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THE UNIVERSITY OF TULSA
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
THE UNIVERSITY OF TULSA
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 ...................................................................................................
CHAPTER I
xii
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 SinglePhase 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 .....................................................................
x
98
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)...............................................
xiii
77
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) .....
xiv
85
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) .....................................................................................
xv
94
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 ................................................
xvi
125
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
Erosion
Flow
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]:
Ve =
C
(I-1)
ρ
Where, Ve is the erosional velocity limit in ft/sec, ρ is the density of the carrier fluid in
lbm/ft3, 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.
5
Some of the
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 w V 2 cos θ − 3 sin θ sin θ for θ ≤ 18.5 o
2
⎧⎪ cρ w ( V sin θ) 2
⎫⎪
=⎨
cot 2 θ⎬ for θ > 18.5 0
12σ o
⎪⎩
⎪⎭
(II-1)
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 cos 2 θ + K sin 2 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.
h = FM FS FP Fr / D
where,
WVL1.73
(D / D0 )2
(II-3)
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
For carbon steel material, Shadley proposed FM = 1.95 x 10-5 / B-0.59 (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
1018
316 Stainless Steel
Yield
Tensile
Brinell
Material Factor
Strength
Strength
Hardness
for VL in m/sec
(Ksi)
(Ksi)
(B)
(FM x 106)
90.0
99.5
210
0.833
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]
FP (for steel)
Reference Stagnation
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
⎧⎪ ⎛
ρ µ
0.25
Fr / D = exp ⎨− ⎜ 0.1 f 0.f3 + 0.015 ρ f
+ 0.12
⎜
dp
⎪⎩ ⎝
⎫
⎞⎛ r
⎟⎜ − C ⎞⎟⎪⎬
std
⎟⎝ D
⎠⎪⎭
⎠
(II-4)
where, ρf is the fluid density in kg/m3, 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
Elbow:
L = L o { 1 −1.27 tan −1(1.01 D −1.89 ) + D0.129
Tee:
L = L o { 1.35 −1.32 tan −1(1.63 D −2.96 ) + D0.247
18
}
(II-5)
}
(II-6)
The simplified particle tracking model used in this erosion model assumes a onedimensional 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 twophase 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
Re o =
where,
ρ m Vo dp
(II-7)
µm
Vo
= equivalent flowstream velocity, m/sec
ρm
= mixture density of fluid in the stagnation zone, kg/m3
µm
= mixture viscosity of fluid in the stagnation zone, pa-s or N-s/m2
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
φ=
where
Lρm
dp ρP
(II-8)
L = equivalent stagnation length, m
ρp = density of particles, kg/m3.
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
0.9
Re o =
ρ m Vo d p
µm
0.8
0.7
VL/Vo
0.6
0.5
0.4
100
0.3
Reo = 1
10
1000
0.2
10000
0.1
100000
0.0
1E-2
1E-1
1E+0
⎛ L
Φ=⎜
⎜ dp
⎝
1E+1
⎞⎛ ρ m
⎟⎜
⎟⎜ ρ p
⎠⎝
1E+2
1E+3
⎞
⎟
⎟
⎠
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.
Vo = λnL VSL + (1 − λ L ) n VSG
where,
⎡ VSL ⎤
λ=⎢
⎥
⎣ VSL + VSG ⎦
(II-9)
0.11
(II-10)
⎡
⎛
V ⎞⎤
n = ⎢1− exp ⎜⎜ − 0.25 SG ⎟⎟⎥
VSL ⎠⎦
⎝
⎣
20
(II-11)
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
h = KV L 1.73 .
(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
Equivalent Stagnation Length
Stagnation
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
Flow
Churn
Flow
Slug
Flow
Bubble
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:
VSL =
QL
AP
(II-16)
26
VSG =
where,
QG
AP
(II-17)
VSL= Superficial Liquid Velocity, ft/sec
VSG = Superficial Gas Velocity, ft/sec
QL = Volumetric Liquid Flow Rate (ft3/ Sec)
QG = Volumetric Flow Rate (ft3/ Sec)
Ap = Cross-Sectional Area of the Pipe (ft2)
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 underpredicted 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 ( 7.25 x 10−7 We1.25 Re0F.25 )
ρ J 2 D ⎛ ρG − ρ F
⎜⎜
We = G G
σ
⎝ ρG
29
(II-18)
1/ 3
⎞
⎟⎟
⎠
(II-19)
Re F =
ρF J F D
µF
(II-20)
where,
E = Entrainment Fraction
We = Weber Number
ReF = Liquid Reynolds number
ρF = Liquid phase density or film density (lb/ft3)
ρG =Gas phase density (lb/ft3)
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. SelmerOlsen [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
33.4 mm
33.4 mm
3.0
3.0
0.034 m/sec
0.9 m/sec
29 m/sec
29 m/sec
Distilled H2O with 1%
NaCl
Distilled H2O with
1% NaCl
Gas Property
Nitrogen
CO2
Pressure
1.5 barg
10 barg
Particle
200 µm Quartz
200 µm Quartz
316L Stainless Steel
316L Stainless Steel
1.5%
1.5%
Annular
Annular
Pipe Diameter
Turning radius ratio (r/D)
Superficial Liquid Velocity
Superficial Gas Velocity
Liquid Property
Elbow Material
Solid Particle Volume
Concentration
Flow configuration
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
m/sec (95.15 ft/sec) and VSL = 0.034 m/sec (0.11 ft/sec) at approximately 35O 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.
