Jon Michael Throneberry, 2010, "Solid Particle Erosion in Slug Flow"

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T H E U N I V E R S I T Y O F T U L S A

THE GRADUATE SCHOOL

Solid Particle Erosion in Slug Flow

by Jon-Michael Throneberry

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science

in the Discipline of Mechanical Engineering

The Graduate School

The University of Tulsa

2010

T H E U N I V E R S I T Y O F T U L S A

THE GRADUATE SCHOOL

SOLID PARTICLE EROSION IN SLUG FLOW

by Jon-Michael Throneberry

A THESIS

APPROVED FOR THE DISCIPLINE OF

MECHANICAL ENGINEERING

By Thesis Committee

, Co-Chair Brenton S. McLaury

, Co-Chair Siamack A. Shirazi

Yongli L. Zhang

Daniel W. Crunkleton

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means (electronic, mechanical, photocopying, recording or otherwise) without the prior written permission of the author.

iii

ABSTRACT

Jon-Michael Throneberry (Master of Science in Mechanical Engineering)

Solid Particle Erosion in Slug Flow

Directed by Dr. Brenton S. McLaury and Dr. Siamack A. Shirazi

182 pp., Chapter 4: Summary, Conclusions, and Recommendations

(147 words)

Solid particle erosion is proven to be a worthy adversary to the oil and gas industry in relation to the economic losses that it is capable of inducing on the upstream production process from pipe damage and maintenance. Slug flow is one of the leading multi-phase flow patterns encountered by the industry, so a firm understanding of solid particle erosion in slug flow is vital to ensure an equitable energy product. Experimental erosion measurements were collected through the use of electrical resistance probes while varying superficial velocities, liquid viscosity, and sand size within the slug flow regime.

The measured results were compared with the one-dimensional mechanistic model and were then used to develop a new two-dimensional approach for predicting erosion rates in slug flow. The calculated erosion trends and magnitudes were greatly improved over the previous model and are now much more representative of the measured values.

ACKNOWLEDGEMENTS

I would like to convey my genuine gratefulness to each professor that served on my thesis committee being Dr. McLaury, Dr. Shirazi, Dr. Zhang, and Dr. Crunkleton.

Each of you have intrigued me during lecture and inspired me to never stop seeking knowledge from life and all of its remarkable facets. Special thanks Dr. Shirazi, because you are the whole reason that I had the opportunity to extend my career in academia to the master’s degree level. Thank you Dr. McLaury for providing the insight and direction that I needed to succeed in the completion of this work and graduate school. I offer my sincere thankfulness to Dr. Zhang, because the application of my experimental research would not be possible without your expertise. I thank you Dr. Rybicki for all of the insightful comments and suggestions that you presented me with throughout my research and studies. I present my gratitude to the member companies of the Erosion/Corrosion

Research Center that funded my experimentation. I am also much obliged to Ed Bowers and his ability to transcend the deep dark chasm between theory and scientific experimentation.

I am indebted to David Chernicky, Janet McGehee, and Jerry Breaux at New

Dominion LLC for challenging many of my skill sets and allowing my academic endeavor for a fundamental understanding of this existence come to fruition by means of real-world application.

TABLE OF CONTENTS

Page

ABSTRACT ...... iv

ACKNOWLEDGEMENTS ...... v

TABLE OF CONTENTS ...... vii

LIST OF TABLES ...... ix

LIST OF FIGURES ...... x

LIST OF GRAPHS ...... xii

CHAPTER 1: INTRODUCTION ...... 1 Solid Particle Erosion ...... 1 Erosion in Industry ...... 2 Erosion/Corrosion Research Center...... 3 Sand Production Pipe Saver ...... 4 Multi-Phase Flow...... 4 Objectives and Approach ...... 5 Objectives of Work ...... 6 Approach ...... 7

CHAPTER 2: LITERATURE REVIEW ...... 12 Multi-Phase Flow ...... 12 Slug Flow ...... 19 Slug Flow Modeling ...... 22 Sand Production Pipe Saver ...... 26 Program Capabilities and Interfacing ...... 27 General Erosion Prediction ...... 27 Slug Flow Erosion Prediction ...... 32 Electrical Resistance Probes ...... 35 ER Probe Theory ...... 36 ER Probe Types ...... 37 ER Probe Evaluation ...... 38

vi ER Probe Evaluation in Slug Flow ...... 41

CHAPTER 3: RESULTS AND DISCUSSION ...... 44 1-Dimensional Slug Flow Modeling ...... 44 1-D Mechanistic Slug Flow Model Development ...... 44 Elbow Model ...... 50 Angle-Head Model ...... 50 1-D Slug Flow Model Results of Previous Boom Loop Experiments 53 Elbow Model ...... 53 Angle-Head Model ...... 56 Experimental Facility ...... 61 Description of Facility ...... 61 Operating Procedure ...... 66 Data Acquisition Procedure ...... 70 Experimental Results ...... 74 Effects of Superficial Velocities ...... 87 Effects of Viscosity ...... 97 Combined Effects of Superficial Velocities and Viscosity ...... 99 Effects of Sand Particle Size ...... 108 Effects and Correlation of Probe Location ...... 110 2-Dimensional Slug Flow Modeling ...... 117 2-D Mechanistic Slug Flow Model Development ...... 120 2-D Slug Flow Model Results ...... 128 2-D Slug Flow Model Evaluation ...... 135 Uncertainty Analysis ...... 139 Uncertainty Analysis of Boom Loop ...... 140 Uncertainty Analysis of Erosion Measurements ...... 142 Uncertainty Analysis of Erosion Predictions ...... 147

CHAPTER 4: SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS ...... 153

NOMENCLATURE ...... 160

BIBLIOGRAPHY ...... 164

APPENDIX A: EXPERIMENTAL CALCULATIONS ...... 168 APPENDIX B: STANDARD OPERATING PROCEDURE ...... 173

vii

LIST OF TABLES

Page

2.2.1 Empirical Material Factor, FM , for Different Materials ...... 30

2.2.2 Sand Sharpness Factor, FS , for Different Types of Sand ...... 31

2.2.3 Penetration Factor, FP , for Elbow Geometry ...... 31

3.1.1 Calculated and Measured Results for the Elbow Probe ...... 54

3.1.2 Calculated and Measured Results for the Angle-Head Probe ...... 57

3.2.1 Surface Tension Measurements for Experimental Liquid Viscosities ...... 68

3.3.1 Experimental Conditions and Erosion Rates for Elbow Probes ...... 76

3.3.2 Experimental Conditions and Erosion Rates for Angle-Head Probe ...... 77

3.3.3 Test Matrix for 20 μm Sand Particles with Corresponding Test Number ..... 86

3.3.4 Test Matrix for 300 μm Sand Particles with Corresponding Test Number ... 87

3.3.5 Correlation of Elbow Section to Angle-head Probe ...... 113

3.3.6 Correlation of Probe at 90° to the Probe at 45° in the Elbow ...... 116

3.6.1 Uncertainties in Boom Loop Measurements ...... 141

3.6.2 Electrical Resistance Probe Measurement Uncertainties ...... 146

3.6.3 Error in 2-D Model Predictions Caused by Turbulence ...... 149

3.6.4 Uncertainties in 2-D Model Predictions for 20 μm Particles ...... 151

3.6.5 Percent Uncertainties in 2-D Model Predictions for 20 μm Particles ...... 152

B.1 Boom Loop Wiring Scheme ...... 176

viii

LIST OF FIGURES

Page

2.1.1 Flow Patterns in Horizontal Pipes for Multi-Phase Flow ...... 16

2.1.2 Flow Pattern Map for Horizontal Flow ...... 18

2.1.3 Example of Flow Pattern Map for Horizontal Flow in 3” Pipe Using Superficial Velocities ...... 19

2.1.4 Slug Flow Schematic ...... 24

2.3.1 ER Probe Data Acquisition Hardware and Connections ...... 37

2.3.2 Angle-Head and Flat-Head ER Probes ...... 38

3.1.1 Illustration of Stagnation Length and Particle Velocity ...... 45

3.1.2 Diagram of Slug Unit and Slug Body (Not to Scale) ...... 47

3.1.3 Stagnation Length Distribution Components ...... 49

3.1.4 Reduction in Cross-Sectional Area Caused by the Protruding Probe ...... 51

3.1.5 Variables for Area Calculation of Pipe at the Angle-Head Probe ...... 51

3.1.6 Fraction of Particles that Impact Angle-Head Probe Face ...... 52

3.2.1 Experimental Schematic of the Boom Loop ...... 61

3.2.2 Boom and Test Sections of Boom Loop ...... 64

3.2.3 Probe Locations for the Elbow Geometry in the Test Section ...... 65

3.2.4 Angle-Head Probe Orientation ...... 66

3.2.5 Concentration of CMC versus Liquid Viscosity ...... 69

3.2.6 ER Probe Output Panel with Matching Final and Initial Temperatures ...... 72

3.2.7 ER Probe Output Panel with Different Final Temperatures ...... 73

3.3.1 Flow Pattern Map of Experimental Conditions for Horizontal Flow in 3” Pipe with Liquid Viscosity of 1 cP ...... 88 3.3.2 Flow Pattern Map of Experimental Conditions for Horizontal Flow in 3” Pipe with Liquid Viscosity of 10 cP ...... 89

3.3.3 Flow Pattern Map of Experimental Conditions for Horizontal Flow in 3” Pipe with Liquid Viscosity of 40 cP ...... 90

3.4.1 1-D Particle Tracking Particle Trajectory ...... 118

3.4.2 2-D Particle Tracking Particle Trajectories ...... 119

3.4.3 Stagnation Zone in Tee and Elbow ...... 122

3.4.4 Flow Velocity Contours and Stagnation Zone for Direct Impingement Geometry...... 123

3.4.5 Illustration of 2-D Particle Tracking Particle Arrangement ...... 124

3.4.6 Slug Unit Reduction for Increasing Liquid Viscosity from Zhang et al (2003) Slug Flow Model ...... 138

3.6.1 Sand Size Distribution for 20 µm Silica Flour ...... 150

B.1 ER Probe Coefficient String ...... 177

LIST OF GRAPHS

Page

3.1.1 Erosion Results for Elbow Probe with Large Particles ...... 55

3.1.2 Erosion Results for Elbow Probe with Small Particles ...... 56

3.1.3 Erosion Results for Angle-Head Probe with Large Particles ...... 58

3.1.4 Erosion Results for Angle-Head Probe with Small Particles ...... 59

3.3.1 Measured Angle-Head Erosion Rates for 1 cP Liquid Viscosity and 20 μm Particle Diameter ...... 79

3.3.2 Measured Elbow Section Erosion Rates for 1 cP Liquid Viscosity and 20 μm Particle Diameter ...... 80

3.3.3 Measured Angle-Head Erosion Rates for 10 cP Liquid Viscosity and 20 μm Particle Diameter ...... 81

3.3.4 Measured Elbow Section Erosion Rates for 10 cP Liquid Viscosity and 20 μm Particle Diameter ...... 81

3.3.5 Measured Angle-Head Erosion Rates for 40 cP Liquid Viscosity and 20 μm Particle Diameter ...... 82

3.3.6 Measured Elbow Section Erosion Rates for 40 cP Liquid Viscosity and 20 μm Particle Diameter ...... 83

3.3.7 Measured Angle-Head Erosion Rates for Increasing Liquid Viscosity and 300 μm Particle Diameter ...... 84

3.3.8 Measured Elbow Section Erosion Rates for Increasing Liquid Viscosity and 300 μm Particle Diameter ...... 84

3.3.9 Effects of Superficial Liquid Velocity on Erosion Rates for Angle-Head Probe with Increasing Vsg ...... 92

xi 3.3.10 Effects of Superficial Liquid Velocity on Erosion Rates for Elbow Section with Increasing Vsg ...... 93

3.3.11 Effects of Superficial Gas Velocity on Erosion Rates for Angle-Head Probe with Constant Nominal Vsl = 2.5 ft/s and Increasing Vsg ...... 94

3.3.12 Effects of Superficial Gas Velocity on Erosion Rates for Elbow Section with Constant Nominal Vsl = 2.5 ft/s and Increasing Vsg ...... 95

3.3.13 Effects of Superficial Gas Velocity on Erosion Rates for Elbow and Straight Section with Constant Nominal Vsl = 2.5 ft/s and Increasing Vsg ...... 96

3.3.14 Effects of Viscosity on Erosion Rates for Angle-Head Probe with Constant Nominal Vsl and Vsg ...... 97

3.3.15 Effects of Viscosity on Erosion Rates for Elbow Section with Constant Nominal Vsl and Vsg ...... 98

3.3.16 Combined Effects of Superficial Liquid Velocity and Viscosity on Erosion Rates for Angle-Head Probe with Constant Nominal Vsg = 150 ft/s ...... 99

3.3.17 Combined Effects of Superficial Liquid Velocity and Viscosity on Erosion Rates for Elbow Section with Constant Nominal Vsg = 150 ft/s ...... 100

3.3.18 Combined Effects of Superficial Liquid Velocity and Viscosity on Erosion Rates for Angle-Head Probe with Constant Nominal Vsg = 50 ft/s ...... 101

3.3.19 Combined Effects of Superficial Liquid Velocity and Viscosity on Erosion Rates for Elbow Section with Constant Nominal Vsg = 50 ft/s ...... 102

3.3.20 Combined Effects of Superficial Gas Velocity and Viscosity on Erosion Rates for Angle-Head Probe with Constant Nominal Vsl = 1.5 ft/s ...... 103

3.3.21 Combined Effects of Superficial Gas Velocity and Viscosity on Erosion Rates for Elbow Section with Constant Nominal Vsl = 1.5 ft/s ...... 103

3.3.22 Combined Effects of Superficial Gas Velocity and Viscosity on Erosion Rates for Angle-Head Probe with Constant Nominal Vsl = 2.5 ft/s ...... 105

3.3.23 Combined Effects of Superficial Gas Velocity and Viscosity on Erosion Rates for Elbow Section with Constant Nominal Vsl = 2.5 ft/s ...... 105

3.3.24 Combined Effects of Superficial Gas Velocity and Viscosity on Erosion Rates for Angle-Head Probe with Constant Nominal Vsl = 2.5 ft/s ...... 107

xii 3.3.25 Combined Effects of Superficial Gas Velocity and Viscosity on Erosion Rates for Elbow Section with Constant Nominal Vsl = 2.5 ft/s ...... 107

3.3.26 Effects of Sand Size on Erosion Rates for Angle-Head Probe with Constant Vsl and Increasing Vsg and Viscosity ...... 109

3.3.27 Effects of Sand Size on Erosion Rates for Elbow Section with Constant Vsl and Increasing Vsg and Viscosity ...... 109

3.3.28 Correlation of Probe Location for Angle-Head and Elbow ...... 113

3.3.29 Correlation of Probe at 45° to the Angle-Head Probe ...... 114

3.3.30 Correlation of Probe at 90° to the Angle-Head Probe ...... 115

3.3.31 Correlation of Probe Locations for Elbow Section ...... 116

3.3.32 Correlation of Probe at 90° to the Probe at 45° in the Elbow ...... 117

3.4.1 2-D SPPS Calculated and Measured Erosion Results for Angle-Head Probe with 150 μm Particles and 1 cP Liquid Viscosity...... 129

3.4.2 2-D SPPS Calculated and Measured Erosion Results for Angle-Head Probe with 150 μm Particles and Increasing Liquid Viscosity ...... 131

3.4.3 2-D SPPS Calculated and Measured Erosion Results for Angle-Head Probe with 300 μm Particles and Increasing Liquid Viscosity ...... 132

3.4.4 2-D SPPS Calculated and Measured Erosion Results for Angle-Head Probe with 20 μm Particles and 1 cP Liquid Viscosity ...... 133

3.4.5 2-D SPPS Calculated and Measured Erosion Results for Angle-Head Probe with 20 μm Particles and 10 cP Liquid Viscosity ...... 133

3.4.6 2-D SPPS Calculated and Measured Erosion Results for Angle-Head Probe with 20 μm Particles and 40 cP Liquid Viscosity ...... 134

3.6.1 ER Probe Output with Total Metal Loss Predictions ...... 143

3.6.2 ER Probe Output with Initial Metal Loss Predictions ...... 144

3.6.3 ER Probe Output with Final Metal Loss Predictions ...... 145

3.6.4 Probe Measurement Percent Difference as a Function of Metal Loss ...... 147

xiii

CHAPTER 1

INTRODUCTION

Solid Particle Erosion

Solid particle erosion is a mechanical process in which material is removed by impingement of solid particles that are transported within a carrier fluid. The process of erosion occurs on a microscopic level, but over time it can produce results that appear macroscopically. The erosion process truly comes in many forms, because it is both naturally occurring and induced within man-made systems. Erosion in nature is exemplified through such landscapes as the Double Arch in Utah, the Grand Canyon in

Arizona, and even the beach erosion at Cabrillo National Monument in California. These are all prime examples of naturally occurring erosion that contain such marvel that millions of people travel great distances to see them each year. On the other hand, there are lesser known cases of erosion that are not desirable. An example is the cost associated with the maintenance and repair of eroded pipelines.

Fluid flow is not always erosive, and it typically only becomes erosive after solid particles are supplemented to the flowing system. The particles amalgamate with the fluid and are transported throughout the system thereby causing the flow to be transformed into a destructive force. Erosion is not a binary process in the sense that it can only be either “on” or “off”. There are varying degrees of erosivity for any system which depends

1 heavily on the flow conditions within it. An appropriate goal for a company is to limit the erosion to a tolerable level for a given system.

Erosion in Industry

Industry today is full of processes that entail solid particle entrainment within a carrier fluid that flows throughout a system. These processes are prone to erosion.

Perhaps the most common industry for solid particle erosion to be found is the oil and natural gas industry, and for that reason this study will focus primarily on that specific trade. The impact of oil and gas production runs deep, and can be seen in the residential, commercial, and industrial sectors alike. Improving the upstream and downstream process efficiency is important to ensuring an equitable energy product for both consumers and producers.

One of the recognizable focal points of investigation for oil and gas operators is the well-known problem identified as erosion. Erosion is the process of abrasion by which material is worn away from a pipe’s surface by solid impinging sand particles.

Erosion occurs in the process of retrieving oil and gas from wells, when sand is extracted along with the produced fluids. The sand particles become entrained in the liquid, gas, or multi-phase flow and are transported through the entire gathering system. This means that every valve, elbow, tee, joint of pipe, or any other fitting in the pipeline will witness particle impingements from the entrained sand in the flow. Erosion is a leading factor in pipeline failures and replacements and is therefore of the upmost importance. Pipe and fitting erosion can be severe enough to cause a hazardous spill and/or complete shutdown of systems that in turn create noteworthy economical impacts throughout the entire production and gathering processes.

2 Erosion/Corrosion Research Center

Erosion/Corrosion Research Center (E/CRC) at The University of Tulsa is

currently funded by a group of 23 oil and gas production related companies from around

the world. The center provides experimental research and computational modeling

regarding the effect of particle erosion in pipelines. The experimental approach

incorporates the combination of both tests conducted in flow loops and direct

impingement testing. Flow loop analysis is used to achieve more of a macroscopic

perspective of erosion with emphasis geared towards fluid properties, particle properties,

flow regime, and geometry. The direct impingement investigations, however, examine erosion with more of a microscopic standpoint amid observation focal points including the erosivity of a specific material, erosion patterns, and the effect of impact angle.

Computational modeling provides numerous benefits. Perhaps the most practical use of the modeling is its complementary accompaniment to the experimental data with regard to interpretation of the results. Direct comparisons between modeling and experimental results are tremendously useful as well, but some of the experimental conditions in question are not obtainable with the current testing apparatus available to the center.

Computational modeling can fill the gaps in data that experimentation is lacking until the actual testing can be conducted and completed on a flow loop that is capable of the required flow conditions.

A goal of E/CRC is to create technical tools that facilitate the estimation of erosion as well as provide practical guidelines to enhance the service life of pipelines and pipe fittings in operation.

3 Sand Production Pipe Saver

E/CRC has created a tool that uses empirical evidence, mechanistic erosion

models, and developed correlations to predict pipe erosion. That tool is the computer

program called Sand Production Pipe Saver (SPPS). SPPS runs in Microsoft Excel and

has a VBA interface. The models that are intrinsic to SPPS make it possible to calculate

an erosion rate by simply inputting the known or desired flow conditions. SPPS also has

the flexibility to evaluate and assign the required flow conditions when the maximum

allowable penetration rate is already identified. Since its inception, SPPS has evolved into

an intricate tool that permits pipeline operators to better manage their erosion issues and

to limit the erosion experienced by their lines.

Multi-Phase Flow

Multi-phase flow, for this investigation, is the flow inside a pipeline that

simultaneously includes liquid and gas components. Each of the two phases is capable of

having variations in density, viscosity, and flow rate, further complicating the affair. The

subject of multi-phase flow is much more intricate than the subject of single-phase flow.

The study of multi-phase flow has not yet acquired a perfect mathematical representation

of the existing transport processes and flow mechanisms.

The occurrence of multi-phase flow can result in a variety of flow patterns

observed in a pipeline. Some examples that appear frequently in multi-phase pipe flow

are classified as stratified smooth, stratified wavy, bubble, churn, annular, and slug flow.

Variations in flow pattern are caused by dissimilar volumetric quantities of liquid and gas in a pipeline and the resulting interfacial properties between them. The flow patterns can

be transient, unstable, and not fully-developed. This increases the complexity of multi-

4 phase flow modeling and in turn, the erosion prediction in any given multi-phase flow regime.

Multi-phase flow is of tremendous interest to many industries because of its relevance in industrialized processes. The oil and natural gas industry is no stranger to multi-phase flow occurrences, due to the multi-phase nature of oil and gas production. A single well can produce oil, gas, brine, and sand. The production of any and all the aforementioned phases, can lead to an assortment of flow conditions and flow patterns.

Objectives and Approach

The models in SPPS have been extended to predict erosion in multi-phase flow conditions in addition to single-phase flow conditions. In order to properly verify and validate the SPPS models, for both single-phase and multi-phase flows, their predictions must be judged against Computational Fluid Dynamics (CFD) and experimental results.

Through the years, the E/CRC has compiled a data bank for erosion from previous studies including Bourgoyne (1989), Salama (1998), Mazumder (2004), Antezana (2004),

Madhu (2006), Nuguri (2006), Gundameedi (2008), and Rodriguez (2008). The previous experimental erosion results were inspected to determine specific areas that required additional testing to ensure the overall completeness of the investigation into the accuracy of the SPPS erosion predictions.

The compilation of data suggested that high liquid and gas flow rates occurring in the slug flow regime necessitated further experimentation. Therefore the large outdoor

Boom Loop at The University of Tulsa’s North Campus was used to collect data, because of its ability to produce such flow rates in large pipe diameters. E/CRC had collected a fair degree of erosion data for the slug flow regime, but more was required for further

5 development of the models. The particular information that the data bank lacked was

small particle erosion for the slug flow regime. Therefore, more tests were conducted of this nature to ensure a robust foundation of experimental results for the slug flow model

to build upon.

Objectives of Work

E/CRC regularly searches for possible improvements that can be made to SPPS in

all aspects of its operation. The culmination of this study’s research, testing, and data analysis, will contribute to the improvement of SPPS and its extension to erosion prediction in multiphase flow, namely slug flow. The primary objectives of the research entail two components; both of which can be considered constituents for the other’s completion. The first objective is the general enhancement of the slug flow model erosion predictions in reference to their predicted erosion magnitudes and erosion trends for all test conditions. The second objective is to increase the accuracy of SPPS predictions for small particle erosion in slug flow. The objectives can both be achieved by the implementation of a 2-D approach to particle tracking within the models.

This study will also conduct a sensitivity analysis of the erosion predictions and the corresponding effect of altering various attributes of the mechanistic models themselves, such as the number of particles released in each simulation and the number of steps taken in each cell of the Computational Fluid Dynamics mesh. The investigation

will determine the precision and accuracy of the penetration rate predictions both before and after modifications are made to the model. The computational expense required to run the model will be assessed, so the appropriate metrics between prediction accuracy and the amount of time required to perform the calculations of the model can be

6 optimized. Lastly, an uncertainty analysis for both the Boom Loop flow conditions and

the measured erosion rate will be developed.

Approach

The approach that is best suited for this study relies on the erosion results

obtained by the large scale multi-phase flow loop located at The University of Tulsa’s

North Campus that is known as the Boom Loop. The Boom Loop was developed and

constructed by the E/CRC and TUSMP. This loop is the largest and most energetic flow loop available for use with either program. It was designed to produce the flow

conditions necessary for multi-phase flow regimes and can generate a variety of flow

patterns for use by different studies. This study will more specifically make use of its

ability to produce slug flow.

Electrical Resistance (ER) probes are used for detecting, quantifying, and

recording the solid particle erosion that is taking place in any given system. ER probes

can measure extremely small rates of erosion and corrosion on the order of nanometers.

The probes have been used in previous erosion and/or corrosion studies and yielded satisfactory results. For this reason, ER probes are used extensively at E/CRC for determining metal loss and have been selected as the primary mode of data acquisition

for this work.

Superficial liquid and gas velocities dictate the flow pattern observed in a piping

system. From the fact that superficial velocities affect the flow pattern and the flow

pattern can affect the amount of erosion, it can be concluded that superficial velocities do

in fact influence the erosion seen in a piping system. As a result, the liquid and gas

7 velocities will be varied in this study to determine the corresponding effect on pipe erosion.

The experimental superficial velocities are contrasted over the slug flow regime for groups of representative liquid and gas velocities that the Boom Loop is capable of producing. Not only is the slug flow regime traversed, but the transition from slug to annular flow is navigated as well to provide a more complete outlook on the subject of superficial velocities and flow regime. The experiments associated with this work have superficial liquid velocities ranging from 1.5 to 2.5 ft/s and superficial gas velocities ranging from 50 to 150 ft/s.

Fluid viscosity is another topic of this study. The importance of viscosity is observed by its appearance in many fluid mechanics calculations. Oil and gas production generates both liquids and gases over a broad range of viscosities. The liquids and gases extracted from producing wells are not homogeneous but are mixtures that are comprised of many components with different viscosities. In any type of flow, varying the viscosity of the fluid can produce consequences throughout the entire system. The viscous effects of fluids contribute to such things as the amount of frictional losses experienced, the flow pattern observed, all the way to the erosion pattern and penetration intensity taking place.

Therefore, a firm understanding is needed regarding the effect of viscosity on erosion.

There are three different liquid viscosities that are examined in this study. The lowest viscosity in the experimental range is 1 cP, which is the viscosity of water near standard conditions. Processes in many realms of industry rely on fluids of this viscosity.

Thus it is essential to have a firm understanding of the effects of fluids with a viscosity of

1 cP. This work will further explore increasing viscosities much greater than that of

8 water. The other viscosities include 10 cP and 40 cP. Experimentation requiring increased liquid viscosity is achieved by using a long chain polymer known as a thickener. In this study, carboxy-methylcellulose (CMC) is used. CMC is added to water to increase its viscosity without encouraging gelling. CMC achieves an increased homogeneous viscosity throughout the liquid. Proper results on the effect of viscosity can then be obtained for the study.

Sand size plays a crucial role in this study, because of its known influence on erosion. Varying particle diameter not only determines the amount of erosion from a single particle impact but also the location of the particle in the flow. Larger particles are heavier and tend to settle more easily than smaller particles. Hence, sand size can affect erosion patterns and the location of erosion in pipe fittings. Particle size is only one characteristic of sand that influences erosion. In the oil field, wellbores can produce sand with many variations in particle shape, size, and sharpness.

There are three different sands that E/CRC has at its disposal, and each has been explored in previous studies to varying degrees. Every sand type has been properly examined to determine the average particle diameter and the overall range of particle diameters. This was accomplished by the implementation of sand sieves of varying screen size as well as other techniques. The smallest particle size sand that is investigated is silica flour. The silica flour has an average particle diameter of 20 μm and is classified as sharp because of the jagged edges that are seen on each particle microscopically. The mid-sized particle available is Oklahoma #1 with an average particle diameter of 150 μm and is classified as semi-rounded because of the more rounded edges that are seen microscopically. The largest particle size on hand is California silica sand mesh 60. The

9 average particle size for this sand is 300 μm, and it is also classified as sharp. The use of these three different sand types at the E/CRC provides a detailed view into the effect of particle properties on pipe erosion. Previous data collected from the Boom Loop that used the 150 μm sand is included for comprehensiveness. The experimentation of this study only makes use of the 20 and 300 μm sands but concentrated primarily on the 20 μm sand, since the slug flow model required small particle erosion measurements for comparison.

Probe location is another topic of interest for this work. Each ER probe location is a position where erosion is measured in the experimental flow loop. There are a total of three probe locations that are used on the Boom Loop. It is important to have erosion measurements for several geometries and even multiple locations in a single geometry. It has been observed that a slight change in flow conditions or flow pattern can alter the locale of maximum erosion. Consequently, two probe locations are situated in an elbow, and one probe location is positioned in a straight section of pipe to further understand this effect.

The number of variables accounted for in this research helps demonstrate the breadth of solid particle erosion in pipe flow. The combination of all these factors can truly produce numerous flow characteristics and resulting erosivity for any given system.

This study of erosion in multi-phase flow presents experimental data gathered for varying flow conditions, fluid viscosities, and sand sizes. The study attempts to develop an accurate depiction of how erosion behaves under slug flow conditions and ultimately provide means of accounting for and predicting erosion in the slug flow regime. More

10 particularly, this study focuses on the slug flow erosion models in SPPS and improving their predictions for small particles.

CHAPTER 2

LITERATURE REVIEW

Multi-Phase Flow

In order to properly understand slug flow, it is imperative to begin with the

fundamental theories of multi-phase flow. This section deals with several variables and

introductory concepts of multi-phase pipe flow. All variables can be expressed in either

English or metric units provided that each are used consistently throughout the

progression. To begin, the volumetric flow rate is defined in Equation (2.1.1), where q is

the total volumetric flow rate, qL is the liquid volumetric flow rate, and qG is the gas

volumetric flow rate.

q = qL + qG (2.1.1)

Superficial velocities are of considerable value to multi-phase flow calculations.

