UNIVERSITY OF CALGARY
An Investigation of Solids Deposition from Two-Phase Wax–Solvent–Water Mixtures
by
Adebola Sadiq Kasumu
A THESIS
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF CHEMICAL AND PETROLEUM ENGINEERING
CALGARY, ALBERTA
APRIL, 2014
© ADEBOLA S. KASUMU 2014
Abstract
This study presents an investigation of the thermophysical behaviour and deposition tendency of
“waxy” mixtures, with and without the addition of water as a liquid phase. In the first part, the
wax precipitation temperature (WPT) of several compositions of a multi-component waxy
mixture (comprising a multi-component paraffinic wax dissolved in a multi-component solvent)
was measured at controlled cooling rates. Results indicated that the WPT of a waxy mixture is
not a constant property, as it varied with the cooling rate. Experimental results were used to
express the WPT as a function of the cooling rate and mixture composition. With the WPT being
dependent on the cooling rate, it may not correspond to the thermodynamic liquidus temperature
for the liquid-to-solid phase transformation process.
The deposition of solids from single-phase and two-phase waxy mixtures (second phase
being water) was studied using two different experimental apparatuses. A flow-loop apparatus
was used to study the effects of water content, wax mixture and coolant temperatures, and flow
rate, in two-phase waxy mixtures flowing under turbulent flow conditions. A cold finger
apparatus was used to further investigate the effects of time and stirring rate on wax deposition in
single-phase waxy mixtures, and the effect of water content in two-phase waxy mixtures.
In both sets of experiments, the water content of the deposit was found to be not related
to the water content of the waxy mixture. The deposit mass (on a water-free basis) decreased
with an increase in Reynolds number, the mixture temperature, and/or the coolant temperature.
The deposit mass both increased and decreased with the water content of the waxy mixture,
depending on the deposition time. Results showed the solids deposition from waxy mixtures to
be a fast process; for example, 56% of the deposition process in the cold-finger experiments was
completed in 0.07% of the time to reach steady-state. The deposition data were analyzed with a
ii
steady-state heat-transfer model, which also indicated that the liquid–deposit interface
temperature was close to the wax appearance temperature (WAT) of the waxy mixture. The
predictions from a transient heat-transfer model, based on the moving boundary formulation,
matched satisfactorily the effect of time on the deposition process in the cold-finger experiments.
Overall, the results of this study confirm that the deposition process from waxy mixtures is a
relatively very fast process, and is primarily thermally-driven.
iii
Acknowledgements
I would like to express my sincere gratitude and appreciation to my thesis supervisor, Dr.
Anil K. Mehrotra, for giving me the opportunity to work on this project, and for his
understanding, mentorship, guidance, patience, support, and unflinching willingness to help in all
circumstances throughout the period of my program.
I want to thank Dr. Jalel Azaiez and Dr. Maen Husein for accepting to be on my
supervisory committee. I extend my sincere appreciation to Mr. Jean-Marc Labonté, Ms. Ligaya
Aguinaldo, Mr. George Nerier, Ms. Elaine Baydak, Mr. Paul Stanislav, Ms. Paige Deitsch, Mr.
Mike Grigg, Mr. Andrew Sutton, Mr. Brian Moerke and other departmental staff for their
assistance at various times during my program.
I would like to thank Mr. Sridhar Arumugam, Dr. Hamid Bidmus, Mr. Nelson Fong, Ms.
Samira Haj-Shafiei, Ms. Dalia Serafini, Dr. Nitin Bhat and Dr. Poornima Jayasinghe for their
helpful suggestions and informative discussions. I gratefully acknowledge the financial support
from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Centre
for Environmental Engineering Research and Education (CEERE), and the Department of
Chemical and Petroleum Engineering. I acknowledge the support from scholarships and awards,
including the Dean's Entrance Scholarship, the Queen Elizabeth II Doctoral Scholarship, FGS
Travel Award, the Department of Chemical and Petroleum Engineering Graduate Award, the
Pipeline Engineering Centre Graduate Scholarship, and the Teaching Assistant Excellence
Award.
Lastly, I want to thank members of my family, my father, mother, wife and three lovely
children for their prayers, selfless support, dedication, patience, love and encouragement, not
only during this program, but throughout my life. I couldn't have done it without you!
iv
Alhamdu lillahi rabbi alAAalameen (All praises and thanks be to Allah, the Lord of the worlds)
So, verily, with every difficulty, there is relief:
Verily, with every difficulty there is relief.
(Quran 94: 5 - 6)
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Table of Contents
Abstract ............................................................................................................................... ii
Acknowledgements............................................................................................................ iv
Table of Contents............................................................................................................... vi
List of Tables ..................................................................................................................... xi
List of Figures and Illustrations ........................................................................................ xii
List of Symbols, Abbreviations and Nomenclature......................................................... xvi
CHAPTER ONE: INTRODUCTION..................................................................................1
1.1 Introduction................................................................................................................1
1.2 Objectives and Scope of Study ..................................................................................5
CHAPTER TWO: LITERATURE REVIEW......................................................................9
2.1 Paraffin Waxes...........................................................................................................9
2.1.1 Classification .....................................................................................................9
2.1.2 Crystal Structure ..............................................................................................10
2.1.3 Physical and Thermal Properties .....................................................................11
2.1.3.1 Enthalpy of Fusion.................................................................................14
2.1.3.2 Heat Capacity.........................................................................................14
2.1.3.3 Thermal Conductivity ............................................................................15
2.2 Wax Precipitation ....................................................................................................17
2.2.1 Crystallization..................................................................................................18
2.2.1.1 Nucleation ..............................................................................................18
2.2.1.2 Crystal Growth.......................................................................................19
2.2.2 Wax Appearance Temperature (WAT) ...........................................................20
2.2.3 WAT Measurement Techniques......................................................................20
2.2.4 Wax Precipitation Temperature (WPT)...........................................................24
2.2.5 Wax Disappearance Temperature (WDT).......................................................24
2.2.6 Pour Point Temperature (PPT) ........................................................................25
2.2.7 Rheology..........................................................................................................25
2.3 Wax Deposition .......................................................................................................26
2.3.1 Mechanism of Wax Deposition .......................................................................27
2.3.1.1 Molecular Diffusion...............................................................................27
2.3.1.2 Heat Transfer .........................................................................................28
2.3.2 Structure of the Wax Deposits.........................................................................29
2.3.3 Factors Affecting Wax Deposition..................................................................30
2.3.3.1 Effect of Composition............................................................................30
2.3.3.2 Effect of Temperatures ..........................................................................32
2.3.3.3 Effect of Flow Rate and Shear Rate.......................................................33
2.3.3.4 Effect of Deposition Time and Aging....................................................35
2.3.3.5 Effect of Surface Properties ...................................................................36
2.3.3.6 Effect of Emulsion Characteristics ........................................................37
2.3.4 Experimental Techniques for Wax Deposition ...............................................38
2.3.4.1 Flow Loop Experiments.........................................................................39
2.3.4.2 Cold Spot or Finger................................................................................39
2.3.4.3 Draft Tube Assembly.............................................................................40
vi
2.3.4.4 Co-axial Shearing Cell...........................................................................40
2.3.5 Wax Deposition Modeling ..............................................................................40
2.4 Control and Remediation .........................................................................................43
2.4.1 Mechanical Methods .......................................................................................43
2.4.2 Thermal Methods.............................................................................................44
2.4.3 Chemical Method ............................................................................................45
2.4.4 Biological Methods .........................................................................................46
2.4.5 Cold Flow of "Waxy" Crude oils ....................................................................46
CHAPTER THREE: EXPERIMENTAL...........................................................................48
3.1 Materials ..................................................................................................................48
3.1.1 Paraffin Waxes ................................................................................................48
3.1.2 Solvents ...........................................................................................................49
3.1.3 Comparison of Compositions of Waxes and Solvents ....................................54
3.2 Wax–Solvent Mixtures ............................................................................................54
3.2.1 WPT Measurements ........................................................................................55
3.2.2 WAT, WDT and PPT Measurements ..............................................................56
3.3 WPT–Cooling Rate Experimental Apparatus..........................................................60
3.3.1 Heating Bath ....................................................................................................60
3.3.2 Cooling Bath....................................................................................................60
3.3.3 Cooling Rate Controller ..................................................................................60
3.3.4 Copper Pour Point Tubes.................................................................................62
3.3.5 Underwater Lighting .......................................................................................62
3.3.6 Thermocouple Data Acquisition System.........................................................65
3.4 WPT–Cooling Rate Experiments.............................................................................66
3.4.1 Experimental Procedure for WPT–Cooling Rate Experiments.......................66
3.4.2 Design of Experiments for WPT–Cooling Rate Experiments.........................67
3.5 Flow Loop Wax Deposition Experimental Apparatus.............................................69
3.5.1 Flow Loop Design ...........................................................................................69
3.5.2 Heating Bath and Associated Apparatus .........................................................74
3.5.3 Cooling Bath and Associated Apparatus .........................................................74
3.5.4 Wax Mixture Reservoir ...................................................................................77
3.5.5 Wax Mixture Stirrer ........................................................................................77
3.5.6 Photo/Contact Tachometer ..............................................................................78
3.5.7 Wax Mixture Centrifugal Pump ......................................................................78
3.5.8 Wax Deposition Section ..................................................................................79
3.5.9 Wax Mixture Flow Regulator..........................................................................83
3.5.10 Flow Sensor and Rate Meter .........................................................................84
3.5.11 Wax Mixture Sample Drain...........................................................................84
3.6 Associated Equipment and Measurements ..............................................................85
3.6.1 Centrifuge ........................................................................................................85
3.6.2 Temperature Measurements ............................................................................85
3.6.3 Density Measurements ....................................................................................86
3.6.4 Viscosity Measurements..................................................................................86
3.6.5 Titrator.............................................................................................................86
3.6.6 GC Analysis of Samples..................................................................................87
3.7 Flow Loop Experiments...........................................................................................88
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3.7.1 Experimental Procedure for Flow Loop Experiments.....................................88
3.7.2 Experimental Design for Flow Loop Experiments..........................................90
3.8 Cold Finger Wax Deposition Experimental Apparatus ...........................................93
3.8.1 Cold Finger Design..........................................................................................93
3.9 Associated Equipment and Measurements ..............................................................98
3.9.1 Microscopy ......................................................................................................98
3.10 Cold Finger Experiments .......................................................................................98
3.10.1 Experimental Procedure for Cold Finger Experiments .................................98
3.10.2 Experimental Design for Cold Finger Experiments ....................................100
CHAPTER FOUR: RESULTS OF WPT–COOLING RATE EXPERIMENTS.............102
4.1 Effect of Cooling Rate ...........................................................................................103
4.1.1 Significance of Cooling Rate.........................................................................105
4.2 Effect of Composition............................................................................................109
CHAPTER FIVE: RESULTS OF TWO-PHASE FLOW LOOP WAX DEPOSITION
EXPERIMENTS .....................................................................................................112
5.1 Steady State Heat Transfer Model .........................................................................112
5.2 Estimation of Heat Transfer Coefficients, hh and hc ..............................................118
5.3 Properties of Wax–Solvent, Wax–Solvent–Water Mixtures and Deposit Samples ................................................................................................................121
5.3.1 Density of Wax–Solvent and Wax–Solvent–Water Mixtures.......................121
5.3.2 Specific Heat Capacity of Wax–Solvent and Wax–Solvent–Water
Mixtures .........................................................................................................124
5.3.3 Viscosity of Wax–Solvent and Wax–Solvent–Water Mixtures ....................127
5.3.4 Density of Deposit Samples ..........................................................................130
5.4 Thermal Steady State .............................................................................................131
5.5 Estimation of Liquid–Deposit Temperature (Td) and Deposit Thermal Conductivity (kd)..................................................................................................135
5.6 Effect of Deposit-layer Thickness (xd) on the Rate of Heat Transfer (q) and the Inside Tube-wall Temperature (Twi) ....................................................................137
5.7 Effect of Process Conditions on Flow Loop Wax Deposition...............................139
5.7.1 Effect of Water Content on Deposit Mass.....................................................139
5.7.1.1 Effect of Th on Deposit Mass...............................................................141
5.7.1.2 Effect of Tc on Deposit Mass ...............................................................142
5.7.1.3 Effect of Flow Rate or Reynolds Number on Deposit Mass ...............142
5.7.2 Effect of Wax Mixture Water Content on Deposit Water Content ...............144
5.7.3 Effect of Reynolds Number on Deposit Water Content ................................146
5.7.4 Effect of Reynolds Number on Deposit Mass per unit Area.........................148
5.8 Homogeneity and Stability of Wax–Solvent–Water Mixtures in the Flow Loop .150
CHAPTER SIX: RESULTS OF TWO-PHASE COLD FINGER WAX DEPOSITION EXPERIMENTS .....................................................................................................152
6.1 Steady-State Heat Transfer Model.........................................................................152
6.2 Estimation of Heat Transfer Coefficient, hh ..........................................................158
6.3 Density of Deposit Samples...................................................................................158
6.4 Estimation of Deposit Thermal Conductivity (kd) .................................................161
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6.5 Effect of Deposit-layer Thickness (xd) on the Rate of Heat Transfer (q) ..............163
6.6 Effect of Process Conditions on Cold Finger Wax Deposition .............................165
6.6.1 Effect of Water Content on Deposit Mass.....................................................167
6.6.2 Effect of Deposition Time on Deposit Mass .................................................169
6.6.3 Effect of Stirring Rate on Deposit Mass........................................................169
6.6.4 Effect of Wax Mixture Water-Content on Deposit Water-Content...............172
6.6.5 Effect of Time on Deposit Water-Content ....................................................174
6.7 Short-Duration Experiments ..................................................................................176
6.8 Homogeneity of Wax–Solvent–Water Mixtures During Cold Finger
Experiments .........................................................................................................178
6.9 Aging of Deposit Samples .....................................................................................180
6.9.1 Deposit Sample Microscopy..........................................................................180
6.9.2 Deposit Sample GC Analysis ........................................................................186
CHAPTER SEVEN: PREDICTIONS FROM TRANSIENT HEAT-TRANSFER MODEL
.................................................................................................................................189
7.1 Moving Boundary Problem Formulation...............................................................190
7.2 Model Development for Transient (Unsteady-State) Wax Deposition .................191
7.2.1 Energy Balance Equations and Heat Transfer Considerations......................191
7.3 Model for Transient Heat Transfer during Cold Finger Wax Deposition .............193
7.3.1 Boundary and Initial Conditions ...................................................................196
7.3.1 Thermodynamic Considerations....................................................................197
7.3.2 Simulation Procedure ....................................................................................198
7.3.3 Estimation of Liquid and Solid Phase Properties ..........................................199
7.3.4 Numerical Solution Methodology .................................................................199
7.4 Model Predictions ..................................................................................................200
7.4.1 Predicted WAT Values..................................................................................200
7.4.2 Deposit Thickness Profiles ............................................................................202
7.4.3 Deposit Temperature Profiles........................................................................206
CHAPTER EIGHT: CONCLUSIONS AND RECOMMENDATIONS.........................208
8.1 Conclusions............................................................................................................208
8.2 Recommendations..................................................................................................212
REFERENCES ................................................................................................................214
APPENDIX A: WAX PRECIPITATION TEMPERATURE MEASUREMENT DATA .....................................................................................................................227
APPENDIX B: HEAT TRANSFER COEFFICIENT DATA .........................................229
APPENDIX C: PHYSICAL PROPERTIES DATA........................................................233
APPENDIX D: FLOW LOOP EXPERIMENTAL DATA .............................................236
APPENDIX E: COLD FINGER EXPERIMENTAL DATA ..........................................239
ix
APPENDIX F: ESTIMATION OF LIQUID MIXTURE AND DEPOSIT PHASE
PROPERTIES IN TRANSIENT MODEL .............................................................243
APPENDIX G: COPYRIGHT PERMISSIONS..............................................................247
x
List of Tables
Table ‎3.1
Composition of wax samples used in this study...........................................50
Table ‎3.2
Composition of solvents. ..............................................................................52
Table ‎3.3
Selected physical and chemical properties of Norpar13 (Imperial Oil
MSDS) and Linpar1416V (APCO Industries Ltd. MSDS) ..........................53
Table ‎3.4
Experimentally determined WAT, WDT, and PPT Values..........................58
Table ‎3.5
Operating Conditions for WPT–Cooling Rate Experiments ........................68
Table ‎3.6
Conditions of flow loop wax deposition experiments (Wax concentration = 6 mass%, WAT = 28 °C )...................................................92
Table ‎3.7
Conditions of cold finger wax deposition experiments (Wax concentration = 10 mass%, WAT = 32 °C)................................................101
Table ‎5.1
Density regression constants for equation 5.9. ...........................................122
Table ‎5.2
Regression constants for equation 5.10, the specific heat capacity of mixtures of Bernardin Parowax in Linpar1416V. ......................................126
Table ‎5.3
Viscosity regression constants for viscosity equation 5.11. .......................129
Table ‎5.4
Average Reynolds number, Re, estimated average liquid–deposit interface temperature, Td, and average deposit thermal conductivity,
kd, at different hot and cold stream temperatures . .....................................136
Table ‎6.1
Density regression constants for equation 6.9. ...........................................160
Table ‎6.2
Average estimated deposit thermal conductivities for deposits from 12 h and 24 h experiments. ..............................................................................162
Table ‎6.3
Deposit mass per unit area, Ω for 5 min, 12 h and 24 h experiments.........166
Table ‎6.4
Deposit mass per unit area for short-duration experiments of 30 s and 2 min, in comparison to the deposit mass per unit area at 12 h..................177
xi
List of Figures and Illustrations
Figure ‎3.1
Composition of solvents and wax samples. ....................................................... 51
Figure ‎3.2
Comparison of WAT values for Parowax–Norpar13 mixtures, and WAT, WDT and PPT values for Bernardin Parowax–Linpar 1416V mixtures (Kasumu and
Mehrotra, 2013) .................................................................................................................... 59
Figure ‎3.3
Bath.
