the impact of viscosity on two-phase gas-liquid slug flow
TRANSCRIPT
The Impact of viscosity on two-phase gas-liquid slug flow hydrodynamics
by
Tolani Afolabi, B.S.
A Thesis
In
Petroleum Engineering
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
MASTER OF SCIENCE
Approved
Dr. Ekarit Panacharoensawad Chair of Committee
Dr. Lloyd Heinze, P.E.
Mr. Denny Bullard, P.E.
Mark Sheridan Dean of the Graduate School
May 2018
Copy Left 2018, Tolani Afolabi
Texas Tech University, Tolani A. Afolabi, May 2018
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ACKNOWLEDGMENTS
I thank God for his grace over my life. I want to thank my family, my ever-present
supporters; Professor Oladapo Afolabi, Mrs. Oluwafemi Afolabi, Bolaji and Oladapo
Afolabi for their immeasurable help, faith, and guidance. To all my friends, I say thank you
for your motivational pep talks, support, and understanding. I would like to say a very big
thank you to the faculty, staff, and students of the Petroleum Engineering department of
Texas Tech University who helped throughout the journey. I especially would like to thank
Brendan Allison for all his input and assistant on this project. To Dr. Ekarit who made all
this possible, I want to say a very big thank you for always pushing me to do better. I thank
you for your encouragement and invaluable guidance during this whole process. I also want
to thank my immediate supervisor Raymond Eghorieta for all the good times we had
working together in the lab, analyzing results, and having intellectual discussions on how
to approach the project. To Mr. Minhaz Ur Rahman, Dr. Gordon Christopher, Mr. Srikanth
Tangairala, and Mr. Jiawei Tu I would like to say thank you for your time and help in
conducting the oil rheology and surface tension experiments.
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TABLE OF CONTENTS
ACKNOWLEDGMENTS ................................................................................................ ii
LIST OF TABLES ............................................................................................................ v
LIST OF FIGURES ........................................................................................................ vii
NOMENCLATURE ........................................................................................................ xii
ABSTRACT .................................................................................................................... xiv
1.INTRODUCTION........................................................................................................ 15
2.LITERATURE REVIEW ........................................................................................... 17
2.1 Flow pattern ................................................................................................................ 17
2.2 Slug flow characterization .......................................................................................... 19
3.THEORETICAL APPROACH .................................................................................. 21
Theoretical Pressure Drop Prediction ............................................................................... 21
3.1 Closure Relationships for the Theoretical Pressure Drops ......................................... 30
3.2 Calculation of π»π»π»π»π»π»π»π» from experimental data ............................................................. 32
4.EXPERIMENTAL PROGRAM ................................................................................. 37
4.1 Research Direction ...................................................................................................... 37
4.2 Fluid Description ........................................................................................................ 42
4.3 Facility Description ..................................................................................................... 45
4.4 Operating Procedures .................................................................................................. 49
4.5 General Startup Operating Procedure ......................................................................... 49
4.6 General Shutdown Operating Procedure .................................................................... 50
4.7 Experimental Procedures ............................................................................................ 50
4.7.1 Visual Capturing .............................................................................................. 50 4.7.2 Proper camera setup ......................................................................................... 51 4.7.3 Hydrodynamic Tests ........................................................................................ 51
5.DISCUSSION AND RESULTS .................................................................................. 58
5.1 Experimental Test Matrix ........................................................................................... 58
5.1.1 Test Matrix for Detailed Air-Water Slug Flow Hydrodynamics Experiments 59 5.1.2 Test Matrix of Air-Oil Detailed Hydrodynamics Experiments ....................... 61
5.2 Flow Pattern ................................................................................................................ 64
5.2.1a Flow Pattern Determination Test Matrix ....................................................... 64
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5.2.1b Flow Pattern Definitions ................................................................................ 67 5.2.2 Flow Pattern Result .......................................................................................... 69 5.2.2a Water flow pattern case .................................................................................. 69 5.2.2b Oil flow pattern case ...................................................................................... 71
5.3 Translational Velocity ................................................................................................. 77
5.3.1a Inclination: Zero Degrees ............................................................................... 77 5.3.1b Inclination: Five Degrees ............................................................................... 80
5.4 Drift Velocity Test Matrix .......................................................................................... 85
5.4.1 Drift Velocity Results ...................................................................................... 86 5.5 Hydrodynamics Characterization Result .................................................................... 88
5.5.1 Slug Length .............................................................................................................. 88
5.5.1a Inclination: Zero Degrees ............................................................................... 89 5.5.1b Inclination: Five Degrees ............................................................................... 92 5.5.1c Slug Length Result ......................................................................................... 97
5.5.2 Slug Frequency ........................................................................................................ 98
5.5.2a Inclination: Five Degrees ............................................................................. 101 5.5.2b Slug Frequency Result Comparison............................................................. 107
5.5.3 Liquid Holdup ........................................................................................................ 108
5.5.3a Liquid Holdup Result Comparison .............................................................. 113 5.5.4 Pressure Drop ......................................................................................................... 115
5.5.4a Pressure Drop Result Comparison ....................................................................... 119
CONCLUSION ............................................................................................................. 122
BIBLIOGRAPHY ......................................................................................................... 124
APPENDICES ............................................................................................................... 129
APPENDIX A ................................................................................................................ 129
APPENDIX B ................................................................................................................ 155
CURRICULUM VITAE ............................................................................................... 165
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LIST OF TABLES
4-1 Summary of the total number of tests performed on the flow loop system. ......... 40
4-2 Steady State water experiment at room temperature ........................................... 40
4-3 Steady State water experiment at 90 degrees Fahrenheit ..................................... 41
4-4 Steady State Oil experiment at room temperature ................................................ 41
4-5 Steady State Oil experiment at 90 degrees Fahrenheit ......................................... 42
4-6 Properties of the fluids used for the experiment ................................................... 42
4-7 Pressure drop test table ......................................................................................... 56
5-1 Air β water hydrodynamic Properties for the 4 corner points at each
inclination angle studied in detail ......................................................................... 60
5-2 Water flow properties for air-water detailed slug flow hydrodynamics
experiment............................................................................................................. 60
5-3 Air flow properties for air-water detailed slug flow hydrodynamics
experiment............................................................................................................ 61
5-4 Oil flow properties for air-oil detailed slug flow hydrodynamics
experiment............................................................................................................. 62
5-5 Air flow properties for air-oil detailed slug flow hydrodynamics experiment............................................................................................................. 63
5-6 Relationship between percent pump speed, percent air valve opening
with VSL and VSG for air-water cases. ............................................................... 65
5-7 Summary of the fluid properties used in FLOPATNTM to generate
transition boundaries for the superimposed flow pattern maps. ........................... 66
5-8 Drift velocity test matrix for water at 0 degrees ................................................... 85
5-9 Drift velocity test matrix for oil at 0 degrees ........................................................ 86
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A-1 Experimental data for flow pattern at 150 cP and 0Β° .......................................... 129
A-2 Experimental data for flow pattern at 150 cP and 5Β° .......................................... 136
A-3 Experimental data for flow pattern at 280 cP and 0Β° .......................................... 140
A-4 Experimental data for flow pattern at 280 cP and 5Β° ......................................... 146
B- 1 Fluid Properties and Pressure Drop reading for Air-Water Case ....................... 155
B- 2 Fluid Properties and Experimental Results of Hydrodynamic Parameters
for Air-Water Case ............................................................................................. 156
B- 3 Fluid Properties and Liquid Holdup Result for Air-Water Case ....................... 157
B- 4 Fluid Properties and Pressure Drop reading for Air-Oil Case at 280cP ............ 158
B- 5 Fluid Properties and Experimental Results of Hydrodynamic Parameters
for Air- Oil Case at 280 cP ............................................................................... 159
B- 6 Fluid Properties and Liquid Holdup Result for Air-Oil Case at 280 cP ............. 160
B- 7 Fluid Properties and Pressure Drop reading for Air-Oil Case at 150cP ............. 161
B- 8 Fluid Properties and Experimental Results of Hydrodynamic Parameters
for Air-Oil Case at 150 cP ................................................................................. 162
B- 9 Fluid Properties and Liquid Holdup Result for Air-Oil Case at 150 cP ............. 163
B- 10 Drift Velocity Result for Air-Water Case ........................................................... 164
B- 11 Drift Velocity Result for Air-Oil Case................................................................ 164
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LIST OF FIGURES
2-1 Slug flow pattern identified in air-water .............................................................. 19
4-1 $60,000 flow loop facility equipped with heat exchanger section, metering section, and data acquisition system. .................................................................... 39
4-2 Pressure sensor (top left), Quick closing valve (top right), Flow sensor (bottom half) ......................................................................................................... 39
4-3 Image of oil Surface tension at 23Β° C .................................................................. 43
4-4 Viscosity and temperature relationship for Shell Omala S2G 100 in the flow loop. ............................................................................................................. 44
4-5 Density-Temperature relationship for Shell Omala S2G 100 .............................. 44
4-6 Overall process flow diagram of the facility courtesy Eghorieta (2018) ............. 45
4-7 Detailed facility diagram Eghorieta (2018) ......................................................... 46
4-8 Visualization section of the flow loop ................................................................. 48
4-9 Hand operated drum pump (image courtesy MSCDirect.com) ........................... 49
4-10 Canon EOS 70D image courtesy (Texas Tech Universityβs library) ................... 51
4-11 Typical slug length attributes ............................................................................... 53
4-12 Translational velocity captured using cameras and timer .................................... 54
5-1 Flow pattern map generated for the flow loop system for water at 0Β° superimposed to FLOPATN 2.7 VBA code ........................................................ 70
5-2 Flow pattern map generated for the flow loop system for water at 0Β° superimposed to FLOPATN 2.7 VBA code ........................................................ 71
5-3 Flow pattern map generated for the flow loop system for oil at 0Λ and 280 cP superimposed to FLOPATN 2.7 VBA code ............................................ 72
5-4 Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination where .................................................................. 74
5-5 Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination. ............................................................................ 74
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5-6 Flow pattern map generated for the flow loop system for oil at 5Λ and 280 cP superimposed to FLOPATN 2.7 VBA code ............................................ 75
5-7 Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination ............................................................................. 76
5-8 Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination ............................................................................. 76
5-9 Translational velocity for water at 1 cP in a horizontal pipe. .............................. 79
5-10 Comparison of translational velocity for oil at 150 and 280 cP on a pipe at 0Λ ...................................................................................................................... 79
5-11 Comparison of translational velocity for all fluids types examined (water and oil) at their corresponding viscosities on a pipe at 0Λ. ....................... 80
5-12 Translational velocity for water at 1 cP on a pipe inclined at 5Λ. ........................ 81
5-13 Comparison of translational velocity for oil at 150 and 280 cP in a 5Λ inclined pipe. ................................................................................................... 82
5-14 Comparison of translational velocity for all fluids types examined (water and oil) at their corresponding viscosities on a pipe inclined at 5Λ .......... 82
5-15 Difference between translational velocity for the same viscosity 1 cP, and between inclination angles 5Λ and 0Λ ................................................................... 83
5-16 Difference between translational velocity for the same viscosity 150 cP, and between inclination angles 5Λ and 0Λ ............................................................. 84
5-17 Difference between translational velocity for the same viscosity 280 cP, and between inclination angles 5Λ and 0Λ ............................................................. 84
5-18 Air- water drift velocity experimental data comparison with Bendiksen model.................................................................................................................... 87
5-19 Air- oil drift velocity experimental data comparison with Bendiksen model............................................................................................................. ...... 87
5-20 Dimensionless slug length obtained experimentally for air-water at 0Λ .............. 89
5-21 Dimensionless slug length obtained experimentally for air-oil at 0Λ and 150 cP ............................................................................................................ 90
5-22 Dimensionless slug length obtained experimentally for air-oil at 0Λ and 280 cP ............................................................................................................ 90
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5-23 Comparison of dimensionless slug length obtained experimentally for air-oil at 0Β° ........................................................................................................... 91
5-24 Comparison of dimensionless slug length obtained experimentally for air-water and air-oil at 0Λ ..................................................................................... 91
5-25 Dimensionless slug length obtained experimentally for air-water at 5Λ ............... 92
5-26 Comparison of dimensionless slug length obtained experimentally for air-oil at 5Λ............................................................................................................ 93
5-27 Comparison of dimensionless slug length for air-water and air-oil at 5Λ ............ 93
5-28 Comparison dimensionless slug length for air-water at 0Λand 5Λ ........................ 94
5-29 Comparison of dimensionless slug length for air-oil at 0Λand 5Λ......................... 95
5-30 Comparison of dimensionless slug for air-oil at 0Λ and 5 .................................... 95
5-31 Difference between dimensionless slug length for the same viscosity 1 cP between inclination angles 5Λ and 0Λ ................................................................... 96
5-32 Difference between dimensionless slug length for the same viscosity 150 cP between inclination angles 5Λ and 0Λ ....................................................... 96
5-33 Difference between dimensionless slug length for the same viscosity 280 cP, between inclination angles 5Λ and 0Λ ...................................................... 97
5-34 Comparison of experimental result to theoretical models .................................... 98
5-35 Slug frequency for water at 1 cP in a horizontal pipe. ....................................... 100
5-36 Comparison of slug frequency for oil at 150 and 280 cP in a horizontal pipe ..................................................................................................................... 100
5-37 Comparison of slug frequency for all fluids types examined (water and oil) at their corresponding viscosities in a horizontal pipe. ...................................... 101
5-38 Slug frequency for water at 1 cP in a pipe inclined at 5Λ. .................................. 102
5-39 Comparison of slug frequency for oil at 150 and 280 cP in a pipe inclined at 5Β° .................................................................................................................... 102
5-40 Comparison of slug frequency for all fluids types examined (water and oil) at their corresponding viscosities in a pipe inclined at 5Λ. ................................. 103
5-41 Comparison of slug frequency for air-water test at 0Λ, and 5Λ at 1 cP ............... 104
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5-42 Comparison of slug frequency for air-oil test at 0Λ, and 5Λ at 150 cP ................ 104
5-43 Comparison of slug frequency for air-oil test at 0Β°, and 5Β° at 280 cP ............... 105
5-44 Difference between slug frequency for viscosity at 1 cP between inclination angles of 5Β° and 0Β° ........................................................................... 105
5-45 Difference between slug frequency for viscosity at 150 cP between inclination angles of 5Λ and 0Λ ........................................................................... 106
5-46 Difference between slug frequency for the same viscosity 280 cP between inclination angles 5Β° and 0Β° ............................................................................... 106
5-47 Comparison of Slug frequency result with existing closure relationships at 280 cP................................................................................................................. 107
5-48 Comparison of Slug frequency result with existing closure relationships at 150 cP................................................................................................................. 108
5-49 Gas bubbles observed in the slug body of the air-oil case (high viscosity fluid) .......................................................................................... 110
5-50 Slug liquid holdup for air-oil case (150 and 280) cP at (0 and 5) Β° ................... 111
5-51 Comparison of the difference in slug liquid holdup at the same viscosities and different inclination angles. ......................................................................... 112
5-52 Comparison of the difference in slug liquid holdup at the same inclination angles and different viscosities. ......................................................................... 113
5-53 Comparsion of predicted Slug liquid holdup (HLLS) using the mass balance to Gomez (2000) for 280 cP............................................................................... 114
5-54 Comparsion of predicted Slug liquid holdup (HLLS) using mass balance to Gomez (2000)for 280 cP. .................................................................................. 115
5-55 Pressure drop between ports 3 and 5 (the second half of the visualization section) represented at both viscosities and inclinations. .................................. 116
5-56 Pressure drop between ports 3 and 5 (the second half of the visualization section) represented at both viscosities and inclinations. .................................. 117
5-57 Pressure drop between ports 3 and 5 (the second half of the visualization section) represented at both viscosities and inclinations. .................................. 118
5-58 Comparison of pressure drop observation between experimental and numerical result at 280 cP. ................................................................................. 120
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5-59 Comparison of pressure drop observation between experimental and numerical result at 150 cP. ................................................................................. 121
A 1 Flow pattern map generated for the flow loop system for oil at 0Λ and
150 cP................................................................................................................. 151
A 2 Flow pattern map generated for the flow loop system for oil at 0Λ and 150 cP superimposed to FLOPATN 2.7 VBA code .......................................... 151
A 3 Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination ........................................................................... 152
A 4 Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination ........................................................................... 152
A 5 Flow pattern map generated for the flow loop system for oil at 5Λ and 150 cP................................................................................................................. 153
A 6 Flow pattern map generated for the flow loop system for oil at 5Λ and 150 cP superimposed to FLOPATN 2.7 VBA code .......................................... 153
A 7 Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination ........................................................................... 154
A 8 Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination ........................................................................... 154
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NOMENCLATURE ππ constant [3.14] Ξ±L Gas Void Fraction [-] (~) Dimensionless Variables [-] ΞΈ Inclination Angle [Degrees] ΞΌ Viscosity [Paβs] Ο Density [kg/m3] Ο Surface Tension [N/m] Ο Shear Stress [Pa/m] β Difference [-]
πΉπΉ Film [-] πΊπΊ Gas [-]
πΏπΏ Liquid [-] ππ Mixture [-] ππ Slug [-] ππππ Taylor Bubble [-] ππ Total Slug Unit [m]
A Cross-sectional Area [m2] AP Pipe Cross-Section Area [m2] C0 Flow Distribution Coefficient [-] πΆπΆπΊπΊ Blasius Constant [-] πΆπΆπΏπΏ Blasius Constant [m] D Pipe Diameter [m] πππΉπΉ Hydraulic diameter of liquid phase [m] πππΊπΊ Hydraulic diameter of gas phase [m] f Friction Factor [-] g gravitational acceleration [m/s2] HL Liquid Holdup [-] π»π»πΏπΏππππ Slug Unit Holdup [m] I Interfacial [-] L Length [m] π»π»πΉπΉβ² Trapped Film Length [m] π»π»ππβ² Trapped Slug Body Length [m] π»π»π‘π‘π‘π‘π‘π‘π‘π‘ Length of Pipe in trap section [m] M Molecular Weight [Kg/mol] πππΊπΊ Blasius Constant [-] πππΏπΏ Blasius Constant [-]
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P Pressure Pa
R Universal Gas Constant οΏ½ππππ β ππ β πΎπΎβ1 β ππππππβ1
ππππππ β ππ3 β ππππ β πΎπΎοΏ½
π π ππ Reynolds number [-] RKF45 Runge-Kutta-Fehlberg Method [-]
π»π»πΉπΉ pipe periphery length that are in contact with liquid film [m]
π»π»πΊπΊ pipe periphery length that are in contact with Taylor bubble [m]
π»π»πΌπΌ length of the interface between gas and liquid [m] T Temperature [Β°C or K] πππΉπΉ Film Period [1/s] πππ π Slug body Period [1/s] ππππ Inverse of frequency [1/HZ] π’π’/ππ Velocity [m/s] π’π’π·π·/πππ·π· Drift Velocity [m/s] π’π’πΊπΊπΏπΏππ/πππΊπΊπΏπΏππ Gas Bubble Velocity in slugs [m/s] πππΏπΏ Volume of Liquid Trapped in pipe [ππ3] π£π£π π /πππ π Slug Frequency [HZ] πππππΊπΊ Superficial Gas Velocity [m/s]
πππππΏπΏ Superficial Liquid Velocity [m/s] ππππ Total Volume [ππ3] πππ‘π‘π‘π‘π‘π‘π‘π‘ Maximum/theoretical Volume trapped in pipe [ππ3] πππΊπΊ Gas Mass Flowrate [kg/s] πππΏπΏ Liquid Mass Flowrate [kg/s]
x pickup/shedding rate οΏ½πΎπΎπππ π οΏ½
z Compressibility Factor [-]
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ABSTRACT
The impact of high viscosity on multiphase slug flow hydrodynamic closure relationship
is examined experimentally in a horizontal pipe. The obvious differences observed between
existing low viscosity closure relationships and high viscosity fluid closure relationships
are discussed. The experiment was performed on a flow loop with test section of 0.0381-
m ID and 6-m long clear acrylic visualization section. Superficial liquid and gas velocities
vary from 0.342-m/s to 0.718-m/s and 0.532-m/s to 1.397-m/s respectively for nominal oil
viscosities of 150 cP and 280 cP at inclinations of 0Β° and +5Β° from horizontal. The
experimental results are used to evaluate the existing models for flow pattern and
hydrodynamic predictions. The results obtained for the hydrodynamic parameters are
reported and compared to existing closure relationships developed for high viscosity fluids.
A modification was applied to Taitel and Barneaβs model for slug flow and the results were
validated by comparing the experimental results to existing mechanistic model (original
Taitel and Barneaβs model).
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CHAPTER 1 INTRODUCTION
Heavy crude oil reserves are abundantly available, with current estimates of more
than twice those of conventional light crude oil reserves. The major reserves of heavy crude
oil are in California, Canada, Venezuela, and Russia. In addition to the challenge of
extracting the heavy crude oil from the reservoir, the efficient production of heavy crude
oil is also problematic, owing to its highly viscous nature and our currently inadequate
ability to model its flow. While existing hydrodynamics calculations are accurate for
single-phase low viscosity oil flow, the accuracy does not extend to high viscosity
multiphase flow. Two-phase gas-oil or three-phase gas-oil-water flow are commonly found
in the wellbore and pipeline during the production of oil and gas from the reservoir.
Typically, the gas phase either comes out of the solution as the pressure drops along the
pipeline or is co-produced from the reservoir in addition to crude oil, while the water phase
tends to be co-produced with oil from the reservoir, whether from connate water in
sedimentary rocks, an invading water aquifer, or water from water flooding operations.
Overall, multiphase flow is more common than not in petroleum production.
Conventionally, two-phase flow hydrodynamics calculations have been developed based
on air-water systems or gas-light oil systems. These systems exhibit different behaviors
than observed in a gas-high viscosity oil system, yet hydrodynamics models for the two-
phase flow of gas and high viscosity oil case are not fully developed.
In practice, engineers tend to rely on the two-phase flow equations developed for
low viscosity liquid systems and include a safety factor to account for the uncertainty from
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the prediction. With the underlying datasets for these models being dominated by empirical
work in low-viscosity fluids, a high predictive uncertainty for high-viscosity cases has
resulted and led to a conservative approach in designing onshore and subsea pipeline for
heavy crude oil. The pipe size and pipe pressure rating tend to be oversized to account for
the high uncertainty of two-phase flow model. As a result, a heavy oil reservoir that is
economically feasible to be developed may instead be an unprofitable reservoir due to the
increase in production and facilities design cost. Thus, there is a need to improve the
accuracy of the hydrodynamics calculation of gas and high viscosity fluid cases.
Though various studies on gas-high viscosity oil hydrodynamics have been
conducted, including key works by Gokcal (2008), Brito (2012) and others, there remains
a need for comprehensive empirical studies across a range of viscosities to verify existing
datasets and set the foundation for the development of new closure relationships. As a first
step in developing these closure relationships for unknowns parameters in two-phase flow
models, the validity of the flow loop systems must be determined, particularly for the case
of gas and high viscosity liquid. As slug flow is the predominant flow pattern found in
slightly inclined pipes, the focus of this study is on slug flow patterns in multiphase flow.
The objectives of the present study are to 1) identify the flow pattern of high viscosity slug
flow cases, and to 2) determine the unknown parameters for two-phase slug flow of air and
high-viscosity oil including a) slug length, b) slug frequency, c) drift velocity, d) slug body
liquid holdup and e) flow pattern.
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CHAPTER 2 LITERATURE REVIEW
The study of multiphase fluid behavior is quite complex. Mechanistic models were
developed to study the individual entities that are intertwined with multiphase flow
behavior. Some of the predominant entities are flow pattern, slug length, slug frequency,
liquid holdup, pressure drop and translational velocity, as they are consistent parameters
found in mechanistic models. Existing mechanistic models are a combination of
conservation laws and empirical observations.
2.1 Flow pattern
The importance of accurate flow pattern cannot be over-emphasized as it is the
foundation for pressure drop and liquid holdup predictions (Shoham, 2006). The trail blazer
for the gas-oil flow pattern map is Baker (1954) whose work is still in use in the petroleum
industry. Bakerβs work identified the major flow pattern transition boundaries in horizontal
pipes. Five different flow patterns were identified, stratified smooth, stratified wavy,
Elongated bubbles, dispersed bubbles, and churn flow. Between 1961-1972, researchers
began to identify the major flow patterns in vertical pipes (Griffith and Wallis, 1961). Aziz
and Govier (1972) identified a more comprehensive set of flow patterns, as well as
developed a flow pattern model that is dependent on total pressure gradient by conducting
air-water experiments on a 2.54-cm (1-in) diameter pipe. Taitel and Dukler (1976)
advanced this work, developing a mechanistic and generalized model for flow pattern
identification on horizontal and near horizontal flows in pipes, which applies to steady state
Newtonian fluid and pipe inclination range of Β± 10Λ. In 1987 Barnea developed a unified
model to identify flow patterns for different fluid properties and inclinations ranging from
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Β±90Λ. The first case where fluid viscosity was taken into consideration when identifying
flow patterns was in 1979 when Weismann et al. studied the effect of fluid properties and
pipe diameter 0.051-m (2-in) on flow patterns. They conducted research on air-water and
air-glycerol water solutions at 75 cP and 150 cP and noted that there was little change in
the major flow patterns already identified in the air-water system (separated, intermittent
and dispersed). An observation of their work was that the dispersed flow pattern transition
boundary changed at low liquid rates, while the annular flow transition boundary occurred
at high gas rates. Finally, most of the plug flow that occurred in the air-water experiment
was replaced by slug flow pattern in the high viscous fluids they examined.
Studies into the effects of viscosity on multiphase flow continued throughout the
1990s but were generally performed on low viscosity oil. Those who ventured to study
higher viscosity fluids did so in vertical pipes; an example is Shoham (2000). Gokcal et al.
in 2008 studied fluids of a viscosity range of 181-587 cP, and identified that all flow
patterns exist for the lower range high viscosity oil 181 cP and 257 cP at a low liquid
superficial πππππΏπΏ of 0.01 m/s and a high gas superficial velocity πππππΊπΊ of 10 m/s. They also
observed that existing models by Zhang et al. (2003), Xiao et al. (1990) were not adequate
for air-high viscosity oils. Gokcal et al. made modifications to the existing models, but also
suggested that new models need to be developed to improve pressure drop and liquid
holdup predictions where the old models have failed. To summarize, between 1949-1979
different researchers studied flow patterns based on inclination, pipe size and fluid type
and property, but almost exclusively for low viscosity fluids. It was only in the new
millennium that researchers began to focus on the impact of high viscous fluids on
mechanistic models.
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2.2 Slug flow characterization
Several flow patterns exist when multiphase fluids flow in pipes, but the
predominant pattern present at high gas flow rates, low pressure, and low liquid flow rates
is the slug flow pattern. In 1993 Zhou et al. agreed with the common observation that slug
flow pattern is the most common flow pattern found in production lines due to the fluid
flow rates. At some degree slug flow will inevitably be present during fluid transportation
from the reservoir to the surface facility, anticipating, identifying, and predicting the
pressure drop, liquid holdup, translational velocity and the characteristic hydrodynamic
properties of slugs is paramount. To begin, one needs to identify slug flow pattern correctly.
Figure 2-1 is an image of a slug unit (LU) which comprises the Film length (LF), Slug body
length (LS) and the mixing front (LM).