The superficial velocity, of either the liquid or gas phase, is the volumetric flux of that

phase through the pipe. This is represented by the phase specific volumetric flow rate per

unit area. It is denoted with vSL being the superficial liquid velocity, vSG is the superficial

gas velocity, and AP is the cross-sectional area of the pipe. The calculations for determining both the superficial liquid velocity and superficial gas velocity are shown in

Equation (2.1.2).

qL qG vSL = and vSG = (2.1.2) AP AP

12 The superficial velocity calculation for multi-phase flow is similar in form to the average velocity calculation for single-phase flow. However, it is important not to confuse the superficial velocities with the average or actual velocities. The superficial velocity is a virtual value of what would be observed in the pipe if there was only one of the two phases present.

The mixture velocity, symbolized by vM , can also be referred to as the center of volume velocity. It is the total combined volumetric flow rate of both liquid and gas phases per unit area. The mixture velocity shown in Equation (2.1.3) is analogous to the average velocity calculation for single-phase flow. It is also seen that the mixture velocity is equal to the sum of superficial velocities.

qL + qG vM = = vSL + vSG (2.1.3) AP

The liquid holdup is a vital multi-phase flow characteristic and can be considered the variable that differentiates single and multi-phase flow calculations from one another.

The liquid holdup was conceived for the complications that arise when applying basic conservation equations to multi-phase flow. The representative area that a particular phase fills inside the pipe is needed to complete an analysis of the flow. This can also be found by similarity through the fractional volume of each phase. The liquid holdup is the volume fraction of flow that is occupied by the liquid phase. The gas void fraction is of the same nature as the liquid holdup, but it is the volume fraction of the gas phase. It is mathematically bound to the liquid holdup by unity as seen in Equation (2.1.4).

H L + α = 1 (2.1.4)

13 The liquid holdup is represented by H L , and the gas void fraction by α . The only

possible values, for multi-phase flow, are shown by the inequalities 0 < H L or α < 1.

These relationships would not hold for the case of single-phase flow, where H L and α must be constrained to an individual integer being the combination of either 0 or 1.

The space and time average of the instantaneous liquid holdup, H L , is seen in

Equation (2.1.5):

∫ ∫ H (r,t)drdt H = L , (2.1.5) L ∫ dr ∫ dt

where H L ()r,t is the instantaneous liquid holdup represented as a differential volume

element. The quantity H L ()r,t is the holdup at any given point in space r at any given point in time t . The volume element condition is simply that it must be either 0 or 1. This is because the volume is taken to be extremely small and can be viewed as only being able to contain a single liquid or gas molecule.

Once the liquid holdup is known or estimated, it can be applied to determine other multi-phase flow characteristics. The first of which is the actual velocity of each phase.

Equation (2.1.6) illustrates the calculations, where vL is the actual liquid velocity, AL is

the cross-sectional area occupied by liquid fraction, vG is the actual gas velocity, and AG is the cross-sectional area occupied by gas fraction. The correlation between the specific phase area in the pipe and the liquid holdup can also be seen by the equations presented.

qL vSL qG vSG vL = = and vG = = (2.1.6) AL H L AG 1− H L

14 Next is the concept of slip velocity, which is the relative velocity of one phase to

the other. Equation (2.1.7) computes the slip velocity, vSLIP , through the difference between the actual gas and liquid velocities.

vSLIP = vG − vL (2.1.7)

The process of solving the liquid holdup simplifies when the slip velocity is equal to zero, and the actual velocities of each phase are equal to one another. The actual velocities for both phases are rarely equal to each other inside a pipe, but assuming them to be allows for a straightforward method of calculating an exploratory liquid holdup.

The no-slip liquid holdup is symbolized by λL and is calculated using Equation (2.1.8).

qL vSL λL = = (2.1.8) qL + qG vSL + vSG

Drift velocity is the relative velocity of one phase to the mixture velocity and is

specific to each phase. It is shown by Equation (2.1.9) where vDL is the liquid drift

velocity and vDG is the gas drift velocity.

vDL = vL − vM and vDG = vG − vM (2.1.9)

Last are the average fluid properties or mixture properties. The mixture density

and mixture viscosity, ρM and μM respectively, are found by Equations (2.1.10) and

(2.1.11). The calculations sum both individual component properties that have been

weighted by their corresponding volumetric fraction. The liquid and gas density, ρL and

ρG respectively, and the liquid and gas viscosity, μL and μG respectively, must be used along with the liquid holdup to determine the mixture properties.

ρ M = ρ L H L + ρG (1− H L ) (2.1.10)

15 μ M = μ L H L + μG (1− H L ) (2.1.11)

Multi-phase flow properties can exist in various manifestations known as flow patterns. The separate flow pattern appearances are caused by dissimilar physical flow mechanisms. Figure 2.1.1 is crucial to understanding multi-phase flow patterns because it provides visual examples of what would be observed in a pipe under different operating conditions.

Stratified- Smooth Stratified Stratified- Wavy

Elongated- Bubble Intermittent

Slug

Annular Annular

Wavy- Annular

Dispersed- Bubble

Direction of flow

Figure 2.1.1: Flow Patterns in Horizontal Pipes for Multi-Phase Flow

Perhaps the most used model for predicting flow pattern in a pipeline is the Taitel and Dukler (1976) model. The model can be applied to horizontal or slightly inclined

16 Newtonian flow if it is considered steady state and fully-developed. It defines slightly inclined as between ±10◦ inclination. The model was tested against experimental data gathered for low pressures in small pipes with great success and is consequently why it is used for flow pattern prediction.

The model accounts for a total of five flow regimes with four regime transition criterions that are analyzed through the use of the above properties along with several dimensionless groups, parameters, and variables. It uses a compounding process that begins with equilibrium stratified flow. Each transition criterion performs a stability analysis of the flow, via mechanistic approaches, to decide if the conditions have been met to transition to the next flow pattern or stay in the current regime. The first is the stratified to non-stratified transition that is known as Transition A. Next is the intermittent or dispersed-bubble to annular transition labeled as Transition B. Then there is the stratified smooth to stratified wavy transition referred to as Transition C. Last is the intermittent to dispersed-bubble transition or Transition D. All of the transitions and flow regimes that are described can be seen graphically in Figure 2.1.2, where the surrounding axes are several of the dimensionless variables needed for the analysis.

Figure 2.1.2: Flow Pattern Map for Horizontal Flow

Figure 2.1.2 formulates a relatively complicated flow pattern map that lacks simple correlation to flow conditions on each of the axes. More substantial axis values are needed so that flow pattern mapping can be more useful to engineers and hydrodynamicists. Therefore, it is more beneficial to map the flow patterns and pattern transition lines using superficial gas and liquid velocities to achieve physical meaning in the map as well as increasing map comprehension. Several fluid properties must be known and taken into account for the map to retain legitimacy. The map must be made for particular cases and cannot be as broad as the previous map. Figure 2.1.3 reveals the flow pattern map for horizontal flow in 3” pipe with 1 cP liquid viscosity where the independent axis is the superficial gas velocity and the dependant axis is the superficial liquid velocity and both are in units of [ft/s]. The flow regime transitions are shown along with the regime labels.

18 100 Dispersed Bubble Regime

10 Slug Regime

1 [ft/s] Annular Regime Superficial Liquid Velocity 0.1 Stratified Stratified Regime Wavy Regime

0.01 0.1 1 10 100 1000 Superficial Gas Velocity [ft/s]

Figure 2.1.3: Example of Flow Pattern Map for Horizontal Flow in 3” Pipe Using Superficial Velocities

To summarize, the subject of multi-phase flow is more convoluted than single- phase flow. This is increasingly apparent for design engineers that must premeditate vital flow characteristics such as the pressure drop, heat transfer, and erosion for any given multi-phase flow system in question. The prediction of flow pattern in itself can be relatively difficult depending on the known and unknown system values. There are several widely accepted multi-phase flow patterns, and each of them possesses distinct flow mechanisms. Each flow pattern necessitates attention to detail in its analysis and modeling to accurately predict the specific flow characteristics. This study will only undertake describing the slug flow pattern in detail.

Slug Flow

Slug flow is important to multi-phase hydrodynamics, and its significance can be seen whilst viewing a flow map and observing the area it possesses in comparison to

19 other multi-phase flow regimes. Minor changes to the flow system can alter the flow characteristics. At the same time even if there are no changes to the system, changes in flow characteristics can occur due to the discontinuous or intermittent nature of slug flow.

The physical peculiarities exhibited by this flow regime are what separate it from the other regimes, and they are also what make the comprehension, analysis, and modeling of the topic difficult.

Slug flow is known to be the leading flow pattern for upward inclined multi-phase flow. When dealing with pipe inclination or declination, in opposition to horizontal flow, gravity plays an important role in the momentum equation which ultimately determines the flow pattern inside a pipe. The slug flow pattern is particularly dominate in the oil and gas industry for this reason. The multiple phases generated from producing formations must travel upward vertically through tubing to reach the surface where they can be separated then transported to a refinery in order to begin downstream processing. The grade, or incline, of any physical land feature that is navigated by a pipeline can also affect slugging. This effect is noticed more for offshore production because the multiple phases must travel longer distances together before it is feasible to separate them. The multi-phase nature of oil and gas production combined with its vertical extraction and varying grade in transmission provide evidence that much of the upstream process of the oil and gas industry encourages slug flow.

The slug flow pattern is further epitomized through its intermittent nature.

Intermittent, in its adjective form, is defined as alternately ceasing or stopping for a time and then beginning again. This is used in reference to the nature of slug flow by the time between produced liquid slugs flowing through a piping section. The intermittency of

20 slug flow adds intricacies to both the investigation and modeling of the regime. However, there are significant physical benefits of the slug flow pattern alongside the added difficulties associated with it. For example, the frictional pressure component, or pressure drop, is found to be smaller for slug flow compared to other flow regimes with comparable volumetric flow rates. This is advantageous for pipeline operatives that must transmit fluids over long distances because smaller and cheaper pumps can be implemented with intrinsically lower operating expenses.

Before moving on to the modeling of slug flow, one more characteristic will be explained. The final trait left to discuss is the difference of horizontal and vertical slug flow. The flow mechanisms remain basically the same, but the visual appearance of the two are not the same. The experimental data for this work was gathered for horizontal slug flow, and therefore horizontally orientated slug flow is discussed in great depth.

Vertical slug flow however is not, so a brief summary of vertically orientated slug flow will now be presented for completeness. There are two primary characteristics that separate horizontal and vertical slug flow, although there are other details that can be assumed minor in comparison. The first is visually apparent, and it is the shape of the

Taylor bubble or gas pocket. The gas pocket is bullet shaped and approximately axis- symmetric about the pipe axis when the flow is vertical. This is not the case for horizontal slug flow as seen in Figure 2.1.1 where the gas pocket is on the top of the pipe and completely stratified from the liquid film. Next is the vertical flow characteristic of the liquid film. It is seen that for vertical slug flow the liquid film may be falling or traveling in the opposite direction than the other fluid components. For horizontal flow,

21 the liquid film is the slowest moving constituent, but it is still traveling in the same direction as the others.

Slug Flow Modeling

The next section attempts to characterize slug flow both by declaration and mathematical analysis. The effort commences with explaining its integral components and flow mechanisms before any models are introduced. It is through the work of Dukler and Hubbard (1975) that allowed such information to be available and later built upon for more recent models. The primary physical components include the combination of a gas pocket, a liquid film, and a liquid body. The gas pocket is known as the Taylor bubble, and it takes up noticeably more pipe volume than the liquid slug. The Taylor bubble length is approximately 100 times the diameter of the pipe that it is traveling in and is much longer in relation to the length of the liquid body. The liquid body is generally referred to as the liquid slug. These three constituents are the framework of the complete slug unit.

Next is the topic of slug flow mechanics, which is distinguished by the flow of alternating Taylor bubbles and liquid slugs. Slug flow exhibits unsteady flow behavior such as varying durations of time between each intermittent liquid slug production as well as dissimilarities in the actual slug and Taylor bubble lengths. No two slugs or

Taylor bubbles are identical, but they can be averaged then assumed constant for modeling purposes. The velocities of the three slug unit components are arranged by increasing magnitude starting with the liquid film, followed by the Taylor bubble, and ending with the slug body which has the highest velocity of them all.

22 The most imperative concept of all the slug flow mechanisms is that which allows the slug body to travel faster than both the Taylor bubble and liquid film. The key to understanding this phenomenon is the constant scooping and shedding of liquid from the liquid film into and out of the slug body which forms a turbulent mixing zone that develops at the leading edge of the slug body. The transport process can be portrayed by following a lone liquid particle that is part of the slower moving liquid film. When the faster moving slug body reaches the particle in the liquid film it is picked up and engulfed by the liquid slug then transported at an increased translational velocity within the slug for a period of time before it is shed behind the slug back into the liquid film and consequently decelerated to the film velocity. The contents within the liquid slug are constantly changing due to the transport process. Under steady state slug flow conditions the rate at which the liquid from the film is picked up or scooped is equal to the rate that the liquid is shed from the slug. This relationship allows the length of the slug body to remain constant throughout the flow.

The primary mechanisms involved in slug flow have been described, but now can be presented and further explained by a model that depicts their actions mathematically.

The most widely accepted interpretation of slug flow is by Taitel and Barnea (1990).

Their comprehensive study presents a schematic for slug flow that was built upon the work of Dukler and Hubbard (1975), except this model accounts for inclination angles ranging from horizontal to upward vertical flow. The model is based on a liquid mass balance over the entire slug unit. The schematic proposed by Taitel and Barnea (1990) is shown by Figure 2.1.4.

Figure 2.1.4: Slug Flow Schematic

Where LU is the slug unit length, LS is the slug body length, LF is the liquid film length,

LM is the mixing zone length, VTB is the translational or interface velocity, VGTB is the gas pocket velocity in the stratified region, VLTB is the liquid film velocity in the stratified region, VGLS is the gas velocity in the slug body, and VLLS is the liquid velocity in the slug body.

There are three additional velocity variables left to discuss. The slug velocity, V;S

gas velocity, VG ; and film velocity, VF , are represented in Equation (2.1.12), Equation

(2.1.13), and Equation (2.1.14) respectively. The slug body travels faster than any other flow component. In fact, the slug body travels at the mixture velocity that was explained earlier in Equation (2.1.3).

qL + qG VS = = VM (2.1.12) AP

24 VG = VTB − VGTB (2.1.13)

VF = VTB − VLTB (2.1.14)

The proposed model requires a total of four closure variables to be specified as input parameters in order to properly use the model. Those variables include the liquid holdup in the liquid slug, the slug frequency or slug length, the translational velocity, and the velocity of the bubbles in the liquid slug. Perhaps the most critical of which is the liquid holdup in the liquid slug. Several attempts have been made over the years to accurately represent this value. Gregory et al. (1978) proposed a relationship that is directly related to the mixture velocity in units of [m/s]. The equation is only valid under horizontal slug flow conditions but is used as a stepping stone in an iterative process of calculating the holdup in the liquid slug. Equation (2.1.15) reveals the calculation.

1 H LLS = 1.39 (2.1.15) ⎛ V ⎞ 1+ ⎜ M ⎟ ⎝ 8.66 ⎠

In order to gain a better understanding of the liquid holdup in the liquid slug for non-horizontal flow, Gomez et al. (2000) has more recently developed a correlation that incorporates inclination angle into the holdup calculation as seen in Equation (2.1.16).

⎡ ⎛ −3 −6 ⎞⎤ HLLS = 1.0× exp⎢− ⎜7.85×10 θ + 2.48×10 ReLS ⎟⎥ (2.1.16) ⎣ ⎝ ⎠⎦

Where ReLS is the liquid slug Reynolds number defined by Equation (2.1.17).

(ρ L ×VM × d ) Re LS = (2.1.17) μ L

The relationship shown by Equation (2.1.16) has been validated through experimentation and found to yield adequate results for pipe inclinations of 0° < θ < 90° .

25 The most widely accepted slug flow modeling has been reviewed along with the associated flow mechanisms. However, a firm understanding of solid particle erosion within the slug flow pattern is needed. The next section explains the resulting E/CRC slug flow erosion model.

Sand Production Pipe Saver

Sand Production Pipe Saver (SPPS) was developed by E/CRC and has its origins in the mid-1990s. In 1999, McLaury and Shirazi extended the semi-empirical model to calculate erosion in multi-phase flows. SPPS was formed from data collected from research centers such as Texas A&M University, Harwell, DNV, and at The University of

Tulsa from E/CRC. McLaury and Shirazi (1999), Mazumder (2004), McLaury (2006),

Gundameedi (2008), and Rodriguez (2008) have all been key contributors to the progress of extending the model to multi-phase flow.

SPPS is a tool provided by E/CRC that attempts to predict the nature of physically occurring processes involving fluid flow. SPPS has the ability to be modified and improved to better capture the erosion that is transpiring in any flow regime. The model has already traversed many obstacles and continues to become better equipped to handle more flow conditions.

Experimental data has been gathered and continues to grow in the effort to validate this model for multi-phase flow conditions. E/CRC and SPPS focus research on erosion in geometries such as elbows, sharp bends, contractions, expansions, plugged tees, and tees. These geometries are rigorously studied including straight sections of pipe.

Albeit erosion is assumed negligible in the comparison of straight pipe sections to other pipe fittings, but the correlations between them are extremely useful.

Program Capabilities and Interfacing

As mentioned earlier, SPPS runs in Microsoft Excel and has a VBA interface.

Results are obtained from the program by inputting the system conditions that are under consideration into the software’s spreadsheet, clicking run, and then reading the results from the output section. In contrast to all of the programs capabilities it is a relatively small piece of software.

SPPS has the ability to predict erosion rates for numerous flow situations in every flow regime. SPPS has such capabilities due to the flow regime dependant models that are native to the program. There are several uses for SPPS that include calculating a penetration or erosion rate from the known flow conditions as well as calculating a threshold velocity. The threshold velocity is calculated by SPPS to determine the proper system conditions in which only an acceptable amount of erosion will take place, and therefore increase the service life of any given pipeline. SPPS can also be used to aid in the evasion of major failures and hazardous spills, help maintenance scheduling, and allow for cost to benefit projections for any pipeline in question.

General Erosion Prediction

There have been many contributions to erosion prediction since the recognition of the phenomenon’s significance. Industry, academia, and institutions alike have all worked towards understanding erosion as a whole. This section attempts to explore those contributions in expectation of ultimately providing a fundamental understanding of the current erosion predictions in SPPS.

27 As mentioned earlier, SPPS has the ability to calculate a maximum allowable threshold velocity which limits erosion. This has stemmed from the American Petroleum

Institute (API) recommended Practice API RP 14E, which affirms that if flow velocities stay below this limit severe erosion can be avoided. Equation (2.2.1), which is taken from

API RP 14E, is used to calculate the threshold velocity Ve , through the use of the density of the carrier fluid ρ , and a system constant C .

C Ve = (2.2.1) ρ

API RP 14E recommends two different values for the constant C depending on the system being used. It is recommended that C = 125 for intermittent service or C =

100 for continuous service. Appraisal of Equation (2.2.1) makes clear some of the generalizations it poses for any system in question. For instance, the equation does not consider the pipe size or pipe material, nor does it account for the sand size or rate. The equation does not include the pipe orientation or the flow regime within the pipe.

Further examination of Equation (2.2.1) and its implied results lead to other queries: the allowable erosional velocity is lower for higher density fluids like water, and the allowable erosional velocity is higher for lower density fluids like air. Conversely, results found in this study and others have found this not to be completely true. Erosion in gas flow is found to be greater than the erosion in liquid flow at comparable velocities.

E/CRC has used the equation as a stepping stone while searching for a more mechanistic approach that captures details of a particular flow system.

The 1-D SPPS model penetration rate calculation is shown by Equation (2.2.2) below.

28 e WVL h = FM FS FP Fr / D , (2.2.2) D / Do

Where h is the penetration rate, FM is the empirical constant related to material

properties, FS is the empirical sand sharpness factor, FP is the penetration factor for

steel based on 1” pipe diameter, Fr / D is the penetration factor for long radius elbows, W

is the sand production rate, VL is the characteristic particle impact velocity, D is the pipe

diameter, Do is the reference 1 inch pipe diameter, and e is the exponent typically determined experimentally.

All of the factors in the penetration rate calculation are known, either through assumptions or empirical methods, except for the characteristic particle impact velocity

VL . Y. L. Zhang (2007) developed an exponent of 2.41 for the impacting velocity. The exponent is based on the specific system that is trying to be imitated. The exponent was determined by the use of Computational Fluid Dynamics (CFD) and experimental data.

Other exponents have been used in the equation such as 1.73, which was based on results obtained by E/CRC and others.

The characteristic impact velocity concept was developed at E/CRC and presented by McLaury (1993); it was based on CFD studies and the use of the stagnation length concept. The stagnation length is the length from the wall at which a particle begins to decrease in velocity due to the boundary caused by the wall. The characteristic particle impact velocity must be modeled for each flow regime to properly predict the penetration rate or amount of erosion taking place. When a particle reaches its stagnation length, its inherent momentum transfer equation is solved and an impact velocity is calculated. The stagnation length concept is described in further detail in the model development section.

29 The model can use either a one or two-dimensional approach to the calculation of VL . A much more detailed explanation of the model is discussed in previous E/CRC Advisory

Board reports. It is proposed that the two-dimensional approach could be more beneficial to the model as a whole, especially for small particles.

The empirical constant for a material, FM , is proposed for carbon steel to be

−5 −0.59 FM = 1.95×10 × B . B is the Brinell hardness factor. Table 2.2.1 contains material properties for both 316 Stainless Steel and 1018 Steel and their corresponding empirical

material factors, FM , to give examples of the magnitude of these values. Please note that

these values are strictly for VL values in [m/s].

Table 2.2.1: Empirical Material Factor, FM , for Different Materials

Yield Tensile Brinell Material Material Type Strength Strength Hardness Factor 6 [Ksi] [Ksi] [B] [ FM x 10 ]

316 Stainless Steel 35 85 183 0.918

1018 Steel 90 99.5 210 0.833

Next, the sand sharpness factor used by SPPS is explored with example values for the three sand types. The sands used for this study include sharp and semi-rounded. Table

2.2.2 reveals the sand sharpness factor, FS , for three different sharpness types.

30 Table 2.2.2: Sand Sharpness Factor, FS , for Different Types of Sand

Sand Sharpness

Sharpness Description Example Factor, FS

Sharp Angular Corners Silica Flour 1.00 Rounded Oklahoma # 1 Semi-Rounded Corners Sand 0.53

Rounded Spherical Proppant 0.20

Table 2.2.3 reveals the penetration factor, FP , for steel in a 90˚ elbow in both metric and English units. Note that the reference stagnation length is for 1” pipe.

Table 2.2.3: Penetration Factor, FP , for Elbow Geometry

Reference Stagnation for Steel Length for 1" Pipe, Lo FP

Geometry [mm] [in] [mm/kg] [in/lb]

90˚ Elbow 30 1.18 206 3.68

The penetration rate calculation for SPPS includes the penetration factor for long

radius elbows, Fr / D . The penetration factor concept is attributed to Wang (1996), who used CFD results obtained from his research to develop the penetration factor equation for long radius elbows which can be seen below in Equation (2.2.3). This equation is for

3 use with metric units only. The fluid density ρ f is in units of [kg/m ], the fluid viscosity

μ f is in units of [Pa*s], and the particle diameter d p is in units of [meters]. Cstd is the radius to diameter ratio of a standard elbow, which is generally assumed to be equal to

1.5.

⎡ 0.4 0.65 ⎤ ⎛ ρ μ f ⎞⎛ r ⎞ F = exp⎢− ⎜0.1 + 0.015ρ 0.25 + 0.12⎟⎜ − C ⎟⎥ (2.2.3) r / D ⎜ d 0.3 f ⎟ D std ⎣⎢ ⎝ p ⎠⎝ ⎠⎦⎥

31 An estimation of the equivalent stagnation length for an elbow was obtained through experimental erosion testing coupled with CFD modeling where particles were tracked in the fluid phases. It was found that the equivalent stagnation length, L , can be

assumed solely as a function of pipe diameter, D ; a reference stagnation length Lo for 1” pipe. The length L can be calculated through Equation (2.2.4) below.

−1 −1.89 0.129 L = Lo {1−1.27 tan (1.01× D )+ D } (2.2.4)

The above equations, along with many others, are shaped by both experimental data and CFD results to form the erosion predictions that SPPS yields. E/CRC has collected such experimental data and CFD results to compare with SPPS erosion predictions. Additional erosion information is continuously collected by the center so the

SPPS models can be systematically updated from the results to ensure accurate erosion predictions.

Slug Flow Erosion Prediction

Since SPPS was created, it has undergone many changes and modifications to better predict erosion in multi-phase flows and more particularly the erosion occurring in the slug flow regime. Mazumder (2004) played a significant role through the mechanistic models proposed in his work. Each flow regime was treated separately thus introducing regime dependant models to further increase the value of SPPS erosion predictions in multi-phase flows. The study also marked the beginning of slug flow erosion predictions within SPPS that were later built upon to take the form they are today.

The current version of SPPS uses the slug flow calculations from the unified hydrodynamic model presented by Zhang et al. (2003). The model is derived from the dynamics of slug flow and is capable of determining flow pattern transition boundaries

32 for all flow patterns, but it is only utilized in calculating and representing slug flow characteristics. This model for slug flow is primarily based on a balance of the surface free energy of dispersed spherical gas bubbles and the turbulent kinetic energy of the liquid phase. Using this approach, an equation was proposed for calculating the slug body liquid holdup shown in Equation (2.2.5).

1 H LLS = (2.2.5) TSM 1+ 0.5 3.16[]()ρ L − ρG gσ where

1 ⎛ f d ρ H (V − V )(V −V ) d ρ (1 − H )(V − V )(V −V )⎞ ⎜ S 2 L LF T F S F C LF T C S C ⎟ (2.2.6) TSM = ⎜ ρ SVS + + ⎟ Ce ⎝ 2 4 LS 4 LS ⎠ and

2.5 − sin(θ ) C = . (2.2.7) e 2

Further clarification of the terms for the previous equations is needed. There are three subscripts that are employed for reference to the correct properties to use in the equations. The liquid phase properties are represented by the subscript L, the gas core

properties by C, and the slug body properties by S. H LF is the liquid holdup in the liquid

film region, LS is the length of the liquid slug, fS is the friction factor of the liquid slug,

VT is the translational velocity, and VF is the liquid film velocity. The liquid film velocity and the holdup in the liquid film region can be calculated through solving the momentum equations set forth by Zhang (2004). However, the length of the liquid slug and the translational velocity terms require closure relationships. The translational velocity can be satisfied by using a correlation proposed by Nicklin (1962), and the slug

33 length can be found through an approach recommended by Taitel et al. (1980) and

Barnea and Brauner (1985). The suggested approach for determining the slug length is seen in Equation (2.2.8).

2 2 Ls = [32.0cos ()θ +16.0sin ()θ ] d (2.2.8)

SPPS utilizes the liquid holdup of both the slug body and film region to determine the fraction of the liquid that is contained in the slug body. SPPS assumes that the slug body is the principal source for the erosion that occurs in slug flow. This approach was suggested by Chen et al. (2006) by assuming that the slippage between the slug body and gas pocket allows the liquid slug to entrain any sand particles that may possibly be in the gas pocket as it overtakes and filters through the slug. Therefore, it can be assumed that no solid particles are combined within the gas phase of the Taylor bubble for fully developed slug flow. The last slug unit component left to detail is the liquid film. SPPS assumes that sand particles are in fact entrained in the liquid of the liquid film, but the resulting erosion is considered negligible. This assumption is easily understood due to the low velocities experienced in the liquid film region. Consequentially, the slug body is the only source of erosion that is accounted for in the SPPS slug flow model.

The slug body is the only flow component that SPPS considers erosive in slug flow. The amount of sand inside the slug body is required to predict the erosion caused by each passing slug. The fraction of liquid in the slug body and the sand concentration in the liquid are the only values needed to calculate the total amount of sand held inside the slug body. The sand concentration is assumed known by the researcher based upon the desired conditions of the experiment. Therefore, only the slug body liquid fraction needs to be solved. Equation (2.2.9) is the equation used for calculating the slug body liquid

34 fraction with previously explained nomenclature and variables. Note that the slug body liquid fraction is the fraction of liquid in the slug body with respect to the total amount of liquid in the entire slug unit.

L H V Slug Body Liquid Fraction = S LLS M (2.2.9) LS H LLSVM + LF H LFVF

The amount of sand possessed in each liquid slug can now be calculated through the aforementioned method to be used by the slug flow model. The amount of sand in the slug body alone is not enough information to estimate erosion. The erosion prediction is accomplished by the application of additional techniques offered by SPPS. The remainder of the operations performed to predict erosion in slug flow is further discussed in the mechanistic slug flow modeling sections.

Electrical Resistance Probes

For this study, Electrical Resistance (ER) probes were employed for metal loss measurements. The probes are manufactured by Cormon Ltd., a British company, and

CorrOcean, a Norwegian company. E/CRC has been conducting research with the

Cormon probes for some time now. Therefore, a great deal of the work conducted by

E/CRC relies heavily on the use, accuracy, and precision of ER probes. Studies have been conducted that formally evaluate the performance of ER probes. The studies were carried out by Hedges and Bodington (2004) and Evans et al. (2004). There have been ER probe evaluations performed by The University of Tulsa Sand Management Projects (TUSMP) by Antezana (2004) and Pyboyina (2006). The most recent studies conducted by the research centers here at The University of Tulsa were performed by Gundameedi (2008) and Rodriguez (2008).

35 ER probes have substantial benefits compared to other methods of determining metal loss. Unlike metal coupons or samples, ER probes are more advantageous. ER probes do not have to be installed and removed prior to and following the experiment to determine mass loss. ER probes can be left in the experimental apparatus to ensure that correct placement is not an issue. ER probes output real-time metal loss and temperature readings to allow measurements and calculations to be performed in a much timelier manner, unlike metal samples that need to be weighed and installed, then retrieved and weighed again to determine a mass loss. ER probes exhibit extremely high sensitivity that allows for metal loss measurements on the order of nanometers.

