the impact of viscosity on two-phase gas-liquid slug flow

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

ii

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 𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 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


iv

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


v

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 – 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


vi

A-1 Experimental data for flow pattern at 150 cP and 0° .......................................... 129



A-4 Experimental data for flow pattern at 280 cP and 5° ......................................... 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


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


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


vii

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 23° 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 University’s 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 0° superimposed to FLOPATN 2.7 VBA code ........................................................ 70

5-2 Flow pattern map generated for the flow loop system for water at 0° superimposed to FLOPATN 2.7 VBA code ........................................................ 71

5-3 Flow pattern map generated for the flow loop system for oil at 0˚ 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


viii

5-6 Flow pattern map generated for the flow loop system for oil at 5˚ 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 0˚ ...................................................................................................................... 79

5-11 Comparison of translational velocity for all fluids types examined (water and oil) at their corresponding viscosities on a pipe at 0˚. ....................... 80

5-12 Translational velocity for water at 1 cP on a pipe inclined at 5˚. ........................ 81

5-13 Comparison of translational velocity for oil at 150 and 280 cP in a 5˚ 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 5˚ .......... 82

5-15 Difference between translational velocity for the same viscosity 1 cP, and between inclination angles 5˚ and 0˚ ................................................................... 83

5-16 Difference between translational velocity for the same viscosity 150 cP, and between inclination angles 5˚ and 0˚ ............................................................. 84

5-17 Difference between translational velocity for the same viscosity 280 cP, and between inclination angles 5˚ and 0˚ ............................................................. 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 0˚ .............. 89

5-21 Dimensionless slug length obtained experimentally for air-oil at 0˚ and 150 cP ............................................................................................................ 90

5-22 Dimensionless slug length obtained experimentally for air-oil at 0˚ and 280 cP ............................................................................................................ 90


ix

5-23 Comparison of dimensionless slug length obtained experimentally for air-oil at 0° ........................................................................................................... 91

5-24 Comparison of dimensionless slug length obtained experimentally for air-water and air-oil at 0˚ ..................................................................................... 91

5-25 Dimensionless slug length obtained experimentally for air-water at 5˚ ............... 92

5-26 Comparison of dimensionless slug length obtained experimentally for air-oil at 5˚............................................................................................................ 93

5-27 Comparison of dimensionless slug length for air-water and air-oil at 5˚ ............ 93

5-28 Comparison dimensionless slug length for air-water at 0˚and 5˚ ........................ 94

5-29 Comparison of dimensionless slug length for air-oil at 0˚and 5˚......................... 95

5-30 Comparison of dimensionless slug for air-oil at 0˚ and 5 .................................... 95

5-31 Difference between dimensionless slug length for the same viscosity 1 cP between inclination angles 5˚ and 0˚ ................................................................... 96

5-32 Difference between dimensionless slug length for the same viscosity 150 cP between inclination angles 5˚ and 0˚ ....................................................... 96

5-33 Difference between dimensionless slug length for the same viscosity 280 cP, between inclination angles 5˚ and 0˚ ...................................................... 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 5˚. .................................. 102

5-39 Comparison of slug frequency for oil at 150 and 280 cP in a pipe inclined at 5° .................................................................................................................... 102

5-40 Comparison of slug frequency for all fluids types examined (water and oil) at their corresponding viscosities in a pipe inclined at 5˚. ................................. 103

5-41 Comparison of slug frequency for air-water test at 0˚, and 5˚ at 1 cP ............... 104


x

5-42 Comparison of slug frequency for air-oil test at 0˚, and 5˚ at 150 cP ................ 104

5-43 Comparison of slug frequency for air-oil test at 0°, and 5° at 280 cP ............... 105

5-44 Difference between slug frequency for viscosity at 1 cP between inclination angles of 5° and 0° ........................................................................... 105

5-45 Difference between slug frequency for viscosity at 150 cP between inclination angles of 5˚ and 0˚ ........................................................................... 106

5-46 Difference between slug frequency for the same viscosity 280 cP between inclination angles 5° and 0° ............................................................................... 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) ° ................... 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



5-58 Comparison of pressure drop observation between experimental and numerical result at 280 cP. ................................................................................. 120


xi

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 0˚ and

150 cP................................................................................................................. 151

A 2 Flow pattern map generated for the flow loop system for oil at 0˚ 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 5 Flow pattern map generated for the flow loop system for oil at 5˚ and 150 cP................................................................................................................. 153

A 6 Flow pattern map generated for the flow loop system for oil at 5˚ and 150 cP superimposed to FLOPATN 2.7 VBA code .......................................... 153




xii

NOMENCLATURE 𝜋𝜋 constant [3.14] αL Gas Void Fraction [-] (~) Dimensionless Variables [-] θ Inclination Angle [Degrees] μ Viscosity [Pa∙s] ρ Density [kg/m3] σ Surface Tension [N/m] τ Shear Stress [Pa/m] ∆ Difference [-]

𝐹𝐹 Film [-] 𝐺𝐺 Gas [-]

𝐿𝐿 Liquid [-] 𝑀𝑀 Mixture [-] 𝑆𝑆 Slug [-] 𝑇𝑇𝑇𝑇 Taylor Bubble [-] 𝑈𝑈 Total Slug Unit [m]

A Cross-sectional Area [m2] AP Pipe Cross-Section Area [m2] C0 Flow Distribution Coefficient [-] 𝐶𝐶𝐺𝐺 Blasius Constant [-] 𝐶𝐶𝐿𝐿 Blasius Constant [m] D Pipe Diameter [m] 𝑑𝑑𝐹𝐹 Hydraulic diameter of liquid phase [m] 𝑑𝑑𝐺𝐺 Hydraulic diameter of gas phase [m] f Friction Factor [-] g gravitational acceleration [m/s2] HL Liquid Holdup [-] 𝐻𝐻𝐿𝐿𝑆𝑆𝑈𝑈 Slug Unit Holdup [m] I Interfacial [-] L Length [m] 𝐻𝐻𝐹𝐹′ Trapped Film Length [m] 𝐻𝐻𝑆𝑆′ Trapped Slug Body Length [m] 𝐻𝐻𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 Length of Pipe in trap section [m] M Molecular Weight [Kg/mol] 𝑛𝑛𝐺𝐺 Blasius Constant [-] 𝑛𝑛𝐿𝐿 Blasius Constant [-]


xiii

P Pressure Pa

R Universal Gas Constant �𝑃𝑃𝑃𝑃 ∗ 𝑔𝑔 ∗ 𝐾𝐾−1 ∗ 𝑚𝑚𝑚𝑚𝑙𝑙−1

𝑚𝑚𝑚𝑚𝑙𝑙 ∗ 𝑚𝑚3 ∗ 𝑃𝑃𝑃𝑃 ∗ 𝐾𝐾�

𝑅𝑅𝑒𝑒 Reynolds number [-] RKF45 Runge-Kutta-Fehlberg Method [-]

𝐻𝐻𝐹𝐹 pipe periphery length that are in contact with liquid film [m]

𝐻𝐻𝐺𝐺 pipe periphery length that are in contact with Taylor bubble [m]

𝐻𝐻𝐼𝐼 length of the interface between gas and liquid [m] T Temperature [°C or K] 𝑇𝑇𝐹𝐹 Film Period [1/s] 𝑇𝑇𝑠𝑠 Slug body Period [1/s] 𝑇𝑇𝑈𝑈 Inverse of frequency [1/HZ] 𝑢𝑢/𝑉𝑉 Velocity [m/s] 𝑢𝑢𝐷𝐷/𝑉𝑉𝐷𝐷 Drift Velocity [m/s] 𝑢𝑢𝐺𝐺𝐿𝐿𝑆𝑆/𝑉𝑉𝐺𝐺𝐿𝐿𝑆𝑆 Gas Bubble Velocity in slugs [m/s] 𝑉𝑉𝐿𝐿 Volume of Liquid Trapped in pipe [𝑚𝑚3] 𝑣𝑣𝑠𝑠/𝑓𝑓𝑠𝑠 Slug Frequency [HZ] 𝑉𝑉𝑆𝑆𝐺𝐺 Superficial Gas Velocity [m/s]

𝑉𝑉𝑆𝑆𝐿𝐿 Superficial Liquid Velocity [m/s] 𝑉𝑉𝑇𝑇 Total Volume [𝑚𝑚3] 𝑉𝑉𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 Maximum/theoretical Volume trapped in pipe [𝑚𝑚3] 𝑊𝑊𝐺𝐺 Gas Mass Flowrate [kg/s] 𝑊𝑊𝐿𝐿 Liquid Mass Flowrate [kg/s]

x pickup/shedding rate �𝐾𝐾𝑔𝑔𝑠𝑠�

z Compressibility Factor [-]

http://maths.cnam.fr/IMG/pdf/RungeKuttaFehlbergProof.pdf


xiv

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 0° and +5° 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 Barnea’s model for slug flow and the results were

validated by comparing the experimental results to existing mechanistic model (original

Taitel and Barnea’s model).


15

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


16

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.


17

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. Baker’s 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 ± 10˚. In 1987 Barnea developed a unified

model to identify flow patterns for different fluid properties and inclinations ranging from


18

±90˚. 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 𝑉𝑉𝑆𝑆𝐿𝐿 of 0.01 m/s and a high gas superficial velocity 𝑉𝑉𝑆𝑆𝐺𝐺 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.