Figure 2-1: Slug flow pattern identified in air-water
In 1984 Crowley et al. discovered that liquid viscosity has a greater effect on slug
flow than gas density in a study of the effect of fluid properties on slugs using gas-water
(1 cP) and a gas-Newtonian fluid of 400 cP. The major experimental studies in slug flow
of air-high viscosity oil were conducted by Gokcal (2005), Gokcal (2008), Jeyachandra
(2011), Foletti et al. (2011), Wang (2012), Brito (2012), and Al-Safran et al. (2015). These
studies serve as a backbone for further advancements in this field. In the early development
LM
LS LU
LF
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stage, Gokcal (2005) constructed a flow loop facility. His test section was 50.8-mm (2-in)
ID with inclination angles ranging from -2Β° to 2Β°. Gokcal (2005) focused only on horizontal
flow. The ranges for the superficial velocity of liquid (πππππΏπΏ) and gas (πππππΊπΊ) were 0.01 m/s to
1.75 m/s and 0 to 20 m/s, respectively. The oil viscosites used in the Gokcal (2005) study
were 181, 257, 378, and 587 cP. Gokcal (2005) provided the data on flow pattern, total
liquid holdup, and pressure drop. The study was not focused to a specific flow pattern.
Thus, the flow patterns corresponding to the liquid holdup and pressure drop data were not
explicitly described. Gokcal (2005) compared his pressure drop results with Xiao (1990)
and the TUFFP (2003) mechanistic model prediction. The results showed that Xiao (1990)
and TUFFP (2003) cannot adequately predict the flow pattern for high viscosity oil cases.
The review from Zhang et al. (2012) is recommended for further detailed study.
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CHAPTER 3 THEORETICAL APPROACH
Theoretical Pressure Drop Prediction
The theoretical pressure drop values in this section are calculated from Taitel and
Barnea slug flow model. The first step in the pressure drop calculation was to determine
the film height as a function of distance (film profile) in the gas pocket zone. Once the film
profile is calculated, the pressure drop over a slug unit length is calculated from
ββππππ = ππππππ sinππ π»π»ππ +πππππππππ΄π΄ππ
π»π»ππ + οΏ½πππΉπΉπ»π»πΉπΉ + πππΊπΊπ»π»πΊπΊ
π΄π΄ππ
πΏπΏπΉπΉ
0ππππ
(3-1)
where βππππ is the pressure drop over a slug unit length, ππππ is the average density of the slug
unit, ππ is the gravitational acceleration, ππ is the inclination angle (positive for an upward
inclined pipe), π»π»ππ is the slug unit length, ππππ is the wall shear stress in the liquid slug body,
ππ is the inner diameter of the pipe, π΄π΄ππ is the cross sectional area of the pipe based on the
pipe ID, π»π»ππ is the slug body length, π»π»πΉπΉ is the film length, πππΉπΉ is the wall shear stress caused
by liquid film, πππΊπΊ is the wall shear stress caused by the gas pocket. π»π»πΉπΉ and π»π»πΊπΊ are the pipe
periphery length that are in contact with liquid film and Taylor bubble, respectively. πππΉπΉ,
π»π»πΉπΉ, πππΊπΊ, and π»π»πΊπΊ are a function of position in the film zone. The wall shear stress in the film
zone was calculated from
πππΉπΉ =12πππΉπΉπππΏπΏ|πππΏπΏππππ|πππΏπΏππππ (3-2)
where πππΏπΏ is the liquid density, π’π’πΏπΏππππ is the velocity of liquid in the film (change with
location), and πππΉπΉ is the Fanning friction factor in the film zone calculated from
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πππΉπΉ = πΆπΆπΏπΏ(π π πππΉπΉ)βπππΏπΏ (3-3)
where πΆπΆπΏπΏ and πππΏπΏ are the constants in Blasius type friction factor formula. They were
calculated based on the value of Reynolds number of the liquid film, π π πππΉπΉ, as
πΆπΆπΏπΏ = οΏ½ 16 π π πππΉπΉ β€ 2100
0.046 π π πππΉπΉ > 2100 (3-4)
and
πππΏπΏ = οΏ½ 1 π π πππΉπΉ β€ 2100
0.2 π π πππΉπΉ > 2100 (3-5)
π π πππΉπΉ is defined as
π π πππΉπΉ =
πππΏπΏπππΉπΉ|πππΏπΏππππ|πππΏπΏ
(3-6)
where πππΉπΉ is the hydraulic diameter of liquid film flow. πππΉπΉ was calculated from
πππΉπΉ =
4π΄π΄πΉπΉπ»π»πΉπΉ
(3-7)
π΄π΄πΉπΉ is the flow cross section area occupied by liquid. For the wall shear stress in the gas
pocket part, πππΊπΊ was calculated from
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πππΊπΊ =12πππΊπΊπππΊπΊ|πππΊπΊππππ|πππΊπΊππππ (3-8)
where π’π’πΊπΊππππ is the gas phase velocity inside the Taylor bubble, and πππΊπΊ is the Fanning
friction factor of gas inside the Taylor bubble. πππΊπΊ was calculated by the similar method
used for πππΉπΉ as follows:
πππΊπΊ = πΆπΆπΊπΊ(π π πππΊπΊ)βπππΊπΊ (3-9)
πΆπΆπΊπΊ and πππΊπΊ are defined from
πΆπΆπΊπΊ = οΏ½ 16 π π πππΊπΊ β€ 21000.046 π π πππΊπΊ > 2100 (3-10)
and
πππΊπΊ = οΏ½ 1 π π πππΊπΊ β€ 21000.2 π π πππΊπΊ > 2100 (3-11)
Reynolds number of gas in the gas pocket is defined as
π π πππΊπΊ =
πππΊπΊπππΊπΊ|πππΊπΊππππ|πππΊπΊ
(3-12)
where πππΊπΊ is the hydraulic diameter of the gas in the Taylor bubble. π΄π΄πΊπΊ is the flow cross
section area occupied by gas. It is defined as
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πππΊπΊ =4π΄π΄πΊπΊ
π»π»πΊπΊ + π»π»πΌπΌ (3-13)
π»π»πΌπΌ is the length of the interface between gas and liquid. In this study, the gas-liquid interface
was found to be smooth (no wave) and flat for both water and oil cases.
Taitel and Barnea film profile equation can be written as
ππβπΏπΏππππ =
πππΉπΉπ»π»πΉπΉπ΄π΄πΉπΉ
β πππΊπΊπ»π»πΊπΊπ΄π΄πΊπΊ
β πππΌπΌπ»π»πΌπΌ οΏ½1π΄π΄πΉπΉ
+ 1π΄π΄πΊπΊοΏ½+ (πππΏπΏ β πππΊπΊ)ππ sinππ
(πππΏπΏ β πππΊπΊ)ππ cosππ β πππΏπΏπ’π’πΉπΉ(ππππππ β πππΏπΏπΏπΏππ)π»π»πΏπΏπΏπΏπππ»π»πΏπΏππππ2
πππ»π»πΏπΏππππππβπΏπΏ
β πππΊπΊπ£π£πΊπΊ(ππππππ β πππΊπΊπΏπΏππ) πΌπΌπΏπΏπππΌπΌππππ2πππ»π»πΏπΏππππππβπΏπΏ
(3-14)
where
πππΉπΉ = ππππππ β πππΏπΏππππ (3-15)
πΌπΌπΏπΏππ = 1 β π»π»πΏπΏπΏπΏππ (3-16)
where π»π»πΏπΏπΏπΏππ is liquid holdup at the slug body.
and
πΌπΌππππ = 1 β π»π»πΏπΏππππ (3-17)
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The length ππ in ππβπΏπΏ/ππππ equation is defined to be positive in the opposite direction of the
flow. In other words, at ππ = 0, π»π»πΏπΏ = π»π»πΏπΏπΏπΏππ, and at ππ = π»π»πΉπΉ, π»π»πΏπΏ = π»π»πΏπΏππππππ (or liquid holdup at
the end of the film zone). The geometric parameters are a function of the film height. They
are given as
οΏ½ΜοΏ½π΄πΊπΊ = 0.25οΏ½arccosοΏ½2βοΏ½πΏπΏ β 1οΏ½ β οΏ½2βοΏ½πΏπΏ β 1οΏ½οΏ½1 β οΏ½2βοΏ½πΏπΏ β 1οΏ½
2οΏ½
(3-18)
οΏ½ΜοΏ½π΄πΏπΏ = 0.25οΏ½ππ β arccosοΏ½2βοΏ½πΏπΏ β 1οΏ½ + οΏ½2βοΏ½πΏπΏ β 1οΏ½οΏ½1 β οΏ½2βοΏ½πΏπΏ β 1οΏ½2οΏ½ (3-19)
οΏ½ΜοΏ½π»πΊπΊ = arccos(2βοΏ½πΏπΏ β 1) (3-20)
οΏ½ΜοΏ½π»πΏπΏ = ππ β arccos(2βοΏ½πΏπΏ β 1) (3-21)
οΏ½ΜοΏ½π»πΌπΌ = οΏ½1 β οΏ½2βοΏ½πΏπΏ β 1οΏ½2
(3-22)
where the dimensionless length is the length scaled by ππ, and the dimensionless area is the
area scaled by ππ2. Specifically, this can be written as βοΏ½πΏπΏ = βπΏπΏπ·π·
, οΏ½ΜοΏ½π»πΊπΊ = πππΊπΊπ·π·
, οΏ½ΜοΏ½π»πΏπΏ = πππΏπΏπ·π·
, οΏ½ΜοΏ½π»πΌπΌ = πππΌπΌπ·π·
, οΏ½ΜοΏ½π΄πΊπΊ = π΄π΄πΊπΊπ·π·2
, and οΏ½ΜοΏ½π΄πΏπΏ = π΄π΄πΏπΏπ·π·2
. The value of πππ»π»πΏπΏπΏπΏπΏπΏππβπΏπΏ
in the film profile equation is calculated from
the equation below.
πππ»π»πΏπΏππππππβπΉπΉ
=4ππππ
οΏ½1 β οΏ½2βπΉπΉππ
β 1οΏ½2
(3-23)
The π»π»πΏπΏππππ parameter is only a function of the liquid height. This can be written as
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π»π»πΏπΏππππ =4π΄π΄πΏπΏππππ2 = 1 β
1ππ οΏ½arccosοΏ½2βοΏ½πΏπΏ β 1οΏ½ β οΏ½2βοΏ½πΏπΏ β 1οΏ½οΏ½1 β οΏ½2βοΏ½πΏπΏ β 1οΏ½2οΏ½
(3-24)
For the moving frame of reference at the speed of π’π’ππππ, the interface is stationary with
respect to the frame of reference. Then, the mass balance in this frame of reference can be
written as
(ππππππ β πππΏπΏπΏπΏππ)πππΏπΏπ΄π΄πππ»π»πΏπΏπΏπΏππ = (ππππππ β πππΏπΏππππ)πππΏπΏπ΄π΄πππ»π»πΏπΏππππ (3-25)
where the above π»π»πΏπΏππππ and π’π’πΏπΏππππ are a function of position. By rearranging this mass
balance equation, we have
πππΏπΏππππ = π’π’ππππ β
(ππππππ β πππΏπΏπΏπΏππ)π»π»πΏπΏπΏπΏπππ»π»πΏπΏππππ
(3-26)
and
πππΉπΉ =(ππππππ β πππΏπΏπΏπΏππ)π»π»πΏπΏπΏπΏππ
π»π»πΏπΏππππ
(3-27)
The value of π’π’πΏπΏπΏπΏππ was from
ππππ = πππππΏπΏ + πππππΊπΊ = πππΏπΏπΏπΏπππ»π»πΏπΏπΏπΏππ + πππΊπΊπΏπΏππ(1 β π»π»πΏπΏπΏπΏππ) (3-28)
The values of πππππΏπΏ and πππππΊπΊ are known based on the flow rate of liquid and gas,
respectively. For the π»π»πΏπΏπΏπΏππ and πππΊπΊπΏπΏππ , they can be determined based on either existing
closure relationships or experimental data. Once, π»π»πΏπΏπΏπΏππ and πππΊπΊπΏπΏππ are obtained πππΏπΏπΏπΏππ can be
calculated from Equation 3.30 From Equation 3.26 πππΏπΏππππ is only a function of film height,
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βπΏπΏ, because π»π»πΏπΏπΏπΏππ is a constant, and π»π»πΏπΏππππ is only a function of βπΏπΏ as shown in Equation
3.24. From Equation 3.2 and 3.6, we can see that, πππΉπΉ is also only a function of βπΏπΏ, because
it is based on πππΏπΏππππ and πππΉπΉ values (πππΉπΉ is a direct function of βπΏπΏ). Similarly, it can be shown
that πππΊπΊππππ is also only a function of βπΏπΏ. By using the same mass balance in the moving
frame of reference for gas phase, we have,
(ππππππ β πππΊπΊπΏπΏππ)(1β π»π»πΏπΏπΏπΏππ) = (ππππππ β πππΊπΊππππ)(1 β π»π»πΏπΏππππ) (3-29)
or
πππΊπΊππππ = ππππππ β
(ππππππ β πππΊπΊπΏπΏππ)(1β π»π»πΏπΏπΏπΏππ)(1 β π»π»πΏπΏππππ)
(3-30)
The values of ππππππ, πππΊπΊπΏπΏππ, and π»π»πΏπΏπΏπΏππ in Equation 3.30 are not a function of location in
the film. Therefore, πππΊπΊππππ is only a function of π»π»πΏπΏππππ or only the function of βπΏπΏ as per
Equation 3.30. Thus, πππΊπΊ is also only a function of βπΏπΏ. πππΌπΌ can be assumed to equal to πππΊπΊ for
a smooth film profile. For a wavy interface,
πππΌπΌ =
12πππΌπΌπππΊπΊ|πππΊπΊππππ β πππΏπΏππππ|(πππΊπΊππππ β πππΏπΏππππ) (3-31)
where πππΌπΌ = 0.0142 for a horizontal and an inclined pipe.
With all the above equations, the right hand side of ππβπΏπΏ/ππππ (Equation 3.14) is only
a function of βπΏπΏ and can be solved numerically by using Runge-Kutta-Fehlberg method
(RKF45). The initial condition for starting π π πΎπΎπ π 45 or βπΏπΏ at ππ = 0 is calculated from π»π»πΏπΏπΏπΏππ
based on Equation 3.24 (solve βοΏ½πΏπΏ for a known π»π»πΏπΏπΏπΏππ numerically). The film profile
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calculation needs to stop at a film length of π»π»πΉπΉ. This π»π»πΉπΉ must allow a mass balance. The
mass balance equation can be written as
πππΏπΏ = οΏ½πππΏπΏπΏπΏπππππΏπΏπ΄π΄πππ»π»πΏπΏπΏπΏππππππ + οΏ½ πππΏπΏπππππππΏπΏπ΄π΄πππ»π»πΏπΏππππππππ
πππΉπΉ
0οΏ½
1ππππ
(3-32)
or
πππΏπΏ = οΏ½πππΏπΏπ»π»πππ΄π΄πππ»π»πΏπΏπΏπΏππ + οΏ½ πππΏπΏπ΄π΄πππ»π»πΏπΏπππππππ»π»
πΏπΏπΉπΉ
0οΏ½
1ππππ
β π₯π₯ (3-33)
if the integration in space is used. The variables πππΉπΉ, ππππ, π»π»πΉπΉ, and π₯π₯ in Equation 3.32-3.33
are the film period, slug unit period, film length, and mass shedding-pickup rate,
respectively. Mathematically, they can be written as
πππΉπΉ =π»π»πΉπΉππππππ
, (3-34)
ππππ =
π»π»ππππππππ
, (3-35)
π»π»πΉπΉ = π»π»ππ β π»π»ππ , (3-36)
and
π₯π₯ = (ππππππ β πππΏπΏπΏπΏππ)πππΏπΏπ΄π΄πππ»π»πΏπΏπΏπΏππ = (ππππππ β πππΏπΏππππ)πππΏπΏπ΄π΄πππ»π»πΏπΏππππ (3-37)
In general, the appropriate film profile is unknown before ππβπΏπΏ/ππππ equation is
solved. This is because to know which π»π»πΉπΉ that can give a mass balance in Equation 3.33,
the film profile is needed to do the calculation of β« πππΏπΏπ΄π΄πππ»π»πΏπΏπππππππ»π»πΏπΏπΉπΉ0 .
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Numerically, the appropriate film length can be determined together with the film profile
by using an iterative method such as a Newton-Raphson method. Equation 3.33 can be
adjusted to be a one function one unknown equation as
β±(π»π»πΉπΉ) = 0 = πππΏπΏ,π π π π πΉπΉ βπππΏπΏ,πππππ‘π‘πππ‘π‘ (3-38)
where πππΏπΏ,π π π π πΉπΉ is the liquid mass flow rate output from RKF45 calculation and πππΏπΏ,πππππ‘π‘πππ‘π‘ is
the liquid mass flow rate input based from
πππΏπΏ,πππππ‘π‘πππ‘π‘ = π’π’πππΏπΏπ΄π΄πππππΏπΏ (3-39)
Function β±(π»π»πΉπΉ) is dependent upon the input value π»π»πΉπΉ . If a correct π»π»πΉπΉ value is
given, then the function β±(π»π»πΉπΉ) return zero. This makes β±(π»π»πΉπΉ) to be a one equation one
unknown which can be solved numerically by using a root-finding algorithm such as a
Newton-Raphson method as discussed earlier.
The answer from film profile calculation allows the integration term,
β« πππΉπΉπππΉπΉ+πππΊπΊπππΊπΊπ΄π΄ππ
πΏπΏπΉπΉ0 ππππ , in Equation 3.1 to be solved numerically. This is done by using a
trapezoidal method. To use this method, the function value (the terms inside the
integration) at every point on the film must be specified. This can be done by using
Equations 3.2,3.8,3.20, and 3.21 for πππΉπΉ , πππΊπΊ , π»π»πΉπΉ , and π»π»πΊπΊ , respectively. This gives the
frictional pressure drop in the film zone.
For the frictional pressure drop in the slug body or πππππππ·π·π΄π΄ππ
π»π»ππ, ππππ can be calculated from
ππππ =12πππππππΏπΏ|ππππ|ππππ (3-40)
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where π’π’ππ is from Equation 3.28 ππππ is from
ππππ = πΆπΆππ(π π ππππ)βππππ (3-41)
πΆπΆππ and ππππ are defined from
πΆπΆππ = οΏ½ 16 π π ππππ β€ 21000.046 π π ππππ > 2100 (3-42)
π π ππππ is defined as
π π ππππ =ππππππππππππππ
(3-43)
ππππ is defined as
ππππ = πππΏπΏπ»π»πΏπΏπΏπΏππ + πππΊπΊ(1 β π»π»πΏπΏπΏπΏππ) (3-44)
ππππ is defined as
ππππ = πππΏπΏπ»π»πΏπΏπΏπΏππ + πππΊπΊ(1 β π»π»πΏπΏπΏπΏππ) (3-45)
The gravitational term in Equation 3.1 is based on ππππ. ππππ can be calculated from
ππππ = π»π»πΏπΏπππππππΏπΏ + (1 β π»π»πΏπΏππππ)πππΊπΊ (3-46)
where
π»π»πΏπΏππππ =
π»π»πΏπΏπΏπΏπππ»π»ππ + β« π»π»πΏπΏπππππΏπΏπΉπΉ0 πππ»π»π»π»ππ
(3-47)
3.1 Closure Relationships for the Theoretical Pressure Drops
The air-water and air-oil slug flow pressure drop results are compared to the
theoretical prediction in this section. The theoretical pressure drops are calculated by using
existing closure relationships to estimate the unknown parameters. These unknown
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parameters are π»π»πΏπΏπΏπΏππ , π»π»ππ , π’π’ππππ , and π’π’πΊπΊπΏπΏππ . They were calculated from Gomez et al. 2000
correlation, the value suggested in Zhang et al. 2003, Bendiksen 1984 correlations, and
Zuber and Hench 1962 correlation, respectively. Slug body liquid holdup can be written as
π»π»πΏπΏπΏπΏππ = πππ₯π₯πποΏ½β(0.45 Γ ππ + 2.48 Γ 10β6π π πππΏπΏππ)οΏ½ (3-48)
where ππ is the inclination angle in radians and π π πππΏπΏππ is the Reynolds number for liquid in
slug defined as
π π πππΏπΏππ =πππΏπΏπππππππππΏπΏ
, (3-49)
The slug body length is calculated from (Zhang et al. 2003)
π»π»ππππ
= (32.0 cos2 ππ + 16.0 sin2 ππ) (3-50)
The translational velocity, ππππππ, was calculated from
ππππππ = πΆπΆ0πππ π + πππ·π· (3-51)
where
πΆπΆ0 = οΏ½1.2 for π π πππΏπΏππ β₯ 21002 for π π πππΏπΏππ < 2100 (3-52)
and the Bendiksen 1984 drift velocity correlation is
πππ·π· = 0.54οΏ½ππππ cos ππ + 0.35οΏ½ππππ sinππ (3-53)
For π’π’πΊπΊπΏπΏππ, the closure relationship from Zuber and Hench is used. It is given here as
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πππΊπΊπΏπΏππ = πΆπΆ1π’π’ππ + 1.53 οΏ½
ππππ(πππΏπΏ β πππΊπΊ)πππΏπΏ2
οΏ½0.25
π»π»πΏπΏπΏπΏππ0.5 sinππ (3-54)
For the case of the near horizontal flow as in this study, πΆπΆ1 for π’π’πΊπΊπΏπΏππ equation is 1 and ππ is
the gas-liquid surface tension.
3.2 Calculation of π»π»πΏπΏπΏπΏππ from experimental data
This section describes the calculation method used to calculate π»π»πΏπΏπΏπΏππ value from the
experimental data. The test section can be closed with a quick closing valves. Once two
quick closing valves close, they trap gas and liquid inside. The maximum capacity of the
quick closing valves trapped volume is πππ‘π‘π‘π‘π‘π‘π‘π‘. The volume of liquid trapped inside the quick
closing valves section is πππΏπΏ. The trapped liquid volume, πππΏπΏ, come from both slug film and
slug body. This can be written as
πππΏπΏ = π΄π΄πππ»π»πΏπΏπππππ»π»πΉπΉβ² + π΄π΄πππ»π»πΏπΏπΏπΏπππ»π»ππβ² (3-55)
By dividing both sides with the capacity of the quick closing valves section, we have
πππΏπΏπππ‘π‘π‘π‘π‘π‘π‘π‘
=π΄π΄πππ»π»πΏπΏπππππ»π»πΉπΉβ² + π΄π΄πππ»π»πΏπΏπΏπΏπππ»π»ππβ²
π΄π΄πππ»π»π‘π‘π‘π‘π‘π‘π‘π‘
(3-56)
The π»π»πΉπΉβ² and π»π»ππβ² here are equal to π»π»πΉπΉ and π»π»ππ. The prime sign is used to indicate that
the length of film or slug that is measures from the fluid drained in the trap section.
Incomplete slug body length (or film length) can also be trapped in the quick closing valve
section. When the incomplete film is trapped, we have π»π»πΉπΉβ² < π»π»πΉπΉ. When the incomplete slug
body is trapped, we have π»π»ππβ² < π»π»ππ . The parameter π»π»π‘π‘π‘π‘π‘π‘π‘π‘ here is the length of the quick
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closing valve section where π΄π΄πππ»π»π‘π‘π‘π‘π‘π‘π‘π‘ = πππ‘π‘π‘π‘π‘π‘π‘π‘π‘π‘ . By canceling π΄π΄ππ in both numerator and
denominator and rearranging equation, we have
πππΏπΏππππ
= π»π»πΏπΏπππππ»π»πΉπΉβ²
π»π»ππ+ π»π»πΏπΏπΏπΏππ
π»π»ππβ²
π»π»ππ
(3-57)
Experimentally, several slugs were captured by using quick closing valves. Each
time the liquid trapped inside the quick closing valve section can be determined and the
trapped volume πππΏπΏ can be obtained. Simultaneously, the camera is used to capture the
picture of the slug trapped inside the quick closing valve section. The picture analysis can
identify the trapped slug body length, π»π»ππβ² . By using linear regression analysis, the plot
between πΏπΏππβ²
πΏπΏπΏπΏ (as a horizontal axis) versus πππΏπΏ
πππΏπΏ (as a vertical axis) is used to solve for the slope
π»π»πΏπΏπΏπΏππ and the intercept is π»π»πΏπΏπππππΏπΏπΉπΉβ²
πΏπΏπΏπΏ. From experimental observations, the film length in the
trap section is longer than the slug length. Thus, πππΏπΏ/ππππ value is more sensitive to the film
length, not the slug length. This causes the linear regression analysis to give a more
accurate value on π»π»πΏπΏπππππΏπΏπΉπΉβ²
πΏπΏπΏπΏ compared to the slope value, π»π»πΏπΏπΏπΏππ. With the confidence in the
intercept value, the π»π»πΏπΏππππ is obtained from the intercept value where π»π»πΉπΉβ² is calculated from
π»π»ππ β π»π»ππβ². With the above approach, π»π»πΏπΏππππ is obtained in this experimental study. Then,
π»π»πΏπΏππππ value was verified with the film height picture to ensure that the obtained holdup
value of the liquid film agrees with the liquid height value from the picture.