Haake D8 Immersion Circulator immersed in a Haake DC1-V Refrigerated 61
Figure ‎3.4
Haake PG 20 Temperature Programmer ............................................................ 61
Figure ‎3.5
Fabricated copper tube used for WPT measurements........................................ 63
Figure ‎3.6
Underwater LED light, model QL-72C. ............................................................ 64
Figure ‎3.7
Schematic of bench-scale apparatus for flow loop wax deposition experiments. .......................................................................................................................... 72
Figure ‎3.8
Bench-scale setup for flow loop wax deposition experiments........................... 73
Figure ‎3.9
Coolant bath with the annealed copper tubing connected to coolant bath recirculator. ........................................................................................................................... 76
Figure ‎3.10
Position of Wax mixture centrifugal pump........................................................ 79
Figure ‎3.11
Cross-section of Aluminum deposition tube (Fong, 2007)................................ 80
Figure ‎3.12
Picture of entrance flange. a) inner side, b) outer side (Fong, 2007)................. 81
Figure ‎3.13
Plexiglass body of wax deposition section. a) Side view, b) Front view: entrance section (Fong, 2007)............................................................................................... 82
Figure ‎3.14
Plexiglass body of wax deposition section (Fong, 2007)................................... 83
Figure ‎3.15
Schematic of cold finger apparatus. ................................................................... 95
Figure ‎3.16
Assembled cold finger apparatus. ...................................................................... 96
Figure ‎3.17
Dismantled cold finger apparatus. ..................................................................... 97
Figure ‎4.1
Variation of WPT with cooling rate for different Conros Parowax–Norpar13 mixture compositions.......................................................................................................... 104
Figure ‎4.2
Comparison of calculated and experimental WPT values for Conros Parowax–Norpar13 mixtures (dotted curves show 95% confidence limits)....................... 107
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Figure ‎4.3. The effect of cooling rate on the wax precipitation temperature and liquid-to-solid phase transformation for w29 = 6 mass%. ........................................................................... 108
Figure ‎4.4
Variation of WPT with Parowax–Norpar13 mixture composition at different cooling rates as predicted by Equation 4.1. ........................................................................ 110
Figure ‎5.1
Temperature profile during wax deposition..................................................... 114
Figure ‎5.2
Predicted effects of deposit-layer thickness on fractional thermal resistances (kd = 0.38 W m–1 K–1
, Re = 10000)..................................................................................... 117
Figure ‎5.3
Comparison of experimental and correlated overall heat transfer coefficient, Ui, for wax mixtures (obtained from experiments performed under non-depositing conditions)........................................................................................................................... 120
Variation of the density of Bernardin Parowax-Linpar1416V mixtures with
Figure ‎5.4
Temperature. ....................................................................................................................... 123
Figure ‎5.5
Specific heat capacities of Bernardin Parowax-Linpar1416V mixtures. ......... 125
Figure ‎5.6
Viscosities of various Bernardin Parowax-Linpar1416V mixtures at wax concentrations from 0-10 mass%........................................................................................ 128
Figure ‎5.7
Variation of deposit mass per unit area,  with time for extended experiments. ........................................................................................................................ 132
Approach to thermal steady-state during deposition shown by the difference
Figure ‎5.8
in coolant temperature for 1-hour experiments at Thi = (WAT+7ºC) and Tci = (WAT–
10ºC) for wax mixtures with 0, 10, 20 and 30 vol% water content. ................................... 134
Figure ‎5.9
Predicted effect of deposit-layer thickness (xd) on the rate of heat transfer and inside tube-wall temperature (Twi)................................................................................ 138
Figure ‎5.10Effect of the water content in the wax mixtures on the deposit mass per unit area, Ω................................................................................................................................. 140
Figure ‎5.11
Variation in the deposit mass at different water contents; (a) Effect of waxy
mixture temperature, Th, (b) Effect of coolant temperature, Tc, and (c) Effect of Reynolds number, Re.......................................................................................................... 143
Figure ‎5.12 .......... Comparison of the water content of deposit to the water content of the wax mixture ......................................................................................................................... 145
Figure ‎5.13
Variation of the water content of the deposits with Reynolds Number, Re..... 147
Figure ‎5.14
Variation of water-free deposit mass per unit area, Ω, with Reynolds
number, Re, for all deposition experiments at Th = (WAT+7 ºC) and Tc = (WAT–10 ºC). 149
xiii
Comparison of the water content of the waxy mixture in the reservoir with Figure ‎5.15
the water content of the waxy mixture flowing in the flow-loop. ...................................... 151
Predicted effects of deposit-layer thickness on fractional thermal resistances Figure ‎6.1
(0% water content). ............................................................................................................. 157
Figure ‎6.2
Predicted effect of deposit-layer thickness (xd) on the rate of heat transfer, q,
for Th = (WAT+3) oC, (Tc = WAT–15) oC, and hh = 980 W m-1 K-1. .................................. 164
Figure ‎6.3
Effect of the water content in the wax mixtures on the deposit mass per unit
area, Ω, at different deposition times.................................................................................. 168
Variation of deposit mass per unit area, Ω with deposition time, t. (a) single
Figure ‎6.4
phase mixtures at stirring rates of 250 and 500 rpm; (b) two-phase mixtures at a constant stirring rate of 500 rpm. ...................................................................................................... 171
Comparison of the water content of deposit to the water content of the wax Figure ‎6.5
mixture for different deposition times. ............................................................................... 173
Figure ‎6.6
Variation of the water content of the deposits with time, for different wax mixture water content. ........................................................................................................ 175
Comparison of the water content of the waxy mixture in the reservoir with Figure ‎6.7
the water content of samples taken. .................................................................................... 179
Figure ‎6.8
Microscopy pictures of deposit sample from 5 min experiment at 500 rpm stirring rate. ......................................................................................................................... 182
Microscopy pictures of deposit sample from 12 h experiment at 500 rpm Figure ‎6.9
stirring rate. ......................................................................................................................... 183
Microscopy pictures of deposit sample from 5 min experiment at 250 rpm Figure ‎6.10
stirring rate. Scale is the same as that of Figure 6.8............................................................ 184
Figure ‎6.11
Microscopy pictures of deposit sample from 12 h experiment at 250 rpm stirring rate. Scale is the same as that of Figure 6.8............................................................ 185
Figure ‎6.12
GC analyses of 10 mass% wax mixture and deposit samples from 5 min experiment and 12 h experiments at 500 rpm stirring rate. ................................................ 187
GC analyses of 10 mass% wax mixture and deposit samples from 5 min Figure ‎6.13
experiment and 12 h experiments at 250 rpm stirring rate. ................................................ 188
Figure ‎7.1
Cross-sectional view of wax deposition on cold finger with different phases and their relative temperatures............................................................................................ 195
Figure ‎7.2
Predicted and experimental values of WAT for Bernardin Parowax–
Linpar1416V mixtures. ....................................................................................................... 201
xiv
Figure ‎7.3... Deposit thickness profile from transient heat transfer model compared to deposit thickness from experimental data for single-phase experiments at 250 and 500 rpm. 204
Deposit thickness profile from transient heat transfer model compared to Figure ‎7.4
deposit thickness from experimental data for two-phase experiments 500 rpm................. 205
Figure ‎7.5
Predictions of temperature profile across the deposit layer at different deposition times, ranging from 5 min to 24 h. .................................................................... 207
xv
List of Symbols, Abbreviations and Nomenclature
a1, a2 = regression constants in eq 5.9 b1, b2 = regression constants in eq 5.11 c1, c2 = regression constants in eq 5.10. d1, d2, d3 = regression constants in eq 5.13 e1, e2 = regression constants in eq 6.9 f1, f2, f3 = regression constants in eq 4.1 A = surface area (m2) Ah = Actual flow rate (gal min–1) Ai = inside surface area of tube (m2) Cc = average specific heat capacity of coolant (J kg–1 K–1) Ch = average specific heat capacity of wax–solvent (hot) mixture (J kg–1 K–1)
Cp,L = paraffin liquid heat capacity (J K–1 kmol–1)
Cp,LCH2 = empirical specific heat capacity methylene contribution (J K–1 kmol–1)
Cp,LCH3 = empirical specific heat capacity methyl contribution (J K–1 kmol–1)
Cw = volume fraction concentration of wax out of solution at the wall
D = internal pipe diameter (m)
Dm, DB = diffusion coefficient (m2 s–1)
Fc = Flowrate of coolant (m3 s–1)
Fh = Flowrate of wax-solvent solution (m3 s–1) hc = heat transfer coefficient for coolant (W m–2 K–1) hh = heat transfer coefficient for wax–solvent (hot) mixture (W m–2 K–1) kd = average thermal conductivity of deposit (W m–1 K–1) xvi
km = thermal conductivity of metal (W m–1 K–1) kw = Wada and Jamieson thermal conductivity (W m–1 K–1)
L = length of aluminum or copper tube (m)
M = molar mass (kg kmol–1)
md = mass of deposited wax (kg)
m c = mass rate of coolant (kg s–1)
m h
= mass rate of wax–solvent mixture (kg s–1)
n = carbon number
Oh = Rate meter reading (gal min–1)
q = rate of heat transfer at steady state (W)
qgain = rate of heat gain by the coolant from the surroundings, (W)
Rc = thermal resistance of coolant (K W–1)
Rd = thermal resistance of deposit layer (K W–1)
Rh = thermal resistance of wax–solvent mixture (K W–1)
Rm = thermal resistance of metal tube wall (K W–1)
Re = Reynolds number
r2 = coefficient of determination
ri = inside metal tube radius (m)
ro = outside metal tube radius (m)
T = temperature (°C or K)
Tc = average temperature of coolant  0.5Tci + 0.5Tco (°C)
Tci = inlet temperature of coolant (°C)
Tco = outlet temperature of coolant (°C)
xvii
Td = average temperature at the interface of deposit and wax–solvent mixture or oil (°C) Tdavg = average deposit temperature ≡ 0.5(Td+Twi) (°C)
Th = average temperature of wax–solvent mixture  0.5Thi + 0.5Tho (°C)
Thi = inlet temperature of wax–solvent mixture (°C)
Tho = outlet temperature of wax–solvent mixture (°C)
Twi = temperature at the inside metal tube surface (°C)
Two = temperature at the outside metal tube surface (°C)
t = time (s)
Ui = overall heat transfer coefficient based on tube inside surface area (W m–2 K–1) xd = deposit layer thickness (m) Greek Letters
, ,  = empirical constants in eq 5.8
 = viscosity of wax–solvent mixture (Pa s)
c = viscosity of continuous phase (Pa s)
m = viscosity of mixxture (Pa s)
ρsoln = density of wax–solvent mixture (kg m–3)
ρd = density of deposit (kg m–3)
φd = volume fraction of dispersed phase
θc = ratio of coolant (convective) thermal resistance and total thermal resistance
θd = ratio of deposit (conductive) thermal resistance and total thermal resistance
θh = ratio of wax–solvent mixture (convective) thermal resistance and total thermal resistance
θm = ratio of tube-wall (conductive) thermal resistance and total thermal resistance
xviii
 = mass of deposit per unit deposition surface area (kg m–2)
 = Jamieson factor
Acronyms
GC = gas chromatograph
PPT = Pour point temperature (°C)
WAT = wax appearance temperature (°C)
WPT = wax precipitation temperature (°C)
WDT = wax disappearance temperature (°C)
xix
Chapter One: Introduction
1.1 Introduction
Crude oils are complex mixtures containing several components, including paraffins,
aromatics, naphthenes, asphaltenes and resins. The higher molecular weight paraffins (or n­
alkanes) are referred to as waxes. At reservoir conditions, with temperatures in the range of 70­
150°C and pressures in the range of 50-100 MPa, these waxes remain dissolved in the crude oil,
which behaves as a Newtonian fluid (Lee, 2008). At the lower temperatures and pressures that
exist during crude oil transportation, the high molecular weight n-alkanes or waxes tend to form
macro and micro crystalline structures that precipitate out of the oil and deposit on the cooler
walls of the pipeline (Venkatesan et al., 2005). The precipitated wax imparts complex nonNewtonian and nonlinear characteristics to the flow properties of the crude oil (Chang and
Boger, 1998).
The temperature at which the first crystals of paraffin wax start to appear in the crude oil
is called the Wax Appearance Temperature (WAT) or the Cloud Point Temperature (CPT). It has
been shown that a "waxy" mixture containing as small as 2 mass% of wax is sufficient to
undergo deposition (Holder and Winkler, 1965a), provided the temperature of the contact surface
is less than or equal to the WAT of the crude oil or "waxy" mixture. Determination of the WAT
and the amount of wax precipitated at a given temperature are critical for understanding the
crude oil rheology and solids deposition (Ronningsen et al., 1991; Hansen et al., 1991; Pedersen
et al., 1991; Roehner and Hanson, 2001).