ER Probe Theory

The guiding principal that gives the ER probes their abilities is, as their name infers, electrical resistance. Metal loss, by erosion and/or corrosion, is detected by the change in resistance of an electrode. There is an exposed electrode, known as the working electrode, that is placed in the flow and a reference electrode that is protected from exterior elements inside the probe. The resistance of the working electrode changes when it is eroded or corroded. The resistance is then compared to that of the reference electrode that has not been affected by either erosion or corrosion. The amount of metal loss that has occurred on the working electrode in the flow can then be calculated by the comparison to the reference electrode. This metal loss provides the penetration rate for a particular flow condition. The penetration rate from an ER probe is then compared to the penetration rate calculated by SPPS to validate the model for any particular case. The resistance of each element is calculated through Equation (2.3.1), where R is the element

36 resistance, ρ is the resistivity of the element material, L is the length of the element, and

A is the cross-sectional area of the element.

L R = ρ × (2.3.1) A

ER probes must be used alongside the provided hardware and software to obtain a reading for metal loss. The probe itself is located in the experimental flow loop with a set of wires that connects to the data acquisition setup. Figure 2.3.1 provides insight into the set of connections that allows successful data acquisition. As seen in Figure 2.3.1, the ER probes must be connected to a transmitter unit and then the signal is conveyed through an isolating barrier device before finally reaching a computer where the software is installed to complete the process and ascertain metal loss readings.

ER Probe IS Barrier

Transmitter Unit Laptop

Figure 2.3.1: ER Probe Data Acquisition Hardware and Connections

ER Probe Types

There are two types of ER probes, which are the angle-head and flat-head probes.

Angle-head probes are employed in straight sections of pipe and protrude into the flow.

Flat-head probes are utilized in bends and are placed flush with the wall. Figure 2.3.2 below shows pictures of the two probe types used in this study. The picture of the angle- head probe is located on the left and the picture of the flat-head probe is located on the right.

Figure 2.3.2: Angle-Head and Flat-Head ER Probes

ER Probe Evaluation

British Petroleum (BP) sponsored studies that included the testing of hardware and software to determine the proper candidate for accurately measuring erosion and corrosion in flow lines. Hedges and Bodington (2004) performed these studies that concentrated efforts to establish what particular type of equipment could sufficiently acquire data under given test conditions. There was a large quantity of tools available to attain the data, but all methods needed to be evaluated and compared. The methods that were tested and compared in the study include the following: an acoustic sand detector, an ultrasonic sand detector, a standard ultrasonic probe, a high sensitivity ultrasonic probe, a flexible ultrasonic mat, and ER probes. Hedges and Bodington (2004) performed multi-phase flow experiments that involved high pressures with varying sand size. The study concluded that out of all the previously mentioned equipment that was investigated, the acoustic sand detector and the ER probe provided acceptable results for erosion measurements. However, Hedges and Bodington (2004) report that the ER probe’s

38 primary disadvantage lies solely on the fact that there is no clear distinction that the output measurements are caused by erosion, corrosion, or the synergistic effect.

Antezana (2004) conducted studies for E/CRC in multiphase annular flows that focused on the effects of probe location relative to the metal loss measured by the probe.

ER probes were the primary means of data acquisition, which led to another key objective involved in the study: assess the sensitivity of the ER probes. The test matrix for the experiments included varying sand rates from 1 to 60 grams per minute of sand that possessed a mean particle diameter of 150 µm. A key discovery to determining the probe sensitivity was observed. It was detected that there is an inherent noise output range for every ER probe. Several conclusions were drawn from the study. It was found that the effect on probe location was noticeable. The resulting consequence was that the probes downstream of a vertical section in the system have a greater erosion ratio than probes downstream of a horizontal section in the system. Antezana (2004) argued that this is a result of dissimilarities in the distribution of the sand inside the pipe between the different flow patterns. Finally, Antezana (2004) estimated a range of ±25 nanometers for the noise output range of the ER probes. The evaluation of the ER probes as effective tools for measuring metal loss was proven successful.

The next scientific exploration that was reviewed is another BP sponsored study accomplished by Evans et al. (2004), which travels further into the use of ER probes for measuring erosion and corrosion. The work focuses on the evaluation of three different erosion-corrosion inhibitors while imitating high gas production conditions. ER probes were the primary mode of data acquisition. Three different types of probe materials were tested. Those three materials included regular carbon steel, 13Cr steel, and a 25Cr duplex

39 stainless steel. The study subsequently revealed properties of the different ER probe materials in addition to the inhibitor efficiency. Of the findings concerning the ER

Probes, two conclusions were met. The data collected for the 25Cr duplex stainless steel

ER probe yielded no suggestion of the combined effect of erosion-corrosion but revealed only metal loss caused by erosion. The metal loss rates sampled from the regular carbon steel and 13Cr steel probes were higher than the 25Cr duplex stainless steel ER probe. In fact, the regular carbon steel and 13Cr steel produced a larger metal loss rate than the pure erosion and pure corrosion components combined. The probes showed a greater loss rate when both the erosion and corrosion components are combined in the flow than if the loss rates are summed from both the pure erosion and pure corrosion. The phenomenon is known as the synergistic effect.

Another study was performed which relied on the use of ER Probes. Pyboyina

(2006) used ER probes to predict sand rates in primarily single-phase gas flows while still including multiphase annular flows. Not only did Pyboyina (2006) run real-world experiments, but Computational Fluid Dynamics (CFD) was also used to compare the prediction of sand rate. The conclusions gathered from the results include peculiar findings in both single phase-gas flows and in multi-phase annular flows. For the plugged tee geometry, under single-phase gas only experiments, it was observed that lower sand concentrations produced more erosion than higher sand concentrations. The mechanism behind this phenomenon is the particle interactions with the gas flow, which actually creates a “sand shield” on the face of the probe protecting it from any high energy impacts and therefore decreasing measured erosion. The multi-phase annular flow experiments gave way to another conclusion, which states that erosion in annular flow

40 decreases as the liquid flow rate increases. The liquid film on the outer diameter of the pipe acts like a protective barrier by slowing down impinging particles.

ER Probe Evaluation in Slug Flow

The two most current works performed at The University of Tulsa’s research centers are by Gundameedi (2008) and Rodriguez (2008). Both researchers utilized the

Boom Loop at North Campus and concentrated their studies in slug and annular flow regimes in the 3” test section. This study is a continuation of their research in slug flow and the further development of the slug flow models in SPPS.

Gundameedi (2008) set out to analyze the performance of ER probes and acoustic monitors in slug flow. The study was funded by Petrobras, a member company of

E/CRC. The range of flow conditions that were used by Gundameedi (2008) is approximately the same for this study. Gundameedi (2008) focused on data acquisition for the angle-head probe in a straight section of pipe in the test section as well as a

Clamp-On acoustic sand monitor located on the first elbow of the test section. The procedure used varies slightly from the procedure of this study. The sand concentration was incrementally increased to a final desired value, while the response of both the angle- head probe and the acoustic sand monitor were observed during the tests. The objective was to understand the behavior of the ER probe and acoustic monitor under the varying sand rates and improve the slug flow models from the results. Contribution to the angle- head and elbow models were made. The surface area, in the erosion calculation, was modified for the elbow model which improved the accuracy of its predictions. It was concluded that the results from the acoustic monitor supported the results from the ER probe.

41 Rodriguez (2008) had goals similar to the objectives of this study. Angle-head and flat-head probes were used to measure the erosion in a straight section of pipe and in an elbow respectively. Unlike Gundameedi (2008), who focused on erosion measured by an angle-head probe, Rodriguez (2008) collected data in the elbow with a flat-head probe oriented at 45 degrees from parallel to the incoming flow in addition to the angle-head probe in a straight section of pipe. The flow conditions that were used in the study fall into the slug flow region and cascade over onto the transition to the annular flow regime.

The liquid viscosity was varied from 1 cP to 40 cP, and particle sizes used range from 20 to 300 µm. Rodriguez (2008) developed the concept of stagnation length distribution for the slug flow models. It was determined that the slug body should be divided into 500 increments to accurately depict the impacting velocity of particles in the slug flow models. Further explanation can be found in the results section. It was concluded that the models do not accurately predict small particle erosion. The results of the study serve as a preliminary mode of evaluation for the content of this research. Data from Rodriguez

(2008) is to be built on by this research to improve the database of erosion results at

E/CRC.

The review of these studies reveals that ER probes were a crucial element to the experimentation. Not only were the ER probes involved in the rigorous testing schemes associated with the studies, but they were also the focal point of data collection. This forced the ER probe measurements and capabilities to be open for scrutiny from many researchers. Some of the studies evaluated the probes themselves while other studies evaluated metal loss rates using the ER probe’s output. The successful progression of ER probes is apparent through each of the trials put forth by scientists that have been curious

42 with regard to the abilities possessed by the probes. The previous work conducted in this area has proven that ER probes collect relatively accurate and precise data, and they are suitable components to use as the basis of erosion monitoring.

CHAPTER 3

RESULTS AND DISCUSSION

1-Dimensional Slug Flow Modeling

The previous data collected and reviewed for this study was acquired on the

Boom Loop with ER probes while the test section on the boom was in the horizontal position. The erosion or penetration rates from the experiments were input into a database to be compared to the calculated rates from SPPS.

1-D Mechanistic Slug Flow Model Development

The slug flow models in SPPS were developed at The University of Tulsa’s research centers, and data is constantly being collected to continuously develop and validate them. Several assumptions are made for the modeling of slug flow. The model assumes that there is no sand entrained in the Taylor bubble. This means that particles are transported solely by the liquid phase in the slug unit. The next assumptions are for the two other components of the slug unit, besides the Taylor bubble. The liquid film is the slowest moving component of the slug unit, and the slug body is the fastest moving component of the slug unit. The slug body’s velocity is equal to the mixture velocity of the gas and liquid phases as seen in Equation (2.1.3). This being said, along with the assumption of no entrained sand in the gas phase or Taylor Bubble, it can be concluded that the slug body is the primary source of erosion in slug flow. Therefore, further assumptions are needed in the slug body. These include that the sand particles are

44 homogenously distributed throughout the slug body, and a no slip condition applies to the particles that are suspended in the slug body. The no slip condition only holds true for the entrained particles in the liquid until they approach the wall. Once the particles reach this point, the stagnation length concept is then applied.

The stagnation length concept has been developed for the slug flow models in

SPPS to estimate the associated impacting velocities under different flow conditions. As seen in Equation (2.2.2), the characteristic impacting velocity is crucial to calculating the penetration rate. Correctly modeling and predicting impacting velocity increases the accuracy of the penetration rate calculation. The stagnation length is the length at which the particle must travel through the fluid before impacting the wall, while the fluid is constantly reducing the particle velocity as it approaches the wall. Therefore, stagnation length actually dictates the total amount that the particle velocity has diminished. The longer the stagnation length, the less significant the impacting velocity will be for the same original velocity. An illustration of stagnation length is seen in Figure 3.1.1.

Figure 3.1.1: Illustration of Stagnation Length and Particle Velocity

45 The particle’s velocity is constantly decreasing from its original velocity as it travels through the stagnation length and reaches its impacting velocity at the wall. This means that an entrained particle in the slug body travels at the same velocity as the slug body, due to the no slip condition, until it reaches the appropriate stagnation length. Then, the particle must overcome the viscous effects caused by travelling through the fluid of the slug body in order to impact the wall. This can also be viewed as a trade of energy from the particle’s momentum to the losses caused by drag. The corresponding velocity at which the particle reaches the wall is the characteristic impacting velocity of the particle or VL.

In order to apply the stagnation length concept to the slug flow models in SPPS, the mixture properties must first be defined. The properties of most concern are density and viscosity, because they are responsible for the drag or fluid resistance on the particle.

They determine the decrease in velocity of the particle as it travels through the stagnation length before impacting the wall. The two apparent choices for mixture properties that apply to slug flow are the slug unit properties and the slug body properties. The slug unit properties are calculated using Equation (3.1.1) and Equation (3.1.2), and the slug body properties are found through Equation (3.1.3) and Equation (3.1.4).

(ρLVSL + ρGVSG ) ρSlugUnit = (3.1.1) VSL +VSG

(μLVSL + μGVSG ) μSlugUnit = (3.1.2) VSL +VSG

ρSlugBody = ρL H LLS + ρG (1− H LLS ) (3.1.3)

μ SlugBody = μ L H LLS + μG (1− H LLS ) (3.1.4)

46 The mixture properties will vary significantly between the slug unit and the slug body. A diagram containing each slug flow component is shown in Figure 3.1.2 to help with visualization of the topic.

Figure 3.1.2: Diagram of Slug Unit and Slug Body (Not to Scale)

The cause for the difference in mixture property values, between the slug unit and the slug body, is the gas in the Taylor Bubble. Gas has a much lower density and viscosity than liquid. Therefore, the slug unit will have both a lower mixture density and mixture viscosity than the slug body. Choosing the slug unit properties for use in the stagnation length would employ relatively lower fluid properties which produce higher impacting velocities. From Equation (2.2.2), it is apparent that the higher impacting velocities would yield an increased calculated penetration rate. The slug unit properties are not used because they over predict the characteristic impacting velocity. Instead, the slug body properties are used. The assumptions used by the slug flow models rectify the use of the slug body properties. The assumptions state that the slug body is the primary source of erosion because the sand particles are transported solely by the liquid phase and the slug body has the highest liquid holdup. The majority of the entrained sand travels in

47 the liquid of the slug body, so using the slug body properties actually helps keep the slug flow models mechanistic in nature. Therefore, the slug body properties are used in the stagnation length approach to determine the drag forces on each particle. Equation (3.1.3) and Equation (3.1.4) show the calculations of slug body density and viscosity

respectively, where H LLS is the liquid holdup in the slug body. The stagnation length must finally be applied to each of the entrained particles to determine their impact velocities.

The particle tracking used in the stagnation length concept is one-dimensional.

The particle is only allowed to travel along a path that is perpendicular to the wall at all times. The 1-D approach does not let the particle deflect up or down and therefore only accounts for the particle’s axial velocity. This is not representative of the particle’s actual velocity, which can also have a radial component. The 1-D approach encounters errors, specifically for small particles, in the approximation of impacting velocity.

Particle impacting velocity is not constant throughout the slug body. There are relatively higher impacting velocities towards the front of the of the slug body, and there are relatively lower impacting velocities towards the rear of the slug body. This is caused by the difference in stagnation length for the different particle locations relative to the wall. The slug flow model must account for this behavior. The stagnation length distribution approach splits the slug body, the primary source of erosion, into two components. The two components are the slug front and the slug tail. Figure 3.1.3 illustrates the approach.

Figure 3.1.3: Stagnation Length Distribution Components

The entire slug body is split into 500 segments or stagnation lengths. The slug front erosion contribution is accounted for by the first 499 increments in stagnation length. All the particles in the slug tail share a common stagnation length and impact velocity that is equal to the 500th stagnation length. This is done to ensure that an accurate portrayal is achieved of the impact velocity over the entire slug body, since different stagnation lengths produce different impact velocities.

The elbow and angle-head models share the same fundamental concepts. They both follow and make use of the assumptions stated earlier for slug flow. Both models apply the stagnation length concept, as well as the stagnation length distribution approach. There are only a few differences between the two. Three areas where the models differ include the definition of the slug front, the local velocity seen by the probe, and the fraction of sand particles used in the erosion calculation.

49 Elbow Model: The elbow model defines the slug front as one pipe diameter at the front of the slug body. One pipe diameter was chosen for the length because it is the maximum height of a vortex in the flow and is the maximum distance traveled by the slug before it impacts the wall. The elbow model defines the slug tail as the remainder of the slug body after the slug front. As mentioned earlier, the slug tail shares a single stagnation length and therefore a single impact velocity. Depending on the length of the entire slug body, the slug tail may or may not have as much of an impact on the overall erosion prediction as the slug front.

Angle-Head Model: The first difference seen between the two models is that the angle-head model defines the slug front as one probe diameter of the slug body, unlike the elbow model that defines it as one pipe diameter. The slug tail is defined as the remainder of the slug body after the slug front. The angle-head model also has the slug tail share a single stagnation length and impact velocity for each particle entrained in it.

The second difference observed between the models is the velocity at the probe.

The angle-head probe encounters a higher local velocity than the flat-head probe. This is caused by the angle-head probe protruding into the flow, where the flat-head probe is placed flush with the wall. Conservation of mass dictates that the reduction in area caused by the probe protruding into the flow will increase the local velocity near the probe.

Figure 3.1.4 is included to help explain this visually.

Figure 3.1.4: Reduction in Cross-Sectional Area Caused by the Protruding Probe

The probe reduces the cross-sectional area of the pipe creating higher local velocities that need to be accounted for by the angle-head model. Figure 3.1.5 shows a schematic of the variables necessary for the cross-sectional area calculation of the pipe with the intrusive probe in the flow path.

Figure 3.1.5: Variables for Area Calculation of Pipe at the Angle-Head Probe

Equation (3.1.5) is used to calculate the flow area around the angle-head probe,

and then the local velocity at the probe can be found by using Equation (3.1.6). Where A1

is the cross-sectional area of the pipe, A2 is the reduced cross-sectional area of pipe at the

51 intrusive probe, d probe is the probe diameter, h is the height to the center of the probe

face, hface is the height from the center to the outer edge of the probe face, V1 is the

average velocity in the pipe without obstructions, and V2 is the average local velocity at the intrusive probe.

A2 = A1 − (d probe × h + 0.5×π × h face × d probe ) (3.1.5)

A1 V2 = V1 (3.1.6) A2

The increased velocity at the angle-head probe is found by multiplying the ratio of the cross-sectional areas by the original velocity in the pipe. Note that the effect on velocity, resulting from the angle-head probe, is more significant for smaller diameter pipes. The effect is dramatically decreased as the pipe size increases.

The third and final difference between the two models is that the angle-head probe only experiences impingements from a fraction of the entrained sand particles in the slug body. The orientation of the probe only allows for a relatively small fraction of particles to impact the probe face. The elbow probe experiences impingements from a different percentage of particles. Figure 3.1.6 illustrates the fraction of particles in the slug body that actually impact the angle-head probe face.

Figure 3.1.6: Fraction of Particles that Impact Angle-Head Probe Face

52 1-D Slug Flow Model Results of Previous Boom Loop Experiments

The objective of this section is to present both the previous slug flow experimental results and their corresponding erosion predictions from the 1-D slug flow models in SPPS. Then there will be a discussion regarding the strengths and weaknesses of the SPPS models in comparison to the real-world measurements.

Elbow Model: The erosion results from both the elbow model and the elbow probe are presented in Table 3.1.1. The test conditions are found along with their corresponding erosion rates in units of [mil/lb].

53 Table 3.1.1: Calculated and Measured Results for the Elbow Probe

Measured SPPS Calculated Test Erosion V V Viscosity Sand Size 1‐D Elbow Number sg sl Rate of Probe Erosion Rate @ 45° [ft/s] [ft/s] [cP] [micron] [mil/lb] [mil/lb] 1 50 1.44 40 150 1.05E‐05 9.35E‐06 6 88 2.63 1 150 3.15E‐05 1.89E‐04 7 50 2.63 1 150 1.81E‐05 4.78E‐05 9 88 2.60 1 150 5.27E‐05 1.89E‐04 11 50 1.49 20 150 2.98E‐05 1.32E‐05 14 49 1.43 20 150 1.16E‐06 1.30E‐05 16 50 1.43 1 150 2.67E‐05 5.96E‐05 19 88 2.63 40 300 1.17E‐04 2.97E‐04 22 88 2.63 40 300 5.03E‐05 2.97E‐04 23 88 2.63 20 300 1.14E‐04 4.83E‐04 24 90 2.63 1 300 1.82E‐04 5.60E‐04 25 51 2.63 1 300 1.06E‐04 1.52E‐04 26 51 1.45 1 300 1.02E‐05 1.87E‐04 27 50 1.45 1 150 3.59E‐05 5.91E‐05 28 50 2.62 1 150 4.34E‐05 4.78E‐05 32 91 2.63 20 150 1.01E‐04 6.81E‐05 33 91 2.63 20 150 7.41E‐05 6.81E‐05 35 50 1.44 1 300 1.50E‐04 1.82E‐04 36 50 2.61 1 300 7.98E‐05 1.46E‐04 39 50 1.44 20 300 7.26E‐05 5.58E‐05 40 50 1.44 20 300 5.64E‐05 5.58E‐05 41 82 2.51 1 300 1.03E‐04 4.40E‐04 43 83 2.56 1 20 1.96E‐05 5.49E‐06 44 50 1.44 1 20 No Data 2.20E‐06 48 83 2.41 20 20 1.75E‐05 1.44E‐06 51 70 2.60 1 300 1.53E‐04 2.97E‐04 53 70 2.60 1 150 4.87E‐05 1.03E‐04 55 70 2.60 1 20 3.65E‐05 3.67E‐06 57 70 2.60 20 300 NM 1.97E‐04 59 70 2.74 40 300 NM 1.04E‐04 60 70 2.60 40 300 NM 1.03E‐04 63 70 2.64 1 300 1.27E‐04 2.97E‐04 65 50 1.43 1 300 5.02E‐05 1.83E‐04 66 50 2.62 1 300 1.30E‐04 1.46E‐04

54 The SPPS erosion predictions are plotted along with the measured erosion for the elbow and are shown in Graph 3.1.1. This graph shows the erosion of the large sand particles that have an average particle diameter of 300 µm. The penetration rate in units of [mil/lb] is represented on the vertical axis, and the test velocities are on the horizontal axis. Calculated erosion from SPPS is represented by the black columns, and the measured erosion from the Boom Loop is shown by the white columns. Viscosity is increasing from the left to right.

1‐D SPPS Comparisons to Previous Slug Flow Experiments Elbow Probe with Increasing Liquid Viscosity for 300 micron Particle Diameter 6.0E‐04

5.0E‐04

4.0E‐04 Calculated

Rate Elbow 3.0E‐04

[mil/lb] Measured Erosion Elbow 2.0E‐04

1.0E‐04 45 90

0.0E+00 Vsl 1.43 1.44 1.45 2.61 2.62 2.63 2.64 2.60 2.51 2.63 1.44 1.44 2.63 2.63 2.63 Vsg 50 50 51 50 50 51 70 70 82 90 50 50 88 88 88 µ 1 1 1 1 1 1 1 1 1 1 20 20 20 40 40 Experimental Conditions [ft/s] and [cP] Graph 3.1.1: Erosion Results for Elbow Probe with Large Particles

The elbow model is sufficient in capturing the proper erosion magnitudes and is also able to detect the overall erosion trends. This again validates the mechanistic nature of the slug flow models. The next graph represents the comparison between measured and calculated erosion for the 20 and 150 µm particles in the elbow. The black dotted

55 lines represent the change in sand size between each data set. Graph 3.1.2 is arranged with increasing viscosity from left to right. The smallest sand size begins from the left.

1‐D SPPS Comparisons to Previous Slug Flow Experiments Elbow Probe with Increasing Liquid Viscosity for 20 and 150 micron Particle Diameters 2.0E‐04

1.8E‐04

1.6E‐04 20 µm 150 µm 1.4E‐04

1.2E‐04 Calculated

Rate Elbow 1.0E‐04

[mil/lb] Measured

Erosion 8.0E‐05 Elbow 6.0E‐05

4.0E‐05 45

90 2.0E‐05

0.0E+00 Vsl 1.44 2.60 2.56 2.41 1.43 1.45 2.63 2.62 2.60 2.63 2.60 1.49 1.43 2.63 2.63 1.44 Vsg 50 70 83 83 50 50 50 50 70 88 88 50 49 91 91 50 µ 1 1 1 20 1 1 1 1 1 1 1 20 20 20 20 40 Experimental Conditions [ft/s] and [cP] Graph 3.1.2: Erosion Results for Elbow Probe with Small Particles

The elbow model overpredicts for the 150 µm particle size with 1 cP liquid, but underpredicts for increased viscosities with the same particle size. The elbow model underpredicts for the smallest 20 µm sand size. The elbow model captures neither erosion magnitude nor trend for the smallest particles. On average, the model overpredicts by a factor of 2.2 for the experimental conditions examined in this study.

Angle-Head Model: The erosion results from both the angle-head model and the angle-head probe are in Table 3.1.2. The test conditions are found along with their corresponding measured erosion.

56 Table 3.1.2: Calculated and Measured Results for the Angle-Head Probe

Measured SPPS Calculated Test Erosion V V Viscosity Sand Size 1‐D Angle‐Head Number sg sl Rate of Angle‐ Erosion Rate Head Probe [ft/s] [ft/s] [cP] [micron] [mil/lb] [mil/lb] 1 501.44401503.07E‐05 4.97E‐04 6 88 2.63 1 150 4.77E‐04 1.13E‐02 7 50 2.63 1 150 8.55E‐05 3.10E‐03 9 88 2.60 1 150 3.78E‐04 1.13E‐02 11 50 1.49 20 150 9.99E‐05 1.53E‐03 16 50 1.43 1 150 1.15E‐04 3.88E‐03 19 88 2.63 40 300 1.65E‐03 3.74E‐02 22 88 2.63 40 300 1.58E‐03 3.74E‐02 23 88 2.63 20 300 3.71E‐03 3.73E‐02 24 90 2.63 1 300 2.51E‐03 2.83E‐02 25 51 2.63 1 300 2.34E‐04 8.59E‐03 26 51 1.45 1 300 1.61E‐04 1.06E‐02 27 50 1.45 1 150 8.85E‐05 3.85E‐03 28 50 2.62 1 150 7.43E‐05 3.10E‐03 32 91 2.63 20 150 7.03E‐04 1.35E‐02 33 91 2.63 20 150 6.19E‐04 1.35E‐02 35 50 1.44 1 300 3.75E‐04 1.04E‐02 36 50 2.61 1 300 2.03E‐04 8.31E‐03 39 50 1.44 20 300 2.00E‐04 9.12E‐03 40 50 1.44 20 300 2.29E‐04 9.12E‐03 41 82 2.51 1 300 1.67E‐03 2.28E‐02 43 83 2.56 1 20 3.74E‐04 1.88E‐04 44 50 1.44 1 20 4.90E‐05 5.55E‐05 48 83 2.41 20 20 1.76E‐04 6.21E‐05 51 70 2.60 1 300 6.86E‐04 1.59E‐02 53 70 2.60 1 150 2.52E‐04 6.33E‐03 55 70 2.60 1 20 9.56E‐05 1.05E‐04 57 70 2.60 20 300 1.13E‐03 2.00E‐02 59 70 2.74 40 300 6.59E‐04 2.02E‐02 60 70 2.60 40 300 6.56E‐04 2.01E‐02 63 70 2.64 1 300 6.10E‐04 1.59E‐02 65 50 1.43 1 300 9.83E‐05 1.04E‐02 66 50 2.62 1 300 3.08E‐04 8.30E‐03

57 The results have been plotted on graphs so that the information can be better visualized. Graph 3.1.3 and Graph 3.1.4 illustrate the calculated erosion versus the measured erosion for the angle-head probe. The calculated erosion is shown in black columns, and the measured erosion is shown in white columns. The vertical axis represents the erosion rate and the horizontal axis shows the test conditions. The graph shows increasing viscosity from left to right.

1‐D SPPS Comparisons to Previous Slug Flow Experiments Angle‐Head Probe with Increasing Liquid Viscosity for 300 micron Particle Diameter 4.0E‐02 4.0E‐03

3.5E‐02 3.5E‐03

3.0E‐02 3.0E‐03

2.5E‐02 2.5E‐03 Scale Scale

Rate Rate

2.0E‐02 2.0E‐03 [mil/lb] [mil/lb] Erosion Erosion 1.5E‐02 1.5E‐03 Measured Calculated Calculated 1.0E‐02 1.0E‐03 Angle‐ Head 5.0E‐03 5.0E‐04 Measured Angle‐ 0.0E+00 0.0E+00 Head Vsl 1.43 1.45 2.61 2.63 2.60 2.64 2.51 2.63 1.44 2.60 2.63 2.60 2.74 2.63 2.63 Vsg 50 51 50 51 70 70 82 90 50 70 88 70 70 88 88 µ 1 1 1 1 1 1 1 1 20 20 20 40 40 40 40 Experimental Conditions [ft/s] and [cP] Graph 3.1.3: Erosion Results for Angle-Head Probe with Large Particles

Graph 3.1.3 displays results for 300 µm particles. The angle-head model does not capture the erosion magnitudes, but it does capture the erosion trends quite well for the larger particles as gas and liquid velocities vary. This is an indication that the model is successful at simulating all the physical mechanisms that help influence erosion on the angle-head probe. It can also be seen that the model over predicts for all of the test conditions shown here. The majority of the total conditions reported over predicted by roughly a factor of 26, but the erosion trends between the model and the data are fair.

58 The following graph arranges the data similar to the previous graph, but instead shows the calculated and measured erosion for the smaller 20 and 150 µm sand particles.

Graph 3.1.4 continues to show measured and 1-D calculated erosion rates. Viscosity is increasing from left to right. The black dotted line represents the change between sand particle sizes.

1‐D SPPS Comparisons to Previous Slug Flow Experiments Angle‐Head Probe with Increasing Liquid Viscosity for 20 and 150 micron Particle Diameters 1.4E‐02 1.4E‐03

1.2E‐02 1.2E‐03 20 µm 150 µm 1.0E‐02 1.0E‐03 Scale Scale

8.0E‐03 8.0E‐04 Rate Rate

[mil/lb] 6.0E‐03 6.0E‐04 [mil/lb] Erosion Erosion Measured Calculated 4.0E‐03 4.0E‐04 Calculated Angle‐ 2.0E‐03 2.0E‐04 Head Measured Angle‐ 0.0E+00 0.0E+00 Head Vsl 1.44 2.60 2.56 2.41 1.43 1.45 2.62 2.63 2.60 2.63 2.60 1.49 2.63 2.63 1.44 Vsg 50 70 83 83 50 50 50 50 70 88 88 50 91 91 50 µ 1 1 1 20 1 1 1 1 1 1 1 20 20 20 40 Experimental Conditions [ft/s] and [cP] Graph 3.1.4: Erosion Results for Angle-Head Probe with Small Particles

It is apparent that the angle-head model predictions for the smaller sand particles do not correspond to the measured rates in comparison to the larger particle predictions.