With the above method, π»π»πΏπΏππππ was obtained. The slug length, π»π»ππ, and translational
velocity, ππππππ are also determined based on the pictures taken. The methods used to do the
image analysis and to obtain these parameters are explained in Chapter 4. With these
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information, the slug body liquid holdup calculated from the measured value of
π»π»πΏπΏππππ,π»π»ππ , πππ»π»π»π» , and ππππππ was calculated from Equation 3.33. It is written here again as
πππΏπΏ = οΏ½πππΏπΏπ»π»πππ΄π΄πππ»π»πΏπΏπΏπΏππ + οΏ½ πππΏπΏπ΄π΄πππ»π»πΏπΏπππππππ»π»
πΏπΏπΉπΉ
0οΏ½
1ππππ
β π₯π₯ (3-58)
The mass flow rate of liquid, πππΏπΏ, was known based on the flow meter reading. ππππ
value is calculated based on the measured slug frequency (ππππ = 1πππ»π»π»π»
). The integration from
zero to π»π»πΉπΉ requires the film profile information. The film profile can be obtained by
integrating ππβπΉπΉ/ππππ Equation 3.14 numerically. Yet, to start the integration, the liquid
holdup in the slug body is needed to specify the initial liquid height at ππ = 0. The pickup
rate term, π₯π₯, in Equation 3.33 is also a function of π’π’πΏπΏπΏπΏππ and π»π»πΏπΏπΏπΏππ as shown in Equation
3.37, shown here again as
π₯π₯ = (ππππππ β πππΏπΏπΏπΏππ)πππΏπΏπ΄π΄πππ»π»πΏπΏπΏπΏππ (3-59)
For a horizontal flow case,
πππΏπΏπΏπΏππ = πππΊπΊπΏπΏππ = ππππ = πππππΏπΏ + πππππΊπΊ (3-60)
Which means that for a horizontal flow case, the only unknown in the mass balance
Equation 3.33 is π»π»πΏπΏπΏπΏππ . Therefore, once all the parameters from the experimental
measurement are identified, the mass balance Equation 3.33 is only a function of π»π»πΏπΏπΏπΏππ. To
solve this, the secant method was used. This was done by 1) giving two initial guesses of
π»π»πΏπΏπΏπΏππ, 2) calculating the film profile by solving Equation 3.14 with RKF45 of those two
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cases, 3) using a trapezoidal method to carry out the integration term in Equation 3.33, 4)
calculate the difference between the mass flow rate from Equation 3.33 the actual input
mass flow rate, and 5) assigning the new guess value of π»π»πΏπΏπΏπΏππ to be
π»π»πΏπΏπΏπΏππ,ππ = π»π»πΏπΏπΏπΏππ,ππβ1 β (π’π’οΏ½π»π»πΏπΏπΏπΏππ,ππβ1οΏ½π»π»πΏπΏπΏπΏππ,ππβ1 β π»π»πΏπΏπΏπΏππ,ππβ2
π’π’οΏ½π»π»πΏπΏπΏπΏππ,ππβ1οΏ½ β π’π’οΏ½π»π»πΏπΏπΏπΏππ,ππβ2οΏ½) (3-61)
where subscripts ππ, ππ β 1, and ππ β 2 indicate the value of π»π»πΏπΏπΏπΏππ in each iteration. The first
two guess of π»π»πΏπΏπΏπΏππ are π»π»πΏπΏπΏπΏππ,1 and π»π»πΏπΏπΏπΏππ,2. The function π’π’ give the difference between the
calculated πππΏπΏ from Equation 3.33 and the input value of πππΏπΏ calculated from πππΏπΏ =
πππΏπΏπ΄π΄πππ’π’πππΏπΏ. The function π’π’ can be written as
π’π’(π»π»πΏπΏπΏπΏππ) = πππΏπΏ,πππππ‘π‘πππ‘π‘ βπππΏπΏ,π‘π‘πππ‘π‘π‘π‘πππ‘π‘(π»π»πΏπΏπΏπΏππ) (3-62)
The iteration for secant method is carried out until there is no difference in the
second digits of π»π»πΏπΏπΏπΏππ value from one iteration to the next iteration, e.g. π»π»πΏπΏπΏπΏππ,3 = 0.652 and
π»π»πΏπΏπΏπΏππ,4 = 0.653
For the case of an inclined flow, πππΊπΊπΏπΏππ > ππππ > πππΏπΏπΏπΏππ. The reason that πππΊπΊπΏπΏππ is slightly
more than πππΏπΏπΏπΏππ value in the slightly upward inclined pipe is that gas has less density than
liquid and gas bubbles tend to accumulate on the top part of the pipe in the slug body zone.
Thus, πππΏπΏπΏπΏππ in this case was estimated from
ππππ = πππΏπΏπΏπΏπππ»π»πΏπΏπΏπΏππ + πππΊπΊπΏπΏππ(1 β π»π»πΏπΏπΏπΏππ) (3-63)
and the value of πππΊπΊπΏπΏππ was estimated from Equation 3.54. With this approach, it leads to the
mass balance equation with the only unknown as π»π»πΏπΏπΏπΏππ. Thus, the π»π»πΏπΏπΏπΏππ value allows a mass
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balance across the film-slug interface can be obtained by using secant method and the
RKF45 calculation of the film profile as in the case of the horizontal flow.
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CHAPTER 4 EXPERIMENTAL PROGRAM
4.1 Research Direction
The goal of the research performed at the Texas Tech University Terry Fuller Flow
Loop Lab is to bridge the gap that exists between the experimental information that is
available between low viscosity and high viscosity slug flow models in pipes. Currently,
there is a plethora of experimental and numerical data for low viscosity multiphase flow in
both horizontal and vertical pipes, but few exist for multiphase air-medium and air-high
viscosity oil. Therefore, a comprehensive experimental steady state and transient state
study on the hydrodynamic behavior of air and medium viscosity oil at varying
temperatures and angles is highly relevant to the present and future of the petroleum
industry. Comprehensive tests at different angles (0Β°, 1Β°, 5Β°) and temperatures (70Β° F and
90Β° F) were selected and parameters of interest recorded for optimal comparison with
existing mechanistic models, in particular Dukler and Hubbardβs influential 1975
mechanistic model in horizontal pipes (as referenced in Ovadia Shohamβs Mechanistic
Modeling of Gas-liquid Two-phase Flow in Pipes). Although the 1975 model by Dukler
and Hubbard is valid for only horizontal flow, the seven critical parameters that they
specify and that we obtain from the flow loop experiments provide a sufficiently versatile
dataset for the development of new closure relationships for near-horizontal angles as well.
The seven variables consist of two input variables (HLLS, and Ο s) and three output variables
(LS, VTB, ΞP), while the sixth and seventh parameters are drift velocity and flow pattern
characterization respectively. To ensure the accuracy of the results, the original flow loop
built by Gomes and Carestiato (2016) was modified by Eghorieta (2018) as detailed in
Figure 4-1. Some of the modifications entailed include adding three quick closing valves
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(QVC), three differential pressure sensors, two pressure transducers that record data at
1HZ, three new capacitance sensors that record data at 1000 HZ, and a pulley, shown in
Figure 4-1- Figure 4-8. The intentions of these modifications was to capture these seven
parameters listed above, but upon commencement of the experiments it was observed that
the capacitance sensors worked well in air-water experiments, but not in air-oil
experiments. Therefore the majority of the experimental data reflects manual capture
procedures (see 4.7: Experimental Procedures). The test matrix for the experiment was
determined after performing flow pattern characterization experiment on the flow loop
system, which illuminated the different flow patterns present in the system (see Chapter 5
for detailed discussion of the test matrix for the water experiments at different angles using
percent valve openings).
To provide a reliable foundation for the main objective of this research, the
modified flow loop was first validated with the analysis of the experimental results and
compared to the existing models. The air-water experiments were performed at varying
angles (0,1,5) Β° and temperatures (70, 90) Β°, enabling shifts in slug flow behavior to be
validated against well-established air-water datasets in a variety of common conditions.
Upon validating the system, the air-medium viscosity oil part of the experiment was then
conducted. A total of 8502 tests were performed for both air-water and air-high viscosity
oil experiments. Table 4-1 is the summation of all the tests performed for both water and
oil cases and Tables 4-2 to 4-5 show the breakdown of each test that was performed in the
flow loop lab. In all data presented in this report, the key parameters needed for a broad-
scope steady state hydrodynamic experiment, ultimately aiding in establishing new
relationships for high viscosity multiphase flow in pipes, are consistently reported, these
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seven parameters being slug frequency, slug length, liquid holdup, pressure drop,
translational velocity, flow pattern, drift velocity, surface tension and viscosity.
Figure 4-1: $60,000 flow loop facility equipped with heat exchanger section, metering section, and data acquisition system.
Figure 4-2: Pressure sensor (top left), Quick closing valve (top right), Flow sensor (bottom half)
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Table 4-1: Summary of the total number of tests performed on the flow loop system.
Experiments Performed
Number of Tests for water and
oil case
Flow Pattern 1120
Slug Length 4400
Slug Frequency 132
Pressure Drop 132
Translational Velocity 2200
Drift Velocity 210
Slug Liquid Holdup 308
Total Number of Test 8502
Table 4-2: Steady State water experiment at room temperature SteadyState Experiment Water at room temperature
Number of Tests for Zero Degree
Number of Tests for One Degree
Number of Tests for Five Degree
Total Number of Tests
Pressure Drop 48 48 48 144 Slug Frequency 48 48 48 144 Slug Length 16 (800 pictures
for each point) 16 (800 pictures for each point)
16 (800 pictures for each point)
48 (800 pictures for each point)
Liquid Holdup 112 112 112 336 Drift Velocity 48 48 48 144 Translational Velocity
16 (800 pictures for each point)
16 (800 pictures for each point)
16 (800 pictures for each point)
48 (800 pictures for each point)
Flow Pattern 1 1 1 3
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Table 4-3: Steady State water experiment at 90 degrees Fahrenheit SteadyState Experiment Water at room temperature
Number of Tests for Zero Degree
Number of Tests for One Degree
Number of Tests for Five Degree
Total Number of Tests
Pressure Drop 48 48 48 144 Slug Frequency 48 48 48 144 Slug Length 16 (800 pictures
for each point) 16 (800 pictures for each point)
16 (800 pictures for each point)
48 (800 pictures for each point)
Liquid Holdup 112 112 112 336 Drift Velocity 48 48 48 144 Translational Velocity
16 (800 pictures for each point)
16 (800 pictures for each point)
16 (800 pictures for each point)
48 (800 pictures for each point)
Flow Pattern 1 1 1 3
Table 4-4: Steady State Oil experiment at room temperature Steady State Experiment Oil at Room Temperature
Number of Tests for Zero Degree
Number of Tests for Five Degree
Number of Tests
Pressure Drop 24 24 48 Slug Frequency 24 24 48 Slug Length 8 8 16 (800 pictures for
each point) Liquid Holdup 56 56 112 Drift Velocity 8 8 16 Translational Velocity 8 8 16 (800 pictures for
each point) Flow Pattern 1 1 2
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Table 4-5: Steady State Oil experiment at 90 degrees Fahrenheit Steady State Experiment Oil at 90 Β°F
Number of Tests for Zero Degree
Number of Tests for Five Degree
Number of Tests
Pressure Drop 24 24 48 Slug Frequency 24 24 48 Slug Length 8 8 16 (800 pictures for
each point) Liquid Holdup 56 56 112 Drift Velocity 8 8 16 Translational Velocity 8 8 16 (800 pictures for
each point) Flow Pattern 1 1 2
4.2 Fluid Description
The flow loop lab utilizes two types of fluids: gas and liquid. The gas is compressed
air supplied at 100 psig at 70 Β°F and stepped down to 70 psig for use in the facility. The
liquids used are City of Lubbock water (treated through reverse osmosis) as explained by
Gomes and Carestiato (2016) and mineral oil (Shell Omala S2G 100). The oil was pumped
into the liquid tank in September 2017 for the commencement of the air-oil phase of the
experimental plan. Table 4-6 is the summary of the fluid property for each of the fluids
used in the flow loop laboratory.
Table 4-6: Properties of the fluids used for the experiment Properties Air Water Mineral Oil Name Compressed gas Distilled water Shell Omala S2G 100 Inlet Temperature (ΛF)
Varies based on room temperature
Varies based on room temperature - 90
Varies based on room temperature - 90
Inlet Pressure (psig) 70 14.7 14.7 Density Viscosity (cP) @ (212ΛF)
1 150 and 280
Color Colorless Dyed green Brown
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Surface tension was measured with KrussTM Drop Shape Analyzer (pendant drop),
model DSA25B at 73.4 Β°F (23 Β°C) and 89.6 Β°F (32Β° C). The surface tension values at 73.4
Β°F is 31.20-mN/m and at 89.6 Β°F is 30.6-mN/m, these values are used for all the subsequent
calculations needing surface tension values.
Figure 4-3: Image of oil Surface tension at 23Β° C
The manufacturer provided the oil viscosity which can be found in the MSDS sheet
for Shell Omala S2G 100, but for better accuracy the viscosity was measured again in the
laboratory using by using a TA InstrumentsTM HR-3 Rheometer at the proposed
experimental temperature. Due to the inconsistency in fluid temperature due to viscous
dissipation of the oil the actual viscosity observed for each experiment is recorded. The
relationships between the fluid viscosity, fluid density and temperature at which the
experiment was run is shown below in Figure 4-4 and Figure 4-5.
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Figure 4-4: Viscosity and temperature relationship for Shell Omala S2G 100 in the flow loop.
Figure 4-5: Density-Temperature relationship for Shell Omala S2G 100
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4.3 Facility Description
The 1.5-inch ID (2-inch OD) flow loop system at the Terry Fuller Petroleum
Engineering department is where all the experimental procedures discussed were
performed with the exception of the surface tension and some part of the viscosity
experiments, Figure 4-6 and Figure 4-7 are process flow diagrams (PFD) of the modified
flow loop. The overall range of inclination angles of the flow loop is from (-1)Β° to (+ 20)Β°.
For the experiments conducted, the flow loop was raised from 0Β° to (+10)Β° for drift velocity
experiments and 0Β°, 1Β° and 5Β° for steady state water and 0Β° and 5Β° for steady state oil.
Figure 4-6: Overall process flow diagram of the facility courtesy Eghorieta (2018)
Heat Exchanger
Test Section
Liquid Reservoir
Gas Flowmeter
Liquid Flowmeter
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Figure 4-7: Detailed facility diagram Eghorieta (2018)
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The flow loop system has a visualization section that is 6.02m long and made of
clear acrylic pipe that is divided into two halves with the aid of the newly installed Quick
Closing Valves (QCV). The QCVs are 0.71m, 2.76m and 6.02m away from the pipe inlet.
These valves allow for the entrapment and observation of slugs in the pipe and thus during
the experiment one can measure and document the liquid holdup, translation velocity, drift
velocity, slug frequency, and identify different flow patterns. Also present in the
visualization section are capacitance sensors intended for data collection (liquid holdup
and slug frequency), two pressure transducers and three differential pressure meters are
used for collecting pressure drop information of along the visualization section of the flow
loop. Figure 4-8 shows detailed information about the visualization section of the flow
loop from the pipe inlet, Eghorieta (2018).
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Figure 4-8: Visualization section of the flow loop
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4.4 Operating Procedures
Oil Transfer
On September 4th, 2017, Shell Omala S2G 100 mineral/gear oil was transferred out
of the 55-gallon storage tank from the manufacturer into the 80-gallon liquid tank using a
hand operated drum pump Figure 4-9. This oil transfer was done after two days of drying
the entire flow loop system and ensuring that there was no water in the system.
Figure 4-9: Hand operated drum pump (image courtesy MSCDirect.com)
4.5 General Startup Operating Procedure
The first step required before any of the seven-steady state hydrodynamic test can
be performed is to understand how to operate the flow loop system safely and properly. To
do so a quick walk through of the lab is described below. The first step before starting up
the lab is to check the position in which the valves were left during the previous experiment
(open or closed) before proceeding to adjust the valves for the next set of experiments. For
example, if one is conducting experiment that requires the heat exchanger then the liquid
line is redirected to the shell in tube exchanger to heat up the oil before running the
experiment. Also, it is important to lift or drop the flow loop to the desired inclination angle
for the test before turning on the power supply to the flow loop system. Next lift the power
lever to the pump system and flip the switch of the pump box to operate the liquid pump.
Next, open the gas valve to allow gas to flow into the system. To open the valve, the valve
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needs to be parallel to the gas line and when the valve is in a perpendicular position it
means the valve is closed. The final step is to set desired liquid and gas flow rate and begin
the experiment when ready. More detailed information on the general operating procedure
for the flow loop system can be found in Eghorieta (2018).
4.6 General Shutdown Operating Procedure
Once the test matrix for the day is completed the liquid flow rate is set to 0% and
the main switch at the pump box can be flipped to the off position. The gas flow rate is
then stepped up at gradually at 20% valve opening increment till the valve is completely
open at 100%; to flush the rest of the fluid out of the visualization section and into the
liquid tank. The process lasts for about 5-10 minutes depending on the fluid in the
visualization section. The gas valve at the mixing point is then shut off afterwards to
prevent liquid from flowing into the gas line when the system is restarted for another test.
The gas valve is also set perpendicular to the gas line to stop gas flow into the laboratory.
4.7 Experimental Procedures
4.7.1 Visual Capturing
Two Digital SLR canon EOS 70D cameras were used in visually recording
information for slug frequency, slug length, and translational velocity via videos and
pictures, which are then analyzed for verifying and validating existing models and
developing closure relationships for the modified flow loop system.
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Figure 4-10: Canon EOS 70D image courtesy (Texas Tech Universityβs library)
4.7.2 Proper camera setup
Proper setup of the camera entails zooming in on the capacitance sensor and
focusing the camera on it, then zooming out the camera lens to capture more of the subject
area (pipe length).
4.7.3 Hydrodynamic Tests
Flow Pattern
Flow pattern is very important when gathering hydrodynamic behavior of a fluid.
The flow pattern identification experiment aids in finding the boundaries of different flow
patterns present on the flow loop system at 0Β°, 1Β° and 5Β° for water and for oil 0Β°, and 5Β°.
The objectives of flow pattern characterization is to identify slug flow pattern that are
present on the modified flow loop system and establish a comparison of the resulting
experiment to existing flow pattern models by using the FLOPATNTM VBA code as shown
in Chapter 5. To begin the flow pattern test, the temperature, pressure, and densities of the
fluids are recorded by opening ports 1, 3 and 5 on the visualization section of the flow loop.
The variations present in oil mass flow rates at different temperatures and viscosity require
Variable Frequency Drive (VFD) and a gas flow control valve to regulate the liquid and
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gas flow rates for consistent inlet oil and gas flow. The range for oil is 5 β 75% and 5 β
90% for gas at 5% increments. These percentages are then matched to their corresponding
liquid and gas flow rate. The flow rates are then converted to liquid and gas superficial
velocity (VSL and VSG) respectively. To perform the flow pattern experiment, ensure that
the gas and liquid inlet valves as well as all the QCVs on the visualization section are in
the open position. The experiment is mainly dependent on visual inspection and the
identification of the flow pattern is on the observer. The gas and liquid are sent at the
desired gas and liquid flow rate and allowed to reach steady state and the flow pattern is
then identified at the visualization section of the flow loop. It takes the flow loop about a
minute to reach steady state, after which the flow pattern is identified. A total of 1592 test
points for the experiments are 675 for water and 917 for oil. A total of 5 flow pattern tests
were performed on the flow loop based on angle and inclination and each test lasting 4
hours.
Slug Frequency
Slug frequency is the number of slugs per unit of time (slugs per minute) at a
location. The reference location for capturing slugs for the experiment is at the capacitance
sensor and its surrounding areas. A slug can be reliably identified from its visual profile.
There are three main attributes of the slug unit (LU) that one needs to look for when
identifying a slug: the front scoop or mixing front (LM), the bridging of the pipe (LS), which
is also known as the slug and finally the bullet like front of the tail (LF) known as Taylor
bubble signifies the end of the slug. These attributes of the slug are shown in Figure 4-11
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Figure 4-11: Typical slug length attributes
To accurately capture slug frequency, the camera needs to be setup properly as
discussed in 4.7.2 Proper camera setup. The pump rates of both gas and liquid are set to
the desired superficial velocities from the test matrix and allowed to stabilize for one
minute before recording the slug movement for the ensuing 60 seconds. There are three
capacitance sensors on the visualization section. These are 1.13m, 3.47m, and 6.33m away
from the mixing tee respectively. The same technique described above is used to capture
the slug frequency at each sensor. The total number of tests performed to obtain slug
frequency for water was 144 (16 x 3 x 3), while the total number of tests for oil was 48 (8
x 3 x 2). The slug frequency was then analyzed with Final Cut Pro (2017) in which the
video was slowed to 5% of its original speed and markers placed and counted for each slug
passing through the pipe for each video of a given time.
Translational Velocity and Slug Length
Translational velocity and slug length tests were performed simultaneously with
the following procedure. The length of the visualization section where the slugs are
captured using a camera and timer is first identified. The camera is then set to high bust
mode to capture slugs at 0.14 Β΅sec. Once the camera is focused on the desired location of
LM
LS LU
LF
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the visualization section, an iPad timer, and camera are used to capture picture of the slugs
continuously. A good image captures both the slug and the time stamp recorded on the
timer as shown in Figure 4-12. An average of 800 pictures is taken for each test point in
the test matrix. The test lasts about 30 minutes for each test point (VSL and VSG) and the
minimum number of people required for this test is 1. To analyze the translational velocity,
the Taylor bubbles of the slug of interest are tracked either by using the slug tail β slug tail
or slug front β slug front but not slug tail β slug front or vice versa. The difference in time
between these slug tails or slug front is used calculate the velocity of the slugs.
ππππππ = π»π»πππ’π’ππ οΏ½πππππππππππππππ‘π‘ππ οΏ½πππππππ‘π‘π‘π‘
β π π πππ’π’ππ οΏ½πππππππππππππππ‘π‘ππ οΏ½πππππππ‘π‘πππ‘π‘π‘π‘
πππ‘π‘πππππππππππ‘π‘π‘π‘ β πππ‘π‘πππππππππππ‘π‘πππ‘π‘π‘π‘
(4-1)
The slug length is obtained from the same picture used for VTB. The tape rule
attached to the visualization section is used to determine the length of the slug body. Of
the 800 pictures captured for the VTB and the slug length test only 100 pictures were viable
for analyzing VTB and 50 pictures for slug length.
Figure 4-12: Translational velocity captured using cameras and timer
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Drift Velocity
A brief overview of the drift velocity test is described here as Eghorieta (2018)
gives a very detailed description of the test. The synopsis of the test is that the visualization
section is raised to the desired inclination angle (0 ,1,3,5,7, and 10) degrees and then filled
with liquid (single phase). The two types fluids on which the drift velocity test was
performed on are water and oil. For the oil test two different viscosities are examined (280
and 150) cP. It is important to visually inspect for any gas bubbles trapped in the section.
It is paramount that there are no gas bubbles along the visualization section as that could
affect the result of the test. Next, the trap section is drained by opening valve 36 and it is
from opening this valve that air is introduced into the test section. For the success of the
test, close valve 36 after draining the trap section when performing a No Drain Test. Two
types of tests are performed for the drift velocity, the Drain and No Drain Test. A stopwatch
is used to record the time it takes for the air bubble to travel from the inlet to the outlet of
the visualization section and the three capacitance sensors are used as distance markers.
The third step is ensuring that the QCV opened (parallel to the pipe) and the stopwatch is
synchronized to when the test begins. The drift velocity is then calculated by dividing the
difference in distance with the difference in time between C1-C2, C2-C3 and C1-C3.
Where C stands for capacitance sensor and the numbers 1-3 indicates the position of the
sensor away from the pipe inlet.
Pressure Drop
Pressure drop is an important parameter when studying hydrodynamic behavior of
slugs as the fluidβs resistance to flow occurring across the visualization section is needed.
Pressure drop is measured with pressure transducers and differential pressure sensors as
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labeled in Figure 4-2. There are five pressure sensors on the visualization section and each
sensor gives the pressure drop across the distance of the section. The test runs for
approximately 15 minutes and for each test points three different readings are taken at 3
minutes interval and 1- 2 minute spacing between each test. Below is a table of how
pressure test across the whole visualization section is obtained.
Table 4-7: Pressure drop test table
Test Location DP1, 2, 5 DP34 DP135
Test Time (2:11-2:14) PM (2:16- 2:19) PM (2:21-2:24) PM
To obtain pressure reading in the first half of the visualization section, PT1, and
DP1 sensors are used along with ports 1,2 and 5, which are connected to DP 1. For the
second half of the loop PT2, DP2 sensors as well as port 3, 4, and 5 are used to gather the
pressure information that is sent to the data acquisition system and later uploaded to a
computer. The pressure readings gotten from each test is then sifted before any statistical
analysis can be performed as the data acquisition system records at 1HZ.
Liquid Holdup
The test for liquid holdup is very similar to that of translational velocity in that
pictures of the slug are taken for numerical validation. The first step to starting the
experiment is to follow the general operating procedures. Next setup the cameras in a
similar manner as explained previously. A very important step of the liquid holdup test is
capturing the slug movement on both cameras from QCV 2 to 3. This test requires a
minimum of two people for it to be successful performed. The reason for this is that one
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person needs to open and close QCV 2 and 3 when required, while the other person
observes the slug movement in the pipe and captures the slug with the cameras on high
bust mode while at the same time alerting the first person to shut the QCVs. The gas inlet
valve at the mixing tee is closed and the liquid is diverted into the liquid tank. The
visualization section is then lifted with a pulley to drain the fluid trapped between QCV 1
and 2, before draining and measuring the fluid trapped in QCV 2 and 3 with a 2000 mL
polyethylene measuring cylinder with +/- 20 mL error. Immediately the fluid is drained
into the cylinder the volume of the liquid is recorded and again at time greater than 10
minutes. For each point on the test matrix the liquid holdup test is repeated 7 times for
repeatability and accuracy.
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CHAPTER 5 DISCUSSION AND RESULTS
The observed results of high viscosity oil in phase air-oil flow in horizontal pipes
is discussed in this chapter. The experimental study was performed on mineral oil (Shell
Omala S2G 100) at two different viscosities 150 cP and 280 cP and inclination angles of
0Β° and 5Β°. The corresponding temperature for the viscosities are 70Β°F and 90Β°F, and a total
of 32 test were performed for both viscosities. The subsequent sections in this chapter will
discuss the test matrix and experimental results of air-water and air-oil two-phase flow
tests. These sections will be grouped based into the parts listed: flow pattern, translational
velocity, drift velocity, pressure drop, and slug flow hydrodynamic parameters - liquid
holdup, slug length, and slug frequency.
5.1 Experimental Test Matrix
Water flow pattern identification test was the first batch of experiment conducted
when validating the flow loop system modified by Eghorieta (2018). The flow pattern
identification tests were followed by the drift velocity, pressure drop, and slug flow
hydrodynamics tests for air-water cases. Upon the completion of the water experiments,
the flow loop system including the liquid tank was drained and dried before oil was
introduced. The same tests listed above are duplicated for oil at the same inclinations used
for the water test, but different viscosities and superficial gas and liquid velocities. In this
section, the test matrices for water experiments and oil experiments are shown separately
and grouped based on the gas and liquid fluid properties.
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5.1.1 Test Matrix for Detailed Air-Water Slug Flow Hydrodynamics Experiments
A total of 48 pairs of πππππΏπΏ and πππππΊπΊ were studied for the air-water case, but only 12
of these points were studied in detail as shown in the tables below. The 48 operating
conditions were achieved by using the pump speed of 35, 45, 55, and 65 and the percent
air valve opening of 45, 50, 55, and 60 at the inclination angle of 0, 1, and 5Β°. From Table
5-1 only the four corners points are studied in detail to obtain slug flow hydrodynamics
measurements. The detailed measurements include liquid holdup, translational velocity,
slug frequency, pressure drop and slug length measurements. Table 5-1 shows the detailed
hydrodynamics characteristics on the 12 operation points at the boundary. The selected
percent pump speed was at 35 and 65. The selected percent air valve opening are at 45 and
60. The tests were conducted at the inclination angle of 0, 1, and 5Β°. Totally, the test of 2
(% pump speed) x 2 (% air valve opening) x 3 (angles) were conducted. Table 5-2 and
Table 5-3 shows the detailed fluid properties for the four boundary points studied at each
inclination.
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Table 5-1: Air β water hydrodynamic Properties for the 4 corner points at each inclination angle studied in detail
Test name
Liqu
id
Hol
dup
[HLL
S]
Tran
slat
iona
l V
eloc
ity
[m/s
]
Slug
Len
gth
[m]
Slug
Fr
eque
ncy
[HZ]
Pres
sure
D
rop
[psi
g]
1-L35_G45_A0 1-L35_G60_A0 1-L65_G45_A0 1-L65_G60_A0 1-L35_G45_A1 1-L35_G60_A1 1-L65_G45_A1 1-L65_G60_A1 1-L35_G45_A5 1-L35_G60_A5 1-L65_G45_A5 1-L65_G60_A5
0.841 0.648 0.745 0.701 0.869 0.829 0.809 0.652 0.840 0.859 0.798 0.718
2.698 5.275 3.506 4.488 3.113 4.220 3.202 5.174 3.374 4.875 3.703 5.158
0.626 0.646 0.489 0.730 0.629 0.671 0.513 0.725 0.567 0.703 0.485 0.664
0.967 0.800 1.983 1.800 1.067 0.767 2.367 1.717 1.150 1.067 2.483 1.950
2.62 3.38 4.82 6.34 2.68 3.41 4.82 6.32 2.97 3.66 5.20 6.61
Table 5-2: Water flow properties for air-water detailed slug flow hydrodynamics experiment.
