T H E U N I V E R S I T Y O F T U L S A
THE GRADUATE SCHOOL
DEVELOPMENT AND VALIDATION OF A MECHANISTIC MODEL TO PREDICT
EROSION IN SINGLE-PHASE AND MULTIPHASE FLOW
by Quamrul Hassan Mazumder
A dissertation submitted in partial fulfillment of
the requirements for the degree of Doctor of Philosophy
in the Discipline of Mechanical Engineering
The Graduate School
The University of Tulsa
2004 T H E U N I V E R S I T Y O F T U L S A
THE GRADUATE SCHOOL
DEVELOPMENT AND VALIDATION OF A MECHANISTIC MODEL TO PREDICT
EROSION IN SINGLE-PHASE AND MULTIPHASE FLOW
by Quamrul Hassan Mazumder
A DISSERTATION
APPROVED FOR THE DISCIPLINE OF
MECHANICAL ENGINEERING
By Dissertation Committee
, Chair Dr. Siamack A. Shirazi
Dr. Brenton S. McLaury
Dr. Joseph D. Smith
Dr. Keith D. Wisecarver
Dr. Mauricio G. Prado
ii ABSTRACT
Mazumder,Quamrul Hassan (Doctor of Philosophy in Mechanical Engineering)
Development and Validation of a Mechanistic Model to Predict Erosion in Single-Phase and Multiphase Flow
Directed by Dr. Siamack A. Shirazi 190 pp., Chapters 10
(153 words)
Erosion in multiphase flow is a complex phenomenon due to existence of different flow patterns. The complexity of erosion increases significantly with entrained
sand particles in the flow. Entrained sand particles in production fluids can severely erode
pipes and cause failures creating potential safety risk for personnel and environment. A
mechanistic model to predict erosion in multiphase flow has been developed in order to
understand and evaluate the effect of liquid and gas rates on erosion results. The model
uses sand particle velocities in the liquid and gas phases separately in calculating erosion
in multiphase flow. The experimental erosion results for elbows were compared with the
model predictions showing good agreement.
Local thickness loss measurements were made in elbow specimens to determine
the location of maximum erosion at different liquid and gas velocities. Thickness loss
measurement showed the erosion profile in the elbow specimen and location of maximum
erosion in elbow specimen.
iii ACKNOWLEDGEMENTS
I would like to express my deepest appreciation and gratitude to my advisor Dr.
Siamack A. Shirazi, who played a key role in all aspects of my research and graduate
study. His encouragement, patience, understanding and support enabled me to complete
such a formidable task Special thanks to Dr. McLaury for his valuable comments and
meaningful suggestions during this research. I would also like to equally thank Dr.
Joseph Smith, Dr. Prado, and Dr. Wisecarver for serving on my Dissertation committee
and providing their expertise. Special thanks to the member companies of the Erosion/
Corrosion Research Center for providing funding that supported this work. I would like
to thank Dr. Rybicki and Dr. Shadley for their support during my study in the department
of Mechanical Engineering.
The author is very grateful to Honeywell Corporation for the support during this
study at The University of Tulsa.
iv DEDICATION
I would like to dedicate this work to God, the most merciful, the most beneficial, who provided me the strength, courage and wisdom to accomplish this work.
I would also like to dedicate this work to my mother Zainab Akhter, my father
Mamtazuddin Mazumder, whose encouragement, inspiration, and support helped me to achieve this academic accomplishment that they will never be able to witness; my lovely wife Shirin Mazumder, my son Fardin Mazumder and my daughter Samia Mazumder, who provided me continued support during my graduate study.
v TABLE OF CONTENTS
Page
ABSTRACT...... iii
ACKNOWLEDGEMENTS...... iv
DEDICATION...... v
TABLE OF CONTENTS...... vi
LIST OF TABLES...... x
LIST OF FIGURES ...... xii
CHAPTER I INTRODUCTION AND BACKGROUND ...... 1
Introduction...... 1
Background ...... 4
Research Goals...... 7
Approach ...... 8
CHAPTER II LITERATURE REVIEW ...... 10
Erosion Phenomenon and Erosion Models...... 12
Multiphase Flow and Flow Patterns ...... 24
Entrainment in Multiphase Flow ...... 27
Sand Distribution in Multiphase Flow...... 30
Annular Film Thickness and Film Velocity ...... 31
Droplet Velocity in Annular Flow ...... 34
Characteristic Thickness Loss Profile in Elbow ...... 35
vi CHAPTER III EXPERIMENTAL FACILITY AND EROSION TEST PROCEDURE ...... 40
Description of the Single-Phase Flow Loop and Test Section (L/D≈ 50) 42
Description of the Multiphase Flow Loop and Test Section (L/D≈ 160) 43
Experimental Procedure for Thickness Loss in Elbow ...... 49
CHAPTER IV EXPERIMENTAL EROSION RESULTS FOR SINGLE-PHASE
FLOW ...... 54
Stage I Erosion Test: Mass Loss Measurements in L/D ≈ 50 Test Section ...... 56
Stage II Erosion Test: Mass Loss Measurements in Multiphase Test
Section ...... 59
Stage III Thickness Loss Measurements of Elbow Specimen in Single-
Phase Flow ...... 66
CHAPTER V EXPERIMENTAL EROSION RESULTS FOR MULTIPHASE FLOW ...... 70
Stage I Erosion Test: Mass Loss Measurements in Multiphase Flow.... 71
Stage II Thickness Loss Measurements of Elbow Specimen in Multiphase
Flow ...... 89
CHAPTER VI COMPARISON OF SINGLE PHASE AND MULTIPHASE
EROSION TEST RESULTS ...... 97
CHAPTER VII: DEVELOPMENT OF MECHANISTIC MODELS ...... 104
Model for Annular Flow...... 105
Validation of Droplet Velocity Calculation ...... 111
Validation of Film Velocity Calculation...... 113
vii Validation of Film Thickness Calculation ...... 115
Validation of Entrainment Calculation...... 118
Model for Mist Flow ...... 119
Model for Slug Flow...... 121
Model for Churn Flow...... 124
Model for Bubble Flow...... 125
CHAPTER VIII VALIDATION OF THE MECHANISTIC MODELS ...... 128
Comparison of Predicted Erosion with Measured Erosion in Single
Phase Flow ...... 128
Comparison of Predicted Erosion with Literature Data in Multiphase
Flow ...... 133
Comparison of Predicted Erosion with Multiphase Flow Experimental
Data ...... 138
CHAPTER IX UNCERTAINTY ANALYSIS OF MODEL PREDICTIONS..... 147
Types of Uncertainty ...... 147
Sources of Uncertainty ...... 148
Uncertainty Estimates in Erosion Prediction...... 152
CHAPTER X SUMMARY, CONCLUSIONS AND RECOMMENDATIONS . 156
Summary...... 156
Conclusion ...... 159
Single-Phase Flow ...... 159
Multiphase Flow ...... 159
viii Mechanistic Model...... 160
Recommendation...... 162
NOMENCLATURE ...... 163
BIBLIOGRAPHY...... 168
APPENDIX A ...... 176
APPENDIX B ...... 178
APPENDIX C ...... 185
APPENDIX D ...... 188
ix LIST OF TABLES
Page
Table II-1: Empirical Material Factor (FM) for Different Materials [4] ...... 17
Table II-2: Sand Sharpness Factors (FS) for Different Types of Sand [4]...... 17
Table II-3: Penetration Factors (FP) for Elbow and Tee Geometries [4]...... 18
Table II-4: Flow Conditions of Selmer-Olsen [31] Experimental Data ...... 36
Table II-5: Flow Condition of Eyler [44] Experimental Erosion Data ...... 39
Table IV-1: Stage I Single-Phase Erosion Test Conditions...... 57
Table IV-2: Single-Phase Erosion Test Results at Different Orientations ...... 58
Table IV-3: Single-Phase Erosion Test Conditions (Multiphase Test Section) ...... 61
Table IV-4: Single-Phase Erosion Test Results in the Multiphase Test Section...... 63
Table IV-5: Summary of Erosion Test Results in Single-Phase Flow...... 66
Table IV-6: Results of Thickness Loss Measurement in Elbow Specimen (Single-Phase
Flow)...... 69
Table V-1: Erosion Test Conditions in Multiphase Flow (L/D ≈160)...... 72
Table V-2: Erosion Test Results of 316 Stainless Steel Specimen (150µm Sand).... 76
Table V-3: Erosion Test Results Summary of Aluminum Specimen (150µm Sand) 82
Table V-4: Summary of Thickness Loss Measurements of Aluminum Specimen.... 96
Table VI-1: Comparison of Single-Phase and Multiphase Erosion Test Results in 316 Stainless Steel Elbow Specimen...... 98
x Table VI-2: Erosion Reduction Factors in Multiphase Flow Compared to
Single-Phase (Air) Flow ...... 100
Table VII-1: Comparison of Calculated and Measured [43] Droplet Velocities ...... 113
Table VII-2: Comparison of Calculated and Measured [41] Film Velocities ...... 115
Table VII-3: Comparison of Measured and Mechanistic Model Predicted Film
Thickness ...... 117
Table VIII-1: Comparison of Mechanistic Model Predictions with Bourgoyne [50]
Erosion Data in Single-Phase Flow ...... 129
Table VIII-2: Comparison of Mechanistic Model Predictions with Tolle and Greenwood
[57] Erosion Data in Single-Phase Flow...... 130
Table VIII-3: Comparison of Mechanistic Model Predictions with Experimental Results in Single-Phase Flow ...... 131
Table VIII-4: Comparison of Mechanistic Model Predictions with Literature [3]
Reported Erosion Data in Annular Flow ...... 136
Table VIII-5: Comparison of Mechanistic Model Predictions with Literature [3]
Reported Erosion Data in Slug/Churn and Bubble Flows ...... 137
Table VIII-6: Comparison of Mechanistic Model Predictions with Literature [3.50]
Reported Erosion Data in Mist Flow ...... 138
Table VIII-7: Comparison of Mechanistic Model Predictions with Experimental
Measurements of Multiphase Flow...... 139
Table IX-1: Sources of Measurement Uncertainty of Erosion Experiment ...... 152
Table IX-2: Uncertainties in Mechanistic Model Predicted Penetration Rates ...... 153
Table IX-2: Percent Uncertainties in Predicted Penetration Rates ...... 154
xi LIST OF FIGURES
Page
Figure I-1: Sand Particle Erosion of Elbow in Single-Phase Flow...... 3
Figure I-2: Sketch of Elbow and Plug Tee Geometries ...... 5
Figure II-1: Direct and Random Impingement in Elbow and Pipe...... 15
Figure II-2: Effect of Different Factors on Particle Impact Velocity [4]...... 20
Figure II-3: Schematic Description of Stagnation Length Model [17]...... 22
Figure II-4: Major Flow Patterns in Horizontal Pipe...... 25
Figure II-5: Major Flow Patterns in Vertical Pipe...... 25
Figure II-6: Roll Wave Mechanism of Entrainment Formation in Annular Flow .... 29
Figure II-7: Selmer-Olsen [31] Measurement (VSG = 95.15 ft/sec, VSL = 0.11 ft/sec) 37
Figure II-8: Selmer-Olsen [31] Measurement (VSG = 95.15 ft/sec, VSL = 2.95 ft/sec) 38
Figure II-9: Erosion Profile in Outer Wall of an Elbow [44] ...... 39
Figure III-1: Photograph of the Single-Phase Erosion Test Section...... 42
Figure III-2: Schematic of the Single-Phase Erosion Test Section...... 42
Figure III-3: Schematic of the One-inch Multiphase Flow Loop ...... 45
Figure III-4: Sand Injection in Multiphase Test Section from Slurry Tank ...... 46
Figure III-5: Horizontal and Vertical Test Cells in Multiphase Flow Loop...... 47
Figure III-6: Photograph of Erosion Specimen in the Horizontal Test Cell...... 49
Figure III-7: Thickness Loss Measurement Locations in the Elbow Specimen ...... 50
Figure III-8: Scratches in the Elbow Specimen Used for Erosion Measurement...... 51
xii Figure III-9: Scratch Measurement of Elbow Specimen Using Profilometer...... 52
Figure IV-1: Average Hardness of 316L Stainless Steel Elbow Specimen...... 55
Figure IV-2: Sand Size Distribution of Oklahoma No.1 Sand ...... 55
Figure IV-3: Test Cells in Vertical (Left) and Horizontal (Right) Orientations...... 56
Figure IV-4: Single Phase Erosion Test Results in Different Flow Orientation...... 59
Figure IV-5: Erosion Test with Air and Sand in the Multiphase Test Section...... 60
Figure IV-6: Mass Loss of 316 SS Elbow Specimen in Single-Phase
Horizontal Flow ...... 64
Figure IV-7: Mass Loss of 316 SS Elbow Specimen in Single-Phase
Vertical Flow ...... 64
Figure IV-8: Erosion Test Results in Single-Phase Flow with 95%
Confidence Interval...... 65
Figure IV-9: Thickness Loss Measurement of Elbow Specimen (Vgas = 112 ft/sec,
Aluminum, 55 degrees)...... 68
Figure IV-9: Thickness Loss Profile of Elbow Specimen in Single-Phase Flow
(Vgas = 112 ft/sec, Aluminum) ...... 68
Figure V-1: Average Hardness of 6061-T6 Aluminum Elbow Specimen...... 71
Figure V-2: One-inch Horizontal Flow Map Showing Erosion Test Conditions ...... 73
Figure V-3: One-inch Vertical Flow Map Showing Erosion Test Conditions ...... 73
Figure V-4: Mass Loss of Stainless Steel Specimen at Different Sand Throughput
(VSG = 32 ft/sec, VSL = 0.10 ft/sec, 150 micron Sand)...... 77
xiii Figure V-5: Mass Loss of Stainless Steel Specimen at Different Sand Throughput
(VSG = 62 ft/sec, VSL = 0.10 ft/sec, 150 micron Sand)...... 78
Figure V-6: Mass Loss of Stainless Steel Specimen at Different Sand Throughput
(VSG = 90 ft/sec, VSL = 0.10 ft/sec, 150µm Sand)...... 78
Figure V-7: Mass Loss of Stainless Steel Specimen at Different Sand Throughput
(VSG = 112 ft/sec, VSL = 0.10 ft/sec, 150 micron Sand)...... 79
Figure V-8: Mass Loss of Stainless Steel Specimen at Different Sand Throughput
(VSG = 32 ft/sec, VSL = 1.0 ft/sec, 150 micron Sand)...... 80
Figure V-9: Mass Loss of Stainless Steel Specimen at Different Sand Throughput
(VSG = 62 ft/sec, VSL = 1.0 ft/sec, 150 micron Sand)...... 80
Figure V-10: Mass Loss of Stainless Steel Specimen at Different Sand Throughput
(VSG = 90 ft/sec, VSL = 1.0 ft/sec, 150 micron Sand)...... 81
Figure V-11: Mass Loss of Stainless Steel Specimen at Different Sand Throughput
(VSG = 112 ft/sec, VSL = 1.0 ft/sec, 150 micron Sand)...... 81
Figure V-12: Comparison of Mass Loss Between Aluminum and Stainless Steel with
95% Confidence Interval (VSG = 32 ft/sec, VSL = 0.10 ft/sec, 150 micron Sand) ..... 83
Figure V-13: Comparison of Mass Loss Between Aluminum and Stainless Steel with
95% Confidence Interval (VSG = 112 ft/sec, VSL = 0.10 ft/sec, 150 micron Sand) ... 84
Figure V-14: Comparison of Mass Loss Between Aluminum and Stainless Steel with
95% Confidence Interval (VSG = 32 ft/sec, VSL = 1.0 ft/sec, 150 micron Sand) ...... 85
Figure V-15: Comparison of Mass Loss Between Aluminum and Stainless Steel with
95% Confidence Interval (VSG = 112 ft/sec, VSL = 1.0 ft/sec, 150 micron Sand) ..... 85
xiv Figure V-16: Schematic of Sand and Liquid Distribution in Vertical and Horizontal
Annular Flows...... 86
Figure V-17: Mass Loss in Test Sections with Different L/D Ratios and Pressures
(VSG = 50- 62 ft/sec, VSL = 1.0 ft/sec, Aluminum, 150 micron sand)...... 88
Figure V-18: Mass Loss in Test Sections with Different L/D Ratios and Pressures
(VSG = 100-112 ft/sec VSL = 1.0 ft/sec, Aluminum, 150 micron Sand) ...... 88
Figure V-19: Thickness Loss measurement of Elbow Specimen at VSG = 32 ft/sec,
VSL = 1.0 ft/sec, Aluminum, 45 degrees ...... 89
Figure V-20: Thickness Loss Measurement of Elbow Specimen at VSG = 90 ft/sec,
VSL = 1.0 ft/sec, Aluminum, 45 degrees ...... 90
Figure V-21: Thickness Loss Measurement of Elbow Specimen at VSG = 112 ft/sec,
VSL = 1.0 ft/sec, Aluminum, 45 degrees ...... 90
Figure V-22: Thickness Loss Measurement of Elbow Specimen at VSG = 112 ft/sec,
VSL = 0.1 ft/sec, Aluminum, 55 degrees ...... 91
Figure V-23: Thickness Loss Profile of Elbow Specimen at Different Gas Velocities
(Vertical, VSL = 0.1 ft/sec) ...... 92
Figure V-24: Thickness Loss Profile of Elbow Specimen at Different Gas Velocities
(Horizontal, VSL = 0.1 ft/sec) ...... 92
Figure V-25: Thickness Loss Profile of Elbow Specimen at Different Gas Velocities
(Vertical, VSL = 1.0 ft/sec) ...... 93
Figure V-26: Thickness Loss Profile of Elbow Specimen at Different Gas Velocities
(Horizontal, VSL = 1.0 ft/sec) ...... 94
xv Figure V-27: Photograph of Vertical Elbow Specimen Holder After Several Erosion Tests ...... 94
Figure VI-1: Comparison of Erosion Ratios at Different Liquid Rate
(316 SS Specimen, Horizontal Orientation) ...... 99
Figure VI-2: Comparison of Erosion Ratios at Different Liquid Rate
(316 SS Specimen, Vertical Orientation)...... 99
Figure VI-3: Sand and Liquid Distribution in Single-Phase and Multiphase Flow... 101
Figure VI-4: Comparison of Calculated Entrainment Fractions at 0.10 ft/sec and
1.0 ft/sec Superficial Liquid Velocities ...... 103
Figure VI-5: Comparison of Calculated Droplet Velocities at 0.10 ft/sec and
1.0 ft/sec Superficial Liquid Velocities ...... 103
Figure VII-1: Schematic Description of Annular Flow ...... 105
Figure VII-2: Comparison of Calculated Droplet Velocity with Experimental
Data [43] ...... 112
Figure VII-3: Comparison of Calculated Film Velocity with Experimental
Data [41] ...... 114
Figure VII-4: Comparison of Calculated Film Thickness with Measured
Film Thickness...... 116
Figure VII-5: Comparison of Measured Entrainments [47] with Ishii [29]
Model Predictions ...... 118
Figure VII-6: Andreussi [48] Proposed Transition for Annular to Mist Flow ...... 120
Figure VII-7: Schematic Description of Slug Flow in Vertical pipe...... 122
Figure VII-8: Schematic Description of Churn Flow ...... 125
xvi Figure VII-9: Schematic Description of Bubble Flow...... 127
Figure VIII-1: Comparison of Experimental Erosion Results with Mechanistic Model
Predictions in Single-Phase Flow ...... 132
Figure VIII-2: Comparison of Previous Model and Mechanistic Model Predictions
With Experimental Data in Single-Phase (Air) Flow ...... 132
Figure VIII-3: Two-inch Vertical Flow Map with Erosion Test Conditions...... 134
Figure VIII-4: One-inch Vertical Flow Map with Erosion Test Conditions ...... 134
Figure VIII-5: Comparison of Measured Erosion with Mechanistic Model Predictions for Annular, Mist, Slug/Churn and Bubble Flows…………………………………. 140
Figure VIII-6: Comparison of Old Model and Mechanistic Model Predictions with
Experimental Erosion Data at Superficial Gas Velocity of 32 ft/sec...... 141
Figure VIII-7: Comparison of Old Model and Mechanistic Model Predictions with
Experimental Erosion Data at Superficial Gas Velocity of 62 ft/sec...... 142
Figure VIII-8: Comparison of Old Model and Mechanistic Model Predictions with
Experimental Erosion Data at Superficial Gas Velocity of 90 ft/sec...... 143
Figure VIII-9: Comparison of Old Model and Mechanistic Model Predictions with
Experimental Erosion Data at Superficial Gas Velocity of 112 ft/sec...... 143
Figure VIII-10: Comparison of Old Model and Mechanistic Model Predictions with
Experimental Erosion Data at Different Liquid Velocities...... 144
Figure VIII-11: Comparison of Old Model and Mechanistic Model Predictions with
Experimental Erosion Data at Superficial Liquid Velocity of 0.10 ft/sec ...... 145
Figure VIII-12: Comparison of Old Model and Mechanistic Model Predictions with
Experimental Erosion Data at Superficial Liquid Velocity of 1.0 ft/sec ...... 146
xvii Figure IX-1: Uncertainty Range of Mechanistic Model Predictions Compared to
Experimental Data in Multiphase Flow ...... 155
xviii CHAPTER I
INTRODUCTION AND BACKGROUND
Introduction
Erosion is a micro-mechanical process by which material is removed from metal
or non-metal surfaces by impact of solid particles entrained in the carrier fluid. The
entrained solid particles remove material from the inner wall of pipes, fittings, valves,
and other process equipment potentially causing severe damage. Damage to piping and equipment reduces the operational reliability and increases the risk of failure resulting in significant financial loss to the industry and danger to the personnel and environment.
Transportation of fluid is essential in several industries to meet production and
operational needs. In the oil and gas industry, crude oil and natural gas are extracted
from the reservoirs and transported to the refineries and gas processing plants using
piping, fittings and other equipment. The extracted fluid from the reservoir contains sand
particles that may cause erosion damage to the inner surfaces of fluid handling
equipment. In coal gasification, erosion adds to corrosion problems causing severe
damage to valves and fittings. In the mining industry, transportation of slurry such as
iron ores, potash and coal causes erosion to the piping and equipment. In the aerospace
industry, high velocity intake air with sand particles causes erosion to heat exchangers,
engine and rotorcraft blades, and other components. Erosion damage can cause
unscheduled repair, removal and replacement of equipment interrupting production and
1 in some cases result in shutdown of the production process. The safety of operating
personnel and environment can also be in jeopardy when harmful chemicals or gases
discharge to the surrounding environment. The end result is lost revenue, harm to
personnel and increased operational cost that are highly undesirable. To optimize
operational efficiencies by minimizing equipment loss and production downtime due to
erosion, it is important to reduce damage due to erosion. One of the approaches to
minimize or control erosion is to reduce flow velocities during production and
transportation that also reduces the production rate. Another approach is to use sand
screens; the screen material may erode after a period of time or sand particles may clog
the screen. Selecting appropriate erosion resistant materials can also reduce erosion rate.
In the oil and gas industry, elbow, tees, pumps, valves, chokes and other fittings
are used in piping systems to transport fluids. Within these geometries, as the flow
direction changes, the entrained sand particles in the fluid can cross the streamlines and
approach the inner walls. These particles can impact the equipment walls at high
velocities that can be detrimental to the metal surface. Repeated impact of a large
number of particles at high velocities results in material removal from the equipment
wall. Figure I-1 shows the erosion damage in a one-inch elbow due to sand particles entrained in single-phase gas flow. This elbow was used in the single-phase erosion experiments conducted during this study. The eroded elbow shows higher erosion at the outer wall. From the non-uniform thickness loss pattern, maximum localized erosion was observed near the downstream pipe of the elbow. Based on this observation, it is necessary to predict the location and magnitude of maximum erosion to estimate the process equipment life.
2 1.0 inch ID
Maximum Flow Erosion
Figure I-1: Sand Particle Erosion of Elbow in Single-Phase Flow
Erosion in a single-phase flow with entrained sand particles in the carrier fluid is a complex phenomenon. The complexity of erosion increases significantly for a multiphase flow with sand particles in the carrier fluid due to different multiphase flow patterns,
distribution of sand particles and their corresponding particle impact velocities that cause
erosion. Among various factors that influence erosion, particle impact velocity is known
to be the most significant factor. Lack of understanding of particle impact velocities and
their effect on the erosion process presents a challenge in analysis of the erosion
mechanism. Therefore, a better understanding of the particle impact velocity is essential
to understand the multiphase erosion process. Most of the available erosion prediction
models are empirical and based on a single-phase gas or liquid carrier fluid. The
accuracy of the empirical models is limited to the flow conditions that were used in
development of the models. To address the complexities associated with a multiphase
erosion problem, a number of assumptions must be made to simplify the problem. The
validity of these assumptions must be carefully evaluated to qualify that the assumptions
were reasonable.
3 Background
American Petroleum Institute (API) Recommended Practice API RP 14E [1]
provides guidelines for maximum allowable threshold velocity to limit erosion. API RP
14E states that if the production velocities are kept below this limit, severe erosion
damage can be avoided. The following equation is used to calculate the threshold
velocity [1]:
C Ve = (I-1) ρ
Where, Ve is the erosional velocity limit in ft/sec, ρ is the density of the carrier fluid in
3 lbm/ft , and C is a constant. API RP 14E recommends using C =100 for continuous
service and C =125 for intermittent service. Equation (I-1) does not consider sand size,
sand rate, wall material, flow regimes in multiphase flow, or flow orientation (horizontal
or vertical). Equation (I-1) states that the allowable erosional velocity would be higher
for a low density fluid (such as gas) compared to a high density fluid (such as liquid).
However, experimental results showed higher erosion rates in gas compared to liquid at
similar velocities.
It may not be economically feasible to limit the fuid velocity as recommended by
Equation (I-1) because of potential conflict between lower flow rate and production
demand. Therefore a different approach to the problem is required to attain a more
acceptable solution. The erosive sand particle impact velocity primarily depends upon
the geometry and fluid velocity. Elbows and plug tees are the most commonly used
geometries for redirecting flows in the piping systems. These geometries are also most
susceptible to erosion damage. Analysis by Wang [2] showed long radius elbows (r/D >
1.5, where r is the turning radius of the centerline of the elbow and D is the inside
4 diameter of the elbow) have lower erosion compared to a standard elbow. Field
experience also showed long radius elbows and plug tees having lower erosion than
standard elbow. Figure I-2 shows schematics of an elbow and plug tee.
Figure I-2: Sketch of Elbow and Plug Tee Geometries.
In confined piping systems, plug tees are often used instead of long radius elbows
due to lack of space. Higher strength alloys such as duplex stainless steel are also used to
extend the service life of the equipment from erosion damage. Although these materials
increased the service life of the equipment, it may be cost prohibitive to use these expensive materials in large complex piping systems.
Multiphase flow is commonly observed in chemical, oil and gas, nuclear and other fluid handling industries. Unlike single-phase flow, multiphase flow phenomenon is very complicated with lack of clear understanding of all the flow mechanisms. The presence of different phases with different properties and different velocities result in different flow patterns such as annular, slug, churn, and bubble flow. These flow patterns are characterized by the interfacial properties between the phases. Some of the
5 multiphase flow patterns are transient, unstable, and not fully developed. Due to these
complex phenomena, the erosion prediction in multiphase flow is far more challenging
than single-phase flow.
Simplified erosion prediction models for straight pipe, elbows, and plug tees have been developed at the Erosion/ Corrosion Research Center of The University of Tulsa using empirical erosion data and CFD modeling. To account for solid size and liquid-gas mixture, Salama [3] modified Equation (I-1) to predict erosion. McLaury and Shirazi [4] developed a semi-empirical erosion prediction model that accounts for pipe size and geometry, sand size, pipe material, fluid velocities and densities. These models are based
on empirical erosion data and do not consider the effect of flow regimes on erosion in
multiphase flow.
The work presented here is an improvement of the previous model developed at
E/CRC [4] and development of a mechanistic erosion prediction model for multiphase
flow. This new mechanistic model accounts for multiphase flow behavior and flow
regimes in predicting erosion. The effect of particle velocities and their distribution in liquid and gas phases were considered in the model. As this model accounts for the important variables that cause erosion, this model is more general and can predict erosion over a wide range of flow velocities. To simplify the complexities of multiphase flow and due to limited availability of experimental erosion data, a number of assumptions were necessary during the model development process. These assumptions were based on careful evaluation of erosion mechanism, two-phase flow theory and past experience with erosion characteristics.
6 Research Goals
The primary objective of this research is to investigate erosion behavior in multiphase flow and to develop a mechanistic model to predict erosion in elbows for a wide range of single and multiphase flow conditions. This mechanistic model should be able to predict erosion considering the significant parameters that affect erosion. The model should compute the solid particle velocity and their concentration in both gas and liquid phases of multiphase flow. The model should rely on principles of fluid mechanics, two-phase flow theories, and physical mechanisms that cause erosion.
Results of the mechanistic model can be used to predict erosion and study the effects of different parameters that influence erosion.