Wax deposition, which occurs when a “waxy” crude oil or mixture is exposed to a
temperature below the solubility temperature of the wax in the crude oil is a serious problem
1
during the production, transportation and processing of crude oil because wax deposition can
damage oil reservoir formations and wells, and cause blockage of pipelines and process
equipment. The deposition of wax in pipelines and process equipment leads to increased pressure
drop, increased pumping power requirements and/or reduction in pumping efficiency. In extreme
cases, the pipeline can become completely blocked, leading to "pump attack". Wax deposition
can be compared to the accumulation of cholesterol in the human blood vessels, which leads to
the obstruction of blood flow through the body from the heart. In severe cases, this will
ultimately lead to a heart attack. Wax deposition problems are more severe in cold environments,
most notably in subsea conditions, where temperatures at the bottom of the ocean can reach 4 oC
(Venkatesan et al., 2005). With deepwater oil recovery becoming increasingly more prevalent,
the implication is that crude oil is transported over greater distances and that the exposure to low
temperatures is increased. Problems associated with wax precipitation and deposition are
expected to become worse and so is the cost of its control and remediation. In an extreme case,
repeated wax deposition problems forced an oil platform to be abandoned at a cost of $100
million (Singh et al., 2000). The United States Minerals Management Service states that severe
wax related plugs were reported in Gulf of Mexico flow lines between 1992 and 2002 (Makagon
et al., 2003). The U.S. Department of Energy (DOE) states that the remediation of plugged
pipelines in water at depths of 400 m can cost $1 million/mile (Venkatesan et al., 2005). Finding
effective control and mitigation measures for the problem of wax deposition, especially in subsea
pipelines, is thus very important.
Wax-related problems are typically dealt with by using mechanical, thermal, chemical
and/or any combination of these methods (Svetgoff, 1984; McClafin and Whitfil, 1984; Woo et
al., 1984; Bernadiner, 1993; Hunt, 1996; Ferworn et al., 1997; Bello et al., 2006). In recent
2
years, other unconventional methods, such as bacterial and electromagnetic treatments,
(Balakirev et al., 2001; Towler and Rebbapragada, 2004), piezoelectric energy (Sulaiman et al.,
2011), and vacuum-insulated tubing (Singh et al., 2007) have also been tried with limited
success. All of these methods have their limitations and increase the production and processing
costs considerably. For example, chemical treatments are highly selective to a particular „waxy‟
mixture considered (Ferworn et al., 1997). An emerging technology proposed to control wax
deposition is “cold flow”. In this method, crude oil is subjected to systematic cooling to
precipitate wax crystals, giving rise to a slurry that is transported through pipelines. Several
reasons have been suggested for the reduced deposition of solids observed during “cold flow”.
These include reduced thermal driving force, the preferential crystallization of wax onto the
suspended solid crystals flowing in the slurry that act as nucleation sites, and a lowering of the
WAT of the remainder liquid phase (Merino-Garcia and Correra, 2008; Bidmus and Mehrotra,
2009; Deo, 2011).
The process of deposit formation from 'waxy' mixtures or crude oils is complex, and it
may involve several processes and considerations, such as crystallization kinetics, mass transfer,
heat transfer, fluid dynamics, rheology, solid–liquid multiphase equilibria, and thermophysical
and transport properties (Cole and Jessen, 1960; Turner, 1971; Burger et al., 1981; Coutinho,
1995; Creek et al., 1999; Singh et al., 2000; Bidmus and Mehrotra, 2004; Fong and Mehrotra,
2007). A number of mechanisms have been suggested for explaining the process of wax
deposition and for estimating the amount of deposition that will occur in a system under a
particular set of operating conditions. These include molecular diffusion, shear dispersion,
Brownian diffusion, gravity settling, and heat transfer. Of these, molecular diffusion and heat
transfer are currently regarded as the most relevant mechanisms. In the molecular diffusion
3
mechanism, it is assumed that deposits are formed as a result of the radial transport of wax
molecules due to a radial concentration gradient (Burger et al., 1981; Majeed et al., 1990;
Svendson, 1993; Creek et al., 1999; Kok and Saracoglu, 2000; Singh et al., 2000-2001; RamirezJaramillo et al., 2004; Farayola et al., 2010). Another inherent assumption in the molecular
diffusion modeling approach is that the deposit–liquid interface temperature is variable, which is
predicted to increase with deposit growth from an initial value close to the pipe-wall temperature
and ultimately to the WAT at steady state.
More recently, heat transfer has been identified as a more important mechanism or
approach for wax deposition. In the heat-transfer mechanism, the deposit formation and growth
is taken to be a (partial) solidification or freezing process involving crystallization (Bott and
Gudmunsson, 1977; Ghedamu et al., 1997; Cordoba and Schall, 2001; Bidmus and Mehrotra,
2004; Parthasarathi and Mehrotra, 2005; Bhat and Mehrotra, 2005; Fong and Mehrotra, 2007;
Mehrotra and Bhat, 2007; Tiwary and Mehrotra, 2009; Bidmus and Mehrotra, 2009; Kasumu and
Mehrotra, 2013; Arumugam et al., 2013). In the models based on the heat-transfer approach,
involving (partial) freezing or solidification, the release of the latent heat of phase change
accompanies the growth of a wax deposit layer close to the pipe wall, which is held at a
temperature lower than the WAT of the flowing “waxy” crude oil. An assumption made in the
heat-transfer mechanism is that the liquid–deposit interface temperature is equal to the WAT of
the crude oil, or waxy mixture, throughout the deposition process. This assumption has been
confirmed through measurements involving batch cooling experiments under static and sheared
conditions (Bidmus and Mehrotra, 2008a; Bidmus and Mehrotra, 2008b). It is pointed out that
the heat-transfer based deposition mechanism is able to explain solids deposition under both “hot
flow” (where the oil temperature > WAT) and “cold flow” (where the oil temperature < WAT)
4
conditions (Bidmus and Mehrotra, 2009; Bidmus and Mehrotra, 2012). Under steady-state
conditions, the liquid–deposit interface temperature in both the molecular diffusion approach and
the heat transfer approach is taken to be equal to the WAT, which has been confirmed from
several experimental investigations (Bidmus and Mehrotra, 2004; Parthasarathi and Mehrotra,
2005; Fong and Mehrotra, 2007; Tiwary and Mehrotra, 2009; Bidmus and Mehrotra, 2008a;
Bidmus and Mehrotra, 2008b; Bidmus and Mehrotra, 2009; Kasumu and Mehrotra, 2013).
Most wax deposition studies have focused on single-phase oil and two-phase oil–gas
flow. However, water is inevitably found in the produced oil and its fraction in the oil stream,
called the water-cut, generally increases with the lifetime of a production well. The wax
deposition process is not well established for two-phase oil–water flow conditions, perhaps due
to the increased complexity caused by the addition of the water phase and the difficulty in
obtaining consistent results with oil–water mixtures (Couto et al.; 2008). Various researchers
have reported different results on the effect of water on wax deposition (Li et al., 1997; AbdelWaly, 1999; Gao, 2003; Sarica and Volk, 2004; Couto et al., 2008; Bruno et al., 2008; Zhang et
al., 2010a; Zhang et al., 2010b; Hoffmann et al., 2012; Kasumu and Mehrotra, 2013;
Panacharoensawad and Sarica, 2013).
1.2 Objectives and Scope of Study
Crude oils are complex mixtures with varying compositions and properties, depending on
the source. Solutions of multi-component paraffin waxes dissolved in multi-component solvents
at various concentrations were used to represent complex paraffinic crude oils. This enhanced the
isolation and understanding of the variables that were studied without introducing additional
uncertainties, in addition to eliminating the limitations that sometimes accompany the use of
actual crude oil samples. In this study, novel experimental apparatuses were assembled and
5
procedures were developed to study the deposition of wax from wax–solvent and wax–solvent–
water mixtures of known compositions under various operating conditions. The main objectives
of the study were:
1. To prepare well-defined mixtures of multi-component waxes in paraffinic solvents, that
were used to represent “waxy” crude oils.
2. To measure and correlate physical properties of the materials and mixtures used.
3. To design and fabricate experimental apparatuses that were suitable, effective and
economical in achieving the objectives of this study.
4. To investigate the onset of wax precipitation and to express the wax precipitation
temperature as a function of cooling rate and mixture composition.
5. To investigate the effects of the presence of water, and other process variables on wax
deposition in a two-phase turbulent flow wax deposition process using a flow loop
apparatus.
6. To confirm that the deposition process in the flow loop apparatus, for both single- and
two-phase mixtures, can be explained using a simple steady-state heat transfer model.
7. To investigate the effects of water, time and shear rate on the wax deposition process in
both single- and two-phase mixtures using the cold finger wax deposition apparatus.
8. To confirm that the deposition process in the cold finger wax deposition apparatus, for
both single- and two-phase mixtures, can be explained using a simple steady-state heat
transfer model.
9. To model the transient behavior of the cold finger wax deposition process and compare
the predictions with experimental results.
6
Chapter 2 presents a critical review of the existing literature on wax deposition from
crude oils and paraffinic mixtures. The literature review presented includes the classification and
properties of paraffinic waxes, crystallization, the rheological behavior of "waxy" crude oils, and
mechanisms of wax deposition. It also includes methods for measuring the wax appearance
temperature (WAT), factors affecting wax deposition, methods for studying the wax deposition
process, structure and properties of wax deposits, and the methods of remediation and control of
wax deposition.
In Chapter 3, a detailed description of the experimental apparatuses and associated
equipment used, and experimental procedures applied in the various parts of this study are
presented. The three sets of experiments carried out in this study are discussed, namely WPT–
cooling rate experiments, one- and two-phase flow loop wax deposition experiments, and oneand two-phase cold finger wax deposition experiments. The design of experiments, materials
used, sample preparation methods, and methods of analyses for each set of experiments are also
described in this chapter.
In Chapter 4, results are presented from the WPT–cooling rate experiments. The effects
of cooling rate and composition on the wax precipitation temperature of "waxy" are discussed.
Results reported in this chapter have been published recently in Fuel by Kasumu et al. (2013).
In Chapter 5, the equations used to represent the physical properties of the systems
studied are presented. The physical properties studied include Bernardin Parowax–Linpar1416V
(and Bernardin Parowax–Linpar1416V–water) mixture density and viscosity, the correlations
used to estimate the specific heat capacity, and the deposit density correlation that was used to
determine deposit thickness. Results from the flow loop wax deposition experiments are also
presented. The steady-state heat transfer model used for the wax deposition process is described.
7
Effects of process parameters such as the water content of the wax mixture, wax mixture
temperature, coolant temperature, and flow rate or Reynolds number, and the deposition time are
described. Data regarding the liquid–deposit interface temperature and the deposit thermal
conductivity are also reported and discussed. Results reported in this chapter have been
published recently in Energy & Fuels by Kasumu and Mehrotra (2013).
In Chapter 6, results from the cold finger wax deposition experiments are presented.
Effects of process variables such as stirring rate, time (aging) and water content are discussed.
The steady-state heat transfer model is used to analyze the steady state experimental data from
the cold finger experiments.
In Chapter 7, a transient-state mathematical model is presented, which is based on the
model presented by Bhat and Mehrotra (2005) that utilizes the moving boundary problem
framework. The transient model was modified and used to describe the growth of the deposit
layer on the outside of a cylindrical pipe with time. Predictions from this model are presented
and compared with the experimental results from the cold finger wax deposition experiments.
Chapter 8 presents a summary of the important conclusions and contributions of this
study. Also included are recommendations for future work in this area of research.
8
Chapter Two: Literature Review
Crude oils are complex mixtures containing several different components, including
alkanes, aromatics, naphthenes, resins, high molecular weight waxes and asphaltenes. Crude oils
containing high fractions of paraffins or waxes, are called paraffin-base or “waxy” crude oils,
while those with a significant amount of asphaltenes are called asphalt-base or “asphaltic” crude
oils (Singh et al., 1999). High molecular weight paraffin waxes are soluble in crude oil under
reservoir conditions of high pressure and temperature. However, at lower conditions of pressure
and temperature during extraction of crude oil, precipitation and deposition of paraffin wax
within the reservoir as well as in the well-bore can occur. Wax deposition will also occur in
production pipelines when the pipeline wall temperature becomes lower than the wax appearance
temperature (WAT) of the flowing "waxy" crude oil (Chen et al., 1997).
2.1 Paraffin Waxes
2.1.1 Classification
Paraffin wax is mostly derived from petroleum crude oil. These petroleum waxes can be
classified as micro-crystalline wax or macro-crystalline/paraffin wax (Srivastava et al., 1993).
Paraffin waxes are a mixture of normal alkanes (n-alkanes) of different chain length (C18C65)
that tend to form clusters and precipitate from crude oil, under suitable conditions, to form wax
solids. Microcrystalline waxes consist of a mixture of iso-alkanes, n-alkanes, and cyclo-alkanes.
Iso-alkanes also form clusters and precipitate from crude oils; however, they tend to delay the
formation of a deposit due to their branched nature, and therefore produce unstable wax solids.
Cyclo-alkanes, or naphthenes, are stiff and bulky in nature and tend to disrupt the wax nucleation
process during deposit formation (Hammami and Raines, 1999).
9
Since paraffin waxes are made up of mainly n-alkanes, they are considered a natural
starting point for understanding the physical and thermal properties of the wax. The n-alkanes
are linear chains of aliphatic hydrocarbons belonging to a family of compounds, the paraffin
series. In this series all members contain carbon and hydrogen in a ratio given by the formula
CnH2n+2 (Turner, 1971). An important characteristic of high molecular weight n-alkanes is their
low solubility in paraffin-base, aromatic, naphthene-base, and other oil solvents at room
temperatures.
2.1.2 Crystal Structure
Below their melting point or melting point range, paraffins form a crystalline structure
from either their individual compounds or mixtures with one another. Their crystals are mainly
rhombic or monoclinic in shape and usually display a low order of symmetry (Mozes et al.,
1982). Crystallization starts when paraffins are cooled to temperatures below their melting
point, with nucleus formation (nucleation), which occurs in parallel with the crystal growth. The
relative rates of nucleation and crystal growth determine the final structure of the paraffin wax.
Similar to many other crystalline substances, the paraffin wax crystal structure changes further at
the equilibrium transition temperature, which is below the melting point.
C21 to C36 n-alkanes display a well-defined transition point below their melting point
where the α-phase, which is stable below the melting point, changes into the β-phase with the
release of a relatively large amount of heat (Mazee, 1949). Generally, n-alkanes between C19
and C29 having an odd number of carbon atoms have an orthorhombic structure at ambient
temperature. However, n-alkanes between C18 and C26 with even carbon numbers have a triclinic
structure, while those between C28 and C36 have a monoclinic structure. The different structural
10
morphologies are determined by the carbon number, thermal history, temperature and purity of
the sample (Turner, 1971; Srivastava et al., 1993).