19

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


20

stage, Gokcal (2005) constructed a flow loop facility. His test section was 50.8-mm (2-in)

ID with inclination angles ranging from -2° to 2°. Gokcal (2005) focused only on horizontal

flow. The ranges for the superficial velocity of liquid (𝑉𝑉𝑆𝑆𝐿𝐿) and gas (𝑉𝑉𝑆𝑆𝐺𝐺) 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.


21

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

−∆𝑝𝑝𝑈𝑈 = 𝜌𝜌𝑈𝑈𝑔𝑔 sin𝜃𝜃 𝐻𝐻𝑈𝑈 +𝜏𝜏𝑆𝑆𝜋𝜋𝜋𝜋𝐴𝐴𝑃𝑃

𝐻𝐻𝑆𝑆 + �𝜏𝜏𝐹𝐹𝐻𝐻𝐹𝐹 + 𝜏𝜏𝐺𝐺𝐻𝐻𝐺𝐺

𝐴𝐴𝑃𝑃

𝐿𝐿𝐹𝐹

0𝑑𝑑𝑑𝑑

(3-1)

where ∆𝑝𝑝𝑈𝑈 is the pressure drop over a slug unit length, 𝜌𝜌𝑈𝑈 is the average density of the slug

unit, 𝑔𝑔 is the gravitational acceleration, 𝜃𝜃 is the inclination angle (positive for an upward

inclined pipe), 𝐻𝐻𝑈𝑈 is the slug unit length, 𝜏𝜏𝑆𝑆 is the wall shear stress in the liquid slug body,

𝜋𝜋 is the inner diameter of the pipe, 𝐴𝐴𝑃𝑃 is the cross sectional area of the pipe based on the

pipe ID, 𝐻𝐻𝑆𝑆 is the slug body length, 𝐻𝐻𝐹𝐹 is the film length, 𝜏𝜏𝐹𝐹 is the wall shear stress caused

by liquid film, 𝜏𝜏𝐺𝐺 is the wall shear stress caused by the gas pocket. 𝐻𝐻𝐹𝐹 and 𝐻𝐻𝐺𝐺 are the pipe

periphery length that are in contact with liquid film and Taylor bubble, respectively. 𝜏𝜏𝐹𝐹,

𝐻𝐻𝐹𝐹, 𝜏𝜏𝐺𝐺, and 𝐻𝐻𝐺𝐺 are a function of position in the film zone. The wall shear stress in the film

zone was calculated from

𝜏𝜏𝐹𝐹 =12𝑓𝑓𝐹𝐹𝜌𝜌𝐿𝐿|𝑉𝑉𝐿𝐿𝑇𝑇𝑇𝑇|𝑉𝑉𝐿𝐿𝑇𝑇𝑇𝑇 (3-2)

where 𝜌𝜌𝐿𝐿 is the liquid density, 𝑢𝑢𝐿𝐿𝑇𝑇𝑇𝑇 is the velocity of liquid in the film (change with

location), and 𝑓𝑓𝐹𝐹 is the Fanning friction factor in the film zone calculated from


22

𝑓𝑓𝐹𝐹 = 𝐶𝐶𝐿𝐿(𝑅𝑅𝑒𝑒𝐹𝐹)−𝑛𝑛𝐿𝐿 (3-3)

where 𝐶𝐶𝐿𝐿 and 𝑛𝑛𝐿𝐿 are the constants in Blasius type friction factor formula. They were

calculated based on the value of Reynolds number of the liquid film, 𝑅𝑅𝑒𝑒𝐹𝐹, as

𝐶𝐶𝐿𝐿 = � 16 𝑅𝑅𝑒𝑒𝐹𝐹 ≤ 2100

0.046 𝑅𝑅𝑒𝑒𝐹𝐹 > 2100 (3-4)

and

𝑛𝑛𝐿𝐿 = � 1 𝑅𝑅𝑒𝑒𝐹𝐹 ≤ 2100

0.2 𝑅𝑅𝑒𝑒𝐹𝐹 > 2100 (3-5)

𝑅𝑅𝑒𝑒𝐹𝐹 is defined as

𝑅𝑅𝑒𝑒𝐹𝐹 =

𝜌𝜌𝐿𝐿𝑑𝑑𝐹𝐹|𝑉𝑉𝐿𝐿𝑇𝑇𝑇𝑇|𝜇𝜇𝐿𝐿

(3-6)

where 𝑑𝑑𝐹𝐹 is the hydraulic diameter of liquid film flow. 𝑑𝑑𝐹𝐹 was calculated from

𝑑𝑑𝐹𝐹 =

4𝐴𝐴𝐹𝐹𝐻𝐻𝐹𝐹

(3-7)

𝐴𝐴𝐹𝐹 is the flow cross section area occupied by liquid. For the wall shear stress in the gas

pocket part, 𝜏𝜏𝐺𝐺 was calculated from


23

𝜏𝜏𝐺𝐺 =12𝑓𝑓𝐺𝐺𝜌𝜌𝐺𝐺|𝑉𝑉𝐺𝐺𝑇𝑇𝑇𝑇|𝑉𝑉𝐺𝐺𝑇𝑇𝑇𝑇 (3-8)

where 𝑢𝑢𝐺𝐺𝑇𝑇𝑇𝑇 is the gas phase velocity inside the Taylor bubble, and 𝑓𝑓𝐺𝐺 is the Fanning

friction factor of gas inside the Taylor bubble. 𝑓𝑓𝐺𝐺 was calculated by the similar method

used for 𝑓𝑓𝐹𝐹 as follows:

𝑓𝑓𝐺𝐺 = 𝐶𝐶𝐺𝐺(𝑅𝑅𝑒𝑒𝐺𝐺)−𝑛𝑛𝐺𝐺 (3-9)

𝐶𝐶𝐺𝐺 and 𝑛𝑛𝐺𝐺 are defined from

𝐶𝐶𝐺𝐺 = � 16 𝑅𝑅𝑒𝑒𝐺𝐺 ≤ 21000.046 𝑅𝑅𝑒𝑒𝐺𝐺 > 2100 (3-10)

and

𝑛𝑛𝐺𝐺 = � 1 𝑅𝑅𝑒𝑒𝐺𝐺 ≤ 21000.2 𝑅𝑅𝑒𝑒𝐺𝐺 > 2100 (3-11)

Reynolds number of gas in the gas pocket is defined as

𝑅𝑅𝑒𝑒𝐺𝐺 =

𝜌𝜌𝐺𝐺𝑑𝑑𝐺𝐺|𝑉𝑉𝐺𝐺𝑇𝑇𝑇𝑇|𝑉𝑉𝐺𝐺

(3-12)

where 𝑑𝑑𝐺𝐺 is the hydraulic diameter of the gas in the Taylor bubble. 𝐴𝐴𝐺𝐺 is the flow cross

section area occupied by gas. It is defined as


24

𝑑𝑑𝐺𝐺 =4𝐴𝐴𝐺𝐺

𝐻𝐻𝐺𝐺 + 𝐻𝐻𝐼𝐼 (3-13)

𝐻𝐻𝐼𝐼 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

𝑑𝑑ℎ𝐿𝐿𝑑𝑑𝑑𝑑 =

𝜏𝜏𝐹𝐹𝐻𝐻𝐹𝐹𝐴𝐴𝐹𝐹

− 𝜏𝜏𝐺𝐺𝐻𝐻𝐺𝐺𝐴𝐴𝐺𝐺

− 𝜏𝜏𝐼𝐼𝐻𝐻𝐼𝐼 �1𝐴𝐴𝐹𝐹

+ 1𝐴𝐴𝐺𝐺�+ (𝜌𝜌𝐿𝐿 − 𝜌𝜌𝐺𝐺)𝑔𝑔 sin𝜃𝜃

(𝜌𝜌𝐿𝐿 − 𝜌𝜌𝐺𝐺)𝑔𝑔 cos𝜃𝜃 − 𝜌𝜌𝐿𝐿𝑢𝑢𝐹𝐹(𝑉𝑉𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐿𝐿𝐿𝐿𝑆𝑆)𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇2

𝑑𝑑𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇𝑑𝑑ℎ𝐿𝐿

− 𝜌𝜌𝐺𝐺𝑣𝑣𝐺𝐺(𝑉𝑉𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐺𝐺𝐿𝐿𝑆𝑆) 𝛼𝛼𝐿𝐿𝑆𝑆𝛼𝛼𝑇𝑇𝑇𝑇2𝑑𝑑𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇𝑑𝑑ℎ𝐿𝐿

(3-14)

where

𝑉𝑉𝐹𝐹 = 𝑉𝑉𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐿𝐿𝑇𝑇𝑇𝑇 (3-15)

𝛼𝛼𝐿𝐿𝑆𝑆 = 1 − 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 (3-16)

where 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 is liquid holdup at the slug body.

and

𝛼𝛼𝑇𝑇𝑇𝑇 = 1 − 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇 (3-17)


25

The length 𝑑𝑑 in 𝑑𝑑ℎ𝐿𝐿/𝑑𝑑𝑑𝑑 equation is defined to be positive in the opposite direction of the

flow. In other words, at 𝑑𝑑 = 0, 𝐻𝐻𝐿𝐿 = 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆, and at 𝑑𝑑 = 𝐻𝐻𝐹𝐹, 𝐻𝐻𝐿𝐿 = 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇𝑒𝑒 (or liquid holdup at

the end of the film zone). The geometric parameters are a function of the film height. They

are given as

�̃�𝐴𝐺𝐺 = 0.25�arccos�2ℎ�𝐿𝐿 − 1� − �2ℎ�𝐿𝐿 − 1��1 − �2ℎ�𝐿𝐿 − 1�

2�

(3-18)

�̃�𝐴𝐿𝐿 = 0.25�𝜋𝜋 − arccos�2ℎ�𝐿𝐿 − 1� + �2ℎ�𝐿𝐿 − 1��1 − �2ℎ�𝐿𝐿 − 1�2� (3-19)

�̃�𝐻𝐺𝐺 = arccos(2ℎ�𝐿𝐿 − 1) (3-20)

�̃�𝐻𝐿𝐿 = 𝜋𝜋 − arccos(2ℎ�𝐿𝐿 − 1) (3-21)

�̃�𝐻𝐼𝐼 = �1 − �2ℎ�𝐿𝐿 − 1�2

(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 ℎ�𝐿𝐿 = ℎ𝐿𝐿𝐷𝐷

, �̃�𝐻𝐺𝐺 = 𝑆𝑆𝐺𝐺𝐷𝐷

, �̃�𝐻𝐿𝐿 = 𝑆𝑆𝐿𝐿𝐷𝐷

, �̃�𝐻𝐼𝐼 = 𝑆𝑆𝐼𝐼𝐷𝐷

, �̃�𝐴𝐺𝐺 = 𝐴𝐴𝐺𝐺𝐷𝐷2

, and �̃�𝐴𝐿𝐿 = 𝐴𝐴𝐿𝐿𝐷𝐷2

. The value of 𝑑𝑑𝐻𝐻𝐿𝐿𝐿𝐿𝐿𝐿𝑑𝑑ℎ𝐿𝐿

in the film profile equation is calculated from

the equation below.

𝑑𝑑𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇𝑑𝑑ℎ𝐹𝐹

=4𝜋𝜋𝜋𝜋

�1 − �2ℎ𝐹𝐹𝜋𝜋

− 1�2

(3-23)

The 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇 parameter is only a function of the liquid height. This can be written as


26

𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇 =4𝐴𝐴𝐿𝐿𝜋𝜋𝜋𝜋2 = 1 −

1𝜋𝜋 �arccos�2ℎ�𝐿𝐿 − 1� − �2ℎ�𝐿𝐿 − 1��1 − �2ℎ�𝐿𝐿 − 1�2�

(3-24)

For the moving frame of reference at the speed of 𝑢𝑢𝑇𝑇𝑇𝑇, the interface is stationary with

respect to the frame of reference. Then, the mass balance in this frame of reference can be

written as

(𝑉𝑉𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐿𝐿𝐿𝐿𝑆𝑆)𝜌𝜌𝐿𝐿𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 = (𝑉𝑉𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐿𝐿𝑇𝑇𝑇𝑇)𝜌𝜌𝐿𝐿𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇 (3-25)

where the above 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇 and 𝑢𝑢𝐿𝐿𝑇𝑇𝑇𝑇 are a function of position. By rearranging this mass

balance equation, we have

𝑉𝑉𝐿𝐿𝑇𝑇𝑇𝑇 = 𝑢𝑢𝑇𝑇𝑇𝑇 −

(𝑉𝑉𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐿𝐿𝐿𝐿𝑆𝑆)𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇

(3-26)

and

𝑉𝑉𝐹𝐹 =(𝑉𝑉𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐿𝐿𝐿𝐿𝑆𝑆)𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆

𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇

(3-27)

The value of 𝑢𝑢𝐿𝐿𝐿𝐿𝑆𝑆 was from

𝑉𝑉𝑆𝑆 = 𝑉𝑉𝑆𝑆𝐿𝐿 + 𝑉𝑉𝑆𝑆𝐺𝐺 = 𝑉𝑉𝐿𝐿𝐿𝐿𝑆𝑆𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 + 𝑉𝑉𝐺𝐺𝐿𝐿𝑆𝑆(1 − 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆) (3-28)

The values of 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺 are known based on the flow rate of liquid and gas,

respectively. For the 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 and 𝑉𝑉𝐺𝐺𝐿𝐿𝑆𝑆 , they can be determined based on either existing

closure relationships or experimental data. Once, 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 and 𝑉𝑉𝐺𝐺𝐿𝐿𝑆𝑆 are obtained 𝑉𝑉𝐿𝐿𝐿𝐿𝑆𝑆 can be

calculated from Equation 3.30 From Equation 3.26 𝑉𝑉𝐿𝐿𝑇𝑇𝑇𝑇 is only a function of film height,


27

ℎ𝐿𝐿, because 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 is a constant, and 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇 is only a function of ℎ𝐿𝐿 as shown in Equation

3.24. From Equation 3.2 and 3.6, we can see that, 𝜏𝜏𝐹𝐹 is also only a function of ℎ𝐿𝐿, because

it is based on 𝑉𝑉𝐿𝐿𝑇𝑇𝑇𝑇 and 𝑑𝑑𝐹𝐹 values (𝑑𝑑𝐹𝐹 is a direct function of ℎ𝐿𝐿). Similarly, it can be shown

that 𝑉𝑉𝐺𝐺𝑇𝑇𝑇𝑇 is also only a function of ℎ𝐿𝐿. By using the same mass balance in the moving

frame of reference for gas phase, we have,

(𝑉𝑉𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐺𝐺𝐿𝐿𝑆𝑆)(1− 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆) = (𝑉𝑉𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐺𝐺𝑇𝑇𝑇𝑇)(1 − 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇) (3-29)

or

𝑉𝑉𝐺𝐺𝑇𝑇𝑇𝑇 = 𝑉𝑉𝑇𝑇𝑇𝑇 −

(𝑉𝑉𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐺𝐺𝐿𝐿𝑆𝑆)(1− 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆)(1 − 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇)

(3-30)

The values of 𝑉𝑉𝑇𝑇𝑇𝑇, 𝑉𝑉𝐺𝐺𝐿𝐿𝑆𝑆, and 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 in Equation 3.30 are not a function of location in

the film. Therefore, 𝑉𝑉𝐺𝐺𝑇𝑇𝑇𝑇 is only a function of 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇 or only the function of ℎ𝐿𝐿 as per

Equation 3.30. Thus, 𝜏𝜏𝐺𝐺 is also only a function of ℎ𝐿𝐿. 𝜏𝜏𝐼𝐼 can be assumed to equal to 𝜏𝜏𝐺𝐺 for

a smooth film profile. For a wavy interface,

𝜏𝜏𝐼𝐼 =

12𝑓𝑓𝐼𝐼𝜌𝜌𝐺𝐺|𝑉𝑉𝐺𝐺𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐿𝐿𝑇𝑇𝑇𝑇|(𝑉𝑉𝐺𝐺𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐿𝐿𝑇𝑇𝑇𝑇) (3-31)

where 𝑓𝑓𝐼𝐼 = 0.0142 for a horizontal and an inclined pipe.

With all the above equations, the right hand side of 𝑑𝑑ℎ𝐿𝐿/𝑑𝑑𝑑𝑑 (Equation 3.14) is only

a function of ℎ𝐿𝐿 and can be solved numerically by using Runge-Kutta-Fehlberg method

(RKF45). The initial condition for starting 𝑅𝑅𝐾𝐾𝑅𝑅45 or ℎ𝐿𝐿 at 𝑑𝑑 = 0 is calculated from 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆

based on Equation 3.24 (solve ℎ�𝐿𝐿 for a known 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 numerically). The film profile


28

calculation needs to stop at a film length of 𝐻𝐻𝐹𝐹. This 𝐻𝐻𝐹𝐹 must allow a mass balance. The

mass balance equation can be written as

𝑊𝑊𝐿𝐿 = �𝑉𝑉𝐿𝐿𝐿𝐿𝑆𝑆𝜌𝜌𝐿𝐿𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆𝑇𝑇𝑆𝑆 + � 𝑉𝑉𝐿𝐿𝑇𝑇𝑇𝑇𝜌𝜌𝐿𝐿𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇𝑑𝑑𝑑𝑑

𝑇𝑇𝐹𝐹

0�

1𝑇𝑇𝑈𝑈

(3-32)

or

𝑊𝑊𝐿𝐿 = �𝜌𝜌𝐿𝐿𝐻𝐻𝑆𝑆𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 + � 𝜌𝜌𝐿𝐿𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇𝑑𝑑𝐻𝐻

𝐿𝐿𝐹𝐹

0�

1𝑇𝑇𝑈𝑈

− 𝑥𝑥 (3-33)

if the integration in space is used. The variables 𝑇𝑇𝐹𝐹, 𝑇𝑇𝑈𝑈, 𝐻𝐻𝐹𝐹, and 𝑥𝑥 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

𝑇𝑇𝐹𝐹 =𝐻𝐻𝐹𝐹𝑉𝑉𝑇𝑇𝑇𝑇

, (3-34)

𝑇𝑇𝑈𝑈 =

𝐻𝐻𝑈𝑈𝑉𝑉𝑇𝑇𝑇𝑇

, (3-35)

𝐻𝐻𝐹𝐹 = 𝐻𝐻𝑈𝑈 − 𝐻𝐻𝑆𝑆 , (3-36)

and

𝑥𝑥 = (𝑉𝑉𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐿𝐿𝐿𝐿𝑆𝑆)𝜌𝜌𝐿𝐿𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 = (𝑉𝑉𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐿𝐿𝑇𝑇𝑇𝑇)𝜌𝜌𝐿𝐿𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇 (3-37)

In general, the appropriate film profile is unknown before 𝑑𝑑ℎ𝐿𝐿/𝑑𝑑𝑑𝑑 equation is

solved. This is because to know which 𝐻𝐻𝐹𝐹 that can give a mass balance in Equation 3.33,

the film profile is needed to do the calculation of ∫ 𝜌𝜌𝐿𝐿𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇𝑑𝑑𝐻𝐻𝐿𝐿𝐹𝐹0 .