T hic k nes s los s in m ic rons
110
Vsg=95.15 ft/sec, Vsl=0.11 ft/sec
Max. Erosion
90
70
30
50
30
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
Total:Vsg=95.15,Vsl=2.95 ft/sec
Vsg=95.15,Vsl=2.95 ft/sec
Vsg=95.15,Vsl=2.95 t/sec
Vsg=95.15, Vsl=2.95 ft/sec
Max. Erosion
Thickness loss in microns
240
190
30
O
140
90
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 4
Test 7
Erosion Rate in mils/lbs
0.035
Test 2
Test 5
Test 8
0.030
Test 3
Test 6
Average-Eyler
Max Erosion
0.025
0.020
0.015
30o
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.
z ≥ 600 D
*
JG
=
*
JG
Re f
(III-1)
JG
⎡ σ g ∆ρ ⎛ ρ ⎞ 2 / 3 ⎤
⎢
⎜⎜ G ⎟⎟ ⎥
2
⎢ ρ G ⎝ ∆ρ ⎠ ⎥
⎣
⎦
40
1/ 4
(III-2)
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)
ρG = Gas density (lb/ ft3)
∆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 singlephase flow and approximately 115 ft/sec for two-phase flow.
44
Cyclone
Separator
Filter
Vertical
Erosion
Specimen
Slurry tank
Pressure Gage P2
4.12 m
Water tank
Horizontal
Erosion
Specimen
Drain
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* = m*2
(III-3)
ρ1Q1 = ρ 2Q 2
(III-4)
47
Q 2 = Q1
where,
⎡ P1g + 14.7 ⎤
⎡P ⎤
ρ1
= Q1 ⎢ 1a ⎥ = Q1 ⎢
⎥
ρ2
⎣ P2a ⎦
⎣⎢ P2g + 14.7 ⎦⎥
(III-5)
m* = mass flow rate (lbs/sec)
ρ1, ρ2 = Densities at location 1 and 2 (lb/ft3)
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 one48
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 singlephase 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
Pick-up
Surtronic 3P
Profilometer
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
Average Brinell Hardness (BHN)
240
230
220
210
200
4
7
8
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%
Sample one
40%
Sample two
Percent Sand
35%
30%
25%
20%
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
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
316 SS
316 SS
316 SS
0.014
0.013
0.006
Mass of Sand Used (lbs)
Elbow Specimen Material
Calculated Sand Volume
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
Orientation Velocity
(ft/sec)
Pressure at
Flow
Test
Sand
Section Throughput
meter P1 Pressure,
(Psig)
P2 (Psig)
(grams)
Mass
Erosion
Calc.
Loss
Ratio
Max. Pen.
(grams) (grams/
Rate *
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
Mass Loss in Grams
Vert. to Hor
1.2E-01
Vert-Hor.
8.0E-02
Flow
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 singlephase 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)
1.0 (2.2)
1.0 (2.2)
1.0 (2.2)
Test Time (minute)
30
30
30
Particle Diameter (µm)
150
150
150
18.9 (62)
27.4 (90)
34.1 (112)
316 SS
316 SS
316 SS
0.024
0.016
0.013
Mass of Sand Used for Each Test, kg (lbs)
Fluid Velocity, m/sec (ft/sec)
Elbow Specimen Material
Sand Volume Concentration (%)
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
Test
Sand
Mass Average Average
Flow
Air
Test
Orientation Velocity
(ft/sec)
Pressure
Section
Throughput
Loss
Mass
Erosion
at Flow
Pressure
(grams)
(grams)
Loss
Ratio
meter P1
P2 (Psig)
(grams)
(Psig)
Horizontal
Horizontal
Horizontal
Vertical
Vertical
Vertical
62
90
112
62
90
112
18
27
32
18
27
32
5
6
6
5
7
6
63
1000
0.0045
1000
0.0059
1000
0.0049
1000
0.0082
1000
0.0056
1000
0.0072
1000
0.0122
1000
0.0099
1000
0.0082
1000
0.0041
1000
0.0037
1000
0.0051
1000
0.0090
1000
0.0125
1000
0.0097
1000
0.0154
1000
0.0170
1000
0.0168
0.0051
5.10 E-6
0.0070
7.00E-6
0.0101
1.01E-5
0.0043
4.30E-6
0.0104
1.04E-5
0.0164
1.64E-5
0.035
Vg=62 ft/sec-Hor
Mass Loss (grams)
0.03
Vg=90 ft/sec- Hor
0.025
Vg =112 ft/sec- Hor
0.02
0.015
0.01
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.