Crystals of paraffin wax appear in three different characteristic forms, namely plates,
needles and mal-crystalline shapes. Crystals with the mal-crystalline shape are small
underdeveloped crystals that often agglomerate. The conditions of crystallization and the
chemical composition of the wax determines the form of the wax crystal. Turner (1971) reported
that fast cooling tends to produce needles and mal-crystalline forms while slow crystallization
favors the growth of plates. It is most likely that all the forms are typically produced during a
single crystallization, but with one of them usually being the predominant one under a given set
of conditions. It was found that the size of the crystal varies with the composition of the system
(Anderson 2001).
2.1.3 Physical and Thermal Properties
Paraffins or n-alkanes belong to a homologous series where each successive member of
the series is different from the next by the CH2 group. They are relatively inert and have little
affinity for most chemical reagents, thus the name „paraffins‟, which is derived from the Latin
words for “little affinity.” They are less dense than water and do not dissolve easily in water.
An alkane molecule is held together entirely by covalent bonds, which are directed in a
symmetrical way, such that the slight bond polarities tend to cancel out resulting in either a nonpolar or very weakly polar molecule. The non-polar molecules are held together by weak and
short-range van der Waals forces that act only between the surfaces of the molecules. Thus, it is
observed that the larger the n-alkane molecule (implying a larger surface area), the stronger the
11
intermolecular forces (Morrison and Boyd, 1992). That is why, as shown in Table 2.1, there is a
smooth gradation in physical properties of n-alkanes as the carbon number increases.
The first four members of the group, with carbon numbers C1 to C4 are gases at 20°C and
atmospheric pressure, while the C5 to C17 members are liquids and members with higher carbon
numbers higher than C17 are solids under the same conditions. The density of succeeding
members of the group increases rapidly initially, but levels off at about 800 kg/m3. The boiling
point increases with molecular weight, however, the rate of increase decreases progressively for
each additional CH2. For this reason, the lower n-alkanes are more easily separated by fractional
distillation than the higher members of the homologous series. A slight irregularity exists at the
beginning of the series, with ethane and propane having a lower melting point than methane.
After that, the melting point increases with molecular weight for the higher n-alkanes. Branched
alkanes or iso-alkanes do not show the same gradation in physical properties, and they usually
have a lower melting and boiling point than their corresponding n-alkane. This is due to the
reduced surface area of their molecules.
12
Table 2.1
Physical properties of some n-alkanes (Barton and Ollis, 1979)
Compound
Formula
Melting point
Boiling point
d420
(°C)
(°C)
(g cm-3)
Methane
CH4
–182.6
–161.6
0.4240 (at b.p.)
Ethane
C2H6
183.3
88.5
0.5462 (at b.p.)
Propane
C3H8
187.1
42.2
0.5824 (at b.p.)
Butane
C4H10
138.4
0.5
0.6011 (at 0°C)
Pentane
C5H12
129.7
36.1
0.6263
Hexane
C6H14
94.0
68.7
0.6594
Heptane
C7H16
90.5
98.4
0.6838
Octane
C8H18
56.8
125.7
0.7026
Nonane
C9H20
53.7
150.8
0.7177
Decane
C10H22
29.7
174.1
0.7301
Dodecane
C12H26
9.7
216.3
0.7487
Tetradecane
C14H30
5.5
253.6
0.7627
Hexadecane
C16H34
18.1
287.1
0.7733
Octadecane
C18H38
28.0
317.4
0.7767
Eicosane
C20H42
36.4
345.1
0.7777
Pentacosane
C25H52
53.3
259*
0.7785
Triacontane
C30H62
66.0
304*
0.7795
Tetracontane
C40H82
81.4


Pentacontane
C50H102
92.1
421*

Hectane
C100H202
115.3

*
*
Values obtained at 15 mm Hg.
13
2.1.3.1 Enthalpy of Fusion
The latent heat of fusion is the energy involved during the transition between solid and
liquid phases. Even though n-alkanes may also undergo solid-to-solid phase changes, involving
latent heat of transition, it has been suggested that heats of transition can be ignored for most
industrial purposes (Mullin 1973). While it has generally been observed that the latent heat of
fusion for n-alkanes increases linearly with their molecular weight, there is some disagreement as
to whether this increase is for only odd- or even-numbered n-alkanes, or for both (Hammami,
1994).
Dollhopf et al. (1981) observed that the plot of ΔHtot (the sum of heats of fusion and
transition) versus 1/n gave straight lines of the form
for even n:
 3
H tot  H  1  
 n
2.1
for odd n:
 4.4 
H tot  H  1 

n 

2.2
where ΔH∞ is the melting enthalpy of polyethylene, extrapolated from the linear plots of the
experimental data for odd- and even-numbered paraffins, and has a value of 4.12 kJ/mol CH2.
High molecular weight n-alkanes have relatively high values of latent heat of fusion, in the range
about 150–300 kJ/kg. They are thus thought to be a useful means of energy storage and/or
thermal protection (Haji-Sheikh et al., 1982).
2.1.3.2 Heat Capacity
The heat capacity of paraffins is an important factor in the determination of the amount of
thermal energy associated with a given temperature change in a paraffinic mixture.
Some
empirical correlations have been developed to describe the heat capacities of paraffins up to
14
polyethylene in the solid and liquid states, as a function of temperature. Heat capacity values for
paraffins up to tritriacontane (C33) were obtained using a calorimeter (Finke, 1954; Huffman,
1931; Parks, 1930; Spaght, 1932). Various equations, empirical in nature, were proposed by
some researchers (Broadhurst, 1962; Karasz and Hamblin 1963; Pan et al., 1986; Wunderlich
and Dole, 1957; and Richardson, 1965) to describe the heat capacities of paraffins up to
polyethylene in the solid and liquid states as a function of temperature. A summary and
comparison of all these equations was provided by Dole (1967). Jin and Wunderlich (1991)
proposed equations 2.3a - 2.3c relating the heat capacity to carbon number (n), temperature, and
the empirical contributions from CH2 and CH3 groups. It was reported that the heat capacities in
the liquid state can be generated within an rms error of ±1.7%.
CH 3
C p ,l  2C p ,l
CH 2
 ( n  2 )C p ,l
2.3a
2
2C CH
p ,l  17.33  0.04551T
2.3b
3
2C CH
p,l  30.41  0.01479T
2.3c
where Cp,l is the specific heat capacity of the pure liquid component in J mol K, T is
temperature in K. However, there was no noticeable odd/even carbon number effect on the
liquid heat capacities.
2.1.3.3 Thermal Conductivity
The thermal conductivity is an important parameter because the deposition of waxes in
flowing crude oil is believed to be a thermally driven process (Kasumu and Mehrotra, 2013;
Fong and Mehrotra, 2007; Parthasarathi and Mehrotra, 2005; Bidmus and Mehrotra, 2004;
15
Guthrie et al., 2004; Cordoba and Schall, 2001a; Ribeiro et al., 1997; Brown et al., 1993; Khan
et al., 1993; Sharma et al., 1982).
The thermal conductivity of over 83 organic liquids were measured by Filippov (1968)
over a temperature range, and the results were tabulated. Dick and McCready (1954) also
measured the thermal conductivity of over 19 organic compounds, it was observed that thermal
conductivity increased with increasing chain length while it decreased in the presence of side
chains for molecules with the same carbon number. Data obtained by Filippov (1968) and Wada
et al. (1985) also agree with Dick and McCready‟s (1954) observations. Tufeu et al. (1968)
found the thermal conductivity of the alcohols to initially decrease rapidly with carbon number
and then increase slowly from C5. Missenard (1968) plotted the thermal conductivity data at 0°C
against the carbon number for organic acids, alcohols, organic iodide derivatives and n-alkanes.
While each group had a different smooth curve, all the curves converged to a common limiting
value between 0.155 to 0.160 W m–1 K–1.
Measurements of thermal conductivity of paraffins have shown an increase with
temperature (le Roux et al., 1974; Haji-Sheikh et al., 1982).
However, in each case an
irregularity or initial decrease in the thermal conductivities was noticed at certain temperatures,
depending on the paraffin wax composition. These temperatures were usually within the range
at which a solid-solid phase transition occurred in the waxes. This peculiar behavior of thermal
conductivity was attributed to the release of latent heat. The data by Wada et al. (1985) and
Vásquez and Briano (1993) also indicate that the thermal conductivities of liquid paraffins and
petroleum fractions decrease with temperature. Wada et al. (1985) found that the thermal
conductivity for n-alkanes such as n-undecane (n-C11), n-tetradecane (n-C14), n-pentadecane (n­
C15), n-hexadecane (n-C16) ranged from 0.120.15 W m–1 K–1 depending on the temperature.
16
Stryker and Sparrow (1990) found the thermal conductivity value of solid n-eicosane (n-C20) to
be 0.380.42 W m–1 K–1, depending on the temperature and the method of sample preparation.
Warth (1956) gave the following relationship for estimating the thermal conductivities of
paraffins in terms of their average molecular weight:
k w  2.4  10 4 M
2.4
Wada (1985) gave a basic relationship for paraffins up to C16 as follows:
kw = An2 + Bn + C – [D(1/n)2 + E(1/n) + F]T
2.5
where kw is the thermal conductivity (W m–1 K–1), A–F are constants, n is carbon number, and T
is temperature (range: 20–90 °C). Jamieson (1979) also developed a correlation in the form of:
kw = A(1 + B 1/3 + C2/3 + D








where  = 1 – T/Tc, Tc is the critical temperature, A is the pseudo-critical thermal conductivity, B
is a constant, C = 1 – 3B, and D = 3B. Equation 2.6 is valid for paraffins with carbon number up
to 25 and a temperature range of melting point to 0.9Tc. Typical conductivity values for paraffin
hydrocarbons reported in literature range from 0.10 to 0.42 W m–1 K–1 (Dick and McCready,
1954; Missenard, 1968; Filipov, 1968; Jamieson et al., 1974; Stryker and Sparrow, 1990;
Bidmus, 2003; Fong and Mehrotra, 2007).
2.2 Wax Precipitation
Paraffins precipitate as wax deposits in crude oils due to either evaporation of volatile
light components, or a drop in the temperature of the system (Svetgoff, 1984). Wax precipitation
occurs during the formation of solid wax crystals out of solution from a liquid phase, while wax
deposition occurs during the formation and growth of a layer of precipitated solid on a surface
(Hammami et al., 2003). Even though precipitation is necessary for deposition to occur, it is
17
possible to have wax precipitation without causing wax deposition. Furthermore, whereas
precipitation is mainly a function of thermodynamic variables such as composition, pressure and
temperature, deposition also depends on heat and mass transfer, flow hydrodynamics, and solidsolid and surface-solid interactions (Hammami et al., 2003). Normal paraffins are the most
readily precipitated, during the cooling of a “waxy” mixture, followed by naphthenes and iso­
paraffins, while aromatics tend to stay in the liquid phase (Pan et al., 1996).
2.2.1 Crystallization
As the temperature of a liquid crude oil is decreased, the energy of molecular motion
decreases, and the molecules move closer together. As time progresses, the molecules begin to
have a more ordered arrangement with the degree of order mostly determined by the shapes of
the molecules and their ability to fit together in adjacent positions (Turner, 1971). Typically, a
degree of super-saturation is required before the beginning of precipitation. At the WAT (or
freezing point in the case of a melt), the short-range intermolecular attractive forces are greater
than the energy of molecular motion and the molecules are bound together into a crystal. The
two distinct stages involved during this process, namely nucleation and growth (Hammami,
1994), are discussed in the following sub-sections.
2.2.1.1 Nucleation
The process of crystallization starts with the formation of a nucleus, which is the smallest
stable particle of wax crystal possible under the system conditions. As the liquid temperature is
decreased, molecules form an ordered arrangement of clusters of adjacently aligned chains.
Molecules continue to attach and detach from these ordered sites until the clusters become stable
after having reached a critical size. This process of attaching and detaching of molecules is
18
called nucleation and the stable clusters formed are the nuclei. Any smaller particle emerging
from the liquid would be unstable and tends to re-dissolve into the solution (Turner, 1971).
Nucleation may be spontaneous (homogenous nucleation), or it may be induced artificially
(heterogeneous nucleation). Homogenous nucleation is mainly a thermal process that usually
occurs from a pure sample with nucleation sites that are time dependent.
Heterogeneous
nucleation may be either thermal or athermal and all the nucleation sites are activated
instantaneously (Turner, 1971). Heterogeneous nucleation occurs either on the surface of a wall
or as a result of foreign particles in the solution.
2.2.1.2 Crystal Growth
If the temperature is kept at or below the WAT (or freezing point), following the
formation of the nuclei, more molecules attach themselves successively to the nucleation sites,
becoming part of the growing lamellar structure. Nearby molecules locate suitable parts of the
nucleation sites where they can fit into in an orderly manner. Intermolecular attractive forces
draw these molecules into place. Once in place, these molecules themselves provide suitable
sites to receive other molecules. A site having the highest possible number of neighboring
molecules bordering its position will be favored due to the higher magnitude of the attractive
forces occurring there (Keating, 1964). Growth occurs most easily at the edge of a partially
completed layer of molecules. During the crystallization of paraffins, a monomolecular layer is
formed by the side-by-side addition of molecules to form each consecutive layer, which is a
relatively fast process. The initial addition of a subsequent layer on an existing layer is slower,
because further growth on a geometrically perfect crystal only occurs if the clustering of
molecules on the surface nucleates a new layer (Hammami, 1994).
19
2.2.2 Wax Appearance Temperature (WAT)
The highest temperature at which the first wax crystals start to appear, upon cooling of a
“waxy” crude oil or mixture, is called the wax appearance temperature (WAT). The WAT is an
important parameter in wax precipitation and deposition. The WAT is also called the cloud point
temperature (CPT) and is essential for determining the tendency of crude oil towards wax
precipitation and deposition (i.e., crude oils with a high WAT will be more likely to undergo wax
precipitation and deposition). No wax precipitation or deposition will occur as long as the crude
oil temperature is above the WAT. Once the temperature drops below the WAT, wax molecules
will begin to crystallize out of solution and wax deposition can occur. Factors that favor an
increase in WAT also tend to favor increased wax deposition.
An important distinction exists between the liquidus temperature and the experimentally
determined WAT. The liquidus temperature defines the true solid–liquid phase boundary,
whereas the experimental WAT is the temperature at which the first crystals are detected upon
cooling. This value can vary depending on the sensitivity of the measurement technique, thermal
or cooling history and the cooling rate; hence, it can be very subjective. The experimental WAT
would be lower that the liquidus temperature and should be within the solid–liquid phase
envelope (Bhat and Mehrotra, 2004).
2.2.3 WAT Measurement Techniques
The WAT of a “waxy” crude oil sample is the highest temperature that wax solids can be
detected when the sample is cooled. Different equipment and methods have been developed to
determine the WAT of crude oils. The measured temperature depends on the oil composition,
the measurement technique, thermal history, the residence time of measurement, and the fluid
properties relating to crystal nucleation and growth (Hammami et al., 2003). Generally, higher
20
cloud point temperatures are obtained with more sensitive methods of measurement. Increases in
system pressure can decrease the measured cloud point temperature, particularly if the sample
contains solution gas (Monger-McClure et al., 1999).
(1) Visual Method (ASTM Standard D 2500-09)
The ASTM standard test method for determination of WAT is a visual measurement technique.