29

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

ℱ(𝐻𝐻𝐹𝐹) = 0 = 𝑊𝑊𝐿𝐿,𝑅𝑅𝑅𝑅𝐹𝐹 −𝑊𝑊𝐿𝐿,𝑖𝑖𝑛𝑛𝑡𝑡𝑖𝑖𝑡𝑡 (3-38)

where 𝑊𝑊𝐿𝐿,𝑅𝑅𝑅𝑅𝐹𝐹 is the liquid mass flow rate output from RKF45 calculation and 𝑊𝑊𝐿𝐿,𝑖𝑖𝑛𝑛𝑡𝑡𝑖𝑖𝑡𝑡 is

the liquid mass flow rate input based from

𝑊𝑊𝐿𝐿,𝑖𝑖𝑛𝑛𝑡𝑡𝑖𝑖𝑡𝑡 = 𝑢𝑢𝑆𝑆𝐿𝐿𝐴𝐴𝑃𝑃𝜌𝜌𝐿𝐿 (3-39)

Function ℱ(𝐻𝐻𝐹𝐹) is dependent upon the input value 𝐻𝐻𝐹𝐹 . If a correct 𝐻𝐻𝐹𝐹 value is

given, then the function ℱ(𝐻𝐻𝐹𝐹) return zero. This makes ℱ(𝐻𝐻𝐹𝐹) 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,

∫ 𝜏𝜏𝐹𝐹𝑆𝑆𝐹𝐹+𝜏𝜏𝐺𝐺𝑆𝑆𝐺𝐺𝐴𝐴𝑃𝑃

𝐿𝐿𝐹𝐹0 𝑑𝑑𝑑𝑑 , 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 𝜏𝜏𝐹𝐹 , 𝜏𝜏𝐺𝐺 , 𝐻𝐻𝐹𝐹 , and 𝐻𝐻𝐺𝐺 , respectively. This gives the

frictional pressure drop in the film zone.

For the frictional pressure drop in the slug body or 𝜏𝜏𝑆𝑆𝜋𝜋𝐷𝐷𝐴𝐴𝑃𝑃

𝐻𝐻𝑆𝑆, 𝜏𝜏𝑆𝑆 can be calculated from

𝜏𝜏𝑆𝑆 =12𝑓𝑓𝑆𝑆𝜌𝜌𝐿𝐿|𝑉𝑉𝑆𝑆|𝑉𝑉𝑆𝑆 (3-40)


30

where 𝑢𝑢𝑆𝑆 is from Equation 3.28 𝑓𝑓𝑆𝑆 is from

𝑓𝑓𝑆𝑆 = 𝐶𝐶𝑆𝑆(𝑅𝑅𝑒𝑒𝑆𝑆)−𝑛𝑛𝑆𝑆 (3-41)

𝐶𝐶𝑆𝑆 and 𝑛𝑛𝑆𝑆 are defined from

𝐶𝐶𝑆𝑆 = � 16 𝑅𝑅𝑒𝑒𝑆𝑆 ≤ 21000.046 𝑅𝑅𝑒𝑒𝑆𝑆 > 2100 (3-42)

𝑅𝑅𝑒𝑒𝑆𝑆 is defined as

𝑅𝑅𝑒𝑒𝑆𝑆 =𝜌𝜌𝑆𝑆𝑉𝑉𝑆𝑆𝜋𝜋𝜇𝜇𝑆𝑆

(3-43)

𝜌𝜌𝑆𝑆 is defined as

𝜌𝜌𝑆𝑆 = 𝜌𝜌𝐿𝐿𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 + 𝜌𝜌𝐺𝐺(1 − 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆) (3-44)

𝜇𝜇𝑆𝑆 is defined as

𝜇𝜇𝑆𝑆 = 𝜇𝜇𝐿𝐿𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 + 𝜇𝜇𝐺𝐺(1 − 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆) (3-45)

The gravitational term in Equation 3.1 is based on 𝜌𝜌𝑈𝑈. 𝜌𝜌𝑈𝑈 can be calculated from

𝜌𝜌𝑈𝑈 = 𝐻𝐻𝐿𝐿𝑆𝑆𝑈𝑈𝜌𝜌𝐿𝐿 + (1 − 𝐻𝐻𝐿𝐿𝑆𝑆𝑈𝑈)𝜌𝜌𝐺𝐺 (3-46)

where

𝐻𝐻𝐿𝐿𝑆𝑆𝑈𝑈 =

𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆𝐻𝐻𝑆𝑆 + ∫ 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇𝐿𝐿𝐹𝐹0 𝑑𝑑𝐻𝐻𝐻𝐻𝑈𝑈

(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


31

parameters are 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 , 𝐻𝐻𝑆𝑆 , 𝑢𝑢𝑇𝑇𝑇𝑇 , and 𝑢𝑢𝐺𝐺𝐿𝐿𝑆𝑆 . 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

𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 = 𝑒𝑒𝑥𝑥𝑝𝑝�−(0.45 × 𝜃𝜃 + 2.48 × 10−6𝑅𝑅𝑒𝑒𝐿𝐿𝑆𝑆)� (3-48)

where 𝜃𝜃 is the inclination angle in radians and 𝑅𝑅𝑒𝑒𝐿𝐿𝑆𝑆 is the Reynolds number for liquid in

slug defined as

𝑅𝑅𝑒𝑒𝐿𝐿𝑆𝑆 =𝜌𝜌𝐿𝐿𝑉𝑉𝑆𝑆𝜋𝜋𝜇𝜇𝐿𝐿

, (3-49)

The slug body length is calculated from (Zhang et al. 2003)

𝐻𝐻𝑆𝑆𝜋𝜋

= (32.0 cos2 𝜃𝜃 + 16.0 sin2 𝜃𝜃) (3-50)

The translational velocity, 𝑉𝑉𝑇𝑇𝑇𝑇, was calculated from

𝑉𝑉𝑇𝑇𝑇𝑇 = 𝐶𝐶0𝑉𝑉𝑠𝑠 + 𝑉𝑉𝐷𝐷 (3-51)

where

𝐶𝐶0 = �1.2 for 𝑅𝑅𝑒𝑒𝐿𝐿𝑆𝑆 ≥ 21002 for 𝑅𝑅𝑒𝑒𝐿𝐿𝑆𝑆 < 2100 (3-52)

and the Bendiksen 1984 drift velocity correlation is

𝑉𝑉𝐷𝐷 = 0.54�𝑔𝑔𝜋𝜋 cos 𝜃𝜃 + 0.35�𝑔𝑔𝜋𝜋 sin𝜃𝜃 (3-53)

For 𝑢𝑢𝐺𝐺𝐿𝐿𝑆𝑆, the closure relationship from Zuber and Hench is used. It is given here as


32

𝑉𝑉𝐺𝐺𝐿𝐿𝑆𝑆 = 𝐶𝐶1𝑢𝑢𝑆𝑆 + 1.53 �

𝑔𝑔𝑔𝑔(𝜌𝜌𝐿𝐿 − 𝜌𝜌𝐺𝐺)𝜌𝜌𝐿𝐿2

�0.25

𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆0.5 sin𝜃𝜃 (3-54)

For the case of the near horizontal flow as in this study, 𝐶𝐶1 for 𝑢𝑢𝐺𝐺𝐿𝐿𝑆𝑆 equation is 1 and 𝑔𝑔 is

the gas-liquid surface tension.