The 150 µm particle predictions are much higher than the 20 µm particle predictions. The model overpredicts for the 150 µm particles much like the 300 µm size. However, the model more accurately predicts the measured rates for the smallest particle size, the 20

µm silica flour. The elbow model does not consistently overpredict the way the angle- head model does, excluding the 20 µm particle erosion. The elbow model is mildly more sparatic when comparing trends from both sets of experimental results. The 1-D angle-

59 head model overpredicts by an average factor of 26 across all of the experimental conditions between the calculated and measured erosion rates.

The angle-head model has both strengths and weaknesses associated with it. The model is very capable of capturing erosion trends, and although it is a conservative model and overpredicts, the amount the model overpredicts is somewhat steady for all the varying superficial velocities. The model is mechanistic in nature which accounts for its ability to capture the erosion trends even if the magnitude is not exact. The 1-D particle tracking used to estimate the impacting velocity is relatively more sufficient for the smaller particle sizes, but does not correlate to the other sand size results. The weaknesses of the model include the magnitude of erosion predictions for the larger sand sizes because the discrepancy between the calculated and the actual erosion becomes larger as particle size increases. Overall the elbow model is the better performer of the two 1-D slug flow models in SPPS.

The elbow model has strengths and weaknesses associated with it like the angle- head model. The elbow model is mechanistic in nature like the angle-head model. The two models do not share all the same characterisics as each other when comparing their results. The elbow model overpredicts for most test conditions except the increased viscosity 150 µm erosion results. The magnitude of erosion was significantly improved from the model used in the previous version of SPPS. It still does not exactly predict erosion, but the erosion trends can be seen. This holds true except for the the predicted erosion for the smallest sand size, the 20 µm silica flour.

60 Experimental Facility

Description of Facility

The Boom Loop at The University of Tulsa’s North Campus was crucial to the completion of the experiments for this project. The key components of the flow loop itself are the two test sections, the mixing tank (or slurry tank), the collecting tank, the liquid side injection point, and the gas side injection point. Further detail of the flow loop is explained later, and a schematic of the flow loop is included in Figure 3.2.1.

ER Boom Probes

Gas & Test Sections Liquid Liquid Angle Head ER Probe (used 3 in diameter pipes or higher) Sand Gas Monitor

V22 V11 V12 V21 Gas & Flow Liquid meter Collecting Gas Slurry Tank Tank

V1 Stirrer

Pump1a) Pump1b)

1 2 3

Pump2a) Pump2b) Compressors

Figure 3.2.1: Experimental Schematic of the Boom Loop

The flow loop possesses the ability to either recirculate the liquid and entrained sand particles or provide a once-through method for the tests. The recirculation method is

61 better suited for high liquid rates, while the once-through method is better apt for lower liquid rates and gas only flows. For this particular study, the recirculation method was used due to the relatively high liquid rates involved in slug flow. The boom is also adjustable for any degree of inclination between horizontal and vertical. This work only focuses on horizontal flow and does not place emphasis on any other degree of inclination.

The Boom Loop is powered primarily by pneumatics. There are two independent

Ingersol Rand diesel compressors mounted on trailers that each yields a maximum gas flow rate of 400 standard cubic feet per minute [scfm]. The two compressors serve a single purpose. They are the solitary mode of providing the gas flow to the actual test section. The compressors are configured in parallel so their maximum flow rate is effectively doubled; as opposed to being configured in series where their pressure would be doubled. There is another compressor that is a Caterpillar Sullair that yields a maximum gas flow rate of 375 cubic feet per minute. The primary function of this compressor is to provide a sufficient amount of pressurized gas to drive the principal set of pumps for the flow loop.

The Boom Loop is comprised of four pumps. There are two sets of Ingersol Rand

ARO pneumatic diaphragm pumps in two different sizes. The smaller size pumps are 2” outlet non-metallic pumps. These pumps are powered by an electric compressor that provides a 100 standard cubic feet per minute flow rate. This compressor is located behind the Boom Loop’s shed and is not shown in the schematic in Figure 3.2.1. The larger size pumps are 3” outlet metallic pumps. These pumps are powered by the

Caterpillar Sullair diesel compressor mentioned earlier. The correct size of pump to use

62 for experimentation is dependent on application and desired flow conditions. The 3” pumps provide a higher liquid flow rate than that of the 2” pumps. For this study, the 3” pumps were used to reach the desired liquid flow rates that are involved in the promotion of slug flow.

The Boom Loop employs a mixing tank known as the slurry tank. The slurry tank has a maximum capacity of 230 gallons of liquid. The slurry tank houses both the liquid and sand particles that are injected in the flow. The desired sand concentration in the liquid is achieved by adding the proper proportion of sand to the liquid in the tank. The sand particles are suspended in the liquid through the use of a ½ horsepower electric motor with an attached mixing rod that is submerged in the slurry tank. This countermeasure discourages the sand from settling on the bottom of the tank, so the mixture remains homogeneous for the duration of the experiments. The slurry tank is key to the determination of the superficial liquid velocities for the system. The slurry tank makes it possible to average the liquid flow rate by measuring the depth of liquid in the tank along with the time associated with its discharge. The volume of the slurry tank is known and therefore depth increments can be translated into volume. The measured volume and elapsed time produce a volumetric liquid rate. The cross-sectional area of the pipe and the volumetric flow rate are then used in Equation (2.1.2) to determine the superficial liquid velocity of the system.

The Boom Loop employs another tank that is vital to its operation and ability to produce multi-phase flows. That tank is a phase separator that has three separate orifices in which flow can pass through. There is an inlet to the tank that receives all phases from the test section. There are two outlets on the tank located at the top and bottom. The tank

63 separates the phases by allowing the gas to escape from the top of the tank to the atmosphere, while the solid/liquid mixture remains in the bottom of the tank where it can be pumped back into the slurry tank or a separate holding tank. The collecting tank enables a recirculation method or a once-through method to be used.

The Boom Loop tower is where the test sections are located. The boom and two test sections are 18 meters long. The length is necessary to promote a fully-developed flow by the time the flow reaches the ER probes in the elbow and the angle-head probe in the straight section. There are several different sizes of test sections that can be outfitted on the boom, but only two can be situated on it at once. The arrangement of the boom can allow for experiments to be run on different size test sections simultaneously under the same flow rates (not velocities). There are 2”, 3”, and 4” test sections available to the system. This study focuses on the use of the 3” test section only. The arrangement of the boom can be seen in Figure 3.2.2 below.

Upper Test Section

Lower Test Section

Figure 3.2.2: Boom and Test Sections of Boom Loop

The test sections mounted on the boom have strategically located ER probes.

There are a combined total of three ER probes available for data acquisition in the test

64 section. There are two regions of the test section where probes can be located. The configuration of the two regions was chosen to best suit the study of erosion on the system. The flow travels through 18 meters of straight pipe before approaching an elbow.

As mentioned earlier, it is crucial to have this amount of uninterrupted length in the test section so the flow can be assumed fully developed. Two probes are located in the elbow, which monitor erosion. The first probe is oriented at 45 degrees and the second is oriented at 90 degrees. Figure 3.2.3 offers a diagram of the probe locations in the elbow geometry for the test section.

Flow

ER Probes 45

Figure 3.2.3: Probe Locations for the Elbow Geometry in the Test Section

The second region, where a single angle-head probe is located, is downstream of the elbow. The flow will pass through the first elbow and then through another elbow.

Before the flow exits the test section, it will pass through a length of straight section to the angle-head probe. The angle-head probe is placed at the far end of the straight length to promote fully-developed flow by the time the flow reaches it. The angle-head probe operates under the same guiding principals as the flat-head probe. The only difference being that the angle-head probe is used to measure erosion in straight pipe sections as

65 opposed to other geometries like the elbow. The angle-head probes are of significance to industry, particularly in the field where it is common that the only accessible region to place an erosion measuring device is in a straight section of pipe. Readings from the probes located in the elbow section and straight section can be correlated to obtain valid erosion measurements. Figure 3.2.4 visually describes the orientation of the angle-head probe in the straight test section.

Flow

Probe Face Figure 3.2.4: Angle-Head Probe Orientation

Operating Procedure

The Boom Loop is the largest experimental flow loop for erosion experiments available to the research centers at The University of Tulsa. The size and power involved in creating the desired flows in the loop require more than a single researcher to safely accomplish the experiments. Safety is of great concern and can be viewed as the reason for multiple researchers. Although, most of the tasks involved with operating the loop can be carried out by a single individual.

The startup procedure for the Boom Loop can vary depending on the type of test that is going to be executed. There would not be a need to prep the gas side of the flow

66 loop if a liquid only test was going to be run. This study delves into multi-phase flow, so there is always the need to start both the gas and liquid phases for an experiment. The first task to initiate the startup procedure for the loop is to close all valves associated with the injection of both the liquid and gas phases. The gas phase is always started first.

Begin by checking the fluids of the three compressors, including fuel, and fill all to the appropriate levels. Decide if the flow conditions require one or two of the large compressors for the gas flow rate to reach the proper superficial gas velocity in the test section. Start the diesel compressors to fuel the gas flow rate required to run the large 3”

ARO diaphragm pumps, and let them warm up while the rest of the flow loop is prepared for the test.

The slurry for the liquid phase is the next step to beginning the test. The amount of setup time revolves around the viscosity of the liquid for the test. If the experiment calls for a 1 cP liquid, then water is added to the slurry tank. If the test requires a viscosity greater than 1 cP, then CMC is added accordingly. CMC is mixed with water in a separate bucket with a mortar mixer drill. The mixing process of the CMC and water is much easier and efficient in small batches, because it produces fewer clumps and clots that keep the blend from becoming a homogeneous mixture with a constant viscosity. The viscous concoction is thoroughly mixed then placed in the slurry tank. This step is repeated until the desired amount is added to the slurry tank.

There are several key points involved with the use of CMC as a liquid thickener in this study. It was found that CMC does affect the density of the liquid, but the change is considered negligible in comparison. It was also found that CMC alters the surface tension of the liquid. Rodriquez (2008) measured the surface tension using a Du-Nouy

67 ring tensiometer. The results are presented in Table 3.2.1 where the viscosity of the liquid was increased using CMC and water. The surface tension measurement is provided for three viscosities. The surface tension is an important parameter that influences bubble and droplet formation in multi-phase flow. The corollary effect between the two is that as surface tension decreases bubble size will also decrease.

Table 3.2.1: Surface Tension Measurements for Experimental Liquid Viscosities

Viscosity Surface Tension [cp] [dyne/cm]

1 72

20 67.6

40 65.4

Rodriquez (2008) also provided a relationship for the amount of CMC needed to obtain a desired viscosity in water. The relationship was obtained empirically for the concentration of CMC and its resulting liquid viscosity. A graph of the CMC concentration versus liquid viscosity relationship is shown in Figure 3.2.5. The horizontal axis represents the concentration of CMC to the total volume of water. The concentration is a percentage found by dividing the weight of CMC in [lb] by the volume of water in

[gal]. The vertical axis is the ensuing liquid viscosity measured in [cP]. The best fit equation of the data is shown on the graph. This information can yield the amount of

CMC to add to water in order to achieve the desired liquid viscosity for a known volume of water during experimentation.

68 CMC Concentration vs. Liquid Viscosity from Experimental Measurements 120

100

80 y = 5.5716e0.9708x R2 = 0.9984 60 [cP] Viscosity

0 0 0.5 1 1.5 2 2.5 3 3.5 Concentration [lb/gal]

Figure 3.2.5: Concentration of CMC versus Liquid Viscosity

The slurry tank must be filled to the proper level with water or the water CMC mixture. The level of liquid required in the slurry tank varies with flow regime and flow conditions. An example of this is portrayed by the difference in fluid levels of the tank between annular flow and slug flow experimentation. Slug flow requires more liquid in the tank than annular flow because slug flow has a much greater liquid holdup than annular flow. In other words, more liquid is in the test section for slug flow which in turn reduces the amount of liquid in the slurry tank.

The compressors are warmed up and ready to be engaged and the slurry tank is mixed and filled accordingly. The next step is to begin the flow of each phase. The gas phase is always begun first. The inlet and outlet conditions of the gas phase are read from temperature and pressure gauges located near the entrance and exit of the flow loop. An electronic flow meter is located just upstream of the adjustment valve but downstream of

69 the compressors. The reading is taken from the flow meter and the superficial gas velocity is calculated through the use of compressibility relationships which are tabulated in a spreadsheet. The gas flow rate is adjusted by the valve until the proper gas velocity is met.

The liquid flow rate is begun after the gas flow rate has been established. It is important for the gas flow rate to be at operating conditions when the liquid flow starts.

This is due to the back pressure produced by the gas flow that affects the performance of the pneumatic diaphragm pumps in a non-linear manner. The liquid flow rate is calculated by determining the decrease of the liquid volume in the tank and the amount of time it took for that decrease to occur. The dimensions of the tank are known, so the internal volume per unit length can be found. Split times are taken for each unit length the liquid level has dropped. The split times are then averaged to increase the overall accuracy of the measurement. After the average time per unit length decrease in volume and the volume per unit length are known, the liquid flow rate can be calculated. With the liquid flow rate and internal pipe diameter of the test section both known; the superficial liquid velocity is attained. After the superficial liquid and gas velocities have been achieved, the data acquisition can commence.

Data Acquisition Procedure

Baseline measurements are recorded from the probes before sand is added to the flow. The beginning and end of each test is important to the ER probes. This is because of the temperature fluctuations in the test section. The fluctuations occur because the gas phase can reach temperatures up to 130° F, and the liquid temperature is close to ambient or 70° F. ER probes are highly dependent on temperature, since the electrical resistance

70 of a material is constantly changing with temperature. Consequently, the initial and final temperatures need to be the same to ensure that an accurate metal loss measurement is obtained. This can be accomplished by one of two methods. When the test is completed, either the liquid or gas phase can be shut off. Shutting off the gas phase and introducing fresh water from an auxiliary tank encourages the temperature to decrease since the gas phase is the primary source of heating without causing further erosion. Or vice versa, shutting off the liquid phase promotes the temperature to increase since the liquid is the key source of cooling the probes.

Once the base temperature is established for the ER probes, the sand can be added to the slurry tank to commence erosion on the test section. The essential amount of sand is then added to the liquid in the slurry tank to reach the desired concentration. For the purposes of this study, the sand concentration was immediately brought to the desired amount instead of gradually increasing it over time. The time was noted at the start of the sand injection so the total sand run time could be found at the end of the experiment. The

Cormon software features crosshairs that can be moved along the data on the output graph to mark time and metal loss. The initial crosshair is placed where the sand flow began. There is a final crosshair that is placed on the output graph when the sand flow stops. The metal loss values are shown for each crosshair in the lower right side of the panel. These are used to determine the difference of local metal losses at the separate points and in turn calculate the penetration rate to compare with SPPS.

To further understand the operations of correctly acquiring data, an illustration of temperature matching in placement of the crosshairs for the ER probe output is shown in

71 Figure 3.2.6 below. Notice the effect of temperature on the measured metal loss of the ER probe without erosion occurring in the test section.

Pure Effect of Temperature Without Erosion

Metal Loss

Temperature

Measured Metal Loss and Temperature for Each Crosshair

Figure 3.2.6: ER Probe Output Panel with Matching Final and Initial Temperatures

Figure 3.2.7 illustrates the incorrect placement of the final crosshair on the ER probe output panel compared to the correct placement. The improper placement does not account for temperature variations and assumes the metal loss at the end of the sand injection is correct. The metal loss readings from both crosshair placements still use the same total sand injection time to calculate the penetration rate. Therefore, the period of time associated with the un-corrected metal loss is the same for the temperature corrected metal loss. The duration of time that an experiment lasts is purely dependant on the erosion rates under the specific test conditions. A test with relatively high erosion rates takes less time to run than a test with relatively low erosion rates because the metal loss rate is much greater.

72 Beginning of Corrected Metal Loss Sand Injection

Difference of Metal Loss If Not Corrected for Temperature End of Sand Injection

Measured Metal Loss and Temperature for Each Crosshair

Figure 3.2.7: ER Probe Output Panel with Different Final Temperatures

The measured metal loss and temperature for the two scenarios are found in the bottom left corner of the panels in Figure 3.2.6 and Figure 3.2.7. The temperature corrected method produces a metal loss of 184 nanometers, while the uncorrected method produces a metal loss of 75 nanometers. The uncorrected method only accounts for approximately 41% of the metal loss. Temperature compensation is essential for ER probes when running experiments on the Boom Loop. The loop is located outside where the temperature fluctuates throughout the day and there is a relatively large temperature difference between the liquid and gas phases.

Once the sand injection has ceased and the metal loss has been determined, the only task left to accomplish in the experimental procedure is to flush or clean the entire system then shut it down. The procedure varies with sand size because the filtration methods involved with the different particle diameters. The relatively larger diameters of the 300 and 150 µm sand sizes allows the slurry to be gravity strained through a filter bag open to atmospheric conditions. Whereas the smaller 20 µm silica flour must be

73 forcefully pumped through filter cartridges due to the pressure drop associated with the small pores. The arrangement of the system requires the slurry to be pumped from the collecting tank when filtering the larger particles, and pumped from the slurry tank when filtering the smaller particles. Once the filtration is complete, both the separated sand and water are disposed of properly. Finally, flush the loop with fresh water to ensure the removal of all sand particles and debris for the subsequent experiment.

Experimental Results

The objective of this section is to present and explain the experimental results that were obtained using the Boom Loop and the aforementioned flow conditions and test procedure. All of the metal loss measurements were acquired while the pipe and boom of the Boom Loop were orientated horizontally. Table 3.3.1 includes the flow conditions and erosion rates for the elbow test section that include results from the probes at both

45° and 90° orientations. Table 3.3.2 includes the flow conditions and the erosion results from the intrusive angle-head probe in the straight test section. Note that test numbers 6,

15, and 26 where omitted from both of these tables. This is strictly for the fact that no sand was injected into the flow during these three experiments, and they were only used to get baseline measurements for each of the viscosities used throughout the entire matrix of test conditions. There are also cells that contain NA, an acronym for not applicable, because there was not any recorded result for the corresponding probe at that flow condition. This was due to either lack of data acquisition equipment or technical difficulty during the experiment.

Tables 3.3.1 and 3.3.2 are arranged chronologically by increasing test number, which is shown in the first column. Next the superficial gas and liquid velocities

74 respectively are shown in units of feet per second [ft/s]. The following column is for the experimental viscosity in units of centiPoise or [cP]. The next column is the sand particle size in units of micrometers or [µm]. The subsequent column yields the sand concentration, which relates the amount of sand to the amount of water in the flow as a percentage by weight and should not to be confused with a percentage by volume.

Finally, the measured erosion rate is presented for the corresponding probe and test condition.

The erosion rate values are presented as they were calculated from the metal loss measurements of the ER probes and the total sand throughput during each experiment.

The erosion rates are presented in [mil/lb]. This is clarified by thousandths of an inch of material thickness loss [mil] per pound of the total amount of sand injected into the test sections [lb] for the duration of the test.

75 Table 3.3.1: Experimental Conditions and Erosion Rates for the Elbow Probes

Erosion Erosion Test Sand Sand Con- V V Viscosity Rate of Rate of Number sg sl Size centration Probe @ 45° Probe @ 90° [ft/s] [ft/s] [cP] [micron] [% weight] [mil/lb] [mil/lb] 1 90 2.63 1 300 0.5 2.44E-05 1.10E-04 2 90 2.63 1 300 0.5 NA 1.19E-04 3 51 2.63 1 300 0.5 NA 1.10E-04 4 88 2.63 1 300 0.5 2.49E-04 4.75E-05 5 150 2.40 1 300 0.5 5.05E-04 1.39E-04 7 90 2.74 1 20 0.5 6.90E-05 NA 8 50 1.47 1 20 0.5 5.24E-05 3.49E-05 9 80 1.60 1 20 0.5 3.35E-05 1.87E-05 10 100 1.50 1 20 0.5 4.62E-05 2.95E-05 11 50 2.62 1 20 1.0 7.49E-06 4.63E-06 12 150 2.62 1 20 1.0 4.52E-05 9.80E-06 13 150 1.61 1 20 1.0 9.99E-05 1.68E-05 14 125 1.63 1 20 1.0 8.21E-05 7.88E-06 16 50 1.51 10 20 1.0 7.44E-06 8.33E-06 17 100 1.48 10 20 1.0 2.93E-05 1.36E-05 18 50 2.45 10 20 1.0 3.60E-06 2.84E-06 19 100 2.40 10 20 1.0 1.67E-05 4.01E-06 20 75 1.49 10 20 1.0 1.04E-05 4.67E-06 21 75 2.41 10 20 1.0 2.22E-05 3.55E-06 22 125 2.42 10 20 1.0 3.64E-05 1.34E-05 23 150 2.47 10 20 1.0 5.80E-05 1.52E-06 24 125 1.50 10 20 1.0 7.49E-05 6.78E-06 25 150 1.40 10 20 1.0 1.55E-04 7.84E-06 27 50 1.51 40 20 1.0 1.16E-05 4.25E-06 28 100 1.52 40 20 1.0 4.91E-05 1.19E-05 29 50 2.57 40 20 1.0 1.32E-05 4.30E-06 30 100 2.59 40 20 1.0 1.01E-05 7.16E-06 31 150 2.35 40 20 1.0 5.74E-05 2.37E-05 32 150 1.44 40 20 1.0 7.92E-05 3.62E-05 33 75 1.58 40 20 1.0 1.86E-05 1.20E-05 34 125 1.47 40 20 1.0 1.00E-04 1.69E-05 35 75 2.40 40 20 1.0 6.12E-06 3.31E-06 36 125 2.36 40 20 1.0 2.36E-05 1.05E-05 37 50 2.54 10 300 0.5 6.69E-05 8.43E-06 38 100 2.40 10 300 0.5 2.30E-04 5.28E-05 39 150 2.55 10 300 0.5 2.53E-04 3.61E-05 40 50 2.59 40 300 0.5 2.40E-05 8.26E-06 41 100 2.64 40 300 0.5 4.72E-05 3.71E-06 42 150 2.52 40 300 0.5 5.86E-04 2.21E-05 43 75 2.62 1 20 1.0 1.63E-05 8.71E-06 44 125 2.11 1 20 1.0 7.08E-05 1.78E-06

76 Table 3.3.2: Experimental Conditions and Erosion Rates for the Angle-Head Probe

Erosion Test Sand Con- Rate of V V Viscosity Sand Size Number sg sl centration Angle-Head Probe [ft/s] [ft/s] [cP] [micron] [% weight] [mil/lb] 1 90 2.63 1 300 0.5 NA 2 90 2.63 1 300 0.5 1.83E-03 3 51 2.63 1 300 0.5 7.24E-04 4 88 2.63 1 300 0.5 9.40E-04 5 150 2.40 1 300 0.5 8.38E-03 790.42.741200.57.26E-04 8 50 1.47 1 20 0.5 7.13E-05 9 80 1.60 1 20 0.5 3.33E-04 10 100 1.50 1 20 0.5 1.24E-03 11 50 2.62 1 20 1.0 3.69E-05 12 150 2.62 1 20 1.0 2.19E-03 13 150 1.61 1 20 1.0 2.30E-03 14 125 1.63 1 20 1.0 1.49E-03 16 50 1.51 10 20 1.0 4.36E-05 17 100 1.48 10 20 1.0 7.30E-04 18 50 2.45 10 20 1.0 1.99E-05 19 100 2.40 10 20 1.0 7.06E-04 20 75 1.49 10 20 1.0 2.43E-04 21 75 2.41 10 20 1.0 2.00E-04 22 125 2.42 10 20 1.0 1.29E-03 23 150 2.47 10 20 1.0 1.93E-03 24 125 1.50 10 20 1.0 2.00E-03 25 150 1.40 10 20 1.0 2.32E-03 27 50 1.51 40 20 1.0 1.44E-05 28 100 1.52 40 20 1.0 4.06E-04 29 50 2.57 40 20 1.0 8.74E-06 30 100 2.59 40 20 1.0 1.67E-04 31 150 2.35 40 20 1.0 1.43E-03 32 150 1.44 40 20 1.0 1.67E-03 33 75 1.58 40 20 1.0 1.65E-04 34 125 1.47 40 20 1.0 1.42E-03 35 75 2.40 40 20 1.0 1.39E-04 36 125 2.36 40 20 1.0 9.07E-04 37 50 2.54 10 300 0.5 3.08E-04 38 100 2.40 10 300 0.5 1.71E-03 39 150 2.55 10 300 0.5 3.93E-03 40 50 2.59 40 300 0.5 1.62E-04 41 100 2.64 40 300 0.5 1.22E-03 42 150 2.52 40 300 0.5 3.42E-03 43 75 2.62 1 20 1.0 9.19E-05 44 125 2.11 1 20 1.0 1.59E-03

77 The experimental results tables have been presented to numerically reveal the erosion phenomena occurring; however, the results can further be explained and visualized graphically. The following graphs are presented for all measured erosion rates with the first data set being dedicated to 20 μm particle erosion followed by the 300 μm particle erosion data set. Within each set, the straight section and elbow section have been separated to increase the comprehension of each graph due to the difference of magnitude between the erosion rates.

The angle-head probe measurements from the straight pipe section are shown first while the flat-head probe measurements in the elbow section follow. The straight section graphs represent the measured angle-head probe erosion rate with black columns, whereas the elbow section graphs represent erosion rates of the probe at 45° with black columns and erosion rates of the probe at 90° with white columns. This particular scheme for each graph and probe will continue throughout the experimental results section unless otherwise stated.

The following graphs include the erosion rate in [mil/lb] on the vertical axis and the flow conditions on the horizontal axis namely the superficial liquid and gas velocities and the liquid viscosity in a multitude of combinations. When applicable, the superficial liquid and gas velocities and liquid viscosity are contained on the horizontal axis in [ft/s] and [cP] correspondingly. The graphs are arranged by increasing superficial gas velocity within each set of superficial liquid velocities. The 20 μm sand data contains two sets of superficial liquid velocities, whereas the 300 μm sand data only contains one superficial liquid velocity. Graph 3.3.1 and Graph 3.3.2 show the erosion rate results gathered from

78 the Boom Loop using a 1 cP viscosity liquid and 20 μm diameter particles for the straight section and elbow section, respectively.

2.5E‐03

2.0E‐03 Angle‐Head Probe

1.5E‐03 Rate

[mil/lb]

Erosion 1.0E‐03

5.0E‐04

0.0E+00 Vsl 1.47 1.60 1.50 1.63 1.61 2.62 2.62 2.74 2.11 2.62 Vsg 50 80 100 125 150 50 75 90 125 150 Superficial Velocities [ft/s]

Graph 3.3.1: Measured Angle-Head Erosion Rates for 1 cP Liquid Viscosity and 20 μm Particle Diameter

79 1.0E‐04

8.0E‐05 Probe @ 45°

Probe @ 90°

6.0E‐05

Rate

90 [mil/lb]

Erosion 4.0E‐05

2.0E‐05

0.0E+00 Vsl 1.47 1.60 1.50 1.63 1.61 2.62 2.62 2.74 2.11 2.62 Vsg 50 80 100 125 150 50 75 90 125 150 Superficial Velocities [ft/s]

Graph 3.3.2: Measured Elbow Section Erosion Rates for 1 cP Liquid Viscosity and 20 μm Particle Diameter

Graph 3.3.3 and Graph 3.3.4 represent their respective section experimental erosion rate results like the previous graphs, except the liquid viscosity has increased to

10 cP and the superficial velocities slightly vary from before. The test conditions contained within the graphs continue to use 20 μm diameter particles to yield the erosion results.

80 2.5E‐03

2.0E‐03 Angle‐Head Probe

1.5E‐03 Rate

[mil/lb]

Erosion 1.0E‐03

5.0E‐04

0.0E+00 Vsl 1.51 1.49 1.48 1.50 1.40 2.45 2.41 2.40 2.42 2.47 Vsg 50 75 100 125 150 50 75 100 125 150 Superficial Velocities [ft/s]

Graph 3.3.3: Measured Angle-Head Erosion Rates for 10 cP Liquid Viscosity and 20 μm Particle Diameter

1.6E‐04

Probe @ 45° 1.2E‐04 Probe @ 90°

Rate

8.0E‐05 45 90 [mil/lb] Erosion

4.0E‐05

0.0E+00 Vsl 1.51 1.49 1.48 1.50 1.40 2.45 2.41 2.40 2.42 2.47 Vsg 50 75 100 125 150 50 75 100 125 150 Superficial Velocities [ft/s]

Graph 3.3.4: Measured Elbow Section Erosion Rates for 10 cP Liquid Viscosity and 20 μm Particle Diameter

81 Graph 3.3.5 and Graph 3.3.6 continue to illustrate the experimental erosion results from each test section further increasing the liquid viscosity to 40 cP. 40 cP is the highest liquid viscosity examined during this study. The graphs continue to represent the results of the 20 μm diameter particle erosion.

1.8E‐03

1.5E‐03 Angle‐Head Probe

1.2E‐03 Rate

9.0E‐04 [mil/lb] Erosion

6.0E‐04

3.0E‐04

0.0E+00 Vsl 1.51 1.58 1.52 1.47 1.44 2.57 2.40 2.59 2.36 2.35 Vsg 50 75 100 125 150 50 75 100 125 150 Superficial Velocities [ft/s]

Graph 3.3.5: Measured Angle-Head Erosion Rates for 40 cP Liquid Viscosity and 20 μm Particle Diameter

82 1.0E‐04

8.0E‐05 Probe @ 45°

Probe @ 90°

6.0E‐05

Rate

90 [mil/lb]

Erosion 4.0E‐05

2.0E‐05

0.0E+00 Vsl 1.51 1.58 1.52 1.47 1.44 2.57 2.40 2.59 2.36 2.35 Vsg 50 75 100 125 150 50 75 100 125 150 Superficial Velocities [ft/s]

Graph 3.3.6: Measured Elbow Section Erosion Rates for 40 cP Liquid Viscosity and 20 μm Particle Diameter

Finally, the 300 μm diameter particle erosion rates collected from experimentation are offered in Graph 3.3.7 and Graph 3.3.8. These differ from the previous graphs, because there was a smaller amount of experimental test conditions involving the 300 μm diameter particles, and all the results fit on a single graph. The only difference is that now there are multiple liquid viscosities included on a single graph.