Test name
Pum
p sp
eed
[%]
Tem
pera
ture
[Β°
F]
ππ πΏπΏ [k
g/m
3 ]
ππ πΏπΏ [
cP]
πππΏπΏ
[g/s
]
π’π’ πππΏπΏ
[m/s
]
π π ππ πππΏπΏ
[-]
1-L35_G45_A0 1-L35_G60_A0 1-L65_G45_A0 1-L65_G60_A0 1-L35_G45_A1 1-L35_G60_A1 1-L65_G45_A1 1-L65_G60_A1 1-L35_G45_A5 1-L35_G60_A5 1-L65_G45_A5 1-L65_G60_A5
0.661 0.661 1.213 1.208 0.660 0.658 1.203 1.205 0.659 0.654 1.203 1.206
74.09 75.12 74.38 74.62 74.01 75.42 75.82 75.97 70.46 71.71 71.70 73.14
992.4 992.7 993.0 990.7 992.5 991.9 985.8 989.2 992.5 991.7 988.1 990.3
1 1 1 1 1 1 1 1 1 1 1 1
727.60 727.89 1336.84 1328.23 727.26 724.68 1315.94 1323.18 725.44 719.74 1319.49 1325.45
0.661 0.661 1.213 1.208 0.660 0.658 1.203 1.205 0.659 0.654 1.203 1.206
25 25 46 46 25 25 45 45 25 25 45 45
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Table 5-3: Air flow properties for air-water detailed slug flow hydrodynamics experiment.
Test name
Air
valv
e op
enin
g [%
]
Tem
pera
ture
[Β°
F]
ππ πΊπΊ [k
g/m
3 ]
ππ πΊπΊA [
cP]
πππΊπΊ
[g/s
]
π’π’ πππΊπΊ
[m/s
]
π π ππ πππΊπΊ
[-]
1-L35_G45_A0 1-L35_G60_A0 1-L65_G45_A0 1-L65_G60_A0 1-L35_G45_A1 1-L35_G60_A1 1-L65_G45_A1 1-L65_G60_A1 1-L35_G45_A5 1-L35_G60_A5 1-L65_G45_A5 1-L65_G60_A5
45 60 45 60 45 60 45 60 45 60 45 60
74.09 75.12 74.38 74.62 74.01 75.42 75.82 75.97 70.46 71.71 71.70 73.14
1.422 1.480 1.599 1.721 1.425 1.480 1.593 1.714 1.454 1.507 1.632 1.742
0.01854 0.01856 0.01854 0.01855 0.01853 0.01857 0.01858 0.01859 0.01844 0.01847 0.01847 0.01851
0.305 0.610 0.306 0.609 0.303 0.604 0.300 0.606 0.312 0.614 0.310 0.615
1.463 2.809 1.305 2.410 1.447 2.780 1.284 2.407 1.460 2.773 1.292 2.404
4274 8533 4287 8518 4239 8442 4194 8454 4386 8620 4350 8621
5.1.2 Test Matrix of Air-Oil Detailed Hydrodynamics Experiments
For air-oil slug flow experiment, the detailed measurements were conducted at
every test point. These measurements are pressure drop, slug frequency, liquid holdup,
translational velocity, and slug length. Air-oil hydrodynamics experiments were conducted
at about 70 and 90 Β°F. At each temperature, the tests were conducted at the inclination
angle of 0Λ and 5Λ. The πππππΏπΏ and πππππΊπΊ were controlled by selecting the desired percent pump
speed and percent air valve opening. The test matrix describing the pair of the pump speed
and percent air valve opening is shown Table 5-4 and Table 5-5 for liquid and gas
properties respectively. These test matrices also include the superficial Reynolds number,
and other flow related properties.
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Table 5-4: Oil flow properties for air-oil detailed slug flow hydrodynamics experiment.
Test name
Pum
p sp
eed
[%]
Tem
pera
ture
[Β°
F]
ππ πΏπΏ [k
g/m
3 ]
ππ πΏπΏ [
cP]
πππΏπΏ
[g/s
]
ππ πππΏπΏ
[m/s
]
π π ππ πππΏπΏ
[-]
280-L20_G30_A0 20 72.6 863 252 339 0.345 45 280-L20_G45_A0 20 73.1 860 248 335 0.342 45 280-L25_G35_A0 25 76.6 859 221 422 0.431 64 280-L30_G40_A0 30 76.5 856 222 506 0.519 76 280-L35_G30_A0 35 77.9 860 212 604 0.616 95 280-L35_G45_A0 35 82.3 856 185 597 0.612 108 280-L40_G30_A0 40 76.5 859 221 685 0.700 103 280-L40_G40_A0 40 83.8 856 178 689 0.707 130 280-L20_G30_A5 20 72.2 862 256 337 0.343 44 280-L20_G45_A5 20 75.6 859 228 335 0.342 49 280-L25_G35_A5 25 79.5 858 202 425 0.434 70 280-L30_G40_A5 30 80.9 856 193 509 0.521 88 280-L35_G30_A5 35 81.9 857 188 601 0.615 107 280-L35_G45_A5 35 83.8 856 178 599 0.614 113 280-L40_G30_A5 40 82.0 856 187 686 0.703 122 280-L40_G40_A5 40 85.6 854 169 683 0.702 135 150-L20_G30_A0 20 93.5 856 136 343 0.351 84 150-L20_G45_A0 20 90.1 855 149 338 0.346 76 150-L25_G35_A0 25 91.1 855 145 428 0.440 99 150-L30_G40_A0 30 91.0 854 146 512 0.527 118 150-L35_G30_A0 35 90.6 855 147 603 0.618 137 150-L35_G45_A0 35 90.4 855 148 602 0.618 136 150-L40_G30_A0 40 92.5 853 140 693 0.712 165 150-L40_G40_A0 40 91.7 853 143 688 0.707 161 150-L20_G30_A5 20 87.9 856 158 339 0.348 72 150-L20_G45_A5 20 89.2 855 153 339 0.348 74 150-L25_G35_A5 25 90.6 854 147 427 0.438 97 150-L30_G40_A5 30 89.6 855 151 513 0.526 114 150-L35_G30_A5 35 91.3 855 144 607 0.622 140 150-L35_G45_A5 35 91.7 853 143 599 0.616 140 150-L40_G30_A5 40 97.6 852 123 698 0.718 190 150-L40_G40_A5 40 90.8 853 146 684 0.703 156
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Table 5-5: Air flow properties for air-oil detailed slug flow hydrodynamics experiment.
Test name
Air
valv
e op
enin
g [%
]
Tem
pera
ture
[Β°
F]
ππ πΊπΊ [k
g/m
3 ]
ππ πΊπΊA [
cP]
πππΊπΊ
[g/s
]
ππ πππΊπΊ
[m/s
]
π π πππππΊπΊ
[-]
280-L20_G30_A0 30 71.8 1.715 0.0185 1.16 0.592 2092 280-L20_G45_A0 45 72.0 1.764 0.0185 2.38 1.186 4305 280-L25_G35_A0 35 74.3 1.761 0.0186 1.52 0.762 2747 280-L30_G40_A0 40 75.0 1.896 0.0186 1.90 0.881 3422 280-L35_G30_A0 30 75.4 1.933 0.0186 1.16 0.527 2081 280-L35_G45_A0 45 77.0 1.936 0.0188 2.39 1.093 4296 280-L40_G30_A0 30 73.2 2.124 0.0186 1.91 0.795 3458 280-L40_G40_A0 40 78.3 1.964 0.0188 1.92 0.866 3448 280-L20_G30_A5 30 73.4 1.714 0.0185 1.15 0.589 2083 280-L20_G45_A5 45 77.4 1.713 0.0186 2.32 1.186 4168 280-L25_G35_A5 35 76.7 1.733 0.0187 1.53 0.779 2752 280-L30_G40_A5 40 81.1 1.819 0.0187 1.89 0.911 3374 280-L35_G30_A5 30 78.4 1.863 0.0187 1.17 0.553 2093 280-L35_G45_A5 45 77.7 1.919 0.0188 2.36 1.091 4243 280-L40_G30_A5 30 74.9 1.965 0.0188 1.18 0.535 2136 280-L40_G40_A5 40 79.1 1.947 0.0188 1.90 0.867 3413 150-L20_G30_A0 30 72.3 1.500 0.0191 1.19 0.722 2164 150-L20_G45_A0 45 71.6 1.576 0.019 2.40 1.381 4373 150-L25_G35_A0 35 77.3 1.590 0.019 1.51 0.854 2723 150-L30_G40_A0 40 77.8 1.688 0.019 1.91 1.015 3435 150-L35_G30_A0 30 72.9 1.736 0.019 1.19 0.624 2173 150-L35_G45_A0 45 70.4 1.824 0.019 2.42 1.206 4416 150-L40_G30_A0 30 79.3 1.770 0.019 1.17 0.595 2107 150-L40_G40_A0 40 77.3 1.830 0.019 1.92 0.946 3467 150-L20_G30_A5 30 71.4 1.569 0.0189 1.18 0.682 2156 150-L20_G45_A5 45 71.0 1.603 0.0189 2.39 1.355 4368 150-L25_G35_A5 35 78.7 1.615 0.019 1.51 0.839 2719 150-L30_G40_A5 40 74.4 1.732 0.019 1.93 1.003 3493 150-L35_G30_A5 30 71.5 1.756 0.019 1.18 0.610 2146 150-L35_G45_A5 45 71.8 1.824 0.019 2.37 1.183 4324 150-L40_G30_A5 30 71.3 1.766 0.0192 1.19 0.622 2184 150-L40_G40_A5 40 72.0 1.887 0.019 1.94 0.933 3535
A The air viscosity was calculated based on the oil temperature by using Sutherlandβs formula
Texas Tech University, Tolani A. Afolabi, May 2018
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5.2 Flow Pattern
5.2.1a Flow Pattern Determination Test Matrix
For both the water and oil case experiments, the pump-speed and air-inlet valve-
opening-percentage are used to control the liquid and gas flow rates. For the water test, 2
inclination angles (0, 1, and 5) Β° are examined at temperature range of 70-76 Β°F. A total of
484 tests was performed on flow pattern for the water cases for both the 0Β° and 1Β°. The
pump-speeds opening and air inlet valve opening percentages used for both air-water and
air-oil flow pattern experiments range from 5, 10, 15, β¦, 70, 100. The percent pump speed
and the percent valve opening are then converted to their corresponding πππππΏπΏ and πππππΊπΊ based
on the measured value of the gas flow rate, liquid flow rate, density, and pressure.
Equations 5.1 and 5.2 are used to solve for the gas and liquid superficial velocities are
shown below.
π£π£πππΊπΊ =πππΊπΊ
πππΊπΊπ΄π΄ππ (5-1)
π£π£πππΏπΏ =πππΏπΏ
πππΏπΏπ΄π΄ππ (5-2)
Where, πππΊπΊ and πππΏπΏ are gas and liquid mass flow rate respectively
Two inclination angles at 0 Β° and 5Β° were examined for the oil flow pattern
determination experiments. The nominal temperatures for the oil test are 70 and 90 Β°F
which correspond to the nominal viscosities of 280 cP and 150 cP respectively. A total of
four combinations, 2 (viscosities) x 2 (angles), of the flow pattern test were conducted and
these resulted in 917 pairs of πππππΏπΏ and πππππΊπΊ. A modification was made to the air- oil flow
pattern experiment by recording the pressure drop at the pipe inlet (PT1) was used as the
Texas Tech University, Tolani A. Afolabi, May 2018
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pressure value in the density ideal gas equation to back calculate the value of gas density,
πππΊπΊ in Equation 5.3. For the air- water case the gas density used to calculate all πππππΊπΊ values
are 1.22 π π πΎπΎππ3 . The observed behavior of pressure drop during the flow pattern experiment is
shown in the sections below. The relationship between the pump speed, valve opening
percentage, πππππΏπΏ and πππππΊπΊ is given below in Table 5-6 for air-water and in APPENDIX A for
air-oil cases, respectively.
πππΊπΊ =ππ β πππ π β ππ
(5-3)
The units used in Equation 5-3 are P in Pascal, M in πΎπΎπππ‘π‘π‘π‘
, R in 8.314 πππ‘π‘βπΎπΎβπ π β1βπππ‘π‘π‘π‘β1
πππ‘π‘π‘π‘βππ3βπππ‘π‘βπ π and
T in K
Table 5-6: Relationship between percent pump speed, percent air valve opening with πππππΏπΏ and πππππΊπΊ for air-water cases.
% pump speed
πππππΏπΏ (m/s)
% air valve opening
πππππΊπΊ (m/s)
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0.099 0.194 0.289 0.383 0.478 0.573 0.668 0.763 0.858 0.952 1.047 1.142 1.237 1.332 1.427 1.521 1.616 1.711 1.806 1.901
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0.056 0.111 0.167 0.334 0.612 0.834 1.113 1.391 1.946 2.113 2.668 3.389 4.274 5.267 6.204 7.028 8.935 10.719 11.889 12.584
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The size of the flow pattern table for air-oil case is quite large and it can be found
in APPENDIX A; therefore only the nominal fluid properties for the test points studied in
detail shown in Table 5-2, Table 5-3, Table 5-4, and Table 5-5 for liquid and gas
respectively. These fluid properties are used to generate the transition boundaries and then
superimposed unto the flow pattern map generated experimentally. Table 5-7 is a summary
of the fluid properties inputted into FLOPATNTM 2.7 to generate the transition boundary
superimposed to the experimental flow pattern map generated by the flow loop. The
simulator code was provided by Ovadia Shoham. The figures below demonstrate how the
flow patterns observed in the flow loop compare to the transition boundaries generated
with FLOPATNTM 2.7.
Table 5-7: Summary of the fluid properties used in FLOPATNTM to generate transition boundaries for the superimposed flow pattern maps.
Incl
inat
ion
[Λ]
Surfa
ce
Tens
ion
[N/m
]
Liqu
id
Den
sity
[K
g/m
3 ]
Gas
Den
sity
[K
g/m
3 ]
Liqu
id
Vis
cosi
ty
[Kg/
m.s]
G
as
Vis
cosi
ty
[Kg/
m.s]
Dia
met
er
[m]
Inte
rface
0
5
1
0
0
5
5
0.0072
0.0072
0.0072
0.0311
0.0306
0.0311
0.0306
992.1981
990.6370
989.8523
858.4257
854.3507
857.1383
854.3507
1.5550
1.5550
1.5550
1.8870
1.6890
1.8340
1.7190
0.0010
0.0010
0.0010
0.2800
0.1500
0.2800
0.1500
1.8452E-5
1.8452E-5
1.8452E-5
1.8452E-5
1.9006E-5
1.8703E-5
1.8998E-5
0.04
0.04
0.04
0.04
0.04
0.04
0.04
smooth
smooth
smooth
smooth
smooth
smooth
smooth
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5.2.1b Flow Pattern Definitions
The experiments conducted for flow pattern tests in this study fall with the
inclination range of horizontal to near-horizontal flow and it is for this reason that the
definitions and criteria proposed by Shoham (2006) and the most important attributes of
the flow patterns from his definitions are summarized below. Shoham (2006) identified the
flow patterns that occur in horizontal and near-horizontal flow. These flow patterns are
Stratified flow (Smooth and Wavy), Intermittent (Elongated Bubble and Slug flow),
Annular and Dispersed-Bubble Flow.
Stratified Flow (SS or SW) occurs at low gas and liquid flow rates, where the
fluids are separated and do not comingle due to gravity. The two types of stratified flow
are Stratified -Smooth and Stratified-Wavy. Stratified smooth occurs at lower flow rates
than Stratified-Wavy and the interface between the gas and liquid is smooth while the
interface between the gas and liquid for stratified-wavy is wavy.
Intermittent Flow (EB or S) There are two types of intermittent flow, elongated
bubble flow and slug flow. based on the gas and liquid flow rate. As the name implies the
fluid phases occur in alternately or intermittently, that is the slug liquid fills the pipe cross-
sectional area and the next liquid phase is separated by gas pockets. The fast-moving slugs
overtake the slow-moving liquid film ahead of it. The slug body may be aerated by small
bubbles which we noticed was present in the air-water case, but absent for the high
viscosity oil used in this study. The elongated bubble is the limited case of slug flow as the
liquid slug is free of entrained bubbles. It is important to note that elongated bubbles occur
at relatively lower gas rates and a higher gas rates slug flow occurs.
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Annular Flow (A) occurs at very high gas rates and the liquid flow is a thing film
that surrounds the pipe with the gas phase flows at the core; like a sandwich. The interface
between the two fluid phases is wavy and thus leads to high shear stress. Apart from the
regular annular flow pattern Shoham (2006) identified wavy-annular flow which is a
combination of the transition boundary between stratified-wavy, slug and annular flow, but
not fully developed to be any of the flow patterns individually. The last flow pattern to be
discussed in the reference material is Dispersed bubble flow.
Dispersed bubble (DB) occurs at very high liquid flow rates and the gas bubbles
are distributed uniformly across the cross-sectional area of the pipe. The uniformity in flow
implies that the two fluid phases are moving at the same velocity and the flow is classified
as homogenous no-slip. For more details on the flow patterns listed above refer to Shoham
(2006).
The flow patterns identified outside of the definitions above will be discussed
below.
Short Slugs and Short Bubbles (SSL and SB) occur at high πππππΏπΏ (πππ π
) rates and
low πππππΊπΊ (πππ π
) and were identified during the flow pattern experiment for air-high viscosity
oil case. This flow pattern is intermittent just like slug flow; the difference is that the slugs
are very short and are suspended at the top of the pipe. Short slugs replace the dispersed
bubble flow region in Figure 5-3.
Roll Wave (RW) was identified by Hiroaki Matsubara et al (2011) when they
studied the effect of liquid viscosity on flow patterns of gas-liquid two-phase flow in a
horizontal pipe and used pressure drop signals to distinguish the difference between rolling
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wave and stratified flow. We identified rolling wave as well in this study at high πππππΊπΊ (πππ π
)
for the air-high viscosity oil study. The similarity between wavy-annular identified by
Shoham (2006) and Roll wave suggests that the authors might be referring to the same
phenomenon.
5.2.2 Flow Pattern Result 5.2.2a Water flow pattern case
For the 0Β° flow pattern test, several flow patterns were individually identified by
visually inspection at the different gas and liquid flow rates before they were converted to
their corresponding πππππΏπΏ (πππ π
) and πππππΊπΊ (πππ π
). The calculated πππππΏπΏ (πππ π
) and πππππΊπΊ (πππ π
) were then
plotted on a logarithmic graph. In Figure 5-1, annular (A), elongated (EB) bubbles, slugs
(SL), stratified Smooth (SS), and stratified wavy (SW) flow as well as transition flows
such as elongated bubbles transitioning into slug flow (EB/SL) or slug flow to annular
flow (SL/A) at low fluid rates and high fluid rates. No new flow pattern was observed, but
the boundaries generated in FLOPATNTM 2.7 do not align with what was observed in the
flow loop. Three-fourths of the identified SS and SW flow patterns are above the stratified
boundary, thus shifting the annular flow into intermittent flow. This does not make either
of the results wrong, as one result is what was observed visually in the flow loop and the
other a boundary generated from numerical simulation. Further investigation is needed to
determine the root cause of the observed shift in flow pattern observation and boundaries.
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Figure 5-1: Flow pattern map generated for the flow loop system for water at 0Β° superimposed to FLOPATN 2.7 VBA code
The same test was performed for the water test at 1Β°. Here, fewer flow patterns were
observed at the raised angle. The flow patterns observed in Figure 5-2 are annular (A),
elongated (EB) bubbles, slugs (SL), and stratified wavy (SW) flow as well as transition
flows such as elongated bubbles transitioning into slug flow (EB/SL) or slug flow to
annular flow (SL/A) at low fluid rates and high fluid rates respectively. The missing flow
pattern is stratified smooth (SS). With an increase in inclination, the intermittent flow
region for water increased in the vertical direction (πππππΏπΏ); that is with EB and SL flow
pattern replaced SS flow pattern. The transition boundaries are beginning to converge with
the experimental data as all the intermittent flow patterns are within the boundary, but some
of the annular flow pattern (A) can be found in the intermittent section similar to the case
of 0Β° where the transition boundary is below the boundary observed from the flow loop.
ππ πππΏπΏ[ππ π π
]/
πππππΊπΊ[πππ π
]/
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Figure 5-2: Flow pattern map generated for the flow loop system for water at 0Β° superimposed to FLOPATN 2.7 VBA code
5.2.2b Oil flow pattern case
In addition to using the same methodology used in the air-water flow pattern test, a
pressure drop measurement was added to the air-oil flow pattern map experiment. The
results of the test are illustrated in Figure 5-3 -Figure 5-8. The flow patterns were identified
by visual inspection and converted to their corresponding πππππΏπΏ and πππππΊπΊ , then plotted on a
logarithmic graph. Flow patterns identified in the flow loop for the air- oil case at 280 cP
are, annular (A), elongated (EB) bubbles, roll wave (RW), slugs (SL), short slugs (SSL),
and stratified wavy (SW), as well as transition flows such as elongated bubbles
transitioning into slug flow (EB/SL), or slug flow into annular flow (SL/A) are identified
in the flow loop. For the air-oil case at 280 cP, the predominant flow pattern observed is
the slug flow pattern, and when compared to air-water case shows an increase in the types
of flow pattern is observed in the flow loop. Similar to the case of water the flow pattern is
superimposed onto the transition boundary generated and similar to the case of water where
ππ πππΏπΏ[ππ π π
]
πππππΊπΊ[πππ π
]
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three-fourths of the flow pattern identified was above the transition boundary as shown in
Figure 5-2. Majority of the flow patterns identified in Figure 5-3 are found in the
intermittent flow pattern region of the map. In Figure 5-3, some of the flow patterns
identified in the intermittent case spill over into the dispersed bubble transition boundary;
the annular flow identified in the flow loop is also found in the intermittent flow area.
Figure 5-3: Flow pattern map generated for the flow loop system for oil at 0Λ and 280 cP superimposed to FLOPATN 2.7 VBA code
An interesting effect is observed when the pressure drop along the pipe is
incorporated into the flow pattern experiment, as the flow pattern continuously changes in
the pipe. Figure 5-4 and Figure 5-5 are 3-D maps showing how pressure drop changes
along the pipe with respect to πππππΏπΏ and πππππΊπΊ. The labels of the figures correspond to the
section of the pipe depicted, with DP1_DL which is the pressure drop per unit length in the
first half of the visualization section (the section between capacitance sensors 1 and 2), and
DP3_DL corresponds to the second half of the visualization section (the section between
ππ πππΏπΏ[ππ π π
]
πππππΊπΊ[πππ π
]
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capacitance sensors 2 and 3). For a relevant diagram of the flow loop itself, refer to Figure
4-3. The color gradient from blue to red shows an increase in pressure drop per unit length,
where dark blue is the lowest pressure drop per unit length observed and dark red the
highest. In the case of pressure drop close to the inlet, the highest-pressure gradient
corresponds to the transition boundary of SL/A on the flow pattern map. Looking at the
map from the coolest color (blue) to the hottest color (red) the flow patterns identified by
the pressure map are continually evolving as shown by the gradual color transition in
shown in Figure 5-4 and Figure 5-5 which is contrary to the abrupt changes observed during
visual identification of the flow pattern. The pressure drop results does corroborate the
results of the flow pattern identified visually and highlight that flow pattern does not
change abruptly, but gradually. Another interesting observation when comparing Figure
5-4 and Figure 5-5 is that DP1_DL (Figure 5-4) is identical to DP3_DL (Figure 5-5) even
when there is an increase in pressure drop per unit length. Thus, validating that the same
flow pattern is observed in the both halves of the visualization section.
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Figure 5-4: Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination
Figure 5-5: Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination.
For the air-oil case at 280 cP at 5Β°, the predominant flow pattern observed is still
the slug flow pattern, and when compared to the flow pattern case of 280 cP at 0Β° additional
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types of flow pattern are observed in the flow loop. Some of the newly identified flow
patterns are short bubbles (SB), stratified wavy- annular (SW/A) shown in Figure 5-6.
Figure 5-6: Flow pattern map generated for the flow loop system for oil at 5Λ and 280 cP superimposed to FLOPATN 2.7 VBA code
The same effect in regard to pressure drop along the pipe first noted when performing the
flow pattern experiment at 0Β° and 280 cP is also found for 5Β° and 280 cP. The pressure
drop observed is much lower than the pressure per unit length at 0Β°, and the same pressure
drop signature is observed with the flow pattern continuously changing in the pipe. Figure
5-7 and Figure 5-8 are also 3-D maps showing how pressure drop per unit length changes
along the pipe with respect to πππππΏπΏ and πππππΊπΊ. As discussed previously, DP1_DL corresponds
to the pressure drop per unit length at the first half of the visualization section (the section
between capacitance sensors 1 and 2), while DP3_DL refers to the same parameter for the
second half of the visualization section (the section between capacitance sensors 2 and 3)
ππ πππΏπΏ[ππ π π
]
πππππΊπΊ[πππ π
]
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see (Figure 4-3) The same explanations and observations described for the air-oil case at
280 cP and 0Β° pressure drop results apply to the case of 280 cP and 5Β°.
Figure 5-7: Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination
Figure 5-8: Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination
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Once the flow pattern for the higher viscosity oil was performed and documented,
the heat exchanger section along with a heating coil was used to reduce the viscosity of the
oil to a nominal viscosity of 150 cP by raising the temperature from 75Β°F to 90Β°F. For the
0Β° flow pattern test, the same flow patterns observed for oil at 280 cP were observed
visually and thus the results are shown in APPENDIX A.
5.3 Translational Velocity
5.3.1a Inclination: Zero Degrees
Experimentally it was observed that translational velocity ( ππππππ ) of fluids
decreases as the viscosity of the fluid increases from 1-280 cP. Translational velocity is
highly driven by superficial gas velocity πππππΊπΊ. The experimental methodology for obtaining
translational velocity data can be found in Chapter 4. Translational velocity is need as a
closure relationship in Taitel and Barnea mechanistic model. Equation 5.4 is the original
closure relationship for ππππππ , while Equation 5.5 is the modified ππππππ equation by
Bendiksen, this equation considers the effect of inclination, but neither equation considers
the effect of viscosity on ππππππ.