3.2 Calculation of 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 from experimental data

This section describes the calculation method used to calculate 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 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 𝑉𝑉𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡. The volume of liquid trapped inside the quick

closing valves section is 𝑉𝑉𝐿𝐿. The trapped liquid volume, 𝑉𝑉𝐿𝐿, come from both slug film and

slug body. This can be written as

𝑉𝑉𝐿𝐿 = 𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇𝐻𝐻𝐹𝐹′ + 𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆𝐻𝐻𝑆𝑆′ (3-55)

By dividing both sides with the capacity of the quick closing valves section, we have

𝑉𝑉𝐿𝐿𝑉𝑉𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡

=𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇𝐻𝐻𝐹𝐹′ + 𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆𝐻𝐻𝑆𝑆′

𝐴𝐴𝑃𝑃𝐻𝐻𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡

(3-56)

The 𝐻𝐻𝐹𝐹′ and 𝐻𝐻𝑆𝑆′ here are equal to 𝐻𝐻𝐹𝐹 and 𝐻𝐻𝑆𝑆. 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 𝐻𝐻𝐹𝐹′ < 𝐻𝐻𝐹𝐹. When the incomplete slug

body is trapped, we have 𝐻𝐻𝑆𝑆′ < 𝐻𝐻𝑆𝑆 . The parameter 𝐻𝐻𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 here is the length of the quick


33

closing valve section where 𝐴𝐴𝑃𝑃𝐻𝐻𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 𝑉𝑉𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 . By canceling 𝐴𝐴𝑃𝑃 in both numerator and

denominator and rearranging equation, we have

𝑉𝑉𝐿𝐿𝑉𝑉𝑇𝑇

= 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇𝐻𝐻𝐹𝐹′

𝐻𝐻𝑇𝑇+ 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆

𝐻𝐻𝑆𝑆′

𝐻𝐻𝑇𝑇

(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 𝑉𝑉𝐿𝐿 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, 𝐻𝐻𝑆𝑆′ . By using linear regression analysis, the plot

between 𝐿𝐿𝑆𝑆′

𝐿𝐿𝐿𝐿 (as a horizontal axis) versus 𝑉𝑉𝐿𝐿

𝑉𝑉𝐿𝐿 (as a vertical axis) is used to solve for the slope

𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 and the intercept is 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇𝐿𝐿𝐹𝐹′

𝐿𝐿𝐿𝐿. From experimental observations, the film length in the

trap section is longer than the slug length. Thus, 𝑉𝑉𝐿𝐿/𝑉𝑉𝑇𝑇 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 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇𝐿𝐿𝐹𝐹′

𝐿𝐿𝐿𝐿 compared to the slope value, 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆. With the confidence in the

intercept value, the 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇 is obtained from the intercept value where 𝐻𝐻𝐹𝐹′ is calculated from

𝐻𝐻𝑇𝑇 − 𝐻𝐻𝑆𝑆′. With the above approach, 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇 is obtained in this experimental study. Then,

𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇 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, 𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇 was obtained. The slug length, 𝐻𝐻𝑆𝑆, and translational

velocity, 𝑉𝑉𝑇𝑇𝑇𝑇 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


34

information, the slug body liquid holdup calculated from the measured value of

𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇,𝐻𝐻𝑆𝑆 , 𝜈𝜈𝐻𝐻𝐻𝐻 , and 𝑉𝑉𝑇𝑇𝑇𝑇 was calculated from Equation 3.33. It is written here again as

𝑊𝑊𝐿𝐿 = �𝜌𝜌𝐿𝐿𝐻𝐻𝑆𝑆𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 + � 𝜌𝜌𝐿𝐿𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝑇𝑇𝑇𝑇𝑑𝑑𝐻𝐻

𝐿𝐿𝐹𝐹

0�

1𝑇𝑇𝑈𝑈

− 𝑥𝑥 (3-58)

The mass flow rate of liquid, 𝑊𝑊𝐿𝐿, was known based on the flow meter reading. 𝑇𝑇𝑈𝑈

value is calculated based on the measured slug frequency (𝑇𝑇𝑈𝑈 = 1𝜈𝜈𝐻𝐻𝐻𝐻

). The integration from

zero to 𝐻𝐻𝐹𝐹 requires the film profile information. The film profile can be obtained by

integrating 𝑑𝑑ℎ𝐹𝐹/𝑑𝑑𝑑𝑑 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 𝑑𝑑 = 0. The pickup

rate term, 𝑥𝑥, in Equation 3.33 is also a function of 𝑢𝑢𝐿𝐿𝐿𝐿𝑆𝑆 and 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 as shown in Equation

3.37, shown here again as

𝑥𝑥 = (𝑉𝑉𝑇𝑇𝑇𝑇 − 𝑉𝑉𝐿𝐿𝐿𝐿𝑆𝑆)𝜌𝜌𝐿𝐿𝐴𝐴𝑃𝑃𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 (3-59)

For a horizontal flow case,

𝑉𝑉𝐿𝐿𝐿𝐿𝑆𝑆 = 𝑉𝑉𝐺𝐺𝐿𝐿𝑆𝑆 = 𝑉𝑉𝑆𝑆 = 𝑉𝑉𝑆𝑆𝐿𝐿 + 𝑉𝑉𝑆𝑆𝐺𝐺 (3-60)

Which means that for a horizontal flow case, the only unknown in the mass balance

Equation 3.33 is 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 . Therefore, once all the parameters from the experimental

measurement are identified, the mass balance Equation 3.33 is only a function of 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆. To

solve this, the secant method was used. This was done by 1) giving two initial guesses of

𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆, 2) calculating the film profile by solving Equation 3.14 with RKF45 of those two


35

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 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 to be

𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆,𝑛𝑛 = 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆,𝑛𝑛−1 − (𝒢𝒢�𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆,𝑛𝑛−1�𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆,𝑛𝑛−1 − 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆,𝑛𝑛−2

𝒢𝒢�𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆,𝑛𝑛−1� − 𝒢𝒢�𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆,𝑛𝑛−2�) (3-61)

where subscripts 𝑛𝑛, 𝑛𝑛 − 1, and 𝑛𝑛 − 2 indicate the value of 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 in each iteration. The first

two guess of 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 are 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆,1 and 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆,2. The function 𝒢𝒢 give the difference between the

calculated 𝑊𝑊𝐿𝐿 from Equation 3.33 and the input value of 𝑊𝑊𝐿𝐿 calculated from 𝑊𝑊𝐿𝐿 =

𝜌𝜌𝐿𝐿𝐴𝐴𝑃𝑃𝑢𝑢𝑆𝑆𝐿𝐿. The function 𝒢𝒢 can be written as

𝒢𝒢(𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆) = 𝑊𝑊𝐿𝐿,𝑖𝑖𝑛𝑛𝑡𝑡𝑖𝑖𝑡𝑡 −𝑊𝑊𝐿𝐿,𝑡𝑡𝑖𝑖𝑡𝑡𝑡𝑡𝑖𝑖𝑡𝑡(𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆) (3-62)

The iteration for secant method is carried out until there is no difference in the

second digits of 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 value from one iteration to the next iteration, e.g. 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆,3 = 0.652 and

𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆,4 = 0.653

For the case of an inclined flow, 𝑉𝑉𝐺𝐺𝐿𝐿𝑆𝑆 > 𝑉𝑉𝑆𝑆 > 𝑉𝑉𝐿𝐿𝐿𝐿𝑆𝑆. The reason that 𝑉𝑉𝐺𝐺𝐿𝐿𝑆𝑆 is slightly

more than 𝑉𝑉𝐿𝐿𝐿𝐿𝑆𝑆 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, 𝑉𝑉𝐿𝐿𝐿𝐿𝑆𝑆 in this case was estimated from

𝑉𝑉𝑆𝑆 = 𝑉𝑉𝐿𝐿𝐿𝐿𝑆𝑆𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 + 𝑉𝑉𝐺𝐺𝐿𝐿𝑆𝑆(1 − 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆) (3-63)

and the value of 𝑉𝑉𝐺𝐺𝐿𝐿𝑆𝑆 was estimated from Equation 3.54. With this approach, it leads to the

mass balance equation with the only unknown as 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆. Thus, the 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 value allows a mass


36

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.


37

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 (0°, 1°, 5°) and temperatures (70° F and

90° F) were selected and parameters of interest recorded for optimal comparison with

existing mechanistic models, in particular Dukler and Hubbard’s influential 1975

mechanistic model in horizontal pipes (as referenced in Ovadia Shoham’s 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 υs) and three output variables

(LS, VTB, ΔP), 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


38

(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) ° and temperatures (70, 90) °, 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


39

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)


40

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)


Liquid Holdup 112 112 112 336 Drift Velocity 48 48 48 144 Translational Velocity





Flow Pattern 1 1 1 3


41

Table 4-3: Steady State water experiment at 90 degrees Fahrenheit SteadyState Experiment Water at room temperature


Number of Tests for One 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)



Liquid Holdup 112 112 112 336 Drift Velocity 48 48 48 144 Translational Velocity





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

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


42

Table 4-5: Steady State Oil experiment at 90 degrees Fahrenheit Steady State Experiment Oil at 90 °F



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 °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 (˚F)

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) @ (212˚F)

1 150 and 280

Color Colorless Dyed green Brown


43

Surface tension was measured with KrussTM Drop Shape Analyzer (pendant drop),

model DSA25B at 73.4 °F (23 °C) and 89.6 °F (32° C). The surface tension values at 73.4

°F is 31.20-mN/m and at 89.6 °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 23° 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.


44

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


45

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)° to (+ 20)°.

For the experiments conducted, the flow loop was raised from 0° to (+10)° for drift velocity

experiments and 0°, 1° and 5° for steady state water and 0° and 5° 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


46

Figure 4-7: Detailed facility diagram Eghorieta (2018)


47

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).


48

Figure 4-8: Visualization section of the flow loop


49

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


50

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.


51

Figure 4-10: Canon EOS 70D image courtesy (Texas Tech University’s 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 0°, 1° and 5° for water and for oil 0°, and 5°.

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


52

gas flow rates for consistent inlet oil and gas flow. The range for oil is 5 – 75% and 5 –

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


53

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 µsec. Once the camera is focused on the desired location of

LM

LS LU

LF


54

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 – slug tail

or slug front – slug front but not slug tail – slug front or vice versa. The difference in time

between these slug tails or slug front is used calculate the velocity of the slugs.