Mass Loss (grams)
0.05
Vg=90 ft/sec- Vert.
Vg =112 ft/sec- Vert.
0.04
0.03
0.02
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
Average Mass Loss (grams)
Hor-Vert.
1.6E-02
Vert.-Hor
1.2E-02
8.0E-03
4.0E-03
0.0E+00
62
90
112
Gas Velocity (ft/s ec)
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
Velocity
Orientation
Sand
Mass Loss
(ft/sec)
Through for 1.0 kg
put (kg)
(grams)
Average
Average
Maximum
Erosion Pen. Rate * Pen. Rate*
Ratio
(mils/lb)
(mils/lb)
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.
66
In this section, erosion experiments to
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
Max. Erosion
120
Vgas=112-After-55 deg
Depth of scratch in microns
80
Vgas=112-After-55 deg
40
45O
0
-40
42.5 micron
-80
-120
0
0.5
1
1.5
2
2.5
3
3.5
4
Traverse distance in mm
Figure IV-9. Thickness Loss Measurement of Elbow Specimen (Vgas = 112 ft/sec,
Aluminum, 55 degrees)
50
Vgas=112
Vgas=112
Vgas=112
Vgas=112
Thickness loss in microns
45
40
(Average)
(Reading 1)
(Reading 2)
(Reading 3)
Max. Erosion
35
30
25
20
45O
15
10
5
0
0
10
20
27.5 35
45
55
62.5
70
90
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 (SinglePhase 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.
A v erage B rinell H ardnes s (B H N )
90
80
70
60
50
2
6
21
E lbow S pec im en 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
Gas Velocity
Liquid Vel.
Orientations
Size
Material
(ft/sec)
(ft/sec)
32
0.1
Horizontal/
Vertical
150
Aluminum/
316 SS
Stratified
Wavy /
Annular
1.0
Horizontal/
Vertical
150
Aluminum/
316 SS
Slug /
Annular
0.1
Horizontal/
Vertical
150
Aluminum/
316 SS
Annular
1.0
Horizontal/
Vertical
150
Aluminum/
316 SS
Annular
0.1
Horizontal/
Vertical
150
Aluminum/
316 SS
Annular
1.0
Horizontal/
Vertical
150
Aluminum/
316 SS
Annular
0.1
Horizontal/
Vertical
150
Aluminum/
316 SS
Annular
1.0
Horizontal/
Vertical
150
Aluminum/
316 SS
Annular
62
90
112
(microns)
Observed
Flow Pattern
in Horizontal/
Vertical
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,
72
the
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.
Superficial Liquid Velocity (ft/sec)
100
Dispersed Bubble
10
Intermittent/ Slug
1
Annular
0.1
Stratified
Smooth
Stratified
Wavy
Erosion Test
Conditions
0.01
1
10
100
1000
Superficial Gas Velocity (ft/sec)
Figure V-2. One-Inch Horizontal Flow Map Showing Erosion Test Conditions
Superficial Liquid Velocity (ft/sec)
100
Erosion Test
Conditions
Dispersed
Bubble flow
10
1
Churn flow
Annular
0.1
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 liquidsand 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)
Superficial Superficial Test
Gas
Velocity
Liquid
Flow
Sand
Total Average Calc.
Calc.
Section Orientation Through Mass Erosion Ave. Pen. Max Pen.