ππππππ = πΆπΆ0ππππ + ππππ
(5-4)
ππππππ = πΆπΆ0ππππ + 0.54οΏ½ππππ πππππ π ππ + 0.35οΏ½ππππ sin(ππ)
(5-5)
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Where; πΆπΆ0 is the flow distribution coefficient, ππππ is the mixture velocity and ππππ is
the drift velocity are in units of πππ π
. The method for obtaining and analysing translational
velocity and drift velocity is described in Chapter 4. For the air-water test, the translational
velocity was performed for 4 test points and 3 inclination angles, but only inclinations 0Β°
and 5Β° are reported in this discussion. Figure 5-9-Figure 5-17 show all the observations and
results obtained for translational velocity at the different viscosities (1, 150 amd 280) cP
and different inclination angles ( 1 and 5) Β° exaimined. The 3-D heat map represents the
data gathered from the experimental program for (1, 150 and 280 ) cPΒ°. In the maps blue
represent the slowest ππππππ values observed at πππππΏπΏ and πππππΊπΊ pairs, while red represents the
fastest ππππππ values observed at πππππΏπΏ and πππππΊπΊ pairs. Figure 5-9 shows that at 1 cP and 0Β° the
fastest ππππππ is at a high πππππΊπΊ and low πππππΏπΏ and the slowest ππππππ is at low πππππΏπΏ and low πππππΊπΊ
rates. The effect of viscosity is examined experimentally for 150 and 280 cP oil. The
observation of the impact of viscosity on ππππππ shows that an increase in fluid viscosity
reduces ππππππ. At both viscosities, a similar trend is observed as shown in Figure 5-10, ππππππ
decreased as the oil viscosity increased from 150 β 280 cP. In summary ππππππ for fluid
viscosity at 0Β° is influenced more by πππππΊπΊ and an increase in fluid viscosity decreases ππππππ.
To demonstrate the full impact of viscosity on ππππππ Figure 5-11 combines all fluids
examined. Althoug the air-water case is not examined at exactly the same πππππΏπΏ and πππππΊπΊ
pairs, it still supports the experimental claim.
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Figure 5-9: Translational velocity for water at 1 cP in a horizontal pipe.
Figure 5-10 : Comparison of translational velocity for oil at 150 and 280 cP on a pipe at 0Λ
ππ πππΊπΊ
[ππ/π π
]
πππππΏπΏ [ππ/π π ]
ππ πππΊπΊ
[ππ/π π
]
πππππΏπΏ [ππ/π π ]
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Figure 5-11: Comparison of translational velocity for all fluids types examined (water and oil) at their corresponding viscosities on a pipe at 0Λ.
5.3.1b Inclination: Five Degrees
For the same fluids viscosities, the inclination angle of the pipe is raised from 0Β°
to +5Β°. While slight differences result relative to the previously discussed fluids, the overall
effect of inclination at 5Β° is not quite clear. ππππππ seems to be driven by high πππππΊπΊ and high
πππππΏπΏ rates when the pipe is inclined. The 3-D heat map represents the data gathered from
the experimental program for 1 cP and 5Β°. In the maps the color blue represent the slowest
ππππππ values observed at πππππΏπΏ and πππππΊπΊ pairs, while red the hot color represents the fastest ππππππ
values observed at πππππΏπΏ and πππππΊπΊ pairs. Figure 5-12 shows that at 1 cP and 5Β° the fastest
ππππππ is at high πππππΊπΊ and high πππππΏπΏ rates and the slowest ππππππ is at low πππππΏπΏ and low πππππΊπΊ rates..
The impact of viscosity on ππππππ shows that an increase in viscosity reduces ππππππ. At both
πππππΏπΏ [ππ/π π ]
ππ πππΊπΊ
[ππ/π π
]
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viscosities, a similar trend is observed as shown in Figure 5-13, ππππππ decreased as the oil
viscosity increased from 150 β 280 cP.
In summary ππππππ for fluid viscosity at 5Β° is influenced by both superficial velocities
and an increase in fluid viscosity decreases ππππππ. To demonstrate the full impact of viscosity
on ππππππ on Figure 5-14 combines all fluids examined. Althoug the air-water case is not
examined at exactly the same πππππΏπΏ and πππππΊπΊ pairs, it still supports the experimental claim.
Figure 5-12: Translational velocity for water at 1 cP on a pipe inclined at 5Λ.
ππ πππΊπΊ
[ππ/π π
]
πππππΏπΏ [ππ/π π ]
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Figure 5-13: Comparison of translational velocity for oil at 150 and 280 cP in a 5Λ inclined pipe.
Figure 5-14: Comparison of translational velocity for all fluids types examined (water and oil) at their corresponding viscosities on a pipe inclined at 5Λ
ππ πππΊπΊ
[ππ/π π
]
πππππΏπΏ [ππ/π π ]
ππ πππΊπΊ
[ππ/π π
]
πππππΏπΏ [ππ/π π ]
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Having examined the effect of viscosity on ππππππ through a comparison of fluids
from low to high viscosities, we turn to the effect of inclination on ππππππ for the same set of
viscosities. As before, a 3D heat-map represents the difference between inclination angles
0Β° and 5 Β° at 1 cP (Figure 5-15), 150 cP (Figure 5-16), and 280 cP (Figure 5-17). Looking
at all three, the results are inconclusive, without any clear trend in the direction of higher
or lower values.
Figure 5-15: Difference between translational velocity for the same viscosity 1 cP, and between inclination angles 5Λ and 0Λ
ππ πππΊπΊ
[ππ/π π
]
πππππΏπΏ [ππ/π π ]
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Figure 5-16: Difference between translational velocity for the same viscosity 150 cP, and between inclination angles 5Λ and 0Λ
Figure 5-17: Difference between translational velocity for the same viscosity 280 cP, and between inclination angles 5Λ and 0Λ
πππππΏπΏ ππ πππΊπΊ
[ππ/π π
]
πππππΏπΏ [ππ/π π ]
ππ πππΊπΊ
[ππ/π π
]
πππππΏπΏ [ππ/π π ]
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5.4 Drift Velocity Test Matrix
For the drift velocity test (Vd), two methods were used. These methods are the drain
and no-drain methods. For the drain method, the drain valve is kept in the open position
while the liquid phase is drained continuously from the test section as the bubble travels
along the pipe from the inlet to the outlet of the visualization test section. For the no-drain
method, a constant volume of a gas pocket is introduced into the test section via the trap
section before the experiment begins. This is done by shutting the QCVβs before draining
the trap section between the mixing tee and the QCV-1. It should be noted that both the
drain and no-drain tests were performed on the inclination angles of 0Β°, +1Β°, +3Β°, +5Β°, +7Β°,
and +10Β° for both the air-water and the air-oil cases, though the drain and no-drain data is
only presented in this section for the air-water case (see supplementary data in APPENDIX
for all drift velocity experiment). The distance between C1-C2 and C2-C3 is 2.0193-m and
3.1877-m respectively. For the water test the temperature of the fluid was not considered
as only one viscosity was examined. The test matrix table for oil will have an additional
column for fluid temperature. Table 5-9 and Table 5-10 are samples of the test matrix for
the No Drain drift velocity on air-water and air-oil experiments.
Table 5-8: Drift velocity test matrix for water at 0 degrees
Trav
el T
ime
to C
1 [s
]
Trav
el T
ime
to C
2 [s
]
Trav
el T
ime
to C
3 [s
]
Vd
at C
1-C
2 [m
/s]
Vd
at C
2-C
3 [m
/s]
Vd
at C
1-C
3 [m
/s]
10.327 11.813 12.369 11.341 10.562
17.842 19.347 19.909 18.875 18.089
29.782 31.424 32.036 30.967 30.015
0.269 0.268 0.268 0.268 0.268
0.267 0.264 0.263 0.264 0.267
0.268 0.266 0.265 0.265 0.268
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Table 5-9: Drift velocity test matrix for oil at 0 degrees
Tem
pera
ture
[ΛF
]
Trav
el T
ime
to C
1 [s
]
Trav
el T
ime
to C
2 [s
]
Trav
el T
ime
to C
3 [s
]
Vd
at C
1-C
2 [m
/s]
Vd
at C
2-C
3 [m
/s]
Vd
at C
1-C
3 [m
/s]
90.4 90.2 90.1 90 90.2 90.1 90.1 90.1 90.2 90.1
1.9 1.91 1.85 1.99 1.92 1.91 1.92 2.14 1.85 1.91
10.99 11.01 10.98 10.97 11.02 10.96 10.98 11.26 10.97 10.92
25.33 25.23 25.18 25.26 25.26 25.25 25.3 25.55 25.21 25.22
0.222 0.222 0.221 0.225 0.222 0.223 0.223 0.221 0.221 0.224
0.222 0.224 0.224 0.223 0.224 0.223 0.223 0.223 0.224 0.223
0.222 0.223 0.223 0.224 0.223 0.223 0.223 0.222 0.223 0.223
5.4.1 Drift Velocity Results
The observation between the experimental results and the modified drift velocity
equation for the water and oil cases at each inclination are shown in Figure 5-18 and Figure
5-19 respectively. Figure 5-18 demonstrates that there is no difference between drain and
no-drain technique and that when performing the drift velocity test either technique can be
used, especially at 0Β°. Also, we observed that Bendiksen over-estimates drift velocity
values for both air-water and air-oil cases, which will in turn inflate ππππππ results. The same
impact of viscosity that was observed for translational velocity applies to drift velocity, in
that as fluid viscosity increases both ππππππ and Vd decrease. The relationship is this way
because of the governing relationship between both parameters; they are directly
proportional to each other as shown in Equations 5.4 and 5.5. For more details on drift
velocity for this flow loop see Eghorieta (2018).
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Figure 5-18: Air- water drift velocity experimental data comparison with Bendiksen model.
Figure 5-19: Air- oil drift velocity experimental data comparison with Bendiksen model.
0.20.220.240.260.28
0.30.320.340.360.38
0.4
0 2 4 6 8 10 12
Drift
vel
ocity
[m/s
]
Inclination angle [Degrees]
no draindrainBendiksen
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5.5 Hydrodynamics Characterization Result
5.5.1 Slug Length
Slug length (LS) is one of the input parameters needed when performing
hydrodynamic characterization calculations when using Dukler and Hubbard (1975) or
Taitel and Barnea (1990) mechanistic models. The closure relationships for slug length
developed by Dukler et al. (1975) and Zhang et al. (2003) are compared to the experimental
results. These equations are good approximations for low viscosity fluids and Zhang et al.
(2003) modified the equation to include inclination angles, but we suspect that the
equations are not sufficiently accurate for high viscosity fluids. Therefore, the relationship
between slug length and viscosity at different angles are examined and illustrated in Figure
5-20-Figure 5-34. The equation proposed by each group is shown in Equation 5.6 and
Equation 5.7
π»π»ππ = 30 β ππ (5-6)
π»π»π π = (32.0 cos2 ππ + 16.0 sin2 ππ) β ππ (5-7)
where D is the pipe diameter in inches and ΞΈ is in degrees.
The working hypothesis is that viscosity affects slug length, that is the higher the
viscosity the shorter the slug length. The results are separated into three categories to
determine which of the three 3 parameters has more impact on slug length. These
parameters are viscosity, inclination, and superficial velocities. To better represent the
effect of viscosity on slug length a 3-D heat map is utilized to present the experimental
results. The map uses superficial velocities of liquid and gas (πππππΏπΏ and πππππΊπΊ) as it y-axis and
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x-axis respectively, with the dimensionless slug length grouped by inclination and viscosity
presented as the z-axis. The same color scheme discussed previously is used in the
subsequent maps. The immediate observation in terms of viscosity for the maximum
lengths observed is a 52.6% reduction in slug length from 1 cP (water) to 280 cP (oil)
shown in Figure 5-20-Figure 5-22. Knowing the drastic effect of viscosity on slug length
prompted the present fine-grained comparison of slug length with the same fluid at
different viscosities. With the difference of 130 cP in the oil viscosity (that is, reducing the
viscosity of the oil from 280 -150 cP), a 22% increase in slug length resulted. Figure 5-23-
Figure 5-24, illustrates the experimental observations and results obtained from the flow
loop system from low to high viscosity fluids in a horizontal pipe.
5.5.1a Inclination: Zero Degrees
Figure 5-20: Dimensionless slug length obtained experimentally for air-water at 0Λ
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Figure 5-21: Dimensionless slug length obtained experimentally for air-oil at 0Λ and 150 cP
Figure 5-22: Dimensionless slug length obtained experimentally for air-oil at 0Λ and 280 cP
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Figure 5-23: Comparison of dimensionless slug length obtained experimentally for air-oil at 0Β°
Figure 5-24: Comparison of dimensionless slug length obtained experimentally for air-water and air-oil at 0Λ
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5.5.1b Inclination: Five Degrees
With prior knowledge that slug length reduces as the fluid viscosity increases for
horizontal pipes, a subsequent interest in the effect of a 0Λ - 5Λ inclination of the relevant
fluids is piqued. The hypothesis is that inclination also influences slug length; but does the
effect exist, and at what magnitude? Figure 5-25-Figure 5-27 summarize the results
obtained for inclination angle 5Λ. Once again, the maximum lengths observed at each
viscosity is used to approximate the reduction in slug length as viscosity increase from 1
cP (water) to 280 cP (oil). A 44% reduction is noticed when water (1 cP) is replaced by
oil at (280 cP). At a difference of 130 cP in oil viscosity the increase in slug is not as
impressive as it was for the horizontal pipe with only a 2.56% observed increase is, but is
still important to note.
Figure 5-25: Dimensionless slug length obtained experimentally for air-water at 5Λ
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Figure 5-26: Comparison of dimensionless slug length obtained experimentally for air-oil at 5Λ
Figure 5-27: Comparison of dimensionless slug length for air-water and air-oil at 5Λ
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To further illustrate that inclination has no major impact on slug length, Figure
5-28-Figure 5-30 combines the observed slug lengths for each fluid at inclination angles of
0Λ and 5Λ at each viscosity examined. The slug length for water and oil case show an
agreement that the increase in slug length is driven by πππππΏπΏ . The longest slug length is
observed at the test points high πππππΏπΏ rates and the shortest slug lengths are observed at low
πππππΊπΊ and low πππππΏπΏ rates.
Figure 5-28: Comparison dimensionless slug length for air-water at 0Λand 5Λ
The difference in the length of the averages of the dimensionless slug length is
examined and illustrated in Figure 5-31-Figure 5-33. At the different nominal viscosities
(1, 150 and 280) cP the difference between the inclination angle of 0Β° and 5Β°. A positive
difference value indicates that the slug length is longer at the higher inclination than the
lower one, and a negative value means that the lower angle (0Β°) experiences longer slug
length at the test point been analyzed.
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Figure 5-29: Comparison of dimensionless slug length for air-oil at 0Λand 5Λ
Figure 5-30: Comparison of dimensionless slug for air-oil at 0Λ and 5
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Figure 5-31: Difference between dimensionless slug length for the same viscosity 1 cP between inclination angles 5Λ and 0Λ
Figure 5-32: Difference between dimensionless slug length for the same viscosity 150 cP between inclination angles 5Λ and 0Λ
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Figure 5-33: Difference between dimensionless slug length for the same viscosity 280 cP, between inclination angles 5Λ and 0Λ
5.5.1c Slug Length Result
The comparison of the experimental results to existing closure relationships by
Taitel and Dukler and Zhang indicate that at high fluid viscosities the slug length estimation
provided in Equation 5-6 and 5-7 are inadequate as they tend to overestimates slug length
as shown in Figure 5-34. Closure relationship that takes into consideration the effect of
viscosity is needed to for proper estimation of slug length in high viscosity fluids.
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Figure 5-34:Comparison of experimental result to theoretical models
5.5.2 Slug Frequency
Slug frequency and slug length are intertwined as either one of the parameter is
needed as an input parameter for both Dukler and Hubbard (1975) or Taitel and Barnea
(1990) mechanistic model and are both affected by πππππΏπΏ. In 2000 Zabaras revised Gregory
and Scott (1969) and expanded the range of its applicability from 0 to 11Λ for small pipes
of 0.0254 to 0.20-m pipe ID. Zabarasβ Equation 5.8 does consider inclination as an input
parameter and it is for this reason it was used as a comparison to the experimental data.
The unit of the parameters in Equation 5.8 are all in English units.
πππ»π»π»π» = 0.0226 β οΏ½
πππππΏπΏππππ
οΏ½1.2
οΏ½212.6ππππ
+ πππποΏ½1.2
β [0.836 + 2.75(sinππ)0.25] (5-8)
Gokcal (2008) developed a linear relationship using regression analysis between
dimensionless slug frequency and a combination of dimensionless inverse viscosity and
45Β° line
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velocity ratio for high viscosity fluids. The result of the relationship are Equations 5.9 and
5.10 and all the parameters involved in these equations are in SI unit.
ππππ = ππ
32 β
οΏ½πππΏπΏ(πππΏπΏ β πππΊπΊ)πππππΏπΏ
(5-9)
πππ π = 2.816 β οΏ½
1ππππ0.612οΏ½ β οΏ½
πππππΏπΏπποΏ½
(5-10)
Like the hypothesis of used for slug length, a hypothesis was developed for slug
frequency with respect to viscosity and inclination; Slug frequency increases as viscosity
and inclination increases. Figure 5-35-Figure 5-48 use the same map coordinates that were
used for dimensionless slug length where the superficial velocities of liquid and gas
(πππππΏπΏand πππππΊπΊ) are y-axis and x-axis respectively, and the frequency grouped by inclination
and viscosity is represented as the z-axis. The illustrations below show that the slug
frequency is directly proportional to viscosity; the slower the occurrence of the slug
frequency the lower the fluid viscosity. Blue represents the slow occurring slug frequency
and red represents the fast-moving slug frequency. Next the experimental data are grouped
by viscosity and inclination to better observe which of the two variables has a greater effect
on slug frequency. Figure 5-35-Figure 5-40, group all the slug frequencies observed
experimentally at the same inclination, but different viscosities to illustrate the impact of
viscosity on slug frequency. It is valid to conclude that for horizontal and near horizontal
pipes slug frequency increases with increasing fluid viscosity despite the inclination. The
figures below complement these observations.
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5.5.2a Inclination: Zero Degrees
Figure 5-35: Slug frequency for water at 1 cP in a horizontal pipe.
Figure 5-36: Comparison of slug frequency for oil at 150 and 280 cP in a horizontal pipe
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Figure 5-37: Comparison of slug frequency for all fluids types examined (water and oil) at their corresponding viscosities in a horizontal pipe.
5.5.2a Inclination: Five Degrees
The same results were observed for the effect of viscosity on slug frequency on a
horizontal pipe applies to inclined pipe of 5Λ. The frequency of the slugs increases as
viscosity and inclination increase. The next step is to determine which of the variable
(viscosity and inclination) has a greater impact on slug frequency. The results for slug
frequency are also promising because unlike slug length, inclination also has an impact on
slug frequency. Thus, it is correct to say that fluid viscosity and inclination are driving
forces for this closure relationship parameter. The impact of inclination is examined by
comparing the results of the slug frequency tests based on inclination (0 and 5) Β° for each
of viscosity (1, 150 and 280) cP. The conclusion is validated by the promising results
observed in Figure 5-41-Figure 5-46 .
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Figure 5-38: Slug frequency for water at 1 cP in a pipe inclined at 5Λ.
Figure 5-39: Comparison of slug frequency for oil at 150 and 280 cP in a pipe inclined at 5Β°
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Figure 5-40: Comparison of slug frequency for all fluids types examined (water and oil) at their corresponding viscosities in a pipe inclined at 5Λ.
At the same viscosities and different inclinations, the difference in slug length at
each inclination is not significant enough for inclination to impact how fast the slugs are
moving through the pipe as the test points overlap or are not too far from each other at the
two inclinations used in the experiment. Figure 5-44-Figure 5-46 helps visualize the
difference in slug frequency at the different inclinations and viscosities. A positive
difference value indicates that the slug frequency occurs more frequently at the higher
inclination than the lower one; and a negative value means that the lower angle (0Β°)
experiences more slug frequency at the test point been analyzed.
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Figure 5-41: Comparison of slug frequency for air-water test at 0Λ, and 5Λ at 1 cP
Figure 5-42: Comparison of slug frequency for air-oil test at 0Λ, and 5Λ at 150 cP
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Figure 5-43: Comparison of slug frequency for air-oil test at 0Β°, and 5Β° at 280 cP
Figure 5-44: Difference between slug frequency for viscosity at 1 cP between inclination angles of 5Β° and 0Β°
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Figure 5-45: Difference between slug frequency for viscosity at 150 cP between inclination angles of 5Λ and 0Λ
Figure 5-46: Difference between slug frequency for the same viscosity 280 cP between inclination angles 5Β° and 0Β°
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5.5.2b Slug Frequency Result Comparison
The comparison of the experimental results to existing closure relationships by
Zabaras and Gokcal indicate that for high fluid viscosities Zabaras is inadequate as it
underestimates the sensitive input parameter to both Dukler and Hubbard (1975) or Taitel
and Barnea (1990) mechanistic model especially at 0Β°. Gokcalβs Equation 5.10, does a
better job at estimating the slug frequency with a maximum percent error of 22 % from the
experimental data while Zabaras has a maximum percent error of 73% from the
experimental data.
Figure 5-47: Comparison of Slug frequency result with existing closure relationships at 280 cP.
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Figure 5-48: Comparison of Slug frequency result with existing closure relationships at 150 cP.
5.5.3 Liquid Holdup
Slug liquid holdup is the ratio of liquid in the slug body to the slug unit and it is a
necessary closure relationship parameter because βit is critical for predicting average liquid
holdup and pressure gradient.β (Al-Safran et al. 2015). Researchers of multiphase flow
have come to a consensus that the traditional liquid holdup equations are not adequate at
predicting the liquid holdup value for high viscosity multiphase fluids. Dating as far back
as 2015 Al-Safran stated that OLGA, one of the top simulators created by Schlumberger
for multiphase flow does not accurately predict pressure gradient and liquid holdup for
high viscosity fluids; it is for this reason that the liquid holdup obtained experimentally
from the flow loop system are reported for high viscosity fluids. The hypothesis proposed
for the case of slug liquid holdup is that as liquid viscosity increases there would be a
comparable increase in the slug liquid holdup. Both the results obtained for air-water and
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air-oil cases agree with the hypothesis. The approach for back-calculating HLLS and the
method of capturing HLLS in the lab are explained in Chapter 3 and Chapter 4. The back-
calculation method for HLLS requires one to know the fluid property parameters and
experimental result for slug length, slug frequency and translational velocity beforehand.
With the aid of Taitel and Barneaβ s mechanistic model the HLLS value is solved using
Newton Raphson to obtain equilibrium in mass, that is mass-in equals mass-out.
Experimental observations in this study for slug body holdup indicate that HLLS increases
as fluid viscosity and inclination increase. Also, like slug length and frequency, HLLS is
greatly impacted by πππππΏπΏ. The viscosity of the fluid has a huge impact on how much liquid
is in the slug body. With water the bubbles are dispersed evenly throughout the slug body
and the slug body volume is much lower than what is observed for the air-oil case. When
the slugs move through the pipe the film height of the oil case appears to be constant and
the slug body moves over it. Also, the bubbles in the fluid do not disperse evenly as
observed in low viscosity fluids. Figure 5-61 is an example of bubble movement through
the slug body. To better represent the effect of viscosity on HLLS a 3-D heat map is used to
display the experimental results. The map uses superficial velocities of liquid and gas (πππππΏπΏ
and πππππΊπΊ) as x-axis and y-axis respectively, and the dimensionless slug length grouped by
inclination and viscosity is represented as the z-axis. Blue indicates the lowest HLLS value
observed and red indicates the highest value of HLLS observed. The results are grouped
based on viscosity and inclination to demonstrate which of the variable has more impact
on HLLS . Figure 5-50-Figure 5-54 are used to illustrate these experimental observations.
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Figure 5-49: Gas bubbles observed in the slug body of the air-oil case (high viscosity fluid)
In Figure 5-50, the two viscosities and inclinations of fluid are looked at
simultaneously to give a snapshot of the fluid behavior. As shown in the legend, the circle
represents the fluid viscosity of 280 cP and an inclination of 0Β°, while the square represents
the same viscosity (280 cP) at 5 Β°. The same fluid is then examined at 150 cP and
inclinations of 0Β° and 5Β°; for this fluid downward facing triangle is for the fluid viscosity
at 150 cP and inclination at 0Β° and upward facing triangle is for 150 cP and 5Β°. The take-
away is that πππππΏπΏ does indeed affect HLLS in all cases, the higher the liquid superficial
velocity the higher the HLLS value.
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Figure 5-50: Slug liquid holdup for air-oil case (150 and 280) cP at (0 and 5) Β°
In Figure 5-51, the impact of inclination on HLLS is observed for both viscosities.
As shown in the legend, the circle represents the fluid viscosity of 280 cP, and the
downward facing triangle represents the fluid viscosity of 150 cP. The way the impact of
inclination is determined for both viscosities is by taking the difference of the averages of
a test point at the different inclinations. If the difference is positive, it indicates that more
fluid is in the slug body at the raised angle of 5Β° than at 0Β°. A negative value shows that for
that test point 0Β° has more HLLS . For fluid viscosity at 150 cP, the inclination angle of 5Β°
always has more volume of liquid in the slug body than at 5Β°. For the case of fluid viscosity
at 280 cP, not all the values are positive as was observed for 150 cP, more data and analysis
need to be performed to determine why the observation is not consistent.
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Figure 5-51: Comparison of the difference in slug liquid holdup at the same viscosities and different inclination angles.
In Figure 5-52, the impact of viscosity on HLLS is observed at both inclinations. As
shown in the legend, the circle represents the inclination angle at 0Β°, and the downward
facing triangle represents the inclination angle at 5Β°. It is important to note that the value
to the left of each symbol is for inclination angle at 5Β°. The way the impact of viscosity is
determined for at both inclinations is by taking the difference of the averages of a test point
at the different viscosities. If the difference is positive, indicates that more fluid is in the
slug body at viscosity of 280 cP than at 150 cP. A negative value shows that for that test
point 280 cP has more HLLS value. For both inclinations, the difference at each test point is
positive thus indicating that as viscosity increases HLLS value also increases in the slug
body. Compared to the observation made at the difference in inclinations and same
viscosity the results here are very consistent.
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Figure 5-52: Comparison of the difference in slug liquid holdup at the same inclination angles and different viscosities.
5.5.3a Liquid Holdup Result Comparison
A comparison is made between the calculated HLLS and Gomez (2000). Gomezβs
equation seems to be versatile as it is for inclination angle within the range of 0Λ β€ ππ β€
90Β° and it is also dependent on fluid viscosity. The limitation to this equation is that it was
developed for low viscosity fluids and thus will overestimate slug liquid holdup at higher
viscosity With Equation 5.11 the theoretical value of HLLS can be determined as it is one
of the closure relationship for slug flow mechanistic models. The units for the parameters
in the equation are in SI units and ππ is in degrees.
π»π»πΏπΏπΏπΏππ = 1 β πΈπΈπΈπΈππ[β(7.85 β 10β3ππ + 2.48 β 10β6π π πππΏπΏππ)] (5-11)
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Figure 5-53 and Figure 5-54, put into perspective by how much Gomez (2000)
deviates from Newton Raphson method which uses the other experimental results obtained
to determine π»π»πΏπΏπΏπΏππ when mass balance (mass-in is equal to mass-out) is achieved . Gomez
(2000) overestimates the result of slug liquid holdup compared to the Newton Raphson
approach employed to solve for HLLS.
In Figure 5-53 and Figure 5-54, it is observed that not only does Gomezβs
correlation overestimate HLLS but it also does not accurate portray that HLLS increases with
inclination as is observed when the mass balance is used solve HLLS. Here the HLLS values
at 5Β° are lower than at 0Β° for both 280 cP and 150 cP. When solving for HLLS using Taitel
and Barneaβs mechanistic model.