𝑉𝑉𝑇𝑇𝑇𝑇 = 𝐻𝐻𝑙𝑙𝑢𝑢𝑔𝑔 �𝑓𝑓𝑓𝑓𝑚𝑚𝑛𝑛𝑑𝑑𝑑𝑑𝑃𝑃𝑡𝑡𝑙𝑙 �𝑓𝑓𝑖𝑖𝑛𝑛𝑡𝑡𝑡𝑡

− 𝑠𝑠𝑙𝑙𝑢𝑢𝑔𝑔 �𝑓𝑓𝑓𝑓𝑚𝑚𝑛𝑛𝑑𝑑𝑑𝑑𝑃𝑃𝑡𝑡𝑙𝑙 �𝑖𝑖𝑛𝑛𝑖𝑖𝑡𝑡𝑖𝑖𝑡𝑡𝑡𝑡

𝑑𝑑𝑡𝑡𝑚𝑚𝑒𝑒𝑓𝑓𝑖𝑖𝑛𝑛𝑡𝑡𝑡𝑡 − 𝑑𝑑𝑡𝑡𝑚𝑚𝑒𝑒𝑖𝑖𝑛𝑛𝑖𝑖𝑡𝑡𝑖𝑖𝑡𝑡𝑡𝑡

(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


55

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 fluid’s resistance to flow occurring across the visualization section is needed.

Pressure drop is measured with pressure transducers and differential pressure sensors as


56

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


57

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.


58

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

0° and 5°. The corresponding temperature for the viscosities are 70°F and 90°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.


59

5.1.1 Test Matrix for Detailed Air-Water Slug Flow Hydrodynamics Experiments

A total of 48 pairs of 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺 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 5°. 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 5°. 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.


60

Table 5-1: Air – 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

[°

F]

𝜌𝜌 𝐿𝐿 [k

g/m

3 ]

𝜇𝜇 𝐿𝐿 [

cP]

𝑊𝑊𝐿𝐿

[g/s

]

𝑢𝑢 𝑆𝑆𝐿𝐿

[m/s

]

𝑅𝑅𝑒𝑒 𝑆𝑆𝐿𝐿

[-]


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


61

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

[°

F]

𝜌𝜌 𝐺𝐺 [k

g/m

3 ]

𝜇𝜇 𝐺𝐺A [

cP]

𝑊𝑊𝐺𝐺

[g/s

]

𝑢𝑢 𝑆𝑆𝐺𝐺

[m/s

]

𝑅𝑅𝑒𝑒 𝑆𝑆𝐺𝐺

[-]


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 °F. At each temperature, the tests were conducted at the inclination

angle of 0˚ and 5˚. The 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺 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.


62

Table 5-4: Oil flow properties for air-oil detailed slug flow hydrodynamics experiment.

Test name

Pum

p sp

eed

[%]

Tem

pera

ture

[°

F]

𝜌𝜌 𝐿𝐿 [k

g/m

3 ]

𝜇𝜇 𝐿𝐿 [

cP]

𝑊𝑊𝐿𝐿

[g/s

]

𝑉𝑉 𝑆𝑆𝐿𝐿

[m/s

]

𝑅𝑅𝑒𝑒 𝑆𝑆𝐿𝐿

[-]

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


63

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

[°

F]

𝜌𝜌 𝐺𝐺 [k

g/m

3 ]

𝜇𝜇 𝐺𝐺A [

cP]

𝑊𝑊𝐺𝐺

[g/s

]

𝑉𝑉 𝑆𝑆𝐺𝐺

[m/s

]

𝑅𝑅𝑒𝑒𝑆𝑆𝐺𝐺

[-]

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 Sutherland’s formula


64

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) ° are examined at temperature range of 70-76 °F. A total of

484 tests was performed on flow pattern for the water cases for both the 0° and 1°. 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, …, 70, 100. The percent pump speed

and the percent valve opening are then converted to their corresponding 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺 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.

𝑣𝑣𝑆𝑆𝐺𝐺 =𝑊𝑊𝐺𝐺

𝜌𝜌𝐺𝐺𝐴𝐴𝑃𝑃 (5-1)

𝑣𝑣𝑆𝑆𝐿𝐿 =𝑊𝑊𝐿𝐿

𝜌𝜌𝐿𝐿𝐴𝐴𝑃𝑃 (5-2)

Where, 𝑊𝑊𝐺𝐺 and 𝑊𝑊𝐿𝐿 are gas and liquid mass flow rate respectively

Two inclination angles at 0 ° and 5° were examined for the oil flow pattern

determination experiments. The nominal temperatures for the oil test are 70 and 90 °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 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺. 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


65

pressure value in the density ideal gas equation to back calculate the value of gas density,

𝜌𝜌𝐺𝐺 in Equation 5.3. For the air- water case the gas density used to calculate all 𝑉𝑉𝑆𝑆𝐺𝐺 values

are 1.22 𝑅𝑅𝐾𝐾𝑚𝑚3 . 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, 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺 is given below in Table 5-6 for air-water and in APPENDIX A for

air-oil cases, respectively.

𝜌𝜌𝐺𝐺 =𝑃𝑃 ∗ 𝑀𝑀𝑅𝑅 ∗ 𝑇𝑇

(5-3)

The units used in Equation 5-3 are P in Pascal, M in 𝐾𝐾𝑚𝑚𝑡𝑡𝑡𝑡

, R in 8.314 𝑃𝑃𝑡𝑡∗𝐾𝐾∗𝑅𝑅−1∗𝑚𝑚𝑡𝑡𝑡𝑡−1

𝑚𝑚𝑡𝑡𝑡𝑡∗𝑚𝑚3∗𝑃𝑃𝑡𝑡∗𝑅𝑅 and

T in K

Table 5-6: Relationship between percent pump speed, percent air valve opening with 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺 for air-water cases.

% pump speed

𝑉𝑉𝑆𝑆𝐿𝐿 (m/s)

% air valve opening

𝑉𝑉𝑆𝑆𝐺𝐺 (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


66

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

[˚]

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


67

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.


68

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 𝑉𝑉𝑆𝑆𝐿𝐿 (𝑚𝑚𝑠𝑠

) rates and

low 𝑉𝑉𝑆𝑆𝐺𝐺 (𝑚𝑚𝑠𝑠

) 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


69

wave and stratified flow. We identified rolling wave as well in this study at high 𝑉𝑉𝑆𝑆𝐺𝐺 (𝑚𝑚𝑠𝑠

)

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 0° 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 𝑉𝑉𝑆𝑆𝐿𝐿 (𝑚𝑚𝑠𝑠

) and 𝑉𝑉𝑆𝑆𝐺𝐺 (𝑚𝑚𝑠𝑠

). The calculated 𝑉𝑉𝑆𝑆𝐿𝐿 (𝑚𝑚𝑠𝑠

) and 𝑉𝑉𝑆𝑆𝐺𝐺 (𝑚𝑚𝑠𝑠

) 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.


70

Figure 5-1: Flow pattern map generated for the flow loop system for water at 0° superimposed to FLOPATN 2.7 VBA code

The same test was performed for the water test at 1°. 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 (𝑉𝑉𝑆𝑆𝐿𝐿); 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 0° where the transition boundary is below the boundary observed from the flow loop.

𝑉𝑉 𝑆𝑆𝐿𝐿[𝑚𝑚 𝑠𝑠

]/

𝑉𝑉𝑆𝑆𝐺𝐺[𝑚𝑚𝑠𝑠

]/


71

Figure 5-2: Flow pattern map generated for the flow loop system for water at 0° 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 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺 , 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


]


]


72

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 0˚ 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 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺. 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


]


]


73

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.


74

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 5°, the predominant flow pattern observed is still

the slug flow pattern, and when compared to the flow pattern case of 280 cP at 0° additional


75

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 5˚ 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 0° and 280 cP is also found for 5° and 280 cP. The pressure

drop observed is much lower than the pressure per unit length at 0°, 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 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺. 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)


]


]


76

see (Figure 4-3) The same explanations and observations described for the air-oil case at

280 cP and 0° pressure drop results apply to the case of 280 cP and 5°.




77

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 75°F to 90°F. For the

0° 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 ( 𝑉𝑉𝑇𝑇𝑇𝑇 ) of fluids

decreases as the viscosity of the fluid increases from 1-280 cP. Translational velocity is

highly driven by superficial gas velocity 𝑉𝑉𝑆𝑆𝐺𝐺. 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 𝑉𝑉𝑇𝑇𝑇𝑇 , while Equation 5.5 is the modified 𝑉𝑉𝑇𝑇𝑇𝑇 equation by

Bendiksen, this equation considers the effect of inclination, but neither equation considers

the effect of viscosity on 𝑉𝑉𝑇𝑇𝑇𝑇.