Velocity Pressure
(ft/sec)
(ft/sec)
(Psig)
112
0.1
26
112
0.1
26
90
0.1
22
90
0.1
22
62
0.1
15
62
0.1
15
32
0.1
9
32
0.1
9
112
1.0
25
112
1.0
25
90
1.0
21
90
1.0
21
62
1.0
19
62
1.0
19
32
1.0
9
32
1.0
9
-put (kg) Loss
Ratio
(grams)
Rate *
Rate *
(mils/lb) (mils/lb)
Horizontal 10.80 1.39E-2 1.26E-6 4.58E-03 7.29E-03
Vertical
10.80 3.20E-2 2.85E-6 1.05E-02 2.40E-02
Horizontal 16.20 8.60E-3 4.98E-7 1.89E-03 3.19E-03
Vertical
16.20 1.81E-2 1.07E-6 3.98E-03 6.44E-03
Horizontal 19.80 4.20E-3 2.01E-7 7.53E-04 1.26E-03
Vertical
19.80 9.90E-3 4.81E-7 1.78E-03 3.30E-03
Horizontal 19.80 4.79E-3 2.48E-7 8.60E-04 1.57E-03
Vertical
19.80 8.07E-3 4.45E-7 1.45E-03 2.64E-03
Horizontal 20.40 7.30E-2 3.17E-6 1.27E-02 2.14E-02
Vertical
20.40 1.80E-1 9.20E-6 3.13E-02 5.80E-02
Horizontal 27.20 1.60E-2 6.41E-7 2.09E-03 3.66E-3
Vertical
27.20 7.90E-2 3.00E-6 1.03E-02 1.94E-02
Horizontal 23.80 5.90E-3 2.44E-7 8.77E-04 1.37E-03
Vertical
23.80 1.50E-2 6.13E-7 2.24E-03 3.94E-03
Horizontal 40.80 1.00E-3 2.12E-8 8.70E-05 1.59E-04
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
Mass Loss (grams)
8.E-03
32H0.1(Horizontal) 316 SS
6.E-03
4.E-03
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
Mass Loss (grams)
62V0.1 (Vertical) 316 SS
62H0.1 (Horizontal) 316 SS
9.E-03
6.E-03
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
90H0.1(Horizontal) 316 SS
Mass Loss (grams)
1.6E-02
1.2E-02
8.0E-03
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
Mass Loss (grams)
112H0.1(Horizontal) 316SS
3.E-02
2.E-02
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
Mass Loss (grams)
32H1.0 (Horizontal) 316SS
4.5E-03
3.0E-03
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)
62V1.0 (Vertical) 316SS
1.6E-02
Mass Loss (grams)
62H1.0 (Horizontal) 316SS
1.2E-02
8.0E-03
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
Mass Loss (grams)
90V1.0 (Vertical) 316SS
7.5E-02
90H1.0 (Horizontal) 316SS
5.0E-02
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
Mass Loss (grams)
112H0.1(Horizontal) 316SS
3.E-02
2.E-02
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)
Superficial Superficial
Gas
Velocity
Liquid
Test
Flow
Section
Velocity Orientation Pressure
Sand
Through
put (kg)
Average
Mass
Loss
Average
Erosion
Ratio
Calc. *
Calc. *
Ave.
Max.
Pen. Rate Pen. Rate
(ft/sec)
(ft/sec)
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
(Psig)
(grams)
(mils/lb) (mils/lb)
* 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
32V0.1 (Vertical) 316SS
32H0.1 (Horizontal) 316 SS
Mass Loss (grams)
8.E-03
6.E-03
4.E-03
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
112H0.1 (Horizontal) Alum
112V0.1 (Vertical) 316SS
112H0.1 (Horizontal) 316SS
Mass Loss (grams)
6.0E-02
4.5E-02
3.0E-02
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
32V1.0 (Vertical) 316SS
32H1.0 (Horizontal) 316SS
Mass Loss (grams)
6.0E-03
4.5E-03
3.0E-03
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
Mass Loss (grams)
112H1.0 (Horizontal) 316 SS
112V1.0 (Vertical) Alum
3.E-01
112H1.0 (Horizontal) Alum
2.E-01
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.
Mass Loss (grams)
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
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)
Mass Loss (grams)
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.
L/D =160, VSG = 112 fps, 25 psig, Hor.
3.0E-01
2.0E-01
`
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
Depth of scratch in microns
120
32H1.0-Before-45 deg.
100
80
60
10.2 Micron
40
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.
Depth of scratch in micron
90
90H1.0-Before-45 deg
40
-10
Thickness Loss
17.6 micron
-60
-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
11 2H1.0-Bef ore 45
Depth of s cratc h in micron
11 2H1.0-A f ter 45
80
40
0
-40
Th ick ne s s
Lo s s 22.3 µm
-80
-120
0
0.5
1
1.5
2
2 .5
3
3.5
4
Traverse dis tanc e in m m
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
Depth of scratch in microns
140
112V0.1-After-55 deg
120
100
80
60
22.8 micron
40
20
0
0
0.5
1
1.5
2
2.5
3
3.5
4
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.
Thickness loss in microns
25
Vsg =112, Vsl=0.1 (Ver.)
Vsg = 90, Vsl = 0.1 (Ver.)
Vsg = 62, Vsl = 0.1 (Ver.)
Vsg = 32, Vsl = 0.1 (Ver.)
20
15
10
5
0
0
10
20
27.5
35
45
55
62.5
70
90
Location in the elbow
Figure V-23. Thickness Loss Profile of Elbow Specimen at Different Gas Velocities
(Vertical, VSL = 0.1 ft/sec)
Thickness loss in microns
20
Vs g = 112, Vsl = 0.1(Hor.)
Vs g = 90, Vs l = 0.1 (Hor.)
Vs g = 62, Vs l = 0.1 (Hor.)
Vs g = 32, Vs l = 0.1 (Hor.)
16
12
8
4
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
Vs g =112, Vs l =1.0-Vert.
Vs g =90, Vsl =1.0-Vert.
Vs g = 62, Vs l = 1.0-Vert.
Vs g = 32, Vs l = 1.0-Vert.