Figure 5-53: Comparsion of predicted Slug liquid holdup (HLLS) using the mass balance to Gomez (2000) for 280 cP.
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Figure 5-54: Comparsion of predicted Slug liquid holdup (HLLS) using mass balance to Gomez (2000)for 280 cP.
5.5.4 Pressure Drop
Pressure drop is very important to know when fluid is moving from one point to
another, inaccurate prediction of pressure drop across a pipe can affect whether or not a
fluid gets to its destination safely and efficiently. Researchers of multiphase flow have
come to an agreement that the traditional liquid holdup equations are not adequate at
predicting the liquid holdup value for high viscosity multiphase fluids which then affects
the prediction of pressure drop in the pipe. Dating as far back as 2015 Al-Safran stated that
OLGA, one of the top simulators created by Schlumberger for multiphase flow does not
accurately predict pressure gradient and liquid holdup for high viscosity fluids; it is for this
reason that the pressure gradient values obtained experimentally from the flow loop system
are reported for high viscosity fluids. It is observed that pressure drop per unit length
across the visualization section increases as fluid viscosity increases because of the shear
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forces and resistance of the fluid to flow; thus the higher the fluid viscosity the higher the
pressured drop observed.
In Figure 5-55, the circle represents the fluid viscosity of 280 cP and an inclination
of 0Β°, while the square represents the same viscosity (280 cP) at 5 Β°. The same fluid is then
examined at 150 cP and inclinations of 0Β° and 5Β°; for this fluid downward facing triangle
is for the fluid viscosity at 150 cP and inclination at 0Β° and upward facing triangle is for
150 cP and 5Β°. Blue indicates low pressure values and as the color goes towards red the
pressure value increases as well. The take-away is that πππππΏπΏ does affect the outcome of
pressure across a pipe. At higher liquid superficial velocity, the pressure drop per unit
length across the pipe also increases.
Figure 5-55:Pressure drop between ports 3 and 5 (the second half of the visualization section) represented at both viscosities and inclinations.
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In Figure 5-56, the impact of inclination on pressure is observed for both viscosities.
As shown in the legend, circle represents the fluid viscosity of 280 cP, and the downward
facing triangle represents the fluid viscosity of 150 cP. The way the impact of inclination
is observed for both viscosities is by taking the difference of the pressure drop of each test
point at the different inclinations. If the difference is positive, it indicates that pressure at
the raised angle of 5Β° is more than the pressure at 0Β°. A negative value shows that for that
test point 0Β° has more pressure drop across the section than 5Β° at the same test point. The
difference in pressure between the inclination angle also supports the claim that pressure
drop is greater at higher viscosity. The difference between 5Β° and 0Β° is much small at 280
cP than at 150 cP which indicates that the pressure at 280 cP is higher than the pressure at
150 cP when the inclination angle is 5Β°.
Figure 5-56: Pressure drop between ports 3 and 5 (the second half of the visualization section) represented at both viscosities and inclinations.
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In Figure 5-57, the impact of viscosity on pressure gradient is observed at both
inclinations. As shown in the legend, the circle represents the inclination angle at 0Β°, and
the downward facing triangle represents the inclination angle at 5Β°. It is important to note
that the values to the left of each symbol are for inclination angle at 5Β°. The impact of
viscosity is determined at both inclinations is by taking the difference of the averages of a
test point at the different viscosities. If the difference is positive, it indicates that more
pressure drop is seen at a fluid viscosity of 280 cP than at 150 cP. For both inclinations,
the difference at each test point is positive thus indicating that as viscosity increases
pressure gradient also increases across the pipe.
Figure 5-57: Pressure drop between ports 3 and 5 (the second half of the visualization section) represented at both viscosities and inclinations.
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5.5.4a Pressure Drop Result Comparison
A comparison is made between the experimentally observed pressure drop, Taitel
and Barneaβs (TTBN) and modified Taitel and Barneaβs (modified TTBN) mechanistic
model. The full detail of how the theoretical pressure drop is obtained can be found in
Chapter 3. The modified TTBN model uses the experimental closure relationship results
(slug length, translational velocity, slug frequency and the fluids physical properties) to
arrive at an estimated pressure drop result when the mass balance for the system is
achieved. The modified Taitel and Barnea mechanistic model does a better job at predicting
the pressure drop compared to just inputting the closure relationship parameters developed
for low viscosity fluids in TTBN mechanistic model. In Figure 5-58 and Figure 5-59 blue
represents the color of the results obtained from modified TTBN and the color green
represents the result of obtained from TTBN when the regular closure relationships
recommended are used to solve for pressure drop. The upward facing blue triangle and
green circle are the results for modified TTBN and TTBN at 0Β° while the downward facing
blue triangle and the green star are modified TTBN and TTBN at 5Β°respectively.
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Figure 5-58: Comparison of pressure drop observation between experimental and numerical result at 280 cP.
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Figure 5-59: Comparison of pressure drop observation between experimental and numerical result at 150 cP.
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CONCLUSION
Promising results were obtained from the 8502 experimental results obtained over
the span of 4 months on the impact of high viscosity fluids on multiphase fluid (air-oil) in
pipes. With these results new data has been added to the research environ for multiphase
fluid that would help in advancing or creating new closure relationships for future slug
flow hydrodynamic characterization in steady state. The objectives of this study were met
and the conclusions to each will be discussed below.
1) Identify the flow pattern of high viscosity slug flow cases.
The flow patterns identified for the flow loop system is shown in chapter 5.1, and
it is obvious that flow pattern is paramount when studying slug flow behavior. Detailed
attention is needed when recording the fluid properties (superficial velocities, densities,
pressure gradient, temperature, surface tension, and viscosities) that flow pattern is
dependent on these parameters and without this information, the result obtained
experimentally will be rendered useless or tedious to mine.
2) Determine the unknown parameters for two-phase slug flow of air and high-
viscosity oil including
a) slug length,
b) slug frequency,
c) drift velocity,
d) slug body liquid holdup, and
e) flow pattern
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The closure relationship result obtained from the flow loop lab, does in fact show
that more work still needs to be done for accurate prediction closure parameters on high
viscosity fluid. The existing models are not accurate and thus over predict or under predict
pressure gradient, liquid holdup.
The impact of high viscosity on the unknown parameters are listed below.
β’ Slug length decreases as viscosity increases
β’ Slug frequency increase as viscosity increases.
β’ Translational velocity decreases as viscosity increases
β’ Liquid holdup increases as viscosity increases.
β’ Pressure drop increases with increasing viscosity
β’ Existing drift velocity correlation over estimates the actual drift velocity for high
viscosity fluids.
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APPENDICES APPENDIX A
Video Files The links below is where all the raw experimental data is uploaded for all the tests
discussed in this report. Raw Experimental Data Files or
https://www.youtube.com/watch?v=mtnFpP8tbuI&t=2s
Flow pattern Table for air-oil case Table A-1: Experimental data for flow pattern at 150 cP and 0Β°
Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
EB EB EB EB EB EB EB/SSL B/SSL SSL SSL SSL SSL SSL EB EB EB EB EB EB EB/SSL SSL/SL SSL
5 10 15 20 25 30 35 40 45 50 55 60 65 5
10 15 20 25 30 35 40 45
5 5 5 5 5 5 5 5 5 5 5 5 5
10 10 10 10 10 10 10 10 10
79 170 256 326 423 504 584 663 744 816 887 959
1020 79
170 256 326 423 504 584 663 744
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
0.093061 0.174073 0.262256 0.351219 0.432384 0.518318 0.600854 0.684881 0.769677 0.842592 0.919264 0.989166
0.90587 0.086955 0.170881 0.259273 0.351301 0.434137 0.518257
0.60142 0.684009
0.76712
0.057426 0.057079 0.055221 0.053172 0.042663 0.042857 0.040179 0.039412 0.037463 0.036489 0.035564 0.039785 0.038533 0.114873 0.106171 0.097691 0.102491 0.088457
0.08528 0.080742 0.077377 0.075274
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Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SSL SSL SSL SSL EB EB EB/SL EB/SL EB/SL EB/SL SL SSL/SL SSL/SL SSL/SL SSL/SL SSL SSL SL SL EB/SL SL SL SL SL SL SL SL SL SSL/SL SSL/SL SL SL SL SL SL SL SL SL SL SL
50 55 60 65 5
10 15 20 25 30 35 40 45 50 55 60 65 5
10 15 20 25 30 35 40 45 50 55 60 65 5
10 15 30 35 40 45 50 55 60
10 10 10 10 15 15 15 15 15 15 15 15 15 15 15 15 15 20 20 20 20 20 20 20 20 20 20 20 20 20 25 25 25 25 25 25 25 25 25 25
816 887 959
1020 79
170 256 326 423 504 584 663 744 816 887 959
1020 79
170 256 326 423 504 584 663 744 816 887 959
1020 79
170 256 504 584 663 744 816 887 959
0.02 0.02 0.02 0.02 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13
0.844322 0.91453
0.993183 0.953439 0.082863 0.167831 0.257194 0.347151 0.433985 0.433985 0.520196 0.607294 0.690347 0.777602 0.847895 0.986414 1.045597 0.082863 0.168854 0.260602 0.349124 0.435013 0.433934 0.521104 0.773081 0.689396 0.773081 0.849761
0.9253 1.036646 0.082863 0.173008 0.258279 0.601744
0.60662 0.601744 0.850493 0.773749 0.850493 0.987537
0.072978 0.07052
0.068549 0.077776 0.256087 0.242558 0.238745 0.230949
0.21764 0.21764
0.210013 0.203807 0.196108 0.185697 0.180877
0.17204 0.203845
0.42241 0.39731
0.433494 0.369518 0.344729 0.346436 0.331013 0.298376 0.310878 0.298376 0.286937 0.277532 0.264652 0.673763 0.703915 0.617357 0.485126 0.517293 0.485126 0.460474 0.476507 0.460474 0.429903
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Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL
65 20 25 30 35 40 45 50 55 60 65 15 20 25 30 35 40 45 50 55 60 65 20 25 30 35 40 45 50 55 60 65 20 25 30 35 40 45 50 55
25 30 30 30 30 30 30 30 30 30 30 35 35 35 35 35 35 35 35 35 35 35 40 40 40 40 40 40 40 40 40 40 45 45 45 45 45 45 45 45
1020 326 423 504 584 663 744 816 887 959
1020 256 326 423 504 584 663 744 816 887 959
1020 326 423 504 584 663 744 816 887 959
1020 326 423 504 584 663 744 816 887
0.13 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.28 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35
1.036289 0.34707
0.348016 0.51941 0.52044
0.690266 0.690266 0.690266 1.032941 0.923287 1.032941 0.258279 0.348138 0.348138 0.604343 0.690266 0.604343 0.690266 0.851224 0.923178 0.824848 0.993261
0.34707 0.348097 0.519166 0.519166 0.690103 0.690103 0.690103 0.849161 0.982493 1.026508 0.348138 0.348138 0.605232
0.52044 0.605232 0.772173 0.772173 0.772173
0.537799 0.822267 0.784216 0.737541 0.730441 0.671591 0.671591 0.671591 0.590936 0.614325 0.590936
1.07412 1.02841 1.02841
0.924444 0.891506 0.924444 0.891506 0.772622 0.809261 0.672124
0.68491 1.276404 1.283096 1.182513 1.182513 1.067818 1.067818 1.067818 0.981609 0.882323
0.85623 1.532218 1.532218 1.343671 1.340994 1.343671 1.194303 1.194303 1.194303
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Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL RW/SL SL SL SL SL SL SL SL SL SL SL SL
60 65 5
10 15 20 25 30 35 40 45 50 55 60 65 5
10 15 20 25 30 35 40 45 50 55 60 65 5
10 15 20 25 30 35 40 45 50 55 60
45 45 50 50 50 50 50 50 50 50 50 50 50 50 50 55 55 55 55 55 55 55 55 55 55 55 55 55 60 60 60 60 60 60 60 60 60 60 60 60
959 1020
79 170 256 326 423 504 584 663 744 816 887 959
1020 79
170 256 326 423 504 584 663 744 816 887 959
1020 79
170 256 326 423 504 584 663 744 816 887 959
0.35 0.35 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.68
0.967703 0.993047 0.082854 0.167812 0.257344 0.345962 0.430597 0.430597 0.519044 0.688505 0.688505 0.688505 0.848762
0.9685 0.9685
0.080808 0.167831 0.256229 0.346989 0.431102 0.431102 0.688586 0.603988 0.688586 0.770292 0.770292 0.948909 0.948909 0.081821 0.166847 0.256259 0.345017 0.431051 0.517771 0.520013 0.769261 0.685574 0.769261 0.892898 0.949606
1.136946 1.065813 2.383652 2.087319 2.101349 1.897042 1.630559 1.630559
1.69574 1.520441 1.520441 1.520441 1.415371
1.33818 1.33818
2.698715 2.591233 2.486028 2.311824 2.180641 2.180641 1.919358 1.921865 1.919358 1.771196 1.771196 1.662227 1.662227 3.523019 3.208272 3.041068 2.829811 2.672412
2.40624 2.557478 2.139793 2.254824 2.139793 2.026425 1.865398
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Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SL RW RW/SL SL/SW SL SL SL SL SL SL SL SL SL SL SW SL/SW SL/SW SL/SW SL SL/A SL SL/A SL SL SL SL SL SW SL/SW SL/SW SL/SW SL/SW SL/A SL SL/A SL/A SL SL SL SL
65 5
10 15 20 25 30 35 40 45 50 55 60 65 5
10 15 20 25 30 35 40 45 50 55 60 65 5
10 15 20 25 30 35 40 45 50 55 60 65
60 65 65 65 65 65 65 65 65 65 65 65 65 65 70 70 70 70 70 70 70 70 70 70 70 70 70 75 75 75 75 75 75 75 75 75 75 75 75 75
1020 79
170 256 326 423 504 584 663 744 816 887 959
1020 79
170 256 326 423 504 584 663 744 816 887 959
1020 79
170 256 326 423 504 584 663 744 816 887 959
1020
0.68 0.86 0.86 0.86 0.86 0.86 0.86 0.86 0.86 0.86 0.86 0.86 0.86 0.86 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.06 1.27 1.27 1.27 1.27 1.27 1.27 1.27 1.27 1.27 1.27 1.27 1.27 1.27
0.949606 0.080789 0.167792 0.255293 0.346165 0.431928
0.5188 0.5188
0.605693 0.766928 0.845668 0.897233 0.900221 0.900221
0.08078 0.166808 0.255234 0.345138 0.428994 0.516923 0.604592 0.683271 0.742712 0.833096 0.875059 0.873205 0.873205 0.080789 0.165823 0.254209 0.342016 0.431051 0.516015 0.602603
0.68113 0.761595 0.828038 0.870419 0.870419 0.870419
1.865398 4.271858 4.127793 3.751651
3.48211 3.198051 3.014078 2.999082
2.92158 2.627906 2.478579
2.26596 2.387002 2.387002 5.493116 5.104192 4.413171 4.086961 3.683337 3.625756 3.359896 3.237828 2.872228
2.96602 2.645967 2.855549 2.855549 6.307295 5.719164 5.292439 4.824584 4.646071
4.15197 3.849439 3.804635 3.615478 3.349964 3.156299 3.156299 3.156299
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Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SW SL/SW SL/SW SL/SW SL/A SL/A SL/A SL/A SL/A SL SL/A SL SL SW SW SL/A SL/A SL/A SL/A SL/A SL/A SL/A SL/A SL/A SL/A SL/A SW/A SW/A SL/A SL/A SL/A SL/A SL/A SL/A SL/A SL/A SL/A SL/A
5 10 15 20 25 30 35 40 45 50 55 60 65 5
10 15 20 25 30 35 40 45 50 55 60 65 5
10 15 20 25 30 35 40 45 50 55 60
80 80 80 80 80 80 80 80 80 80 80 80 80 85 85 85 85 85 85 85 85 85 85 85 85 85 90 90 90 90 90 90 90 90 90 90 90 90
79 170 256 326 423 504 584 663 744 816 887 959
1020 79
170 256 326 423 504 584 663 744 816 887 959
1020 79
170 256 326 423 504 584 663 744 816 887 959
1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.79 1.79 1.79 1.79 1.79 1.79 1.79 1.79 1.79 1.79 1.79 1.79 1.79 2.05 2.05 2.05 2.05 2.05 2.05 2.05 2.05 2.05 2.05 2.05 2.05
0.079766 0.166827 0.254238 0.345138
0.43095 0.515954 0.599046 0.677088 0.759802 0.831621 0.870112 0.870112 0.870112 0.079757 0.167851 0.255234 0.343284 0.428015 0.515833 0.597663
0.67891 0.756798 0.824945
0.83948 0.83948
0.848628 0.079757
0.16787 0.255264 0.342016 0.427865 0.514196 0.598623 0.676929 0.739704 0.816695 0.816695 0.816695
7.142698 6.756193 5.977919 5.319624 4.926619 4.669389 4.321791 4.142388 3.909754 3.804509 3.697092 3.697092 3.697092 8.489536 8.031926 7.553223 6.626927 6.047194 5.337182 5.304667 4.879576 4.624456 4.478943 4.621808 4.621808 4.181331 9.846071 8.965656 8.328526 6.888737 6.552684 6.287574 5.861765 5.412337 5.106847
5.26586 5.26586 5.26586
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Table A-1: Experimental data for flow pattern at 150 cP and 5Β° Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
EB EB EB SL SL SL SL SL SL SL RW/SL RW/SL RW RW RW RW RW/A A EB EB SL SL SL SL SL SL SL RW/SL RW/SL RW/SL RW/SL RW/SL RW/A A EB EB/SL SL
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 15 15 15
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 10 15 20 25 30 40 45 50 55 60 65 70 75 80 85 90 5
10 15
83 83 83 83 83 83 83 83 83 83 83 83 83 83 83 83 83 83
169 169 169 169 169 169 169 169 169 169 169 169 169 169 169 169 255 255 255
0.01 0.03 0.04 0.08 0.13 0.18 0.23 0.28 0.35 0.43 0.53 0.68 0.87 1.07 1.25 1.44 1.75 2.02 0.03 0.04 0.08 0.13 0.18 0.28 0.35 0.43 0.53 0.68 0.87 1.07 1.25 1.44 1.75 2.02 0.01 0.03 0.04
0.077667 0.082834 0.083788 0.082796 0.082796 0.082776 0.081754 0.082767 0.081764 0.083788 0.081745 0.080723 0.080714 0.080723 0.080723 0.080732 0.079701 0.079711 0.171061 0.169997 0.171041 0.169997 0.171001 0.169957 0.169977 0.168953 0.168973 0.167929 0.167909 0.167909 0.166886 0.167929 0.165842 0.166866 0.258248 0.258218 0.258279
0.048877 0.142734 0.218094
0.40526 0.662407 0.900518 1.127403 1.533812 1.855452 2.125387 2.765248 3.469441 4.635253 5.389379 6.478077 7.138496 8.580499 9.725836 0.146659 0.193303 0.393228 0.624427 0.950998 1.451748 1.623567
2.01901 2.549244 3.168592 3.924731 4.932648 5.602883 6.675959 7.498438 8.793165 0.046694 0.140106 0.187849
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Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SL SL SL SL SL SL RW/SL RW/SL RW/SL RW/A SL/A SL/A EB EB/SL EB/SL SL SL SL SL SL RW/SL RW/SL RW/SL SL/A SL/A SL/A EB EB/SL SL SL SL SL SL SL RW/SL RW/SL SL/A SL/A SL/A EB/SL
15 15 15 15 15 15 15 15 15 15 15 15 20 20 20 20 20 20 20 20 20 20 20 20 20 20 25 25 25 25 25 25 25 25 25 25 25 25 25 30
20 25 30 50 55 60 65 70 75 80 85 90 5
10 15 20 25 50 55 60 65 70 75 80 85 90 5
10 15 20 50 55 60 65 70 75 80 85 90 5
255 255 255 255 255 255 255 255 255 255 255 255 339 339 339 339 339 339 339 339 339 339 339 339 339 339 423 423 423 423 423 423 423 423 423 423 423 423 423 514
0.08 0.13 0.18 0.43 0.53 0.68 0.87 1.07 1.25 1.44 1.75 2.02 0.01 0.03 0.04 0.08 0.13 0.43 0.53 0.68 0.87 1.07 1.25 1.44 1.75 2.02 0.01 0.03 0.04 0.08 0.43 0.53 0.68 0.87 1.07 1.25 1.44 1.75 2.02 0.01
0.257254 0.258309 0.259394 0.256289 0.255204 0.255204 0.255204 0.255204 0.254149 0.254149
0.25412 0.25412
0.364912 0.348797 0.346786 0.347934 0.345922 0.345922 0.348016 0.345881 0.345922 0.346908 0.344815 0.343788 0.343708 0.342722 0.433527 0.434707 0.432232 0.434036 0.427638 0.431675 0.432703 0.431675 0.429519 0.430546 0.428541 0.427514 0.425278 0.526686
0.371557 0.607126 0.927726 1.978157 2.421036 2.975143 3.877175 4.518055 5.305727 5.877113 6.749997 7.828571 0.042376
0.13137 0.177934 0.350321 0.575249 1.877635 2.300861 2.816117 3.466167 4.088955 4.798583 5.884454 6.315211 7.325578 0.041415 0.128672 0.173296 0.344693 1.753055