To validate the model, available erosion data from the literature and field will be gathered. After review of the available data, further erosion experiments will be conducted to complement the data. Erosion experiments will be conducted in both single-phase and multiphase flow. The effect of different factors such as liquid rate, gas rate, flows orientation (horizontal/ vertical) that contribute to erosion will be studied and evaluated. As the elbow is one of the most important geometries for evaluation of erosion, an elbow specimen will be used during the experiments. The goal of the mechanistic model is to develop a generalized erosion prediction procedure that is capable of predicting erosion over a wide range of multiphase flow conditions. The mechanistic model predictions will be compared with previous empirical erosion models developed by Salama [1998] and McLaury [2000].
7 Approach
The mechanistic model development process involves the following steps. The
semi-empirical erosion prediction procedure previously developed at the Erosion/
Corrosion Research Center of The University of Tulsa was evaluated by using available
experimental erosion data reported in the literature. The semi-empirical model uses
superficial liquid and gas velocities to calculate the initial particle velocity, Vo that is used to calculate particle impact velocity at the wall. The model does not account for the effect of different flow regimes in multiphase flow. The mechanistic model developed in this research first calculates the flow regimes. The corresponding liquid and gas velocities were then calculated using two-phase flow equations. For example, in annular flow, the sand entrainments in the liquid and gas phases were estimated using experimental data and correlations. Using the sand particle velocities and entrainments in different phases, the corresponding erosion rates were calculated separately for gas and liquid phases using erosion equations. Finally, the erosion rates for gas and liquid phases are added together to compute the total erosion rate for the flow condition.
The erosion rate or penetration rate is defined as the rate of wall thickness loss due to sand particle impact on the wall. A dimensionless parameter used to define erosion is the erosion ratio. Erosion ratio is calculated by dividing the mass loss from the pipe wall by the mass of sand particles that causes erosion.
To validate the mechanistic model, the predicted erosion rates using the model were compared with available erosion data reported in the literature and experimental erosion data gathered during this research. Experiments were conducted at different
8 multiphase flow conditions to complement the available erosion data reported in the literature. Erosion experiments were conducted using both mass loss and thickness loss measurement procedures. The mass loss data provides information about the average erosion rate. Whereas, the thickness loss measurements provide information about the characteristic erosion profile, location and magnitude of maximum erosion.
Experimental investigations of thickness loss measurements were conducted in both single and multiphase flows. The ratio of maximum to average thickness loss was computed that can be used to estimate the maximum thickness loss from mass loss data.
9 CHAPTER II
LITERATURE REVIEW
This research mainly focused on understanding the physical phenomenon of solid
particle erosion on metal surfaces by evaluating the factors that affect erosion and
development of a generalized mechanistic model to predict erosion in single and multiphase flows. Another part of the research is to conduct erosion experiments to
determine the location of maximum erosion and the characteristic erosion profile in the
elbow geometry. Most of the currently available erosion prediction models are based on
empirical data and assumptions that are unable to accurately predict erosion in flow
conditions beyond the experimental conditions. While some of these models are only
valid for predicting the erosion in single-phase flow. This creates a need for a
generalized multiphase erosion prediction model.
To develop a mechanistic model for multiphase flow, experimental, theoretical,
analytical and mechanistic approaches can be used. Each of these approaches has their
unique advantages and disadvantages. The experimental approach requires using a
geometry of interest (such as pipe, elbow, and tee) and/or a representative test specimen
to conduct the erosion tests under specific flow conditions. The erosion ratio (mass loss
of the geometry/ mass of the sand that causes erosion) and/or penetration rates (thickness
loss per unit sand throughput, mils/lb) are then calculated from the mass loss or thickness
10 loss data, geometry, flow and test conditions. This experimental erosion data can be used
to validate erosion models.
One of the main disadvantages of the experimental approach is the cost and time
required to conduct erosion tests at different flow conditions and using different
geometries. Construction of a multiphase erosion test loop may be a very expensive and
time-consuming project. Gathering reliable and useful erosion data often requires experiments to be run for long periods of time and then repeating the tests. The above constraints can make the experimental approach cost-prohibitive and time consuming.
The theoretical or analytical approach requires a clear understanding of the different
variables and their interactions that cause erosion in multiphase flow. The understanding of these variables and their effect on erosion is still being developed and evaluated. A
lack of clear understanding of these variables prevents the development of an accurate
theoretical or analytical erosion prediction model.
Considering the above factors, the development of a mechanistic model using
multiphase flow theory, erosion equations and then validating the model with
experimental erosion data appears to be a more feasible and practical approach in
addressing the erosion problem. The work presented here discusses the efforts in the
development of a mechanistic model substantiated by experimental investigations to
validate the mechanistic model.
In order to understand the erosion phenomenon in multiphase flow, it is essential
to have knowledge and understanding of several concepts. First, a good understanding of the solid particle erosion process in single-phase and multiphase flow is important. The major factors that affect solid particle erosion are impact velocity, impingement angle,
11 wall material, particle shape, size, density, carrier fluid properties (density, viscosity),
and carrier fluid velocity. Among these factors, particle impact velocity has the greatest
influence on erosion, as erosion rate is a function of the exponent of the impact velocity.
Second, knowledge of multiphase flow and how the erodent solid particles are distributed in different phases is essential. In a two-phase gas-liquid flow, the gas and liquid have different spatial distributions with their corresponding velocities that influence the solid particle velocity. Particle impact velocities can be calculated from the corresponding gas
and liquid phase velocities. The third important factor is the fraction of solid particles
entrained in the gas and liquid phases. In multiphase flow, gas bubbles can be entrained
in the liquid phase and liquid droplets can be entrained in the gas phase. The particles
entrained in the liquid and gas phases will have velocities similar to the corresponding
phase velocities.
Finally, to calculate the erosion caused by solid particles, one must understand how the particles impact the wall of the geometry causing removal of the wall material.
The remainder of this chapter discusses the above factors and how they contribute to erosion.
Erosion Phenomenon and Erosion Models
Erosion is a process by which material is removed from the inner surface of a
fluid-handling device as a result of repeated impact of small solid particles. In ductile
materials erosion is caused by localized plastic strain and fatigue resulting in material
removal from the surface. In brittle material, impacting particles cause surface cracks
and chipping of micro-size metal pieces.
12 Erosion behavior in a single-phase gas was investigated by Brinell [5] as early as
1921. One of the first erosion models developed by Finnie [6] in 1958 was based on the
assumption that erosion is a result of the micro-cutting mechanism. Later, other
investigators demonstrated that micro-cutting is not the primary erosion mechanism for
ductile material. In 1982 Levy [7] proposed the platelet mechanism of erosion in ductile
material. To determine the effects of specific steel microstructures on erosion, Levy
analyzed the eroded surfaces by using a Scanning Electron Microscope (SEM). From
the micrographs, Levy observed that the platelets from the metal surfaces are initially
extruded due to impact of smaller solid particles; the platelets are then forged into
distressed conditions and are eventually removed from the surfaces by further subsequent
impacts. A work hardening zone developed underneath the platelet zone during the
erosion process. After the removal of metals from the platelet zone, the steady-state
erosion process begins.
Particle impact velocity has been recognized as the most significant contributing factor for erosion and erosion-corrosion by several investigators. Experimental results
show the erosion rate to be proportional to the particle impact velocity or flow velocity
raised to an exponent. The value of this velocity exponent was reported to be between
0.8 and 8.0 by different investigators depending upon the flow conditions, material
properties, corrosion, and other parameters that contribute to mass loss [8]. Stoker [9]
proposed the erosion rate to be proportional to the cube of the air velocity in single-phase
gas flow. Finnie [10] and Tilly [11] proposed erosion rates to be proportional to the
particle impact velocity, impact angle and wall material properties. Finnie [12] presented
the following empirical equation to predict erosion.
13 ER = cρ V 2 cosθ − 3 sinθ sinθ for θ≤18.5o { w ( 2 ) } 2 (II-1) ⎪⎧cρ (V sinθ) 2 ⎪⎫ 0 = ⎨ w cot θ⎬ for θ >18.5 ⎩⎪ 12σo ⎭⎪
where, ER is the erosion ratio, c is an empirical constant (nominal value for c is
0.50), V is the particle impact velocity, θ is the particle impact angle, ρw is the density of
the wall material, σo is the yield strength of the target wall material. Tilly [13] presented the following erosion model where he expressed erosion in terms of particle impact angle with different coeffcients for ductile and brittle materials.
ER = J cos2 θ + K sin2 θ (II-2)
where, ER = Erosion in cc/kg, θ is the particle impact angle, J and K are the coefficients based on material properties. Tilly proposed J=0 for pure brittle material and K=0 for pure ductile material. Many materials exhibit a combination of brittle and ductile erosion so that the ductile term predominates at small angles and the brittle term predominates at large angles.
Ahlert [14] conducted an experimental investigation of erosion on dry and wetted surfaces at different impingement angles. His experimental results showed that erosion on dry surfaces depends upon the impingement angle with higher erosion rates at a 15-30 degree impingement angle. Erosion behavior on wet surfaces was similar at all impingement angles between 15-60 degrees. Contrary to the lower expected erosion for a wetted specimen than a dry specimen, the wetted specimen showed 2-3 times more mass loss than the dry specimen. Further investigation of the eroded surfaces was conducted using a Scanned Electron Microscope (SEM). The SEM micrographs revealed larger and deeper craters in the wetted specimen surface that extruded more metal. The displaced
14 material from the craters is pushed upwards, piling up at the edge of the crater and eventually breaking apart from the surface. For dry specimens, the craters were comparatively smaller and removed less material from the surface.
Erosion as a result of particles entrained in flow systems adds another dimension to the complexity of erosion prediction. Erosion due to particle impact can be caused by two mechanisms: 1) direct impingement, and 2) random impingement. In geometries like elbows and plug tees that are used to redirect the flow, the entrained particles can cross the flow streamlines. At high velocity, these particles approach the wall with a high
momentum causing direct impingement to the wall. In geometries like straight pipe,
where the mean flow directions do not change, particles approach the wall due to
turbulent fluctuations causing random impingement to the wall. Figure II-1 shows direct impingement in an elbow and random impingement in a straight pipe.
Figure II-1: Direct and Random Impingement in Elbow and Pipe
Generalized models such as the computational fluid dynamics (CFD) based
erosion models [15] which take into account details of flow effects and pipe geometry
require a significant computational effort to simulate the particles’ trajectories,
impingement angles and speeds. Blatt [16] studied the particle velocity close to the target
wall of a pipe with sudden expansion in a two-phase liquid-particle flow and proposed that the flow velocity in the form of the power law influence the erosion rate with
15 exponents of 2.0. Salama [3] proposed an erosion prediction model using mixture density and mixture velocities to account for multiphase flow. The model considers particle diameter, sand production rate, a geometry constant and calculates erosion rate using an
exponent of 2.0 of mixture velocity. McLaury and Shirazi [17] developed a mechanistic
model for predicting the maximum penetration rate in a geometry, such as elbows and
tees, that was based on a CFD-based erosion model. The mechanistic model for
multiphase flow was based on extensive empirical information gathered at The
University of Tulsa, Louisiana State University, Harwell and Det Norske Veritas (DNV)
for erosion in multiphase flow. The model uses a characteristic impact velocity of the
particles while taking into account factors such as pipe geometry and size, sand size and
density, flow velocity, and fluid properties. The model also can be used to determine the
threshold velocity for a corresponding maximum allowable penetration rate.
Shadley [4] proposed a simplified stagnation length model for predicting erosion in
simple geometries. According to the model the maximum penetration rate for a simple
geometry such as elbows and tees the following equation can be used.
WV 1.73 h = F F F F L (II-3) M S P r / D 2 (D / D0)
where, h = penetration rate in mm/year
FM, FS = empirical factors for material and sand sharpness
FP = penetration factor for steel based in 1” pipe diameter, (mm/kg)
Fr/D = penetration factor for long radius elbows
W = sand production rate, (kg/s)
16 VL = characteristic particle impact velocity, (m/s)
D = pipe diameter, (mm)
D0 = 25.4 mm
-5 -0.59 For carbon steel material, Shadley proposed FM = 1.95 x 10 / B (for VL in m/sec) where B is the Brinell hardness factor. Table II-1 shows FM for 1018 Steel and
316 Stainless Steels.
Table II-1. Empirical Material Factor (FM) for Different Materials [4]
Material Type Yield Tensile Brinell Material Factor
Strength Strength Hardness for VL in m/sec
6 (Ksi) (Ksi) (B) (FM x 10 )
1018 90.0 99.5 210 0.833
316 Stainless Steel 35 85 183 0.918
For known pipe diameter, D, and sand production rate, W, the values of FS and FP
are provided in Table II-2 and Table II-3.
Table II-2. Sand Sharpness Factors (FS) for Different Types of Sand [4]
Description of Sharpness Sand Sharpness Factor, FS
Sharp (angular corners) 1.0
Semi-Rounded (rounded corners) 0.53
Rounded (spherical glass beads) 0.20
17 Table II-3. Penetration Factors (FP) for Elbow and Tee Geometries [4]
Reference Stagnation FP (for steel)
Length for 1” Pipe, Lo
Geometry mm inch mm/kg in/lb
90o Elbow 30 1.18 206 3.68
Tee 27 1.06 206 3.68
The penetration factor Fr/D is obtained by Wang [2] using the following equation
⎧ ⎛ 0.4 0.65 ⎞ ⎫ ⎪ ⎜ ρf µf 0.25 ⎟⎛ r ⎞⎪ Fr / D = exp ⎨− 0.1 + 0.015ρf + 0.12 ⎜ − Cstd ⎟⎬ (II-4) ⎜ d 0.3 ⎟ D ⎩⎪ ⎝ p ⎠⎝ ⎠⎭⎪
3 where, ρf is the fluid density in kg/m , µf is the fluid viscosity in Pa-s, dp is the particle
diameter in m, Fr/D is the elbow radius factor for long radius elbow, Cstd is the r/D ratio
for a standard elbow (Cstd=1.5).
The equivalent stagnation length for an elbow and tee geometries were obtained
by flow modeling, erosion testing and particle tracking of sand in gas and liquid phases.
The equivalent stagnation length (L) is a function of pipe diameter and can be calculated
−1 −1.89 0.129 Elbow: L = Lo{}1−1.27 tan (1.01D )+D (II-5)
−1 −2.96 0.247 Tee: L = Lo{}1.35−1.32 tan (1.63D )+D (II-6)
18 The simplified particle tracking model used in this erosion model assumes a one-
dimensional flow field in the stagnation zone that has a linear velocity profile in the
direction of particle motion. For single-phase flow, the initial particle velocity, Vo, can be assumed to be the same as the flowstream velocity which may not be accurate for two- phase flow. Assuming the “equivalent characteristic flowstream velocity” before the particles reach the stagnation zone is known, the characteristic particle impact velocity was calculated using a simplified particle tracking model developed at the Erosion/
Corrosion Research Center [4]. The chracteristic particle impact velocity depends upon a number of parameters such as particle Reynolds number, density and viscosity of fluids, particle size and density. The particle Reynolds number, Reo, is calculated as
ρm Vo dp Reo = (II-7) µm
where, Vo = equivalent flowstream velocity, m/sec
3 ρm = mixture density of fluid in the stagnation zone, kg/m
2 µm = mixture viscosity of fluid in the stagnation zone, pa-s or N-s/m
dp = diameter of particles, m.
A dimensionless parameter, φ, is used that is proportional to the ratio of mass of
fluid displaced to the mass of the impinging particles
L ρ φ = m (II-8) dp ρP where L = equivalent stagnation length, m
3 ρp = density of particles, kg/m .
19 Using the dimensionless parameter φ, particle Reynolds number Reo, and Vo, the
particle impact velocity VL can be determined from Figure II-2.
1.0
ρm Vo dp 0.9 Re = o µ 0.8 m
0.7
0.6 o
/V 0.5 L V 0.4 100 0.3 10 Reo = 1 1000 0.2 10000 0.1 100000 0.0 1E-2 1E-1 1E+0 1E+1 1E+2 1E+3 ⎛ L ⎞⎛ ρ ⎞ Φ = ⎜ ⎟⎜ m ⎟ ⎜ ⎟⎜ ⎟ ⎝ dp ⎠⎝ ρp ⎠
Figure II-2. Effect of Different Factors on Particle Impact Velocity [4]
The equivalent flowstream velocity, Vo, must be specified to calculate the particle
Reynolds number, Reo. For single-phase flow, it is assumed to be the average flow
velocity. For two-phase phase, the following ad hoc equations are used to calculate the
equivalent flowstream velocity.
n n Vo = λL VSL + (1− λL ) VSG (II-9)
0.11 ⎡ VSL ⎤ where, λ = ⎢ ⎥ (II-10) ⎣VSL + VSG ⎦
⎡ ⎤ ⎛ VSG ⎞ n= ⎢1−exp⎜− 0.25 ⎟⎥ (II-11) ⎣ ⎝ VSL ⎠⎦
20 The exponent n is used so that when (VSG/VSL) < 1, Vo = Vm = VSL + VSG.
For a given geometry, material, sand sharpness and sand rate, all the terms in Equation
(II-3) become constant except the characteristic impact velocity, VL and can be written as
1.73 h = KVL . (II-12)
The term VL in the equation represents the characteristic particle impact velocity of particles, which must be deduced by solving a simplified particle tracking equation.
The investigators [17] developed a method for calculating VL, which is obtained through creating a simple model of the stagnation layer representing the pipe geometry. The stagnation zone is a region that the particles must travel through to penetrate and strike the pipe wall for erosion to occur. This approach is graphically displayed in Figure II-3.
The severity of erosion in this zone depends on a series of factors such as fitting geometry, fluid properties and sand properties. It was demonstrated that for elbows with different diameters the stagnation length varies. A simplified particle-tracking model is used to compute the characteristic impact velocity of the particles; the model assumes movement in one direction with linear fluid velocity profile. Initial particle velocity is assumed to be the same as the flowstream velocity, Vo. Validity of this assumption is limited to single-phase flow when there is no-slip between the particles and fluid.
21 Stagnation Equivalent Stagnation Length Zone
L
Particle Initial Position
Tee Stagnation Zone vo
x
Elbow
Figure II-3. Schematic Description of Stagnation Length Model [17]
During this study, a preliminary mechanistic model was developed to calculate the initial particle velocity, Vo to predict erosion in multiphase annular flow [18] while considering the effect of sand distribution in the liquid film and gas core regions in annular flow. The multiphase flow mechanism and corresponding phase characteristic behavior was considered in the model. To account for the sand velocity distribution in annular flow, it was assumed that sand is uniformly distributed in the liquid phase and there is no slip between liquid and sand particles in the flow. The velocities of liquid film and entrained liquid droplets in the gas core were used in calculating the initial particle velocity. The characteristic flowstream velocity (that is assumed to be the same as initial particle velocity) was calculated using a mass weighted average of the flow velocities in
the film and the entrained droplets. The initial particle velocity, Vo, was calculated by the following equation.
Vo = (1 - E)Vfilm + EVd (II-13)
22 where,
E = fraction of liquid entrained in the gas core (mass of liquid in gas core/ total
mass of liquid)
Vfilm= average liquid film velocity, m/sec
Vd = average liquid droplet velocity in gas core, m/sec
The preliminary mechanistic model [17] predictions were compared with available erosion data reported in the literature [3] and showed reasonably good agreement. The preliminary mechanistic model was later extended to slug, churn, and bubble flow regimes considering the sand particle impact velocity and by using an improved entrainment model proposed by Ishii [29]. For slug flow, it was assumed that the sand is uniformly distributed in the liquid phase, and the mass fraction of sand in the liquid slug is equal to the mass fraction of liquid in the liquid slug. The characteristic initial particle velocity (Vo) for slug flow was calculated as
Vo = HLLS x VLLS (II-14) where, HLLS is the liquid holdup in the liquid slug, and VLLS is the liquid velocity of the liquid slug. For bubble and churn flows, the characteristic initial particle velocity was assumed to be the same as mixture velocity as below.
Vo = VSL + VSG (II-15)
The extended preliminary mechanistic model [19] predicted erosion rates in annular, slug, bubble and churn flow regimes were compared with the available literature data [3, 50]. The model predictions also showed favorable agreement with the erosion data reported in the literature for different sand sizes, pipe sizes, geometries, wall materials, and flow regimes.
23 Multiphase Flow and Flow Patterns
A physical understanding of the flow characteristics with more than one phase is much more complex than single-phase as the phases are distributed in different configurations. The reason is that the phases do not uniformly mix and that small-scale interactions between the phases can have a profound effect on the macroscopic properties of the flow [20]. The interface between the phases can be highly unstable, irregular and transient. The interfacial forces between the phases develop different flow configurations or flow patterns in multiphase flow. The flow pattern changes with the change of phase velocities and properties. Another factor that influences the flow pattern is the flow orientation and inclination angle of the pipe. For example, different flow patterns may exist at similar liquid and gas phase velocities for horizontal, vertical or inclined pipes.
Flow configurations have different spatial distributions of the gas-liquid interface, resulting in unique flow characteristics such as entrainment, and different velocity profiles of the phases [21]. Different flow patterns were also observed in horizontal and vertical flows. The major flow patterns observed in horizontal multiphase flow are stratified, slug, annular and dispersed bubble flow as shown in Figure II-4. In vertical flow the major flow patterns observed are annular, churn, slug and bubble flows as shown in Figure II-5.
24 Stratified Flow
Slug Flow
Annular Flow
Dispersed Bubble Flow
Figure II-4. Major Flow Patterns in Horizontal Pipe
Annular Churn Slug Bubble Flow Flow Flow Flow
Figure II-5. Major Flow Patterns in Vertical Pipe
25 Due to the large number of variables and complex nature, a rigorous solution of multiphase flow systems is not possible. Generalized models have been developed to solve multiphase flow problems. The homogeneous model assumes the mixture of the phases as a pseudo single-phase fluid with an average velocity and properties. In the homogeneous model, conservation of mass and momentum equations are solved for the total mass flow rate, and average mixture density and velocity. The limitation of this model is that this model assumes no slippage between the phases and that is true only for dispersed bubble flow. Another approach is the separated flow model where gas and liquid phases are assumed to flow separately. In this model each phase is analyzed using a single-phase flow method based on the hydraulic diameter concepts for each of the phases. The separated flow model is limited to horizontal stratified flow as the phases are usually mixed in two-phase flow. The drift flux model assumes phases to be mixed homogeneously, but allows relative slip between the phases. The two-fluid model is a multiphase model in which both the mass and momentum equations are solved for each phase by considering several physical effects [22].
Flow velocities of the gas and liquid phases greatly influence the particle impact velocity. In two-phase flow, superficial gas and liquid velocities are used in the calculation of particle velocity. The superficial velocity of a phase is the velocity that would occur if only that phase was flowing in the pipe. Therefore, the superficial velocities are the volumetric flow rates per unit area of the pipe as shown in Equation
II-16 and Equation II-17:
Q L VSL = (II-16) A P
26 Q G VSG = (II-17) A P
where, VSL= Superficial Liquid Velocity, ft/sec
VSG = Superficial Gas Velocity, ft/sec
3 QL = Volumetric Liquid Flow Rate (ft / Sec)
3 QG = Volumetric Flow Rate (ft / Sec)
2 Ap = Cross-Sectional Area of the Pipe (ft )
Due to differences in flow behaviors in multiphase flow, the particle impact velocities may be different for different flow regimes. For example, the particle impact velocity in annular flow may depend upon the annular liquid film velocity and gas core velocity. In slug flow, particle impact velocity may depend upon the liquid slug velocity and liquid holdup in the liquid slug. In churn and bubble flows, it may depend upon the superficial liquid and gas velocities. Due to different flow characteristics in different flow regimes, the attempt to develop a single model for all flow regimes may not be practically possible. Therefore, different erosion prediction models will be required for different flow regimes.
Entrainment in Multiphase Flow
Entrainment is the fraction of liquid in the gas core in annular flow and it is defined as the ratio of rate of liquid droplets in the gas phase to the total liquid rate. The difference between liquid holdup and entrainment is that liquid holdup is the ratio of the liquid volumetric flow rate to the total volumetric flow rate. This definition of liquid holdup assumes both phases move at the same velocity with no slippage between the phases which can exist only in homogeneous flow or in dispersed bubble flow with high 27 liquid and low gas flow rates.
In annular flow, entrainment is considered to result from a balance between the rate of atomization of the liquid layer flowing along the pipe wall and the rate of deposition of drops [23]. As the liquid flow rate increases, both atomization and deposition rate decrease. At high gas velocities, droplet turbulence controls the deposition, and at low gas velocities, gravitational settling controls the deposition [24].
The gravitational forces act on the drops resulting in an asymmetric distribution of horizontal flows with higher droplet concentration in the lower half of the pipe. The asymmetry disappears in horizontal flow at higher gas velocities and the entrainment distributions in horizontal and vertical pipes become similar.
In annular flow, accurate prediction of solid particles entrained in the gas and liquid phases is important for erosion prediction. The mechanism that causes droplet entrainment in the gas core can also cause solid particles to be entrained in the gas core.
The entrained sand particles in the gas core impact the pipe wall at high velocity causing erosion damage. Although a number of empirical entrainment correlations are available in the literature, the accuracy is limited to certain flow conditions. Wallis [25] proposed an entrainment correlation using superficial gas velocity, fluid properties and surface tension. The correlation did not consider the effect of liquid rate and therefore under- predicted entrainment at higher liquid velocities. Asali, Leman and Hanratty [26] proposed a correlation to calculate entrainment. The correlation requires a liquid film thickness as an input parameter that is usually unknown in most cases and therefore can not be used effectively. Olieman [27] developed a correlation using seven different input parameters and their corresponding exponents using Harwell well data reported by
28 Whalley [28]. The parameter estimates were calculated at different Reynolds numbers.
The correlation provided good entrainment results but the accuracy was limited to flow conditions of the data being used. Ishii [29] stated that for liquid Reynolds numbers larger than 160 (ReL > 160), the droplet entrainment mechanism is due to the shearing-off of roll wave crests produced by highly turbulent gas flow as shown in Figure II-6.
VFilm
Deposition
Entrained droplets Roll wave
VGas
Figure II-6 Roll Wave Mechanism of Entrainment Formation in Annular Flow [29]
The semi-empirical correlation proposed by Ishii appears to provide accurate entrainment prediction over a wide range of flow conditions. The entrainment model uses a form of dimensionless Weber number and liquid Reynolds number as shown in
Equations II-18 through II-20.
E = tanh(7.25x10−7 We1.25 Re0.25) F (II-18)
2 1/ 3 ρG JG D ⎛ ρG −ρF ⎞ We= ⎜ ⎟ (II-19) σ ⎝ ρG ⎠
29 ρF JF D ReF = (II-20) µF where,
E = Entrainment Fraction
We = Weber Number
ReF = Liquid Reynolds number
3 ρF = Liquid phase density or film density (lb/ft )
3 ρG =Gas phase density (lb/ft )
D = Hydraulic diameter (inches)
JG = Volumetric flux of gas or superficial gas velocity (ft/sec)
JF = Volumetric flux of liquid or superficial liquid velocity (ft/sec)
Sand Distribution in Multiphase Flow
The presence of sand in multiphase flow adds to the complexity of the erosion problem. Therefore, the sand entrainment and distribution patterns need to be considered in the mechanistic model. Santos [30] measured sand distribution in multiphase flow using an intrusive probe of 4.7 mm (0.185 inch) diameter inside a one-inch pipe with air and water annular flow. Sand and water samples were collected from five different uniformly spaced locations across the pipe at superficial gas velocities of 25, 50, 75 and
100 ft/sec and superficial liquid velocity of 1.0 ft/sec in both horizontal and vertical pipes. The probe was placed at 900 mm upstream of the erosion test cell to minimize flow disturbances to the erosion specimen. The sand concentration in the collected sample was measured by weighing the wet sample and then after drying the sample. The 30 percentage of sand was calculated by dividing the amount of sand collected by the total sand throughput during the experiment. The percentage of liquid was calculated by dividing the amount of liquid collected by the total liquid throughput during the experiment. The percentage of sand in water was nearly the same in both the gas core and liquid film region in vertical pipe. In the horizontal pipe, a higher amount of sand in water was measured at the bottom section of the pipe where a thicker liquid film is present.
Selmer-Olsen [31] conducted similar sand distribution experiments in a 26.6 mm pipe and collected sand and water samples using an intrusive probe. Experiments were conducted at superficial gas velocity of 31.0 m/sec and superficial liquid velocity of 0.9 m/sec using gaseous nitrogen and water with 200 µm sand. Their experimental results showed similar sand and liquid concentrations in the gas core and annular liquid film region for vertical annular flow.
Annular Film Thickness and Film Velocity
In annular flow, a fraction of the liquid flows along the pipe wall as a thin liquid film and the remaining liquid flows in the gas core as entrainment. Understanding the liquid film formation process, film thickness, and velocity is essential in development of the erosion prediction model in annular flow.
The interface between the circumferential annular liquid film and the gas core region is always under different forms of pressure waves developing from the turbulent forces. In most cases, the interface is very unstable and wavy. The annular liquid film can be divided into a continuous liquid layer adjacent to the wall and a wavy disturbed
31 layer [32]. The average film thickness is the distance from the wall to a point above the continuous layer that includes approximately half of the thickness of the disturbed layer.
Film thickness decreases with increasing gas flow rates and increases with increasing liquid flow rate. The film thickness distribution is nearly uniform in vertical annular flow, whereas in horizontal flow the film is asymmetric due to gravitational forces. At very high gas velocities, the liquid film becomes very thin, unstable, discontinuous and dissipates into droplets resulting in mist flow.