Thickness loss in microns
30
25
20
15
10
5
0
0
10
20
27.5
35
45
55
62.5
70
90
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)
Vsg = 62, Vsl =1.0 (Hor)
Vsg = 32, Vsl =1.0 (Hor)
Thickness loss in microns
25
20
15
10
5
0
0
10
20
27.5
35
45
55
62.5
70
90
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 in c h ID
L oc ation of
M ax im um
E ro sio n
Center
Line
Flo w
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
Superficial Superficial
Gas
Velocity
(ft/sec)
Liquid
Flow
Orientation Through Thickness Maximum Thickness Maximum
Velocity (Horizontal
(ft/sec)
Sand Maximum Location of Average Ratio of
put
Loss
/ Vertical) (grams) (micron)
Thickness
Loss
Loss
to Average
(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
Gas
Velocity/
Superficial
Flow
Single Phase Flow
Multiphase Flow
Multiphase Flow
(VSL = 0 ft/sec)
(VSL = 0.1 ft/sec)
(VSL = 1.0 ft/sec)
Average Average
Orientation Erosion
Gas Velocity (Horizontal /
Ratio
Average Average Average
Pen.
Average
Penetr.
Erosion
Penetr.
Rate*
Erosion
Rate*
Ratio
Rate*
mils/lb)
Ratio
(mils/lb)
(mils/lb)
(ft/sec)
Vertical)
32
Horizontal
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
N/A
N/A
N/A
N/A
2.42E-07 8.60E-04 2.45E-08 8.70E-05
32
Vertical
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
Erosion Ratio
Gas Vel = 62 ft/sec-Hor
Gas Vel = 90 ft/sec
Gas Vel = 112 ft/sec
1.E-05
1.E-06
1.E-07
0
0.1
1.0
Superficial Liq. Vel. (ft/sec)
Figure VI-1. Comparison of Erosion Ratios at Different Liquid Rate
(316 SS Specimen, Horizontal Orientation)
1.0E-04
Erosion Ratio
Gas Vel = 62 ft/sec-Vert.
Gas Vel = 90 ft/sec
Gas Vel = 112 ft/sec
1.0E-05
1.0E-06
1.0E-07
0
0.1
1.0
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
Liquid
Flow
Velocity
Orientation
Superficial Gas Velocity
(ft/sec)
(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 crosssectional 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
Vsl=0.1 ft/sec
0.50
Entrainment Fraction
0.558
0.40
0.340
0.316
0.30
0.20
0.182
0.102
0.10
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
Droplet Velocity (m/sec)
Vsl=0.1 ft/sec
28.602
27.0
27.987
23.592
23.0
22.602
19.0
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
annular liquid film
VCore.
. . .
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 ⎜ ⎟ − τ i Si − ρ G A C g sin θ = 0
⎝ dL ⎠ C
(VII-1)
⎛ dP ⎞
− A F ⎜ ⎟ + τ i Si − τ F S F − ρ L A F g sin θ = 0
⎝ dL ⎠ F
(VII-2)
By eliminating the pressure gradient terms from the above equations, the
combined momentum equation for annular two-phase flow can be written as,
τF
⎡ 1
SF
1 ⎤
− τiSi ⎢
+
⎥ + (ρ L − ρG ) g sin θ = 0
AF
⎣ AC AF ⎦
where, τ F
= Film shear stress (kg/m-sec)
τi
= Gas core shear stress (kg/m-sec)
AF
= Cross-sectional area of the film (m2)
AC
= Cross-sectional area of the gas core (m2)
SF
= Wetted perimeter of the film (m)
Si
= Wetted perimeter of the gas core (m)
ρL
= Density of liquid film (kg/m3)
106
(VII-3)
ρG
= Density of the gas core (kg/m3)
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:
A C = (1 − 2 δ )2 A P
(VII-8)
The cross-sectional area of the film:
AF = 4 δ (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,
VFilm = VSL
(1 − E ) D
4δ ( D − δ )
2
(VII-10)
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.
E = tanh ( 7.25 x 10 −7 We1.25 Re L
where,
2
We =
ρ G VSG D ⎛ ρ L − ρ G
⎜⎜
σ
⎝ ρG
Re L =
and
ρ L VSL D
µL
⎞
⎟⎟
⎠
0.25
)
(VII-11)
(VII-12)
(VII-13)
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,
VG
⎡D⎤
= VSG ⎢ ⎥
⎣Dc ⎦
2
(VII-14)
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
SR =
Vd
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
Centerline Droplet Velocity (m/sec)
[43] are presented in Table VII-1 at different superficial gas and liquid velocities.
40
35
30
25
Rel = 750 (Calc. Mech. Model)
Rel = 750 (Dukler)
Rel=2250 (Calc. Mech. Model)
Rel =2250 (Dukler)
20
15
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
Calculated
VSG
VSL
Liquid
(m/sec)
(m/sec)
Reynolds
Measured
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.
Calculated Film Velocity (m/sec)
5.0
Calculated-Mechanistic Model
Perfect Agreement
4.0
3.0
2.0
1.0
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
Velocity, VSL
(m/sec)
Superficial Gas
Velocity, VSG
(m/sec)
Measured Film
Velocity, VFilm
(m/sec)
Calculated Film
Velocity, VFilm
(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 SelmerOlsen [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.