The sample is cooled down from a temperature that is at least 14 oC above the expected WAT of
the sample. The temperature at which the first wax crystals appear is noted as the WAT of the
sample. This method can only be used for petroleum products and biodiesel fuels that are
transparent in layers 40mm in thickness, and with a cloud point below 49 oC. Tiwary (2002)
modified this method by cooling in steps of 1°C and leaving the sample at each temperature step
for 15 minutes before checking visually for the appearance of wax crystals. The WAT values
obtained using this slightly modified approach were found to compare well with those obtained
from other methods.
(2) Filter Plugging (FP)
In this method, a solution of preheated and pre-filtered oil is passed through a capillary to a filter.
Both the filter and the oil sample are submersed in a programmable temperature bath. As the oil
is cooled at a steady rate, pressure drop across the capillary and filter is noted, and a comparison
of these pressure drops is used to determine the cloud point (Monger-McClure et al., 1999). An
increase in differential pressure drop indicates the occurrence of wax crystal formation (MongerMcClure et al., 1999). This method is preferred measuring the WAT of live oils, but is not
suitable for viscous crude oils.
21
(3) Viscometry
Precipitation of wax from "waxy" mixtures changes the flow behavior of the mixture gradually
from Newtonian to non-Newtonian (Tiwary, 2002). The rheology of the crude oil and its nonNewtonian behavior in the presence of wax crystals is utilized in this method. At temperatures
above the WAT, the sample is Newtonian and its viscosity is a function of temperature only
(Tiwary, 2002). When the temperature falls below the WAT, precipitation of wax crystals
makes the rheological properties of the sample become increasingly dependent on the shear rate
as well. Therefore, by using a rheometer to measure the viscosity of the sample as it is cooled,
the temperature at which the viscosity-temperature relationship suddenly starts to change can be
recorded as the WAT. Ronningsen et al. (1991) described WAT measurements using this
method.
(4) Solids Deposition System (SDS)
This method of measuring WAT is based on the transmission of light through the sample being
tested. The intensity of light transmission through the sample should change dramatically in the
presence of wax crystals. As a known volume of sample is cooled isobarically, while mixing
continuously, the average transmitted light power and the corresponding temperature are
automatically recorded with time using a computerized data acquisition system. The test is
stopped a few degrees below the temperature at which there is a dramatic drop in the intensity of
the transmitted light (Hammami and Raines, 1999).
(5) Cross Polar Microscopy (CPM)
This method has been found to give the highest value for WAT measurements when compared
with other methods, and is thus regarded as one of the most accurate methods (Ronningsen et al.,
1991). The CPM method is based on the theory that all crystalline materials rotate the plane of
22
polarization of transmitted light while liquid hydrocarbons do not. This method requires a light
source, an infrared filter, a polarizer, a temperature controller and a microscope. The sample is
enclosed in glass cover slides that are placed on the variable temperature microscope stage and
viewed through the crossed polarizer. As the sample is cooled, the appearance of wax crystals
are observed as isolated points of light using a video camera by the eye (Monger-McClure,
1999). CPM is the method of choice for limited sample volumes.
(6) Differential Scanning Calorimeter (DSC)
The DSC technique measures the heat released from the sample during the crystallization. As
with the CPM method, only a small quantity of sample is required for this method. The heat
released or absorbed and the variable specific heats exhibited by the isolated sample as during
cooling or heating is determined as the temperature changes. As the heat released is very small
at the onset of wax crystallization, care must be taken to obtain a stable baseline and use as large
a sample as possible without distorting the DSC signal. The temperature at which a melting peak
occurs in the heat flow-temperature curve (thermogram) is taken to be the WAT (Tiwary, 2002).
(7) Fourier Transform Infrared (FTIR)
The increase in energy scattering associated with solid formation due to wax
crystallization is used for detecting the WAT in this method.
The mid-infrared spectrum
between 650 and 4000 cm-1 contain wavelengths in which little energy is absorbed by
hydrocarbons. This spectrum is used because a wavelength that indicates wax crystal formation
is in this region and can be detected by spectral subtraction (Monger-McClure et al., 1999).
Similar to FP, the FTIR method is suitable for live oil measurements. Near infrared spectroscopy
has also been used as a method of determining the WAT (Alex et al., 1991).
23
2.2.4 Wax Precipitation Temperature (WPT)
The wax precipitation temperature (WPT) has been used to describe the highest
temperature at which the first wax crystals are observed while cooling a “waxy” crude oil or
mixture at a controlled and specified cooling rate. Cooling rate influences the phase transition
temperature and is known to affect the kinetics of crystallization. The effect of cooling rate on
the phase-change temperature for waxy mixtures and crude oils has been described in several
studies. Increased cooling rates have been reported to give lower temperature for the onset of
crystallization due to the super-cooling effects and the roles of nucleation and crystallization
kinetics (Hammami and Mehrotra, 1995; Guo et al., 2006; Paso et al., 2009; Kasumu et al.,
2013). Kasumu et al. (2013) reported experimental results for the effect of cooling rate on WPT
for several prepared solutions of a wax in a multicomponent solvent. They provided a correlation
for the effect of cooling rate and wax concentration on the measured WPT. Their correlation was
used by Arumugam et al. (2013) to predict the transition from the 'hot flow' to the 'cold flow'
regime in a waxy mixture flowing in a pipeline.
2.2.5 Wax Disappearance Temperature (WDT)
The wax disappearance temperature (WDT) is the temperature at which the wax crystals
in a “waxy” mixture become completely dissolved in solution while heating the mixture from a
temperature well below its WAT. The thermodynamic liquidus temperature was found to be
closer to the WDT than the WAT; in addition, the WDT was found to be an average of 3°C
higher than the WAT for prepared waxsolvent mixtures comprising a multi-component wax
(C20C40) dissolved in different paraffinic solvents (Bhat and Mehrotra, 2004).
24
2.2.6 Pour Point Temperature (PPT)
The pour point temperature (PPT) is the lowest temperature at which crude oil or a
“waxy” mixture will flow or pour. The oil flow properties is affected by the PPT, which is
dependent on the amount of paraffin wax present in the oil. The PPT is the temperature at which
the interlocking gel structure, formed as a result of crystallization of wax crystals from the oil,
causes the viscosity and flow properties of the oil to change dramatically. It can be determined
by cooling a sample in steps of 1°C and determining the lowest temperature at which the liquid
sample is able to move (Bhat and Mehrotra, 2004; Fong and Mehrotra, 2007). The PPT depends
on the carrying capacity of the fluid solvent. Tiwary (2002) measured the PPT of mixtures
containing wax dissolved in different hydrocarbon solvents with widely varying melting points
and found the difference between the various PPT to be less than 5°C.
2.2.7 Rheology
At temperatures below the WAT, wax crystals precipitate and a rapid increase in
viscosity occurs with the onset of non-Newtonian flow behavior (Wardhaugh and Boger, 1991).
The crude oil is converted into a complex non-Newtonian fluid whose flow properties are
difficult to measure in a reliable and repeatable manner, by the presence of crystallized wax. The
non-Newtonian behavior is in part caused by orthorhombic wax crystallites in solution that
flocculate together which results in a gel-like mixture with increased viscosity (Dirand et al.,
1998).
These crude oils, with precipitated wax crystals in them, are thixotropic in nature, and
their viscosity decreases isothermally with time, during flow at any particular shearing rate
(Cawkwell and Charles, 1987; Tiwary and Mehrotra 2004, Vignati et al., 2005). Because of the
25
yield stress exhibited in this condition, significant pressures are required to restart the flow of
gelled crude oil after shut down. Matveenko et al. (1995) studied the time-dependent thixotropic
behavior of a highly paraffinic crude oil and found the system to be pseudo-plastic with
pronounced thixotropic properties. Below the PPT, the crude oil no longer flows but was found
to display viscoelastic rheological properties (Silva and Coutinho, 2004; Visintin et al., 2005).
The flow behavior of gelled “waxy” crude oils is affected by many factors, the most important
being the thermal history, shear history, aging and composition (Tiwary, 2002; Kané et al.,
2004).
2.3 Wax Deposition
The precipitation and deposition of wax is of significant importance in the production,
transportation and processing of crude oil because wax deposition can damage oil reservoir
formations and wells, and cause blockage of pipelines and process equipment. The deposition of
wax in pipelines and process equipment leads to increased pressure drop, increased pumping
power requirements and/or reduction in efficiency.
Most wax deposition studies reported in the literature have focused on single-phase oil
and two-phase oil–gas flow. However, water is inevitably found in the produced oil and its
fraction in the oil stream, called the water-cut, generally increases with the lifetime of a
production well. Relatively few studies have been conducted to study the effects of water on the
deposition process (Abdel-Waly, 1999; Couto et al., 2008; Bruno et al., 2008; Zhang et al.,
2010a; Zhang et al., 2010b). A literature review showed that the wax deposition process is not
well established for two-phase oil–water flow conditions, perhaps due to the increased
26
complexity caused by the addition of the water phase and the difficulty in obtaining consistent
results with oil–water mixtures (Couto et al., 2008).
2.3.1 Mechanism of Wax Deposition
A number of mechanisms have been suggested for explaining the process of wax
deposition, and estimating the amount of deposition that will occur in a system under a particular
set of operating conditions. Such mechanisms include molecular diffusion, shear dispersion,
Brownian diffusion, gravity settling and heat transfer. Molecular diffusion and heat transfer are
currently regarded as the most relevant mechanisms.
2.3.1.1 Molecular Diffusion
The molecular diffusion mechanism is based on the assumption that a radial temperature
gradient is created when oil flows in a pipeline with the pipeline wall temperature lower than the
WAT of the oil, which gives rise to a concentration gradient that causes the diffusion of wax
from the region of higher concentration within the bulk, towards the wall where the
concentration of dissolved wax is lower. In the underlying pseudo-steady state mathematical
model, the amount of deposit is obtained from the rate of mass transfer at the liquid–deposit
interface, and an energy balance is used to back-calculate the liquid–deposit interface
temperature. An inherent assumption in the molecular diffusion modeling approach is that the
deposit–liquid interface temperature is variable, which is predicted to increase with deposit
growth from an initial value close to the pipe-wall temperature and ultimately to the WAT at
steady state. This mechanism of wax deposition is the most widely studied and has been
reported as a dominant mechanism (Burger et al., 1981; Weingarten and Euchner, 1986;
27
Svendson, 1993; Brown et al., 1993; Erickson et al., 1993; Hsu and Brubaker., 1995; Creek et
al., 1999; Singh et al., 2000, 2001).
2.3.1.2 Heat Transfer
In the heat-transfer mechanism, the deposit formation and growth is taken to be a (partial)
solidification or freezing process involving crystallization (Ghedamu et al., 1997; Cordoba and
Schall, 2001a; Bidmus and Mehrotra, 2004, 2008a, 2008b, 2009, 2012; Mehrotra and Bidmus,
2005; Bhat and Mehrotra, 2005, 2006, 2008; Mehrotra and Bhat, 2007, 2010; Parthasarathi and
Mehrotra, 2005; Fong and Mehrotra, 2007; Tiwary and Mehrotra, 2009; Arumugam et al., 2012,
2013; Kasumu and Mehrotra, 2013). The rate of heat transfer through the deposit layer is
dependent on the thermal driving force between the bulk “waxy” oil or mixture temperature and
the cooler pipe-wall temperature. The overall rate of heat transfer is influenced by the convective
(from the flowing crude oil and surroundings) and the conductive (from the pipe wall and deposit
layer) thermal resistances in series.
Mathematical models have been developed based on the moving boundary problem
formulation for heat transfer associated with phase transformation (Bhat and Mehrotra, 2005,
2006, 2008; Mehrotra and Bhat, 2007, 2010; Arumugam et al., 2012, 2013). In the models based
on this heat-transfer approach, involving (partial) freezing or solidification, the release of the
latent heat of phase change accompanies the growth of a wax deposit layer close to the pipe wall,
which is held at a temperature lower than the WAT of the flowing “waxy” crude oil. An
assumption made in the heat-transfer mechanism is that the liquid–deposit interface temperature
is equal to the WAT of the crude oil, or waxy mixture, throughout the deposition process. This
assumption has been confirmed through measurements involving batch cooling experiments
under static and sheared conditions (Bidmus and Mehrotra, 2008a, 2008b). It is pointed out that
28
the heat-transfer based deposition mechanism is able to explain solids deposition under both “hot
flow” (with the wax mixture or crude oil temperature above the WAT) and “cold flow” (with the
wax mixture or crude oil temperature below the WAT) conditions (Bidmus and Mehrotra, 2009,
2012; Arumugam et al., 2013).
2.3.2 Structure of the Wax Deposits
The structure of wax deposits formed in pipelines during the deposition process is
lamellar in nature and is similar to that of pure n-alkanes except for a conformational disorder
that occurs in the interfacial region. The packing of the sub-cell is orthorhombic at room
temperature and hexagonal at higher temperatures (Clavell-Grunbaum et al., 1997). Observation
of the deposits with a cross-polarized microscope by Holder and Winkler (1965a) revealed that
the wax crystallites have structures of platelets that overlap and interlock. The crystallization of
the paraffins thus leads to the formation of gel deposits with a complex morphology (Singh et al.,
2000). Gelling occurs when an adequate amount of solid paraffin crystals, enough for the
formation of a solid network structure, have been formed.
Wax deposits are therefore composed of liquid oil entrapped in a network of solid
paraffin wax. Wax-oil gelation is due to the flocculation of orthorhombic wax crystallites that
appear in solution during cooling (Dirand et al., 1998). The conditions at which the gel was
deposited and the rate of gelation affects the composition of the gel. Studies have shown that as
little as 2% of precipitated paraffin wax is sufficient to form a gel deposit (Holder and Winkler,
1965b; Singh et al., 2000).
29
2.3.3 Factors Affecting Wax Deposition
Wax deposition starts to occur as soon as the pipe wall temperature becomes equal to or
lower than the WAT, thus factors affecting the WAT are also important to wax deposition. For
the single-phase oil some important factors considered to affect the value of WAT are
composition, temperature, flow or shear rate and deposition time (Hammami and Raines, 1999).
In addition to these, other factors that come into play in a two-phase oil–water emulsion include
water content, flow pattern, emulsion characteristics, and deposition surface properties (Bruno et
al., 2008; Zhang et al., 2010a, 2010b).
2.3.3.1 Effect of Composition
The lower the paraffin content in the crude oil, the less likely it is that deposition will
occur. For the single phase wax deposition, it was shown that when different wax-solvent
mixture compositions are exposed to similar temperature conditions with respect to their
respective WAT, the same amount of deposition occurs (Bidmus and Mehrotra, 2004;
Parthasarathi and Mehrotra, 2005; Fong and Mehrotra, 2007). However, when all the mixtures
were exposed to identical operating conditions, those with a higher wax composition produced
more solid deposits. Increasing the wax content of a crude oil increases its WAT, which in turn
increases the possibility of deposition.
Hammami and Raines (1999) suggested that while both n-paraffins and iso-paraffins tend
to cluster together and precipitate from crude oil as wax solids, the iso-paraffins tend to delay the
formation of wax nuclei and usually form unstable solids. Naphthenes or cyclo-paraffins tend to
disrupt the wax nucleation process because they are stiff and bulky in nature, while aromatics are
good solvents for paraffin waxes. Patton and Casad (1970) observed that an oil mixture
30
containing lighter paraffin waxes formed unstable deposits that easily flaked off the deposition
surface while the oil mixture with heavier waxes formed structurally stronger deposits.