Henstock [33] developed an empirical correlation for film thickness in vertical upward and downward annular air-water flows. The non-dimensional film thickness was shown to be a function of the film liquid Reynolds number. Leman [34] performed experimental measurements of film thickness using conductance probes with 2.0 and 4.6 centistokes liquids and air. The experimental film thickness measurements agreed with the Henstock film thickness measurement.
Fukano [35] analyzed the liquid film formation mechanism in horizontal annular flow using direct numerical simulation (DNS). The analysis demonstrated that the liquid is transferred from the bottom of the pipe in the circumferential direction as a liquid film by pumping action of the disturbance waves. The pressure gradient within the disturbance waves in the circumferential direction effects the formation of the asymmetric shape of the film.
Gonzales [36] conducted experimental investigation to determine the effect of pipe inclination angle on the annular film thickness distribution. Film thicknesses were measured at eight different locations around the circumference of the pipe using conductance probes with the pipe at vertical 90o, 75o, 60o and 45o inclination angles. For
32 vertical upward flow, the film thickness was nearly uniform at 60 ft/sec superficial gas velocity and superficial liquid velocities of 0.020 to 0.20 ft/sec. The film thickness increased with the increased liquid velocity for the same gas velocity. As the inclination angle of the pipe deviated from vertical position, the film thickness increased at the bottom and decreased at the top of the pipe. At a 60o-inclination angle, the film thickness at the bottom of the pipe was approximately 7 times more than the film thickness at the top of the pipe. The film thickness ratio increased from 7 to 13 as the inclination angle changed from 60o to 45o. Flores [37] experimentally demonstrated that the secondary flows in the gas core were the dominant mechanism in controlling the film thickness in horizontal annular flow. These secondary flows consisted of two counter-rotating vortices that sheared a liquid film up the wall of the pipe.
Ansari [38] presented a procedure to calculate the dimensionless film thickness to pipe diameter ratio. The film thickness and corresponding film velocities were calculated using a mass balance of liquid between the film and the droplets in the gas core. Selmer-
Olsen [31] measured film thickness of vertical, annual flow in a 26.6-mm diameter pipe using an ultrasonic thickness measuring method that was capable of measuring film thicknesses below 0.25 mm. He reported that at a superficial gas velocity of 14.2 m/sec, the film thickness increased as the liquid velocity increased from 0.5 – 2.2 m/sec.
Zabaras and Dukler [39] studied the film flow rate by measuring the instantaneous local film thickness in a 50.8 mm diameter vertical pipe with air-water annular flow. In their experiment, they placed two 0.05-inch diameter platinum wires 2.5 mm apart along the diameter of the pipe. The film thickness was obtained by measuring the conductivity of the wires. The experimental results showed that the film thickness increased with
33 increased liquid rate and decreased with increased gas flow rate. They also measured the fluctuation of the annular film thickness and observed that the film thickness can fluctuate as much as 50% of the average thickness.
Weidong [40] conducted experimental measurements of film thickness in a 40 mm diameter pipe using 5 parallel conductance probes at 5 circumferential positions.
The film thickness measurements were taken using an ultrasonic probe at superficial gas velocities of 33.65 and 33.85 m/sec and superficial liquid velocities of 0.044 and 0.057 m/sec. Their experimental results showed similar trends as obtained by other investigators; larger film thickness was measured at higher liquid rates with same gas rate.
Adsani [41] measured film velocity in vertical annular flow using two conductance probes that measured the conductance of salt-water solution injected upstream of these probes. As the salt-water solutions passed the probes, conductance spikes were observed. The film velocities were calculated at different liquid and gas velocities by measuring the time between the two spikes. The experimental film velocity measurements agreed well with the calculated film velocity using the method presented by Ansari [41].
Droplet Velocity in Annular Flow
Liquid droplets entrained in the gas core may contain solid particles that travel at a higher velocity as compared to that of particles in the annular film that move at a lower velocity. The velocity of liquid droplets will be slightly less than the gas core velocity due to slippage between the droplets and the gas velocities. Therefore, a good
34 understanding of the droplet velocities and an accurate calculation of the droplet velocity are essential in predicting erosion in annular flow. In absence of available experimental data for sand velocity, the sand particle velocity is assumed to be similar to the droplet velocity.
Lopes [42] conducted experiments in air-water annular flow in a 51-mm diameter vertical pipe conducting simultaneous measurements of drop size, droplet axial and radial velocities. The drop sizes had a strong dependence on the superficial gas velocity and smaller dependence on superficial liquid velocity. As the gas velocities increase, the drop sizes decrease.
Fore and Dukler [43] measured the droplet size and velocity distribution in a 50.8 mm vertical pipe with air and liquids of different viscosity. They observed that the droplet size increases with increased liquid rate and viscosity for the same gas velocity.
Experimental results showed a higher slip ratio exists at higher gas and liquid velocities.
At superficial gas velocities between 18-33 m/sec and at liquid Reynolds number (ReL) of
750-3000, the measured slip ratio at the centerline of the pipe was 0.77-0.82. The average droplet velocity at the centerline of the pipe was approximately 80% of the local gas velocity. A simplified procedure to calculate the average droplet velocity has been developed during this study considering the gas core velocity and slip between the droplets and gas velocities.
Characteristic Thickness Loss Profile in Elbow
Selmer-Olsen [28] performed thickness loss measurements of a 26.6 mm, 316L stainless steel elbow with r/D ratio of 3.0 in multiphase vertical annular flow with 200
35 micron quartz particles of 1.5% volume concentration at two different flow conditions.
Table II-4 shows the experimental conditions. Wall thickness was measured at 14 different locations along the length of the elbow before and after each test using both ultrasonic and precision micrometers. One experiment was reported for test condition 1 and 3 experiments were reported for test condition 2.
Table II-4: Flow conditions of Selmer-Olsen [31] Experimental Data
Description Test condition 1 Test Condition 2
Pipe Diameter 33.4 mm 33.4 mm
Turning radius ratio (r/D) 3.0 3.0
Superficial Liquid Velocity 0.034 m/sec 0.9 m/sec
Superficial Gas Velocity 29 m/sec 29 m/sec
Liquid Property Distilled H2O with 1% Distilled H2O with NaCl 1% NaCl
Gas Property Nitrogen CO2 Pressure 1.5 barg 10 barg
Particle 200 µm Quartz 200 µm Quartz
Elbow Material 316L Stainless Steel 316L Stainless Steel
Solid Particle Volume 1.5% 1.5% Concentration
Flow configuration Annular Annular
Figures II-7 and II-8 show the experimental results of Selmer-Olsen thickness loss measurements. Although the experiments were repeated multiple times, the data shows a high degree of dispersion. Figure II-7 shows the maximum thickness loss for VSG = 29
O m/sec (95.15 ft/sec) and VSL = 0.034 m/sec (0.11 ft/sec) at approximately 35 from the inlet of the elbow that is approximately 5 degrees downstream from the intersection point 36 of the centerline of inlet flow and outer wall of the elbow. Figure II-7 shows the maximum thickness loss for VSG = 29 m/sec (95.15 ft/sec) and VSL = 0.9 m/sec (2.95 ft/sec) at approximately 40o from the inlet of the elbow that is approximately 10 degrees downstream from the intersection point of the centerline of inlet flow and outer wall of the elbow. The test was repeated three times and shows a high degree of dispersion of the data.
Vsg=95.15 ft/sec, Vsl=0.11 ft/sec 110 Max. Erosion
90
70 30
50
30
Thickness loss in microns in loss Thickness 10
-10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Location in Elbow-Degrees
Figure II-7. Selmer-Olsen [31] Measurement (VSG= 95.15 ft/sec, VSL =0.11 ft/sec).
37 290 Max. Erosion Total:Vsg=95.15,Vsl=2.95 ft/sec Vsg=95.15,Vsl=2.95 ft/sec 240 Vsg=95.15,Vsl=2.95 t/sec Vsg=95.15, Vsl=2.95 ft/sec
190 30O
140
90 Thickness loss in microns 40
-10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Location in Elbow-Degrees
Figure II-8. Selmer-Olsen [31] Measurement (VSG = 95.15 ft/sec, VSL= 2.95 ft/sec)
Eyler [44] studied the erosion behavior of an elbow installed in a pneumatic flow loop with air/sand transport system. Thickness loss measurements were taken at 19 different locations along the length of the elbow in approximately 5 degree increments from the inlet. Table II-5 shows the test conditions of the experiment. Thickness loss measurements were performed using a precision micrometer and an ultrasonic thickness gage. Each experiment was performed using 600 lbs of sand to measure the thickness loss at the outer wall of the elbow. Figure II-9 shows the experimental results for 8 different erosion experiments and their average values. A high degree of scatter was observed among the test data. The maximum erosion was observed at 35 degrees from the inlet of the elbow. The centerline of inlet flow intersects the outer wall of the elbow at approximately 30 degrees. Therefore the location of maximum erosion was approximately 5 degrees downstream from the centerline of the inlet flow.
38 Table II-5: Flow Condition of Eyler [44] Experimental Erosion Data
Description Test condition 1
Pipe Diameter 41 mm
Turning radius ratio (r/D) 3.25
Gas Velocity 25.24 m/sec
Gas Property Air
Particle 100 µm Sand
Elbow Material Carbon Steel
Particle/ Fluid mass ratio 0.75%
Flow configuration Vertical
0.040 Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 0.035 Test 7 Test 8 Average-Eyler
0.030 Max Erosion
0.025
0.020
0.015 30o
Erosion Rate mils/lbs in 0.010
0.005
0.000 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 Location in Elbow- Degrees
Figure II-9. Erosion Profile in Outer Wall of an Elbow [44].
39 CHAPTER III
EXPERIMENTAL FACILITY AND EROSION TEST PROCEDURE
Erosion experiments were conducted in both single and multiphase flow conditions in different stages by measuring the mass loss and the thickness loss of elbow specimen. In stage one, erosion experiments were conducted by measuring mass loss of an elbow specimen to determine the average erosion. The final stages of erosion experiments were conducted to measure the thickness loss of an elbow specimen at 10 different locations along the length of the specimen. The objective of the thickness loss measurement experiment was to determine the characteristic erosion profile of the specimen surface and determine the location of maximum erosion. The test section was designed and constructed with sufficient length for multiphase flow to become fully developed. Ishii and Mishima [29] proposed a correlation to calculate the minimum axial distance required for the entrainment to reach an equilibrium condition or the multiphase flow to become fully developed.
J* z ≥ 600D G (III-1) Ref
J J* = G (III-2) G 1/ 4 ⎡ 2 / 3 ⎤ σ g∆ρ ⎛ ρG ⎞ ⎢ ⎜ ⎟ ⎥ ⎢ 2 ∆ρ ⎥ ⎣ ρG ⎝ ⎠ ⎦
40 where, z = Axial distance from the inlet, ft
D = Hydraulic diameter, ft
* J G= Dimensionless gas flux
JG = Volumetric gas flux (superficial gas velocity), ft/sec
Ref = Liquid Reynolds number (ρFDVFilm / µFilm)
3 ρG = Gas density (lb/ ft )
∆ρ =Density difference between gas and liquid phases
σ = Surface tension (lb/ft)
g = Acceleration due to gravity (ft/sec2)
Oliemen [24] reported 728 different test cases from Harwell data bank for entrainment measurement. The pipe lengths used in these experiments were between
170-900 times the diameter of the pipe. Using the above correlation and previous experimental set-ups reported in the literature, a multiphase erosion test section was constructed to have greater than 150 pipe diameters upstream of the test section
(L/D>150). This ensures that the entrainment reaches the equilibrium condition at higher gas velocity and the flow becomes fully developed.
For the single-phase one-inch erosion test section, the length of the straight pipe section upstream of the specimen is 4 feet or approximately 50 times the pipe diameter
(L/D ≈ 50) as the single-phase flow becomes fully developed at L/D < 50. To compare single-phase erosion results with the multiphase erosion data, single-phase erosion tests were also conducted using the multiphase test section.
41 Description of the Single-Phase Flow Loop and Test Section (L/D ≈ 50)
A one-inch single-phase test section was used to conduct erosion experiments.
Figure III-1 shows a photograph and Figure III-2 shows a schematic of the erosion test section. The flow loop consists of two Ingersoll-Rand gas compressors model T-30 capable of delivering 200 ACFM flow at 150 psig, one ABB TRI-WIRL vortex flow meter, two pressure gages and approximately 18 feet of one-inch pipe. Sand is injected into the gas stream using a vibratory feeder and nozzle as shown in Figure III-1.
Erosion Test Cell
Pressure
Gage, P2
Vibratory Sand Injection Feeder
Pressure
Gage, P1
Flow Meter Flow From Compressor
Figure III-1. Photograph of the Single-Phase Erosion Test Section
Figure III-2. Schematic of the Single-Phase Erosion Test Section
42 By adjusting the spring tension and slope of the vibratory feeder the sand feed rate to the test section was controlled. The gas-sand mixture then flows from the sand injection point to the erosion test specimen holder through a one-inch clear fiberglass pipe. After the test sections, the sand is collected in a filter for disposal. The maximum attainable gas velocity in the test section is approximately 230 ft/sec for single-phase flow. The test section can be rotated by changing the bolts of the pipe flange that connect the horizontal pipe sections. By rotating the pipe, the flow orientation of the test cell can be changed from horizontal to vertical. This allows erosion testing in both horizontal and vertical orientations to evaluate the effect of flow orientation on erosion. For example, when the flow upstream to the specimen is vertical and the downstream flow is horizontal the test was identified as a vertical test. The upstream flow direction towards the elbow specimen is used in defining the flow orientation.
Description of Multiphase Flow Loop and Test Section (L/D ≈ 160)
Two different one-inch multiphase test sections were used to conduct erosion experiments. The major difference between the two loops is the flow development length upstream of the erosion test cell and the test section pressures. The ratio between the length of the straight pipe section (L) upstream of the elbow and the diameter of the pipe
(D) is used to define the L/D ratio of the test section. Initial erosion tests were performed in the test section with L/D ratio of 70 with test section pressure of 30 psig. Realizing the shortcomings and inconsistencies of erosion data from this test section, another one-inch multiphase test section was constructed with L/D ratio of 160. During this research, most of the multiphase erosion tests were conducted in the L/D ≈ 160 test section. The erosion
43 test data of L/D ≈ 70 test section was presented to compare the effect of L/D on erosion results.
Figure III-3 shows a schematic of the flow loop with L/D ≈160. The flow loop consists of two Ingersoll-Rand gas compressors model T-30 capable of delivering 200
ACFM flow at 170 psi, one 20 gpm pump, one 8 gallon slurry tank, one 100 gallon slurry tank, one positive displacement pneumatic pump, one ABB TRI-WIRL vortex flow meter, two pressure gauges, one cyclone separator, one filter and approximately 40 feet of one-inch schedule 40 and fiberglass pipes. Sand and liquids are mixed in the slurry tank and injected into the gas stream. The sand-water mixture from the 8-gallon tank is injected in the test section through a 0.188-inch diameter nozzle and by pressurizing the tank with a pressure slightly higher than the test section pressure. A pneumatically driven positive displacement pump is used to inject the sand-water mixture from the 100-gallon tank to the test section. The gas-liquid-sand mixture then flows through the one-inch pipe section to the erosion test sections. The one-inch transparent section of fiberglass pipe is used upstream of the erosion test specimens for multiphase flow pattern visualization. After the test sections, the mixture flows through a cyclone separator where the gas-liquid and sand are separated. After discharging the liquid-sand mixture from the bottom of the cyclone separator, the remaining gas-liquid-sand mixture then flows through a filter where the sand is separated and the liquid flows to a large water tank. The maximum attainable gas velocity in the test section is 150 ft/sec for single- phase flow and approximately 115 ft/sec for two-phase flow.
44 Cyclone Filter Separator
Vertical Erosion Specimen Slurry tank
Pressure Gage P2 4.12 m
Water tank Hori zontal Erosion Drain Specimen 4.0 m
Pressure Gage P1 p Flowmeter
Compressors
Figure III-3. Schematic of the One-inch Multiphase Flow Loop
Two different erosion specimens were used concurrently during the test. One placed downstream of the horizontal pipe section and the other placed downstream of the vertical pipe section. The erosion specimens were placed inside a test cell. The flow development length for the horizontal pipe section is 4.0 meters (13.12 feet) and the length of the pipe upstream of the vertical specimen is 4.12 meters (13.50 feet).
Therefore the L/D ratio is approximately 160 for both horizontal and vertical test sections and the test section pressure was approximately 9-26 psig (1.4 barg) depending on the flow condition.
45 Figure III-4 shows a photograph of the sand and water injection to the multiphase test section from the smaller 8-gallon slurry tank. This tank was used to conduct erosion tests at a superficial liquid velocity of 0.1 ft/sec. The sand-water flow rate to the test section was controlled with a ball valve downstream of the injection nozzle. For erosion tests at a liquid velocity of 1.0 ft/sec, a larger 100 gallon tank was used to mix the sand and water. Figure III-5 is a photograph of the multiphase flow loop showing the horizontal and vertical erosion test cells and the pressure gage (P2) that was used to determine the test section pressure and to calculate the velocity of gas in the test cells.
8 Gallon Slurry Tank
Sand + Water Injection
Gas Flow
Figure III-4. Sand Injection in Multiphase Test Section from Slurry Tank
46
Vertical Erosion Specimen
13.50 feet
Pressure Gage, P2
Horizontal Erosion Specimen
Figure III-5. Horizontal and Vertical Test Cells in Multiphase Flow Loop
The pressure gage P1 is located approximately 12 inches upstream of the flow meter and P2 is located between the horizontal and vertical test cells as shown in Figure
III-5. The flow velocity was calculated by using the ACFM reading from the flow meter and P1 and P2 from the pressure gages using mass balance (assuming constant temperature):
* * m1 = m2 (III-3)
ρ1Q1 = ρ2Q2 (III-4)
47 ⎡ ⎤ ρ1 ⎡P1a ⎤ P1g +14.7 Q2 = Q1 = Q1 ⎢ ⎥ =Q1 ⎢ ⎥ (III-5) ρ2 ⎣P2a ⎦ ⎣⎢ P2g +14.7 ⎦⎥ where, m* = mass flow rate (lbs/sec)
3 ρ1, ρ2 = Densities at location 1 and 2 (lb/ft )
P1a, P2a = Pressure at location 1 and 2 (psia)
P1g, P2g = Pressure at location 1 and 2 (psig)
Q1, Q2 = Volumetric flow rate (CFM)
Two different slurry tanks (8 gallon, 100 gallon) were used to premix the sand and water that were injected in the test section. Before the experiment, the slurry tank was filled with predetermined amount of water. Sand was weighed and slowly mixed in the water to maintain the required sand concentration of 2%. Electric motor driven stirrers were used in both tanks to assure mixing of sand and water during the test. The
8-gallon slurry tank was used during the experiment with a superficial liquid rate of 0.10 ft/sec, and the 100-gallon slurry tank was used during the tests with a superficial liquid rate of 1.0 ft/sec. The liquid velocity was calculated by using a stop watch recording the time to empty a volume of water-sand mixture. During the experiments, the 8-gallon tank was pressurized to approximately 30 psig to assure continuous and nearly homogeneous sand-water injection to the test section. The 100-gallon tank was open to atmosphere that required a pneumatic positive displacement pump to inject sand-water mixture in the test section. Detail description of the multiphase erosion test procedure is provided in Appendix B. Description of the test equipment is provided in Appendix C.
A photograph of the erosion test cell with the elbow specimen is shown in Figure
III-6. The test cell is made of two halves of PVC. A 90o-elbow specimen of ¼ inch by
¼ inch cross-section is placed inside the test cell that simulates the outer wall of a one- 48 inch elbow with r/D ratio of 1.5.
Test Cell
Erosion Specimen
Figure III-6. Photograph of Erosion Specimen in the Horizontal Test Cell
Experimental Procedure for Thickness Loss in Elbow
To prevent localized erosion damage, it is important to understand the characteristic erosion profile in an elbow. A limited number of studies found in the literature provide information about the location of maximum erosion in elbows in single- phase or multiphase flows. Experiments were conducted to determine the maximum thickness loss in elbows for both single and multiphase flows. Aluminum elbow specimens were used to gain more accurate thickness loss measurements due to lower density of Aluminum. Figure III-7 shows the location of scratches on the elbow specimen in degrees from inlet to outlet.
Before making the scratches, the specimen surface was carefully polished using
300, 400 and 600 grit sandpapers and the initial surface roughness and scratch depths were measured with the profilometer. Making the scratches creates burrs at both sides of
49 the scratches. These burrs were also polished using 600 grit sand papers so that the specimen surface adjacent to the scratch shows a smooth profile free of burrs.
0.5D
90o
70
62.5
55 45
35 27.5 20 10 0 -0.5D
Figure III-7. Thickness Loss Measurement Locations in the Elbow Specimen
Two scratches were made at 12 different locations on the elbow specimen surface in an X or V-shape configuration as shown in Figure III-8. The depth of the scratches and the relative distances between the scratches were measured using a profilometer before and after each erosion test. Single-phase thickness loss erosion experiment was conducted at 112-ft/sec-gas velocity in vertical flow. In multiphase flow, thickness loss erosion experiments were conducted at superficial gas velocities of 110, 90, 62, and 32 ft/sec and superficial liquid velocities of 0.1 ft/sec and 1.0 ft/sec in horizontal and vertical configurations. The location and magnitude of maximum thickness loss in the elbow specimen was determined from the thickness loss measurement.
50 Elbow Specimen
Primary Scratch
Secondary Scratch
Figure III-8. Scratches in the Elbow Specimen Used for Erosion Measurement.
A Surtronic 3P profilometer was used to measure the depth of the scratches and the relative distance between the scratches before and after each test. Figure III-9 shows the profilometer used in measuring the depth of the scratches in the elbow specimen.
The profilometer has two parts: the battery-operated display traverse unit and the pick-up.
The display units contain a drive motor, which traverses the pick-up across the elbow specimen surface with scratches. The measuring stroke starts from the extreme outward position, and at the end of the measurement, the pick-up returns to the initial position.
The traverse length was selected to be less than the width of the specimen so that the pick-up did not travel to the end of the specimen to avoid an error in measurement. The display traverse unit was mounted on a wooden block and the elbow specimen was mounted on a specimen holder for proper control of the relative vertical distance between
51 the pick-up and the elbow specimen surface during scratch depth measurements.
The pick-up is a variable reluctance type transducer that is supported on the surface to be measured by a red skid, a curved support projecting from the underside of the pick-up near the stylus. As the pick-up traverses across the surface, movements of the diamond stylus relative to the skid are detected and converted to a proportional electrical signal.
Elbow Specimen Traverse Direction Holder
Surtronic 3P Surtronic 3P Profilometer Pick-up Display Unit
Figure III-9. Scratch Measurement of Elbow Specimen Using Profilometer
The radius of curvature of the skid is much greater than the roughness spacing, so it rides across the surface without being affected by the roughness of the surface providing a datum representing the surface profile and scratch depth relative to the surface. The stylus tip radius is 10 microns and it can measure scratch depths of up to
400 microns peak-to-peak. The measurement accuracy of the stylus is ± 2 % of full scale. During scratch depth measurements, the pick-up was adjusted so that it is parallel
52 to the elbow specimen surface being measured to ensure that the stylus records the depth of the scratch accurately.
53 CHAPTER IV
EXPERIMENTAL EROSION RESULTS FOR SINGLE-PHASE FLOW
Erosion experiments were conducted in three different stages in single-phase flow using mass loss and thickness loss measurement methods. In stage I, mass loss of
316 stainless steel elbow specimens were recorded in the single-phase test section with
L/D ≈ 50. In stage II, mass loss measurements of 316 stainless steel specimen were recorded using the multiphase test section with L/D ≈ 160. The single-phase and the multiphase test sections are described in Chapter III of this dissertation. The multiphase test section had two different test cells compared to one test cell in the single-phase test section. In the single-phase test section, sand was injected to the one-inch pipe of the test section using a 0.125 inch diameter nozzle that flowed to the horizontal test cell impacting the specimen. In the multiphase test section, the sand-air mixture was discharged from the horizontal test cell in the vertically upward direction and impacted the elbow specimen in the vertical test cell. The elbow specimen had a cross-section of
0.25” by 0.25” that matched the outer wall of a standard one-inch elbow (r/D = 1.5).
The elbow specimens were hardness tested using a Rockwell hardness tester.
Each specimen was hardness tested three times and the average hardness values are shown in Figure IV-1. The hardness range of all three specimens was between 228-233
BHN that is well within the required hardness range of 316 Stainless steel material.
54 240
230
220
210 Average Brinell HardnessAverage (BHN)
200 478 Elbow Specimen No.
Figure IV-1. Average Hardness of 316L Stainless Steel Elbow Specimen.
Two different sand samples were analyzed using different sizes of sieve and weighing the amount of sand on each sieve. Figure IV-2 shows the sand size distribution of Oklahoma no. 1 sand used in the test with average sand size of approximately 150 µm.
Analysis of both sand samples shows similar sand distribution.
45%
40% Sample one Sample two 35%
30%
25%
20%
Percent Sand Percent 15%
10%
5%
0% <53 53-125 126-150 151-177 178-212 213-250 >250 Sand Size in micron
Figure IV-2. Sand Size Distribution of Oklahoma no. 1 Sand
55 To study the effect of erosion at different flow orientation, erosion tests were conducted at different orientations. For example with vertical inlet flow to the specimen and horizontal outlet flow from the specimen, the test was identified as vertical (Ver) test as shown on the left section of Figure IV-3. The horizontal to vertical (Hor) orientation is shown on the right part of Figure IV-3. In stage I of single-phase erosion tests, erosion tests were also conducted with horizontal flows both upstream and downstream of the elbow that was designated as Hor-Hor test in Table IV-2.
Figure IV-3. Test Cells in Vertical (Left) and Horizontal (Right) Orientations.
Stage I Erosion Test: Mass Loss Measurement in the L/D ≈ 50 Test Section
Mass loss measurements of the elbow specimen were recorded in horizontal to horizontal and vertical to horizontal orientations at 105, 112 and 228 ft/sec gas velocities using the single-phase test section with L/D ≈ 50. During each test 2000 grams of sand was injected in the test section for each test condition using a vibratory feeder and sand injection nozzle. The readings from the pressure gauges located downstream of the sand injection nozzle and immediately before the test section were used to calculate the flow
56 velocity. Table IV-1 shows the erosion test conditions for stage I single-phase erosion tests. The sand volume concentration was calculated by dividing the sand throughput by gas velocity and time required to inject the sand. Appendix A describes the sand volume concentration calculation procedure for single-phase flow.
Table IV-1: Stage I -Single-Phase Erosion Test Conditions Pipe Diameter (inch) 1.0 1.0 1.0
Mass of Sand Used (lbs) 4.408 4.408 4.408
Test Time (minute) 60 60 60
Particle Diameter (µm) 150 150 150
Fluid Velocity (ft/sec) 105 112 228-230
Elbow Specimen Material 316 SS 316 SS 316 SS
Calculated Sand Volume 0.014 0.013 0.006 Concentration (%) *
* Refer to Appendix A for sand volume concentration calculation procedure
The elbow specimen was weighed three times before and after each test and the average weight of the specimen was used to determine the mass loss. Table IV-2 shows the average mass loss, erosion ratio and calculated maximum penetration rates at 105,
112, and 228-230 ft/sec air velocities in different orientations. Appendix A describes the penetration rate and sand volume concentration calculation procedures. The maximum penetration rate was calculated by multiplying the penetration rate with the maximum to average thickness loss ratio determined from thickness loss measurement experiments.
57 Table IV-2: Single-Phase Erosion Test Results at Different Orientations (L/D ≈ 50).
Flow Air Pressure at Test Sand Mass Erosion Calc. Orientation Velocity Flow Section Throughput Loss Ratio Max. Pen.
(ft/sec) meter P1 Pressure, (grams) (grams) (grams/ Rate *
(Psig) P2 (Psig) grams) (mils/lb)
Hor-Hor 105 28 2 2000 0.0093 4.65E-6 5.23E-2
Hor-Hor 112 31 3 2000 0.0211 1.06E-5 1.19E-1
Hor-Hor 228 60 5 2000 0.1024 5.12E-5 5.76E-1
Vertical 105 28 2 2000 0.0103 5.15E-6 5.79E-2
Vertical 111 30 3 2000 0.0228 1.14E-5 1.28E-1
Vertical 230 62 6 2000 0.1554 7.77E-5 8.75E-1
* Refer to Appendix A for penetration rate calculation procedure
Figure IV-4 shows the Stage I erosion experimental results with higher mass loss in the vertical specimen. The difference in mass loss between the horizontal and vertical specimens was higher at higher gas velocities. There was no significant difference between horizontal and vertical specimens although vertical specimens consistently showed higher mass loss. The difference was approximately 10% at 105 ft/sec gas velocity and was approximately 52% at 228 ft/sec gas velocity. The mass loss increased by a factor of 11-15 as the gas velocity increased from 105 to 228 ft/sec. The rate of increase in mass loss was also higher in vertical to horizontal orientation with increased gas velocity.