2.13947 2.635843 3.264228
3.91198 4.574255 4.905422 5.768145 6.761535 0.041176
Texas Tech University, Tolani A. Afolabi, May 2018
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Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
EB/SL SL SL SL SL SL SL SL SL SL SL/A SL/A SL/A SL/A SL/A EB/SL EB/SL EB/SL SL SL SL SL SL SL/A SL/A SL/A SL/A SL/A SL/A B/SSL B/SSL SL SL SL SL SL SL SL SL/A SL/A
30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 35 35 35 35 35 35 35 35 35 35 35 35 35 35 40 40 40 40 40 40 40 40 40 40 40
10 15 20 25 30 40 50 55 60 65 70 75 80 85 90 5
10 15 20 35 50 55 60 65 70 75 80 85 90 5
10 15 45 50 55 60 65 70 75 80
514 514 514 514 514 514 514 514 514 514 514 514 514 514 514 591 591 591 591 591 591 591 591 591 591 591 591 591 591 670 670 670 670 670 670 670 670 670 670 670
0.03 0.04 0.08 0.13 0.18 0.28 0.43 0.53 0.68 0.87 1.07 1.25 1.44 1.75 2.02 0.01 0.03 0.04 0.08 0.23 0.43 0.53 0.68 0.87 1.07 1.25 1.44 1.75 2.02 0.01 0.03 0.04 0.35 0.43 0.53 0.68 0.87 1.07 1.25 1.44
0.529022 0.530966 0.529812 0.527879 0.529094 0.529812 0.527693 0.526315 0.526541 0.524853 0.522856 0.522195 0.521766
0.52364 0.522133 0.604627
0.61482 0.615705
0.61482 0.607896 0.611658 0.612616 0.611587 0.609599 0.607468 0.607468 0.607682 0.606367 0.605409 0.691949 0.698566 0.697945 0.695883 0.693198
0.69176 0.692546 0.690323 0.691272 0.689293 0.687313
0.131214 0.167084
0.3309 0.543025 0.733759 1.135721 1.710842 2.043663
2.53157 3.107321 3.607329 4.302075 4.606905 5.553113 6.321901 0.047908 0.121103 0.162246 0.319888 0.876424 1.573087 1.930957 2.405839 2.924879 3.369471
3.88355 4.371769 5.245008 5.808377 0.039055 0.117688 0.156918 1.278118 1.559893 1.859481
2.30101 2.780597 3.217524 3.740518 4.190639
Texas Tech University, Tolani A. Afolabi, May 2018
139
Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SL/A A SSL SSL SL SL SL SL SL SL/A SL/A SL/A SL/A SSL SSL SL SL SL SL SL SL/A SL/A SL/A SL/A SSL SSL SSL/SL SL SL SL SL SL SL SL/A SL/A SL/A SL/A SSL SSL SSL
40 40 45 45 45 45 45 45 45 45 45 45 45 50 50 50 50 50 50 50 50 50 50 50 55 55 55 55 55 55 55 55 55 55 55 55 55 60 60 60
85 90 5
10 15 45 60 65 70 75 80 85 90 5
10 15 20 60 65 70 75 80 85 90 5
10 15 20 25 55 60 65 70 75 80 85 90 5
10 15
670 670 749 749 749 749 749 749 749 749 749 749 749 831 831 831 831 831 831 831 831 831 831 831 886 886 886 886 886 886 886 886 886 886 886 886 886 966 966 966
1.75 2.02 0.01 0.03 0.04 0.35 0.68 0.87 1.07 1.25 1.44 1.75 2.02 0.01 0.03 0.04 0.08 0.68 0.87 1.07 1.25 1.44 1.75 2.02 0.01 0.03 0.04 0.08 0.13 0.53 0.68 0.87 1.07 1.25 1.44 1.75 2.02 0.01 0.03 0.04
0.683351 0.682401 0.773354 0.698566 0.697945 0.695883 0.771017 0.770201
0.76917 0.768139 0.766928 0.757829 0.757651 0.855326 0.856258 0.858223
0.93111 0.803487 0.911068 0.845233 0.869378 0.884242 0.837614 0.827104 0.925138 0.856359 0.934757
0.93111 1.001215 1.002485 0.994898 0.938668 0.900962 0.894349 0.879292 0.844537 0.829167
0.99941 1.001097 0.939552
4.873449 5.45373
0.037825 0.117688 0.156918 1.278118
2.25431 2.669558
3.14562 3.721711 3.970896 4.856561 5.196248 0.036511 0.109533 0.146704 0.282381 1.951505 2.451947 3.050124 3.407815 3.715135 4.488075 5.159019 0.035588 0.110008 0.140603 0.282381 0.440555 1.661417 2.013457 2.492156 2.995328 3.340511
3.61498 4.365359 5.150837 0.034576
0.10247 0.161413
Texas Tech University, Tolani A. Afolabi, May 2018
140
Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SSL/SL SL SL SL SL SL/A SL/A SL/A SSL SSL SSL SSL/SL SL SL SL
60 60 60 60 60 60 60 60 65 65 65 65 65 65 65
20 25 55 60 65 70 75 80 5
10 15 20 25 55 60
966 966 966 966 966 966 966 966
1038 1038 1038 1038 1038 1038 1038
0.08 0.13 0.53 0.68 0.87 1.07 1.25 1.44 0.01 0.03 0.04 0.08 0.13 0.53 0.68
0.93111 1.060735 1.002485 0.925082 0.930782 0.918183 0.901676 0.902389 1.063179 1.062302 1.037935 1.063179 1.060735 1.002485
0.97871
0.282381 0.42853
1.661417 1.698474 2.512515 2.940225 3.239225 3.641174 0.033889 0.100062
0.16542 0.322943
0.42853 1.661417 1.975777
Table A-2: Experimental data for flow pattern at 280 cP and 0Β° Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
EB EB EB SL SL SL SL SL SW/SL SW/RW RW RW SW SW/A SW/A EB EB EB SL
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 5 5 5
5 10 20 25 30 35 40 45 50 55 60 65 70 75 80 5
10 20 25
47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 81 81 81 81
0.02 0.03 0.09 0.13 0.17 0.23 0.29 0.35 0.42 0.52 0.67 0.85 1.04 1.24 1.43 0.02 0.03 0.09 0.13
0.046742 0.04788 0.04895
0.047913 0.046889 0.048927 0.046883 0.046878 0.046878 0.047897 0.046878 0.045853 0.046861 0.046861 0.047875 0.085563 0.079414 0.084603 0.082584
0.10195 0.152378 0.457391 0.673034 0.858492 1.118066 1.464759 1.864135 2.121375 2.692639 3.447646 4.241144 5.031297 6.149755
7.00023 0.10098
0.151442 0.494133
0.67316
Texas Tech University, Tolani A. Afolabi, May 2018
141
Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SL SL SL SL SL SL SL/RW RW RW SW/A SW/A EB EB SL SL SL SL SL SL SL RW/SL RW RW/SL SW/A A A EB EB EB/SL SL SL SL SL SL SL RW/SL SL/A SL/A SL/A A
5 5 5 5 5 5 5 5 5 5 5
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 15 15 15 15 15 15 15 15 15 15 15 15 15 15
30 35 40 45 50 55 60 65 70 75 80 5
10 20 25 30 35 40 45 50 55 60 65 70 75 80 5
10 20 25 30 35 40 45 50 55 60 65 70 75
81 81 81 81 81 81 81 81 81 81 81
166 166 166 166 166 166 166 166 166 166 166 166 166 166 166 250 250 250 250 250 250 250 250 250 250 250 250 250 250
0.17 0.23 0.29 0.35 0.42 0.52 0.67 0.85 1.04 1.24 1.43 0.02 0.03 0.09 0.13 0.17 0.23 0.29 0.35 0.42 0.52 0.67 0.85 1.04 1.24 1.43 0.02 0.03 0.09 0.13 0.17 0.23 0.29 0.35 0.42 0.52 0.67 0.85 1.04 1.24
0.080554 0.080545 0.080554 0.080545 0.080545 0.078506 0.080554 0.079534 0.079525 0.078515 0.078506
0.19245 0.167953 0.168324 0.166361 0.166361 0.166361 0.166361 0.166361 0.165341 0.166381
0.16536 0.16536 0.16432
0.165379 0.164358 0.252585 0.228009 0.255393 0.253291 0.254312 0.254312 0.253291 0.253291 0.253291 0.250519 0.254372 0.252564 0.251541
0.25049
0.838212 1.147604 1.429624 1.785413 2.169085 2.624328 3.372446 4.165431 5.054975 5.834135 6.641774 0.096545 0.146058 0.484338 0.594519 0.773147 1.085497 1.371968 1.636948 1.957399 2.402263 3.075001 3.760983 4.547988
5.23019 5.993828 0.091174 0.142676 0.428268
0.55146 0.713772
0.97065 1.211649
1.44762 1.819866 2.120056
2.78333 3.396046 4.077012 4.718092
Texas Tech University, Tolani A. Afolabi, May 2018
142
Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
A EB/SL EB/SL EB/SL SL SL SL SL SL RW/SL SL/A A A SL SL SL SL SL SL SL SL SL RW/SL SL/A A SSL SL SL SL SL SL SL SL SL/A SL/A A SSL SSL SL SL
15 20 20 20 20 20 20 20 20 20 20 20 20 25 25 25 25 25 25 25 25 25 25 25 25 30 30 30 30 30 30 30 30 30 30 30 35 35 35 35
80 5
10 20 25 30 35 50 55 60 65 70 75 5
10 20 25 40 45 50 55 60 65 70 75 5
10 20 25 40 50 55 60 65 70 75 5
10 20 25
250 340 340 340 340 340 340 340 340 340 340 340 340 426 426 426 426 426 426 426 426 426 426 426 426 512 512 512 512 512 512 512 512 512 512 512 598 598 598 598
1.43 0.02 0.03 0.09 0.13 0.17 0.23 0.42 0.52 0.67 0.85 1.04 1.24 0.02 0.03 0.09 0.13 0.29 0.35 0.42 0.52 0.67 0.85 1.04 1.24 0.02 0.03 0.09 0.13 0.29 0.42 0.52 0.67 0.85 1.04 1.24 0.02 0.03 0.09 0.13
0.25049 0.345107 0.346125 0.342457 0.340859 0.339914 0.334239
0.33897 0.33704
0.336133 0.335147 0.333097 0.333058 0.520146 0.417532 0.471283 0.424911 0.424911 0.419484 0.421536 0.422611 0.421585 0.420559 0.420412 0.419386 0.557808
0.46572 0.513774 0.510576 0.424911 0.508774 0.508893 0.508953 0.506782 0.506782 0.504671 0.611827 0.593243 0.622839 0.592831
5.250664 0.087971 0.130558
0.44652 0.527179 0.686004 0.897464 1.700432 2.048383 2.521757 3.096346 3.780532 4.305523 0.073616 0.119192 0.409542 0.495507 1.102596 1.250698
1.56161 1.89203 2.38709
2.855128 3.419872 3.973482 0.073301
0.11531 0.400825 0.484465 1.102596 1.393541 1.757619
2.2429 2.693704 3.211002 3.650487 0.069276 0.109201 0.367189 0.451894
Texas Tech University, Tolani A. Afolabi, May 2018
143
Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SL SL SL SL/A SL/A SL/A A SSL SSL SL SL SL SL SL SL SL SL SL/A A A A SSL SSL SSL SSL SL SL SL SL SL SL SL/A SL/A SL/A A A SSL SSL SSL SSL
35 35 35 35 35 35 35 40 40 40 40 40 40 40 40 40 40 40 40 40 40 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 50 50 50 50
30 50 55 60 65 70 75 5
10 20 25 30 35 40 50 55 60 65 70 75 80 5
10 20 25 30 35 40 45 50 55 60 65 70 75 80 5
10 20 25
598 598 598 598 598 598 598 648 648 648 648 648 648 648 648 648 648 648 648 648 648 716 716 716 716 716 716 716 716 716 716 716 716 716 716 716 861 861 861 861
0.17 0.42 0.52 0.67 0.85 1.04 1.24 0.02 0.03 0.09 0.13 0.17 0.23 0.29 0.42 0.52 0.67 0.85 1.04 1.24 1.43 0.02 0.03 0.09 0.13 0.17 0.23 0.29 0.35 0.42 0.52 0.67 0.85 1.04 1.24 1.43 0.02 0.03 0.09 0.13
0.672022 0.591111 0.591249 0.590016 0.590085 0.587006 0.584748 0.701576 0.677925
0.66751 0.592831 0.672022 0.747034 0.766467 0.591111 0.591249 0.590016 0.590085 0.663025 0.661921 0.779641 0.798402 0.844289 0.736853 0.672022 0.672022 0.816071 0.766467 0.802428 0.668391 0.668313 0.666182 0.665078 0.735042 0.729994 0.839298
0.87702 0.948653 0.883603
0.88566
0.567201 1.352409 1.678582 2.052156 2.559857 3.057533 3.483262 0.067312 0.103255 0.338654 0.451894 0.567201 0.715618 0.817323 1.352409 1.678582 2.052156 2.559857 2.827824 3.193311 3.428813 0.063668 0.096789 0.338844 0.431991 0.567201 0.692735 0.817323
0.98477 1.323261 1.612524 1.966408 2.359056 2.673092 3.127812 3.320051 0.061096 0.088741 0.272165 0.399053
Texas Tech University, Tolani A. Afolabi, May 2018
144
Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SL SL SL SL SL SL SL SL/A SL/A A A SSL SSL SSL SL SL SL SL SL SL SL SL/A SL/A A A A SSL SSL SSL SL SL SL SL SL SL SL SL/A SL/A SL/A SL/A
50 50 50 50 50 50 50 50 50 50 50 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 60 60 60 60 60 60 60 60 60 60 60 60 60 60
30 35 40 45 50 55 60 65 70 75 80 5
10 20 25 30 35 40 45 50 55 60 65 70 75 80 5
10 20 25 30 35 40 45 50 55 60 65 70 75
861 861 861 861 861 861 861 861 861 861 861 892 892 892 892 892 892 892 892 892 892 892 892 892 892 892 909 909 909 909 909 909 909 909 909 909 909 909 909 909
0.17 0.23 0.29 0.35 0.42 0.52 0.67 0.85 1.04 1.24 1.43 0.02 0.03 0.09 0.13 0.17 0.23 0.29 0.35 0.42 0.52 0.67 0.85 1.04 1.24 1.43 0.02 0.03 0.09 0.13 0.17 0.23 0.29 0.35 0.42 0.52 0.67 0.85 1.04 1.24
0.817482 0.816071 0.766467 0.802428 0.892842 0.879279 0.869781 0.854486 0.866798 0.845431 0.839298 0.904733 0.948653 0.879904 0.944182 0.886273 0.816071 0.766467 0.802428 0.877225 0.882934 0.911774
0.89133 0.869966 0.845431 0.839298 0.948653 0.936861 0.949632 0.944182 0.886273 0.816071 0.766467 0.802428 0.944907 0.920973 0.903702
0.89133 0.869966 0.845431
0.533358 0.692735 0.817323
0.98477 1.15822
1.449163 1.700752 2.131814
2.51332 2.943308 3.320051 0.060223 0.088741 0.301346 0.393493 0.512403 0.692735 0.817323
0.98477 1.135515 1.409825 1.758224 2.202376 2.578276 2.943308 3.320051 0.059161 0.089128 0.315406 0.393493 0.512403 0.692735 0.817323
0.98477 1.162943 1.390172 1.744038 2.202376 2.578276 2.943308
Texas Tech University, Tolani A. Afolabi, May 2018
145
Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
A SSL SSL SL SL SL SL SL SL SL SL SL SL SL SL SL/A SSL SSL SSL SL SL SL SL SL SL SL SL SL SL SL SL/A
60 65 65 65 65 65 65 65 65 65 65 65 65 65 65 65 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70
80 5
10 20 25 30 35 40 45 50 55 60 65 70 75 80 5
10 20 25 30 35 40 45 50 55 60 65 70 75 80
909 932 932 932 932 932 932 932 932 932 932 932 932 932 932 932 954 954 954 954 954 954 954 954 954 954 954 954 954 954 954
1.43 0.02 0.03 0.09 0.13 0.17 0.23 0.29 0.35 0.42 0.52 0.67 0.85 1.04 1.24 1.43 0.02 0.03 0.09 0.13 0.17 0.23 0.29 0.35 0.42 0.52 0.67 0.85 1.04 1.24 1.43
0.839298 0.994853
0.80109 0.973209 0.945926 0.944767 0.816071 0.937351 0.802428 0.982303 0.920973 0.903702
0.89133 0.869966 0.845431 0.839298 0.994738
1.02168 0.966537 0.996498 0.944767 0.816071 0.937351 0.802428 0.959816 0.920973 0.903702
0.89133 0.869966 0.845431 0.839298
3.320051 0.058136 0.092852 0.263913 0.376281 0.501786 0.692735
0.80086 0.98477
1.121752 1.390172 1.744038 2.202376 2.578276 2.943308 3.320051 0.058147 0.095844 0.332573 0.375453 0.501786 0.692735
0.80086 0.98477
1.143215 1.390172 1.744038 2.202376 2.578276 2.943308 3.320051
Texas Tech University, Tolani A. Afolabi, May 2018
146
Table A-3: Experimental data for flow pattern at 280 cP and 5Β° Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
EB EB EB EB SB SB SB SB SB SSL SSL SSL SSL SSL EB EB EB EB EB SSL SL SSL SSL SSL SSL SSL SSL SSL EB EB EB EB/SL SL SL SL SSL SL
5 10 15 20 25 30 35 40 45 50 55 60 65 70 5
10 15 20 25 30 35 40 45 50 55 60 65 70 5
10 15 20 25 30 35 40 45
5 5 5 5 5 5 5 5 5 5 5 5 5 5
10 10 10 10 10 10 10 10 10 10 10 10 10 10 15 15 15 15 15 15 15 15 15
81 166 250 340 426 512 598 648 716 861 892 909 932 954
81 166 250 340 426 512 598 648 716 861 892 909 932 954
81 166 250 340 426 512 598 648 716
0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.081707 0.167767 0.256402
0.34875 0.437429 0.516136 0.602139 0.663612 0.725005 0.902042 0.940216 0.951221 0.970578 0.960947 0.078955 0.169865 0.252897 0.341109 0.426386 0.512083 0.593456 0.593456 0.676293 0.835355 0.898264 0.967717 0.967717
0.93267 0.079057 0.159253 0.247077 0.340042 0.427363 0.512571 0.594694 0.594694 0.676134
0.099049 0.100291 0.105458 0.101601
0.09744 0.092028 0.088166 0.083685 0.081664 0.067796 0.071968 0.070453
0.06275 0.075045 0.147741 0.163409 0.153288
0.14111 0.138763 0.113898 0.115041 0.115041 0.104421 0.097993
0.11287 0.094108 0.094108 0.109599
0.24776 0.224802 0.220005 0.204831 0.196108 0.190743 0.181552 0.181552 0.172582
Texas Tech University, Tolani A. Afolabi, May 2018
147
Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SSL SSL SSL SSL SSL EB/SL SL SL SL SL SL SL SL SL SL SL SL SL SSL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL
50 55 60 65 70 5
10 15 20 25 30 35 40 45 50 55 60 65 70 5
10 15 20 50 55 60 65 70 5
10 15 20 50 55 60 65 70 5
10 25
15 15 15 15 15 20 20 20 20 20 20 20 20 20 20 20 20 20 20 25 25 25 25 25 25 25 25 25 30 30 30 30 30 30 30 30 30 35 35 35
861 892 909 932 954
81 166 250 340 426 512 598 648 716 861 892 909 932 954
81 166 250 340 861 892 909 932 954
81 166 250 340 861 892 909 932 954
81 166 426
0.05 0.05 0.05 0.05 0.05 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.23 0.23 0.23
0.839174 0.90233 0.90233 0.90233
0.979266 0.07803
0.159271 0.245961 0.341189 0.425309 0.513658 0.594415 0.594415 0.677084 0.838978 0.902118 0.902118 0.902118
0.98041 0.078058 0.158281 0.249813 0.341149 0.964278 1.069787 1.069787 1.069787 1.044512 0.079094 0.158281 0.250783 0.341069 1.062586 0.902118 0.902118 0.902118 0.902118 0.078067 0.158299 0.425309
0.16271 0.15853 0.15853 0.15853
0.153509 0.448664
0.41137 0.396083 0.370534 0.348033 0.335585 0.318454 0.318454
0.3056 0.288398 0.281105 0.281105 0.281105 0.276368
0.64033 0.600973
0.57212 0.535216 0.448134 0.386244 0.386244 0.386244 0.422872 0.842385 0.781363 0.740259 0.692984 0.497986 0.522998 0.522998 0.522998 0.522998 1.146585 1.005572 0.919472
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Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL SL/RW SL SL SL SL SL SL SL SL SL SL SL SL SL/RW SL/SW SL SL SL SL SL SL SL SL
30 5
10 25 30 35 5
10 35 40 45 50 55 60 65 70 5
10 15 20 25 30 35 40 45 50 55 60 65 70 5
10 15 20 25 30 35 40 45 50
35 40 40 40 40 40 45 45 45 45 45 45 45 45 45 45 50 50 50 50 50 50 50 50 50 50 50 50 50 50 55 55 55 55 55 55 55 55 55 55
512 81
166 426 512 598
81 166 598 648 716 861 892 909 932 954
81 166 250 340 426 512 598 648 716 861 892 909 932 954
81 166 250 340 426 512 598 648 716 861
0.23 0.29 0.29 0.29 0.29 0.29 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.52 0.52 0.52 0.52 0.52 0.52 0.52 0.52 0.52 0.52
0.425309 0.078049 0.158262 0.513598 0.513598 0.513598 0.080018 0.158281 0.676846 0.676846 0.676846 1.043042 1.043042 1.043042 1.043042 1.043042 0.075959 0.157253 0.249492 0.336605 0.421634 0.512877 0.594607 0.594607 0.672971 0.835404 0.835404 0.835404 1.012974 1.012974 0.076995 0.158244 0.249521 0.336605 0.422808 0.511851 0.593511 0.593511 0.673919 0.969781
0.919472 1.419685 1.356204
1.00327 1.00327 1.00327
1.781067 1.627445 1.122016 1.122016 1.122016 1.031004 1.031004 1.031004 1.031004 1.031004 2.068603 1.954605 1.801839 1.647162 1.461807 1.444904
1.41726 1.41726
1.320484 1.263312 1.263312 1.263312 1.071021 1.071021 2.610576 2.427861 2.211348 2.049405 1.959669 1.808931 1.712653 1.712653 1.632446 1.441019
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Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SL SL SL SL RW SL/SW SL/SW SL/SW SL SL SL SL SL SL SL SL SL/A SL/A RW SL/SW SL/SW SL/SW SL SL SL/A SL/A SL/A SL/A SL/A SL/A SL/A SL/A RW SW/A SL/SW SL/SW SL/A SL/A SL/A SL/A
55 60 65 70 5
10 15 20 25 30 35 40 45 50 55 60 65 70 5
10 15 20 25 30 35 40 45 50 55 60 65 70 5
10 15 20 25 30 35 40
55 55 55 55 60 60 60 60 60 60 60 60 60 60 60 60 60 60 65 65 65 65 65 65 65 65 65 65 65 65 65 65 70 70 70 70 70 70 70 70
892 909 932 954
81 166 250 340 426 512 598 648 716 861 892 909 932 954
81 166 250 340 426 512 598 648 716 861 892 909 932 954
81 166 250 340 426 512 598 648
0.52 0.52 0.52 0.52 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 0.85 1.04 1.04 1.04 1.04 1.04 1.04 1.04 1.04
0.898506 0.927508 0.934268 0.939627 0.076986 0.159271 0.249433 0.338538
0.42266 0.510945 0.592484 0.592484 0.671786 0.818319 0.911056
0.92983 0.941683 0.907651
0.07595 0.159234 0.248378 0.336369 0.421585 0.509979 0.589403 0.589403 0.668704 0.883085 0.937461 0.934268 0.910842 0.964187 0.075932 0.160243
0.24832 0.335343
0.42051 0.508834 0.590292 0.590292
1.431645 1.468479 1.358619 1.367457 3.389905 3.024899 2.797835 2.534119 2.353897 2.206707 2.154347 2.154347 2.012316 1.819658 1.861281 1.626759
1.71474 1.748219 4.089504 3.740087 3.420557 3.030793 2.968787 2.726841 2.492376 2.492376 2.434217 2.222695 2.162175 2.122977 2.275735 2.159555 4.992999 4.585796 4.001876 3.731217 3.535908 3.212613 3.046105 3.046105
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Flow Pattern
Pump Speed [%]
Valve Opening [%]
Liquid Mass flowrate [g/s]
Gas Mass Flowrate [lb/min]
πππππΏπΏ [m/s] πππππΊπΊ [m/s]
SL/A SL/A SL/A SL/A SL/A SL/A SW SW/A SL/SW SL/SW SL/A SL/A A A A SL/A A SL/A SL/A SL/A SW/A SW/A SL/SW SW/A SL/A SL/A A A A A A A A SL/A
45 50 55 60 65 70 5
10 15 20 25 30 35 40 45 50 55 60 65 70 5
10 15 20 25 30 35 40 45 50 55 60 65 70
70 70 70 70 70 70 75 75 75 75 75 75 75 75 75 75 75 75 75 75 80 80 80 80 80 80 80 80 80 80 80 80 80 80
716 861 892 909 932 954
81 166 250 340 426 512 598 648 716 861 892 909 932 954
81 166 250 340 426 512 598 648 716 861 892 909 932 954
1.04 1.04 1.04 1.04 1.04 1.04 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43 1.43
0.66665 0.825612 0.962808 0.962808 0.936433 0.910949 0.078992 0.160243
0.24832 0.336369 0.419386 0.508834 0.588307 0.588307
0.66665 0.856456 0.862524 0.928319 0.928319 0.928319 0.078974 0.160205 0.247207 0.336369 0.419386 0.508834 0.587075 0.587075
0.58817 0.869202 0.906836 0.909921 0.909921 0.909921
2.949925 2.619291 2.555121 2.555121 2.614004 2.447767 5.862696 5.558479 4.743112 4.309675 3.990061 3.723112 3.511571 3.511571 3.307153 2.990148 3.086193 3.013375 3.004627 3.004627 6.600235 5.981925 5.289871 4.914577 4.429941 4.050036 3.776742 3.776742 3.867931 3.354485 3.392176 3.382496 3.382496 3.382496
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Flow Pattern Results for 150 cP Air-Oil Case
Figure A 1: Flow pattern map generated for the flow loop system for oil at 0Λ and 150 cP.