A reduction in paraffin deposition from crude oil, in the presence of asphaltenes has been
reported (Woo et al., 1984; Misra et al., 1995). Deposited asphaltenes could serve as nucleation
sites for additional wax deposition. The presence of impurities and other amorphous solids in the
oil might lower the energy barrier required for the formation of the critical wax nucleus
(Hammami and Raines, 1999). Meray et al. (1993) reported that on adding light fractions to
crude oil, the WAT of the crude decreased by as much as 15°C depending on the amount of light
component added. Similar results were obtained by adding solution gas to the oil, making it live
oil (Brown et al., 1993).
The presence of water has been reported to decrease the amount of wax deposited,
especially on a water-wet surface (Li et al., 1997). Using a cold finger experimental apparatus, a
few studies have reported a decrease in the amount of solids deposition with increasing water cut
for a two-phase oil–water deposition process (Abdel-Waly, 1999; Couto et al., 2008; Zhang et
al., 2010a, 2010b). The same trend was also reported by Bruno et al. (2008) who used a flow
loop experimental set-up. They stated that the increase in water cut diminishes the flow path of
dissolved wax due to a higher concentration of water droplets. Couto et al. (2008) observed no
difference in the amount of wax deposited when salt water was used instead of fresh water. Gao
(2003) conducted oil/water two-phase wax deposition experiments with different water cuts in a
1.5-inch flow loop and found that wax deposition rate in the oil/water two-phase flow was higher
than that in single phase flow. More recently, Hoffmann et al. (2012) performed two-phase,
stratified oil/water flow loop experiments and reported higher deposit mass per unit area at a
lower total flow rate. They also reported higher deposit thicknesses at higher water cuts and
31
attributed this to a higher degree of gelation, resulting from decreased shear stress. Sarica and
Volk (2004) used the Tulsa loop to study two-phase wax deposition in both horizontal and
vertical pipes. They concluded that wax deposition is a flow-pattern dependent phenomenon,
with annular flows producing the thickest deposits in horizontal flow tests. In vertical flow tests,
they reported that an increase in the oil superficial velocity results in thinner deposits. More
recently, Panacharoensawad and Sarica (2013) studied single-phase and two-phase wax
deposition, and they concluded that water did not have a direct impact on the deposit thickness
and the deposit composition, for the case of water-in-oil dispersed flow. They also suggested that
the direct impact of water content on wax deposition is mainly on the change in the shear and
heat transfer behaviors which were found to have a strong impact on wax deposition.
2.3.3.2 Effect of Temperatures
It was thought that the temperature difference between the bulk oil and the pipe wall or
the outside temperature is the driving force required for deposition to occur (Agrawal et al.,
1990; Creek et al., 1999; Wu et al., 2002). However, it has been shown that having a higher
overall temperature difference does not necessarily translate into greater amount of deposition in
wax deposition (Bidmus and Mehrotra, 2004; Mehrotra and Bidmus, 2005; Parthasarathi and
Mehrotra, 2005). Wax deposition decreases as the temperatures of the crude oil and pipe wall or
coolant increase relative to the WAT. Mehrotra and Bidmus (2005) showed that wax deposition
could be prevented if the crude oil flows through a highly conductive pipeline maintained above
a certain temperature given by:
ℎ 𝑟
𝑇ℎ = WAT+ ℎ 𝑐 𝑟𝑜 (WAT− 𝑇𝑐 )
2.7
ℎ ℏ
32
Where ℎ𝑐 and ℎℎ are the outside coolant and inside crude oil heat transfer coefficients
respectively, 𝑟𝑜 and 𝑟ℏ are outside and inside pipe radii respectively, and 𝑇ℎ and 𝑇𝑐 are the crude
oil and coolant temperatures respectively. It was shown that this temperature could be relatively
high for sub-sea pipelines and that it would be energy-intensive and uneconomical to maintain
the crude oil temperature at this value (Mehrotra and Bidmus, 2005). Bidmus and Mehrotra
(2004) indicated that the temperature difference between the oildeposit interface and the pipewall is an important parameter for wax deposition. As the thickness of the wax deposit increases,
it creates a thermal insulation that limits the rate of heat transfer and reduces further increases in
the deposit mass (Cole and Jessen, 1960).
For the two-phase oil–water wax deposition, some studies (Couto et al., 2008; Zhang et
al., 2010a, 2010b) stated that wax deposition increases with the temperature difference between
the bulk emulsion and the deposition surface, as the deposition surface temperature is reduced
below the WAT of the waxy crude oils, while keeping the bulk emulsion temperature constant.
However, Kasumu and Mehrotra (2013) reported results from two-phase deposition studies that
showed that similar to single-phase wax deposition, the important temperature driving forces
were difference between the waxy mixture temperature and the liquid–deposit interface
temperature, and between the liquid–deposit interface temperature and the pipe-wall temperature.
2.3.3.3 Effect of Flow Rate and Shear Rate
For the single phase wax deposition, it has been shown that the deposit mass decreases as
the flow rate of the crude oil or waxy mixture is increased, regardless of flow being laminar or
turbulent (Bidmus and Mehrotra, 2004; Parthasarathi and Mehrotra, 2005; Fong and Mehrotra,
2007; Creek et al., 1999; Patton and Casad, 1970; Bott and Gudmunsson, 1977; Wu et al., 2002;
33
Jennings and Weispfennig, 2005; Tiwary and Mehrotra, 2009). The rate of shear at the wall was
proposed to cause a sloughing or shearing off of the deposits that increases with increasing flow
rate (Creek et al., 1999). This would start to occur when the cohesive and adhesive forces
properties of the paraffin wax molecules and the deposition surface are overcome by the rate of
shear (Bott and Gudmunsson, 1977). A cold spot wax deposition tester used by Abdel-Waly
(1999), however, showed an initial increase followed by a decrease in the amount of wax
deposited on the deposition surface as the shearing rate was increased. Abdel-Waly (1999) stated
that the initial increase in deposition was because more and more paraffin was carried out by the
moving oil rotation, providing a greater opportunity for deposition upon the cold spot surface,
and that the viscous drag was still insufficient to cause wax removal. However, with an increase
in stirring speed, the viscous drag exerted by the solution rotation tended to remove some of the
accumulated wax. Deposits obtained from an increased flow rate have been found to be harder;
containing lower fractions of embedded oil or solvent (Jessen and Howell, 1958; Hsu and
Bubaker, 1995; Creek et al., 1999; Singh et al., 2000-2001; Cordoba and Schall, 2001b; Bidmus
and Mehrotra, 2004; Fong and Mehrotra, 2007; Tiwary and Mehrotra, 2009).
To explain the effect of shear rate on the deposition process, Mehrotra and Bhat (2007)
proposed a model of the deposit comprising of individual cubical cages made of solid wax, with
embedded liquid oil. They proposed that the application of a shear stress causes the tilting of the
cubical cage, which causes a portion of the liquid phase to be “squeezed” out of the deposit. It
was shown that the shear stress causes an enrichment of the solid wax phase in the deposit at
high flow rates.
34
2.3.3.4 Effect of Deposition Time and Aging
The rate of wax deposition on a surface decreases with time due to the thermal insulation
provided by the initially deposited solids (Cole and Jessen, 1960). Thus, the amount of
deposition increases with time, irrespective of the operating conditions, until it reaches an
asymptotic value at steady state conditions. Using small scale laboratory set-ups, studies have
shown that a thermal pseudo-steady state is attained in less than 30 minutes during deposition
from waxsolvent mixtures under laminar and turbulent conditions (Bidmus and Mehrotra, 2004;
Parthasarathi and Mehrotra, 2005; Fong and Mehrotra, 2007; Tiwary and Mehrotra, 2009,
Kasumu and Mehrotra, 2013). Laboratory studies also showed a negligible increase in the mass
of the deposit after 4 hours.
The wax content in the deposit has also been reported to increase with time (Creek et al.,
1999; Singh et al., 1999-2001; Cordoba and Schall, 2001a, 2001b; Wu et al., 2002; Bidmus and
Mehrotra, 2004; Parthasarathi and Mehrotra, 2005; Fong and Mehrotra, 2007; Tiwary and
Mehrotra, 2009). This leads to a gradual hardening of the deposit layer with time that is referred
to as “aging” (Creek et al., 1999; Singh et al., 1999, 2001). During aging, the gel-like structured
deposit comprising a 3-dimensional network of solid wax with liquid oil entrapped in it
undergoes a characteristic change with time, whereby it becomes richer in heavier paraffin
content while the lighter paraffin content or the amount of entrapped oil simultaneously
decreases. Singh et al. (2000) proposed a counter diffusion process in which wax molecules with
carbon number below a certain critical value diffused out of the deposit while those with carbon
number above this critical value diffused into the deposit. They observed that the aging process
depended on the operating conditions and that it was a stronger function of the temperature
difference across the deposit than of the compressive force due to the flow rates. Creek et al.
35
(1999) explained deposit aging using the phenomena of Ostwald ripening or the self-organization
of the wax molecules in the deposit. From their laboratory studies, Fong and Mehrotra (2007)
observed the aging process to be more pronounced at higher Reynolds numbers.
2.3.3.5 Effect of Surface Properties
Wax deposition is affected by the material and properties of the pipeline inner surface.
Studies indicate that the adhesion of the deposit onto a surface is a function of either wettability
(free surface energy) and/or surface roughness. The theory that supports wettability suggests that
paraffin deposit crystals are held in place by adsorption forces. These adsorption forces are
dependent on the free surface energy possessed by both the paraffin and the surface (Patton and
Casad, 1970). Cole and Jessen (1960) studied the effect of wettability on paraffin deposition in
single-phase wax deposition experiments and observed that the amount of deposit decreased with
decreasing free surface energy for a given temperature difference. They found that the
temperature difference and the free surface energy acted independently in determining the
amount of wax depositing. As the free surface energy of a deposition surface is reduced, a
resultant decrease in the adsorption forces occurs. This results in a decrease in the amount of
paraffin that can be retained on the deposition surface for the flow conditions present (Bott and
Gudmundsson, 1977). More recently, Quintella et al. (2006) observed less deposition in
pipelines lined with polypropylene than with those lined with high-density polyethylene and a
vinyl acetate copolymer. This result was attributed to the higher contact angle (and hence, lower
wettability) between the flowing crude oil and the polypropylene lined pipes. Li et al. (1997)
performed two-phase oil–water wax deposition experiments in steel as well as glass-layered
tubes and found that more wax was deposited on the steel tubes than was deposited on the glasslayered tubes. This occurrence was attributed to the greater wettability of the steel tube surfaces.
36
The surface roughness theory suggests that the roughness of the deposition surface is
responsible for the adherence of the deposit onto the surface. The rougher the surface, the greater
the frictional force on that surface that will keep the deposit from flaking away due to shear or
flow rates. Jorda (1966) carried out wax deposition experiments using a cold spot test apparatus
and concluded that the quantity, adhesion and the mean molecular weight of the paraffin that
accumulates on the deposition surface increases as the surface roughness increases. He attributed
the lower amount of wax observed on plastic coated surfaces when compared to metallic surfaces
to the smoother surface of the plastic coated surfaces. However, (Patton and Casad, 1970)
performed similar experiments and concluded that there was no correlation between surface
roughness and amount of deposit. They found that paraffin waxes of lower molecular weight slid
off or flaked off smooth surfaces while high molecular weight paraffins did not. The lower
amount of deposit observed for plastic-coated surfaces was attributed to thermal insulation
provided by the plastic layer.
2.3.3.6 Effect of Emulsion Characteristics
Wax deposition in a multiphase flow is a complex process influenced by emulsion
characteristics. For the two-phase oil–water system, emulsion preparation patterns including the
stirring speed, stirring temperature, and addition method of the water phase have an extremely
significant effect on emulsion characteristics (Zhang et al., 2010a). During the course of
emulsion preparations, different droplet sizes and distributions generated by varying the mixing
speed of the stirrer or varying the water cut may have a significant effect on the wax deposition.
Using a cold-finger apparatus, Zhang et al. (2010a) studied the effect of emulsion characteristics
on wax deposition from water-in-waxy crude oil emulsions under static cooling conditions and
reported that wax deposition rate decreases as the stirring speed at which the emulsions were
37
prepared, increases. In other words, the wax deposition rate decreases with the decreasing droplet
diameters of the dispersed phase and the resulting increasing amount of smaller droplets.
However, Couto et al. (2008) performed cold finger experiments on two-phase oil–water
emulsions using emulsions prepared at different speeds, the differences in the deposit mass
observed for both mixing speeds were within the error band of the measurements. This means
that either the emulsions prepared had comparable properties or the differences in their
characteristics did not affect the deposition process for the range of parameters tested. They
could not determine which of the above explanations to be valid as the emulsions were not
thoroughly characterized.
2.3.4 Experimental Techniques for Wax Deposition
Different types of experimental apparatuses and procedures have been developed over the
years to study the wax deposition problem (Bidmus and Mehrotra 2004). The principle behind
the operation and design of wax deposition experiments is to create a temperature difference
between a surface and the crude oil mixture or sample. This produces the thermal gradient that
induces deposition of wax on the surface. The apparatus should be capable of providing a means
of measuring and monitoring the amount of deposit obtained under different operating
conditions. The deposition data thus obtained can be correlated with an appropriate model. Four
types of deposition experimental apparatus that have been developed over the years (Ellison et
al., 2000, Bidmus and Mehrotra, 2004; Zougari et al., 2006). These are discussed in the
following sub-sections.
38
2.3.4.1 Flow Loop Experiments
The preferred apparatus for studying wax deposition is the flow or pipe loop system
because it is the nearest in design to actual field conditions. This design has a double pipe heat
exchanger in which cold fluid is pumped through the shell side and the oil mixture pumped
through the tube side (Bidmus and Mehrotra, 2004). The oil is heated in a reservoir or tank and
pumped through a pipeline in the form of a flow loop. Incorporated in the flow loop is the heat
exchanger section. A large volume of oil is required in this method to maintain the flow loop,
and in reality the loop system does not completely simulate actual field conditions. Also, the
initial wax composition of the oil would change gradually as deposition occurs although this may
not be significant in a flow loop with a large oil reservoir and a relatively small heat exchanger
or deposition section.
2.3.4.2 Cold Spot or Finger
After the flow loop, the cold finger apparatus is the next most commonly used
experimental setup for wax deposition. It consists of a temperature-controlled cold deposition
surface, usually in the shape of a metal finger that is submerged in a sample of the oil mixture at
a temperature above its WAT. A cold spot is similar to a cold finger except that a flat disk is
used as the deposition surface as opposed to a cylindrical surface. The warm oil mixture may be
stirred with an agitator to simulate shear stress on the surface of the cold finger. The oil mixture
close to the cold finger is cooled and wax deposits form on the surface of the cold finger. The
main advantage of this setup over the pipe loop system is that less oil is required and it is
economical and easy to set up.
39
2.3.4.3 Draft Tube Assembly
The draft tube assembly is similar to the cold finger setup. It consists of an oil mixture
reservoir that has a concentric tube heat exchanger or draft tube inserted within it down the
centre (Bidmus and Mehrotra, 2004). Coolant flows through the annulus of the draft tube while
deposition occurs on the inside wall of the inner tube. Flow of the oil mixture is created by an
axial flow impeller placed at the exit of the draft tube.