58 1.6E-01 Hor.to Hor Vert. to Hor 1.2E-01
Vert-Hor. 8.0E-02 Flow
MassLoss in Grams 4.0E-02
0.0E+00 105 112 228 Gas Velocity (ft/sec)
Figure IV-4. Single-Phase Erosion Test Results in Different Orientation (L/D ≈ 50)
Stage II Erosion Test: Mass Loss Measurements in Multiphase Test Section
The objectives of the single-phase (air) erosion test using the multiphase flow section with L/D ≈ 160 are:
1. Conduct experiment in horizontal to vertical orientation as the single-phase
flow loop with L/D ≈ 50 did not allow erosion testing in horizontal and
vertical test cells at the same time.
2. Investigate the effect of test section pressure on erosion as the pressure in the
single-phase test section was higher compared to the multiphase test section.
3. Evaluate the effect of flow development length (L/D) on erosion in single-
phase flow.
4. Compare the differences in erosion in single and multiphase flows using the
same test section that will eliminate the effect of test section.
59 Sand was injected in the test section using a nozzle, ball valve and a 2 inch
diameter, 4 feet long transparent sand injection tubes as shown in Figure IV-5.
Pneumatic pressure was applied at the top of the sand injection tube and the tube
was connected to the test section at the bottom using a ball valve and nozzle. The
ball valve and the sand tube pressure controlled the sand flow rate to the test
section. The mass flow rate of sand was measured using a stop watch and
graduation in the sand injection tube.
Figure IV-5. Erosion Test with Air and Sand in the Multiphase Test Section
The injected sand traveled horizontally with the flowing gas to the horizontal test cell impacting the elbow specimen. The air-sand mixture then flows upward towards the vertical test cell where it impacts the elbow specimen. The sand-air mixture then flows to
60 the cyclone separator and a filter where the sand is separated from air. Two pressure gages, one located near the flow meter and the other one between the horizontal and vertical test cells, and a flow meter reading (ACFM) were used to calculate the gas velocity at the test section.
Table IV-3: Single-Phase Erosion Test Conditions (Multiphase Test Section) Pipe Diameter, meter (inch) 0.0254 (1.0) 0.0254 (1.0) 0.0254 (1.0)
Mass of Sand Used for Each Test, kg (lbs) 1.0 (2.2) 1.0 (2.2) 1.0 (2.2)
Test Time (minute) 30 30 30
Particle Diameter (µm) 150 150 150
Fluid Velocity, m/sec (ft/sec) 18.9 (62) 27.4 (90) 34.1 (112)
Elbow Specimen Material 316 SS 316 SS 316 SS
Sand Volume Concentration (%) 0.024 0.016 0.013
Erosion tests were conducted at 62, 90 and 112 ft/sec air velocities using 150 µm
Oklahoma no. 1 sand. Table IV-3 shows the single-phase erosion test conditions using the multiphase test section. The material of the elbow specimen was 316 stainless steel in this test. During each test 1000 grams (2.2 lbs) of sand was used and each test condition was repeated three times. The sand was injected in 30 minutes to maintain a sand injection rate of 33 grams per minute for each test. The elbow specimen was weighed three times before and after each test and the average weight was used to determine the mass loss during each test condition. During the test, the test section pressure and airflow rate was monitored closely to maintain similar pressure and flow
61 rates. The pressure to the sand injection tube and ball valve was also adjusted periodically to maintain uniform sand flow rate and sand injection time.
Table IV-4 shows the erosion test results for three different air velocities with the mass loss data for each 1000 grams of sand throughput during each test. Each test condition was repeated three times with 1000 grams of sand. The test section pressures
(P1, P2) for each test condition are listed in the table. The mass loss of the specimens in horizontal and vertical orientations and the erosion ratio (mass loss/ sand throughput) are shown in the Table IV-4. The erosion ratio was calculated for each test condition using the average mass loss.
Figures IV-6 and IV-7 show the cumulative mass loss in horizontal and vertical elbow specimens at 62, 90, and 112 ft/sec gas velocities using 150 µm sand. Trend lines are drawn through the data with zero intercepts. The mass loss in the vertical elbow specimen was higher than the horizontal specimen (except for 62 ft/sec gas velocity) for the same test condition. Larger differences between vertical and horizontal specimen were observed at higher gas velocities. For example, at 62 ft/sec, the mass loss of the vertical specimen was slightly less than the horizontal specimen, while the mass loss of the vertical specimen was 49% higher at 90 ft/sec and 62% higher at 112 ft/sec.
62 Table IV-4: Single-Phase Erosion Test Results in the Multiphase Test Section Flow Air Test Test Sand Mass Average Average Orientation Velocity Pressure Section Throughput Loss Mass Erosion (ft/sec) at Flow Pressure (grams) (grams) Loss Ratio
meter P1 P2 (Psig) (grams) (Psig)
1000 0.0045 Horizontal 62 18 5 0.0051 5.10 E-6 1000 0.0059
1000 0.0049
1000 0.0082 Horizontal 90 27 6 0.0070 7.00E-6 1000 0.0056
1000 0.0072
1000 0.0122 Horizontal 112 32 6 0.0101 1.01E-5 1000 0.0099
1000 0.0082
1000 0.0041 Vertical 62 18 5 0.0043 4.30E-6 1000 0.0037
1000 0.0051
1000 0.0090 Vertical 90 27 7 0.0104 1.04E-5 1000 0.0125
1000 0.0097
1000 0.0154 Vertical 112 32 6 0.0164 1.64E-5 1000 0.0170
1000 0.0168
63 0.035 Vg=62 ft/sec-Hor 0.03 Vg=90 ft/sec- Hor 0.025 Vg =112 ft/sec- Hor
0.02
0.015
0.01 Mass Loss (grams) Loss Mass 0.005
0 0 1000 2000 3000 4000 Sand Throughput (grams)
Figure IV-6. Mass Loss of 316 SS Elbow Specimen in Single-Phase Horizontal Flow
0.06 Vg=62 ft/sec-Vert. 0.05 Vg=90 ft/sec- Vert.
0.04 Vg =112 ft/sec- Vert.
0.03
0.02 Mass Loss (grams) Loss Mass 0.01
0 0 1000 2000 3000 4000 Sand Throughput (grams)
Figure IV-7. Mass Loss of 316 SS Elbow Specimen in Single-Phase Vertical Flow
64 Figure IV-8 demonstrates how the mass loss increases with increased gas velocity along with higher mass loss in the vertical specimen with 95% confidence interval. At 62 ft/sec gas velocity, the mass loss in the horizontal specimen appears to be slightly higher than the mass loss in the vertical specimen. The probable reason for this result may be contributed by a high level of measurement uncertainty of the scale
(±0.50 mg) associated with small mass loss measurements.
2.0E-02
Hor-Vert. 1.6E-02 Vert.-Hor
1.2E-02
8.0E-03
Average Mass Loss (grams) Loss Mass Average 4.0E-03
0.0E+00 62 90 112 Gas Velocity (ft/sec)
Figure IV-8. Erosion Test Results in Single-Phase with 95% Confidence interval
Table IV-5 shows the average penetration rate calculated by dividing the mass loss by the sand throughput, density of specimen material, and test time. The maximum penetration rate was calculated by multiplying the average penetration rate with the maximum to average thickness loss ratio from the thickness loss measurement experiment. The thickness loss data for the single-phase erosion tests are presented in
Stage III Erosion Test in the following section of this chapter. The penetration rate calculation procedure is described in Appendix A.
65 Table IV-5. Summary of Erosion Test Results in Single-Phase Flow
Gas Flow Total Average Average Average Maximum
Velocity Orientation Sand Mass Loss Erosion Pen. Rate * Pen. Rate*
(ft/sec) Through for 1.0 kg Ratio (mils/lb) (mils/lb)
put (kg) (grams)
62 Horizontal 3.0 5.10E-03 5.10E-06 1.81E-02 5.74E-02
90 Horizontal 3.0 7.00E-03 7.00E-06 2.49E-02 7.88E-02
112 Horizontal 3.0 1.01E-02 1.01E-05 3.59E-02 1.14E-01
62 Vertical 3.0 4.30E-03 4.30E-06 1.53E-02 4.84E-02
90 Vertical 3.0 1.04E-02 1.04E-05 3.69E-02 1.17E-01
112 Vertical 3.0 1.64E-02 1.64E-05 5.83E-02 1.85E-01
* Refer to Appendix A for penetration rate calculation procedure
Stage III Thickness Loss Measurements of Elbow Specimen in Single-Phase Flow
To optimize the design of process equipment and piping system that can withstand internal fluid pressure, it is important to identify the location and magnitude of the maximum erosion. So far, no study comparing the thickness loss characteristics of elbows in multiphase horizontal and vertical particle laden annular flow has been presented in the literature. At the Erosion/Corrosion Research Center of The University of Tulsa, erosion studies were conducted in single and multiphase flows in elbows to identify the location of maximum erosion. In this section, erosion experiments to
66 characterize the single-phase erosion profiles in an elbow are presented.
The elbow specimen was prepared by polishing the specimen surface with sand paper until the surface became very smooth. Ten “X” or “V” shaped scratches were made in a aluminum elbow specimen as described in Chapter III. The main reason for selecting aluminum was the ability to make deeper scratches. Due to lower hardness of aluminum, the surface thickness loss during erosion test was expected to be higher reducing the measurement uncertainty. A Surtronic 3P profilometer was used to measure the depth and relative distance between the scratches before and after each test to determine the surface thickness loss. Figures III-8 shows the elbow specimen with scratches and Figure III-9 shows a photograph of the scratch depth measurement of the elbow specimen using the profilometer.
Figure IV-9 shows the scratch depth measurement of the vertical elbow specimen before and after the erosion test at 112 ft/sec single-phase gas velocity. Thickness loss is the difference in scratch depth before and after erosion test. The area between the before and after test thickness profiles was divided by the width of the specimen (4 mm) to determine the average thickness loss. The average thickness loss of 42.5 microns was measured at 55 degrees from the inlet of the elbow. Three different thickness loss readings were recorded at each location before and after tests along the length of the elbow. Figure IV-10 shows three different readings at each scratch location and the average of those three readings. A trend line was drawn through the average data to observe the thickness loss profile in the elbow specimen.
67 120 Max. Erosion
Vgas=112-After-55 deg
80 Vgas=112-After-55 deg
40 45O
0
-40 42.5 micron Depth of scratch in microns -80
-120 00.511.522.533.54 Traverse distance in mm
Figure IV-9. Thickness Loss Measurement of Elbow Specimen (Vgas = 112 ft/sec, Aluminum, 55 degrees) 50 Vgas=112 (Average) Vgas=112 (Reading 1) 45 Vgas=112 (Reading 2) Vgas=112 (Reading 3) 40 Max. Erosion 35
30
25
20 45O 15
Thickness loss in microns loss in Thickness 10
5
0 0 102027.535455562.57090 Location in the elbow
Figure IV-10. Thickness Loss Profile of Elbow Specimen in Single-Phase Flow (Vgas =112 ft/sec, Aluminum) 68 The thickness loss data for 112 ft/sec gas velocity are presented in Table IV-6.
The average thickness loss along the length of the elbow specimen was calculated by adding the average thickness loss of each of the ten locations shown in Figure III-1 and then dividing by 10. The calculated average thickness loss was 13.4 microns and the ratio of maximum to average thickness loss was 3.17. The maximum to average thickness loss ratio was used to calculate the maximum penetration rate from the mass loss measurement data.
Table IV-6. Results of Thickness Loss Measurement in Elbow Specimen (Single- Phase Flow)
Pipe Diameter (inch) 1.0
Mass of Sand Injected (lb) 2.204
Test Time 60
Fluid Velocity (ft/sec) 112
Maximum Thickness Loss (micron) 42.5
Location of Maximum Thickness Loss (degrees) 55o
Average Thickness Loss (micron) 13.4
Ratio of Maximum to Average Thickness Loss 3.17
Material of Specimen 6061-T6 Aluminum
69 CHAPTER V
EXPERIMENTAL EROSION RESULTS FOR MULTIPHASE FLOW
Erosion experiments were conducted in multiphase flow at superficial gas velocities of 32, 62, 90, and 112 ft/sec and at superficial liquid velocities of 0.1 and 1.0 ft/sec using 150 µm sand. The ratio of mass of sand to water was maintained at approximately 2% during each test. Experiments were conducted in two different stages.
In a stage I erosion tests, mass loss measurements were recorded and in stage II test, thickness loss measurements of the elbow specimen surface were recorded. The erosion data presented in this chapter is primarily for mass loss in a 316 stainless steel specimen.
Mass loss measurements were also recorded for an aluminum elbow specimen to compare the relative difference in erosion between stainless steel and aluminum. An aluminum specimen was used to conduct thickness loss measurements as lower density of aluminum is expected to result in larger thickness loss reducing measurement uncertainties in the experimental data.
Hardness of three 6061-T6 aluminum specimens was tested using a Barber
Coleman model GYZJ934-1 hardness tester that is suitable for soft metals like aluminum.
Three different hardness readings were recorded for each specimen and the average hardness values were computed. The average Barber Coleman Hardness readings for three specimens were converted to equivalent Brinell hardness numbers and presented in
70 Figure V-1. The Brinell hardness of the elbow specimens was 80-82.5; that meets the minimum hardness requirement for 6061-T6 material per SAE AMS 2656 specification.
90 )
80
70
60 Average Hardness Brinell (BHN
50 2621 Elbow Specimen No.
Figure V-1. Average Hardness of 6061-T6 Aluminum Elbow Specimen.
Stage I Erosion Test: Mass Loss Measurements in Multiphase Flow
Two different elbow specimens were used in the experiment, one in the horizontal test cell with upstream horizontal flow, and the other one in the vertical test cell with upstream vertical flow. Sand and water were mixed in a slurry tank with an electric motor driven stirrer and then injected in the test section through a nozzle. Two different flow loops were used with different flow development lengths and pressures in the test sections. The flow development length, L, is the length of straight pipe section upstream of the elbow specimen. A dimensionless L/D ratio was calculated by dividing the pipe length with the diameter of the pipe. The L/D ratios for the two test sections were
71 approximately 70 and 160 with test section pressures of 30 psig and 9-26 psig, respectively. Table V-1 lists the erosion test conditions for multiphase flow.
Table V-1. Erosion Test Conditions in Multiphase Flow (L/D ≈ 160) Superficial Superficial Flow Sand Specimen Observed Flow Pattern Gas Velocity Liquid Vel. Orientations Size Material in Horizontal/ (ft/sec) (ft/sec) (microns) Vertical
32 0.1 Horizontal/ 150 Aluminum/ Stratified Vertical 316 SS Wavy / Annular
1.0 Horizontal/ 150 Aluminum/ Slug / Vertical 316 SS Annular
62 0.1 Horizontal/ 150 Aluminum/ Annular Vertical 316 SS
1.0 Horizontal/ 150 Aluminum/ Annular Vertical 316 SS
90 0.1 Horizontal/ 150 Aluminum/ Annular Vertical 316 SS
1.0 Horizontal/ 150 Aluminum/ Annular Vertical 316 SS
112 0.1 Horizontal/ 150 Aluminum/ Annular Vertical 316 SS
1.0 Horizontal/ 150 Aluminum/ Annular Vertical 316 SS
The horizontal and vertical flow maps with the erosion test conditions are shown in Figures V-2 and V-3. Erosion tests were conducted primarily in annular flow except at the superficial gas velocity of 32 ft/sec where the horizontal flow pattern was different.
At 32 ft/sec superficial gas velocity and 0.1 ft/sec superficial liquid velocity, the
72 observed flow pattern was stratified wavy. At the same gas velocity and at superficial liquid velocity of 1.0 ft/sec, the observed flow pattern was intermittent/slug.
100
Dispersed Bubble 10
Intermittent/ Slug
1 Annular
0.1 Stratified Smooth Stratified Erosion Test Wavy Conditions Superficial Liquid Velocity (ft/sec) Liquid Superficial 0.01 1 10 100 1000 Superficial Gas Velocity (ft/sec)
Figure V-2. One-Inch Horizontal Flow Map Showing Erosion Test Conditions 100 Erosion Test Dispe rse d Conditions Bubble flow 10 Velocity (ft/sec) 1 Churn flow Annular
0.1 Superficial Liquid
0.01 1 10 100 1000 Superficial Gas Velocity (ft/sec)
Figure V-3. One-Inch Vertical Flow Map Showing Erosion Test Conditions
Erosion tests were repeated 4 to 9 times for each test condition using a large amount of sand to validate the accuracy and repeatability of the data. Before and after
73 each test, the elbow specimen was washed and dried using heated air from an industrial grade hand held electric dryer. The specimen was then allowed to cool before taking the weight measurement using a precision digital scale. Each specimen number and their weights were recorded on the data sheet. To ensure placement of the correct specimens in the horizontal and vertical test cells, the specimen numbers were verified in the test cell. The test cell was then closed using rubber gaskets and clamps to prevent leakage during the test.
The sand and water were mixed in the slurry tank with a pre-calculated mass of water and mass of sand to obtain 2% sand concentration by mass. An electric motor driven stirrer was used during the test to maintain the homogeneous characteristic of the sand-water solution. The time required to empty the tank was used to determine the liquid flow rate and superficial liquid velocity. The 8-gallon slurry tank used during the tests with 0.1 ft/sec of liquid was pressurized with air at a pressure slightly higher than the test section pressure to ensure continuous flow of sand-water mixture to the test section. The 100-gallon tank used during erosion test with 1.0 ft/sec liquid rate was open to atmosphere. A pneumatic, positive displacement pump was used to flow the liquid- sand mixture to the test section. A ball valve was used to control the sand-water injection rate. The detailed erosion test procedure is described in Appendix B.
The sand-water mixture injected to the test section was mixed with the air and then flowed through a one-inch pipe section and reached the horizontal test cell impacting the specimen. The mixture then flowed vertically upward through another one-inch pipe section and impacted the elbow specimen located in the vertical test cell.
The fluid discharged from the vertical test cell went through a cyclone separator where
74 the sand and water were separated. The mixture then flowed through an air-filter where the remaining sand was separated from the air.
The erosion test results for the 316 stainless steel specimen are reported in Table
V-2. The average erosion ratio was determined from the slopes of the trend lines of
Figures V-4 through V-11. The penetration rate is the surface thickness loss per unit mass of sand throughput and expressed in mils per pound or mm per kilogram. The measured mass loss was divided by the sand throughput, density of specimen material, surface area of the specimen to calculate the average penetration rate. The maximum penetration rate was calculated using the ratio of maximum to average thickness loss from the thickness loss data. The maximum to average thickness loss ratio was determined from thickness loss experiments and are listed in Table V-4 of this chapter. It was assumed that this ratio would be similar for aluminum and stainless steel. Appendix
A describes the penetration rate calculation procedure. Appendix B describes the erosion test procedure for multiphase flow.
75 Table V-2. Erosion Test Results of 316 Stainless Steel Specimen (150µm Sand)
SuperficialSuperficial Test Flow Sand Total Average Calc. Calc. Gas Liquid Section Orientation Through Mass Erosion Ave. Pen.Max Pen. Velocity Velocity Pressure -put (kg) Loss Ratio Rate * Rate * (ft/sec) (ft/sec) (Psig) (grams) (mils/lb) (mils/lb)
112 0.1 26 Horizontal 10.80 1.39E-2 1.26E-6 4.58E-03 7.29E-03
112 0.1 26 Vertical 10.80 3.20E-2 2.85E-6 1.05E-02 2.40E-02
90 0.1 22 Horizontal 16.20 8.60E-3 4.98E-7 1.89E-03 3.19E-03
90 0.1 22 Vertical 16.20 1.81E-2 1.07E-6 3.98E-03 6.44E-03
62 0.1 15 Horizontal 19.80 4.20E-3 2.01E-7 7.53E-04 1.26E-03
62 0.1 15 Vertical 19.80 9.90E-3 4.81E-7 1.78E-03 3.30E-03
32 0.1 9 Horizontal 19.80 4.79E-3 2.48E-7 8.60E-04 1.57E-03
32 0.1 9 Vertical 19.80 8.07E-3 4.45E-7 1.45E-03 2.64E-03
112 1.0 25 Horizontal 20.40 7.30E-2 3.17E-6 1.27E-02 2.14E-02
112 1.0 25 Vertical 20.40 1.80E-1 9.20E-6 3.13E-02 5.80E-02
90 1.0 21 Horizontal 27.20 1.60E-2 6.41E-7 2.09E-03 3.66E-3
90 1.0 21 Vertical 27.20 7.90E-2 3.00E-6 1.03E-02 1.94E-02
62 1.0 19 Horizontal 23.80 5.90E-3 2.44E-7 8.77E-04 1.37E-03
62 1.0 19 Vertical 23.80 1.50E-2 6.13E-7 2.24E-03 3.94E-03
32 1.0 9 Horizontal 40.80 1.00E-3 2.12E-8 8.70E-05 1.59E-04
32 1.0 9 Vertical 40.80 5.50E-3 1.28E-7 4.80E-04 7.47E-04 * Refer to Appendix A for penetration rate calculation procedure
Figures V-4 to V-7 show the cumulative mass loss of the 316 stainless steel elbow specimen in horizontal and vertical test cells at superficial gas velocities of 32, 62, 90,
76 and 112 ft/sec and at a superficial liquid velocity of 0.10 ft/sec. Mass loss measurements were recorded after each erosion test using 2.7 kilograms of sand. The mass loss for each test was similar although the vertical specimen had approximately 2 to 4 times more mass loss than the horizontal specimen. Larger mass losses were observed at higher gas velocities for the same liquid velocity.
1.E-02
32V0.1 (Vertical)- 316SS 8.E-03 32H0.1(Horizontal) 316 SS
6.E-03
4.E-03 Mass Loss (grams) 2.E-03
0.E+00 0.0 2.7 5.4 8.1 10.8 13.5 16.2 18.9 21.6 24.3 Sand Throughput (Kg)
Figure V-4. Mass Loss of Stainless Steel Specimen at Different Sand Throughput (VSG = 32 ft/sec, VSL = 0.10 ft/sec, 150 micron Sand)
77 1.E-02
62V0.1 (Vertical) 316 SS 62H0.1 (Horizontal) 316 SS 9.E-03
6.E-03
Mass Loss (grams) 3.E-03
0.E+00 0 2.7 5.4 8.1 10.8 13.5 16.2 18.9 21.6 Sand Throughput (Kg)
Figure V-5. Mass Loss of Stainless Steel Specimen at Different Sand Throughput (VSG = 62 ft/sec, VSL = 0.10 ft/sec, 150 micron Sand)
2.0E-02
90V0.1 (Vertical) 316 SS 1.6E-02 90H0.1(Horizontal) 316 SS
1.2E-02
8.0E-03 Mass Loss (grams) Mass 4.0E-03
0.0E+00 0 2.7 5.4 8.1 10.8 13.5 16.2 18.9 Sand Throughput (Kg)
Figure V-6. Mass Loss of Stainless Steel Specimen at Different Sand Throughput (VSG = 90 ft/sec, VSL = 0.10 ft/sec, 150 micron Sand)
78 4.E-02
112V0.1 (Vertical) 316SS 112H0.1(Horizontal) 316SS 3.E-02
2.E-02
Mass Loss (grams) 1.E-02
0.E+00 0 2.7 5.4 8.1 10.8 13.5 Sand Throughput (Kg) Figure V-7. Mass Loss of Stainless Steel Specimen at Different Sand Throughput (VSG = 112 ft/sec, VSL = 0.10 ft/sec, 150 micron Sand)
Figures V-8 to V-11 illustrate the cumulative mass loss of the 316 stainless steel specimen at superficial gas velocities of 32, 62, 90, and 112 ft/sec and superficial liquid velocity of 1.0 ft/sec. Mass losses for each test using 3400 grams of sand were similar with the vertical specimen having 1.5 to 9.0 times more mass loss than the horizontal specimen. The difference between vertical and horizontal mass loss was smaller at a superficial gas velocity of 112 ft/sec and larger at a superficial gas velocity of 90 ft/sec.
Table V-3 summarizes the erosion test results for the aluminum specimen. The test procedure was similar to the test using the 316 stainless steel specimen. The erosion ratio, average and maximum penetration rates were also calculated using similar methods described in earlier sections of this chapter.
79 6.0E-03 32V1.0 (Vertical) 316SS 32H1.0 (Horizontal) 316SS 4.5E-03
3.0E-03
Mass Loss (grams) Loss Mass 1.5E-03
0.0E+00 0 6.8 13.6 20.4 27.2 34 40.8 Sand Throughput (Kg) Figure V-8. Mass Loss of Stainless Steel Specimen at Different Sand Throughput (VSG = 32 ft/sec, VSL = 1.0 ft/sec, 150 micron Sand)
1.6E-02 62V1.0 (Vertical) 316SS 62H1.0 (Horizontal) 316SS
1.2E-02
8.0E-03 Mass Loss (grams) 4.0E-03
0.0E+00 0.0 6.8 13.6 20.4 27.2
Sand Throughput (Kg) Figure V-9. Mass Loss of Stainless Steel Specimen at Different Sand Throughput (VSG = 62 ft/sec, VSL = 1.0 ft/sec, 150 micron Sand)
80 1.0E-01
90V1.0 (Vertical) 316SS
7.5E-02 90H1.0 (Horizontal) 316SS
5.0E-02
Mass Loss (grams) Mass 2.5E-02
0.0E+00 0 6.8 13.6 20.4 27.2 Sand Throughput (Kg) Figure V-10. Mass Loss of Stainless Steel Specimen at Different Sand Throughput (VSG = 90 ft/sec, VSL = 1.0 ft/sec, 150 micron Sand)
4.E-02
112V0.1 (Vertical) 316SS 112H0.1(Horizontal) 316SS 3.E-02
2.E-02
Mass Loss (grams) 1.E-02
0.E+00 0 2.7 5.4 8.1 10.8 13.5 Sand Throughput (Kg) Figure V-11. Mass Loss of Stainless Steel Specimen at Different Sand Throughput (VSG = 112 ft/sec, VSL =1.0 ft/sec, 150 micron Sand)
81 Table V-3. Erosion Test Results Summary of Aluminum Specimen (150µm Sand)
SuperficialSuperficial Test Average Calc. * Calc. * Sand Average Gas Liquid Flow Section Mass Ave. Max. Through Erosion Velocity Velocity OrientationPressure Loss Pen. RatePen. Rate put (kg) Ratio (ft/sec) (ft/sec) (Psig) (grams) (mils/lb) (mils/lb)
112 0.1 Horizontal 26 21.60 3.05E-2 1.41E-6 1.50E-02 2.39E-02
112 0.1 Vertical 26 21.60 5.63E-6 2.61E-6 2.78E-02 6.35E-02
90 0.1 Horizontal 22 32.40 7.23E-3 2.43E-7 2.59E-03 4.37E-03
90 0.1 Vertical 22 32.40 2.31E-2 7.71E-7 8.22E-03 1.33E-02
62 0.1 Horizontal 15 21.60 3.47E-3 1.60E-7 1.70E-03 2.86E-03
62 0.1 Vertical 15 21.60 8.67E-3 7.01E-7 7.47E-03 1.39E-02
32 0.1 Horizontal 9 24.30 4.06E-3 1.67E-7 1.78E-03 3.24E-03
32 0.1 Vertical 9 24.30 7.64E-3 3.14E-7 3.35E-03 6.09E-03
112 1.0 Horizontal 25 20.40 9.30E-2 4.56E-6 4.86E-02 8.19E-02
112 1.0 Vertical 25 20.40 3.20E-1 1.57E-5 1.67E-01 3.10E-01
90 1.0 Horizontal 21 20.40 9.10E-3 4.46E-7 4.75E-03 1.57E-02
90 1.0 Vertical 21 20.40 8.90E-2 4.36E-6 4.65E-02 8.76E-02
62 1.0 Horizontal 19 20.40 1.80E-3 8.82E-8 9.40E-04 1.47E-03
62 1.0 Vertical 19 20.40 1.30E-2 6.37E-7 6.79E-03 1.19E-02
32 1.0 Horizontal 9 20.40 3.40E-3 1.67E-7 1.78E-03 3.25E-03
32 1.0 Vertical 9 20.40 4.40E-3 2.15E-7 2.29E-03 3.57E-03 * Refer to Appendix A for penetration rate calculation procedure. Density of aluminum ( 2600 kg/ m3) was used in the calculation.
82 Figure V-12 shows a comparison of the mass loss between aluminum and stainless steel specimens in horizontal and vertical orientations at VSG = 32 ft/sec with
95% confidence interval bars. The 95% confidence interval was calculated using sample standard deviation and t-statistics of three different mass loss measurements at each test.
Higher mass losses were recorded in the stainless steel specimen in both horizontal and vertical specimens at this low gas velocity. Figure V-13 compares the mass losses between aluminum and stainless steel at superficial gas velocity of 112 ft/sec with 95% confidence interval bars. No significant difference in mass loss was observed between aluminum and stainless steel at this flow condition.