Note that a third flow condition has been included on the horizontal axis in addition to the superficial liquid and gas velocities, and that flow condition is the liquid viscosity in units of [cP]. The liquid viscosity is increasing from left to right, beginning with 1 cP on the left, 10 cP in the center, and 40 cP on the right. Vertical dotted lines have been included in the graphs to help distinguish between the different viscosities.

83 1.0E‐02

8.0E‐03 Angle‐Head Probe

6.0E‐03 Rate

[mil/lb]

Erosion 4.0E‐03

2.0E‐03

0.0E+00 Vsl 2.63 2.63 2.40 2.54 2.40 2.55 2.59 2.64 2.52 Vsg 51 88 150 50 100 150 50 100 150 μ 1 1 1 10 10 10 40 40 40 Experimental Conditions [ft/s] and [cP]

Graph 3.3.7: Measured Angle-Head Erosion Rates for Increasing Liquid Viscosity and 300 μm Particle Diameter

6.0E‐04

5.0E‐04 Probe @ 45°

4.0E‐04 Probe @ 90° Rate

3.0E‐04 45

[mil/lb] 90 Erosion 2.0E‐04

1.0E‐04

0.0E+00 Vsl 2.63 2.63 2.40 2.54 2.40 2.55 2.59 2.64 2.52 Vsg 51 88 150 50 100 150 50 100 150 μ 1 1 1 10 10 10 40 40 40 Experimental Conditions [ft/s] and [cP]

Graph 3.3.8: Measured Elbow Section Erosion Rates for Increasing Liquid Viscosity and 300 μm Particle Diameter

84 The effects attributed to all the different flow conditions will be further analyzed and described in more detail in subsequent sections, but a distinct generalization can already be made from the experimental results. That distinction is that the angle-head probe in the straight section always measures more metal loss or erosion compared to the flat-head probes in the elbow. It will later be discussed that the total amount of metal loss for each probe has a direct correlation to the uncertainty of its measurement and therefore has lead to greater emphasis being placed on the angle-head probe data.

When comparing the data in the ensuing sections, the measured superficial liquid and gas velocities vary slightly from one another throughout the test matrix. In various graphs, the erosion results are evaluated using nominal superficial velocities. The nominal flow conditions are the conditions for which the test was originally intended to be conducted from the initial matrix in the planning phase of this work. Due to the inability to duplicate exact flow conditions time and again, Table 3.3.3 and Table 3.3.4 have been included to increase clarity and provide a reference between the actual and nominal superficial liquid and gas velocities. Table 3.3.3 is the test matrix for the 20 μm sand particles, and Table 3.3.4 is the test matrix for the 300 μm sand particles. The desired flow conditions are listed with the liquid viscosity as the centered header for each block, the superficial liquid velocity is on the vertical axis, and the superficial gas velocity is on the horizontal axis. The value inside each box represents the test number performed at the corresponding nominal conditions shown in the test matrices. These tables can be cross-referenced with Tables 3.3.1 and 3.3.2 to determine the actual superficial velocities of each test.

85 Table 3.3.3: Test Matrix for 20 μm Sand Particles with Corresponding Test Number

Test Matrix For 20 Micron Sand

1 cP

1.58 9 101413

Vsl [ft/s]

2.5 11 43 7 44 12

50 75 100 125 150

Vsg [ft/s]

10 cP

1.51620172425

Vsl [ft/s]

2.51821192223

50 75 100 125 150

Vsg [ft/s]

40 cP

1.52733283432

Vsl [ft/s]

2.52935303631

50 75 100 125 150

Vsg [ft/s]

86 Table 3.3.4: Test Matrix for 300 μm Sand Particles with Corresponding Test Number

Test Matrix For 300 Micron Sand

1 cP

Vsl 2.5 3 1, 2, & 45 [ft/s]

50 100 150

Vsg [ft/s]

10 cP

Vsl 2.5 37 38 39 [ft/s]

50 100 150

Vsg [ft/s]

40 cP

Vsl 2.5 40 41 42 [ft/s]

50 100 150

Vsg [ft/s]

Effects of Superficial Velocities

The superficial liquid and gas velocities used in this study produce patterns exclusively in the slug and annular flow regimes. Slug flow was the premier target flow pattern for the experimentation although the transition from slug to annular was included for comprehensiveness. This section explores the superficial liquid and gas velocities used to gather the experimental data of the study.

87 Figure 3.3.1, Figure 3.3.2, and Figure 3.3.3 illustrate the experimental conditions on flow regime maps. The transition lines of the flow maps were generated using

FLOPATN software developed by Pereyra and Torres (2005). The important details of the flow maps include the superficial liquid velocity on the vertical axis and the superficial gas velocity on the horizontal axis, where they both have units of feet per second and are on logarithmic scales. The lines on the graph are the transition lines between the different flow regimes. The black dots are the experimental flow conditions placed on their corresponding superficial liquid and gas velocities. Several of the flow conditions were repeated with almost identical flow conditions.

Slug Regime Annular Regime

1 [ft/s] Superficial Liquid Velocity

Experimental Flow Stratified Conditions Regime

0.1 10 100 1000 Superficial Gas Velocity [ft/s]

Figure 3.3.1: Flow Pattern Map of Experimental Conditions for Horizontal Flow in 3” Pipe with Liquid Viscosity of 1 cP

Figure 3.3.1 shows experimental conditions with liquid viscosities of 1 cP. Notice that the transition between the slug flow regime and the annular flow regime is well covered by experimentation. The transition lines on the flow pattern maps are not

88 absolute and should not be taken so. They are tools that aid in flow pattern transition estimation. Proper engineering judgment should always be used if actual in-pipe flow observation is not possible. It is possible for different piping systems to produce varying results on the flow pattern map. There were two clear pipe sections on the experimental apparatus that allowed visual inspection of the flow. It was observed during experimentation that as the superficial gas velocity increased there were fewer liquid slugs present, but they did exist and were visible inside the clear test sections. All of the experimental flow conditions exhibited slug flow behavior to varying degrees, yet many appear in the annular flow regime on the flow pattern maps.

The next flow map seen in Figure 3.3.2 covers the experimental liquid viscosity of 10 cP, which is ten times more viscous than the 1 cP liquid shown on the flow map in

Figure 3.3.1. pqy 10

Slug Regime Annular Regime

1 [ft/s]

Superficial LiquidVelocity Stratified Experimental Flow Regime Conditions

0.1 10 100 1000 Superficial Gas Velocity [ft/s]

Figure 3.3.2: Flow Pattern Map of Experimental Conditions for Horizontal Flow in 3” Pipe with Liquid Viscosity of 10 cP

89 It is apparent that the transition lines have moved and are no longer the same shape or size. This is caused by the change in viscosity of the liquid and its consequent effect on multi-phase flow mechanisms. The liquid viscosity plays an important role in determining the flow pattern observed in fluid flow. The increase in viscosity from 1 cP to 10 cP has shifted the slug to annular transition towards the right of the map. This signifies that slug flow can be maintained at relatively higher superficial gas velocities than previously for 1 cP liquid viscosity. Notice that slightly fewer tests have been performed with this viscosity so the transition from slug to annular flow contains a smaller quantity of test conditions. Figure 3.3.3 shows the third and final liquid viscosity of 40 cP. pqy 10

Slug Regime Annular Regime

1 [ft/s] Superficial Liquid Velocity Liquid Superficial

Experimental Flow Conditions

0.1 10 100 1000 Superficial Gas Velocity [ft/s]

Figure 3.3.3: Flow Pattern Map of Experimental Conditions for Horizontal Flow in 3” Pipe with Liquid Viscosity of 40 cP

The 40 cP liquid viscosity is the highest used for this study and is 40 times greater than the viscosity of water at standard conditions. Notice that the transition lines have

90 shifted towards the right again, and the stratified transition no longer exists on this particular scale of the axes. The experimental flow conditions traversing the slug to annular flow transition are even less apparent at this viscosity. It can be concluded that increasing the liquid viscosity effectively shifts the slug to annular transition to higher superficial gas velocities while also affecting the gas to liquid velocity ratios that make up the transition line.

The effects of superficial gas and liquid velocities have been explained in terms of consequences toward observed flow pattern, and before continuing it is essential to note that flow pattern absolutely influences erosion rate and is the primary motive for E/CRC developing regime dependant models within SPPS for predicting erosion rates in the separate flow regimes. Next, the direct effects of superficial gas and liquid velocities on erosion rates will be examined strictly for slug flow.

Throughout the measured experimental erosion rate analysis the effects caused by different flow conditions will be visited and only typical results will be shown for the topics that require emphasis. First, the effects of superficial liquid velocity will analyzed from the experimental results. Graph 3.3.9 and Graph 3.3.10 show the first examples of the effect that liquid velocity has on the measured erosions rates in the slug flow regime.

Each pair of columns on the graphs contain the measured erosion rate as the superficial liquid velocity is increased from approximately 1.5 ft/s to 2.5 ft/s for each of the nominal superficial gas velocities ranging from 50 ft/s to 150 ft/s in increments of 25 ft/s. Note that the erosion rate for the probe at 90° is not on the graph for Vsg = 90 ft/s and Vsl = 2.74 ft/s, because the probe was not available during the test. Also, a graph for the effects of

91 superficial liquid velocity was not included for the 300 μm particles because the test matrix only covered one liquid velocity for that particle diameter.

Measured Experimental Erosion Rates 1 cP Liquid Viscosity and 20 μm Particle Diameter

2.5E‐03

2.0E‐03 Angle‐Head Probe

1.5E‐03 Rate

[mil/lb]

Erosion 1.0E‐03

5.0E‐04

0.0E+00 Vsl 1.47 2.62 1.60 2.62 1.50 2.74 1.63 2.11 1.61 2.62 Vsg 50 50 80 75 100 90 125 125 150 150 Superficial Velocities [ft/s] Graph 3.3.9: Effects of Superficial Liquid Velocity on Erosion Rates for Angle-Head Probe with Increasing Vsg

92 Measured Experimental Erosion Rates 1 cP Liquid Viscosity and 20 μm Particle Diameter

1.0E‐04

Probe @ 45° 8.0E‐05 Probe @ 90°

6.0E‐05

45 Rate

[mil/lb] 4.0E‐05 Erosion

2.0E‐05

0.0E+00 Vsl 1.47 2.62 1.60 2.62 1.50 2.74 1.63 2.11 1.61 2.62 Vsg 50 50 80 75 100 90 125 125 150 150 Superficial Velocities [ft/s] Graph 3.3.10: Effects of Superficial Liquid Velocity on Erosion Rates for Elbow Section with Increasing Vsg

It is seen from both of the graphs that increasing the superficial liquid velocity decreases the amount of erosion measured by each of the ER probes in most of the cases.

This can be explained by the developed E/CRC erosion concepts, but it will be discussed in detail in a later section. The angle-head probe in the straight section is affected the most by liquid velocity followed by the probe at 45° then the probe at 90° in the elbow.

The angle-head data shows a much more linear trend than the elbow data. This is caused by the area of maximum erosion shifting in the elbow section over the variety of superficial velocities tested, whereas the intrusive angle-head probe measures the area of maximum erosion inherently from its geometry and placement.

Next, the effects of superficial gas velocity will be examined for the experimental results. Graphs 3.3.11, 3.3.12, and 3.3.13 show the erosion rate trends for increasing superficial gas velocity. Graphs 3.3.11 and 3.3.12 were made from the measured erosion

93 rates using 40 cP liquid viscosity, 20 μm sand, and increasing the superficial gas velocity while the nominal superficial liquid velocity is held constant at 2.5 ft/s. Graph 3.3.11 represents the straight section probe, and Graph 3.3.12 contains the data from the elbow section.

Measured Experimental Erosion Rates 40 cP Liquid Viscosity, 20 μm Particle Diameter, and Increasing Vsg

1.6E‐03

1.4E‐03

1.2E‐03 Angle‐Head Probe 1.0E‐03 Rate

8.0E‐04

[mil/lb] 6.0E‐04 Erosion

4.0E‐04

2.0E‐04

0.0E+00 Vsl 2.57 2.40 2.59 2.36 2.35 Vsg 50 75 100 125 150 Superficial Velocities [ft/s] Graph 3.3.11: Effects of Superficial Gas Velocity on Erosion Rates for Angle-Head Probe with Constant Nominal Vsl = 2.5 ft/s and Increasing Vsg

94 Measured Experimental Erosion Rates 40 cP Liquid Viscosity, 20 μm Particle Diameter, and Increasing Vsg

7.0E‐05

6.0E‐05 Probe @ 45°

Probe @ 90° 5.0E‐05

4.0E‐05 45 Rate

[mil/lb] 3.0E‐05 Erosion

2.0E‐05

1.0E‐05

0.0E+00 Vsl 2.57 2.40 2.59 2.36 2.35 Vsg 50 75 100 125 150 Superficial Velocities [ft/s] Graph 3.3.12: Effects of Superficial Gas Velocity on Erosion Rates for Elbow Section with Constant Nominal Vsl = 2.5 ft/s and Increasing Vsg

Graph 3.3.13 is presented differently for the 300 μm sand, because the data can fit on a single graph. The elbow erosion rates are offered on the primary vertical axis in grey colums for the probe at 45° and white columns for the probe at 90°. The angle-head rates are on the secondary vertical axis in the black columns. There is an order of magnitude of

10 between the scales of each axis.

95 Measured Experimental Erosion Rates 10 cP Liquid Viscosity, 300 μm Particle Diameter, and Increasing Vsg

4.0E‐04 4.00E‐03

Probe @ 45°

3.0E‐04 3.00E‐03 45

Probe @ 90° 2.0E‐04 2.00E‐03 Rate

[mil/lb] 90 Erosion

1.0E‐04 1.00E‐03 Angle‐Head Probe

0.0E+00 0.00E+00 Vsl 2.54 2.40 2.55 Vsg 50 100 150 Superficial Velocities [ft/s] Graph 3.3.13: Effects of Superficial Gas Velocity on Erosion Rates for Elbow and Angle-Head Probe with Constant Nominal Vsl = 2.5 ft/s and Increasing Vsg

The data from these graphs demonstrate that as the superficial gas velocity increases and all other flow conditions are kept constant the measured erosion rate will increase as well. This can be explained similarly to the effect of superficial liquid velocity on erosion rate except with an adverse effect. The cause for this effect will be discussed in a later section.

To summarize the effects of superficial liquid and gas velocities: increasing liquid velocity decreases erosion and increasing gas velocity increases erosion. Gas velocity has a stronger effect on the measured erosion rate in comparison to the liquid velocity. In other words, gas velocity variations have a tendency to alter the magnitude of erosion to a greater extent than liquid velocity variations.

96 Effects of Viscosity

Now the effects of liquid viscosity will be reviewed. To begin, Graph 3.3.14 and

Graph 3.3.15 present the effects of liquid viscosity on erosion rate for 300 μm sand particles while holding the nominal superficial liquid velocity constant at 2.5 ft/s. Each graph contains three sets of data within it. Each set retains roughly the same superficial gas velocities, but each ensuing column increases the liquid viscosity from 1 cP to 10 cP and then to 40 cP.

Measured Experimental Erosion Rates Increasing Liquid Viscosity and 300 μm Particle Diameter

2.5E‐03

2.0E‐03

Angle‐Head Probe 1.5E‐03 Rate

[mil/lb] 1.0E‐03 Erosion

5.0E‐04

0.0E+00 Vsl 2.74 2.40 2.59 2.11 2.42 2.36 2.62 2.47 2.35 Vsg 90 100 100 125 125 125 150 150 150 μ 1 10 40 1 10 40 1 10 40 Experimental Conditions [ft/s] and [cP] Graph 3.3.14: Effects of Viscosity on Erosion Rates for Angle-Head Probe with Constant Nominal Vsl and Vsg

97 Measured Experimental Erosion Rates Increasing Liquid Viscosity and 300 μm Particle Diameter

8.0E‐05

Probe @ 45° 6.0E‐05 Probe @ 90°

4.0E‐05 45 90 Rate

[mil/lb] Erosion 2.0E‐05

0.0E+00 Vsl 2.74 2.40 2.59 2.11 2.42 2.36 2.62 2.47 2.35 Vsg 90 100 100 125 125 125 150 150 150 μ 1 10 40 1 10 40 1 10 40 Experimental Conditions [ft/s] and [cP] Graph 3.3.15: Effects of Viscosity on Erosion Rates for Elbow Section with Constant Nominal Vsl and Vsg

The angle-head data from Graph 3.3.14 yields a non-linear decrease in erosion rate over all three gas velocities for each viscosity. The elbow data from Graph 3.3.15 however, has features that are not seen in the angle-head results. Some of the elbow test cases present higher magnitudes of erosion occurring for the median liquid viscosity of

10 cP as compared to the lower liquid viscosity of 1 cP even while all other flow conditions are held steady. Rodriquez (2008) experienced the same oddity during experimentation, except the investigational median liquid viscosity was that of 20 cP instead of the 10 cP viscosity that was used for this study. This can be attributed to the area of maximum erosion migrating throughout the elbow because of its flow dependant characteristics that are significantly affected by liquid viscosity.

Generally, the results from the graphs confirm that liquid viscosity has a negative effect on measured erosion rate magnitudes. Increasing the liquid viscosity decreases the erosion rate with all other flow conditions approximately constant. This is analgous to the

98 effects of superficial liquid velocity in the fact that as their magnitudes increase the measured erosion decreases.

Combined Effects of Superficial Velocities and Viscosity

The effects of superficial velocities and liquid viscosity have been discussed and now the combination of all the parameters can be presented. Graph 3.3.16 and Graph

3.3.17 show the measured erosion rates for each test section using 20 μm sand particles and a constant superficial gas velocity of 150 ft/s. The liquid velocity is increased nominally from 1.5 ft/s to 2.5 ft/s for each set of liquid viscosities to represent the combined effects of superficial liquid velocity and viscosity.

Measured Experimental Erosion Rates Increasing Liquid Viscosity, 20 μm Particle Diameter, and Vsg = 150 ft/s

2.5E‐03

2.0E‐03 Angle‐Head Probe

1.5E‐03 Rate

[mil/lb]

Erosion 1.0E‐03

5.0E‐04

0.0E+00 Vsl 1.61 2.62 1.40 2.47 1.44 2.35 μ 1 1 10 10 40 40 Experimental Conditions [ft/s] and [cP] Graph 3.3.16: Combined Effects of Superficial Liquid Velocity and Viscosity on Erosion Rates for Angle-Head Probe with Constant Nominal Vsg = 150 ft/s

99 Measured Experimental Erosion Rates Increasing Liquid Viscosity, 20 μm Particle Diameter, and Vsg = 150 ft/s

1.6E‐04

Probe @ 45°

1.2E‐04 Probe @ 90°

45 Rate 8.0E‐05 90 [mil/lb] Erosion

4.0E‐05

0.0E+00 Vsl 1.61 2.62 1.40 2.47 1.44 2.35 μ 1 1 10 10 40 40 Experimental Conditions [ft/s] and [cP] Graph 3.3.17: Combined Effects of Superficial Liquid Velocity and Viscosity on Erosion Rates for Elbow Section with Constant Nominal Vsg = 150 ft/s

The graphs for each test section share two common properties. They are a decrease in erosion rate for an increased liquid velocity and some of the increased liquid viscosities yield a greater erosion rate than the lower viscoities. The angle-head probe and probe at 45° in the elbow have larger erosion rates for 10 cP liquids, but the probe at 90° has higher erosion rates using a 40 cP liquid. The probe at 90° has almost twice the measured erosion rate in 40 cP than in a 1 cP liquid. Graph 3.3.17 indicates that as liquid viscosity increases the area of maximum erosion transfers to a larger angle around the elbow. This being said, the probe located at 45° in the elbow still witnessed more erosion than the probe at 90. Graph 3.3.18 and Graph 3.3.19 portray the combined effects of superficial liquid velocity and liquid viscosity in the same manner as previously shown except now the superficial gas velocity is held constant at 50 ft/s.

100 Measured Experimental Erosion Rates Increasing Liquid Viscosity, 20 μm Particle Diameter, and Vsg = 50 ft/s 8.0E‐05

6.0E‐05 Angle‐Head Probe Rate 4.0E‐05 [mil/lb] Erosion

2.0E‐05

0.0E+00 Vsl 1.47 2.62 1.51 2.45 1.51 2.57 μ 1 1 10 10 40 40 Experimental Conditions [ft/s] and [cP] Graph 3.3.18: Combined Effects of Superficial Liquid Velocity and Viscosity on Erosion Rates for Angle-Head Probe with Constant Nominal Vsg = 50 ft/s

The angle-head probe data has a more linear profile using the lower gas velocity.

The graph shows that as the liquid viscosity increases erosion rates decline. The difference in magnitude between the measured erosion for each liquid velocity decreases although the percentage drop is approximately constant.

101 Measured Experimental Erosion Rates Increasing Liquid Viscosity, 20 μm Particle Diameter, and Vsg = 50 ft/s

6.0E‐05

5.0E‐05 Probe @ 45°

Probe @ 90° 4.0E‐05

Rate 90 3.0E‐05 [mil/lb] Erosion 2.0E‐05

1.0E‐05

0.0E+00 Vsl 1.47 2.62 1.51 2.45 1.51 2.57 μ 1 1 10 10 40 40 Superficial Liquid Velocity [ft/s] Graph 3.3.19: Combined Effects of Superficial Liquid Velocity and Viscosity on Erosion Rates for Elbow Section with Constant Nominal Vsg = 50 ft/s

The elbow data contains dissimilar traits compared to the angle-head probe in the straight section. The probe at 45° in the elbow experienced greater erosion rates for 40 cP over 10 cP. Perhaps the most intriguing aspect to the elbow data is that the probe at 90° actually measured a higher erosion rate than the probe at 45° for 10 cP at the lower liquid rate. Note that the effects of superficial liquid viscosity cannot be reviewed for the 300

μm particle diameter because only one liquid velocity was included in its test matrix.

Now the combined effects of superficial gas velocity and liquid viscosity will be presented. Graph 3.3.20 and Graph 3.3.21 have been included to demonstrate those effects. The graphs include the measured erosion rate for 20 μm sand particles and a constant nominal superficial liquid velocity of 1.5 ft/s. Each set within the graphs show increasing gas velocity.

102 Measured Experimental Erosion Rates Increasing Liquid Viscosity, 20 μm Particle Diameter, and Increasing Vsg

2.5E‐03

2.0E‐03

Angle‐Head Probe

1.5E‐03 Rate

[mil/lb] 1.0E‐03 Erosion

5.0E‐04

0.0E+00 Vsg 50 100 150 50 100 150 50 100 150 μ 1 1 1 10 10 10 40 40 40 Experimental Conditions [ft/s] and [cP] Graph 3.3.20: Combined Effects of Superficial Gas Velocity and Viscosity on Erosion Rates for Angle-Head Probe with Constant Nominal Vsl = 1.5 ft/s

Measured Experimental Erosion Rates Increasing Liquid Viscosity, 20 μm Particle Diameter, and Increasing Vsg

1.6E‐04

Probe @ 45°

1.2E‐04 Probe @ 90°

45 Rate 8.0E‐05 90 [mil/lb] Erosion

4.0E‐05

0.0E+00 Vsg 50 100 150 50 100 150 50 100 150 μ 1 1 1 10 10 10 40 40 40 Experimental Conditions [ft/s] and [cP] Graph 3.3.21: Combined Effects of Superficial Gas Velocity and Viscosity on Erosion Rates for Elbow Section with Constant Nominal Vsl = 1.5 ft/s

103 The angle-head data from Graph 3.3.20 shows a steady increase in erosion rate as the gas velocity is increased. When the rates are varied over the three viscosities, the lower gas velocities have a linear decay; however, the highest gas velocity does not show the same trend and is held nearly constant for all viscosities. The elbow data from Graph

3.3.21 yields increased erosion rate differences between the gas velocities as the viscosity increases. Both graphs still exhibit the highest erosion rates for the 10 cP liquid viscosity while operating at the highest superficial gas velocity of 150 ft/s except for the probe at

90°.

The 300 μm sand erosion data will now be interpreted with regard to the combined effects of superficial gas velocity and liquid viscosity. Graph 3.3.22 and Graph

3.3.23 consist of the measured erosion rates using 300 μm sand particles and a constant nominal liquid velocity of 2.5 ft/s. The graphs increase the liquid viscosity of each set of columns while increasing the gas velocity within each set. Note that there is not a measured erosion rate for the probe at 45° in the elbow on Graph 3.3.23 for the first experimental condition.

104 Measured Experimental Erosion Rates Increasing Liquid Viscosity, 300 μm Particle Diameter, and Increasing Vsg

9.0E‐03

8.0E‐03

7.0E‐03 Angle‐Head Probe 6.0E‐03

Rate 5.0E‐03

[mil/lb] 4.0E‐03 Erosion 3.0E‐03

2.0E‐03

1.0E‐03

0.0E+00 Vsg 51 90 150 50 100 150 50 100 150 μ 1 1 1 10 10 10 40 40 40 Experimental Conditions [ft/s] and [cP] Graph 3.3.22: Combined Effects of Superficial Gas Velocity and Viscosity on Erosion Rates for Angle-Head Probe with Constant Nominal Vsl = 2.5 ft/s

Measured Experimental Erosion Rates Increasing Liquid Viscosity, 300 μm Particle Diameter, and Increasing Vsg

6.0E‐04

5.0E‐04 Probe @ 45°

Probe @ 90° 4.0E‐04

90 Rate 3.0E‐04 [mil/lb] Erosion 2.0E‐04

1.0E‐04

0.0E+00 Vsg 51 90 150 50 100 150 50 100 150 μ 1 1 1 10 10 10 40 40 40 Experimental Conditions [ft/s] and [cP] Graph 3.3.23: Combined Effects of Superficial Gas Velocity and Viscosity on Erosion Rates for Elbow Section with Constant Nominal Vsl = 2.5 ft/s

105 The angle-head probe data yields nearly constant erosion rates when varied in this manner with an exception for the case of 150 ft/s gas velocity and 1 cP viscosity. The liquid viscosity does not have near the effect on measured erosion as the gas velocity.

The elbow data has scattered results but on average agrees with the angle-head data. To conclude the graphs presented in this section, the effects of superficial gas velocity and liquid viscosity are presented once more in a three-dimensional manner.

Graph 3.3.24 illustrates the combined effects on erosion rate for the angle-head probe measurements. The measured erosion rate is on the vertical axis and the nominal superficial velocities are on the horizontal axis like before except now the liquid viscosity is included on the axis that would protrude out of the page. Following the angle-head probe graph is the probe at 45° data. Graph 3.3.25 for the elbow section results does not exemplify the trends quite as well as the angle-head, but it still demonstrates the general effects. This is caused by the area of maximum erosion migrating in the elbow section while the flat-head probes must remain fixed in the same constant location. The angle- head probe consistently measures the maximum erosion due to the probe placement in the straight section geometry. Therefore, the measurements from the angle-head probe result in more uniform erosion magnitudes as seen in the graph. Further analysis can be found later in the chapter.

106 Measured Experimental Erosion Rates Angle‐Head Probe with 20 μm Particle Diameter

2.5E‐03 1 cP 2.0E‐03 10 cP 1.5E‐03

Rate 40 cP

1.0E‐03 [mil/lb]

Erosion 5.0E‐04

0.0E+00

vsl vsg 2.5 150 2.5 125 2.5 1 cP 100 2.5 10 cP 75 2.5 40 cP Nominal Superficial Velocities Viscosity 50 [ft/s] [cP]

Graph 3.3.24: Combined Effects of Superficial Gas Velocity and Viscosity on Erosion Rates for Angle-Head Probe with Constant Nominal Vsl = 2.5 ft/s

Measured Experimental Erosion Rates Probe at 45° with 20 μm Particle Diameter

8.0E‐05 1 cP

6.0E‐05 10 cP

Rate 40 cP 4.0E‐05 [mil/lb]

Erosion 2.0E‐05 45

0.0E+00

vsl vsg 2.5 150 2.5 125 2.5 1 cP 100 2.5 10 cP 75 2.5 40 cP Nominal Superficial Velocities Viscosity 50 [ft/s] [cP]

Graph 3.3.25: Combined Effects of Superficial Gas Velocity and Viscosity on Erosion Rates for Probe at 45° with Constant Nominal Vsl = 2.5 ft/s

107 Effects of Sand Particle Size

Different sand types have varying physical characteristics that only begin with the particle size. However, particle shape, sharpness, and hardness are contributors to the overall erosion that can be caused by a single particle impingement. It is possible for two sand particles of the same mean diameter, with only varying particle sharpness, to cause a different amount of erosion under the same flow conditions. Erosion is known to increase as the sharpness of the particle increases. It was seen earlier that SPPS takes this aspect into consideration by the use of a sharpness factor in the penetration rate calculation in

Equation 2.2.2. Therefore, this study consisted of two experimental sand types that were used over most of the test matrix to provide insight as to the effect of particle size on erosion.

Graph 3.3.26 and Graph 3.3.27 contain the trend of measured erosion versus average particle diameter. The graphs have a common nominal superficial liquid velocity of 2.5 ft/s for increasing gas velocities within three sets of liquid viscosities. The nominal flow conditions are on the horizontal axis and the measured erosion rate is on the vertical axis. The 20 μm particle erosion rates are represented by the white columns in front of the

300 μm particle erosion rates that are presented with black columns.