2.3.4.4 Co-axial Shearing Cell
The co-axial shearing cell is also similar to the cold finger setup. It consists of an outer
stationary cylinder and a central rotating cylinder, with the oil mixture sample in the annular
space. The cooled deposition surface can either be the outer wall of the central rotating cylinder
or the inner wall of the stationary outer cylinder. The problem with the former approach is the
difficulty in separating the coolant fluid flowing into the inner cylinder from the oil mixture
while this cylinder is rotating simultaneously. The latter approach, where deposition occurs on
the stationary cylinder, is easier to design and set up.
2.3.5 Wax Deposition Modeling
One group of researchers have used the molecular diffusion approach to model the
process of wax deposition from crude oil mixtures (Burger et al., 1981; Majeed et al., 1990;
Svendson, 1993; Singh et al., 1999, 2001; Kok and Saracoglu, 2000; Ramirez-Jaramillo and
Lira-Galeana, 2004). In this approach, the rate of wax deposition is modeled using a modified
form of Fick‟s diffusion equation. The wax deposition flux was estimated this way by Burger et
40
al. (1981) in terms of the wax solubility coefficient for the oil, dC/dT, and the radial temperature
gradient dT/dr, given as:
dmd
 dC  dT 
 Dm A 
 
dt
 dT  dr 
2.8
where md is the mass of the deposit, C is the wax concentration, and Dm is the mass diffusivity.
The molecular diffusion coefficient, Dm, may be estimated from reported correlations. A form of
equation 2.8 was used by Singh et al. (1999, 2000, 2001) to model wax deposition and aging in
wax–solvent mixtures. In their approach, the liquid–deposit interface temperature was back
calculated from an energy balance, which predicted a gradual increase in its initial value, from
close to the pipe-wall temperature, to the WAT at steady state.
To determine the amount of wax deposited at equilibrium conditions, Agrawal et al.
(1990) developed a mathematical equation by correlating the flow rate and the oil and wall
temperatures from wax deposition experiments. Mehrotra (1996) commented on a similar
correlation developed by Khan et al. (1995) and pointed out the limitations of interpolating or
extrapolating an empirical model that has been fitted to experimental data.
Another group of researchers have used the heat transfer approach to model the process
of wax deposition from crude oil mixtures. Mehrotra (1990) suggested the use of a heat transfer
analogy for wax deposition. He assumed that the heat transfer resistances due to the pipe wall
and coolant flow were negligible, and developed the following correlation:
hxd
2 xd

kd
D  2 xd

D
 ln
 D  2 xd



1
(Td  Tc )
(Th  Td )
2.9
41
The (hxd/kd) parameter was plotted against the temperature differential and flow rate results from
the experiments performed by Agrawal et al. (1990) and was found to give an average value of
0.29 ± 0.19. This was suggested as a possible parameter for scale up.
The pseudo-steady state conditions of wax deposition was examined by Bidmus and
Mehrotra (2004). They suggested a dimensionless scale up parameter, d, defined as defined as
the thermal resistance offered by the wax deposit relative to the overall thermal resistance. It
also represented the ratio of the temperature difference across the deposit layer to the overall
temperature difference, given as:
d 
Rd
T  Twi
 d
Rh  Rd  Rm  Rc
Th  Tc
2.10
where Td is the temperature at the liquiddeposit interface, Twi is the inner wall temperature of
the pipeline, and Th and Tc are the average oil and coolant temperatures respectively. d has been
related to the amount of wax deposited for various process variables (Bidmus and Mehrotra,
2004; Parthasarathi and Mehrotra, 2005; Fong and Mehrotra, 2007; Tiwary and Mehrotra, 2009;
Kasumu and Mehrotra, 2013).
A transient mathematical model based on heat transfer considerations for solids
deposition from “waxy” mixtures in both radial and axial directions for established laminar flow
in a pipeline was presented by Bhat and Mehrotra (2005, 2006). They modeled the solids
deposition via a moving boundary problem formulation. They found that the rate of heat transfer
at the liquid–deposit interface, as well as those in the liquid region and the deposit layer,
influenced the growth of the deposit layer. At steady state, a smaller deposit thickness was
predicted with pipe length for higher mixture temperature, pipe wall temperature, and inlet
42
Reynolds number. Recently, Arumugam et al. (2013) modified the model of Bhat and Mehrotra
(2005), by including a correlation proposed by Kasumu et al. (2013), to predict wax deposition
in a waxy mixture flowing in a pipeline in both the hot flow and cold flow conditions. They were
able to match their predictions with the trends in laboratory experimental data reported by
Bidmus and Mehrotra (2009).
2.4 Control and Remediation
The steps involved in controlling wax deposition, in order of priority includes:
predict/diagnose, prevent and mitigate/remediate the solid deposition (Leontaritis, 1996).
Predicting the extent of wax deposition involves the estimation of WAT of the crude oil and the
knowledge of factors that could affect the wax deposition. The factors can be adjusted, as is
possible, for prevention. In cases where complete prevention fails, remediation becomes
necessary. Various methods are being used in the industry to control the extent of wax deposition
such as chemical treatment, mechanical methods, thermal methods and biological methods. In
addition, a relatively new technology for controlling wax deposition is the 'cold flow' of crude
oil.
2.4.1 Mechanical Methods
These methods involve the use of various mechanical devices to physically scrap off the
wax deposit from the pipe wall. Some of the devices include rod scrapers, paraffin cutters,
plunger lifts and flowline pigs. The removal of wax deposits with these devices is done
periodically. Pigs are the most commonly used mechanical devices to scrap off wax deposits.
Some problems associated with the use of these devices include tubing wear from removal tools,
43
broken tool wirelines, stuck pigs, requiring flowline excavation, and capital expenditure for the
equipment (Newberry et al., 1986; Aiyejina et al., 2011). To mitigate some of the problems,
bypass pigs are used, which allows liquid to flow through in case of an accumulation ahead of
the pigs to disperse the solids accumulated (Wang et al., 2008). In addition, operation of the pigs
at short intervals before there is a large extent of deposition reduces the risk of stuck pigs. Recent
improvements to this technology include the use of remote controlled tools on wheels that reduce
the use of wirelines thereby eliminating the risk of severed lines.
2.4.2 Thermal Methods
Thermal methods involve either the application of external heat on the deposition surface
or the minimization of radiation heat losses from the pipeline. The heat losses can be minimized
by insulating the pipeline or by maintaining a higher pressure in the flow lines to minimize
cooling through dissolved gas expansion (McClaflin and Whitfill, 1984). Singh et al. (2007)
demonstrated improved heat retention for wax control in an arctic environment using vacuuminsulated tubing. For the application of external heat, this can be done using several techniques,
including the injection of hot water, hot oiling, steaming and the use of an electrical heating
element (Becker, 2000). Hot oil serves as both a heater and a solvent for the wax deposits but can
plug perforations, pumps or separators due to eventual cooling (Newberry et al., 1986). Heating
elements are difficult to use in subsea pipelines and long flow lines. The application of heat on
the deposition surface melts the deposit back into the oil.
Methods have also been developed to make use of electromagnetic radiation and
inductive heating to remove wax deposits in pipelines (Balakirev et al., 2001, Sarmento et al.,
2004). Zhang et al. (2013) reported a 50% decrease in oil viscosity and 87.5% decrease in was
44
deposition rate from experiments in which magnetic paraffin control (MPC) was studied in a
laboratory-scale oil circulating platform.
2.4.3 Chemical Method
This method involves the use of solvents, pour point depressants, wax crystal modifiers,
anti-sticking agents or a combination of any of these methods for controlling the deposition of
paraffin wax. A generic wax inhibitor/dispersant and anti-sticking agent was developed and
tested by Groffe et al. (2001), who suggested that the use of the chemical dispersant with antisticking properties can reduce the severity of wax deposition by lowering the WAT and
simultaneously creating less adhesion between the wax deposit and the metal surface. Towler et
al. (2011) observed a 59% reduction in deposition using wax inhibitors which are a combination
of solvents, pour point depressants and wax crystal modifiers especially for crude oil obtained
from the Dakota formation in Wyoming.
The applicability of the chemicals for wax inhibition, however, is highly selective for a
particular composition of the crude oil and the environmental conditions. The chemicals that are
applicable to a particular production field may not be applicable to other fields, or even different
wells within the same field. Ferworn et al. (1997) compared the effectiveness of the four
different solvents used for inhibiting wax depositions with o-xylene, he found that the wax
inhibition ability not only depended on the concentration of the solvents employed, but also on
the type of wax being treated. Becker (2000) suggested a combination of the different methods,
particularly thermal and chemical methods, for efficient and safer means of removing and
controlling deposited solids in pipelines.
45
2.4.4 Biological Methods
In this method, biological agents such as bacteria are used to prevent or remove wax
deposits. The metabolic activity of select bacteria produce organics acids and alcohols that cause
the bio-degradation of alkanes. However, the bacteria blend and treatment volume need to be
determined for different crude oils and reservoir environments (Brown, 1992).
2.4.5 Cold Flow of "Waxy" Crude oils
Most of the methods of control discussed above have limitations, including cost and
selectivity, especially when dealing with long production lines or offshore facilities, and in some
cases can lead to more problems in process equipment further downstream (Newberry et al.,
1986). 'Cold flow' is considered an alternative approach to controlling and reducing solids
deposition problems during the flow of “waxy” crude oil, especially in subsea un-insulated
pipelines where the temperature of the surrounding environment can be well below the WAT of
the fluid being transported.
'Cold flow' occurs when the liquid oil being transported contains suspended solid wax
crystals, in the form of a slurry, and is transported through the pipeline under stable conditions
with no wax deposition (Merino-Garcia and Correra, 2008). This can happen when the crude oil
temperature falls between its WAT and PPT. Although very few studies can be found in the
literature relating to 'cold flow' as a means of preventing wax deposition, there are numerous
patents that suggest methods of creating “waxy” slurries. For application of 'cold flow' as an
effective technology in controlling wax deposition, the precipitated solids in the bulk liquid
phase should only act as nucleation sites and not deposit on the cold walls. Thus, the challenges
faced by the cold flow technology include creating a stable slurry and the ability to cool the
„waxy‟ crude oil to the pipe wall temperature below the WAT without depositing the solids on
46
the pipe wall (Merino-Garcia and Correra, 2008). Studies have shown 'cold flow' technology to
be relatively successful in the prevention of gas hydrate formation during the flow of crude oil
and natural gas (Gudmunsson, 2002).
47
Chapter Three: Experimental
The experimental work included in this thesis is comprised of three parts; WPT–cooling
rate experiments, single- and two-phase flow loop wax deposition experiments, and single- and
two-phase cold finger wax deposition experiments. The experimental apparatuses and associated
equipment, procedures and experimental designs used in all the different sets of experiments are
described in this chapter. The properties and compositional analyses of the materials used are
also discussed. Furthermore, the method of data collection and processing are explained. The
WPT–cooling rate experiments were designed to investigate the effects of cooling rate and
composition. The flow loop wax deposition experiments were designed to investigate the effects
of water content, waxy mixture flow rate, waxy mixture temperature and coolant temperature on
wax deposition. The cold finger experiments were designed to investigate the effects of
deposition time, stirring rate and water content on wax deposition. It is noted that most of the
information presented in this chapter on the WPT–cooling rate experiments have been published
in Fuel by Kasumu et al. (2013), while most of the information on the flow loop wax deposition
experiments have been published in Energy & Fuels by Kasumu and Mehrotra (2013).
3.1 Materials
3.1.1 Paraffin Waxes
Two different paraffin waxes were used in this study. These were Conros Parowax
supplied by Conros Corporation (Ontario, Canada) and Bernardin Parowax, which was available
in retail stores locally. Conros Parowax was obtained in the form of small granules. It consists of
n-alkanes in the range of C20 to C50 with a melting point range of 57–62 °C and a density of 915
kg m–3 at 23 °C (Fong, 2007). Bernardin Parowax was obtained in form of rectangular chunks
48
and consists of n-alkanes in the range of C21 to C58, with a melting point range of 57–61 °C and
density of 912 kg m–3 at 23 °C.
Conros Parowax has an average molecular weight of 414.2 kg kmol–1, equivalent to a
carbon number of about 29 while Bernardin Parowax has an average molar mass of 420.9 kg
kmol–1 that corresponds to a carbon number of about 30. Both paraffin waxes were characterized
by simulated distillation in the In-Situ Combustion Laboratory (University of Calgary), using a
HP 6890 series GC system. Details of the equipment and procedure used for the compositional
analysis are discussed later. The results of the compositional analysis of the waxes are shown in
Table 3.1 and Figure 3.1.
3.1.2 Solvents
It was required that the solvents used in this study be non-volatile at temperatures up to
70 °C. One of the solvents used was Norpar13, a petroleum solvent obtained from Imperial Oil
(Ontario, Canada). Norpar13 consists of n-alkanes ranging from C9 to C16 and has a density of
754 kg m–3 at 23 °C. It has a flash point of 97 °C.
The other solvent used in this study was Linpar1416V obtained from APCO Industries
Ltd. (Ontario, Canada), which consists of n-alkanes ranging from C10 to C20, with a density of
763 kg m–3 at 23 °C. Linpar1416V has a flash point of 117 °C.
The flash point of both solvents, being greater than 90 °C, made it possible for their
mixtures to be heated to 70 °C without the danger of ignition by errant sparks. The results of a
compositional analysis of both solvents are as shown in Table 3.2 and Figure 3.1, while other
properties of the solvents are shown in Table 3.3.
49
Table 3.1
Component
C20
C21
C22
C23
C24
C25
C26
C27
C28
C29
C30
C31
C32
C33
C34
C35
C36
C37
C38
C39
C40
C41
C42
C43
C44
C45
C46
C47
C48
C49
C50
Composition of wax samples used in this study.
Bernardin Parowax
(mass %)
0.07
0.59
2.29
2.57
4.07
6.08
7.12
8.39
10.07
11.40
11.68
11.39
8.58
6.82
4.04
2.43
1.03
0.68
0.07
0.07
0.07
0.07
0.05
0.05
0.07
0.05
0.06
0.04
0.05
0.04
50
Conros Parowax
(mass %)
0.43
1.17
1.80
2.44
3.35
5.23
8.63
10.16
8.85
9.09
8.09
7.07
7.12
4.13
4.94
3.25
3.87
2.26
2.39
1.33
1.23
0.92
0.69
0.34
0.28
0.30
0.20
0.16
0.09
0.09
0.05
80
14
Linpar1416V
Bernardin Wax
Conros Wax
Norpar13
60
10
8
40
6
4
20
2
0
0
10
15
20
25
30
35
40
45
Carbon Number
Figure 3.1
Composition of solvents and wax samples.
51
50
Wax Composition (mass%)
Solvent Composition (mass%)
12
Table 3.2
Composition of solvents.