1.E-02 32V0.1 (Vertical) Alum 32H0.1 (Horizontal) Alum 8.E-03 32V0.1 (Vertical) 316SS 32H0.1 (Horizontal) 316 SS
6.E-03
4.E-03 Mass Loss (grams) Mass 2.E-03
0.E+00 0 5.4 10.8 16.2 21.6 27 Sand Throughput (Kg)
Figure V-12. Comparison of Mass Loss Between Aluminum and Stainless Steel with 95% Confidence Interval (VSG = 32 ft/sec, VSL = 0.10 ft/sec, 150 micron sand)
83 112V0.1 (Vertical) Alum 6.0E-02 112H0.1 (Horizontal) Alum 112V0.1 (Vertical) 316SS 112H0.1 (Horizontal) 316SS
4.5E-02
3.0E-02 Mass Loss (grams) Loss Mass 1.5E-02
0.0E+00 0 5.4 10.8 16.2 21.6 Sand Throughput (Kg) Figure V-13. Comparison of Mass Loss Between Aluminum and Stainless Steel with 95% Confidence Interval (VSG = 112 ft/sec, VSL = 0.10 ft/sec, 150 micron Sand)
Figures V-14 and V-15 compare the differences in mass loss between aluminum and stainless steel specimens at superficial gas velocities of 32 and 112 ft/sec and at superficial liquid velocity of 1.0 ft/sec. Higher mass loss was observed in the aluminum elbow specimen than the stainless steel elbow specimen at these test conditions. Further study is necessary to determine the cause of the difference in mass loss between aluminum and stainless steel specimen. After the experiment with aluminum, it was observed that the specimen holder was eroded that may affected the erosion behavior of the aluminum elbow specimen. The difference between the horizontal and vertical mass losses observed during this research has never been recognized by any previous erosion investigator. An attempt to understand the cause of this behavior and a qualitative analysis is provided in the following section.
84 7.5E-03 32V1.0 (Vertical) Alum 32H1.0 (Horizontal) Alum 6.0E-03 32V1.0 (Vertical) 316SS 32H1.0 (Horizontal) 316SS
4.5E-03
3.0E-03 Mass Loss (grams) 1.5E-03
0.0E+00 0 6.8 13.6 20.4 27.2 34 40.8 Sand Throughput (Kg)
Figure V-14. Comparison of Mass Loss Between Aluminum and Stainless Steel with 95% Confidence Interval (VSG = 32 ft/sec, VSL = 1.0 ft/sec, 150 micron Sand)
4.E-01 112V1.0 (Vertical) 316 SS 112H1.0 (Horizontal) 316 SS
3.E-01 112V1.0 (Vertical) Alum 112H1.0 (Horizontal) Alum
2.E-01
Mass Loss (grams) Loss Mass 1.E-01
0.E+00 0 3.4 6.8 10.2 13.6 17 20.4 23.8 Sand Throughput (Kilograms)
Figure V-15. Comparison of Mass Loss Between Aluminum and Stainless Steel with 95% Confidence Interval (VSG = 112 ft/sec, VSL = 1.0 ft/sec, 150 micron Sand)
85 Several factors such as entrainment fraction, droplet velocity, film thickness, liquid and gas velocity have influenced the erosion pattern in horizontal and vertical flows. The amount of liquid and sand entrained in the gas core region was larger in the vertical flow compared to the horizontal flow for the same flow condition. The sand particles in the gas core region traveled at a velocity similar to the high gas velocity and impacted the inner wall of the elbow. The liquid film thickness is nearly uniform for vertical annular flow. On the other hand, in horizontal flow, the liquid film was of asymmetric shape with larger thickness at the lower section of the pipe. The primary cause of this asymmetry is due to gravitational effects on higher density liquid compared to lower density gas. In horizontal flow, a large fraction of sand particles entrained in the liquid film moved at a lower velocity with smaller impact velocities to the wall. The differences in distribution of sand particles in the gas core and liquid film region with different impact velocities resulted in lower erosion rates in horizontal flow than the vertical flow. Figure V-16 shows a schematic description of the sand and liquid distribution in vertical and horizontal annular flow.
Liquid Droplet
Sand Vertical Flow Horizontal Flow Figure V-16. Schematic of Sand and Liquid Distribution in Vertical and Horizontal Annular Flows
86 Figures V-17 and V-18 show a comparison between the erosion results obtained from two different one-inch multiphase test sections with different L/D ratios and test section pressures. One of the test sections has L/D ratio of 70 and the other test section has L/D ratio of approximately 160. The superficial gas velocities during experiments were also different in these two test sections. The superficial gas velocity in the L/D ≈ 70 test section was 50 ft/sec with 30 psig test section pressure compared to VSG = 62 ft/sec with 19 psig test section pressure. The superficial gas velocity in the L/D ≈ 70 test section was 100 ft/sec with 30 psig test section pressure compared to VSG = 112 ft/sec with 25 psig test section pressure. No difference in mass loss between horizontal and vertical specimens was observed in the test section with L/D ≈ 70 and test section pressure of 30 psig. Whereas, higher mass loss was observed in the vertical specimen than the horizontal specimen in the test section with L/D ≈ 160. One of the reasons for this difference is that at L/D ≈ 70 the flow may not be fully developed. One evidence of lack of fully developed multiphase flow for the smaller L/D ratio was the lack of repeatability of the erosion test data in the L/D ≈ 70 test section.
87 2.E-02 L/D=70, VSG = 50 fps, 30 psig, Vert. L/D=70, VSG = 50 fps, 30 psig, Hor. L/D=160, VSG = 62 fps, 19 psig, Vert. 1.E-02 L/D=160, VSG = 62 fps, 19 psig, Hor.
8.E-03
Mass Loss (grams) Mass 4.E-03
0.E+00 0.0 3.4 6.8 10.2 13.6 17.0 20.4 23.8 Sand Throughput (Kg)
Figure V-17. Mass Loss in Test Sections with Different L/D Ratios and Pressures (VSG = 50-62 ft/sec, VSL = 1.0 ft/sec, Aluminum, 150 micron Sand)
4.0E-01 L/D =70, VSG =100 fps, 30 psig, Vert. L/D =70, VSG=100 fps, 30 psig, Hor. L/D =160, VSG=112 fps, 25 psig, Vert. 3.0E-01 L/D =160, VSG = 112 fps, 25 psig, Hor.
2.0E-01
`
Mass Loss (grams) 1.0E-01
0.0E+00 0.0 6.8 13.6 20.4 Sand Throughput (Kilograms)
Figure V-18. Mass Loss in Test Sections with Different L/D Ratios and Pressures (VSG= 100-112 ft/sec, VSL = 1.0 ft/sec, Aluminum, 150 micron Sand)
88 Stage II Thickness Loss Measurements of Elbow Specimen in Multiphase Flow
Figures V-19, V-20, and V-21 show the representative scratch depth measurement of the aluminum elbow specimen before and after erosion tests at superficial gas velocities of 32, 90, and 112 ft/sec and superficial liquid velocity of 1.0 ft/sec. The average thickness loss was computed from the scratch depth measurements taken before and after test. The average thickness losses in horizontal specimens at VSG =32, 90, and
112 were 10.2, 17.6, and 22.3 microns, respectively. It was observed that for the same superficial liquid velocity, thickness loss was higher at higher gas velocity. Figure V-22 shows the representative scratch depth measurement and average thickness loss of 22.8 microns at superficial gas velocity of 112 ft/sec and superficial liquid velocity of 0.10 ft/sec. The average thickness loss was determined similar methods as Figure IV-9.
140
32H1.0-After-45 deg 120 32H1.0-Before-45 deg.
100
80
60
10.2 Micron 40 Depth of scratch in microns
20
0 0 0.5 1 1.5 2 2.5 3 3.5 4 Traverse distance in mm
Figure V-19. Thickness Loss Measurement of Elbow Specimen at VSG =32 ft/sec, VSL =1.0 ft/sec, Aluminum, 45 degrees.
89 140
90H1.0-After-45 deg.
90 90H1.0-Before-45 deg
40
-10
Thickness Loss 17.6 micron -60 Depth of scratch in micron in scratch of Depth
-110
-160 0 0.5 1 1.5 2 2.5 3 3.5 4 Traverse distance in mm
Figure V-20. Thickness Loss Measurement of Elbow Specimen at VSG =90 ft/sec, VSL =1.0 ft/sec, Aluminum, 45 degrees.
120 112H1.0-Before 45
112H1.0-After 45 80
40
0
-40 Thick ness
Depth of scratchDepth of micron in Loss 22.3 µm -80
-120 00.511.522.53 3.54 Traverse distance in mm
Figure V-21. Thickness Loss Measurement of Elbow Specimen at VSG =112 ft/sec, VSL =1.0 ft/sec, Aluminum, 45 degrees. 90 160
112V0.1-Before-55 deg 140 112V0.1-After-55 deg
120
100
80
60 22.8 micron
40 Depth of scratch in microns
20
0 00.511.522.533.54 Traverse distance in mm Figure V-22. Thickness Loss Measurement of Elbow Specimen at VSG = 112 ft/sec, VSL = 0.10 ft/sec, Aluminum, 55 degrees.
Figure V-23 illustrates the vertical specimen thickness loss profile for VSG = 112,
90, 62 and 32 ft/sec and at VSL = 0.10 ft/sec. A thickness loss of 22.8 microns was measured at a high gas velocity of 112 ft/sec compared to the other lower gas velocities.
The maximum thickness loss was measured at approximately 55 degrees from the inlet of the elbow for all vertical flow conditions presented in Figure V-23. Figure V-24 shows the thickness loss profiles of the horizontal specimen at VSG =112, 90, 62 and 32 ft/sec and at VSL =0.1 ft/sec. The maximum thickness loss of 14.6 microns was measured at
VSG =112 ft/sec, VSL =1.0 ft/sec at approximately 45 degrees from the inlet of the elbow.
At VSG = 62 ft/sec, the maximum thickness loss was measured at approximately 35
91 degrees from the inlet. Comparison of Figures V-23 and V-24 shows higher thickness loss in the vertical specimen than the horizontal specimen at the same flow condition.
25 Vsg =112, Vsl=0.1 (Ver.) Vsg = 90, Vsl = 0.1 (Ver.) Vsg = 62, Vsl = 0.1 (Ver.) 20 Vsg = 32, Vsl = 0.1 (Ver.)
15
10
5 Thickness loss in microns in loss Thickness
0 0 102027.535455562.57090 Location in the elbow
Figure V-23. Thickness Loss Profile of Elbow Specimen at Different Gas Velocities (Vertical, VSL = 0.1 ft/sec) 20 Vsg = 112, Vsl = 0.1(Hor.) Vsg = 90, Vsl = 0.1 (Hor.) Vsg = 62, Vsl = 0.1 (Hor.) 16 Vsg = 32, Vsl = 0.1 (Hor.)
12
8
4 Thickness loss in microns in loss Thickness
0 0 10 20 27.5 35 45 55 62.5 70 90 Location in the elbow
Figure V-24. Thickness Loss Profile of Elbow Specimen at Different Gas Velocities (Horizontal, VSL = 0.1 ft/sec) 92 Figures V-25 and V-26 show the thickness loss profile of vertical and horizontal specimens at VSG = 112, 90, 62, and 32 ft/sec and at VSL =1.0 ft/sec. Higher thickness loss was observed at a superficial liquid velocity of 1.0 ft/sec compared to 0.10 ft/sec superficial liquid velocity at the same gas velocities in both horizontal and vertical specimens. The locations of maximum thickness loss were at approximately 55 degrees in vertical flow and approximately 45 degrees in horizontal flow.
35 Vsg =112, Vsl =1.0-Vert. Vsg =90, Vsl =1.0-Vert. 30 Vsg = 62, Vsl = 1.0-Vert. Vsg = 32, Vsl = 1.0-Vert.
25
20
15
10 Thickness loss in microns in loss Thickness 5
0 0 102027.535455562.57090 Location in the elbow
Figure V-25. Thickness Loss Profile of Elbow Specimen at Different Gas Velocities (Vertical, VSL =1.0 ft/sec)
93 30 Vsg =112, Vsl = 1.0 (Hor) Vsg = 90, Vsl = 1.0 (Hor) 25 Vsg = 62, Vsl =1.0 (Hor) Vsg = 32, Vsl =1.0 (Hor)
20
15
10
Thickness loss in microns in loss Thickness 5
0 0 102027.535455562.57090 Location in the elbow
Figure V-26. Thickness Loss Profile of Elbow Specimen at Different Gas Velocities (Horizontal, VSL = 1.0 ft/sec)
1.0 inch ID
Location of Maximum Center Erosion Line
Flow
Figure V-27. Photograph of Vertical Elbow Specimen Holder After Several Erosion Tests
Figure V-27 shows the location of maximum erosion in the elbow specimen holder used in the vertical test cell after several multiphase flow tests. The maximum erosion was observed at 55 degrees from the inlet of the elbow. The centerline of the inlet flow intersected the elbow specimen outer wall at approximately 45 degrees from
94 inlet. Visual inspection of maximum erosion location in the elbow specimen holder was similar to the results obtained from thickness loss measurements.
Table V-4 summarizes the thickness loss measurements in the aluminum elbow specimen. Thickness loss readings were measured three times at each location in the elbow specimen and the average of the readings was used to identify the location of maximum thickness loss. The average of the ten average readings from each location was used to calculate the average thickness loss. Maximum thickness loss was higher in the vertical specimen than the horizontal specimen. Larger thickness loss was observed at superficial liquid velocity of 1.0 ft/sec than 0.10 ft/sec for the same superficial gas velocity. Both of these observations were similar to the erosion results obtained using the mass loss measurement method.
This phenomenon was very interesting and surprising as it is contrary to the previous assumption about the effect of liquid rate on erosion. The expected erosion behavior before this study was reduced erosion rate with increased liquid rate. It was assumed that with higher liquid rate, the liquid film thickness adjacent to the wall would be higher retarding the particle impact velocity and resulting in lower erosion. The experimental evidence presented here undermines the validity of this assumption. At a higher liquid velocity of 1.0 ft/sec, the entrainment is higher in the gas core of annular flow. Therefore, a large number of sand particles entrained in the gas core impacts the elbow specimen surface at high velocity. The effect of this higher impact velocity is more significant than the assumed dampening provided by the thicker liquid film resulting in higher erosion. Further discussion and a quantitative analysis of this erosion mechanism are described in Chapter VI.
95 Table V-4. Summary of Thickness Loss Measurements of Aluminum Specimen
SuperficialSuperficial Flow Sand Maximum Location of Average Ratio of Gas Liquid Orientation Through Thickness Maximum Thickness Maximum Velocity Velocity (Horizontal put Loss Thickness Loss to Average (ft/sec) (ft/sec) / Vertical) (grams) (micron) Loss (micron) Thickness (Degrees) Loss
32 0.1 Horizontal 1000 9.2 45 5.1 1.82
62 0.1 Horizontal 1000 11.9 35 7.1 1.67
90 0.1 Horizontal 1000 12.3 45 7.4 1.69
112 0.1 Horizontal 1000 14.3 45 8.9 1.59
32 0.1 Vertical 1000 10.9 55 6.0 1.82
62 0.1 Vertical 1000 15.9 55 8.6 1.86
90 0.1 Vertical 1000 15.2 55 9.4 1.62
112 0.1 Vertical 1000 22.8 55 9.9 2.28
32 1.0 Horizontal 1000 10.2 45 5.6 1.83
62 1.0 Horizontal 1000 14.9 45 9.5 1.57
90 1.0 Horizontal 1000 17.6 45 10.1 1.75
112 1.0 Horizontal 1000 22.3 45 13.2 1.69
32 1.0 Vertical 1000 9.9 55 7.0 1.56
62 1.0 Vertical 1000 13.7 55 10.0 1.76
90 1.0 Vertical 1000 20.3 55 12.9 1.88
112 1.0 Vertical 1000 29.5 55 15.9 1.85
96 CHAPTER VI
COMPARISON OF SINGLE-PHASE AND MULTIPHASE EROSION TEST
RESULTS
The experimental erosion data for single and multiphase flows are compared in this section to evaluate the effects of liquid rate on erosion. The objective of this study is to understand how the addition of liquid changes erosion behavior from single-phase to multiphase flow. Table VI-I compares the erosion ratios and calculated average penetration rates for both single-phase and multiphase flows with 0.1 ft/sec and 1.0 ft/sec liquid rates. The test results shown in Table VI-1 are for the tests conducted at L/D ≈
160 test section and using the same specimen material, eliminating the variation due to test section configuration and material.
The mass loss in the vertical specimen was higher than the horizontal specimen for both single and multiphase flows. Mass loss increased as the gas velocity increased while maintaining the same liquid rate. During single-phase erosion tests at 32-ft/sec gas velocity, larger fluctuations were observed in the low flow meter readings resulting in unreliable data. Therefore, single-phase erosion test results at 32 ft/sec are not reported in Table VI-1 below. The average erosion ratio and average penetration rate calculation methods are described earlier in Chapter IV.
97 Table VI-1: Comparison of Single-Phase and Multiphase Erosion Test Results in 316 Stainless Steel Elbow Specimen Single Phase Flow Multiphase Flow Multiphase Flow
Gas (VSL = 0 ft/sec) (VSL = 0.1 ft/sec) (VSL = 1.0 ft/sec) Velocity/ Flow Average Average Average Average Average Superficial Orientation Erosion Pen. Average Penetr. Erosion Penetr. Gas Velocity (Horizontal / Ratio Rate* Erosion Rate* Ratio Rate* (ft/sec) Vertical) mils/lb) Ratio (mils/lb) (mils/lb)
32 Horizontal N/A N/A 2.42E-07 8.60E-04 2.45E-08 8.70E-05
62 Horizontal 5.10E-06 1.81E-02 2.12E-07 7.53E-04 2.47E-07 8.77E-04
90 Horizontal 7.00E-06 2.49E-02 5.31E-07 1.89E-02 5.88E-07 2.09E-03
112 Horizontal 1.01E-05 3.59E-02 1.29E-06 4.58E-02 3.58E-06 1.27E-02
32 Vertical N/A N/A 4.08E-07 1.45E-02 1.35E-07 4.80E-04
62 Vertical 4.30E-06 1.53E-02 5.00E-07 1.78E-02 6.30E-07 2.24E-02
90 Vertical 1.04E-05 3.69E-02 1.12E-06 3.98E-03 2.90E-06 1.03E-02
112 Vertical 1.64E-05 5.83E-02 2.96E-06 1.05E-02 8.82E-06 3.13E-02
* Refer to Appendix A for penetration rate calculation procedure
A surprisingly interesting erosion phenomenon was observed as the liquid rate was increased from 0.10 ft/sec to 1.0 ft/sec. Initially, a decrease in mass loss was observed from single-phase (air) test to multiphase test when a small amount of liquid was added at a rate of 0.1ft/sec. With further increase of liquid rate from 0.10 ft/sec to
1.0 ft/sec, the mass loss was increased but remained below the mass loss measured in single-phase tests with air. Figures VI-1 and VI-2 compare the erosion ratios at 62, 90,
98 and 112 ft/sec superficial gas velocities in single-phase and multiphase flow conditions as described above.
1.E-04 Gas Vel = 62 ft/sec-Hor Gas Vel = 90 ft/sec Gas Vel = 112 ft/sec
1.E-05
Erosion Ratio 1.E-06
1.E-07 00.11.0 Superficial Liq. Vel. (ft/sec) Figure VI-1. Comparison of Erosion Ratios at Different Liquid Rate (316 SS Specimen, Horizontal Orientation)
1.0E-04 Gas Vel = 62 ft/sec-Vert. Gas Vel = 90 ft/sec Gas Vel = 112 ft/sec
1.0E-05
Erosion Ratio 1.0E-06
1.0E-07 00.11.0 Superficial Liq. Vel. (ft/sec)
Figure VI-2. Comparison of Erosion Ratios at Different Liquid Rate (316 SS Specimen, Vertical Orientation)
99 To study the effect of liquid rate on erosion, erosion ratios for superficial liquid velocities of 0.10 and 1.0 ft/sec were compared to the single-phase erosion test results.
Table VI-2 compares the effect of liquid rate and flow orientation on erosion ratios at 62,
90 and 112 ft/sec gas velocities. For example, at 62-ft/sec gas velocity when liquid is added at the rate of 0.10 ft/sec, erosion will be reduced by a factor of 24.0 compared to the single-phase erosion test in horizontal flow. The reduction in erosion rate between multiphase flow (with liquid) and single-phase (air) is less at higher gas velocities and vertical flow orientation.
Table VI-2. Erosion Reduction Factors in Multiphase Flow Compared to Single-Phase (Air) Flow Superficial Superficial Gas Velocity Liquid Flow (ft/sec) Velocity Orientation (ft/sec) 62 90 100
0.10 Horizontal 24.0 13.2 7.8
1.00 Horizontal 20.6 11.9 2.8
0.10 Vertical 8.6 9.3 5.5
1.00 Vertical 6.8 3.6 1.9
For proper evaluation of the differences in erosion behavior between single and multiphase flows, it is necessary to have a good understanding about the distribution of sand particles and their corresponding velocities that cause erosion. Figure VI-3 schematically describes the sand distribution patterns in single and multiphase flows. In single-phase flow with air, the distribution of sand particles is more homogeneous across
100 the pipe cross-sectional area than in multiphase flow. These sand particles move at a velocity similar to the high gas velocity and impinge on the elbow surface resulting in erosion. Whereas, in multiphase flow, the sand distribution pattern can be quite different because of the different spatial distribution of liquid and gas phases. The sand particles are entrained in the liquid film, gas core and inside the liquid droplets in the gas core.
The velocity of these sand particles depends upon their corresponding phase velocities and locations in the pipe. The presence of liquid provides a thin liquid film on the elbow surface and lowers the particle impact velocity as particle travels through the liquid film.
Liquid Droplet
Sand Multiphase Flow Single-Phase Flow
Figure VI-3. Sand and Liquid Distribution in Single-Phase and Multiphase Flow
The increase in erosion with increased liquid rate in multiphase flow is contrary to generalized erosion theories that predict lower erosion with increased liquid rates.
Similar observations were reported by Selmer-Olsen [31], although detail analysis was not provided to explain this phenomenon. Selmer-Olsen [31] reported higher erosion at a superficial liquid velocity of 2.95 m/sec compared to 0.11 m/sec at 95.15 m/sec superficial gas velocity as shown in Chapter II.
101 An attempt to explain this phenomenon of higher erosion with higher liquid rate is made in the following paragraphs considering effects of particle velocity and distribution in single and multiphase flows. At higher liquid rates, calculations indicate that the annular liquid film thickness becomes larger with reduction in the gas core cross- sectional area. The smaller gas core area increases the droplet velocity and the velocity of the sand particles resulting in higher erosion. Calculations indicate that higher liquid rate also increases the entrainment fraction in the gas core with more sand particles in the core region.
Figure VI-4 shows the new mechanistic model calculated entrainment fractions at superficial liquid velocities of 0.10 and 1.0 ft/sec at 62, 90, and 112 ft/sec superficial gas velocities. The entrainment fractions are higher at a 1.0 ft/sec liquid rate compared to a
0.10 ft/sec liquid rate for the same superficial gas velocities. It was assumed that the sand entrainment mechanism in the gas core is similar to the droplet entrainment mechanism in annular flow. Therefore, more sand particles are entrained at 1.0 ft/sec liquid velocity than 0.10 ft/sec liquid velocity.
Comparison of calculated droplet velocities for 0.10 and 1.0 ft/sec liquid velocities are provided in Figure VI-5. The calculated droplet velocities at 1.0 ft/sec liquid velocity are slightly higher than those of 0.10 ft/sec liquid velocity for the same superficial gas velocities. According to the calculations, it can be assumed that larger amounts of sand particles impacting the inner wall of the elbow at higher velocities result in more mass loss at a superficial liquid velocity of 1.0 ft/sec as compared to 0.10 ft/sec.
102 0.60 Vsl=1.0 ft/sec 0.558 0.50 Vsl=0.1 ft/sec
0.40
0.340 0.316 0.30
0.20 0.182 Entrainment Fraction Entrainment 0.10 0.102 0.057 0.00 45 60 75 90 105 120 135 Superficial Gas Velocity (m/sec)
Figure VI-4. Comparison of Calculated Entrainment Fractions at 0.10 and 1.0 ft/sec Superficial Liquid Velocities.
31.0 Vsl=1.0 ft/sec Vsl=0.1 ft/sec 28.602
27.0 27.987
23.592 23.0
22.602
19.0 Droplet Velocity (m/sec) Droplet Velocity
17.058
15.722 15.0 45 60 75 90 105 120 135 Superficial Gas Velocity (m/sec)
Figure VI-5. Comparison of Calculated Droplet Velocities at 0.10 and 1.0 ft/sec Superficial Liquid Velocities
103 CHAPTER VII
DEVELOPMENT OF MECHANISTIC MODELS
A mechanistic model is developed to predict erosion in multiphase flow using the characteristic initial particle velocity of sand particles. The characteristic initial particle velocity of sand particles plays an important role in the erosion process due to strong influence of particle velocity on the erosion rate. Thus, the ability to accurately predict the characteristic initial particle velocity in two-phase flow is very important. The early predictive means for characteristic impact velocity was based on a semi-empirical model
[4] for Vo as described earlier in Chapter II. The semi-empirical model did not consider the complex flow behaviors that exist in multiphase flow. The mechanistic model presented in this work calculates an initial sand particle velocity, Vo, based on the physics of two-phase flow and is expected to be more reliable and general because it incorporates the important parameters of multiphase flow that are critical to erosion. Two preliminary mechanistic models [14, 15] were developed during this investigation that calculate the initial particle velocity, Vo, using a mass weighted average of liquid velocities in the film and entrained liquid droplet velocities in the gas core. These preliminary models for annular flow calculate initial particle velocity, Vo, by multiplying the film and droplet velocities with their corresponding entrainment fractions and adding them together.
The new mechanistic model presented here calculates erosion rate separately by using initial sand particle velocities in the liquid and gas phases in annular flow. The
104 total erosion rate is then calculated by adding the individual erosion rates due to sand particles in the liquid and gas phases.
Model for Annular Flow
Annular flow exists at high gas velocity and low liquid velocity. Due to high gas velocity, erosion is usually higher in annular flow than other flow regimes. In gas production wells, the flow is usually annular, gas-liquid, two-phase flow. The gas flows in the core region at high velocity, the liquid flows as a symmetric thin film inside the pipe wall at a slower velocity. A schematic of annular flow is shown in Figure VII-1.
VFilm
Entrained sand ...... and Liquid . . . . droplets in the gas . core ...... Entrained sand particles in the VCore. annular liquid film .. .
δ
D- 2δ D
Figure VII-1. Schematic Description of Annular Flow
105 A fraction of the liquid is entrained in the gas core region as droplets and travels at a velocity similar to the local gas velocity. The gas core to liquid film interface is unstable and wavy with high interfacial shear stress.
Alves [45] developed a model for vertical and sharply inclined annular flow that was later extended by Gomez [46] to the entire range of pipe inclination angles from 0 to
90o. In a fully developed annular flow, the conservation of momentum can be applied separately to the gas core and liquid film since it is assumed that both phases flow separately [38]. The linear momentum (force) balances for the gas (core) and liquid
(film) phases are written as:
⎛ dP ⎞ − A C ⎜ ⎟ − τiSi −ρG A C g sin θ =0 (VII-1) ⎝ dL ⎠C
⎛ dP ⎞ − A F ⎜ ⎟ + τiSi − τFSF − ρL A F g sin θ =0 (VII-2) ⎝ dL ⎠ F
By eliminating the pressure gradient terms from the above equations, the combined momentum equation for annular two-phase flow can be written as,
SF ⎡ 1 1 ⎤ τF − τiSi ⎢ + ⎥ + ()ρL −ρG g sin θ =0 (VII-3) AF ⎣AC AF ⎦
where, τF = Film shear stress (kg/m-sec)
τ i = Gas core shear stress (kg/m-sec)
2 AF = Cross-sectional area of the film (m )
2 AC = Cross-sectional area of the gas core (m )
SF = Wetted perimeter of the film (m)
Si = Wetted perimeter of the gas core (m)
3 ρL = Density of liquid film (kg/m )
106 3 ρG = Density of the gas core (kg/m )
The momentum equation provided as Equation VII-3 combines all the forces that act on the liquid and gas phases and is an implicit equation for annular liquid film thickness. The equation can be solved iteratively for film thickness by considering different geometrical and force variables. For some flow conditions, the iterative method may provide multiple solutions that need to be evaluated for determination of appropriate film thickness. The velocity of the liquid film can be determined [38] from simple mass balance calculation of the liquid phase as shown in Equation VII-10. The film thickness
δ was obtained by using an iterative method proposed by Ansari [38].
It was assumed that sand is uniformly distributed in the liquid phase and travels at the same velocities of the phase they are present. Another assumption was that there is no slip between the sand/liquid and gas phases in the gas core. The velocities of liquid film and liquid droplets entrained in the gas core were considered in calculating the initial particle velocities. Additionally, the mass fractions of sand in the film and in the gas core were assumed to be equal to the mass fraction of liquid in the film and gas core region.
This means that the mass fraction of sand in the annular film and gas core is assumed to be the same as the mass fraction of liquid in these regions. The “characteristic particle initial velocity, Vo” (that is assumed to be the particle initial velocity before the particle reaches the stagnation zone) is calculated separately for liquid and gas phases using the flow velocities in the liquid film and the entrained droplets in the gas core. The characteristic initial sand particle velocity is calculated as:
VoL = Vfilm
VoG = Vd
107 (VII-4) where, VoL = Velocity of sand particles in the liquid film, ft/sec (or m/sec)
VoG = Velocity of sand particles in the gas core, ft/sec (or m/sec)
The entrainment rate, E, is the fraction of liquid entrained in the gas core and is defined as
E = (Mass of liquid in the gas core) / (Total mass of liquid)
Assuming the mass fraction of liquid is equal to the mass fraction of sand, then E is the fraction of sand entrained in the gas core,
E = (Mass of sand in the gas core) / (Total mass of sand)
The fraction of sand entrained in the liquid film,
(1 - E) = (Mass of sand in the liquid film) / (Total mass of sand)
The erosion rate due to sand particles in the liquid phase is calculated by using
VoL and the fraction of sand entrained in the liquid film, (1- E). The erosion rate due to sand particles in the gas phase is calculated by using VoG and the fraction of sand entrained in the gas core, E in the erosion equation II-3 of chapter II. The total erosion rate is calculated by adding the erosion rates due to sand particles in the liquid and gas phases.