𝑉𝑉𝑇𝑇𝑇𝑇 = 𝐶𝐶0𝑉𝑉𝑀𝑀 + 𝑉𝑉𝑑𝑑

(5-4)

𝑉𝑉𝑇𝑇𝑇𝑇 = 𝐶𝐶0𝑉𝑉𝑀𝑀 + 0.54�𝑔𝑔𝑑𝑑 𝑐𝑐𝑚𝑚𝑠𝑠𝜃𝜃 + 0.35�𝑔𝑔𝑑𝑑 sin(𝜃𝜃)

(5-5)


78

Where; 𝐶𝐶0 is the flow distribution coefficient, 𝑉𝑉𝑀𝑀 is the mixture velocity and 𝑉𝑉𝑑𝑑 is

the drift velocity are in units of 𝑚𝑚𝑠𝑠

. 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 0°

and 5° 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) ° exaimined. The 3-D heat map represents the

data gathered from the experimental program for (1, 150 and 280 ) cP°. In the maps blue

represent the slowest 𝑉𝑉𝑇𝑇𝑇𝑇 values observed at 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺 pairs, while red represents the

fastest 𝑉𝑉𝑇𝑇𝑇𝑇 values observed at 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺 pairs. Figure 5-9 shows that at 1 cP and 0° the

fastest 𝑉𝑉𝑇𝑇𝑇𝑇 is at a high 𝑉𝑉𝑆𝑆𝐺𝐺 and low 𝑉𝑉𝑆𝑆𝐿𝐿 and the slowest 𝑉𝑉𝑇𝑇𝑇𝑇 is at low 𝑉𝑉𝑆𝑆𝐿𝐿 and low 𝑉𝑉𝑆𝑆𝐺𝐺

rates. The effect of viscosity is examined experimentally for 150 and 280 cP oil. The

observation of the impact of viscosity on 𝑉𝑉𝑇𝑇𝑇𝑇 shows that an increase in fluid viscosity

reduces 𝑉𝑉𝑇𝑇𝑇𝑇. At both viscosities, a similar trend is observed as shown in Figure 5-10, 𝑉𝑉𝑇𝑇𝑇𝑇

decreased as the oil viscosity increased from 150 – 280 cP. In summary 𝑉𝑉𝑇𝑇𝑇𝑇 for fluid

viscosity at 0° is influenced more by 𝑉𝑉𝑆𝑆𝐺𝐺 and an increase in fluid viscosity decreases 𝑉𝑉𝑇𝑇𝑇𝑇.

To demonstrate the full impact of viscosity on 𝑉𝑉𝑇𝑇𝑇𝑇 Figure 5-11 combines all fluids

examined. Althoug the air-water case is not examined at exactly the same 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺

pairs, it still supports the experimental claim.


79

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 0˚


[𝑚𝑚/𝑠𝑠

]

𝑉𝑉𝑆𝑆𝐿𝐿 [𝑚𝑚/𝑠𝑠]


[𝑚𝑚/𝑠𝑠

]



80

Figure 5-11: Comparison of translational velocity for all fluids types examined (water and oil) at their corresponding viscosities on a pipe at 0˚.

5.3.1b Inclination: Five Degrees

For the same fluids viscosities, the inclination angle of the pipe is raised from 0°

to +5°. While slight differences result relative to the previously discussed fluids, the overall

effect of inclination at 5° is not quite clear. 𝑉𝑉𝑇𝑇𝑇𝑇 seems to be driven by high 𝑉𝑉𝑆𝑆𝐺𝐺 and high

𝑉𝑉𝑆𝑆𝐿𝐿 rates when the pipe is inclined. The 3-D heat map represents the data gathered from

the experimental program for 1 cP and 5°. In the maps the color blue represent the slowest

𝑉𝑉𝑇𝑇𝑇𝑇 values observed at 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺 pairs, while red the hot color represents the fastest 𝑉𝑉𝑇𝑇𝑇𝑇

values observed at 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺 pairs. Figure 5-12 shows that at 1 cP and 5° the fastest

𝑉𝑉𝑇𝑇𝑇𝑇 is at high 𝑉𝑉𝑆𝑆𝐺𝐺 and high 𝑉𝑉𝑆𝑆𝐿𝐿 rates and the slowest 𝑉𝑉𝑇𝑇𝑇𝑇 is at low 𝑉𝑉𝑆𝑆𝐿𝐿 and low 𝑉𝑉𝑆𝑆𝐺𝐺 rates..

The impact of viscosity on 𝑉𝑉𝑇𝑇𝑇𝑇 shows that an increase in viscosity reduces 𝑉𝑉𝑇𝑇𝑇𝑇. At both



[𝑚𝑚/𝑠𝑠

]


81

viscosities, a similar trend is observed as shown in Figure 5-13, 𝑉𝑉𝑇𝑇𝑇𝑇 decreased as the oil

viscosity increased from 150 – 280 cP.

In summary 𝑉𝑉𝑇𝑇𝑇𝑇 for fluid viscosity at 5° is influenced by both superficial velocities

and an increase in fluid viscosity decreases 𝑉𝑉𝑇𝑇𝑇𝑇. To demonstrate the full impact of viscosity

on 𝑉𝑉𝑇𝑇𝑇𝑇 on Figure 5-14 combines all fluids examined. Althoug the air-water case is not

examined at exactly the same 𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺 pairs, it still supports the experimental claim.

Figure 5-12: Translational velocity for water at 1 cP on a pipe inclined at 5˚.


[𝑚𝑚/𝑠𝑠

]



82

Figure 5-13: Comparison of translational velocity for oil at 150 and 280 cP in a 5˚ 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 5˚


[𝑚𝑚/𝑠𝑠

]



[𝑚𝑚/𝑠𝑠

]



83

Having examined the effect of viscosity on 𝑉𝑉𝑇𝑇𝑇𝑇 through a comparison of fluids

from low to high viscosities, we turn to the effect of inclination on 𝑉𝑉𝑇𝑇𝑇𝑇 for the same set of

viscosities. As before, a 3D heat-map represents the difference between inclination angles

0° and 5 ° 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 5˚ and 0˚


[𝑚𝑚/𝑠𝑠

]



84



𝑉𝑉𝑆𝑆𝐿𝐿 𝑉𝑉 𝑆𝑆𝐺𝐺

[𝑚𝑚/𝑠𝑠

]



[𝑚𝑚/𝑠𝑠

]



85

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 QCV’s 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 0°, +1°, +3°, +5°, +7°,

and +10° 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


86

Table 5-9: Drift velocity test matrix for oil at 0 degrees

Tem

pera

ture

[˚F

]

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 0°. Also, we observed that Bendiksen over-estimates drift velocity

values for both air-water and air-oil cases, which will in turn inflate 𝑉𝑉𝑇𝑇𝑇𝑇 results. The same

impact of viscosity that was observed for translational velocity applies to drift velocity, in

that as fluid viscosity increases both 𝑉𝑉𝑇𝑇𝑇𝑇 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).


87

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


88

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

𝐻𝐻𝑆𝑆 = 30 ∗ 𝜋𝜋 (5-6)

𝐻𝐻𝑠𝑠 = (32.0 cos2 𝜃𝜃 + 16.0 sin2 𝜃𝜃) ∗ 𝜋𝜋 (5-7)

where D is the pipe diameter in inches and θ 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 (𝑉𝑉𝑆𝑆𝐿𝐿 and 𝑉𝑉𝑆𝑆𝐺𝐺) as it y-axis and


89

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.


Figure 5-20: Dimensionless slug length obtained experimentally for air-water at 0˚


90

Figure 5-21: Dimensionless slug length obtained experimentally for air-oil at 0˚ and 150 cP

Figure 5-22: Dimensionless slug length obtained experimentally for air-oil at 0˚ and 280 cP


91

Figure 5-23: Comparison of dimensionless slug length obtained experimentally for air-oil at 0°

Figure 5-24: Comparison of dimensionless slug length obtained experimentally for air-water and air-oil at 0˚


92

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 0˚ - 5˚ 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 5˚. 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 5˚


93

Figure 5-26: Comparison of dimensionless slug length obtained experimentally for air-oil at 5˚

Figure 5-27: Comparison of dimensionless slug length for air-water and air-oil at 5˚


94

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

0˚ and 5˚ at each viscosity examined. The slug length for water and oil case show an

agreement that the increase in slug length is driven by 𝑉𝑉𝑆𝑆𝐿𝐿 . The longest slug length is

observed at the test points high 𝑉𝑉𝑆𝑆𝐿𝐿 rates and the shortest slug lengths are observed at low

𝑉𝑉𝑆𝑆𝐺𝐺 and low 𝑉𝑉𝑆𝑆𝐿𝐿 rates.

Figure 5-28: Comparison dimensionless slug length for air-water at 0˚and 5˚

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 0° and 5°. 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 (0°) experiences longer slug

length at the test point been analyzed.


95

Figure 5-29: Comparison of dimensionless slug length for air-oil at 0˚and 5˚

Figure 5-30: Comparison of dimensionless slug for air-oil at 0˚ and 5


96

Figure 5-31: Difference between dimensionless slug length for the same viscosity 1 cP between inclination angles 5˚ and 0˚

Figure 5-32: Difference between dimensionless slug length for the same viscosity 150 cP between inclination angles 5˚ and 0˚


97

Figure 5-33: Difference between dimensionless slug length for the same viscosity 280 cP, between inclination angles 5˚ and 0˚

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.


98

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 𝑉𝑉𝑆𝑆𝐿𝐿. In 2000 Zabaras revised Gregory

and Scott (1969) and expanded the range of its applicability from 0 to 11˚ for small pipes

of 0.0254 to 0.20-m pipe ID. Zabaras’ 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.