Figure A 2: Flow pattern map generated for the flow loop system for oil at 0Λ and 150 cP superimposed to FLOPATN 2.7 VBA code
ππ πππΏπΏ[ππ π π
]/
πππππΊπΊ[πππ π
]/
ππ πππΏπΏ[ππ π π
]/
πππππΊπΊ[πππ π
]/
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Figure A 3: Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination
Figure A 4: Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination
Texas Tech University, Tolani A. Afolabi, May 2018
153
Figure A 5: Flow pattern map generated for the flow loop system for oil at 5Λ and 150 cP
Figure A 6: Flow pattern map generated for the flow loop system for oil at 5Λ and 150 cP superimposed to FLOPATN 2.7 VBA code
ππ πππΏπΏ[ππ π π
]/
πππππΊπΊ[πππ π
]/
ππ πππΏπΏ[ππ π π
]/
πππππΊπΊ[πππ π
]/
Texas Tech University, Tolani A. Afolabi, May 2018
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Figure A 7: Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination
Figure A 8: Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination
Texas Tech University, Tolani A. Afolabi, May 2018
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APPENDIX B
Air-Water Case
Table B- 1: Fluid Properties and Pressure Drop reading for Air-Water Case
cP g/cc m/s F kg/m3 m/s m/s Deg1-L35_G45_A0 1 0.9924 0.661 74.09 1.422 1.463 2.123 01-L35_G60_A0 1 0.9927 0.661 75.12 1.48 2.809 3.47 01-L65_G45_A0 1 0.993 1.213 74.38 1.599 1.305 2.518 01-L65_G60_A0 1 0.9907 1.208 74.62 1.721 2.41 3.617 01-L35_G45_A1 1 0.9925 0.66 74.01 1.425 1.447 2.107 11-L35_G60_A1 1 0.9919 0.658 75.42 1.48 2.78 3.438 11-L65_G45_A1 1 0.9858 1.203 75.82 1.593 1.284 2.487 11-L65_G60_A1 1 0.9892 1.205 75.97 1.714 2.407 3.612 11-L35_G45_A5 1 0.9925 0.659 70.46 1.454 1.46 2.119 51-L35_G60_A5 1 0.9917 0.654 71.71 1.507 2.773 3.427 51-L65_G45_A5 1 0.9881 1.203 71.7 1.632 1.292 2.495 51-L65_G60_A5 1 0.9903 1.206 73.14 1.742 2.404 3.61 5
PT1 PT2(5) DP_12 DP_13 DP_34 DP_35kPa kPa Pa/m Pa/m Pa/m Pa/m
1-L35_G45_A0 119.45 115.94 555.15 562.26 816.32 709.591-L35_G60_A0 124.63 119.5 637.18 761.2 1106.23 990.481-L65_G45_A0 134.56 127.35 1076.18 1107.87 61.05 NA 1-L65_G60_A0 145.07 135.38 1225.75 1362.92 1970.89 1881.831-L35_G45_A1 119.86 116.02 653.77 670.91 843.64 767.511-L35_G60_A1 124.88 118.99 722.13 845.28 1239.23 NA1-L65_G45_A1 134.62 126.72 1125.3 1177.56 1449.65 NA1-L65_G60_A1 144.94 134.53 1219.4 1416.55 2030.18 NA1-L35_G45_A5 121.82 115.89 1005.26 922.74 1038 970.631-L35_G60_A5 126.61 119.3 1149.97 1149 1427.97 1180.561-L65_G45_A5 137.24 126.84 1518.12 1552.45 1762.8 1742.491-L65_G60_A5 146.93 134.49 1522.49 1799.74 2286.52 2204.25
Test Info
Test Name
Pressure
Test Name
Test InfoTests Conditions
Liquid Gas
Texas Tech University, Tolani A. Afolabi, May 2018
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Table B- 2: Fluid Properties and Experimental Results of Hydrodynamic Parameters for Air-Water Case
cP g/cc m/s F kg/m3 m/s m/s Deg1-L35_G45_A0 1 0.9924 0.661 74.09 1.422 1.463 2.123 01-L35_G60_A0 1 0.9927 0.661 75.12 1.48 2.809 3.47 01-L65_G45_A0 1 0.993 1.213 74.38 1.599 1.305 2.518 01-L65_G60_A0 1 0.9907 1.208 74.62 1.721 2.41 3.617 01-L35_G45_A1 1 0.9925 0.66 74.01 1.425 1.447 2.107 11-L35_G60_A1 1 0.9919 0.658 75.42 1.48 2.78 3.438 11-L65_G45_A1 1 0.9858 1.203 75.82 1.593 1.284 2.487 11-L65_G60_A1 1 0.9892 1.205 75.97 1.714 2.407 3.612 11-L35_G45_A5 1 0.9925 0.659 70.46 1.454 1.46 2.119 51-L35_G60_A5 1 0.9917 0.654 71.71 1.507 2.773 3.427 51-L65_G45_A5 1 0.9881 1.203 71.7 1.632 1.292 2.495 51-L65_G60_A5 1 0.9903 1.206 73.14 1.742 2.404 3.61 5
C1 C2 C3 Min Max Mode Avg.slugs/sec slugs/sec slugs/sec m/s m m m m
1-L35_G45_A0 1.15 1.017 0.967 2.698 0.229 1.283 0.597 0.6261-L35_G60_A0 1.317 0.883 0.8 5.275 0.241 1.194 0.635 0.6461-L65_G45_A0 2.533 2.133 1.983 3.506 0.191 0.978 0.419 0.4891-L65_G60_A0 NA 1.867 1.8 4.488 0.292 1.359 0.66 0.731-L35_G45_A1 NA 1.15 1.067 3.113 0.127 1.295 0.47 0.6291-L35_G60_A1 NA 1 0.767 4.22 0.216 1.067 0.813 0.6711-L65_G45_A1 NA 2.483 2.367 3.202 0.203 1.359 0.572 0.5131-L65_G60_A1 NA 1.8 1.717 5.174 0.216 1.397 0.864 0.7251-L35_G45_A5 NA 1.3 1.15 3.374 0.267 1.549 0.381 0.5671-L35_G60_A5 NA 1.2 1.067 4.875 0.381 1.245 0.622 0.7031-L65_G45_A5 NA 2.833 2.483 3.703 0.216 0.953 0.419 0.4851-L65_G60_A5 NA 2.083 1.95 5.158 0.279 1.359 0.457 0.664
Test Info
Test Name
Frequency, Translational Velocity, and Slug LengthTest Info
Tests ConditionsLiquid Gas
Test Name
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Table B- 3: Fluid Properties and Liquid Holdup Result for Air-Water Case
cP g/cc m/s F kg/m3 m/s m/s Deg1-L35_G45_A0 1 0.9924 0.661 74.09 1.422 1.463 2.123 01-L35_G60_A0 1 0.9927 0.661 75.12 1.48 2.809 3.47 01-L65_G45_A0 1 0.993 1.213 74.38 1.599 1.305 2.518 01-L65_G60_A0 1 0.9907 1.208 74.62 1.721 2.41 3.617 01-L35_G45_A1 1 0.9925 0.66 74.01 1.425 1.447 2.107 11-L35_G60_A1 1 0.9919 0.658 75.42 1.48 2.78 3.438 11-L65_G45_A1 1 0.9858 1.203 75.82 1.593 1.284 2.487 11-L65_G60_A1 1 0.9892 1.205 75.97 1.714 2.407 3.612 11-L35_G45_A5 1 0.9925 0.659 70.46 1.454 1.46 2.119 51-L35_G60_A5 1 0.9917 0.654 71.71 1.507 2.773 3.427 51-L65_G45_A5 1 0.9881 1.203 71.7 1.632 1.292 2.495 51-L65_G60_A5 1 0.9903 1.206 73.14 1.742 2.404 3.61 5
1-L35_G45_A0 0.841 0.27 0.3981-L35_G60_A0 0.648 0.26 0.2981-L65_G45_A0 0.745 0.369 0.4731-L65_G60_A0 0.701 0.264 0.3921-L35_G45_A1 0.869 0.241 0.3761-L35_G60_A1 0.829 0.213 0.2881-L65_G45_A1 0.809 0.376 0.541-L65_G60_A1 0.652 0.311 0.3921-L35_G45_A5 0.84 0.255 0.3681-L35_G60_A5 0.859 0.213 0.3131-L65_G45_A5 0.798 0.328 0.4811-L65_G60_A5 0.718 0.274 0.385
Test InfoLiquid Holdup
Test InfoTests Conditions
Liquid Gas
Test Name
Test Name
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158
Air-Oil Case at 280 cP
Table B- 4: Fluid Properties and Pressure Drop reading for Air-Oil Case at 280cP
Β°C Pa.s g/cc m/s kg/m3 m/s m/s Deg280-L20_G30_A0 22.56 0.252 0.8627 0.345 1.694 0.598 0.943 0280-L20_G45_A0 22.85 0.248 0.8604 0.342 1.742 1.198 1.54 0280-L25_G35_A0 24.76 0.221 0.8587 0.431 1.736 0.77 1.201 0280-L30_G40_A0 24.74 0.222 0.8561 0.519 1.873 0.89 1.408 0280-L35_G30_A0 25.51 0.212 0.8596 0.616 1.907 0.532 1.148 0280-L35_G45_A0 27.95 0.185 0.8556 0.612 1.9 1.103 1.715 0280-L40_G30_A0 24.75 0.221 0.8586 0.7 2.093 0.802 1.502 0280-L40_G40_A0 28.77 0.178 0.8558 0.707 1.927 0.874 1.581 0280-L20_G30_A5 22.33 0.256 0.8618 0.343 1.706 0.594 0.936 5280-L20_G45_A5 24.21 0.228 0.8591 0.342 1.707 1.195 1.537 5280-L25_G35_A5 26.4 0.202 0.8582 0.434 1.712 0.784 1.218 5280-L30_G40_A5 27.17 0.193 0.8562 0.521 1.808 0.917 1.439 5280-L35_G30_A5 27.73 0.188 0.8568 0.615 1.839 0.556 1.172 5280-L35_G45_A5 28.75 0.178 0.8556 0.614 1.886 1.098 1.711 5280-L40_G30_A5 27.77 0.187 0.8556 0.703 1.927 0.538 1.241 5280-L40_G40_A5 29.78 0.169 0.8537 0.702 1.912 0.873 1.575 5
PT1 PT2 DP_12 DP_13 DP_34 DP_35kPa kPa Pa/m Pa/m Pa/m Pa/m
280-L20_G30_A0 143.75 129.4 2557.14 2445.82 2277.45 2363.66280-L20_G45_A0 147.96 125.86 2442.1 2461.08 2247.95 2459.37280-L25_G35_A0 148.38 118.89 2255.05 2436.43 2305.62 2447.27280-L30_G40_A0 160.1 119.84 2636.68 3099.4 2787.75 3037.23280-L35_G30_A0 163.36 114.81 2589.85 3267.88 2883.59 3274.47280-L35_G45_A0 164.1 110.12 2162.1 2708.67 2493.38 2845.41280-L40_G30_A0 178.87 111.56 3094.11 3686.4 3386.61 3766.83280-L40_G40_A0 166.92 97.98 1844.51 2766.92 2403.44 2933.12280-L20_G30_A5 144.66 127.45 3021.18 2910.54 2837.46 2825.66280-L20_G45_A5 145.6 122.04 2666.09 2695.87 2592.86 2681.62280-L25_G35_A5 147.15 116.04 2507.52 2726.97 2574.39 2741.82280-L30_G40_A5 155.77 115.12 2692.93 3035.34 2860.12 3102.4280-L35_G30_A5 158.77 109.55 2729.63 3225.95 3003.72 3295.77280-L35_G45_A5 163.36 106.89 2528.21 3145.01 2914.9 3288.52280-L40_G30_A5 166.38 100.74 2654.51 3442.07 3113.15 3563.01280-L40_G40_A5 166.17 95.04 2127.93 3113.7 2762.87 3313.75
Pressure
Test InformationTests Conditions
Liquid Gas
Test Name
Test Information
Test Name
Texas Tech University, Tolani A. Afolabi, May 2018
159
Table B- 5: Fluid Properties and Experimental Results of Hydrodynamic Parameters for Air-Oil Case at 280 cP
C Pa.s g/cc m/s kg/m3 m/s m/s Deg280-L20_G30_A0 22.56 0.252 0.8627 0.345 1.694 0.598 0.943 0280-L20_G45_A0 22.85 0.248 0.8604 0.342 1.742 1.198 1.54 0280-L25_G35_A0 24.76 0.221 0.8587 0.431 1.736 0.77 1.201 0280-L30_G40_A0 24.74 0.222 0.8561 0.519 1.873 0.89 1.408 0280-L35_G30_A0 25.51 0.212 0.8596 0.616 1.907 0.532 1.148 0280-L35_G45_A0 27.95 0.185 0.8556 0.612 1.9 1.103 1.715 0280-L40_G30_A0 24.75 0.221 0.8586 0.7 2.093 0.802 1.502 0280-L40_G40_A0 28.77 0.178 0.8558 0.707 1.927 0.874 1.581 0280-L20_G30_A5 22.33 0.256 0.8618 0.343 1.706 0.594 0.936 5280-L20_G45_A5 24.21 0.228 0.8591 0.342 1.707 1.195 1.537 5280-L25_G35_A5 26.4 0.202 0.8582 0.434 1.712 0.784 1.218 5280-L30_G40_A5 27.17 0.193 0.8562 0.521 1.808 0.917 1.439 5280-L35_G30_A5 27.73 0.188 0.8568 0.615 1.839 0.556 1.172 5280-L35_G45_A5 28.75 0.178 0.8556 0.614 1.886 1.098 1.711 5280-L40_G30_A5 27.77 0.187 0.8556 0.703 1.927 0.538 1.241 5280-L40_G40_A5 29.78 0.169 0.8537 0.702 1.912 0.873 1.575 5
C2 C3 C1 Min Max Avg. SDslugs/sec slugs/sec slugs/sec m/s m m m m
280-L20_G30_A0 2.467 2.15 1.8 2.256 0.165 0.635 0.324 0.115280-L20_G45_A0 2.883 2.017 1.967 3.873 0.1 0.48 0.273 0.075280-L25_G35_A0 2.8 2.274 2.15 2.967 0.165 0.635 0.315 0.106280-L30_G40_A0 3.65 2.833 2.581 3.263 0.125 0.635 0.343 0.127280-L35_G30_A0 4.1 3.45 2.833 3.065 0.152 0.787 0.327 0.155280-L35_G45_A0 3.283 2.65 2.483 4.002 0.127 0.559 0.288 0.093280-L40_G30_A0 4.983 3.717 3.067 3.843 0.12 0.711 0.351 0.147280-L40_G40_A0 4.45 3.083 2.833 3.962 0.127 0.609 0.333 0.118280-L20_G30_A5 2.717 2.15 1.833 2.496 0.127 0.851 0.351 0.155280-L20_G45_A5 2.689 2.131 2.098 3.58 0.178 0.584 0.288 0.079280-L25_G35_A5 3.5 2.433 2.333 3.054 0.025 0.673 0.346 0.133280-L30_G40_A5 3.083 2.65 2.483 3.414 0.178 0.622 0.323 0.11280-L35_G30_A5 3.967 3.167 2.75 2.746 0.114 0.724 0.356 0.142280-L35_G45_A5 3.383 2.9 2.633 4.039 0.102 0.8 0.361 0.168280-L40_G30_A5 5.117 3.717 3.183 3.156 0.102 0.749 0.367 0.162280-L40_G40_A5 4.533 3.383 2.967 3.792 0.089 0.813 0.337 0.172
Test Information
Test Name
Experiments & Camera
Test InformationTests Conditions
Liquid Gas
Test Name
Texas Tech University, Tolani A. Afolabi, May 2018
160
Table B- 6: Fluid Properties and Liquid Holdup Result for Air-Oil Case at 280 cP
Β°C Pa.s g/cc m/s kg/m3 m/s m/s Deg280-L20_G30_A0 22.56 0.252 0.8627 0.345 1.694 0.598 0.943 0280-L20_G45_A0 22.85 0.248 0.8604 0.342 1.742 1.198 1.54 0280-L25_G35_A0 24.76 0.221 0.8587 0.431 1.736 0.77 1.201 0280-L30_G40_A0 24.74 0.222 0.8561 0.519 1.873 0.89 1.408 0280-L35_G30_A0 25.51 0.212 0.8596 0.616 1.907 0.532 1.148 0280-L35_G45_A0 27.95 0.185 0.8556 0.612 1.9 1.103 1.715 0280-L40_G30_A0 24.75 0.221 0.8586 0.7 2.093 0.802 1.502 0280-L40_G40_A0 28.77 0.178 0.8558 0.707 1.927 0.874 1.581 0280-L20_G30_A5 22.33 0.256 0.8618 0.343 1.706 0.594 0.936 5280-L20_G45_A5 24.21 0.228 0.8591 0.342 1.707 1.195 1.537 5280-L25_G35_A5 26.4 0.202 0.8582 0.434 1.712 0.784 1.218 5280-L30_G40_A5 27.17 0.193 0.8562 0.521 1.808 0.917 1.439 5280-L35_G30_A5 27.73 0.188 0.8568 0.615 1.839 0.556 1.172 5280-L35_G45_A5 28.75 0.178 0.8556 0.614 1.886 1.098 1.711 5280-L40_G30_A5 27.77 0.187 0.8556 0.703 1.927 0.538 1.241 5280-L40_G40_A5 29.78 0.169 0.8537 0.702 1.912 0.873 1.575 5
280-L20_G30_A0 0.895 0.895 0.565 0.65 0.708 0.719 0.572280-L20_G45_A0 0.868 0.868 0.549 0.593 0.898 0.506 0.393280-L25_G35_A0 0.829 0.829 0.575 0.633 0.874 0.675 0.547280-L30_G40_A0 0.806 0.806 0.593 0.651 0.944 0.643 0.524280-L35_G30_A0 0.721 0.754 0.693 0.711 0.925 Used 5 points 0.837 0.725280-L35_G45_A0 0.816 0.871 0.576 0.629 0.956 Used 5 points 0.658 0.529280-L40_G30_A0 1.005 0.887 0.541 0.638 0.36 Replaced 0.765 0.648280-L40_G40_A0 1.007 0.945 0.568 0.658 0.832 Replaced 0.722 0.613280-L20_G30_A5 1.033 0.785 0.49 0.566 0.711 Replaced 0.757 0.612280-L20_G45_A5 0.902 0.902 0.538 0.599 0.475 0.506280-L25_G35_A5 0.974 0.888 0.534 0.627 0.778 Replaced 0.652 0.535280-L30_G40_A5 0.839 0.839 0.574 0.636 0.652 0.677 0.546280-L35_G30_A5 0.939 0.939 0.581 0.709 0.971 0.824 0.697280-L35_G45_A5 0.986 0.942 0.543 0.637 0.901 Replaced 0.633 0.501280-L40_G30_A5 0.88 0.88 0.652 0.737 0.329 0.834 0.729280-L40_G40_A5 0.814 0.814 0.615 0.668 0.71 0.729 0.612
Test Information
Test Name
Mass Balance
Test Name
Raw Corr. R2 Remarks
Test InformationTests Conditions
Liquid Holdup
Liquid Gas
QCV Method
Texas Tech University, Tolani A. Afolabi, May 2018
161
Air-Oil Case at 150 cP Table B- 7: Fluid Properties and Pressure Drop reading for Air-Oil Case at 150cP
Β°C Pa.s g/cc m/s kg/m3 m/s m/s Deg150-L20_G30_A0 34.14 0.136 0.8556 0.351 1.426 0.731 1.082 0150-L20_G45_A0 32.29 0.149 0.8547 0.346 1.506 1.397 1.744 0150-L25_G35_A0 32.85 0.145 0.8547 0.44 1.533 0.864 1.303 0150-L30_G40_A0 32.77 0.146 0.8535 0.527 1.63 1.026 1.552 0150-L35_G30_A0 32.55 0.147 0.8545 0.618 1.663 0.63 1.249 0150-L35_G45_A0 32.43 0.148 0.8549 0.618 1.741 1.218 1.836 0150-L40_G30_A0 33.59 0.14 0.8535 0.712 1.71 0.601 1.313 0150-L40_G40_A0 33.18 0.143 0.8535 0.707 1.765 0.955 1.662 0150-L20_G30_A5 31.08 0.158 0.856 0.348 1.509 0.688 1.035 5150-L20_G45_A5 31.77 0.153 0.8553 0.348 1.538 1.366 1.713 5150-L25_G35_A5 32.55 0.147 0.8544 0.438 1.568 0.846 1.283 5150-L30_G40_A5 32.03 0.151 0.855 0.526 1.672 1.011 1.537 5150-L35_G30_A5 32.94 0.144 0.8553 0.622 1.681 0.614 1.236 5150-L35_G45_A5 33.14 0.143 0.853 0.616 1.746 1.191 1.807 5150-L40_G30_A5 36.45 0.123 0.8524 0.718 1.671 0.627 1.345 5150-L40_G40_A5 32.65 0.146 0.8534 0.703 1.811 0.94 1.642 5
PT1 PT2 DP_12 DP_13 DP_34 DP_35kPa kPa Pa/m Pa/m Pa/m Pa/m
150-L20_G30_A0 125.7 119 1241.32 1140.31 1105.87 1124.56150-L20_G45_A0 131.99 116.31 1314.7 1396.34 1329.2 1420.62150-L25_G35_A0 134.58 111.16 1231.93 1444.86 1282.43 1462.53150-L30_G40_A0 143.07 110.13 1415.37 1765.09 1588.31 1844.12150-L35_G30_A0 145.83 104.83 1342.46 1860.21 1656.79 1952.21150-L35_G45_A0 152.61 102.81 1864.97 2014.67 1790.99 2160.93150-L40_G30_A0 150.54 94.38 1061.93 1893.88 1597.13 2045.28150-L40_G40_A0 155.08 90.78 1018.71 1990.62 1660.47 2173.54150-L20_G30_A5 131.74 120.54 1964.65 1869.08 1799.82 1850.17150-L20_G45_A5 134.53 115.83 1804.31 1896.02 1785.49 1898.93150-L25_G35_A5 137.52 110.62 1775.02 2010.18 1856.5 2044.75150-L30_G40_A5 146.42 109.72 1992.03 2381.77 2204.31 2458.59150-L35_G30_A5 147.66 103.49 1866.79 2382.04 2166.19 2470.47150-L35_G45_A5 153.47 101.11 1808.03 2497.17 2270.6 2659.95150-L40_G30_A5 148.42 90.66 1251.69 2157.7 1837.62 2332.66150-L40_G40_A5 158.91 90.63 1630.1 2650.02 2298.45 2855.39
Pressure
Test InformationTests Conditions
Liquid Gas
Test Name
Test Information
Test Name
Texas Tech University, Tolani A. Afolabi, May 2018
162
Table B- 8: Fluid Properties and Experimental Results of Hydrodynamic Parameters for Air-Oil Case at 150 cP
Β°C Pa.s g/cc m/s kg/m3 m/s m/s Deg150-L20_G30_A0 34.14 0.136 0.8556 0.351 1.426 0.731 1.082 0150-L20_G45_A0 32.29 0.149 0.8547 0.346 1.506 1.397 1.744 0150-L25_G35_A0 32.85 0.145 0.8547 0.44 1.533 0.864 1.303 0150-L30_G40_A0 32.77 0.146 0.8535 0.527 1.63 1.026 1.552 0150-L35_G30_A0 32.55 0.147 0.8545 0.618 1.663 0.63 1.249 0150-L35_G45_A0 32.43 0.148 0.8549 0.618 1.741 1.218 1.836 0150-L40_G30_A0 33.59 0.14 0.8535 0.712 1.71 0.601 1.313 0150-L40_G40_A0 33.18 0.143 0.8535 0.707 1.765 0.955 1.662 0150-L20_G30_A5 31.08 0.158 0.856 0.348 1.509 0.688 1.035 5150-L20_G45_A5 31.77 0.153 0.8553 0.348 1.538 1.366 1.713 5150-L25_G35_A5 32.55 0.147 0.8544 0.438 1.568 0.846 1.283 5150-L30_G40_A5 32.03 0.151 0.855 0.526 1.672 1.011 1.537 5150-L35_G30_A5 32.94 0.144 0.8553 0.622 1.681 0.614 1.236 5150-L35_G45_A5 33.14 0.143 0.853 0.616 1.746 1.191 1.807 5150-L40_G30_A5 36.45 0.123 0.8524 0.718 1.671 0.627 1.345 5150-L40_G40_A5 32.65 0.146 0.8534 0.703 1.811 0.94 1.642 5
C2 C3 C1 Min Max Avg. SDslugs/sec slugs/sec slugs/sec m/s m m m m
150-L20_G30_A0 1.667 1.367 1.217 2.503 0.191 0.673 0.326 0.097150-L20_G45_A0 1.717 1.3 1.267 3.89 0.178 0.597 0.334 0.088150-L25_G35_A0 2 1.6 1.583 3.246 0.216 0.749 0.367 0.128150-L30_G40_A0 2.483 2.117 1.833 3.609 0.165 0.711 0.381 0.114150-L35_G30_A0 3.4 2.633 2.483 2.916 0.178 0.749 0.414 0.162150-L35_G45_A0 3.233 2.317 2.117 4.491 0.216 0.635 0.36 0.089150-L40_G30_A0 4.183 3.25 3.05 3.069 0.216 0.775 0.425 0.147150-L40_G40_A0 3.583 2.7 2.3 3.778 0.178 0.813 0.414 0.181150-L20_G30_A5 2.283 1.883 1.667 2.545 0.165 0.584 0.333 0.091150-L20_G45_A5 2.017 1.583 1.5 3.821 0.178 0.679 0.367 0.103150-L25_G35_A5 2.35 1.917 1.75 3.392 0.216 0.889 0.385 0.124150-L30_G40_A5 2.75 2.267 2.067 3.602 0.229 0.749 0.374 0.095150-L35_G30_A5 3.567 2.733 2.5 2.894 0.076 0.838 0.408 0.182150-L35_G45_A5 3.617 2.5 2.25 3.915 0.127 0.775 0.367 0.12150-L40_G30_A5 4.164 3.083 2.567 3.085 0.203 0.686 0.389 0.111150-L40_G40_A5 3.933 2.917 2.583 3.925 0.178 0.914 0.417 0.166
Test Information
Test Name
Experiments & Camera
Test InformationTests Conditions
Liquid Gas
Test Name
Texas Tech University, Tolani A. Afolabi, May 2018
163
Table B- 9: Fluid Properties and Liquid Holdup Result for Air-Oil Case at 150 cP
Β°C Pa.s g/cc m/s kg/m3 m/s m/s Deg150-L20_G30_A0 34.14 0.136 0.8556 0.351 1.426 0.731 1.082 0150-L20_G45_A0 32.29 0.149 0.8547 0.346 1.506 1.397 1.744 0150-L25_G35_A0 32.85 0.145 0.8547 0.44 1.533 0.864 1.303 0150-L30_G40_A0 32.77 0.146 0.8535 0.527 1.63 1.026 1.552 0150-L35_G30_A0 32.55 0.147 0.8545 0.618 1.663 0.63 1.249 0150-L35_G45_A0 32.43 0.148 0.8549 0.618 1.741 1.218 1.836 0150-L40_G30_A0 33.59 0.14 0.8535 0.712 1.71 0.601 1.313 0150-L40_G40_A0 33.18 0.143 0.8535 0.707 1.765 0.955 1.662 0150-L20_G30_A5 31.08 0.158 0.856 0.348 1.509 0.688 1.035 5150-L20_G45_A5 31.77 0.153 0.8553 0.348 1.538 1.366 1.713 5150-L25_G35_A5 32.55 0.147 0.8544 0.438 1.568 0.846 1.283 5150-L30_G40_A5 32.03 0.151 0.855 0.526 1.672 1.011 1.537 5150-L35_G30_A5 32.94 0.144 0.8553 0.622 1.681 0.614 1.236 5150-L35_G45_A5 33.14 0.143 0.853 0.616 1.746 1.191 1.807 5150-L40_G30_A5 36.45 0.123 0.8524 0.718 1.671 0.627 1.345 5150-L40_G40_A5 32.65 0.146 0.8534 0.703 1.811 0.94 1.642 5
150-L20_G30_A0 1.044 0.951 0.54 0.605 0.797 Replaced 0.613 0.488150-L20_G45_A0 1.528 0.806 0.445 0.484 0.745 Replaced 0.432 0.327150-L25_G35_A0 1.352 0.816 0.489 0.547 0.677 Replaced 0.593 0.49150-L30_G40_A0 0.811 0.811 0.566 0.613 0.582 0.585 0.482150-L35_G30_A0 0.991 0.991 0.577 0.723 0.777 0.706 0.616150-L35_G45_A0 0.817 0.817 0.59 0.628 0.817 0.573 0.476150-L40_G30_A0 0.938 0.938 0.624 0.757 0.253 0.706 0.636150-L40_G40_A0 0.94 0.94 0.602 0.687 0.272 0.667 0.561150-L20_G30_A5 0.898 0.898 0.556 0.63 0.652 0.664 0.533150-L20_G45_A5 1.137 0.822 0.454 0.507 0.862 Replaced 0.476 0.355150-L25_G35_A5 0.95 0.855 0.532 0.596 0.739 Replaced 0.634 0.525150-L30_G40_A5 0.875 0.875 0.564 0.631 0.776 0.625 0.506150-L35_G30_A5 0.925 0.925 0.586 0.705 0.702 0.753 0.648150-L35_G45_A5 0.923 0.923 0.53 0.613 0.859 0.612 0.488150-L40_G30_A5 0.953 0.953 0.62 0.727 0.928 0.774 0.67150-L40_G40_A5 1.402 0.784 0.456 0.546 0.735 Replaced 0.679 0.575
Test Information
Test Name
Mass Balance
Test Name
Raw Corr. R2 Remarks
Liquid HoldupQCV Method
Texas Tech University, Tolani A. Afolabi, May 2018
164
Drift Velocity Data
Table B- 10: Drift Velocity Result for Air-Water Case T
[ ] [Pa.s] [N/m] [kg/m3] [deg] [m/s]70.5 8.90E-04 72.8 0.990896 0 0.2648770.5 8.90E-04 72.8 0.990896 1 0.26590470.5 8.90E-04 72.8 0.990896 3 0.26873670.5 8.90E-04 72.8 0.990896 5 0.27922870.5 8.90E-04 72.8 0.990896 7 0.2802570.5 8.90E-04 72.8 0.990896 10 0.290596
Table B- 11: Drift Velocity Result for Air-Oil Case
T [ ] [Pa.s] [N/m] [kg/m3] [deg] [m/s]70.62 0.2703 30.68 0.854351 0 0.04732970.62 0.2703 30.68 0.854351 1 0.13209170.62 0.2703 30.68 0.854351 3 0.17101570.62 0.2703 30.68 0.854351 5 0.18318670.62 0.2703 30.68 0.854351 7 0.19329670.62 0.2703 30.68 0.854351 10 0.20339390.19 0.1487 31.22 0.857782 0 0.09181990.02 0.1494 31.22 0.857782 1 0.19604390.01 0.1494 31.22 0.857782 3 0.2165890.15 0.1488 31.22 0.857782 5 0.22300890.25 0.1484 31.22 0.857782 7 0.23178690.18 0.1487 31.22 0.857782 10 0.237797
Texas Tech University, Tolani A. Afolabi, May 2018
165
CURRICULUM VITAE Tolani A. Afolabi
Tolani Afolabi is a Petroleum Engineer with a professional and research-focused background in multiphase flow hydrodynamics and flow assurance; She has significant familiarity with midstream processing and surface facility operations and design; and rigorous training in drilling, production, reservoir engineering, formation evaluation, well completions and facilities design.
Relevant Experience
08/16 to 05/18 Masterβs Thesis Research, Texas Tech University, Lubbock TX
β’ Designed experimental procedures for the research β’ Managed and supervised 8-10 undergraduate students during the
experimental phase of the research and 4-6 students during the data analysis phase of the research.
β’ Used excel VBA to solve mathematical models to obtain results for both theoretical and experimental data.
β’ Implemented python and matplotlib for visualization of the experimental results
07/14 to 08/14 Afren Inc. USA, Woodlands, TX
Summer Intern
Responsible for performing Rock typing using mathematical models/Excel, reviewing Seismic Interpretation in the Gulf of Mexico, and drawing contour maps to determine possible reservoirs.
β’ Mentored by a reservoir engineer in understanding the importance of PVT analysis and its effect on the reservoir.
05/12 to 07/13 Pilot Energy Solutions LLC., Houston, TX
Process Engineer
Responsible for performing mass/energy balances on plant equipment (Absorbers, Distillation Towers, and Separators), processing of simulations for Goldsmith/Booker Plants (Dehydration, Fractionators, and Amine Sweetening System), reviewing/updating process flow/piping (AS Built)/instrumentation diagrams (P & IDs), and acting as a vendor liaison while also purchasing equipment.
β’ Utilized activated charcoal to mitigate asphaltene influx into the processing plant.
Texas Tech University, Tolani A. Afolabi, May 2018
166
Education
M.S., Petroleum Engineering, Texas Tech University, Lubbock TX, Graduation, 05/18
GPA-3.85
Thesis: The impact of viscosity on two-phase gas-liquid slug flow hydrodynamics
B.Sc., Petroleum Engineering Texas Tech University, Lubbock TX, GPA-3.37
B.Sc., Chemical Engineering/Minor Chemistry, Texas Tech University, Lubbock TX, GPA-3.28
B.A., French, Texas Tech University, Lubbock TX, GPA-3.28
Academic Honors
β’ Presidentβs List, Summer 2011 & 2016
β’ Deanβs Honor List, 2010, 2013 to 2015
β’ National Deanβs List, 2007 to 2008 β’ Bill & Mabeth Sanderson
Academic Scholarship, 2008 to 2012
β’ International Student Laureate Program (ISLP) delegate to China 2008
Leadership Positions
β’ President of Ladies in Petroleum β’ Coordinator of the Ladies in
Petroleum β’ Residence Hall Community Advisor β’ Treasurer of the French Club β’ Assistant Supervisor of the FLOW LOOP LAB