ERLiquid = f (VoL, (1-E)) (VII-5)
108 ERGas = f (VoG, E) (VII-6)
ERTotal = ERLiquid + ERGas (VII-7)
The entrainment rate, E, is calculated using the Ishii [29] model as described below. The liquid film thickness, δ, is assumed to be uniform or the cylindrical gas core to be of uniform diameter, DC. Also, the gas core is considered to be composed of homogeneous gas and tiny liquid droplets with no relative slip between the gas and the entrained liquid droplets. Thus, various geometric parameters can be easily expressed.
The cross-sectional area of the gas-core:
2 A C = ( 1 − 2 δ ) A P (VII-8)
The cross-sectional area of the film:
AF = 4δ (1 − δ ) AP (VII-9)
Where AP is the cross-sectional area of the pipe and δ is the ratio of the film thickness to the pipe diameter, D.
The velocity of the film can be determined from simple mass balance calculations
[38] yielding,
(1 − E)D 2 V = V (VII-10) Film SL 4δ(D − δ)
Where VSL is the superficial liquid velocity, D is the pipe diameter, and E is the fraction of the total liquid entrained in the gas core. Liquid entrainment in the gas core is an important parameter for predicting erosion in annular flow. Although a number of
109 empirical entrainment correlations are available in the literature, the accuracy is limited to the flow conditions that were used to develop the correlation. Among the available entrainment correlations, the correlation proposed by Ishii [29] appears to provide accurate entrainment prediction over a wide range of flow conditions. The entrainment model shown in Equation VII-11 uses dimensionless Weber number and liquid Reynolds number. The model is for quasi-equilibrium conditions and can be applied to a region away from the entrance region of the flow.
−7 1.25 0.25 E= tanh (7.25 x10 We Re L ) (VII-11)
ρ V 2 D ⎛ ρ − ρ ⎞ where, G SG L G (VII-12) We = ⎜ ⎟ σ ⎝ ρ G ⎠
ρL VSL D and Re L = (VII-13) µ L
In this investigation, a method for calculating the droplet velocity is proposed by assuming no relative slip between the gas and liquid film. The diameter of the gas core is calculated as:
Dc = D - 2δ
The average gas core velocity,
2 ⎡ D ⎤ (VII-14) VG = VSG ⎢ ⎥ ⎣D c ⎦
In annular flow, droplets generate from the disturbances in the wavy liquid film surfaces near the wall, accelerate in the gas core and deposit back on to the film. The droplet acceleration in the gas core contributes to erosion due to high impact velocity of sand particles entrained in the gas core and the droplets. The droplet velocities in the gas
110 core are less than the gas velocity, VG, due to interphase slip between the gas and droplets.
The mean slip ratio, SR, is defined with the droplet velocity, Vd, as
Vd S R = VG
(VII-15)
The droplet velocity is calculated by multiplying the gas core velocity by the above slip ratio. For annular flow at superficial liquid Reynolds number (ReL) between
750 and 3000, experimental results of Fore and Dukler [43] measured the average slip ratio between the droplet and gas core velocities to be approximately 0.80. The droplet velocity is calculated by multiplying the average gas velocity by the slip ratio between droplet and gas velocities.
Droplet velocity, Vd = VGSR (VII-16)
Thus, by using Vfilm, E, and Vd, VoL, VoG, the total erosion rate due to sand particles in the liquid and gas phases are calculated by using Equations VII-5, VII-6, and
VII-7.
Validation of Droplet Velocity Calculation
In the present mechanistic model, it is assumed that the sand particles are carried by the annular liquid film near the wall and the liquid droplets entrained in the gas core.
The mechanism of sand particle entrainment in the gas core is assumed to be similar to the mechanism of liquid droplet formation and entrainment from the liquid film to the gas core. The sand particle velocities are also assumed to be similar to the liquid film
111 velocity and the liquid droplet velocities in the gas core based on the assumption that there is no slip between the sand particles and liquid. The calculated average droplet velocities from Equation VII-16 were multiplied by a factor of 1.2 to calculate the mean centerline droplet velocity in the gas core assuming that the flow is fully developed turbulent flow. Because in a fully developed turbulent flow the maximum velocity at the center of the pipe is approximately 20% higher than the average flow velocity.
The calculated centerline droplet velocities are compared with the measured droplet velocities in Figure VII-2 showing good agreement. The liquid Reynolds number
(ReL = ρL VSL D / µ L) of Figure VII-2 is the superficial liquid velocity as described in
Equation VII-13. The calculated droplet velocities and the measured droplet velocities
[43] are presented in Table VII-1 at different superficial gas and liquid velocities.
40
35
30
25
Rel = 750 (Calc. Mech. Model) 20 Rel = 750 (Dukler) Rel=2250 (Calc. Mech. Model) Rel =2250 (Dukler) Centerline Droplet Velocity15 (m/sec) 15 20 25 30 35 40 Superficial Gas Velocity (m/sec)
Figure VII-2. Comparison of Calculated Droplet Velocity with Experimental Data [43].
112 Table VII-1. Comparison of Calculated and Measured [43] Droplet Velocities
VSG VSL Liquid Calculated Measured (m/sec) (m/sec) Reynolds Droplet Velocity Droplet Velocity
Number (ReL) (m/sec) (m/sec)
18.1 0.012 750 21.56 20.00
20.3 0.012 750 22.67 22.80
23.3 0.012 750 25.85 25.25
26 0.012 750 28.64 28.75
28.4 0.012 750 31.06 31.00
31.5 0.012 750 34.09 33.40
33 0.012 750 35.52 34.80
18.1 0.036 2250 20.22 20.75
20.3 0.036 2250 22.55 23.75
23.3 0.036 2250 25.66 26.75
26 0.036 2250 28.38 30.25
28.4 0.036 2250 30.71 33.00
31.5 0.036 2250 33.63 35.75
33 0.036 2250 34.99 37.75
Validation of Film Velocity Calculation
Calculation of film thickness is another important parameter because it is used to calculate the erosion due to sand particle velocity in the liquid film. To account for the velocity of the solid particles entrained in the annular liquid film, it is important to be able to calculate the film velocity. The mechanistic model assumes the solid particle
113 velocity in the film to be similar to the film velocity. Adsani [41] measured film velocity in upward annular air-water flow from 0.06 to 0.37 m/sec superficial liquid velocity and from 13.72 to 44.81 m/sec superficial gas velocities using two conductance probes. For better conductivity during measurements, a small amount of salt-water solution was injected in the flow [41]. By measuring the time difference between the conductance spikes, the film velocity was calculated [41]. Table VII-2 and Figure VII-3 compare the mechanistic model calculated film velocities with the film velocities measured by Adsani
[41]. The mechanistic model predicted film velocity agrees well with experimental measurements.
5.0 Calculated-Mechanistic Model Perfect Agreement 4.0
3.0
2.0
1.0 Calculated Film Velocity (m/sec)
0.0 0.0 1.0 2.0 3.0 4.0 5.0 Measured Film Velocity (m/sec)
Figure VII-3. Comparison of Calculated Film Velocity with Experimental Data [41].
114 Table VII-2. Comparison of Calculated and Measured [41] Film Velocities
Superficial Liquid Superficial Gas Measured Film Calculated Film
Velocity, VSL Velocity, VSG Velocity, VFilm Velocity, VFilm (m/sec) (m/sec) (m/sec) (m/sec) 0.06 44.69 1.28 1.52 0.06 34.76 1.10 1.24 0.06 27.01 0.97 1.01 0.06 21.45 0.94 0.96 0.10 21.45 1.34 1.26 0.10 27.31 1.50 1.66 0.10 34.76 1.72 1.90 0.10 44.69 1.96 2.12 0.12 44.69 2.17 2.26 0.12 36.15 1.95 2.23 0.12 28.68 1.74 1.97 0.12 20.11 1.46 1.71 0.25 20.11 2.34 2.24 0.25 27.31 2.66 2.62 0.25 34.76 2.94 2.94 0.25 44.69 3.28 3.09 0.37 43.20 4.19 3.86 0.37 28.68 3.57 3.76
Validation of Film Thickness Calculation
Calculation of film thickness is another important parameter because it is used to calculate the gas core diameter and representative sand particle velocity in the gas core region that causes erosion. The mechanistic model calculated annular liquid film
115 thicknesses were compared with the average film thickness measurements by Selmer-
Olsen [31], Gonzales [36], Zabaras [39], and Weidong [40]. The mechanistic model predicted film thicknesses and the measured film velocities at different superficial gas and liquid velocities are listed in Table VII-3. Figure VII-4 shows a comparison of experimental film thickness measurements to the predicted film thicknesses at superficial gas velocities from 14.2 to 33.8 m/sec and superficial liquid velocities from 0.01 to 2.20 m/sec. At higher liquid rates (>0.05 m/sec), the mechanistic model over predicted the film thickness. Due to the wavy interface between the liquid film and gas core, the film thickness may vary significantly from the average film thickness. The fluctuation of the annular film thickness was measured and reported by Zabaras [39] to be as much as 50% of the mean film thickness.
1.60 Selmer Olsen Data Gonzales Data Weidong Data Zabaras Data 1.20 Perfect Agreement Line
0.80
0.40 Model Predicted Film Thickness (mm) Thickness Predicted Film Model 0.00 0.00 0.40 0.80 1.20 1.60 Measured Film Thickness (mm)
Figure VI-4. Comparison of Calculated Film Thickness with Measured Film Thickness
116 Table VII-3. Comparison of Measured and Mechanistic Model Predicted Film Thickness
Vsl Vsg Measured Film Mech. Model Film Velocity (m/sec) (m/sec) Thickness prediction Measured by (mm) (mm)
0.45 14.20 0.42 0.68 Selmer-Olsen [31]
0.90 14.20 0.48 0.86 Selmer-Olsen [31]
1.35 14.20 0.54 0.94 Selmer-Olsen [31]
1.80 14.20 0.68 1.00 Selmer-Olsen [31]
2.20 14.20 0.60 1.03 Selmer-Olsen [31]
0.01 18.29 0.84 0.55 Gonzales [36]
0.01 18.29 1.02 0.71 Gonzales [36]
0.02 18.29 1.19 0.96 Gonzales [36]
0.03 18.29 1.22 1.02 Gonzales [36]
0.05 18.29 1.27 1.37 Gonzales [36]
0.06 18.29 1.50 1.47 Gonzales [36]
0.04 33.65 0.09 0.10 Weidong [40]
0.06 33.85 0.12 0.10 Weidong [40]
0.07 20.05 0.32 0.59 Zabaras [39]
0.07 24.07 0.25 0.38 Zabaras [39]
0.07 28.08 0.20 0.24 Zabaras [39]
0.07 32.09 0.15 0.14 Zabaras [39]
0.07 36.10 0.12 0.08 Zabaras [39]
117 Validation of Entrainment Calculation
The entrainment rate is used in the mechanistic model to determine the fraction of sand particles in the gas core and in the liquid film. Since prediction of entrainment rate is important in development of the mechanistic model, the predicted entrainment rate obtained from the Ishii [29] model were compared to the entrainment measurements by
Azzopardi [47] as shown in Figure VII-5. The predicted entrainment rates using the Ishii model agree well with data at lower gas velocities and slightly overpredict entrainment at higher gas velocities.
1.00 Exp.Data (Vsg=30 m/sec) Exp.Data (Vsg=40 m/sec) Exp.Data (Vsg=50 m/sec) Exp. Data (Vsg=60 m/sec) 0.80 Ishii Model (Vsg =30 m/sec) Ishii Model (Vsg=40 m/sec) Ishii Model (Vsg=50 m/sec) Ishii Model (Vsg=60 m/sec)
0.60
0.40 Entrainment Entrainment
0.20
0.00 0.03 0.06 0.09 0.12 0.15 Superficial Liquid Velocity (m/sec)
Figure VII-5. Comparison of Measured Entrainments [47] with Ishii [29] Model Predictions.
118 Model for Mist Flow
Mist flow commonly exists in gas production wells with high gas velocity and low liquid rate. Higher erosion rates are observed in gas wells with mist flows that can damage production equipment, piping and fittings. At higher gas velocity, the annular liquid film thickness becomes very thin, unstable, wavy and discontinuous. As the velocity increases further, the annular film disappears and breaks into small liquid droplets. These entrained droplets travel with higher velocity (similar to the gas velocity) and can not stay attached to the wall. The sand particles entrained in the gas and liquid droplets travel with a higher momentum impacting the wall of the geometry resulting in erosion damage to the wall. Due to high particle impact velocity and absence of liquid film on the wall, the erosion in mist flow may be higher than other flow regimes.
Although the need to improve understanding of erosion phenomenon in mist flow regime has been realized by the oil and gas industry for a long time, the work performed in defining the mist flow regime is very limited. The available multiphase flow prediction models do not recognize or address the mist-flow regime. Lack of understanding about the mist flow regime prevents development of a mechanistic erosion prediction model in mist flow. The physical phenomenon of mist flow is analyzed and an attempt at a definition of annular to mist flow criteria has been developed in this work.
Andreussi [48] performed an experimental study of the pressure gradient, annular film thickness, liquid entrainment, and drop size distribution in downward air-water vertical annular mist-flow. The experimental results showed that at any liquid flow rate, the gas phase to smooth pipe friction factor is a decreasing function of the film thickness
119 to diameter ratio. The maxima of the friction factor ratio were at the point of entrainment inception. Chien and Ibele [49] reported that the maxima of the gas phase friction factor represent the point of entrainment inception. They defined the annular to mist flow transition as a function of superficial liquid and superficial gas Reynolds numbers.
Figure VII-5 shows the proposed preliminary annular to mist flow transition line proposed by Andreussi. The flow regimes of the flow conditions reported by Salama [3] and Bourgoyne [50] were predicted using the procedure developed by Ansari [38] for annular flow and the mist flow criteria that were described earlier. The predicted flow regimes for the above data are plotted in Figure VII-6. This indicates that the erosion data provided by Bourgoyne [50] is in mist flow regime. Salama [4] and Bourgoyne
[50] erosion results are used later in Chapter VIII to compare with the mechanistic model that is developed during this research.
15.0 Salama [3] Data Andreussi Proposed Transition 12.0 Bourgoyne Data [50]
9.0
Mist Flow 6.0 Annular Flow
3.0 Friction Ratio (fg/fi) Factor
0.0 0.00 0.01 0.02 0.03 0.04 0.05 Film thickness/ Pipe Dia
Figure VII-6. Andreussi [48] Proposed Transition for Annular to Mist Flow.
120 Model for Slug Flow
Slug flow occurs over a wide range of gas and liquid flow rates. It is the dominant flow pattern in upward inclined flow. Slug flow hydrodynamics is very complex with unique and unsteady flow behaviors. It is characterized by an alternate flow of a gas pocket, named Taylor bubble, and liquid slugs that contain numerous small gas bubbles.
A thin liquid film flows downward between the Taylor bubble and the pipe wall in vertical slug flow. The Taylor bubble is assumed to be symmetric around the pipe axis for fully developed vertical slug flow. Figure VII-7 shows a schematic description of slug flow in vertical pipe. For fully developed slug flow, the length of the Taylor bubble is approximately in the order of 100 times the diameter of the pipe.
The slug body of unit length LSU is divided into two parts: the Taylor bubble of length LTB, and the liquid slug of length LLS. The Taylor bubble occupies nearly the entire pipe cross-section and propagates downstream around the wall. The average liquid velocity in the liquid slug is VLLS and the liquid holdup of the liquid slug is denoted by
HLLS.
Due to unsteady hydrodynamic characteristics of slug flow, it has a unique velocity, holdup and pressure distribution. Therefore, the prediction of the liquid holdup, pressure drop, heat and mass transfer are difficult and challenging. Several mechanistic models have been proposed that enable reasonable prediction of the liquid holdup in the slug, slug length, slug frequency and velocities of Taylor bubble and liquid slug. Taitel and Barnea [51] presented a comprehensive analysis of slug flow into a unified model for horizontal, inclined and vertical flows.
121 VLTB
Taylor Bubble (LTB)
LSU
VLLS
HLLS Liquid Slug (LLS)
Figure VII-7. Schematic Description of Slug Flow in Vertical Pipe.
For calculation of erosion in slug flow, it is assumed that sand is uniformly distributed in the liquid phase and the mass fraction of sand in the liquid slug is equal to the mass fraction of liquid in the liquid slug. Assuming that the mass fraction of sand moving with the liquid slug causes the erosion in slug flow, the characteristic initial particle velocity for slug flow can be a calculated as
Vo = VLLS = Velocity of liquid in the liquid slug (VII-17)
The erosion rate in slug flow is calculated by using the fraction of sand particles in the liquid slug and Vo in Equation II-3.
HLLS = (Mass of liquid in the liquid slug / Total mass of liquid)
= (Mass of sand in the liquid slug / Total mass of sand)
Erosion rate in slug flow , ER = f (Vo, HLLS) (VII-18)
122 The erosion calculation method is described in Chapter II . In Equation VII-18,
HLLS is the liquid holdup in the liquid slug and VLLS is the liquid velocity of the liquid slug. The liquid holdup in the slug body, HLLS can be calculated using the Gomez et al.
[46] correlation:
-(0.45.θ +2.48E-6.Re) HLLS = 1.0 e (VII-19)
where, θ is in radians for pipe inclination angle 0 ≤ θ ≤ 900 (θ = 900 for vertical)
The slug superficial Reynolds number is calculated as
ρ V d Re = f m p (VII- 20) µf
where, Vm = VSL + VSG
The velocity of liquid in liquid slug can be calculated as:
Vm − VGLS (1− H LLS ) VLLS = H LLS
(VII- 21) where, VGLS is the velocity of gas in the liquid slug. The calculated initial sand particle velocities in the liquid slug were used in the mechanistic model to calculate erosion rate.
123 Model for Churn Flow
Churn flow is somewhat similar to slug flow except churn flow is more chaotic.
The liquid and gas phases have oscillatory motion and without stable and clear boundaries between the phases. As the gas velocity in slug flow increases, the liquid slug becomes shorter, breaks and mixes with the following slug. Due to this mixing phenomenon, the shape of the Taylor bubble gets distorted resulting in churn flow. Kaya
[52] defined the churn flow pattern as consisting of highly aerated slugs with repeated destruction of liquid continuity in the slug during an oscillatory motion of the slug. Churn flow is normally observed between the slug and annular flow pattern in vertical or nearly vertical upward flow. As the pipe inclination angle changes from vertical to horizontal, churn flow changes to slug flow. Churn flow does not exist in horizontal flow. A schematic of the churn flow is shown in Figure VII-8.
There is no available mechanistic model in the literature to predict hydrodynamic behavior of churn flow due to its highly disordered and chaotic nature. Churn flow exhibits intermittent behavior, similar to slug flow. Hasan [53] attempted to develop a separate model for churn flow by redefining the transitional velocity coefficient as 1.15.
Tengesdal [54] adapted the slug flow model to churn flow with a different closure relationship for the transitional velocity of the Taylor Bubble and void fraction in the liquid-phase based on experimental churn flow data of Schmidt [55] and Majeed [56].
According to Tengesdal, under turbulent flow conditions, the maximum centerline velocity of flow can be approximated as the average mixture velocity.
124 In churn flow, it is assumed that the sand is uniformly distributed in the liquid phase. The velocities of the liquid and sand are assumed to be the same as the mixture velocity. Therefore, the characteristic initial sand particle velocity for churn flow is assumed to be the mixture velocity and is calculated as
Vo = Vm = VSL + VSG (VII-22)
Gas Liquid Bubble Phase
Figure VII- 8. Schematic Description of Churn Flow.
Model for Bubble Flow
Bubble flow is characterized as small gas bubbles that are distributed in the continuous liquid phase. Bubble flow can be classified as bubbly and dispersed bubble flows based on the relative slip between the bubbles and the surrounding liquid phases.
Bubbly flow exists in relatively large pipe diameters with upward vertical or inclined
125 pipes. Due to slippage and buoyancy effects, in bubbly flow, gas bubbles tend to flow near the upper part of inclined pipes. In bubbly flow, slippage between the bubble and liquid phase is present and the bubbles are not distributed homogenously. In dispersed bubble flow, gas bubbles are uniformly distributed in the liquid phase and can be treated as homogeneous flow. Due to homogeneous distribution of gas bubbles, the mixture properties can be used in expressing dispersed bubble flow. In this section, the mechanistic model is developed for dispersed bubble flow.
At lower gas flow rates, smaller and fewer bubbles exist. As the gas flow rate increases, the number of bubbles also increases and the shape of the bubbles changes from smaller round bubbles to larger, irregularly shaped bubbles due to coalescence and collision of bubbles. In bubble flow, it is assumed that the gas phase is approximately uniformly distributed in the form of discrete bubbles that move at different velocities in a continuous liquid phase. Bubble flow occurs at low gas rates. Figure VII-9 schematically describes bubbly flow in a vertical pipe.
In bubble flow, it is also assumed that the sand is uniformly distributed in the liquid phase. The velocities of the liquid and sand in the bubble flow region is assumed to be the same as the mixture velocity. Therefore, the characteristic initial sand particle velocity for bubble flow is assumed to be the mixture velocity and can be calculated using Equation VII-22.
126 Liquid phase Gas Bubbles
Figure VII-9. Schematic Description of Bubble Flow.
127 CHAPTER VIII
VALIDATION OF THE MECHANISTIC MODELS
To validate the mechanistic model, the model predicted erosion rates were compared with the available literature data, single-phase experimental results and multiphase experimental results. The mechanistic model predicted erosion rates were compared to measured erosion rates reported by Salama [3], Bouugoyne [50], and
Greenwood [57]. The measured erosion rates reported in the literature are for single- phase (air), annular, mist, slug/ churn and bubble flow regimes, different sand sizes, and different pipe diameters. To complement the available literature data and to validate the model prediction at other flow conditions, erosion experiments were conducted in multiphase flow at low liquid rates. To validate the model for single-phase flow conditions, erosion experiment were also conducted in single-phase flow with air. The comparisons are presented in the following sections of this chapter.
Comparison of Pedicted Erosion with Measured Erosion in Single-Phase Flow
Bourgoyne [50] investigated erosion behavior in single-phase flow with air and sand in a 52.5 mm diameter elbow. These experiments were conducted with very high sand rates of approximately 350 micron average sand size. The sand was assumed to be of semi-rounded shape with a sharpness factor of 0.53. The measured erosion data and
128 the mechanistic model predicted erosion rates are reported in Table VIII-1. The mechanistic model predictions agree reasonably with the experimental erosion data at high gas velocity and high sand rates. However, at these high gas velocities, the predicted erosion is less than the measured values.
Table VIII-1. Comparison of Mechanistic Model Predictions with Bourgoyne [50] Erosion Data in Single-Phase Flow Air Air Sand Sand Rate Sand Volume Measured Measured Predicted Velocity Velocity Rate (m3/sec) Concentration Erosion Erosion Erosion (m/sec) (ft/sec) (kg/sec) (%) (m/sec) (mil/lb) (mil/lb)
111 364 0.55 2.08E-4 0.0864 6.15E-5 1.99 1.29
141 463 0.198 7.46E-5 0.0245 4.10E-5 3.70 1.96
141 463 0.081 3.06E-5 0.0100 1.55E-5 3.42 1.86
148 486 0.153 5.78E-5 0.0180 3.20E-5 3.74 2.13
32 105 0.046 1.74E-5 0.0248 3.74E-7 0.15 0.18
47 154 0.067 2.55E-5 0.0250 3.32E-7 0.19 0.37
72 236 0.118 4.46E-5 0.0286 1.65E-5 2.50 0.78
93 305 0.130 4.93E-5 0.0244 3.70E-6 0.51 1.21
98 322 0.119 4.52E-5 0.0212 4.23E-6 0.64 1.32
Tolle and Grenwood [57] of Texas A&M investigated single-phase erosion behavior in different pipe fittings to identify fittings that were less susceptible to sand erosion. The pipe diameter used in the experiment was 2.0 inches and the sand size was approximately 300 microns. The sand was assumed to be sharp with a sharpness factor of 1.0. The mechanistic model predicted erosion rates were similar to the measured data as reported in Table VIII-2.
129 Table VIII-2. Comparison of Mechanistic Model Predictions with Tolle and Greenwood [57] Erosion Data in Single-Phase Flow
Air Sand Rate Sand Volume Calculated Calculated Model Pred.
Velocity (lb/sec) Concentration Pen. Rate Pen. Rate Pen. Rate (ft/sec) (%) (in/yr) * (mil/lb) * (mil/lb)
30 1.94E-03 0.0018 2.33 3.81E-02 4.74E-02
40 1.94E-03 0.0013 4.16 6.79E-02 7.81E-02
50 1.93E-03 0.0011 8.16 1.34E-01 1.15E-01
60 1.94E-03 0.0009 9.99 1.63E-01 1.58E-01
70 1.93E-03 0.0008 13.3 2.18E-01 2.06E-01
80 1.95E-03 0.0007 17.8 2.89E-01 2.60E-01
90 1.95E-03 0.0006 19.8 3.22E-01 3.18E-01
100 1.94E-03 0.0005 22.3 3.64E-01 3.82E-01
70 4.28E-02 0.017 107 7.93E-02 3.19E-01
100 4.54E-02 0.013 399 2.78E-01 3.83E-01 * Calculated from erosion ratio
During this investigation, erosion experiments were conducted in single-phase flow with air and sand. A one-inch elbow specimen of 316 stainless steel material was used with average sand size of approximately 150 microns as described in Chapter IV.
The single-phase erosion results and the mechanistic model predictions are presented in
Table VIII-3. The mechanistic model overpredicted the erosion rate for vertical flow conditions by a factor of 3-4 and for all the conditions by a factor of 3-5.
130 Table VIII-3. Comparison of Mechanistic Model Predictions with Experimental Results in Single-Phase Flow
Gas Flow Sand Calc. Max. Pen. Mech. Model Model Velocity Orientation Throughput Rate (Test Data) Predicted Pen. Prediction to (ft/sec) (Horizontal/ (kg) (mils/lb) * Rate (mils/lb) Measured Ratio Vertical)
112 Horizontal 1.00 1.14E-1 N/A** N/A**
112 Vertical 1.00 1.85E-1 5.68E-1 3.0
90 Horizontal 1.00 7.88E-2 N/A** N/A**
90 Vertical 1.00 1.17E-1 3.89E-1 3.3
62 Horizontal 1.00 5.74E-2 N/A** N/A**
62 Vertical 1.00 4.84E-2 2.03E-1** 4.2 * Calculated from mass loss data as described in Appendix A. ** The current model calculates erosion in vertical flow only.
Figure VIII-1 illustrates the mechanistic model predicted penetration rates
(mils/lb) with the experimental erosion data reported by Bourgoyne [50], Greenwood
[57], and single-phase erosion experiments conducted at The University of Tulsa (TU
Data). A perfect agreement line and a factor of 5 to perfect agreement line shows the mechanistic model predictions are within a factor of five for all these flow conditions.
The model was able to predict erosion reasonably well with the experimental erosion data in single-phase flow .
Comparison of the new mechanistic model predicted erosion with the previous
E/CRC model [16] and experimental data is presented in Figure VIII-2. In single-phase flow with air, both the previous E/CRC model and the new mechanistic model have similar predictions and both models resonably agree with the experimental data. 131 1.E+02 TU Data (Horizontal) ) TU Data (Vertical) Bourgoyne Data Tolle and Greenwood Data 1.E+01 Perfect Agreement Factor of 5 x Measured
1.E+00
1.E-01
1.E-02 Model Predicted Erosion (mil/lb Erosion Predicted Model 1.E-03 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02
Measured Erosion (mil/lb)
Figure VIII-1. Comparison of Experimental Erosion Results with Mechanistic Model Predictions in Single-Phase Flow
8.0E-01 Gas Only-Vert. ) Mechanistic Model 6.0E-01 Previous Model
4.0E-01
2.0E-01 Penetration Rate (mils/lbPenetration Rate
0.0E+00 0 25 50 75 100 125 Gas Velocity (ft/sec)
Figure VIII-2. Comparison of Previous Model and Mechanistic Model Predictions with Experimental Erosion Data in Single-Phase (Air) Flow
132 Comparison of Predicted Erosion with Literature Data in Multiphase Flow
The mechanistic model predicted erosion rates were compared with available multiphase erosion data reported in the literature and data gathered during this investigation. Salama [3] reported erosion data at superficial gas velocities between 3.5 and 51.0 m/sec and at superficial liquid velocities between 0.2 and 5.8 m/sec. Two different sand sizes of 150 and 250 microns were used with 49 mm and 26.5 mm elbows made from carbon steel and duplex stainless steel materials. The fluids used were air- water mixture at 2 bar (29.4 psi) and nitrogen-water mixture at 7 bar (103 psi). The flow patterns for the test conditions were not reported by the investigator. Therefore, the flow regimes were calculated using the mechanistic model . A flow map for a two-inch vertical pipe with the flow regimes and literature reported erosion test conditions [3, 50] are presented in Figure VIII-3. Figure VIII-4 shows a one-inch vertical flow map with the literature reported erosion test conditions [3].