Model Predicted Film Thickness (mm)
1.60
1.20
Selmer Olsen Data
Gonzales Data
W eidong Data
Zabaras Data
Perfect Agreement Line
0.80
0.40
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
(m/sec)
(m/sec)
Measured Film Mech. Model
Thickness
prediction
(mm)
(mm)
Film Velocity
Measured by
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
Entrainment
0.80
Exp.Data (Vsg=30 m/sec)
Exp.Data (Vsg=40 m/sec)
Exp.Data (Vsg=50 m/sec)
Exp. Data (Vsg=60 m/sec)
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
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
Friction Factor Ratio (fg/fi)
Salama [3] Data
Andreussi Proposed Transition
12.0
Bourgoyne Data [50]
9.0
Mist
Flow
Annular
Flow
6.0
3.0
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)
122
(VII-18)
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:
HLLS = 1.0 e-(0.45.θ +2.48E-6.Re)
(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
Re =
ρ f Vm dp
(VII- 20)
µf
where, Vm = VSL + VSG
The velocity of liquid in liquid slug can be calculated as:
VLLS =
Vm − VGLS (1 − H LLS )
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
Gas
Bubble
(VII-22)
Liquid
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 singlephase (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
Velocity Velocity
(m/sec)
Sand Sand Rate Sand Volume Measured Measured Predicted
Rate
(m3/sec) Concentration Erosion
Erosion
Erosion
(%)
(m/sec)
(mil/lb)
(mil/lb)
(ft/sec) (kg/sec)
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
Velocity
Sand Rate Sand Volume Calculated Calculated Model Pred.
(lb/sec)
(ft/sec)
Concentration Pen. Rate
Pen. Rate
Pen. Rate
(%)
(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
Velocity
(ft/sec)
Flow
Sand
Calc. Max. Pen. Mech. Model
Orientation Throughput Rate (Test Data) Predicted Pen.
(Horizontal/
(kg)
(mils/lb) *
Model
Prediction to
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
Model Predicted Erosion (mil/lb)
1.E+02
TU Data (Horizontal)
TU Data (Vertical)
Bourgoyne Data
Tolle and Greenwood Data
Perfect Agreement
Factor of 5 x Measured
1.E+01
1.E+00
1.E-01
1.E-02
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
Penetration Rate (mils/lb)
8.0E-01
Gas Only-Vert.
Mechanistic Model
Previous Model
6.0E-01
4.0E-01
2.0E-01
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 airwater 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].
Superficial Liquid Velocity (ft/sec)
1.0E+03
1.0E+02
FLOW MAP
Annular-Salama [3]
Slug/Churn- Salama [3]
Bubble- Salama [3]
Mist - Bourgoyne [50]
Dispersed Bubble
1.0E+01
1.0E+00
Bubble
Slug/ Churn
1.0E-01
1.0E-02
1.0E-02
Annular/
Mist
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
Superficial Liquid Velocity (ft/sec)
Flow Map
1.0E+02
Dispersed
Bubble Flow
Annular-Salama [3]
1.0E+01
1.0E+00
1.0E-01
1.0E-02
1.0E-02
Slug/ Churn
Flow
1.0E-01
1.0E+00
Annular
Flow
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
VSL
VSG
Calc.
Calc.
Sand
Dia. Drop. Vel. Entrain.
(m/sec) (m/sec) (mm)
(m/sec)
Rate
size
Measured
Flow
Model
Erosion Prediction
(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.
VSL
VSG
Dia.
Vel., Vo
Sand Calculated/
Size
Observed
Measured
Model
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
VSL
VSG
Calc.
Calc.
Sand
Dia. Drop. Vel. Entrain
(m/sec) (m/sec) (mm)
(m/sec)
Rate
Size
Measured
Flow
Model
Erosion Prediction
(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
Model Predicted Erosion (mm/kg)
flow regime where the model prediction is lower than the measured erosion.
1.E-01
Annular-Literature
Perfect agreement
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
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
Penentartion Rate (mils/lb)
1.0E-01
Vsg=32 (Vert.-Test)
Vsg=32 (Old Model)
Vsg=32 (Mech.Model)
1.0E-02
1.0E-03
1.0E-04
0
0.1
1.0
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.
mechanistic model
The
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.