𝜈𝜈𝐻𝐻𝐻𝐻 = 0.0226 ∗ �

𝑉𝑉𝑆𝑆𝐿𝐿𝑔𝑔𝑑𝑑

�1.2

�212.6𝜈𝜈𝑀𝑀

+ 𝜈𝜈𝑀𝑀�1.2

∗ [0.836 + 2.75(sin𝜃𝜃)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

45° line


99

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.

𝑁𝑁𝑓𝑓 = 𝜋𝜋

32 ∗

�𝜌𝜌𝐿𝐿(𝜌𝜌𝐿𝐿 − 𝜌𝜌𝐺𝐺)𝑔𝑔𝜇𝜇𝐿𝐿

(5-9)

𝑓𝑓𝑠𝑠 = 2.816 ∗ �

1𝑁𝑁𝑓𝑓0.612� ∗ �

𝑉𝑉𝑆𝑆𝐿𝐿𝜋𝜋�

(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

(𝑉𝑉𝑆𝑆𝐿𝐿and 𝑉𝑉𝑆𝑆𝐺𝐺) 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.


100


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


101

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 5˚. 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) ° 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 5˚.

Figure 5-39: Comparison of slug frequency for oil at 150 and 280 cP in a pipe inclined at 5°


103

Figure 5-40: Comparison of slug frequency for all fluids types examined (water and oil) at their corresponding viscosities in a pipe inclined at 5˚.

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 (0°)

experiences more slug frequency at the test point been analyzed.


104

Figure 5-41: Comparison of slug frequency for air-water test at 0˚, and 5˚ at 1 cP

Figure 5-42: Comparison of slug frequency for air-oil test at 0˚, and 5˚ at 150 cP


105

Figure 5-43: Comparison of slug frequency for air-oil test at 0°, and 5° at 280 cP

Figure 5-44: Difference between slug frequency for viscosity at 1 cP between inclination angles of 5° and 0°


106

Figure 5-45: Difference between slug frequency for viscosity at 150 cP between inclination angles of 5˚ and 0˚

Figure 5-46: Difference between slug frequency for the same viscosity 280 cP between inclination angles 5° and 0°


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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 0°. Gokcal’s 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 “it is critical for predicting average liquid

holdup and pressure gradient.” (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


109

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 Barnea’ 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 𝑉𝑉𝑆𝑆𝐿𝐿. 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 (𝑉𝑉𝑆𝑆𝐿𝐿

and 𝑉𝑉𝑆𝑆𝐺𝐺) 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.


110

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 0°, while the square represents

the same viscosity (280 cP) at 5 °. The same fluid is then examined at 150 cP and

inclinations of 0° and 5°; for this fluid downward facing triangle is for the fluid viscosity

at 150 cP and inclination at 0° and upward facing triangle is for 150 cP and 5°. The take-

away is that 𝑉𝑉𝑆𝑆𝐿𝐿 does indeed affect HLLS in all cases, the higher the liquid superficial

velocity the higher the HLLS value.


111

Figure 5-50: Slug liquid holdup for air-oil case (150 and 280) cP at (0 and 5) °

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 5° than at 0°. A negative value shows that for

that test point 0° has more HLLS . For fluid viscosity at 150 cP, the inclination angle of 5°

always has more volume of liquid in the slug body than at 5°. 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.


112

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 0°, and the downward

facing triangle represents the inclination angle at 5°. It is important to note that the value

to the left of each symbol is for inclination angle at 5°. 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). Gomez’s

equation seems to be versatile as it is for inclination angle within the range of 0˚ ≤ 𝜃𝜃 ≤

90° 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 𝜃𝜃 is in degrees.

𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 = 1 ∗ 𝐸𝐸𝐸𝐸𝑃𝑃[−(7.85 ∗ 10−3𝜃𝜃 + 2.48 ∗ 10−6𝑅𝑅𝑒𝑒𝐿𝐿𝑆𝑆)] (5-11)


114

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 𝐻𝐻𝐿𝐿𝐿𝐿𝑆𝑆 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 Gomez’s

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 5° are lower than at 0° for both 280 cP and 150 cP. When solving for HLLS using Taitel

and Barnea’s mechanistic model.

Figure 5-53: Comparsion of predicted Slug liquid holdup (HLLS) using the mass balance to Gomez (2000) for 280 cP.


115

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


116

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 0°, while the square represents the same viscosity (280 cP) at 5 °. The same fluid is then

examined at 150 cP and inclinations of 0° and 5°; for this fluid downward facing triangle

is for the fluid viscosity at 150 cP and inclination at 0° and upward facing triangle is for

150 cP and 5°. Blue indicates low pressure values and as the color goes towards red the

pressure value increases as well. The take-away is that 𝑉𝑉𝑆𝑆𝐿𝐿 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.


117

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 5° is more than the pressure at 0°. A negative value shows that for that

test point 0° has more pressure drop across the section than 5° 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 5° and 0° 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 5°.

Figure 5-56: Pressure drop between ports 3 and 5 (the second half of the visualization section) represented at both viscosities and inclinations.


118

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 0°, and

the downward facing triangle represents the inclination angle at 5°. It is important to note

that the values to the left of each symbol are for inclination angle at 5°. 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.


119

5.5.4a Pressure Drop Result Comparison

A comparison is made between the experimentally observed pressure drop, Taitel

and Barnea’s (TTBN) and modified Taitel and Barnea’s (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 0° while the downward facing

blue triangle and the green star are modified TTBN and TTBN at 5°respectively.


120

Figure 5-58: Comparison of pressure drop observation between experimental and numerical result at 280 cP.


121

Figure 5-59: Comparison of pressure drop observation between experimental and numerical result at 150 cP.


122

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


123

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.

• Slug length decreases as viscosity increases

• Slug frequency increase as viscosity increases.

• Translational velocity decreases as viscosity increases

• Liquid holdup increases as viscosity increases.

• Pressure drop increases with increasing viscosity

• Existing drift velocity correlation over estimates the actual drift velocity for high

viscosity fluids.


124

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129

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 0°

Flow Pattern

Pump Speed [%]

Valve Opening [%]

Liquid Mass flowrate [g/s]

Gas Mass Flowrate [lb/min]

𝑉𝑉𝑆𝑆𝐿𝐿 [m/s] 𝑉𝑉𝑆𝑆𝐺𝐺 [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




130

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


131

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


132

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


133

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


134

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


135


136

Table A-1: Experimental data for flow pattern at 150 cP and 5° Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


137

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


138

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


139

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


140

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


Pump Speed [%]

Valve Opening [%]




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


141

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


142

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


143

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


144

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


145

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


146


Pump Speed [%]

Valve Opening [%]




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


147

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


148

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


149

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


150

Flow Pattern

Pump Speed [%]

Valve Opening [%]




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


151

Flow Pattern Results for 150 cP Air-Oil Case

Figure A 1: Flow pattern map generated for the flow loop system for oil at 0˚ and 150 cP.

Figure A 2: Flow pattern map generated for the flow loop system for oil at 0˚ and 150 cP superimposed to FLOPATN 2.7 VBA code


]/


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]/


152

Figure A 3: Change in pressure drop per unit length as flow pattern changes for the same viscosity and inclination



153

Figure A 5: Flow pattern map generated for the flow loop system for oil at 5˚ and 150 cP

Figure A 6: Flow pattern map generated for the flow loop system for oil at 5˚ and 150 cP superimposed to FLOPATN 2.7 VBA code


]/


]/


]/


]/


154




155

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


156

Table B- 2: Fluid Properties and Experimental Results of Hydrodynamic Parameters for Air-Water Case


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


157

Table B- 3: Fluid Properties and Liquid Holdup Result for Air-Water Case


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


158

Air-Oil Case at 280 cP

Table B- 4: Fluid Properties and Pressure Drop reading for Air-Oil Case at 280cP

°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


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


Liquid Gas

Test Name


160

Table B- 6: Fluid Properties and Liquid Holdup Result for Air-Oil Case at 280 cP


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


Liquid Holdup

Liquid Gas

QCV Method


161

Air-Oil Case at 150 cP Table B- 7: Fluid Properties and Pressure Drop reading for Air-Oil Case at 150cP


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


Liquid Gas

Test Name

Test Information

Test Name


162

Table B- 8: Fluid Properties and Experimental Results of Hydrodynamic Parameters for Air-Oil Case at 150 cP


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


Liquid Gas

Test Name


163

Table B- 9: Fluid Properties and Liquid Holdup Result for Air-Oil Case at 150 cP


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


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


165

CURRICULUM VITAE Tolani A. Afolabi

[email protected]

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 Master’s Thesis Research, Texas Tech University, Lubbock TX

• Designed experimental procedures for the research • 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.

• Used excel VBA to solve mathematical models to obtain results for both theoretical and experimental data.

• 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.

• 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.

• Utilized activated charcoal to mitigate asphaltene influx into the processing plant.


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

• President’s List, Summer 2011 & 2016

• Dean’s Honor List, 2010, 2013 to 2015

• National Dean’s List, 2007 to 2008 • Bill & Mabeth Sanderson

Academic Scholarship, 2008 to 2012

• International Student Laureate Program (ISLP) delegate to China 2008

Leadership Positions

• President of Ladies in Petroleum • Coordinator of the Ladies in

Petroleum • Residence Hall Community Advisor • Treasurer of the French Club • Assistant Supervisor of the FLOW LOOP LAB

the impact of viscosity on two-phase gas-liquid slug flow

Documents