1.0E+03 FLOW MAP Annular-Salama [3] Slug/Churn- Salama [3] 1.0E+02 Bubble- Salama [3]
ft/sec) Mist - Bourgoyne [50]
Dispersed Bubble 1.0E+01
Bubble 1.0E+00
Slug/ Churn
1.0E-01 Annular/ Mist Superficial Liquid Velocity (
1.0E-02 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 Superficial Gas Velocity (ft/sec)
Figure VIII-3. Two-inch Vertical Flow Map with Erosion Test Conditions 133 1.0E+03 Flow Map Dispersed Annular-Salama [3] 1.0E+02 Bubble Flow ft/sec)
1.0E+01
1.0E+00
Annular Flow 1.0E-01 Slug/ Churn Flow Superficial Liquid Velocity (
1.0E-02 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 Superficial Gas Velocity (ft/sec)
Figure VIII-4. One-inch Vertical Flow Map with Erosion Test Conditions
The mechanistic model predictions of erosion in annular flow regimes are reported in Table VIII-4 with the calculated droplet velocity and entrainment fraction.
The mechanistic model predicted erosion rates agreed well with the erosion data and were higher in most cases showing good agreement with data. Table VIII-5 compares the mechanistic model predicted erosion with the measured erosion in slug/churn and bubble flow regimes. The flow patterns predicted by Ansari [38] model were verified by conducting flow visualization experiments in a two-inch test section with L/D ≈ 150. In vertical pipe in some flow conditions, the observed flow patterns were churn flow that is different than the model predicted slug flow. Based on the flow visualization experiments, erosion rate was calculated using the churn flow model. The predicted erosion rates in slug/churn and bubble flow agree reasonably well with the mechanistic
134 model predictions.
The mechanistic model predictions were also compared to previous empirical erosion models proposed by Salama [3] and the empirical model developed at the
Erosion/ Corrosion Research Center [17]. The literature reported erosion data and the experimental erosion results were compared with the empirical models and the mechanistic model predictions and are presented in Appendix D.
135 Table VIII-4. Comparison of Mechanistic Model Predictions with Literature Reported [3] Erosion Data in Annular Flow.
Elbow Calc. Calc. Sand Measured Model
VSL VSG Dia. Drop. Vel. Entrain. size Flow Erosion Prediction (m/sec) (m/sec) (mm) (m/sec) Rate (micron) Pattern (mm/kg) (mm/kg) Note
1.0 30.0 49 24.8 0.814 150 Annul 5.25E-04 1.41E-03 1
0.5 30.0 49 24.7 0.713 150 Annul 2.46E-03 1.94E-03 1
5.8 20.0 49 18.1 0.565 150 Annul 5.19E-05 1.47E-04 1
3.1 20.0 49 18.0 0.501 150 Annul 6.93E-05 2.46E-04 1
1.0 15.0 49 14.3 0.198 150 Annul 1.47E-04 1.01E-04 1
6.2 9.0 26.5 3.0 0.789 250 Annul 1.80E-04 9.61E-05 2
1.5 14.4 26.5 13.9 0.248 250 Annul 2.30E-04 6.70E-04 2
1.5 14.6 26.5 14.0 0.257 250 Annul 4.20E-04 6.98E-04 2
2.1 34.4 26.5 27.4 0.982 250 Annul 2.83E-03 6.77E-03 2
1.0 35.0 26.5 28.2 0.971 250 Annul 6.56E-03 9.68E-03 2
0.5 34.3 26.5 27.7 0.935 250 Annul 7.20E-03 1.05E-02 2
0.7 37.0 26.5 29.9 0.977 250 Annul 8.03E-03 1.18E-02 2
0.5 38.5 26.5 30.9 0.979 250 Annul 8.03E-03 1.35E-02 2
1.5 44.0 26.5 35.2 0.985 250 Annul 1.05E-02 1.38E-02 2
0.6 51.0 26.5 40.8 0.989 250 Annul 1.34E-02 2.27E-02 2
Notes: (1) Data from Salama [3], air and water at 2 bar, Material: Carbon steel (BHN =160) (2) Data from Salama [3], nitrogen and water at 7 bar, Material: Duplex Stainless Steel
136 Table VIII-5. Comparison of Mechanistic Model Predictions with Literature Reported [3] Erosion Data in Slug/Churn and Bubble Flows.
Elbow Charac. Sand Calculated/ Measured Model
VSL VSG Dia. Vel., Vo Size Observed Erosion Prediction (m/sec) m/sec (mm) (m/sec) (micron) Flow Pattern (mm/kg) (mm/kg) Note
5.0 15.0 49 20.0 150 Slug/ Churn 6.38E-05 2.41E-05 1,4
5.0 10.0 49 15.0 150 Slug/ Churn 1.35E-05 7.08E-06 1, 4
0.7 10.0 49 10.7 150 Slug/ Churn 7.01E-05 8.18E-05 1, 4
0.2 8.0 49 8.2 150 Slug/ Churn 1.23E-04 2.33E-04 1, 4
4.0 3.5 49 7.5 150 Bubble 4.60E-06 3.12E-07 1 (1) Data from Salama [3], air and water at 2 bar, Material: Carbon steel (BHN 160) (4) Model predictions are based on churn flow model.
Bourgoyne reported erosion data [50] at high superficial gas velocities of 72 to
107 m/sec and superficial liquid velocities of 0.12 to 0.53 m/sec with air and water in a
52.5 mm carbon steel elbow. Due to high gas velocity, the calculated entrainment in the gas core region was very high and the flow pattern was assumed to be mist flow as described in Chapter VII. Comparison between the mechanistic model predicted erosion rates and Bourgoyne data presented in Table VIII-6 shows higher model predictions than the experimental data. The reason for this higher prediction may be due to uncertainty of model predictions at higher velocity. Another possible reason is that during the experiment, the elbow material became hot reducing the hardness of material causing larger mass loss. The mechanistic model predicted ersoion rates are also compared with the previous E/CRC semi-empirical [17] model and Salama [3] model and presented in Appendix D
137 Table VIII-6. Comparison of Mechanistic Model Predictions with Literature Reported [3,50] Erosion Data in Mist Flow
Elbow Calc. Calc. Sand Measured Model
VSL VSG Dia. Drop. Vel. Entrain Size Flow Erosion Prediction (m/sec) (m/sec) (mm) (m/sec) Rate (micron) Pattern (mm/kg) (mm/kg) Note
0.7 52.0 26.5 52.0 1.000 250 Mist 1.33E-02 3.38E-02 2
0.53 86.0 52.5 86.0 0.999 350 Mist 1.27E-01 4.64E-02 3
0.53 92.0 52.5 92.0 1.000 350 Mist 1.21E-01 5.24E-02 3
0.12 89.0 52.5 89 0.998 350 Mist 1.08E-01 5.26E-02 3
0.53 84.0 52.5 84 1.000 350 Mist 9.34E-02 4.45E-02 3
0.53 72.0 52.5 72 1.000 350 Mist 5.37E-02 3.06E-02 3
0.12 84.0 52.5 84 1.000 350 Mist 7.51E-02 4.36E-02 3
0.12 92.0 52.5 92.0 1.000 350 Mist 9.94E-02 5.11E-02 3
0.53 107 52.5 107 1.000 350 Mist 1.05E-01 6.27E-02 3
(2) Data from Salama [3], nitrogen and water at 7 bar, Material: Duplex Stainless Steel (3) Data from Bourgoyne [50], air and water at standard conditions,, Material: Assumed Carbon steel (BHN 140)
Comparison of Predicted Erosion with Multiphase Flow Experimental Data
Experiments were conducted at VSG = 32, 62, 90, and 112 ft/sec and at VSL = 0.1 and 1.0 ft/sec in vertical and horizontal flows using 316 stainless steel elbow specimens as discussed in Chapter V. Table VIII-7 compares the calculated maximum penetration rates from the experimental erosion data with the mechanistic model predictions in multiphase flow. The mechanistic model overpredicted erosion for all these flow conditions. In vertical flow, the mechanistic model overpredicted erosion by a factor of
1.34 to 4.32 compared to erosion test data. The overperdiction factor is 1.02 to 17.6 in
138 horizontal flow. The mechanistic model predictions match closely with the experimental results of the vertical elbow specimens.
Table VIII-7. Comparison of Mechanistic Model Predictions with Experimental Measurements of Multiphase Flow
Superficial Superficial Flow Sand Maximum Mechanistic Gas Velocity Liquid Velocity Orientation Through Penetration Rate- Model Prediction (ft/sec) (ft/sec) put (kg) Test (mils/lb) (mils/lb)
112 0.1 Horizontal 10.80 5.82E-3 N/A *
112 0.1 Vertical 10.80 1.92E-2 1.30E-1
90 0.1 Horizontal 16.20 2.55E-3 N/A *
90 0.1 Vertical 16.20 5.15E-3 4.86E-2
62 0.1 Horizontal 19.80 1.01E-3 N/A *
62 0.1 Vertical 19.80 2.64E-3 8.47E-3
32 0.1 Horizontal 19.80 1.25E-3 N/A *
32 0.1 Vertical 19.80 2.11E-3 6.17E-3
112 1.0 Horizontal 20.40 1.72E-2 N/A *
112 1.0 Vertical 20.40 4.63E-2 1.97E-1
90 1.0 Horizontal 27.20 5.53E-3 N/A *
90 1.0 Vertical 27.20 1.55E-2 8.07E-2
62 1.0 Horizontal 23.80 1.10E-3 N/A *
62 1.0 Vertical 23.80 3.15E-3 1.62E-2
32 1.0 Horizontal 40.80 1.27E-4 N/A *
32 1.0 Vertical 40.80 5.97E-4 4.90E-3 * The current model calculates erosion for vertical flow only
139 The model predictions and measurements are exhibited in Figure VIII-5 with a perfect agreeement line and factor of 5 to the perfect agreement line. The mechanistic model predictions are within a factor of 5 of the measured erosion rates for the literature data and TU data that was discussed earlier. The mechanistic model predictions agree well with the measured erosion data in all multiphase flow regimes except for bubble flow regime where the model prediction is lower than the measured erosion.
Annular-Literature
) Perfect agreement 1.E-01 Churn-Literature Mist-Literature Annular-TU Data (Ver) Churn- TU Data (Ver) Bubble- Literature
1.E-03
1.E-05
Factor of 5 to perfect agreement Model Predicted Erosion (mm/kg 1.E-07 1.E-07 1.E-05 1.E-03 1.E-01 Measured Erosion (mm/kg)
Figure VIII-5. Comparison of Measured Erosion with Mechanistic Model Predictions for Annular, Mist, Slug/ Churn, and Bubble Flows
Figure VIII-6 demonstrates how the erosion rate decreases when the liquid rate is increased from 0.1 ft/sec to 1.0 ft/sec at VSG = 32 ft/sec. Both the old E/CRC model and the mechanistic model show trends similar to the experimental results in vertical flow.
140 1.0E-01 Vsg=32 (Vert.-Test) Vsg=32 (Old Model) Vsg=32 (Mech.Model)
1.0E-02
1.0E-03 Penentartion Rate (mils/lb)
1.0E-04 00.11.0 Superficial Liquid Velocity (ft/sec)
Figure VIII-6. Comparison of Old Model and Mechanistic Model Predictions with Experimental Erosion Data at Superficial Gas Velocity of 32 ft/sec
Figure VIII-7 compares the experimental erosion results with mechanistic model predictions in single-phase flow, and multiphase flow with 0.10 ft/sec and 1.0 ft/sec liquid rates at superficial gas velocities of 62, 90 and 112 ft/sec. The effect of liquid rate on erosion is illustrated in these comparisons. Experimental data and the model show that the erosion rate decreases with the addition of small amounts of liquid (0.10 ft/sec liquid rate) when compared with single-phase flow erosion data. Surprisingly, the erosion rate increased with further addition of liquid from 0.10 ft/se to 1.0 ft/sec. The mechanistic model predicted similar trends as the experimental results with higher predicted erosion in all these test conditions. Whereas, the old model was unable to predict this trend and showed decreasing erosion rate as the liquid rate was increased.
Figures VIII-8 and VIII-9 illustrate the effect of liquid rate on erosion at superficial gas 141 velocities of 90 and 112 ft/sec in horizontal and vertical flows. The mechanistic model predictions are higher than the experimental data with trends similar to the experimental results in these conditions. The old model was unable to predict this unusual but interesting trend of lower erosion at higher liquid rate.
1.0E+00 Vsg=62 (Vert.-Test) Vsg=62 (Old Model) Vsg=62 (Mech.Model)
1.0E-01
1.0E-02
1.0E-03 Penetration Rate (mils/lb)
1.0E-04 00.11.0 Superficial Liquid Velocity (ft/sec)
Figure VIII-7. Comparison of Old Model and Mechanistic Model Predictions with Experimental Erosion Data at Superficial Gas Velocity of 62 ft/sec
142 1.0E+00 Vsg=90 (Vert.-Test) Vs g=90 (Old Model) Vsg=90 (Mech.Model)
1.0E-01
1.0E-02 Penetration Rate (mils/lb)
1.0E-03 00.11.0 Superficial Liquid Velocity (ft/sec)
Figure VIII-8. Comparison of Old Model and Mechanistic Model Predictions with Experimental Erosion Data at Superficial Gas Velocity of 90 ft/sec 1.0E+00 Vsg=112 (Vert.-Test) Vsg=112 (Old Model) Vsg=112 (Mech.Model)
1.0E-01 Penetration Rate (mils/lb)
1.0E-02 00.11.0 Superficial Liquid Velocity (ft/sec)
Figure VIII-9. Comparison of Old Model and Mechanistic Model Predictions with Experimental Erosion Data at Superficial Gas Velocity of 112 ft/sec 143 1.0E+00 Vsg=112 (Vert.-Test) Vsg=112 (Old Model) Vsg=112 (Mech.Model)
1.0E-01 Penetration Rate (mils/lb)
1.0E-02 00.11.05 10 Superficial Liquid Velocity (ft/sec)
Figure VIII-10. Comparison of Old Model and Mechanistic Model Predictions with Experimental Erosion Data at Different Liquid Velocities.
To further investigate this erosion behavior, erosion rates were predicted at VSL =
5.0 and 10.0 ft/sec and at VSG = 112 ft/sec. Figure VIII-10 compares the old model and the mechanistic model predictions at different liquid rates. The old model predicted lower erosion as the liquid rate was increased to 5 and 10 ft/sec. Whereas, the mechanistic model shows lower erosion with increased liquid rate of more than 1.0 ft/sec.
The mechanistic model predicted a lower reduction in erosion rate at these high liquid rates compared to the old model. Figure VIII-11 shows the erosion test results, old model and the mechanistic model predictions at superficial gas velocities of 32, 62, 90, and 112 ft/sec and at a superficial liquid velocity of 0.10 ft/sec. The mechanistic model predictions have similar trends as the experimental results and are closer to the data compared to the old model. 144 1.0E+00 Vsl=0.1 ft/sec (Old Model) Vsl=0.1 ft/sec-Vert. Mechanistic Model
1.0E-01
1.0E-02 Penetration Rate (mils/lb)
1.0E-03 0 255075100125 Superficial Gas Velocity (ft/sec)
Figure VIII-11. Comparison of Old Model and Mechanistic Model Predictions with Experimental Erosion Data at Superficial Liquid Velocity of 0.10 ft/sec
Figure VIII-12 demonstrates how the erosion rate increases with increased gas velocity for the same liquid velocity. Comparison between the erosion test results, old model and mechanistic model predictions at superficial gas velocities of 32, 62, 90, and
112 ft/sec and at a superficial liquid velocity of 1.0 ft/sec shows higher predictions by both models. The mechanistic model follows the same trend as the experimental erosion data with better agreement compared to the old model.
145 1.0E+00 Vsl=1.0 ft/sec (Old Model) Vsl=1.0 ft/sec-Vert. Mechanistic Model 1.0E-01
1.0E-02
1.0E-03 Penetration Rate (mils/lb)
1.0E-04 0 25 50 75 100 125 Gas Velocity (ft/sec)
Figure VIII-12. Comparison of Old Model and Mechanistic Model Predictions with Experimental Erosion Data at Superficial Liquid Velocity of 1.0 ft/sec
In spite of the extreme level of complexity of erosion multiphase flow with entrained solid particles and the number of variables that influence the erosion process, the attempt of this study is to provide an effective tool to estimate erosion in both single and multiphase flow within a factor of 5 applied to the perfect agreement line as shown earlier in this chapter.
146 CHAPTER IX
UNCERTAINTY ANALYSIS OF THE MODEL PREDICTIONS
All measurement systems have error in the data since the true value is not known.
A good understanding of the amount of error in the measurement system is necessary for the results to be used to their fullest value. Reporting uncertainty of experimental measurement is as important as the data itself. Uncertainty analysis is a systematic approach of defining the error in the experimental data and is a function of the measurement system. It is important to understand the difference between error and uncertainty. Error is the difference between the true value and the measured value since the true value is unknown; the error is unknown and unknowable. Uncertainty is an estimate of the limits to which an error can be expected to go, under a given set of conditions as part of the measurement system [58]. The difference between uncertainty and error is that uncertainty is an estimate of the error.
Types of Uncertainty
There are two types of errors and uncertainties, random and systematic. The error sources that cause scatter in the measured data are defined as random or precision error. By calculating the standard deviation of the data, the random uncertainty can be defined by the confidence interval that can be calculated by using standard deviation of
147 the data and t- statistic. 95% confidence interval is commonly used in describing data that means that 95% of the time, the population average will be contained with the interval (X ± tSX). X is the sample average, t is the value of t-statistics for 95% confidence interval and Sx is the standard deviation of the average X.
Systematic errors or bias affect experimental data by the same amount for the same condition. Systematic errors can not be detected from the experimental data. In experimental data with low random error and high systematic error, the systematic error may not be detected and the data may appear to be accurate. This may lead to misinterpretation of the data resulting in erroneous decisions by the user. Since the true systematic error of a measurement system may not be known, its limit can be estimated with the systematic uncertainty. There are several types of systematic errors that give rise to different types of systematic uncertainties. Abernethy [59] provided methods for estimating the systematic uncertainties by repeating the same test using different test equipment, different laboratories and by calibrating the measuring equipment. If it is not possible to repeat the experiments using the above methods, the systematic uncertainties can be estimated by the experimenters and by careful review of instrument manufacturers’ literature.
Sources of Uncertainty
The uncertainties in mass loss measurements and the results calculated from those measurements are due to the following sources:
1) Measured weight of the specimens before and after each test.
2) Measured weight of the sand used during each experiment.
3) Flow meter reading used to determine the gas flow rate. 148 4) Pressure gage reading used to calculate the gas velocity.
5) Sand-liquid injection rate from slurry tank to the test section used to
calculate the superficial liquid velocity.
6) Size and shape distributions of the sand used in the experiment.
7) Brinnell hardness of the specimen.
The first two sources of error, measured weight of the specimen and sand are influenced by the accuracy of the balances used. The third source of error is from the accuracy of the flow meter readings used in calculation of the gas velocity. The gas flow rate varied as the compressor started and stopped during the test. The fifth source of error is from the precision of the pressure gage readings that is also used in calculation of gas velocity. The fifth source of error is associated with the measurement of liquid rate from the slurry tank to the test section. As the liquid level changed in the slurry tank, the liquid rate to the test section changed. The uncertainty in sand size distribution was obtained from sample standard deviation of sand size distribution data using t-statistics and 95% confidence interval. The uncertainty of sand shape is not considered in this analysis.
Propagation of uncertainty can be analyzed by using Taylor’s series by neglecting higher order terms [60].
f [(x1 + ∆ x1 ),(x2 + ∆ x2 ), ...... (xn + ∆ xn )] ∂f ∂f ∂f ...... (IX-1) =f ( x1 ,x2 , ...... xn ) + ∆ x1 + ∆ x2 + ...... ∆ xn ∂ x1 ∂ x2 ∂ xn
The above equation can be rewritten by changing the ∆xn’s to un’s merely to
represent the total uncertainties in a better way.
149 f ( x1 + ux1 ), ( x2 + ux2 ), ...... ( xn + uxn ) − f( x1 , xx , . . . . . xn ) ∂f ∂f ∂f . . (IX-2) =uf −Total = ux1 + ux2 + ...... + uxn ∂x1 ∂x2 ∂xn
where,
uf −Total = Total Uncertainty
ux1 = Uncertainty in variable x1
∂f = Change in uncertainty due to changes in variable x1 ∂x1
Equation (IX-2) indicates absolute values because uncertainties are usually
expressed as plus and minus values. The above equation expresses the maximum
uncertainties of a function that is not a reasonable approach as some of the
uncertainties may cancel each other in a system. A more practical approach to
determine the overall uncertainty is to calculate the root mean square (RMS) of
individual uncertainties of a system using the following equation.
2 2 2 ⎡ ∂f ⎤ ⎡ ∂f ⎤ ⎡ ∂f ⎤ uf −RMS = ⎢ux1 ⎥ + ⎢ux2 ⎥ + ...... + ⎢uxn ⎥ . . . . . (IX-3) ⎣ ∂x1 ⎦ ⎣ ∂x 2 ⎦ ⎣ ∂xn ⎦
where, xi = nominal value of variables
uxi = discrete uncertainties
uf = overall uncertainty
The uncertainty Equations (IX-2) and (IX-3) can be used to determine the overall uncertainty associated with the erosion prediction from the mechanistic model. To demonstrate the calculation of the overall uncertainty in predicting erosion, it was
150 assumed that the uncertainties from the sand size distribution, gas velocity and liquid velocity calculations were the dominating factors. In the uncertainty analysis, the above equation is further modified to calculate the change in penetration rate for changes in the sand size, liquid rate and gas rates.
∂f ∂(Pen.Rate) u x1 = u Sand ...... (IX-4) ∂x1 ∂(sand)
∂f ∂(Pen.Rate) u x2 = u liq.vel...... (IX-5) ∂x 2 ∂(liq.vel)
∂f ∂(Pen.Rate) u x3 = u gas vel ...... (IX-6) ∂x 3 ∂(gas vel.)
Table IX-1 lists the systematic and random uncertainties of the measurement systems and equipments used during erosion experiment. The random uncertainties are calculated from statistical analysis of the experimental data. The systematic uncertainties were determined by comparing results from two different measurement methods and estimates based on experience.
151 Table IX-1. Sources of Measurement Uncertainty of Erosion Experiment
Uncertainty Source Units Nomin Systematic Random Total Uncertainty al UncertaintyUncertaintyUncertainty Percent of
Level (B) (SX) (U95) ± nominal
Balance used for mass mg 20 0.10 0.40 mg 0.50 2.5% loss measurement
Balance used for sand grams 1000 10 * 5 15 1.5% measurement
Air Flow Reading CFM 20 0.25 0.50 0.75 3.75%
Pressure Gage Psi 10 0.50 0.50 1.0 10%
Liquid and Sand Rate GPM 2.5 0.05 0.10 0.15 6%
Sand size distribution µm 150 5 * 27 ** 32 21%
Hardness of the BHN 230 3 * 6.2 9.2 4% Specimen
Profilometer thickness µm 15 1.5 * 0.53 1.83 12.2% measurement
* Estimated value of uncertainty ** Calculated using 95% confidence interval of measured sand size distribution data and t-statistics.
Uncertainty Estimates in Erosion Prediction
The influences of uncertainties from sand size, liquid velocity, gas velocity on penetration rate were calculated by changing the value of one parameter at a time in the model. For example, the penetration rate was calculated by changing the sand size from
152 150 to 182 microns (+21%). The penetration rate calculation procedure using erosion prediction model was described in Chapter II. Table IX-2 below shows the mechanistic model predicted penetration rates for experimental test conditions by applying the uncertainties of sand size, liquid rate and gas rate. These input variables assumed to have the greatest influence on total uncertainty in penetration rate. The total uncertainty is the summation of the uncertainties in penetration rates due to changes in these three variables.
Table IX-2. Uncertainties in Mechanistic Model Predicted Penetration Rate
Mech. Mech. Mech. Model SuperficialSuperficial Mech. Model Model Prediction Gas Liquid Model Prediction Prediction With Total Velocity Velocity Pred. Pen. With +21% With + 6% +13.75% Uncer- Measured
VSG VSL Rate Sand Size Liq. Rate Gas Rate tainty Pen Rate (m/sec) (m/sec) (mm/yr) (mm/yr) (mm/yr) (mm/yr) (mm/yr) (mm/yr)
34.3 0.305 1.83E+00 1.87E+00 1.80E+00 2.77E+00 9.50E-01 1.12E+00
27.5 0.305 7.49E-01 7.67E-01 7.36E-01 1.19E+00 4.46E-01 3.54E-01
18.8 0.305 1.50E-01 1.56E-01 1.47E-01 2.36E-01 8.90E-02 7.04E-02
9.08 0.305 4.55E-02 4.82E-02 4.24E-02 5.56E-02 9.70E-03 1.32E-02
34.3 0.0305 1.21E+00 1.22E+00 1.22E+00 1.99E+00 8.00E-01 4.42E-01
27.5 0.0305 4.52E-01 4.56E-01 4.55E-01 7.58E-01 3.13E-01 1.17E-01
18.8 0.0305 7.87E-02 7.96E-02 7.93E-02 1.32E-01 5.48E-02 5.40E-02
9.08 0.0305 5.72E-02 5.79E-02 5.65E-02 7.05E-02 1.33E-02 4.56E-02
153 The percent change in mechanistic model predicted penetration rate due to uncertainties in sand size, liquid rate and gas rate are presented in Table IX-3. The total uncertainty was calculated by adding the absolute value of the individual uncertainty.
Based on the assumed and computed uncertainties associated with the input variables, the mechanistic model predicted penetration rate can have 23 to 70 % uncertainty.
Table IX-3. Percent Uncertainties in predicted Penetration Rates
Superficial Superficial Uncertainty Uncertainty Uncertainty Gas Liquid Due to Due to Due to Overall Overall Velocity Velocity Change in Change in Changes in Total RMS (m/sec) (m/sec) Sand size Liq-Rate Gas-Rate Uncertainty Uncertainty ∂(Pen.Rate) ∂(Pen.Rate) ∂(Pen.Rate)
∂(sand) ∂(liq.vel) ∂(gas vel.) (Uf-Total) (Uf-RMS)
34.3 0.305 2.19% -3.83% 53.01% 59.02% 53.19%
27.5 0.305 2.40% -4.14% 60.61% 67.16% 60.80%
18.8 0.305 4.00% -6.00% 59.33% 69.33% 59.77%
9.08 0.305 5.93% -12.75% 29.01% 47.69% 32.24%
34.3 0.0305 0.83% 0.00% 63.64% 64.46% 63.64%
27.5 0.0305 0.88% -0.22% 67.04% 68.14% 67.04%
18.8 0.0305 1.14% -0.38% 66.96% 68.49% 66.97%
9.08 0.0305 1.22% -2.45% 24.48% 28.15% 24.63%
Figure IX-1 compares the mechanistic model predicted penetration rates for the erosion test conditions that were performed during this investigation. An error bar in each of the predicted penetration rates shows the total uncertainty ranges of the mechanistic model predicted rate.
154 1.E+01
) Perfect Agreement Mech. Model Prediction
1.E+00
1.E-01 Model Predicted Pen-Rate (mm/yr Pen-Rate Predicted Model 1.E-02 1.E-02 1.E-01 1.E+00 1.E+01 Measured Penetration Rate (mm/yr)
Figure IX-1. Uncertainty Range of Mechanistic Model Predictions Compared to Experimental Erosion Data in Multiphase Flow.
155 CHAPTER X
SUMMARY, CONCLUSION, AND RECOMMENDATION
Summary
There are two main goals for this research. The first goal is to study erosion behavior in single and multiphase flow to have a better understanding of erosion mechanisms and relative erosion between single and multiphase flows. The other goal is to develop a mechanistic model that is capable of predicting erosion in both single and multiphase flows. The model should be general and applicable to a wide range of flow conditions in different flow regimes.
For single-phase flow, erosion experiments were conducted in elbows at different gas velocities, different orientations (horizontal to vertical, vertical to horizontal, horizontal to horizontal) using aluminum and stainless steel materials. Two different test sections with different lengths of pipe upstream of the specimen were used to evaluate the effect of pipe length on erosion characteristics. No significant difference in erosion was observed between the test sections. Mass loss measurements were used to calculate the average erosion for the test conditions described above. Thickness loss measurement before and after erosion experiments were used to determine the location and magnitude of erosion. The characteristic thickness loss profile was used to calculate the maximum to average thickness loss ratio.
The volumetric sand concentrations were between 0.006 and 0.024% at air velocities of 62, 90, 112, and 230 ft/sec gas velocities. Due to inaccuracy of flow meter
156 readings at lower gas velocities, no experiments were performed less than 62-ft/sec single-phase gas velocity. Experimental results showed increase in erosion rate with increasing gas velocity and were higher for the vertical specimen than the horizontal specimen.