Penetration Rate (mils/lb)
1.0E+00
Vsg=62 (Vert.-Test)
Vsg=62 (Old Model)
Vsg=62 (Mech.Model)
1.0E-01
1.0E-02
1.0E-03
1.0E-04
0
0.1
1.0
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
Penetration Rate (mils/lb)
Vsg=90 (Vert.-Test)
Vsg=90 (Old Model)
Vsg=90 (Mech.Model)
1.0E-01
1.0E-02
1.0E-03
0
0.1
1.0
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
Penetration Rate (mils/lb)
1.0E+00
Vsg=112 (Vert.-Test)
Vsg=112 (Old Model)
Vsg=112 (Mech.Model)
1.0E-01
1.0E-02
0
0.1
1.0
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
Penetration Rate (mils/lb)
1.0E+00
Vsg=112 (Vert.-Test)
Vsg=112 (Old Model)
Vsg=112 (Mech.Model)
1.0E-01
1.0E-02
0
0.1
1.0
5
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
Penetration Rate (mils/lb)
Vsl=0.1 ft/sec (Old Model)
Vsl=0.1 ft/sec-Vert.
Mechanistic Model
1.0E-01
1.0E-02
1.0E-03
0
25
50
75
100
125
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
Penetration Rate (mils/lb)
Vsl=1.0 ft/sec (Old Model)
Vsl=1.0 ft/sec-Vert.
Mechanistic Model
1.0E-01
1.0E-02
1.0E-03
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 ) , ( x 2 + ∆ x 2 ) , . . . . . . . . . . . ( x n + ∆ x n )]
= f ( x1 , x 2 , . . . . . . x n ) + ∆ x1
∂f
∂f
∂f
+ ∆ x2
+ . . . . . . . . ∆ xn
∂ x1
∂ x2
∂ xn
. . . . . . (IX-1)
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 + u x1 ), ( x 2 + u x 2 ), . . . . . . .( xn + u xn ) − f ( x1 , x x , . . . . . x n )
= uf − Total = u x1
. . (IX-2)
∂f
∂f
∂f
+ ux 2
+ . . . . . . . . . . . . + u xn
∂x1
∂x 2
∂x n
where,
u f −Total
= Total Uncertainty
u x1
= Uncertainty in variable x1
∂f
∂x1
= Change in uncertainty due to changes in variable 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
u f −RMS =
where,
2
⎡
⎡
⎡
∂f ⎤
∂f ⎤
∂f ⎤
⎢u x1
⎥ + ⎢u x 2
⎥ + . . . . . . . . . . . . + ⎢u xn
⎥
∂x 1 ⎦
∂x 2 ⎦
∂x n ⎦
⎣
⎣
⎣
2
. . . . . (IX-3)
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.
u x1
∂f
∂ (Pen.Rate)
= u Sand
∂x1
∂ (sand)
u x2
∂f
∂ (Pen.Rate)
= u liq.vel.
. . . . . . . . . . . . . . . . . . . . . . . . . .. . (IX-5)
∂x 2
∂ (liq.vel)
u x3
∂f
∂ (Pen.Rate)
= u gas vel
∂x 3
∂ (gas vel.)
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . (IX-4)
. . . . . . . . . . . . . . . . . . . . . . . . .. . . . (IX-6)
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
al
Balance used for mass
mg
Total
Uncertainty
Uncertainty Uncertainty Uncertainty Percent of
Level
(B)
(SX)
(U95) ±
nominal
20
0.10
0.40 mg
0.50
2.5%
10 *
5
15
1.5%
loss measurement
Balance used for sand grams 1000
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%
2.5
0.05
0.10
0.15
6%
Liquid and Sand Rate GPM
Sand size distribution
µm
150
5*
27 **
32
21%
Hardness of the
BHN
230
3*
6.2
9.2
4%
µm
15
1.5 *
0.53
1.83
12.2%
Specimen
Profilometer thickness
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.
Superficial Superficial Mech.
Gas
Velocity
Liquid
Model
Mech.
Mech.
Model
Model
Model
Prediction
Prediction Prediction
With
Total
Velocity Pred. Pen. With +21% With + 6% +13.75% Uncer- Measured
VSL
Rate
Sand Size
(m/sec)
(m/sec)
(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
Liq. Rate Gas Rate
tainty
VSG
(mm/yr)
Pen Rate
(mm/yr) (mm/yr) (mm/yr)
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
Due to
Due to
Gas
Liquid
Due to
Velocity
Velocity
Change in
Change in
Changes in
(m/sec)
(m/sec)
Sand size
Liq-Rate
Gas-Rate
∂(Pen.Rate )
∂(Pen.Rate)
∂(Pen.Rate)
∂( sand )
∂(liq.vel)
∂(gas vel.)