108 Measured Experimental Erosion Rates Angle‐Head Probe Sand Size Comparison

1.0E‐02

7.5E‐03

20 μm

Rate 5.0E‐03 300 μm [Mil/lb]

Erosion 2.5E‐03

0.0E+00

Vsl 2.5 2.5 2.5 Vsg 50 100 2.5 2.5 μ 1 150 2.5 1 1 50 100 2.5 10 150 2.5 2.5 10 10 50 100 40 150 40 40

Nominal Experimental Conditions [ft/s] and [cP] Graph 3.3.26: Effects of Sand Size on Erosion Rates for Angle-Head Probe with Constant Vsl and Increasing Vsg and Viscosity

Measured Experimental Erosion Rates Probe @ 45° Sand Size Comparison

6.0E‐04

4.0E‐04 20 μm Rate

300 μm [Mil/lb] 2.0E‐04 Erosion

45 0.0E+00

Vsl 2.5 2.5 2.5 Vsg 50 2.5 100 150 2.5 2.5 μ 1 50 1 1 100 2.5 2.5 10 150 2.5 10 10 50 100 40 150 40 40

Nominal Experimental Conditions [ft/s] and [cP] Graph 3.3.27: Effects of Sand Size on Erosion Rates for Probe at 45° with Constant Vsl and Increasing Vsg and Viscosity

109 The graphs both agree that increasing the average particle diameter increases the measured erosion occuring in both test sections. They also show the overall change in erosion magnitude caused by the difference in particle diameter on each test section. It was found that on average an approximate factor of 8 separates the measured erosion rates recorded between the 300 μm and 20 μm sand particles in both test sections. The elbow section is affected much more than the angle-head probe in the straight section by the change in sand particle diameter at higher gas velocities. The superficial gas velocity of 150 ft/s over the range of viscosities has a factor of 9 between the erosion rate of both particle diameters for the probe at 45° and only a factor of 3 for the angle-head probe.

When compared in the same manner as before for the superficial gas velocity of 50 ft/s the factors vary adversely with a larger value for the angle-head data that is equal to 18 and only 8 for the elbow data. It should also be noted that at lower gas velocities the angle-head probe endured relatively constant factors of difference in erosion under each condition when compared to the probe located at 45° in the elbow.

Effects and Correlation of Probe Location

The experimental results presented thus far have provided details as to the effect of probe location on the measured erosion rate. In general, the angle-head probe in the straight section was subjected to the highest erosion rates followed by the probe at 45° and then by the probe at 90° in the elbow section. Consequently, the uncertainty associated with the angle-head probe measurements is lower than the uncertainty of the elbow measurements. This has lead to greater emphasis being placed on the angle-head probe data and in turn the correlations associated with it.

110 It is critical to understand that the angle-head probe in the straight section always witnesses more metal loss or erosion compared to the flat-head probes in the elbow.

There are many possible reasons for such incidence. The most obvious of which is that the angle-head probe protrudes into the flow reducing the cross-sectional area of the pipe and effectively increasing the local velocity and resulting erosion as explained in the one- dimensional slug flow models section earlier in the chapter. There is another less apparent rationale behind this occurrence that actually stems from the fundamentals of fluid mechanics. The hydrodynamics of each test section are different from one another.

Flow that travels through the elbow section can be viewed as being disrupted more significantly than when it flows through the straight section with the protruding angle- head probe. In other words, entrained particles have more time to respond to deviations of flow in the bend, which ultimately affects impact characteristics. This being said, the angle-head probe is assumed to be measuring the maximum erosion rate of the entire system.

The next detail to discuss is the scatter in the elbow erosion rates for the probe at

45° and probe at 90°. There is more scatter in the results for the elbow probes in comparison to the straight section probe. This is not only attributed to uncertainty in the probe measurements but is further credited to the area of maximum erosion. It is flow dependant and constantly migrates in the elbow section geometry. The flat-head probes are not able to move around in the elbow to track the area of maximum erosion but are fixed in their location. The erosion pattern migration increases the difficulty of analysis for the experimental elbow results. The associated correlations that link probe locations to one another are useful and are possibly the most important attribute of this study when

111 considering field implementation of ER probes. The angle-head probe measurements are in a sense rendered useless without any corollary relationships to other pipe fitting geometries. This is true except when taking the measured erosion rate of the angle-head probe to be the maximum possible erosion rate of the system. The intrusive probe by itself does however show potential to be a worthy sand monitor that can determine the presence of sand production in flow lines.

The reason that the intrusive angle-head probes are more useful in field applications compared to flat-head probes is simply due to installation. Most access fittings, which are used as probe insertion points, are placed in straight sections of pipe. If correlations between angle-head probe erosion and elbow erosion are available, elbow erosion could be determined from angle-head results. This study attempts to establish those correlations beginning with the angle-head and elbow probes on the Boom Loop. In the future, companies could design more access points for different pipe fitting geometries thereby allowing flat-head probes to be used more easily in bends and other locations.

Graph 3.3.28 illustrates the effect of probe location on measured erosion rates.

The horizontal axis is the measured erosion of the angle-head probe in the straight section. The vertical axis contains the measured erosion rates for all the probes. Both of the axes are on logarithmic scales. The data points are arranged by increasing angle-head erosion rates along with the corresponding rates from the elbow in the same horizontal location on the graph. Therefore, the angle-head probe data is arranged in a linear fashion with a slope equal to one. The experimental data was prepared in this manner to gain a representative value that permits suitable comparisons between the probe locations. The

112 correlations allow the erosion rates for an elbow to be estimated if only an angle-head probe is present in a straight pipe section of the system in question.

Correlation of Probe Location Increasing Angle-Head Erosion Rate with Corresponding Elbow Rates

1.0E-02

1.0E-03 Probe @ 45°

y = 0.0678x 1.0E-04 R2 = 0.635

Probe @ 90° [mil/lb]

Erosion Rate y = 0.0129x 1.0E-05 R2 = 0.596

Angle-Head Probe

1.0E-06 y = x

45 2 90 R = 1

1.0E-07 1 1 1 1 .0 .0 .0 .0 E- E- E- E- 05 04 03 02 Angle-Head Erosion Rate [mil/lb]

Graph 3.3.28: Correlation of Probe Location for Angle-Head and Elbow

The graph is important to ER probe users that wish to predict elbow erosion rates through the use of only angle-head probe measurements from a straight pipe section.

Table 3.3.5 contains the necessary information to predict the elbow rates from the angle- head probe rates.

Table 3.3.5: Correlation of Elbow Section to Angle-Head Probe

Angle-Head Probe Correlations

Probe Equation

Elbow Probe at 45° y = 0.0678x Section Probe at 90° y = 0.0129x

113 The far right column in the table represents the linear equation for both elbow probes in relation to the amount of erosion imparted on the angle-head probe. The x in the equation is the input variable of measured erosion on an angle-head probe in a straight section of pipe, and the y represents the erosion in the elbow at that specific location. The following graphs have been included to further explain the information presented in the table along with the acceptable range of estimations for a given probe location. Graphs 3.3.29 and 3.3.30 are on log-log scales with the probe erosion rate on the vertical axis and the angle-head erosion rate on the horizontal axis.

Correlation of Probe Location Increasing Angle-Head Erosion Rate with Corresponding Probe at 45° Rates with Factor of 5 Uncertainty Shown

1.0E-02

45 1.0E-03

1.0E-04 [mil/lb]

Erosion Rate 1.0E-05

1.0E-06

1.0E-07 1 1 1 1 .0 .0 .0 .0 E- E- E- E- 05 04 03 02 Angle-Head Erosion Rate [mil/lb]

Graph 3.3.29: Correlation of Probe at 45° to the Angle-Head Probe

Graph 3.3.29 is applied to the probe at 45° in relation to the angle-head probe.

The experimental data points are shown in the graph along with a solid black linear fit trend line. The dotted lines above and below the trend line represents the range of the correlation prediction. The angle-head correlation to the probe at 45° yields an

114 approximate uncertainty of plus or minus a factor of 5. Graph 3.3.30 is arranged in the same manner as the probe at 45° except for the probe at 90° location correlation.

However, the uncertainty increases to a factor of 15 for the probe at 90° correlation to the angle-head probe.

Correlation of Probe Location Increasing Angle-Head Erosion Rate with Corresponding Probe at 90° Rates with Factor of 15 Uncertainty Shown 1.0E-02

1.0E-03

1.0E-04 [mil/lb]

Erosion Rate Rate Erosion 1.0E-05

1.0E-06

1.0E-07 1 1 1 1 .0 .0 .0 .0 E- E- E- E- 05 04 03 02 Angle-Head Erosion Rate [mil/lb]

Graph 3.3.30: Correlation of Probe at 90° to the Angle-Head Probe

The correlation between the angle-head probe and the elbow section is important to many ER probe using companies. The correlation between the two probes in the elbow section is also important and is explained next. Graph 3.3.31 is arranged for the elbow section by the increasing erosion rate of the probe at 45°. The corresponding rates of the probe at 90° follow. The measured erosion rate is on the vertical axis and the probe at 45° erosion rate is on the horizontal axis. The graph is followed by Table 3.3.6 that includes the equation for predicting the erosion rate for the probe at 90° from the erosion rates of

115 the probe at 45°. The input variable x is the erosion rate of the probe at 45° that must be included to solve the equation and the probe at 90° erosion rate.

Correlation of Probe Location Increasing Probe at 45° Erosion Rate with Corresponding Probe at 90° Rates

1.0E-03

90 1.0E-04 Probe @ 45°

y = x R2 = 1 1.0E-05 [mil/lb]

Erosion Rate Probe @ 90°

y = 0.153x R2 = 0.4408 1.0E-06

1.0E-07 1 1 1 1 .0 .0 .0 .0 E- E- E- E- 06 05 04 03 Probe at 45° Erosion Rate [mil/lb]

Graph 3.3.31: Correlation of Probe Locations for Elbow Section

Table 3.3.6: Correlation of Probe at 90° to the Probe at 45° in the Elbow

Probe at 45° Correlation

Probe Equation Elbow Probe at 90° y = 0.153x Section

The uncertainty of the correlation prediction between the two probes in the elbow is shown in Graph 3.3.32. The probe at 45° correlation to the probe at 90° yields an approximate uncertainty of plus or minus a factor of 7.5. Therefore, the most accurate probe location correlation is the angle-head probe to the probe at 45° in the elbow. That

116 correlation can provide the erosion estimation with an uncertainty of plus or minus a factor of 5.

Correlation of Probe Location Increasing Probe at 45° Erosion Rate with Corresponding Probe at 90° Rates with Factor of 7.5 Uncertainty Shown

1.0E-02

1.0E-03

1.0E-04 [mil/lb]

Erosion Rate Rate Erosion 1.0E-05

1.0E-06

1.0E-07 1 1 1 1 .0 .0 .0 .0 E- E- E- E- 06 05 04 03 Probe at 45° Erosion Rate [mil/lb]

Graph 3.3.32: Correlation of Probe at 90° to the Probe at 45° in the Elbow

It should be stated that the correlations developed between the probe locations are specific to the pipe size used in these experiments. More studies need to be performed to determine how results would change with increases in pipe size.

2-Dimensional Slug Flow Modeling

The desire for accurate erosion prediction has led to developing a 2-dimensional approach to particle tracking due to the shortcomings of the 1-D technique. The greatest deficiencies of the 1-D slug flow models are their predicted erosion magnitudes and their failure to capture small particle erosion. Improvement to the models are needed the most in these areas. The cause for the underprediction of erosion for small particles lies within

117 the 1-D particle tracking in the slug flow models. The 1-D approach forces the particles to travel in a perpendicular path towards the wall at all times and are never allowed to deflect from their linear path. This method encounters errors as a small particle approaches the wall. Small particles cannot overcome the viscous effects near the wall, because they do not have as much momentum as the larger particles. Therefore, the problem is not as prevalent for larger particles that can overcome the forces near the wall to make impacts. However, the smaller particles cannot impact the wall in a 1-D manner and their impact velocity may approach zero. An impact velocity equal to zero yields no erosion, and the models underpredict. The following figures have been included to illustrate the physical differences in particle trajectories between the 1-D and 2-D approaches to particle tracking. Figure 3.4.1 shows the only particle trajectory for every particle at every stagnation length using the 1-D approach.

Figure 3.4.1: 1-D Particle Tracking Particle Trajectory

The particle is only allowed to travel perpendicular to the wall. The forced linear path does not have much affect on the particle’s velocity until the particle nears the wall; this is where the assumed fluid velocity has a steep gradient. When the particle is near the wall, the forced linear path decreases the velocity, moreso than if the particle was allowed

118 to move in a 2-D manner. The 2-D approach allows another degree of freedom in direction that each particle can travel. Therefore, the 2-D particle tracking is more representative of the actual real-world physical sytem that it is attempting to recreate.

Figure 3.4.2 represents possible particle trajectories using 2-D particle tracking. Note that

Figure 3.4.2 is not to any scale and that actual trajectories may differ.

Centerline Figure 3.4.2: 2-D Particle Tracking Particle Trajectories

The addition of the second dimension in particle tracking provides the ability to have a radial component in the particle velocity. The radial velocity component is important for determining the particle trajectory. Figure 3.4.2 shows that the further the particle is released from the centerline of the flow, the greater the radial velocity component can be and furthermore the greater the particle trajectory will be non-linear.

The single component axial velocity produces a linear 1-D particle trajectory towards the wall at all times, but the combination of radial and axial velocity components in the 2-D particle tracking produces non-linear particle trajectories that are more representative of actual trajectories found in experimentation. Also, the 2-D particle tracking accounts for the effect of turbulence on entrained particles. Turbulence is known to have an effect on

119 erosion for all sand types and sizes, but especially for smaller diameter particles that require less energy to be accelerated.

The elbow and angle-head slug flow models can both be improved by implementing a 2-D approach to particle tracking. Therefore, a 2-D advancement in particle tracking needs to be employed in place of the current 1-D approach in order to increase the overall accuracy of the particle impact information estimation of the models.

This will ultimately improve the magnitude of erosion predictions and the ability to capture all the erosion trends for any sand size or test condition.

2-D Mechanistic Slug Flow Model Development

2-D particle tracking can be used to determine more representative particle tracjectories and impact characterisitics for accurately predicting erosion. The application of the 2-D approach to the slug flow models within SPPS will now be outlined. There are several considerations for the 2-D approach to particle tracking. The two primary components for the approach include a stagnation region of a specific geometry and the flow field information within that stagnation region. The 1-D and 2-D modeling techniques are similar to one another in several ways. Both of the models revolve around three core requirements to predict erosion. To begin, the flow properties and mechanics must be obtained under the flow conditions in question to serve as input for the subsequent step. Next, those results are used to establish the impact characteristics of entrained particles through a given geometry. The impact information can then be used in parallel with an erosion equation to finally predict erosion rates.

The first requirement for the 1-D and 2-D models to predict erosion in slug flow is almost identical. The mechanistic slug flow representation used by the 1-D model for

120 determining fluid properties and slug mechanics still applies to the 2-D model. The previous slug flow erosion modeling assumptions also apply to the new 2-D approach. In other words, the new model uses the same procedure and ideology as the old model until the stagnation length or stagnation zone concepts are applied to the slug body. There are further similarties between the two models even after that step in the definition of the slug front and slug tail. The central differences between the two models are the method of acquiring particle impact information and the subsequent equations for calculating erosion.

The process begins with determining the flow field information for the geometry in question. CFD is used along with the slug flow model to determine the flow field. The

2-D flow field is obtained by treating the slug body like single-phase flow that moves at the mixture velocity of the multi-phase flow. The modeled single-phase fluid shares the same properties as the mixture properties of the slug body. The 2-D model can calculate all the necessary properties needed for determining flow field information in the stagnation region. The method has been made applicable to many 2-D geometries through built-in pre-saved cases of representative flow fields with varying Reynolds numbers.

The next step is to evaluate the particle impact information. This is where the models begin to differ from one another. The 1-D modeling uses stagnation length to determine impact velocities, but the 2-D modeling employs a stagnation zone for a certain geometry under known flow conditions to ultimately gain the particle impact information. Figure 3.4.3 illustrates the stagnation zone concept for a tee and elbow

121 geometry. The stagnation zone is the region of the fittings outlined by the black dotted line.

Stagnation Zones

Figure 3.4.3: Stagnation Zone in Tee and Elbow

Although erosion data for a tee pipe fitting was not gathered during experimentation in this study, the above diagram was included to help demonstrate the stagnation zone concept. However, the stagnation zone and erosion modeling of a tee is analgous to that of a direct impingement configuration. Figure 3.4.4 demonstates the

CFD simulated flow velocity field for 2-D direct impingement on a target wall. This is the arrangement that the 2-D slug flow erosion model for the angle-head probe uses for the flow field to eventually calculate particle trajectories and impact information.

122 Contour of Flow Stagnation Zone Velocity (by CFD)

Red: High Velocity Blue: Low Velocity

Nozzle

Target Wall

Figure 3.4.4: Flow Velocity Contours and Stagnation Zone for Direct Impingement Geometry

Next, is a discussion of how the particles are arranged in the 2-D stagnation zone flow field to begin particle trajectory simulations. The two variables associated with particle arrangement are the number of particle groups and the number of particles in each group. The particle groups are arranged axially in the pipe, and the particles in each group are arranged radially in the pipe. The number of particle groups and number of particles in each group can be completely customized. Figure 3.4.5 illustrates these variables of the 2-D approach. It is important to know that both the axial and radial locations where a particle is released, inside any given stagnation region with 2-D particle tracking, influences the particle trajectory and velocity components.

123

Figure 3.4.5: Illustration of 2-D Particle Tracking Particle Arrangement

The particle groups can be viewed analgous to the stagnation length distribution from the 1-D approach, but only regarding particle placement in the slug body with respect to the slug front and tail. The stagnation length distibution only has a single particle in each stagnation length for each simulation, but the stagnation zone approach has many. In fact, the 2-D slug flow model uses 50 particles inside 50 particle groups for a total of 2500 particles that are all released in a single simulation. The slug front erosion component is represented by the first 49 particle groups and the slug tail by the 50th particle group. The 1-D model uses only 500 particles over 500 simulations with the first

499 particles representing the slug front erosion and the slug tail erosion is demonstrated by the 500th particle. The 2-D approach to particle tracking not only changes the number of particles released during a single simulation, but also changes the tracjectory of the particles in the flow in comparison to the 1-D approach as seen earlier. This improves the

124 impact velocity prediction for each particle goup, which yields superior impact velocity and trajectory estimations over the entire stagnation region.

Once the flow field information and the initial particle arrangement for the stagnation zone in question is known, the subroutine that calculates the trajectories will track all of the particles in order to generate the most representative results of the specific system. The impact information is recorded every time a particle impacts the target wall in the simulations. The 2-D tracking currently allows for only a single target wall impact from each particle much like the 1-D model. This being said, the 2-D model can be adjusted to only accept the first impact of each particle or any number that the user defines. The recorded impact properties include the impact locale, the impact angle, and the impact speed. Note that the 2-D approach does not allow particle interaction and consequentially each particle does not know that any other particles exist in the flow during simulations.

The 2-D particle tracking used by the model for calculating impact properties is obtained by integrating the force balance between the particle inertia and external forces that act on each particle in analogy to Newton’s Second Law. The method is represented

in Equation (3.4.1) for Cartesian coordinates, where the particle velocity is VP .

dV F + F + F + F = P (3.4.1) D P B A dt

The left hand side of the equation is the total combined resultant force that acts upon each particle per unit particle mass that is represented by the summation of the force

of drag FD , force of the pressure gradient FP , buoyant force FB , and added mass force

FA . The single component of the resultant force that is attributed with the most influence

125 on each particle is the drag force FD represented by Equation (3.4.2). It can be found from the equation that the drag is dependent upon the slip velocity between the particle and the carrier fluid, and as the slip velocity between the two increases so will the force of drag. The 1-D model does not account for all of the particle body forces that the 2-D model is capable of, but only accounts for the force of drag.

18μ f CD Re r FD = 2 ()V f −VP (3.4.2) ρ d d P 24

The fluid phase velocity is shown by V f , the particle velocity by VP , the particle

density by ρd , the particle diameter by d P , the relative Reynolds number by Rer , and

the coefficient of drag by CD . The relative Reynolds number used by the model is shown

by Equation (3.4.3), where ρ f is the fluid density.

ρ f V f −VP d P Rer = (3.4.3) μ f

The remaining forces that act on each particle in the 2-D simulations can be seen in Equations (3.4.4), (3.4.5), and (3.4.6). They are the forces that account for large

pressure gradients, gravity and/or buoyancy, and added mass or FP , FB , and FA , respectively.

3 1 FP = − ∇P (3.4.4) 2 ρ P

(ρ P − ρ f )g FB = (3.4.5) ρ P

1 ρ f d(V f −VP ) FA = (3.4.6) 2 ρ P dt

126 Further explanation of the above equations is needed beginning with the pressure gradient term. ∇P is the local pressure gradient of the fluid that changes with flow conditions. Next is the buoyant force, which can be significant if the fluids have considerable differences in density or if gravity effects are to be included in the simulations. Last is the added mass force that is required to accelerate the fluid in the surrounding vicinity of the particle. The resulting resistive force on the particle exists when relative motion between the particle and carrier fluid occurs similar to the force of drag. Other forces can be added to the force balance but will not be discussed in detail.

Zhang et al. (2010) proposed a complete analysis of the topic that includes a Discrete

Random Walk (DRW) model or “eddy lifetime” model to account for turbulence through the interaction of entrained particles and turbulent eddies.

Now that the particle trajectories and corresponding impact characteristics have been explained for the 2-D model, the erosion calculation can commence. The aforementioned particle impact information is used to calculate the erosion rate that is location dependant on the target wall. The fixed CFD cells along the target wall of the mesh contain the final particle impact information from the simulation. The calculated erosion rate distribution is then known for the entire impact area of the geometry. The maximum erosion rate or the total erosion rate can be calculated from the distribution.

SPPS is capable of taking the analysis one step further by using the CFD erosion distribution to plot and evaluate the results for different cell size distributions.

The particle impact information can be used in any of the erosion equations that are available, but the 2-D model in SPPS uses the equation recently proposed and validated by Zhang et al. (2009). The applied erosion equation is shown by Equation

127 (3.4.7) where Equation (3.4.8) is the impact angle erosion function that is needed to complete the erosion ratio calculation.

−0.59 n ER = C(HB) FS f (θ )VP (3.4.7)

f ()θ = 1.4234θ 5 − 6.3283θ 4 +10.9327θ 3 −10.1068θ 2 + 5.3983θ (3.4.8)

Completion of the 2-D model outline requires the variables accompanied with the new erosion equation to be made clear. ER is the erosion ratio that has been defined as the amount of wall material metal loss caused by the particle impingements that is

divided by the mass of those particles. HB is the Brinell hardness, FS is the particle

shape coefficient, VP is the particle impact velocity in [m/s], C and n are empirical constants, and the function f (θ ) is the material specific impact angle equation. The particle shape coefficient is equal to 1.0 for sharp angular particles, 0.53 for semi- rounded particles, and 0.2 for fully rounded particles. The particle impact angle, θ , is measured in radians. The empirical constants used are C = 2.17x10-7 and n = 2.41. Note that the hardness and angle functions were developed for carbon steels and both must be modified when predicting the erosion rates of other materials.

2-D Slug Flow Model Results

E/CRC slug flow modeling techniques and procedures that were previously outlined have been applied to the geometry of an angle-head probe in a straight pipe section to obtain the new 2-D SPPS calculated erosion rates. The experimental test matrix of this study did not include 150 μm diameter particles, but the effect of sand size on the

2-D erosion model is important. As a result, previous experimental data that was not collected during this study has been included to exemplify the effect. The data that was

128 not acquired from the experimental results of this research will be listed first and kept separate from the results that were. The results of the new 2-dimensional slug flow erosion model will now be presented.

Graph 3.4.1 reveals the comparison between the calculated 2-D SPPS erosion predictions and measured erosion rates for the angle-head probe using a liquid viscosity of 1 cP and 150 μm diameter particles while varying the superficial velocities within the slug flow regime. The flow conditions in [ft/s] or [cP] are on the independent axis, and the erosion rate in [mil/lb] is presented on the dependant axis. The black columns are the calculated erosion rates and the white columns are the experimentally measured erosion rates. The theme of the graph formatting will be carried out for the remainder of the 2-D results.

2.0E‐03

1.5E‐03 Calculated Angle‐Head

Measured Rate Angle‐Head 1.0E‐03 [mil/lb] Erosion

5.0E‐04

0.0E+00 Vsl 1.4 1.5 1.4 1.5 2.6 2.6 2.6 2.6 2.6 2.6 2.6 Vsg 50 50 90 133 50 50 70 88 88 90 102 Superficial Velocities [ft/s] Graph 3.4.1: 2-D SPPS Calculated and Measured Erosion Results for Angle-Head Probe with 150 μm Particles and 1 cP Liquid Viscosity

129 The improvement in the erosion predictions of the SPPS angle-head model can be seen instantaneously after the 2-D particle tracking and new erosion equation have been applied to the previous slug flow model. The results have caused the 2-D comparisons graph to differ from the 1-D graph. The most significant detail is that the calculated and measured erosion rate magnitudes are nearly identical and can be shown on a single axis scale, whereas previously a secondary vertical axis was utilized to account for the large difference in magnitudes between the two. The 2-D model not only captures the appropriate erosion magnitudes, but it is also capable of accurately predicting the erosion trends found by experimentation. The graph verifies that the 2-D SPPS erosion calculations for 1 cP viscosity liquids and 150 μm diameter particles very mildly underpredicts for most of the measured cases. The 2-D results are more than substantial for dependable real-world application.

The measured and modeled erosion results for increased liquid viscosities are discussed next to complete the 150 μm sand particle effect on erosion rate. Graph 3.4.2 contains both of the erosion rates for 20 and 40 cP liquids over a range of superficial velocities that produce slug flow. The black dotted line separates the two liquid viscosities from one another on the graph.

130 8.0E‐04

6.0E‐04 Calculated Angle‐Head

Measured Rate Angle‐Head 4.0E‐04 [mil/lb] Erosion

2.0E‐04

0.0E+00 Vsl 1.4 1.5 1.5 1.4 2.6 2.6 1.4 1.4 1.4 2.6 2.6 Vsg 50 50 90 91 91 91 50 50 50 78 89 µ 20 20 20 20 20 20 40 40 40 40 40 Experimental Conditions [ft/s] and [cP] Graph 3.4.2: 2-D SPPS Calculated and Measured Erosion Results for Angle-Head Probe with 150 μm Particles and Increasing Liquid Viscosity

The erosion rates of higher liquid viscosities for 150 μm sand particles are captured by the 2-D model to nearly the same degree of accuracy as the 1 cP viscosity erosion rates. The model appears to underpredict for the 20 cP viscosity in most cases, but the 40 cP results contain both high and low predictions. The 2-D angle-head model has an average of 68% error between the calculated and measured values of erosion for the slug flow regime for 150 µm particles.

The 2-D model can be contrasted with the erosion results gathered during the experimentation of this study. Graph 3.4.3 represents the comparisons of the 2-D SPPS calculated erosion rate to the experimentally measured erosion rate for 300 µm diameter particles. All three liquid viscosities are visible on the graph and separated by the black dotted lines for clarity.

131 9.0E‐03

7.5E‐03 Calculated Angle‐Head 6.0E‐03 Measured Rate Angle‐Head 4.5E‐03 [mil/lb] Erosion

3.0E‐03

1.5E‐03

0.0E+00 Vsl 2.63 2.63 2.40 2.54 2.40 2.55 2.59 2.64 2.52 Vsg 51 90 150 50 100 150 50 100 150 µ 1 1 1 10 10 10 40 40 40 Experimental Conditions [ft/s] and [cP] Graph 3.4.3: 2-D Calculated and Measured Erosion Results for Angle-Head Probe with 300 μm Particles and Increasing Liquid Viscosity

The 2-D model captures the erosion magnitudes and erosion trends of the 300 µm particles to a satisfactory degree for all the experimental conditions. All of the modeling results underpredict the measured values with an average of 40% error between them for

300 µm particles.

The 20 µm sand is the only particle size that remains for discussion of the calculated erosion results for the 2-D model. Recall that the previous 1-D models were relatively successful at large particle erosion predictions, but they were completely unable to obtain suitable results for the 20 µm diameter particles. There are a total of three graphs for this particle size and each graph represents a single liquid viscosity. The progression begins with Graph 3.4.4 for 1 cP then transitions to 10 cP for Graph 3.4.5 followed by Graph 3.4.6 which is for the 40 cP liquid viscosity.

132 2.5E‐03

2.0E‐03 Calculated Angle‐Head

1.5E‐03 Measured Rate Angle‐Head [mil/lb] Erosion 1.0E‐03

5.0E‐04

0.0E+00 Vsl 1.47 1.60 1.50 1.63 1.61 2.62 2.62 2.74 2.11 2.62 Vsg 50 80 100 125 150 50 75 90 125 150 Superficial Velocities [ft/s] Graph 3.4.4: 2-D Calculated and Measured Erosion Results for Angle-Head Probe with 20 μm Particles and 1 cP Liquid Viscosity

2.5E‐03

2.0E‐03 Calculated Angle‐Head

1.5E‐03 Measured Rate Angle‐Head [mil/lb] Erosion 1.0E‐03

5.0E‐04

0.0E+00 Vsl 1.51 1.49 1.48 1.50 2.45 2.41 2.40 2.42 2.47 Vsg 50 75 100 125 50 75 100 125 150 Superficial Velocities [ft/s] Graph 3.4.5: 2-D Calculated and Measured Erosion Results for Angle-Head Probe with 20 μm Particles and 10 cP Liquid Viscosity

133 5.0E‐03

4.0E‐03 Calculated Angle‐Head

3.0E‐03 Measured Rate Angle‐Head [mil/lb] Erosion 2.0E‐03

1.0E‐03

0.0E+00 Vsl 1.58 1.52 1.47 1.44 2.57 2.40 2.59 2.35 Vsg 75 100 125 150 50 75 100 150 Superficial Velocities [ft/s] Graph 3.4.6: 2-D Calculated and Measured Erosion Results for Angle-Head Probe with 20 μm Particles and 40 cP Liquid Viscosity

The 2-D model is successful at predicting the measured experimental erosion rates. The application of 2-D particle tracking to the angle-head slug flow model has resulted in dramatic improvements for small particle erosion prediction. The 2-D model can now capture acceptable erosion magnitudes and trends for the 20 μm silica flour, whereas before the 1-D modeling produced unacceptable results. The 10 cP liquid viscosity yields the best fit of calculated to measured erosion rates. The 2-D calculated rates for 20 µm particles underpredict erosion for the 1 cP and 10 cP liquid viscosities but overpredict for the 40 cP viscosity. The 20 μm particles generated an average of 113% error between each experimentally measured erosion rate and the calculated rate by the 2-

D angle-head model for slug flow. In conclusion, the 2-D model has an overall average of

84% error between the calculated and measured erosion rates for all experimental conditions and sand sizes.