Thickness loss of the elbow specimen was measured before and after erosion tests to determine the location and magnitude of maximum erosion. In single-phase flow, maximum erosion was localized at approximately 55 degrees from the inlet of the elbow for one-inch standard elbow. Comparing literature data and experimental thickness loss measurement data, the maximum thickness loss was observed on the outer wall of an elbow approximately at the intersection of centerline of upstream inlet pipe. From the characteristic thickness loss profile of the elbow specimen, the maximum to average thickness loss ratio was determined. This ratio was used along with the surface area and material density to calculate the penetration rate of elbow specimen from the mass loss measurements.
In multiphase flow, erosion experiments were conducted at superficial gas velocities of 32, 62, 90, and 112 ft/sec and superficial liquid velocities of 0.10 and 1.00 ft/sec. Two different multiphase test sections with L/D ≈ 70 and L/D ≈ 160 were used
(L/D = length to diameter ratio of pipe upstream of the elbow specimen) to determine the effect of L/D on erosion behavior. Elbow specimens in horizontal and vertical test cells were used to evaluate the effect of flow orientation on erosion. More mass loss was observed in the vertical specimen than the horizontal specimen in the L/D ≈160 test section. Whereas, similar mass loss was observed in the horizontal and vertical specimens in the L/D ≈ 70 test section. Similar to single-phase experiments, erosion rate increased
157 with increased gas velocity. An interesting and surprising erosion phenomenon was observed when liquid rate was increased from 0.10 ft/sec to 1.0 ft/sec. Higher mass loss was measured at 1.0 ft/sec liquid rate compared to 0.10 ft/sec for the same superficial gas velocity.
Thickness loss measurements were conducted at superficial gas velocities of 32,
62, 90 and 112 ft/sec for superficial liquid velocities of 0.10 and 1.00 ft/sec using horizontal and vertical aluminum specimens. Higher thickness loss was measured at superficial liquid velocity of 1.0 ft/sec than 0.10 ft/sec. This higher erosion behavior with higher liquid rate is similar to the phenomenon observed during erosion experiment using mass loss measurements.
A mechanistic model was developed considering the effects of liquid and gas velocities, sand distribution, entrainment and particle impact velocities. The mechanistic model predicted penetration rates were compared to erosion measurements reported in the literature for annular, mist, slug, churn, and bubble flow regimes. The model predictions showed reasonably good agreement with the measured erosion rates. When compared with the experimental erosion data, the model slightly over predicted erosion in most cases. It was interesting that the mechanistic model predictions showed qualitatively good agreement with the experiment data and predicted higher erosion at superficial liquid velocity of 1.0 ft/sec than 0.10 ft/sec.
158 Conclusions
From the experimental erosion study and the mechanistic erosion prediction model, the following conclusions are made for single-phase and multiphase flows.
I. Single-Phase Flow:
1. Erosion is observed to be higher in the vertical specimen than the
horizontal specimen at similar flow conditions.
2. In a one-inch standard elbow in vertical pipe at 112 ft/sec gas velocity
maximum thickness loss was observed in the outer wall of the elbow at
a location approximately 55 degrees from the inlet of the elbow
3. The ratio of maximum to average erosion in single-phase flow with air
at 112 ft/sec velocity and aluminum elbow specimen was
approximately 3.17.
4. The mechanistic model predicted erosion rates are in good agreement
with the experimental results.
II. Multiphase Flow:
5. Erosion in multiphase flow has a higher dependency on the upstream
pipe length of the elbow. The multiphase flow require larger pipe
length (L/D ≈ 160) to become nearly fully developed compared to
single-phase flow
6. Higher erosion was observed in the vertical specimen than the
horizontal specimen in the test section with L/D ≈160. Erosion in
159 vertical and horizontal specimens was similar in the test section with
L/D ≈ 70.
7. Mass loss was similar in both aluminum and stainless steel specimens
in multiphase flow.
8. Maximum thickness loss in the horizontal specimen is at approximately
45 degrees and at 55 degrees in the vertical specimen in a one-inch
aluminum specimen.
9. The maximum to average thickness loss ratio in aluminum specimen
are 1.6 to 2.2 at superficial liquid velocity of 0.10 ft/sec and superficial
gas velocities of 32, 62, 90, and 112 ft/sec. The maximum to average
thickness loss ratio is 1.6 to 1.9 at superficial liquid velocity of 1.0
ft/sec for the above superficial gas velocities.
10. Erosion rate decreased from single-phase flow to multiphase flow at
smaller liquid rate of 0.10 ft/sec. As the liquid rate increased from
0.10 to 1.0 ft/sec, higher erosion was observed at higher liquid velocity.
This behavior discovered during this study was very interestingly
surprising and different than previous perception about erosion
behavior. The reason for the higher erosion is higher sand entrainment
in the gas core region at higher liquid rate.
160 III. Mechanistic Model
11. The mechanistic model predictions agreed well within a factor of 5
with the literature erosion data for different flow regimes, different pipe
sizes, different sand size and different materials.
12. In general, the mechanistic model predicted higher erosion than the
experimental data in most cases.
13. The mechanistic model predicted higher erosion at superficial liquid
velocity of 1.0 ft/sec compared to 0.10 ft/sec. The previous erosion
prediction model developed at E/CRC was unable to predict this trend
of decreasing erosion rate with increasing liquid rate. This clearly
demonstrates the strength of the mechanistic model to predict erosion
in different flow conditions and flow regimes of multiphase flow.
161 Recommendations
Based on this study of erosion in multiphase flow, the following recommendations are made for future study.
1. Conduct erosion experiments with VSG = 112 ft/sec at VSL= 0.50, 5.0, and 10
ft/sec to validate the mechanistic model predictions and determine the change
of erosion rate with changes in liquid rate.
2. Perform erosion experiments in slug, churn and bubble flow regimes to
further validate the mechanistic model predictions in these flow regimes.
3. Perform experiments at different inclination angles from 0 to 90 degrees to
investigate the effect of inclination angle on erosion behavior.
4. Extend the mechanistic model to horizontal flow as the present model is for
vertical flow only
5. Measure actual particle impact velocity in multiphase flow using LDV
(Laser Doppler Velocimetry) or other similar devices.
6. Conduct erosion experiment in multiphase flow using different sizes of sand
(i.e. 50 µm, 300 µm) to investigate the effect of sand size on erosion.
7. Conduct erosion experiment using fluids with different viscosity to investigate
the effect of viscosity on erosion rate.
8. Conduct thickness loss experiment using stainless steel specimen and compare
the thickness loss behavior of stainless steel with aluminum.
9. Conduct erosion experiments in aluminum to evaluate the effect of material
properties on erosion behavior.
162 NOMENCLATURE
Symbol Description
2 Ap Cross-sectional area of the pipe (ft )
2 AF Cross-sectional area of the film (m )
2 AC Cross-sectional area of the gas core (m )
B Brinell hardness factor
C Constant
Cstd r/D ratio for a standard elbow (Cstd=1.5)
D Pipe diameter, (mm)
D0 25.4 mm dp Particle diameter in m
Dh Hydraulic diameter (inches)
ER Erosion ratio
E Fraction of liquid entrained in the gas core (mass of liquid in gas core/ total mass of liquid) E Entrainment fraction
ERLiquid Erosion rates due to sand particles in the liquid phase
ERGas Erosion rates due to sand particles in the gas phase
163 ERTotal Total erosion
FM , FS Empirical factors for material and sand sharpness
FP Penetration factor for steel based in 1” pipe diameter, (mm/kg)
Fr/D Elbow radius factor for long radius elbow
G Acceleration due to gravity (ft/sec2) h Penetration rate in mm/year
HLLS Liquid holdup in the liquid slug
J Coefficient based on material properties
JG Volumetric flux of gas or superficial gas velocity (ft/sec)
JF Volumetric flux of liquid or superficial liquid velocity (ft/sec)
* J G Dimensionless gas flux
K Coefficient based on material properties
Lo Reference stagnation length for 1” Pipe
L Equivalent stagnation length m* Mass flow rate (lbs/sec)
P1a, P2a Pressure at location 1 and 2 (psia)
164 P1g, P2g Pressure at location 1 and 2 (psig)
Q1, Q2 Volumetric flow rate (CFM)
3 QG Volumetric gas flow rate (ft / Sec)
3 QL Volumetric liquid flow rate (ft / Sec)
Reo Particle Reynolds number
ReF Liquid Reynolds number
Sx Standard deviation of the average X
SR Mean slip ratio
Si Wetted perimeter of the gas core (m)
SF Wetted perimeter of the film (m) uxi Discrete uncertainties
uf Overall uncertainty
Ve Erosional velocity limit in ft/sec
VL Characteristic particle impact velocity, (m/s)
Vo Equivalent flowstream velocity, m/sec
Vo Initial particle velocity
165 Vfilm Average liquid film velocity, m/sec
Vd Average liquid droplet velocity in gas core, m/sec
VLLS Liquid velocity of the liquid slug.
VSL Superficial liquid velocity, ft/sec
VSG Superficial gas velocity, ft/sec
VoG Velocity of sand particles in the gas core, ft/sec (or m/sec)
VoL Velocity of sand particles in the liquid film, ft/sec (or m/sec)
VGLS Velocity of gas in the liquid slug
W Sand production rate, (kg/s)
We Weber number
X Sample average
xi Nominal value of variables
Z Axial distance from the inlet, ft
∆ρ Density difference between gas and liquid phases
δ Liquid film thickness
µf Fluid viscosity in Pa-s
166 2 µm Mixture viscosity of fluid in the stagnation zone, pa-s or N-s/m
φ Dimensionless parameter
3 ρ Density of the carrier fluid lbm/ft
ρw Density of the wall material
3 ρm Mixture density of fluid in the stagnation zone, kg/m
3 ρp Density of particles, kg/m
3 ρF Liquid phase density or film density (lb/ft )
3 ρ1, ρ2 Densities at location 1 and 2 (lb/ft )
3 ρL Density of liquid film (kg/m )
3 ρG Density of the gas core (kg/m )
σo Yield strength of the target wall material
Σ Surface tension (lb/ft)
τF Film shear stress (kg/m-sec)
τC Gas core shear stress (kg/m-sec)
θ Particle impact angle t Value of t-static for 95% confidence interval
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175 APPENDIX A
CALCULATION OF PENETRATION RATE AND SAND VOLUME CONCENTRATION
Penetration Rate Calculation
Superficial liquid velocity, VSL = 112 ft/sec,
Superficial gas velocity, VSG = 1.0 ft/sec Sand throughput = 20.4 kg Elbow specimen material = 316 Stainless Steel Sand throughput = 20.4 Kg Elbow specimen width = 0.25 inches Elbow specimen length = 4.0 inches
Mass Loss: 1.80 E-1 grams (Vertical Specimen)
Calculation:
Erosion Ratio: (Mass Loss)/ (Sand Throughput) = 1.80E-1 / 20,400= 8.82E-6
Elbow specimen surface area = 4.0 inches x 0.25 inches = 1.00 inch2 = 1.00 * (.0254)2 = 6.452E-4 m2
Density of 316 stainless Steel = 7800 Kg / m3
Average Penetration Rate = Erosion Ratio x (1/Density) x (1/ surface area) x (39.37inch/meter) x (1000mil/inch) x (0.454kg / lb)
8.82E-6 x (1 / 7800) m3 / Kg x (1/ 6.452E-4 m2) x (39.37 inch/ m ) x (1000 mil / inch) x 0.454 kg/ lb) = 3.13 E-2 mils/ lb
176 The maximum penetration rate (mils/lb) was calculated by using the maximum to average thickness loss ratio of profilometer thickness loss measurement. For Vsg= 112 ft/sec, Vsl =1.0 ft/sec , vertical specimen, the maximum to average thickness loss ratio is 2.068.
Maximum Penetration Rate: 3.13E-2 x 2.068 = 6.47E-2 mils/lb
Sand Volume Concentration in Single-Phase Flow
The sand volume concentration for single-phase flow is calculated using the following procedure:
Sand throughput = 2 kg (4.408 lbs) Time required to inject sand = 60 minutes Gas velocity = 105 ft/sec Pipe diameter = 1 inch (Area = 0.0005067 ft2) Density of sand particles = 2650 kg/m3
Sand Volume Concentration 3 1 min m3 sec ⎡ ft ⎤ 1 = 2 kg x x x x x ⎢ ⎥ x 2 60 min 60 sec 2650kg 105ft ⎣0.3048 m⎦ 0.0005067 ft = 0.000139 ≈ 0.014 %
177 APPENDIX B
EROSION TEST PROCEDURE FOR MULTIPHASE FLOW
A schematic of the once-through multiphase flow loop is shown in
Figure III-3. The major components of the flow loop are two Ingersoll-Rand gas compressors each with a maximum capacity of 200 cfm, one 20 gpm diaphragm pump, two slurry tanks (8 gallons and 100 gallons), one ABB TRI-WIRL vortex flow meter, two pressure gages (one located at upstream of the flow meter and one between the horizontal and vertical erosion test cells), one cyclone separator, one filter and approximately 40 feet long one-inch pipe.
Liquid is supplied to the sand-liquid slurry tank from city water supply. Sand is mixed with water in the slurry tank using a stirrer and injected to the flowing gas in the one-inch pipe through a ball valve. The 8-gallon slurry tank is used during the test with superficial gas velocity less than 0.5 ft/sec. During the test, the 8-gallon slurry tank is pressurized so that the pressure in the slurry tank is higher than the pressure in the one-inch pipe to assure sand and liquid mixture flow to the pipe. The
8-gallon slurry tank is made of steel and can withstand 50-psig internal pressure.
Gas is supplied from the compressor to the flow loop. This one-inch test section can reach gas velocity up to 130 ft/sec with a pressure of 40 psig. The liquid-sand mixture is injected into the gas stream. The three phases (gas-liquid-sand) flow through the
178 test section. After the test section, the mixture flows to a cyclone separator where the liquid and sand are separated from the gas stream and discharged to a bucket. The liquid, gas and sand flows through a filter where the remaining sand is separated and the liquid flows back to a larger liquid tank.
For superficial liquid velocity of 1.0 ft/sec, the 100-gallon tank is used with a positive displacement pump and the tank is not pressurized. The sand injection nozzle used with the 8-gallon tank is 0.188 inches ID and the sand injection nozzle used with the 100-gallon tank is 0.375 ID.
Test Set-up
Before starting the test, the test condition was determined (gas velocity, liquid velocity, sand size, sand concentration etc.) and the elbow specimen was prepared for the test. Due to critical nature of the test, extreme care must be taken to minimize any uncertainty during the test. The following steps are followed and data are recorded:
1. Prepare the elbow specimen for erosion test. Weigh the specimen using the
scale in the test lab. Take 3 (three) different measurement and record all the
measurements. Average the measured weight. Record the average initial
weight of the specimen in the data sheet.
2. Place the elbow specimen in the test cell as shown in Figure III-4. When
placing the specimens in the test cell, make sure the specimen is placed
properly in the test cell. The perturbation of the specimen in the test cell must
be controlled so that the specimen placement is uniform and consistent among
179 tests. Place the rubber gasket between the test cell and the metal cover.
Tighten all four clamps using sufficient amount of torque to assure the test
cell is sealed properly.
3. Fill-up the slurry tank with water using a plastic hose to a predetermined
height (10.50 inches). The ID of the slurry tank is 12.75 inches.
The volume of water in the slurry tank with 10.38 inches height is:
π x (12.75)2 x[]10.50 =1340 inch3 4
3 3 ⎡meter⎤ 1340 inch x ⎢ ⎥ = 0.02197 Cubic meters = 21.97 Liters ⎣39.37 ⎦
4. Determine the amount of sand to be added to the slurry tank as follows:
For 2% sand concentration, amount of sand required in 21.97 liters (21970
cc) of fluid is: 21970 cc * .02 = 439 grams of sand
NOTE: If erosion test to performed using 50 micron sand, then mix the sand
with the fluid and add to the slurry tank using the funnel at the top of the tank.
If the test requires high viscosity fluid (i.e. Glycerin mixture) then mix sand
with the fluid in a separate bucket and add the sand/fluid mixture through the
funnel located at the top of the tank by opening the ball valve.
180 Start-up and Operation
1. Before starting the compressor, please check the followings:
i) Gate valve located in the horizontal line ( upstream of the flow
meter and pressure gage) is closed.
ii) Ball valve in the sand injection location is closed
2. Start the compressors by turning the start switch ON. Open the gate valve
near the flow meter slowly and carefully. This valve controls gas flow from
the compressor to the test section. Pressure gauge P1 is located near the flow
meter and pressure gauge P2 is located between the horizontal and vertical test
cell as shown in Figure III-3. Observe the flow meter; pressure gage (P1 , P2 )
readings while opening the valve. Record the readings and calculate the gas
velocity as follows:
Superficial gas velocity at the test section,
⎛ ⎞ ⎛ 3 ⎞ ⎡ ⎤ ⎜ ⎟ ⎜ ft ⎟ P1 +14.7 1 ⎡ min ⎤ V2 = x⎢ ⎥x⎜ ⎟x⎢ ⎥ = ft / sec ⎜ min ⎟ P +14.7 ⎜ π 2 2 ⎟ 60Sec ⎝ ⎠ ⎣ 2 ⎦ ⎜ ()1 ft ⎟ ⎣ ⎦ ⎝ 4 12 ⎠
⎛ ⎞ ⎜ 1 ⎟ Cross sectional area of one inch pipe = ⎜ ⎟=0.00542 ft2 ⎜ π 2 ⎟ ⎜ ()1 ⎟ ⎝ 4 12 ⎠
Example: Assume the pressure at P1 is 35 psig and pressure at gage P2 is 30 psig and the flow meter reading is 30 ACFM . The gas velocity at the test cell is calculated as:
181 ⎛ ⎞ ⎛ 3 ⎞ ⎜ ⎟ ⎜ 30ft ⎟ ⎡35 + 14.7⎤ ⎜ 1 ⎟ ⎡ min ⎤ V2 = x⎢ ⎥x x⎢ ⎥ = 101.94ft / sec ⎜ min ⎟ 30+14.7 ⎜ π 2 2 ⎟ 60Sec ⎝ ⎠ ⎣ ⎦ ⎜ ()1 ft ⎟ ⎣ ⎦ ⎝ 4 12 ⎠
Liquid Velocity Calculation Procedure
Measure the time taken to lower one inch of liquid level in the slurry tank.
9.125 inch liquid height in the slurry tank = 10 liters
1 inch of liquid height = 10 / 9.125 = 1.0958 liters/ inch
If it takes 70 seconds to lower the liquid level by one inch, then the flow rate from the slurry tank to the test section are 1.0958/ 70 = 0.015654 liters/sec.
1 liter = 0.0353147 cubic foot
Cross sectional are of one inch pipe =0.00542 ft2
3 2 VSL =0.015654 liters/sec x (0.0353147 ft / liter) x (1/0.00542 ft ) = 0.101 ft/sec
Continue the test until the all the liquid-sand mixture from the slurry tank passes through the erosion test specimens. When test fluid is a Glycerin/ water mixture, then the fluid after the test is collected in a bucket.
Shut Down Procedure
1. Close the ball valve that feeds sand-water mixture from the slurry tank to
the test section.
2. Turn-off the compressors.
3. Close the gate valve located at upstream of the flow meter.
182 4. Remove the elbow specimen from the test cell. Wash the specimen
thoroughly until the specimen is clean and free from any foreign material.
Dry the specimen using hot air and cool down before weighing the
specimen.
5. Weigh the specimen by carefully taking 3 measurements and record all the
measurements in the data sheet. Calculate the average final weight and
record in the data sheet.
6. The mass loss of the elbow specimen is the difference between the average
initial weight ( step 1 of TEST SET UP) and average final weight.
7. Complete the Erosion Test Data Sheet by including the following information:
Sand size
Sand throughput
Superficial gas velocity
Superficial liquid velocity
Liquid viscosity
Specimen weight before test
Specimen weight after test
Test date
Material of the specimen (i.e. 316 ss, Aluminum)
183 EROSION TEST DATA SHEET TEST NO: TEST DATE: TESTED BY: ______SPECIMEN NO. MATERIAL OF SPECIMEN: . SAND SIZE (micron):
VISCOSITY (cp): ______GAS VEL.(VSG) ______ft/sec LIQ. VEL.(VSL)______(ft/sec) Initial Weight of the Specimen:
W1= ______grams W2 = ______grams W3 = ______grams W4 = ______grams
W Before Test : (W1 + W2 + W3 ) / 3 = ______grams
Test Amount of Liquid Time took to Calculated Pressure Test section Flow meter Calculated Comment date sand level lower liquid liquid P1 (Psig) pressure P2 Reading Gas and (grams) in the level by one velocity (psig) (ACFM) Velocity time slurry tank inch (ft/sec) (ft/sec) (inches) (seconds)
Final Weight of the Specimen:
W1= ______grams W2 = ______grams W3 = ______grams W4 = ______grams
W After Test : (W1 + W2 + W3 ) / 3 = ______grams
MASS LOSS (grams) = ( INITIAL WEIGHT – FINAL WEIGHT) = (WBefore test - W After Test) = ______grams
184 APPENDIX C
Description of Test Equipment
The test equipment used to conduct the erosion experiment is described in this appendix. Where applicable, information about the manufacturer, model, operating range, accuracy is provided.
1) Balance used to weigh the test specimens
Equipment Manufacturer: Scientech, Inc.
Equipment Model: SA 210 (Supreme Accuracy) Digital
Maximum Capacity: 200 grams
Readability: 0.1 milligram (0.0001 gram)
Accuracy: ± 0.1 mg
2) Balance used to weight sand
Equipment Manufacturer: Pelouze Controller
Equipment Model: YG1000A Analog Scale
Maximum Capacity: 1000 grams
Incremental measurable weight: 5 grams
Accuracy: ± 2 grams
185 3) Flow meter used to measure gas flow rate
Equipment Manufacturer: ABB Limited
Equipment Model: FV4000/ VR4 Vortex Flow meter
Maximum Capacity: 150 m3/hour
Accuracy: ± 1%
Reproducibility: ± 0.2 of the flow rate
4) Pressure gage near the flow meter
Equipment Manufacturer: Ashcroft
Equipment Model: 3 inch Bourdon tubes pressure gage
Measurement Range: 0 – 200 psi
Measurement Increment: 2 psi
5) Pressure gage between the horizontal and vertical test cells
Equipment Manufacturer: Watts
Equipment Model: 2 inch Bourdon tubes pressure gage
Measurement Range: 0 – 200 psi
Measurement Increment: 5 psi
Accuracy: ± 1%
186 6) Diaphragm pump used to inject sand-water mixture from 100 gallon tank
Equipment Manufacturer: Ingersoll- Rand
Equipment Model: 66605J-388 ARO Diaphragm pump
Maximum capacity: 13 GPM
Liquid inlet/Outlet sizes: ½ inch-14 NPTF
Maximum operating pressure: 100 psi
7) Profilometer used to measure the thickness loss of specimen
Equipment Manufacturer: Taylor Hobson
Equipment Model: Surtronic- 3P
Dimension and Weight: 80 x 135 x 80 mm, 0.60 kg
Measurement Range: 0 – 999.99 micron
Traverse speed of pickup: 0.25 mm/sec
Readout: Four digits digital LCD
Accuracy: ± 2% of the reading,
±1 least significant digit
187 APPENDIX D Table D-1: Comparison for Annular Flow
E/CRC Salama Mechanistic Empirical Empirical Elbow Sand Measured Model Model [17] Model [3]
VSL VSG Dia. size Erosion Prediction Prediction Prediction (m/sec) (m/sec) (mm) (micron) (mm/kg) (mm/kg) (mm/kg) (mm/kg) Note
1.0 30.0 49 150 5.25E-04 1.41E-03 3.47E-04 8.71E-04 1
0.5 30.0 49 150 2.46E-03 1.94E-03 6.38E-04 1.56E-03 1
5.8 20.0 49 150 5.19E-05 1.47E-04 5.48E-05 9.18E-05 1
3.1 20.0 49 150 6.93E-05 2.46E-04 6.56E-05 1.22E-04 1
1.0 15.0 49 150 1.47E-04 1.01E-04 4.23E-05 1.24E-04 1
6.2 9.0 26.5 250 1.80E-04 9.61E-05 1.05E-04 9.95E-05 2
1.5 14.4 26.5 250 2.30E-04 6.70E-04 2.39E-04 4.38E-04 2
1.5 14.6 26.5 250 4.20E-04 6.98E-04 2.46E-04 4.54E-04 2
2.1 34.4 26.5 250 2.83E-03 6.77E-03 1.38E-03 3.45E-03 2
1.0 35.0 26.5 250 6.56E-03 9.68E-03 2.28E-03 6.18E-03 2
0.5 34.3 26.5 250 7.20E-03 1.05E-02 3.06E-03 8.94E-03 2
0.7 37.0 26.5 250 8.03E-03 1.18E-02 3.11E-03 8.97E-03 2
0.5 38.5 26.5 250 8.03E-03 1.35E-02 3.93E-03 1.20E-02 2
1.5 44.0 26.5 250 1.05E-02 1.38E-02 3.07E-03 8.67E-03 2
0.6 51.0 26.5 250 1.34E-02 2.27E-02 6.66E-03 2.20E-02 2 Notes: (1) Data from Salama [3], air and water at 2 bar, Material: Carbon steel (BHN =160) (2) Data from Salama [3], nitrogen and water at 7 bar, Material: Duplex Stainless Steel
188 Table D-2: Comparison for Mist Flow
E/CRC Salama Empirical Empirical Mechanistic Model Model [3] Elbow Sand Measured Model [17] Pred. Prediction VSL VSG Dia. Size Flow Erosion Prediction (m/sec) (m/sec) (mm) (micron) Pattern (mm/kg) (mm/kg) (mm/kg) (mm/kg) Note
0.7 52.0 26.5 250 Mist 1.33E-02 3.38E-02 6.52E-03 2.15E-02 2
0.53 86.0 52.5 350 Mist 1.27E-01 4.64E-02 1.09E-02 4.28E-02 3
0.53 92.0 52.5 350 Mist 1.21E-01 5.24E-02 1.25E-02 5.18E-02 3
0.12 89.0 52.5 350 Mist 1.08E-01 5.26E-02 1.68E-02 1.34E-02 3
0.53 84.0 52.5 350 Mist 9.34E-02 4.45E-02 1.04E-02 4.00E-02 3
0.53 72.0 52.5 350 Mist 5.37E-02 3.06E-02 6.88E-03 2.58E-02 3
0.12 84.0 52.5 350 Mist 7.51E-02 4.36E-02 1.38E-02 1.16E-01 3
0.12 92.0 52.5 350 Mist 9.94E-02 5.11E-02 1.64E-02 1.46E-01 3
0.53 107 52.5 350 Mist 1.05E-01 6.27E-02 1.55E-02 7.92E-02 3
(2) Data from Salama [3], nitrogen and water at 7 bar, Material: Duplex Stainless Steel (3) Data from Bourgoyne [50], air and water at standard conditions,, Material: Carbon steel (BHN 140)
189 Table D-3: Comparison for Slug, Churn and Bubble Flows
E/CRC Salama Mechanistic Empirical Empirical Elbow Calculated/ Measured Model Model [17] Model [3] VSL VSG Dia. Observed Erosion Prediction (m/sec) m/sec (mm) Flow Pattern (mm/kg) (mm/kg) (mm/kg) (mm/kg) Note
5.0 15.0 49 Slug/ Churn 6.38E-05 2.41E-05 1.30E-05 4.96E-05 1,4
5.0 10.0 49 Slug/ Churn 1.35E-05 7.08E-06 5.04E-06 2.10E-05 1, 4
0.7 10.0 49 Slug/ Churn 7.01E-05 8.18E-05 1.74E-05 5.29E-05 1, 4
0.2 8.0 49 Slug/ Churn 1.23E-04 2.33E-04 7.10E-05 7.89E-05 1, 4
4.0 3.5 49 Bubble 4.60E-06 3.12E-07 3.04E-07 3.29E-06 1 (1) Data from Salama [3], air and water at 2 bar, Material: Carbon steel (BHN 160) (4) Model predictions are based on churn flow
Table D-4: Comparison with Experimental Erosion Data
E/CRC Salama Mechanistic Empirical Empirical Elbow Calculated/ Measured Model Model [17] Model [3] VSL VSG Dia. Observed Erosion Prediction (m/sec) m/sec (mm) Flow Pattern (mm/kg) (mm/kg) (mm/kg) (mm/kg)
0.305 34.3 25.4 Annular 3.32E-03 1.10E-02 5.66E-03 1.25E-02
0.305 27.5 25.4 Annular 9.70E-04 4.52E-03 3.53E-03 6.76E-03
0.305 18.8 25.4 Annular 1.93E-04 9.07E-04 1.52E-03 2.32E-03
0.305 9.08 25.4 Annular 3.62E-05 2.74E-04 2.54E-04 2.94E-04
0.0305 34.3 25.4 Annular 1.21E-03 7.28E-03 1.04E-02 4.29E-02
0.0305 27.5 25.4 Annular 3.21E-04 2.72E-03 6.82E-03 2.58E-02
0.0305 18.8 25.4 Annular 1.48E-04 4.74E-04 3.29E-03 1.05E-02
0.0305 9.08 25.4 Annular 1.25E-04 3.46E-04 7.74E-04 1.71E-03
190 191