(Uf-Total)
(Uf-RMS)
Overall
Overall
Total
RMS
Uncertainty Uncertainty
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
Model Predicted Pen-Rate (mm/yr)
1.E+01
Perfect Agreement
Mech. Model Prediction
1.E+00
1.E-01
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
Ap
Cross-sectional area of the pipe (ft2)
AF
Cross-sectional area of the film (m2)
AC
Cross-sectional area of the gas core (m2)
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
E
Fraction of liquid entrained in the gas core (mass of liquid in gas core/ total mass of
liquid)
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)
QG
Volumetric gas flow rate (ft3/ Sec)
QL
Volumetric liquid flow rate (ft3/ 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
µm
Mixture viscosity of fluid in the stagnation zone, pa-s or N-s/m2
φ
Dimensionless parameter
ρ
Density of the carrier fluid lbm/ft3
ρw
Density of the wall material
ρm
Mixture density of fluid in the stagnation zone, kg/m3
ρp
Density of particles, kg/m3
ρF
Liquid phase density or film density (lb/ft3)
ρ1, ρ2
Densities at location 1 and 2 (lb/ft3)
ρL
Density of liquid film (kg/m3)
ρG
Density of the gas core (kg/m3)
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
167
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175
APPENDIX A
CALCULATION OF PENETRATION RATE AND SAND VOLUME
CONCENTRATION
Penetration Rate Calculation
Superficial liquid velocity, VSL =
Superficial gas velocity, VSG =
Sand throughput =
Elbow specimen material =
Sand throughput =
Elbow specimen width =
Elbow specimen length =
Mass Loss:
112 ft/sec,
1.0 ft/sec
20.4 kg
316 Stainless Steel
20.4 Kg
0.25 inches
4.0 inches
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 =
Time required to inject sand =
Gas velocity =
Pipe diameter =
Density of sand particles =
2 kg (4.408 lbs)
60 minutes
105 ft/sec
1 inch (Area = 0.0005067 ft2)
2650 kg/m3
Sand Volume Concentrat ion
3
⎡
⎤
1
min
m3
sec
ft
1
x⎢
= 2 kg x
x
x
x
⎥ x
60 min 60 sec 2650 kg 105 ft ⎣ 0.3048 m ⎦ 0.0005067 ft 2
= 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 inch 3
4
3
⎡ meter ⎤
1340 inch x ⎢
⎥ = 0.02197 Cubic meters = 21.97 Liters
⎣ 39.37 ⎦
3
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,
⎛
⎞
⎟ ⎡ min ⎤
⎛ ft 3 ⎞ ⎡ P1 + 14.7 ⎤ ⎜
1
⎟x ⎢
⎜
⎟x
V2 = ⎜
x
= ft / sec
⎜ min ⎟ P + 14.7 ⎥ ⎜ π
2 2 ⎟ ⎢ 60 Sec ⎥
⎣
⎦
⎦ ⎜ 1
⎝
⎠ ⎣ 2
ft ⎟
⎝ 4 12
⎠
( )
⎛
⎞
⎜
⎟
1
⎜
⎟ = 0.00542 ft 2
Cross sectional area of one inch pipe =
2
π
⎜ 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
⎛
⎞
⎟ ⎡ min ⎤
⎛ 30 ft 3 ⎞ ⎡ 35 + 14.7 ⎤ ⎜
1
⎟x ⎢
⎜
⎟x
V2 = ⎜
x
= 101.94 ft / sec
⎜ min ⎟ ⎣ 30 + 14.7 ⎥⎦ ⎜ π
2 2 ⎟ ⎢ 60 Sec ⎥
⎣
⎦
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
VSL =0.015654 liters/sec x (0.0353147 ft3 / liter) x (1/0.00542 ft2) = 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:
SPECIMEN NO.
TEST DATE:
TESTED BY: ___________
MATERIAL OF SPECIMEN:
VISCOSITY (cp): _______________GAS VEL.(VSG) _______ ft/sec
.
SAND SIZE (micron):
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
Time took to Calculated Pressure Test section Flow meter Calculated Comment
Test Amount of Liquid
lower liquid
level
sand
P1 (Psig) pressure P2 Reading
date
liquid
Gas
level by one velocity
in the
(grams)
(ACFM)
and
(psig)
Velocity
inch
slurry tank
time
(ft/sec)
(ft/sec)
(seconds)
(inches)
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
Mechanistic Empirical
Elbow Sand Measured Model Model [17]
Dia.
size
Erosion Prediction Prediction
VSL
VSG
(mm/kg)
(m/sec) (m/sec) (mm) (micron) (mm/kg) (mm/kg)
Salama
Empirical
Model [3]
Prediction
(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
Mechanistic
VSL
VSG
Elbow
Sand
Dia.
Size
Flow
Measured
Model
Erosion
Prediction
(m/sec) (m/sec) (mm) (micron) Pattern (mm/kg)
(mm/kg)
Salama
Empirical Empirical
Model
Model [3]
[17] Pred. Prediction
(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
Empirical
Empirical
Mechanistic
Elbow Calculated/
VSL
VSG
Dia.
Measured
Model
Erosion
Prediction
Observed
(m/sec) m/sec (mm) Flow Pattern (mm/kg)
Model [17] Model [3]
(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
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
3.12E-07
3.04E-07
3.29E-06
Bubble
4.60E-06
1,4
(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
Mechanistic
Elbow Calculated/
VSL
VSG
Dia.
Observed
Measured
Model
Erosion
Prediction
(m/sec) m/sec (mm) Flow Pattern (mm/kg)
E/CRC
Salama
Empirical
Empirical
Model [17] Model [3]
(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
1
191