134 2-D Slug Flow Model Evaluation

The ability of the angle-head slug flow model to capture accurate erosion magnitudes was greatly increased from the previous 1-D model due to the 2-D particle tracking. However, the capacity of the 2-D model to obtain the experimental erosion trends was passed on from the 1-D model via the mechanistic approach to slug flow modeling and the developed erosion concepts of E/CRC. The four primary flow conditions that critically affect the measured erosion rate of a system are the superficial liquid velocity, superficial gas velocity, liquid viscosity, and sand size. Therefore, the behavior of the 2-D model erosion predictions will be discussed for each one of the flow conditions.

The 2-D erosion ratio equation is calculated, for the most part, as a function of impact characteristics. The slug flow model uses mixture properties in the CFD simulations to determine the forces acting against each particle as it travels through the stagnation zone to ultimately resolve the particle impact information. The mixture properties used by the 2-D model are a function of liquid holdup in the slug body shown by Equation (3.1.3) and Equation (3.1.4). The liquid holdup is a function of fluid properties and velocities shown by Equation (2.2.5), and it is what allows the model to predict the erosion trends. All of the flow conditions, except the sand size, affect the model in this fashion.

The measured erosion rate was found to decrease during experimentation after the superficial liquid velocity was increased. The 2-D model predictions were influenced in the same manner as the measured values. The explanation is that as the superficial liquid velocity climbs in value, the liquid holdup in the slug body will be amplified. Thereby

135 increasing mixture properties, such as viscosity, will shrink the velocity of each sand particle before impact. Thus effectively reducing the amount of erosion throughout the system.

Increasing liquid velocity decreases erosion, but increasing gas velocity increases erosion as seen from the experimental results. The liquid slug body velocity calculation involves the superficial gas velocity as seen in Equation (2.1.12). The slug body velocity actually determines the initial particle velocity in the simulations and therefore has a direct affect on the particle impact velocity. The higher the initial particle velocity, the larger the impact velocity will be for the same geometry. The erosion increase is attributed to the decrease in liquid holdup as the gas velocity rises. The pipe volume will contain more gas and the liquid holdup will become smaller. Gas has a much lower density and viscosity compared to liquid and the mixture properties in the slug body will be lower. The decreased fluid resistance on each sand particle inside the stagnation zone causes impact velocities to be higher with an end result of greater erosion rates for increased superficial gas velocities.

The liquid viscosity affects the erosion rate both directly and indirectly. The liquid viscosity directly affects the erosion rate by changing the shear forces in the liquid and consequently the drag that it imparts on entrained sand particles to lessen their impact velocities. Higher viscosity fluids can potentially trap more gas bubbles that in turn reduce the effective density of the fluid in the slug body and increase erosion. Viscosity indirectly affects the erosion rate much like the superficial liquid and gas velocities do, by means of influencing the liquid holdup.

136 The effect of liquid viscosity on measured erosion rates for slug flow was found to be non-linear. The erosion results of the 2-D model were able to predict the effects of viscosity but not perfectly. The 300 µm results actually improved as the viscosity increased, whereas the smaller 20 and 150 µm results produced more error. The liquid viscosity increasing from the lowest, median, then highest test conditions yielded the following errors: 50%, 44%, and 27% for 300 µm particles; 46%, 64%, and 121% for 150

µm particles; and finally, 81%, 104%, and 169% for 20 µm particles. Therefore, the model contains 61%, 81%, and 125% error respectively, when comparing all of the sand size predictions over the three liquid viscosities.

Examination of the slug flow model proposed by Zhang et al. (2003) yields interesting results as to the effect of liquid viscosity on the hydrodynamic properties that it calculates. The model shows that as liquid viscosity increases, the length of the liquid film decreases. However, the length of the liquid slug body remains constant due to the fact that it is strictly calculated by the diameter of the pipe. The model also shows that the liquid holdup in both the film region and slug body decrease as viscosity is increased. In conclusion, the slug unit must be getting smaller in length and more aerated for increases in viscosity. An illustration of the concept is shown in Figure 3.4.6 where increasing the liquid viscosity results in enlarging the slug body liquid fraction with respect to the entire slug unit.

137

Figure 3.4.6: Slug Unit Reduction for Increasing Liquid Viscosity from Zhang et al. (2003) Slug Flow Model

Recall that it was stated previously in the experimental results that a strange phenomenon occurred that yielded larger erosion rates in the median viscosity than in the lowest viscosity. The aforementioned details of the slug flow model along with physical reasoning can help explain the occurrence of increased erosion rates in the median viscosity over the lowest viscosity. Once the liquid viscosity reached the highest value, the viscous forces imparted on each particle became more dominant and considerably reduced the impact speed and erosion rate. The progression of viscosity affecting the slug body liquid holdup and erosion can also be found in more detail from Rodriguez (2008).

There is one final flow property left for discussion that affects the erosion rate of a given system, and that is the sand size. The modeled predictions follow the increasing trend of measured erosion for increasing sand particle size. The 2-D particle tracking is attributed for the performance of the new angle-head model regarding the effects of sand size on calculated erosion rates. It was found that the model best predicted the rates associated with the 300 μm particles, followed by the 150 μm predictions, and ending

138 with the 20 μm estimations. The percent errors between measured and predicted rates for each of the sand sizes are 40%, 68%, and 113% respectively. The 2-D model predictions yielded an overall average of 84% error in erosion for all sand sizes and experimental conditions.

Uncertainty Analysis

In a perfect world the results that have been presented would be precisely known, but unfortunately every measurement given thus far is an estimate. In fact, the true value cannot even be identified. Therefore, it is common practice to report the uncertainty associated with the experimental measurements and results in order to gain awareness to most aspects of a study. The three areas of uncertainty to assess for this study are the uncertainties of the Boom Loop, ER probe measurements, and the SPPS erosion predictions.

Many of the uncertainties can be found through statistical analysis of the measurements and results or through the manufacturer specifications of the equipment used. However, certain instances of the associated uncertainties need further investigation and explanation to properly account for their error. These are the measurements that have multiple sources of error within them and their propagation of uncertainty becomes more important than any single uncertainty component. The propagation of uncertainty can be analyzed through the exploit of Taylor’s series by neglecting the higher order terms and then modifying the variables in the equation to represent the total uncertainties. Equation

(3.6.1) reveals the series after the process has been completed.

139 f ( x1 + u x1 ),( x2 + u x2 ),...... ( xn + u xn )− f ( x1 , xx ,..... xn ) = (3.6.1) ∂f ∂f ∂f = u f −Total = u x1 + u x2 + ...... + u xn ∂x1 ∂x2 ∂xn

The total uncertainty, u f −Total , is determined through the use of the uncertainty in

variable x1 , ux1 , and the change in uncertainty due to the changes in variable x1 or

∂f ∂x1 . Equation (3.6.1) expresses the maximum uncertainty of a system, but a more practical approach is needed given that different uncertainties have the potential to cancel one another out altogether. Therefore, it is reasonable to calculate the root mean square

(RMS) of each individual uncertainty of the system. The RMS method is found below.

2 2 2 ∂f ∂f ∂f u f −RMS = u x1 + u x2 + ...... + u xn (3.6.2) ∂x1 ∂x2 ∂xn

Equation (3.6.2) shows that the RMS overall uncertainty, u f −RMS , is calculated

using the nominal value of each variable, xi , and the associated discrete uncertainty or

u xi .

Uncertainty Analysis of Boom Loop

The Boom Loop was used to retrieve all of the experimental results, and therefore it is crucial to explain the uncertainty involved with measuring the system. The three core measurements that must be evaluated are the gas velocity, liquid velocity, and the sand rate that the boom loop produces. There are two sources of error in the gas velocity calculation. The gas flow rate is measured by a flow meter and a portion of the uncertainty is based upon the accuracy of the meter. A pressure gauge reading is also used in the gas velocity calculation, so the gauge precision must be included.

140 The liquid velocity and sand rate observe nearly the same uncertainty as one another. This is explained by the sand being homogenously mixed throughout the liquid phase in the slurry tank. However, an extra source of error is added to the sand rate and not to the liquid velocity. That extra source of error is from the balance used to measure the amount of sand added to the slurry tank in order to reach the desired sand concentration in the liquid phase. The liquid flow rate is found by repeatedly measuring the amount of time taken for the liquid level in the slurry tank to decrease one inch. The known volume per inch of the slurry tank is used along with the average measured time to calculate the volumetric flow rate.

Table 3.6.1 lists the uncertainties of the measurements and equipment for the

Boom Loop. The uncertainties in this study were found through one of several methods.

Most of the equipment manufacturers provided statistical analysis of their products and the reported uncertainties were transmitted to the table. Otherwise, the values were established either through numerical analysis or estimated based upon experience with the flow loop.

Table 3.6.1: Uncertainties in Boom Loop Measurements Boom Loop Component Uncertainty

Nominal Uncertainty % Source Units Level Uncertainty of Nominal

Balance grams 1000 15 1.5%

Liquid and Sand Rate GPM 44 8 18.2%

Gas Flow Meter Reading CFM 25 1 4.0%

Pressure Gage Psi 200 5 2.5%

141 The most significant of the columns in the table is the percent uncertainty of the nominal value on the right side. The percentage can help quantify the range of an actual value relative to a measurement. The table reveals that the liquid and sand rate contains the most error of all the Boom Loop measurements. The other uncertainties are nearly negligible in comparison. For example, a measured liquid rate of 44 GPM produces an average velocity of approximately 2.0 ft/s in a 3” diameter pipe. Due to the uncertainty in the measurement the actual average velocity must be in the range of 1.63 - 2.36 ft/s. At the same liquid rate of 44 GPM the sand rate will range from 22.3 – 33.3 g/s with a measured value of 27.8 g/s when using the combination of uncertainty in the sand rate and balance for a total of 19.7%. The superficial gas velocity will range from 93.5 –

106.5 ft/s for a nominal reading of 25 CFM or 100 ft/s in 3” pipe, when considering both sources of uncertainty in its measurement for a total of 6.5%.

Uncertainty Analysis of Erosion Measurements

The uncertainty of the ER probes used for data acquisition on the Boom Loop is an interesting yet difficult topic. Many factors are involved in the measurements that the probes generate. The probe measurements have fluctuations in their readings and are temperature dependant because the resistivity of the probe material changes with temperature. The temperature compensation required for the metal loss reading was discussed in the data acquisition procedure earlier. However, further analysis was conducted to determine the uncertainty in the ER probe metal loss prediction.

Every erosion rate prediction in the study required a metal loss reading from an

ER probe. Two points were selected from the probe output to establish a metal loss and be used with the total sand throughput to calculate an erosion rate. Three graphs have

142 been included to illustrate the uncertainty of the ER probe output. Graph 3.6.1 shows the entire angle-head probe output from test 16 where the metal loss is represented by the gray line and the prediction, overprediction, and underprediction are all marked in black lines on the graph. The predicted metal loss is the solid line, the overprediction is the dashed line, and the underprediction is the dotted line. The total metal loss of the probe is on the vertical axis in units of [µm], and the horizontal axis is the time scale in units of

[s].

Electrical Resistance Probe Output Angle-Head Probe from Test #16

1.557E+02

1.556E+02

1.555E+02 Metal Loss Predicted m] μ

[ Over Prediction Under Prediction 1.554E+02 TotalMetal LossProbe of

1.553E+02

1.552E+02 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Time [s]

Graph 3.6.1: ER Probe Output with Total Metal Loss Predictions

The predicted metal loss has already been temperature compensated and the slope of the metal loss prediction does not follow the actual slope of the measured metal loss.

Graph 3.6.2 and Graph 3.6.3 are shown next, because the scale of Graph 3.6.1 increases the difficulty of comprehending the predictions. Graph 3.6.2 shows the initial metal loss predictions for test 16, and Graph 3.6.3 demonstrates the final metal loss predictions.

143 Note that the initial underprediction is at a local maximum and the final underprediction is at a local minimum. The overprediction is taken in the same manner except it uses opposite local extremes at the initial and final locations. The nominal prediction lies between the two other approaches, and it is the value that was used for the erosion rate calculation.

Electrical Resistance Probe Output Angle-Head Probe from Test #16

1.5532E+02

1.5531E+02

Metal Loss Predicted m] 1.5530E+02 μ

[ Over Prediction Under Prediction Total Metal Lossof Probe 1.5529E+02

1.5528E+02 2500 2550 2600 2650 2700 2750 2800 2850 2900 2950 3000 Time [s]

Graph 3.6.2: ER Probe Output with Initial Metal Loss Predictions

144 Electrical Resistance Probe Output Angle-Head Probe from Test #16

1.5556E+02

1.5555E+02

Metal Loss Predicted m] μ

[ Over Prediction Under Prediction

1.5554E+02 Total Metal Loss of Probe of Loss Metal Total

1.5553E+02 8250 8350 8450 8550 8650 8750 Time [s]

Graph 3.6.3: ER Probe Output with Final Metal Loss Predictions

The process was repeated for many of the ER probe outputs. It was observed that the ER probe erosion rate measurement uncertainty varied greatly over the range of test conditions and is a strong function of the magnitude of metal loss that occurs during an experiment. The angle-head probe and flat-head probes both exhibited approximately the same percent difference in the measurement for the same magnitude of metal loss. Note that the angle-head probe in the straight section is generally submitted to higher metal loss rates compared to the flat-head probes in the elbow. Consequentially, the angle-head probe output is a more precise measurement in comparison to the elbow probes.

Table 3.6.2 contains results of the analysis and presents the uncertainties as a percent difference between the nominal predicted metal loss and either the overprediction or underprediction of metal loss. The percent differences were gathered for both probe types at their maximum, minimum, and approximately median metal loss magnitudes.

145 Table 3.6.2: Electrical Resistance Probe Measurement Uncertainties

ER Probe Measurement Uncertainty

Experimental Predicted Over Under Measurements Probe Type Metal Loss Prediction % Difference Prediction % Difference [nm] [nm] [%] [nm] [%]

Angle-Head 17832 18099 1.5% 17571 1.5% Maximum Metal Loss Flat-Head 1034 1051 1.6% 996 3.7%

Angle-Head 246 260 5.5% 229 7.2% Median Metal Loss Flat-Head 332 353 6.1% 311 6.5%

Angle-Head 61 117 63% 13 130% Minimum Metal Loss Flat-Head 24 43 57% 3 156%

The amount of uncertainty in the metal loss predictions varied with the magnitude of metal loss yet both probe types yield roughly the same percent difference as one another under similar metal loss quantities. The information presented in Table 3.6.2 is shown graphically on Graph 3.6.4 along with an incorporated trend line of the results.

The equation of the trend and the trend to data correlation are included on the graph. The equation can help describe the uncertainty of an ER probe measurement using only the total metal loss recorded during an experiment.

146 ER Probe Measurement Uncertainty Uncertainty vs. Metal Loss

160%

140%

120% y = 41.83x-1.09 100% R² = 0.883

80% [%]

60% Percent Difference Percent 40%

20%

0% 0 200 400 600 800 1000 1200 Metal Loss [nm]

Graph 3.6.4: Probe Measurement Percent Difference as a Function of Metal Loss

The graph portrays the significance that metal loss has on the uncertainty of the measurements. The trend of exponentially decreasing percent difference is seen as the total metal loss increases for each experimental condition. The data suggests that a minimum of 200 nm metal loss should be subjected to an ER probe to obtain proper predictions of the measured metal loss. It was found that the measurement contains less than 10% difference of the nominal value if the 200 nm metal loss threshhold has been met.

Uncertainty Analysis of Erosion Predictions

The two areas of uncertainty involved with the 2-D SPPS slug flow erosion predictions relate to the experimental data collection and CFD simulations. The experimental erosion results collected from the Boom Loop were used to develop, verify,

147 and validate the modeling results. Therefore, the uncertainties of the Boom Loop flow conditions have a direct connection to the uncertainty of the 2-D erosion model predictions. The 2-D particle tracking accounts for the effect of turbulence in the particle trajectory simulations, and turbulence affects every simulation different from the next.

This ultimately results in minor discrepancies of calculated erosion values for identical flow conditions. In other words, the same flow condition inputs do not produce the same exact outputs for the 2-D model.

The 20 µm particles are affected to a greater extent by turbulence in the 2-D particle tracking simulations in comparison to the larger particle diameters. Therefore, the silica flour can be considered to contain the highest turbulence error of all particle diameters. Table 3.6.3 contains the maximum percent error of the erosion rate caused by the effect of turbulence in the simulations for the 20 µm particle experiments. The average erosion rate of the 2-D model predictions are calculated over a total of 6 runs for each case. The maximum value of each case is used to determine the maximum percent error from the average calculated rate.

148 Table 3.6.3: Error in 2-D Model Predictions Caused by Turbulence

Maximum Test Average of Maximum Runs of Each Case Error of Number All Runs of All Runs Each Case [#]123456[mil/lb] [mil/lb] [%] 73.51E‐04 4.65E‐04 2.43E‐04 3.13E‐04 3.33E‐04 2.54E‐04 3.27E‐04 4.65E‐04 42.5% 81.81E‐04 1.67E‐04 1.81E‐04 1.22E‐04 1.23E‐04 1.63E‐04 1.56E‐04 1.81E‐04 16.1% 91.85E‐04 3.37E‐04 2.47E‐04 1.93E‐04 4.11E‐04 3.92E‐04 2.94E‐04 4.11E‐04 39.9% 10 3.81E‐04 6.37E‐04 9.22E‐04 5.75E‐04 4.43E‐04 5.10E‐04 5.78E‐04 9.22E‐04 59.5% 11 7.77E‐05 1.22E‐04 9.39E‐05 1.02E‐04 1.51E‐04 1.17E‐04 1.11E‐04 1.51E‐04 36.7% 12 1.01E‐03 1.68E‐03 1.22E‐03 9.34E‐04 7.99E‐04 1.20E‐03 1.14E‐03 1.68E‐03 47.6% 13 1.23E‐03 7.71E‐04 1.11E‐03 8.65E‐04 2.23E‐03 1.71E‐03 1.32E‐03 2.23E‐03 68.9% 14 1.26E‐03 5.43E‐04 7.84E‐04 7.37E‐04 5.92E‐04 6.63E‐04 7.64E‐04 1.26E‐03 65.3% 16 1.47E‐04 8.89E‐05 1.68E‐04 2.00E‐04 2.01E‐04 2.40E‐04 1.74E‐04 2.40E‐04 37.7% 17 5.28E‐04 9.85E‐04 6.81E‐04 4.72E‐04 4.28E‐04 5.37E‐04 6.05E‐04 9.85E‐04 62.7% 18 1.01E‐04 1.29E‐04 8.12E‐05 2.28E‐04 1.70E‐04 1.45E‐04 1.42E‐04 2.28E‐04 60.1% 19 2.69E‐04 6.23E‐04 3.26E‐04 5.84E‐04 3.99E‐04 7.76E‐04 4.96E‐04 7.76E‐04 56.3% 20 3.16E‐04 5.20E‐04 6.72E‐04 2.81E‐04 2.75E‐04 4.98E‐04 4.27E‐04 6.72E‐04 57.4% 21 3.82E‐04 4.24E‐04 2.42E‐04 2.69E‐04 3.79E‐04 3.01E‐04 3.33E‐04 4.24E‐04 27.5% 22 8.37E‐04 1.11E‐03 1.08E‐03 1.49E‐03 1.34E‐03 1.81E‐03 1.28E‐03 1.81E‐03 42.0% 23 1.62E‐03 7.83E‐04 1.21E‐03 1.54E‐03 1.33E‐03 2.71E‐03 1.53E‐03 2.71E‐03 76.6% 24 1.24E‐03 4.37E‐04 7.62E‐04 9.63E‐04 7.11E‐04 8.14E‐04 8.21E‐04 1.24E‐03 51.0% 25 1.42E‐03 1.20E‐03 2.35E‐03 1.19E‐03 2.03E‐03 1.77E‐03 1.66E‐03 2.35E‐03 41.7% 27 1.05E‐04 1.72E‐04 2.09E‐04 2.37E‐04 3.34E‐04 1.59E‐04 2.03E‐04 3.34E‐04 65.1% 28 1.36E‐03 5.15E‐04 8.76E‐04 6.97E‐04 1.12E‐03 1.11E‐03 9.45E‐04 1.36E‐03 43.7% 29 2.25E‐04 1.24E‐04 2.12E‐04 8.25E‐05 1.97E‐04 1.92E‐04 1.72E‐04 2.25E‐04 30.8% 30 5.91E‐04 1.53E‐03 6.73E‐04 1.19E‐03 9.35E‐04 7.25E‐04 9.41E‐04 1.53E‐03 62.2% 31 2.14E‐03 3.50E‐03 1.84E‐03 2.22E‐03 1.92E‐03 1.85E‐03 2.25E‐03 3.50E‐03 55.8% 32 2.42E‐03 2.49E‐03 3.42E‐03 2.08E‐03 1.82E‐03 2.50E‐03 2.46E‐03 3.42E‐03 39.5% 33 4.52E‐04 4.70E‐04 5.53E‐04 4.32E‐04 3.21E‐04 4.71E‐04 4.50E‐04 5.53E‐04 23.0% 34 1.75E‐03 2.10E‐03 1.33E‐03 1.25E‐03 7.92E‐04 1.66E‐03 1.48E‐03 2.10E‐03 42.1% 35 4.94E‐04 6.96E‐04 9.70E‐04 6.21E‐04 5.01E‐04 4.64E‐04 6.24E‐04 9.70E‐04 55.4% 36 3.11E‐03 1.99E‐03 1.24E‐03 1.58E‐03 2.00E‐03 9.38E‐04 1.81E‐03 3.11E‐03 72.0% 43 2.85E‐04 2.81E‐04 3.27E‐04 3.90E‐04 1.59E‐04 3.02E‐04 2.91E‐04 3.90E‐04 34.3% 44 6.66E‐04 8.06E‐04 3.67E‐04 8.94E‐04 5.73E‐04 7.50E‐04 6.76E‐04 8.94E‐04 32.3%

The propagation of uncertainty can be used to determine the overall uncertainty associated with the erosion predictions of the 2-D slug flow model. The error involved with the liquid velocity, gas velocity, and sand size distribution are considered to be the dominating factors in the erosion calculations. The most prevalent sand size utilized in the test matrix of this study was the 20 µm silica flour, and therefore the uncertainty in sand size distribution will be explored for this sand type only. Figure 3.6.1 displays the

149 sand size distribution of the silica flour that results in a 95% confidence interval of 0 - 58

µm for an uncertainty in particle diameter of 190%.

Figure 3.6.1: Sand Size Distribution for 20 μm Silica Flour

Equation (3.6.2) can be further modified to determine the change in calculated erosion ratio for the change in each particular flow condition. Equation (3.6.3) has been applied to the superficial liquid velocity, Equation (3.6.4) to the superficial gas velocity, and Equation (3.6.5) to the sand size.

∂f ∂(ER) ux1 = uvsl (3.6.3) ∂x1 ∂()vsl

∂f ∂(ER) ux2 = uvsg (3.6.4) ∂x2 ∂()vsg

∂f ∂(ER) ux3 = udp (3.6.5) ∂x3 ∂()d p

Table 3.6.4 contains the numerical influences of uncertainty on the predicted erosion rates caused by the aforementioned experimental conditions and calculated through the use of the above equations. This was accomplished by using the errors in flow condition measurements of the Boom Loop found in Table 3.6.1, and only changing a single parameter value for each SPPS simulation to determine the corresponding effects

150 on the modeled erosion predictions. The total uncertainty is found by summing the differences in erosion rates caused by the changes in superficial liquid velocity,

superficial gas velocity, and sand size.

Table 3.6.4: Uncertainties in 2-D Model Predictions for 20 µm Particles

Avg. Calculated Calculated Calculated Test Total Calculated with +18.2% with +6.5% with 58 µm Number Uncertainty Erosion Rate Vsl Vsg Particles [#] [mil/lb] [mil/lb] [mil/lb] [mil/lb] [mil/lb] 7 3.27E‐04 2.36E‐04 3.76E‐04 4.34E‐04 2.47E‐04 8 1.56E‐04 9.34E‐05 1.48E‐04 1.35E‐04 9.15E‐05 9 2.94E‐04 3.56E‐04 2.87E‐04 2.96E‐04 7.18E‐05 10 5.78E‐04 4.16E‐04 4.35E‐04 4.30E‐04 4.53E‐04 11 1.11E‐04 1.12E‐04 9.68E‐05 7.93E‐05 4.70E‐05 12 1.14E‐03 9.24E‐04 1.15E‐03 8.97E‐04 4.71E‐04 13 1.32E‐03 9.58E‐04 7.99E‐04 1.48E‐03 1.05E‐03 14 7.64E‐04 7.44E‐04 6.42E‐04 6.03E‐04 3.02E‐04 16 1.74E‐04 1.65E‐04 2.65E‐04 1.36E‐04 1.38E‐04 17 6.05E‐04 4.94E‐04 7.23E‐04 4.12E‐04 4.22E‐04 18 1.42E‐04 1.37E‐04 2.06E‐04 9.97E‐05 1.12E‐04 19 7.01E‐04 5.02E‐04 6.21E‐04 5.59E‐04 4.21E‐04 20 4.27E‐04 4.08E‐04 3.88E‐04 2.70E‐04 2.15E‐04 21 3.33E‐04 2.38E‐04 5.56E‐04 2.62E‐04 3.88E‐04 22 1.28E‐03 6.56E‐04 6.55E‐04 1.74E‐03 1.71E‐03 23 1.53E‐03 7.49E‐04 1.52E‐03 1.22E‐03 1.11E‐03 24 8.21E‐04 1.18E‐03 1.22E‐03 1.07E‐03 9.99E‐04 25 1.66E‐03 1.06E‐03 1.16E‐03 9.42E‐04 1.82E‐03 27 2.03E‐04 1.97E‐04 2.05E‐04 2.00E‐04 1.05E‐05 28 9.45E‐04 1.24E‐03 1.52E‐03 5.55E‐04 1.26E‐03 29 1.72E‐04 1.90E‐04 2.37E‐04 2.18E‐04 1.29E‐04 30 9.41E‐04 9.13E‐04 7.72E‐04 1.04E‐03 2.98E‐04 31 2.25E‐03 2.95E‐03 1.57E‐03 1.91E‐03 1.72E‐03 32 2.46E‐03 1.32E‐03 3.74E‐03 2.79E‐03 2.75E‐03 33 4.50E‐04 6.64E‐04 4.90E‐04 6.50E‐04 4.54E‐04 34 1.48E‐03 2.45E‐03 1.32E‐03 9.16E‐04 1.70E‐03 35 6.24E‐04 4.73E‐04 1.02E‐03 6.17E‐04 5.59E‐04 36 1.81E‐03 1.83E‐03 1.97E‐03 1.10E‐03 8.89E‐04 43 2.91E‐04 3.83E‐04 4.02E‐04 1.39E‐04 3.56E‐04 44 6.76E‐04 6.37E‐04 7.80E‐04 7.84E‐04 2.52E‐04

151 Table 3.6.5 contains the percent uncertainty in predicted erosion rates for the 2-D angle-head slug flow model for the 20 µm particle experiments. The overall total uncertainty is the summation of each individual flow condition uncertainty. The overall

RMS uncertainty is calculated by Equation (3.6.2).

Table 3.6.5: Percent Uncertainties in 2-D Model Predictions for 20 µm Particles

Uncertainty Uncertainty Uncertainty Test Overall Total Overall RMS with +18.2% with +6.5% with 58 µm Number Uncertainty Uncertainty Vsl Vsg Particles [#] [%] [%] [%] [%] [%] 7 ‐27.7% 15.1% 32.9% 75.8% 45.6% 8 ‐40.1% ‐5.3% ‐13.3% 58.7% 42.6% 9 21.1% ‐2.6% 0.7% 24.4% 21.3% 10 ‐28.1% ‐24.7% ‐25.6% 78.4% 45.3% 11 1.5% ‐12.6% ‐28.3% 42.5% 31.1% 12 ‐18.9% 1.1% ‐21.3% 41.3% 28.5% 13 ‐27.5% ‐39.5% 12.4% 79.4% 49.7% 14 ‐2.6% ‐15.9% ‐21.1% 39.6% 26.5% 16 ‐5.1% 52.3% ‐22.0% 79.3% 57.0% 17 ‐18.3% 19.5% ‐31.9% 69.7% 41.6% 18 ‐3.4% 45.2% ‐29.9% 78.5% 54.3% 19 ‐28.4% ‐11.4% ‐20.3% 60.1% 36.7% 20 ‐4.4% ‐9.2% ‐36.7% 50.3% 38.1% 21 ‐28.4% 67.0% ‐21.2% 116.6% 75.8% 22 ‐48.7% ‐48.7% 36.3% 133.8% 77.9% 23 ‐51.2% ‐1.1% ‐20.2% 72.5% 55.1% 24 43.3% 48.1% 30.3% 121.7% 71.4% 25 ‐36.4% ‐30.3% ‐43.3% 109.9% 64.1% 27 ‐2.8% 1.0% ‐1.5% 5.2% 3.3% 28 31.2% 60.8% ‐41.2% 133.2% 79.8% 29 10.4% 37.8% 26.6% 74.9% 47.4% 30 ‐2.9% ‐17.9% 10.9% 31.7% 21.2% 31 31.3% ‐29.9% ‐15.1% 76.4% 45.9% 32 ‐46.3% 52.2% 13.4% 111.9% 71.0% 33 47.5% 9.0% 44.5% 101.0% 65.7% 34 65.8% ‐10.8% ‐38.1% 114.6% 76.8% 35 ‐24.3% 64.1% ‐1.2% 89.6% 68.6% 36 1.1% 8.8% ‐39.2% 49.2% 40.2% 43 31.8% 38.3% ‐52.3% 122.4% 72.2% 44 ‐5.8% 15.5% 16.0% 37.3% 23.0%

152

CHAPTER 4

SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS

In this study, experimental data of erosion was collected in the slug flow regime, including the slug to annular transition, in order to compare the erosion predictions of the slug flow models in Sand Production Pipe Saver or SPPS to experimentation. The erosion data was gathered for varying flow conditions from a total of three locations in the flow loop. Several different conditions were varied in order to gain a firm understanding as to the effects of superficial velocities, viscosity, and sand size. The superficial liquid velocities ranged from 1.5 – 2.5 ft/s nominally as well as the superficial gas velocities that ranged from 50 – 150 ft/s. The liquid viscosities studied were 1 cP, 10 cP, and 40 cP.

The average sand particle diameters used were 20 µm and 300 µm. The multi-phase

Boom Loop was to collect the erosion measurements. Two flat-head probes were located in an elbow and an intrusive angle-head probe was located in a straight section of pipe.

The objectives of this study were to collect erosion data under a wide range of flow conditions and then compare the results to the slug flow models in SPPS. The flow conditions included the slug and annular regimes but focused primarily on slug flow. The experimental erosion data was first used to validate the penetration rate predictions of

SPPS. The experimental data was then used to further improve the erosion predictions of

153 the slug flow models in SPPS. A review of the model performance comparing the experimental erosion with the predicted erosion presented the next step of model improvement, increasing accuracy of small particle erosion.

Every aspect of this study helped contribute to the conclusions drawn and overall knowledge gained. First, a brief general description of each flow component effect will be mentioned from the corresponding measured erosion trends. The conclusions associated with the experimentation of this study are listed below.

• Increasing the superficial liquid velocity while operating in the slug flow regime

decreases the magnitude of erosion for all of the probe locations.

• Increasing the superficial gas velocity while operating in the slug flow regime

increases the magnitude of erosion witnessed in the flow loop.

• The effect of superficial gas velocity is more substantial than the effect of

superficial liquid velocity.

• In most cases, increasing the liquid viscosity while operating in the slug flow

regime decreases the magnitude of erosion in the experimental test sections.

However, the effect of liquid viscosity is more predominate at relatively lower

superficial liquid and gas velocities.

• Increasing the sand size and/or sand particle sharpness results in increased

measured erosion rates throughout the flow loop.

• The intrusive angle-head probe consistently witnessed more erosion than the flat-

head probes in the elbow due to the local flow characteristics around the angle-

head probe. Therefore, the angle-head probe is assumed to measure the maximum

possible erosion of the system.

154 • All of the probe locations can be correlated to one another to a relatively

reasonable degree of accuracy. The most significant correlation of which can

estimate the magnitude of erosion imparted in an elbow through the use of an

angle-head probe measurement in a straight section.

• A minimum of 200 nm metal loss should be subjected to each ER probe to

maintain a measurement uncertainty of less than 10%.

The content contained alone in the experimental results of erosion is enough to conclude many things, but the focus of this study is geared more towards the slug flow models and their performance and improvement. The conclusions associated with the 1-D mechanistic slug flow modeling of this study are listed below.

• SPPS contains two 1-D models that are specific to slug flow and mechanistic in

nature. The two models are for an angle-head probe in a straight section and for

flat-head probes in an elbow.

• The stagnation length concept is used to determine the characteristic particle

impact velocity. The stagnation length is the length the particle must travel

through the fluid before impacting the wall, while the particle velocity is

constantly decreasing. The longer the stagnation length is, the lower the impact

velocity will be.

• The mixture properties used for the stagnation length concept are the liquid slug

body properties opposed to the entire slug unit properties. Not only does this

improve the erosion predictions, but it also helps to maintain the mechanistic

nature of the models.

155 • The stagnation length distribution is used to determine the particle impact

velocities over the entire liquid slug. The stagnation length distribution accounts

for the varying impact velocities caused by the difference in stagnation length

throughout the slug body. A particle at the front of the slug body will have a

shorter stagnation length and therefore a higher impact velocity compared to a

particle at the rear of the slug body. There are a total of 500 stagnation lengths

where the first 499 particle impacts represent the slug front contribution to

erosion, and the 500th particle impact symbolizes the slug tail contribution.

• 1-D particle tracking is used along with the stagnation length concept in the 1-D

slug flow models. 1-D particle tracking provides sufficient results for cases with

large sand particles. 1-D particle tracking does not adequately capture the impact

velocities for small particles. This is caused by the forced particle trajectory and

the viscous effects near the wall.

• The 1-D angle-head model successfully captures the general erosion trends seen

in the experimental data. However, the 1-D model is conservative and

overpredicts erosion rate magnitudes by an average factor of approximately 26.

The model captures the effects on erosion caused by varying viscosity and

superficial liquid and gas velocities. The angle-head model does not accurately

predict erosion magnitudes or trends for small particles.

• The 1-D elbow model is more successful than the 1-D angle-head model when

comparing their performance. The magnitudes and trends from the experimental

data are both captured by the elbow model. The 1-D elbow model is also

conservative, but it only overpredicts by a factor of approximately 3 over the

156 range of test conditions. Much like the 1-D angle-head model, the 1-D elbow

model suffers in capturing small particle erosion.

• The area where the 1-D model predictions are not as successful as the others is in

the variation of sand size at increased liquid viscosities. As sand size and viscosity

increase, the model predicts erosion increasing at a higher rate than the

experimental data suggests. Therefore, the discrepancy between the measured and

predicted erosion rates gets larger as sand size and viscosity increase.

The experimental results and 1-D models have been covered in depth and concluded to a satisfactory degree. Finally, the conclusions for the 2-D mechanistic slug flow model in SPPS can be reviewed

• SPPS now contains a 2-dimensional model for an angle-head ER probe in a

straight section that is mechanistic in nature and specific to slug flow. The model

employs a new erosion equation along with 2-D particle tracking in place of the

original 1-D approach to ultimately improve the accuracy and precision of the

SPPS erosion predictions. However, the developed slug flow mechanisms and

erosion assumptions from the 1-D model remain the same.

• The added degree of freedom associated with the 2-D particle tracking allows for

a radial velocity component in addition to the axial component in the flow field,

so the simulated particle trajectories are much more representative of actual

trajectories witnessed in experimentation.

• Contrasting from the 1-D modeling approach, the 2-D particle tracking is capable

of capturing the effects of carrier fluid turbulence and the resulting forces

157 imparted on entrained particles. The magnitude of the turbulence effect varies

with flow conditions and is generally too large to be considered negligible.

• The stagnation zone concept is used in unison with 2-D particle tracking to

determine particle impact characteristics such as the impact angle and impact

velocity. There are 50 particles within 50 particle groups for a total of 2500

particles arranged in the stagnation zone for each flow field simulation in order to

accurately depict impact information. The first 49 groups represent the slug front

contribution to erosion and the 50th group symbolizes the slug tail contribution.

• The 2-D model erosion ratio equation employs an angle function, a particle shape

coefficient, the Brinell hardness, and two empirical constants. The angle function

is for a corrosion resistance alloy, and was not utilized by the 1-D models.

• The error of the SPPS erosion predictions for the angle-head probe was

dramatically improved for the 2-D model in comparison to the previous 1-D

model by a factor of 31. The erosion magnitudes were the most heavily affected

by the advancements, but the trends of erosion magnitudes were enhanced as well.

The 2-D SPPS angle-head model for slug flow has an overall average of 84%

error between the calculated and measured erosion rates over the entire spectrum

of experimental flow conditions and sand sizes.

As time and labor progressed throughout this research interesting topics were traversed that originally were not foreseen, while others were predicted before the study began. Unfortunately many subjects and questions were not addressed due to time constraints. To help improve the continuation of this topic for future research, several recommendations are listed below.

158 • Create a more robust erosion databank to further verify and validate the slug flow

models in SPPS by conducting more experiments under a wider range of slug and

annular flow conditions, but primarily focus on filling in the test matrix of this

study for the experimental conditions that relate to the 150 μm and 300 μm sand

sizes. Do not collect any more 20 μm erosion results until the other matrices have

been completed. Data acquisition should continue to concentrate in the elbow as

well as the straight section. Collect data for all three ER probe locations in the

flow loop: the probe at 45°, the probe at 90°, and the angle-head probe.

• Apply the new erosion equation and 2-D particle tracking technique to the SPPS

elbow model for slug flow. The advancements will be nearly identical to the

angle-head model, except they will use a different geometry in the CFD

simulations.

• Conduct a sensitivity analysis in the CFD mesh for the number of steps taken in

each cell for a given sand size. Smaller particles will require more steps per cell

than larger particles due to the effects of turbulence. Therefore, the CFD modeling

should be considered particle size dependant.

• Conduct a sensitivity analysis for the 2-D particle tracking in the slug flow

models. Vary the amount of particle groups and the number of particles in each

group to gain a firm understanding of their corresponding effect on impact

calculations. Also, determine a median between the accuracy of erosion

predictions and the computational time required to complete them.

159

NOMENCLATURE

q = total volumetric flow rate

qL = liquid volumetric flow rate

qG = gas volumetric flow rate

vSL = superficial liquid velocity

vSG = superficial gas velocity

AP = cross-sectional area of the pipe

vM = mixture velocity

H L = liquid holdup

α = gas void fraction

H L = space and time average of the instantaneous liquid holdup

H L ()r,t = differential volume element of holdup in space and time r = point in space t = point in time

vL = actual liquid velocity

AL = cross-sectional area occupied by liquid fraction

vG = actual gas velocity

AG = cross-sectional area occupied by gas fraction

vSLIP = slip velocity

160 λL = no-slip liquid holdup

vDL = liquid drift velocity

vDG = gas drift velocity

ρM = mixture density

ρL = liquid density

ρG = gas density

μM = mixture dynamic viscosity

μL = liquid dynamic viscosity

μG = gas dynamic viscosity

H LF = liquid holdup in the liquid film

LS = length of the liquid slug

VT = translational velocity

VF = liquid film velocity

Ve = erosional velocity limit, [ft/s]

C = system constant

3 ρ = density of carrier fluid [lbm/ft ] h = penetration rate, [mm/yr]

FM = empirical constant related to material properties

FS = empirical sand sharpness factor

FP = penetration factor for steel based on 1” pipe diameter, [mm/kg]

Fr / D = penetration factor for long radius elbows

161 W = sand production rate, [kg/s]

VL = characteristic particle impact velocity, [m/s]

D = pipe diameter, [any length unit]

Do = reference 1 inch pipe diameter, [same length unit used for D] e = exponent typically determined experimentally

Fr / D = penetration factor for long radius elbows

3 ρ f = fluid density [kg/m ]

μ f = fluid viscosity [Pa/s]

d p = particle diameter [m]

Cstd = r/D ratio of a standard elbow (generally assumed to be 1.5)

L = equivalent stagnation length

Lo = reference stagnation length for 1” pipe

D = pipe diameter

R = element resistance

ρ = resistivity of the element material

L = length of the element

A = cross-sectional area of the element

A1 = cross-sectional area of pipe

A2 = reduced cross-sectional area of pipe at intrusive probe

d probe = probe diameter h = height to the center of the probe face

162 hface = height from the center to the outer edge of the probe face

V1 = average global velocity in pipe

V2 = average local velocity at intrusive probe

FD = force of drag

FP = force of pressure gradient

FB = buoyant force

FA = added mass force

VP = particle velocity

V f = fluid phase velocity

ρd = density of particle

d P = diameter of particle

Rer = relative Reynolds number

CD = coefficient of drag

163

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167

APPENDIX A

EXPERIMENTAL CALCULATIONS

There are four primary calculations associated with the data acquisition of this research. The first three are related to the measurement of experimental flow conditions, and they are needed to complete the final calculation of the measured erosion ratio. The three flow measurements required for the erosion ratio calculation include the superficial liquid velocity, the superficial gas velocity, and the total sand throughput.

The superficial liquid velocity, vsl in [ft/s], is calculated by measuring the

3 volumetric flow rate, Ql in [ft /s], exiting the slurry tank and dividing it by the cross-

2 sectional area of the pipe, Ap in [ft ], shown by Equation (A.1).

Ql vsl = (A.1) Ap

3 The liquid flow rate, Ql in [ft /s], is calculated by using the volume per inch

3 increment of the slurry tank, Vincrement in [ft /in], and the average time taken to discharge

an inch of liquid depth from the tank, taverage in [s/in], as seen in Equation (A.2).

Vincrement Ql = (A.2) taverage

Next the calculation of superficial gas velocity, vsg in [ft/s] shown by Equation

(A.3), is completed by beginning from the continuity equation and progressing through

168 the following equations. The gas mass flow rate, m& g in [lb/s], is needed and must be

3 found using the gas volumetric flow rate, Qg in [ft /s], and multiplying it by the gas

3 density, ρg in [lb/ft ], shown by Equation (A.4). It can be rewritten to solve for final conditions as shown by Equation (A.5).

Qg vsg = (A.3) Ap

m& g = Qg × ρg (A.4)

Q1 × ρ1 Q1 × ρ1 = Q2 × ρ2 or Q2 = (A.5) ρ2

The gas flow rate in the gas line is Q1 and the gas flow rate in the test section is

Q2 . The nomenclature theme continues where the subscript of 1 represents the conditions in the gas line and the subscript of 2 is for the test section conditions. The densities can be calculated through the use of the ideal gas law which is demonstrated by Equation

(A.6).

P1 P2 ρ1 = and ρ2 = (A.6) R ×T1 R ×T2

where R is the universal gas constant in [(ft*lbf)/( °R*lb-mol)], Px is the pressure in

2 3 [lb/ft ], ρx is the gas density in [lb/ft ], and Tx is the temperature in [°R].

Therefore, utilizing the continuity equation again, the superficial gas velocity, vsg in [ft/s], can be written as Equation (A.7) where the volumetric flow rate of the test

3 2 section, Q2 in [ft /s], is divided by, Ap in [ft ], the cross-sectional area of the pipe.

Q2 vsg = (A.7) Ap

169 The calculation is simplified for ease of use while conducting experiments, because the gas velocity is under constant observation and must be checked frequently.

The equation has added two factors for unit conversions of the Boom Loop measurement scales. The pressure read from the gage has to be converted to absolute pressure for the calculation, and the temperature is measured in °F and must be converted to the absolute

Rankine scale in °R. The final product for the gas velocity calculation is shown in

Equation (A.8).

Q1 × (P1 +14.7)× (T2 + 460) vsg = (A.8) Ap × ()()P2 +14.7 × T1 + 460

The last of the calculated experimental flow conditions that is needed for the erosion ratio is the total sand throughput during an experiment. The calculations begin with the continuity equation yet again, except now for the liquid phase. The liquid mass flow rate, m& l in [lb/s], is needed and must be found using the liquid volumetric flow rate,

3 3 Ql in [ft /s], and multiplying it by the liquid density, ρl in [lb/ft ], shown by Equation

(A.9).

m& l = Ql × ρl (A.9)

The mass flow rate of the sand, m& s in [lb/s], is calculated through the use of the

liquid mass flow rate, m& l in [lb/s], and the sand concentration is in units of [% concentration by weight or lb/lb]. The calculation is shown by Equation (A.10).

m& s = m& l ×Sand Concentration (A.10)

Once the mass flow rate of sand, m& s in [lb/s], has been determined the only

required variable left to introduce is the total sand run time, ts in [s], to calculate the total

170 sand throughput in units of [lb], shown by Equation (A.11). The total sand run time is the time that each test injected sand into the test section. The sand quantity results can be converted to any desired units after completion.

TotalSand Throughput = m& s × ts (A.11)

Finally, the erosion ratio calculation can commence after all the required variables were defined. The erosion ratio calculation is epitomized through Equation (A.12). The

ER probe metal loss is taken from the Cormon software and raw test data in units of

[nm], and the sand throughput was previously outlined.

ER Probe Metal Loss Erosion Ratio = (A.12) Total Sand Throughput

This study usually reported the sand rate in [g/s] so the total sand throughput had units of [g]. Therefore, the erosion ratio is in units of [nm/g], but the desired units were

[mil/lb]. Note that a mil is a thousandth of an inch. The last presented calculations are for that unit conversion and the resulting erosion ratio. The unit conversion is shown by

Equation (A.13).

⎡mil ⎤ ⎡nm⎤ ⎢ ⎥ ⇔ ⎢ ⎥ = ⎣ lb ⎦ ⎣ g ⎦ (A.13) ⎛ ML ⎡nm⎤⎞ ⎛ 1 ⎡ m ⎤⎞ ⎛ 39.37 ⎡in⎤⎞ ⎛1000 ⎡mil ⎤⎞ ⎛ 453.59 ⎡ g ⎤⎞ = ⎜ ⎟ × ⎜ ⎟ × ⎜ ⎟ × ⎜ ⎟ × ⎜ ⎟ ⎜ ⎢ ⎥⎟ ⎜ 9 ⎢ ⎥⎟ ⎜ ⎢ ⎥⎟ ⎜ ⎢ ⎥⎟ ⎜ ⎢ ⎥⎟ ⎝ TST ⎣ g ⎦⎠ ⎝10 ⎣nm⎦⎠ ⎝ 1 ⎣m⎦⎠ ⎝ 1 ⎣ in ⎦⎠ ⎝ 1 ⎣lb⎦⎠ 1424444444 434444444 1424 434 [][]nm ⇔ mil []g ⇔ [lb ]

The converted erosion ratio is shown by Equation (A.14). It can be used when the metal loss is collected in [nm] and the sand throughput is reported in [g] to achieve the desired ratio of [mil/lb].

171 ER Probe Metal Loss ⎡nm⎤ ⎡ g mil ⎤ ErosionRatio = ⎢ ⎥ × 0.017858⎢ ⎥ (A.14) Total Sand Throughput ⎣ g ⎦ ⎣lb nm ⎦

172

APPENDIX B

STANDARD OPERATING PROCEDURE OF THE BOOM LOOP

B.1 Preliminary Setup

The preliminary setup of the system must be attained before the system startup is initiated and an experiment is run. This includes proper arrangement of valves, installation of the drain line, preparation of the liquid slurry solution, filling the compressors with diesel, and allowing the compressors to warm up.

Begin by approaching the system and assessing the valve arrangement. Make sure all flow valves supplying the gas and liquid flow to the test section are closed. There are four primary valves that allow flow through the test section. Two valves are for the gas flow and two valves are for the liquid flow. The two valves for the gas flow are located on the West wall inside of the Boom Loop shed, just downstream of the electronic gas flow meters and compressors. The gas flow to the flow meters is supplied from the two beige Ingersoll Rand 400 scfm compressors. The two valves for the liquid flow are found just above the diaphragm pumps. There are two valves in each cluster. The circular type globe valves adjust the gas supplied to the pump to ultimately control liquid flow rate.

The lever type gate valves are used to turn the flow on and off. This is done to be able to achieve the same flow rate while intermittently starting and stopping the flow if needed.

The gas flow to the liquid pumps is supplied by the white Caterpillar 375 scfm

173 compressor. Once all the valves are known to be closed, the compressors are ready to be started and allowed to warm up.

The compressors need to be full of fuel for each test. It is important not to let the compressors run out of fuel. The consequences could be considered catastrophic if the fuel is completely depleted. To begin fueling the compressors, the air supply hose must be connected to the house air (electric compressor) inside the shed in the SW corner. Go to the fuel storage and open it. There is a small pneumatic pump that pumps the fuel from the drums in the storage container to the tanks of the compressors. Unscrew the lid of the drum and place the suction side of the pump in the drum. Open the door of the compressor that needs to be filled then open the cap on the fuel tank. Place the nozzle from the fuel pump into the compressor fuel tank. Attach the air hose to the pump and open the valve. The pump may prime itself if the liquid level in the fuel drum is high enough, otherwise you must prime the pump yourself. To do so, use the suction nozzle in the storage area along with the air supply hose to draw the fuel up into the pump. Once the pump is primed, fueling the compressor can begin.

The drain line for the loop must be installed for running tests. It is crucial to draining and rinsing the system. The drain exit is located on the West wall outside the

Boom Loop shed. The drain hose is coiled up on the ground on the SW corner of the shed. Attach one end of the hose to the drain exit of the system, and the other end is placed in the sump roughly 60 feet south of the SW corner of the shed. The drain hose is to be properly wound and put away after each test.

Many precautions can be made to ensure safe testing and proper use of the equipment without any failures. The most important precaution involves the awareness of

174 the researcher. Let your senses guide you. Sight, sound, and smell can be great indications of what is happening around you. If something doesn’t look, sound, or smell right, chances are that it is not right. Also note that any changes in these, while the loop is running at steady state conditions, are also good indications that something is not right.

Other miscellaneous precautionary measures include the following. Avoid quickly opening any valve, especially for the gas flow from the compressors since their outlet pressure is approximately 200 psi. Always monitor the liquid level in the slurry tank, especially when the mixer is running. If the liquid level gets too low, the mixing rod will become unbalanced while it rotates and quickly shear of at the coupling. This is dangerous for the researcher and the system. Always wear protection! Ear and eye protection are required while running the Boom Loop. If there is a question don’t be afraid to ask.

B.2 Data Acquisition

There are two primary modes of data acquisition for the Boom Loop. Electrical

Resistance probes produced by Cormon and Acoustic Monitors produced by Clampon.

This section explains their procedure when used on the Boom Loop. There are two laptops used for the Boom Loop. One laptop is for ER probe data acquisition and another is used for acoustic monitor data acquisition. There are a total of three ER probes and one acoustic monitor. The acoustic monitor and two flat-head probes are located in an elbow and the angle-head probe is located in a straight section.

Cormon Instructions: Prepare the ER probes for data acquisition by making sure that the probes are installed in the test sections. A wiring diagram for the subsequent

175 steps is found on Figure 2.3.1. Connect each ER probe to the corresponding transmitter unit and then attach each transmitter unit to the wire harness box at the end of the boom.

These connections relay back to the IS barriers in the shed that are already connected to a power source. The wires in the shed are numbered and the boxes should be labeled for future use. The wiring scheme is shown below for all the required connections.

Table B.1: Boom Loop Wiring Scheme

Wire Probe Com Port on PC 15 Angle-Head Com 1 (serial) 14 Probe @ 45° Com 6 13 Probe @ 90° Com 7

Start up the laptop. The Boom Loop laptop password is [praneeth]. Once the probes are setup and the laptop is running, the power can be turned on to the probes. This is done by pushing the switch on the DAQ box up to the on position. Note that this switch also powers the flow meters. The DAQ box is on the East wall inside the shed.

Open the hyper-terminal from the desktop to check connection to boxes and probes. The desired Com port can be selected to view the raw ER probe output data. If the temperature needs to be changed, open the coefficient notepad for the particular probe to get the proper coefficients. Shown below is an example of an ER probe coefficient.

The coefficients vary from probe to probe. Each coefficient represents an important piece of the internal calculations occurring, but only two of them are of concern and need to be adjusted for E/CRC purposes. Those two coefficients include the temperature and averaging coefficients.

176 C000000:0000:000:0000:00000:000: 1 2

1.) Temperature Coefficient 2.) Averaging Coefficient

Figure B.1: ER Probe Coefficient String

When using an ER probe with a new box or a different box, the box needs to be calibrated for that probe. Coefficients come with every probe, and all the coefficient data is located in Ed Bowers’ office at North Campus. The temperature coefficients can be adjusted by trial and error. Open the hyper terminal with the proper com port selected.

Be sure that it is receiving a signal. Check the temperature, which is the right-hand column of the output in the hyper terminal. The number has 4 digits. The last number is a decimal point, so a reading of 0543 would be 54.3 degrees C. To adjust the temperature reading, change the numbers marked by 1.). Increasing the value of the temperature coefficient will decrease the temperature reading, and oppositely, decreasing the value of will increase the temperature. The averaging or Rand Number has two settings that are used. The default value is 1000, but E/CRC changes the averaging coefficient to 0005.

Once the numbers have been changed in Notepad, copy the entire coefficient.

While the hyper terminal is connected and taking data, right click in the terminal and

Paste to Host. There will be a pause and then the coefficients will be displayed. At that moment disconnect the hyper terminal and unplug the DAQ from power until the light on the box fades away. Plug the box back into power and connect the hyper terminal. Check the temperature output and adjust using trial and error to get the correct temperature.

Once the temperature is correct, disconnect the hyper terminal and begin the Cormon software with the correct temperature and coefficients. Open Cormon software, but first

177 make sure that the hyper terminal is disconnected. In Cormon go to options Æ setup Æ select com port and then double click it to name it Æ turn averaging on to each point.

Sand Monitor Instructions: Prepare the monitor by fixing the chassis to the pipe just after the elbow. Apply the acoustic gel to the sensor of the monitor and screw it into the chassis without over tightening. Connect the wire that runs directly back to the shed to the transmitter unit. Connect the transmitter unit to the proper laptop to begin data acquisition. Start up the laptop then click on the Clampon sand monitor icon on the desktop. Double click the monitor that is green and says OK. Uncheck sand rate and velocity (only want RAW displayed). Go back to the other panel (with green OK) and click FileÆ Settings Æ Logging. Under sensor logs click the file tab then name and place the output where it is wanted. Make sure both boxes in the same panel under the prompt say 0. Click OK.

B.3 Liquid Slurry Solution

The preparation of the liquid solution contains two variables, which are the sand concentration and liquid viscosity. The sand concentration is measured as a percent by weight. The larger sands should only have a concentration of 0.5% in the slurry tank, but the smaller silica flour can be safely operated up to 1%. These limits ensure the safety of the liquid pumps and allow the particles to stay in suspension and not settle out to the bottom of the tank, although constant manual stirring is still required in addition to the mixer. This is true especially for the larger particles.

The sand concentration is determined by using the total mass of water in the slurry tank and then adding the correct amount of sand. The tank must be filled to at least

178 200 gallons for slug flow experiments. There is a worksheet in the Boom Loop workbook for calculating these values. Input the volume of water in the tank as marked on the side in gallons into the spreadsheet. Input the desired sand concentration and then the total amount of sand will be output. Use the balance to measure the weight of sand and then gradually pour it into the tank while the mixer is running. It is critical not to let the sand settle to the bottom, both for the safety of the pump and the accuracy of the sand concentration in the test section.

The liquid viscosity is increased by adding CMC and alcohol to the water in the slurry tank. There is another worksheet just for this task. Input the volume of water in gallons and the desired viscosity in cP. The amount of CMC and alcohol to be added will be output. Begin by mixing the CMC and alcohol with the mortar mixer drill in small batches in a 5 gallon bucket. After the concoction is thoroughly mixed, dump and spread the mixture out evenly at the bottom of the slurry tank. After all of the initial mixing is complete then fill the slurry tank with the total amount of water. Turn the mixer on after the liquid level has reached a safe operating height. Let the mixer run for some time until the liquid is homogenous. Use the viscometer from inside the lab to confirm the liquid viscosity. Minor adjustments may need to be made to the mixture. Increase the viscosity by adding more CMC. Decrease the viscosity by adding more water. Be sure to rinse and clean all tools used in the process.

B.4 Gas and Liquid Flow Rates

The gas and liquid volumetric flow rates are imperative to determining the proper superficial velocities of the system. A worksheet was created specifically for these

179 calculations. Open the Excel workbook called conversion sheet large loop. This sheet will output proper superficial gas velocities from the gas flow rate characteristics such as the initial and final temperatures and pressures. The sheet will also calculate the liquid flow rate from the average time taken for the slurry tank to discharge 1 inch of liquid.

The gas flow rate is always begun before the liquid flow rate. The superficial gas velocity is easier to obtain than the superficial liquid velocity, but it requires more inputs.

If the desired flow rate is larger than 12 CFM use the larger line and flow meter on bottom, but if it is less than12 CFM use the smaller line and flow meter on top. P1 and T1 are in the Southwest corner of the shed connected to the gas inlet. P2 is out on the return side of the boom, and T2 is ambient temperature. Note that these values change. The initial values change until the compressors have reached steady-state conditions. The final temperature can vary throughout the day. Read the volumetric gas flow rate in CFM off the flow meter and input the 5 variables into the spreadsheet to determine the Vsg in ft/s. Opening the valve increases the flow rate while closing the valve decreases the flow rate.

After the gas flow rate has been set, the liquid flow rate can be achieved. Flow meters cannot be used and the rate must be found manually. There is only one input needed to determine the Vsl, which is the average time for the liquid level to drop 1 inch inside the slurry tank. The average time is acquired by averaging a minimum of 5 time measurements for 1 inch of discharge. There is a ruler with 1 inch increments that is placed in the tank for the measurements. The measurements should be taken while the mixer is off and there is no fluid being pumped back into the tank. Input the split times

180 into the spreadsheet to find the flow rate in GPM. Input this flow rate for the proper pipe size to also determine the Vsl in ft/s.

B.5 System Shut Down and Emergency Shut Down

The two primary components involved with the shut down process are the gas and liquid flow rates. The startup procedure should be followed in reverse. The system shut down procedure begins with the liquid flow, then gas flow, and then the gas compressors.

Close the liquid flow valves at the liquid pumps followed by the gas flow valves near the gas flow meters, and then the gas compressors can be shut down. The electronics can then be powered down. The normal and emergency procedures are identical unless there is a fire at the compressors. If there is a fire, quickly shut down the gas and liquid flows and seek immediate help. Do not attempt to extinguish the fire.

B.6 System Clean Up

The only remaining task is to clean the system. There are two parts to this step, which are filtering the liquid slurry solution and rinsing the system. After the completion of the experiment and data acquisition, the sand must be filtered before draining the liquid through the drain hose to the sump. The small particles must be forcefully pumped through filter cartridges in the filter housing and out the drain line. Note that the flow should be adjusted so that the differential pressure does not exceed what is shown on the housing pressure gage. The larger particles can be gravity filtered through a filter bag

181 inside the other liquid tank. Note that the flow should be adjusted so that the liquid does not over flow out of the filter bag.

The final step is to rinse the system. This is especially crucial if CMC was used for the experiment. After the system has been drained, rinse the slurry tank until it is clean then begin to fill it back up with water. When the liquid level is sufficient in the slurry tank, pump the clean water through the system at relatively high rates until all of the liquid has been pumped from the tank. Drain all the tanks and lines through the drain hose and out to the sump. Return the drain hose to its original location and orientation for the next experiment.

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