Component
Linpar1416V (mass
%)
Norpar13 (mass
%)
C9
-
0.03
C10
0.19
0.20
C11
0.18
1.80
C12
0.68
13.30
C13
2.91
51.30
C14
66.79
32.80
C15
23.42
0.60
C16
5.24
0.01
C17
0.16
­
C18
0.16
­
C19
0.15
­
C20
0.15
­
52
Table 3.3
Selected physical and chemical properties of Norpar13 (Imperial Oil
MSDS) and Linpar1416V (APCO Industries Ltd. MSDS)
Property
Value
Norpar13
Linpar1416V
Clear Liquid
Light Yellow Oily Liquid
187
201
Boiling Point (oC)
221 – 248
248 – 284
Melting Point (oC)
0
4
Flash Point (oC)
97
118
Auto-Ignition Temperature ( oC)
229
204
Specific Gravity @ 16oC
0.760
0.768
Vapor Pressure @ 20oC (kPa)
0.01
0.01
Solubility in Water @ 25 oC (%)
<0.01
Negligible
2.37 @ 25oC
2.3 - 2.5 @ 40oC
6.48
7.10
Appearance
Average Molecular Weight
Viscosity (cSt)
Vapor Density (g/L, Air = 1)
53
3.1.3 Comparison of Compositions of Waxes and Solvents
In Figure 3.1, the carbon number distributions of the waxes and solvents are presented.
Norpar13 has an average molecular mass of 187 kg kmol–1 and a corresponding carbon number
of approximately 13. The main constituents of Norpar13 are n-C13 and n-C14 with
concentrations of 51.3 and 32.8 mass%, respectively. Linpar1416V has an average molecular
mass of 201 kg kmol–1 and a corresponding approximate carbon number of 14. The main
constituents of Linpar 1416V are n-C14 and n-C15, with concentrations of 64.5 and 22.6 mass%,
respectively. Comparing the composition of the waxes and the solvents, it is seen that there is
no carbon number distribution overlap between Norpar13 and Conros Parowax, and between
Linpar1416V and Bernardin. Thus, all experiments in this study were performed with wax–
solvent mixtures of either Conros Parowax + Norpar13 or Bernardin Parowax + Linpar1416V.
This ensured that any compositional analysis done on the wax–solvent mixtures or wax
deposits in this study could be interpreted easily.
3.2 Wax–Solvent Mixtures
Because crude oils have a large number of different components that could either hinder
or favor the precipitation and deposition of solids, simple and well-defined wax–solvent or wax–
solvent–water mixtures were used, in order to avoid the complexity of crude oils. It was thus
possible to work with different compositions without introducing additional uncertainties. The
confidentiality constraints and huge costs associated with field samples were also avoided.
The compositions of the wax–solvent mixtures used in the WPT–cooling rate
experiments were 2, 4, 6, 8, 10, 15 and 20 mass% Parowax–Norparl3 mixtures.
54
The flow loop wax deposition experiments were performed with 6 mass% Bernardin
Parowax–Linpar1416V mixture, containing 0, 5, 10, 15, 20, 25, and 30 vol% water. The cold
finger wax deposition experiments were performed with 10 mass% Bernardin Parowax–
Linpar1416V mixture, containing 10, 20 and 30 vol% water. Each mixture was prepared by
dissolving the right amount of wax in the solvent, heating the mixture to about 70°C and holding
at this temperature for 1 hour while stirring continuously. Continuous stirring was done to ensure
that the wax was completely dissolved and that the mixture was homogenous. For mixtures that
contained water, the right amount of tap water was added at a temperature close to that of the
wax–solvent mixture. This also ensured that mixtures containing water were well-mixed water­
in-oil transient emulsions. Sample preparation procedures are given in more details in the
sections describing the experimental procedures.
3.2.1 WPT Measurements
The term WPT has been used in this study to define the temperature for the onset of solid
formation under a measured, constant cooling rate, which distinguishes it from the WAT that is
measured using the ASTM method. A constant cooling rate was employed using the equipment
setup described in Section 3.3. Upon gradual cooling at a constant cooling rate, the highest
temperature at which wax crystals were first observed visually (cloudiness) was taken to be the
WPT of the waxy mixture. The measurement was done for the various wax concentrations
ranging from 2 to 20 mass%, at cooling rates of 0.4, 0.3, 0.2, 0.1 and 0.05 oC/min.
55
3.2.2 WAT, WDT and PPT Measurements
The wax appearance temperature (WAT) of seven prepared wax–solvent mixtures,
ranging from 2 to 20 mass% Conros Parowax in Norpar13, were measured at atmospheric
pressure using a modified ASTM D 2500-09 visual method (Tiwary and Mehrotra, 2004). It is
noted that WAT values for Conros Parowax in Norpar13 mixture for some concentrations had
been measured and published by other researchers (Fong and Mehrotra, 2007; Bidmus and
Mehrotra, 2008b; Bidmus and Mehrotra, 2009). The prepared wax–solvent mixture sample was
heated in a pour point tube to a temperature of about 70°C and held for an hour. The sample was
then cooled at a cooling rate of 10°C/h to about 50°C, thereafter, the temperature of the sample
was decreased in steps of 1°C and the sample held at that temperature for 15 min. At each
constant temperature, the samples were checked visually for any sign of turbidity. Holding the
sample at a constant temperature for 15 min ensured uniformity in the sample temperature before
checking visually for any appearance of wax crystals. The highest temperature at which the
sample showed turbidity was recorded as the WAT. Tiwary and Mehrotra (2004) showed that
this method gave WAT values that compared well with WAT measurements from other methods.
The WAT, WDT and PPT of seven prepared wax–solvent mixtures, ranging from 2 to 20 mass%
of Bernardin Parowax in Linpar1416V, were also measured at atmospheric pressure using the
same step-cooling method. The WDT, measured while heating, was taken to be the temperature
at which all of the wax crystals were completely dissolved. The PPT, measured while cooling,
was taken to be the temperature at which the sample ceased to flow. It is noted here that the
actual WAT and PPT values may be higher than those obtained using the step-cooling method,
giving an error of up to +1°C for this method. Similarly, the error associated with the WDT may
be up to –1°C. To determine if the presence of water affected these temperatures, the WAT of
the same mixtures, containing 5 vol% water, was measured and the results showed that the
56
presence of water had no effect on the measured WAT. The results of WAT measurements for
Conros Parowax–Norpar13 mixtures and WAT, WDT and PPT measurements for Bernardin
Parowax–Linpar 146V mixtures and are listed in Table 3.4. The values listed in Table 3.4 are
presented graphically in Figure 3.2. The results in Table 3.4 and Figure 3.2 show that the WAT
of Conros Parowax in Norpar13 is consistently greater than that of Bernardin Parowax in Linpar
1416V at all concentrations, even though the difference reduces slightly at concentrations higher
than 8 mass%.
As expected, the PPT of each Parowax–Linpar1416V mixture is less than its
WAT; however, the difference between the WAT and PPT is not the same at all wax
concentrations. The PPT data show a sharp decline at wax concentrations less than about 10
mass%. Also, the difference between the WDT and WAT for Parowax–Linpar1416V is not the
same at all concentrations, this difference increases progressively at wax concentrations higher
than 8 mass%.
57
Table 3.4
Experimentally determined WAT, WDT, and PPT Values.
wax
Conros Parowax
Bernardin Parowax
concentration
WAT
WDT
PPT
WAT
(mass%)
(oC)
(oC)
(oC)
(oC)
2
28.0*
22.0
2.0
20.0
4
32.0*
27.0
8.0
25.0
6
35.0*
30.0
12.0
28.0
8
36.0
32.0
17.0
30.0
10
38.0**
38.0
22.0
32.0
15
41.0**
43.0
27.0
36.0
20
43.0**
48.0
33.0
38.0
* Bidmus and Mehrotra (2008b, 2009)
** Fong and Mehrotra (2007)
58
50
o
Temperature ( C)
40
30
20
WAT - Conros Wax+Norpar13
WDT - Bernardin Wax+Linpar1416V
WAT - Bernardin Wax+Linpar1416V
WAT - Bernardin Wax+Linpar1416V+5 vol% Water
10
PPT - Bernardin Wax+Linpar1416V
0
0
5
10
15
20
Wax Concentration (mass%)
Figure 3.2
Comparison of WAT values for Parowax–Norpar13 mixtures, and WAT, WDT
and PPT values for Bernardin Parowax–Linpar 1416V mixtures (Kasumu and
Mehrotra, 2013)
59
3.3 WPT–Cooling Rate Experimental Apparatus
3.3.1 Heating Bath
A Polyscience temperature-controlled heated/refrigerated bath with an internal circulator,
model 1187, supplied by VWR Scientific Products, was used to heat prepared wax–mixtures in
copper tubes. Water was used as the heating bath liquid.
3.3.2 Cooling Bath
The cooling bath was a Haake DC1-V Refrigerated Bath. In it was immersed a Haake D8
Immersion Circulator with built-in heating element, which was connected to a temperature
programmer. Figure 3.3 shows the Haake DC1-V Refrigerated Bath with the Haake D8
Immersion Heater/Circulator.
3.3.3 Cooling Rate Controller
A Haake PG 20 Temperature Programmer was used to control the cooling rate. It enabled
temperature to be preset externally and varied following a time-linear program by providing
resistance or voltage signals to the Haake D8 Immersion Circulator connected to it, in which
case, a stepwise change of resistance of 0.1 ohm corresponds to temperature steps of 0.01 oC. It
was possible to set this programmer in such a way that a temperature difference above a starting
temperature could be specified for a heating phase (at a specified heating rate), a holding time for
the hold phase at the attained temperature, and a cooling rate for the cooling phase after the
duration of the hold phase. Figure 3.4 shows the Haake PG 20 Temperature Programmer.
60
Figure 3.3
Haake D8 Immersion Circulator immersed in a Haake DC1-V Refrigerated Bath.
Figure 3.4
Haake PG 20 Temperature Programmer
61
3.3.4 Copper Pour Point Tubes
In order to reduce the thermal resistance from the water bath to wax mixture, 3/8" x 6
inch (OD x L) flanged copper tubes were fabricated and used instead of glass pour point tubes.
The bottom of the copper tubes were retrofitted with transparent plexiglass to facilitate visual
observation of the wax mixture during the experiments. Figure 3.5 shows a photograph of the
fabricated copper tubes.
3.3.5 Underwater Lighting
An underwater LED light, model QL-72C purchased from Gulf Coast Consultants Inc.
(BC, Canada) was used to project light from the bottom of the copper tubes to aid visual
detection of the onset of formation of wax crystals in the wax mixture in the copper tube during
the cooling process. Figure 3.6 shows the underwater lighting.
62
Copper tube flange
Copper tube
Plexiglass bottom
Figure 3.5
Fabricated copper tube used for WPT measurements.
63
Figure 3.6
Underwater LED light, model QL-72C.
64
3.3.6 Thermocouple Data Acquisition System
Thermocouples used for temperature measurements were the 6 inch T-type
thermocouples (Cat. No. TMQSS-062G-6) obtained from Omega (Stamford, Connecticut, USA).
A modular distributed input/output (I/O) system called FieldPoint, obtained from National
Instruments (Austin TX, USA), was used for recording the thermocouple measurements. The
FieldPoint system consisted of three components, namely, FP-TC-120 I/O module, FP-TB-1
terminal base, and the FP-1000 network module. The FP-TC-120 model is an 8-channel input
module for direct measurement of thermocouple signals. It has eight individually calibrated
channel differential inputs for thermocouples. A high accuracy 16 bit resolution analog-to-digital
converter (ADC) with an ultra-stable voltage reference and built-in calibration circuitry digitized
input signals in the FP-TC-120 I/O module. The FP-TB-1 terminal base is a general-purpose
terminal base that was connected to the I/O module. It provided the screw terminals for the
thermocouple wiring connections. It carries communications and power to the I/O module and
could be used for any I/O module. The FP-1000 model network interface module, snapped
together with the terminal base formed a local high-speed bus that was responsible for managing
communications between the host personal computer (PC) and the I/O module. The power
supply to the FieldPoint system was a 1 to 30 VDC adapter connected to screw terminals on the
FP-1000 network interface module. The three individual units, connected together, formed the
FieldPoint system and the thermocouples were wired to the terminal base. The thermocouple
readings were recorded, in degrees Celsius, on the PC through National Instruments software,
LabVIEW.
All of the thermocouples used were calibrated using a mixture of water and ice, and
boiling water. It was found that the temperatures deviated slightly from 0°C and 100°C. These
temperature deviations were corrected for in a calibration file.
65
3.4 WPT–Cooling Rate Experiments
3.4.1 Experimental Procedure for WPT–Cooling Rate Experiments
The compositions of the wax–solvent mixtures used in the experiments of this study were
2, 4, 6, 8, 10, 15 and 20 mass% Parowax–Norparl3 mixtures. After preparing each mixture with
the required amount of wax and solvent, the mixture was heated to 70 °C in the Polyscience bath
before transferring smaller quantities into the copper pour point tubes used for the experiments.
Each mixture was then held in the pour point tubes at this temperature for 2 hours during which
it was agitated vigorously every 30 minutes. The agitation was done to ensure not only complete
dissolution of the wax in the solvent, but also homogeneity in the mixture.
The Haake PG 20 Temperature Programmer connected to a Haake D8 Immersion
Circulator with built-in heating element, which was immersed in a Haake DC1-V Refrigerated
Bath (also at 70 °C) was preset to the desired cooling rate. After the 2 hour hold period, the
flanged copper tube containing the wax–solvent mixture was held in the refrigerated bath
directly above the lit underwater LED light, with aid of sheet of a plexiglass support with holes
drilled in it. One thermocouple was used to monitor the temperature of the wax mixture in the
copper tube while another was used to monitor the temperature of the water in the bath. The
highest temperature at which wax crystals were first observed visually (cloudiness) was taken to
be the WPT of the waxy mixture.
Preliminary experiments showed that due to heat transfer limitations in the cooling bath,
the highest cooling rate that could be used without having a lag in temperature between the water
in the bath and the temperature reading on the programmer was 0.4 °C/min. Thus cooling rates
used for these experiments were 0.4, 0.3, 0.2, 0.1 and 0.05 oC/min and the experiments were
performed for the various wax mixtures. Repeatability was established by repeating one
66
experiment from every block of five experiments, and WPT measurements were found to be
within ±0.8 oC.
3.4.2 Design of Experiments for WPT–Cooling Rate Experiments
The main objective of the WPT–Cooling rate experiments was to determine the effect of
cooling rate on WPT, the experiments were performed at five different cooling rates using seven
different wax mixture compositions. Apart from the preliminary experiments, a total of 42
experiments (including repeat experiments) were performed for this study. Table 3.5 summarizes
the conditions under which the experiments were performed.
67
Table 3.5
Operating Conditions for WPT–Cooling Rate Experiments
Composition
(Mass% Wax)
2
4
6
8
10
Cooling Rate
(oC/min)
Run
Number
0.4
0.4
0.3
0.2
0.1
0.05
0.4
0.3
0.3
0.2
0.1
0.05
0.4
0.3
0.2
0.2
0.1
0.05
0.4
0.3
0.2
0.1
0.1
0.05
0.4
0.3
0.2
0.1
0.05
0.05
CR1
CR1-R
CR2
CR3
CR4
CR5
CR6
CR7
CR7-R
CR8
CR9
CR10
CR11
CR12
CR13
CR13-R
CR14
CR15
CR16
CR17
CR18
CR19
CR19-R
CR20
CR21
CR22
CR23
CR24
CR25
CR25-R
68
Block
Number
1
2
3
4
5
Composition
(Mass% Wax)
Cooling Rate
(oC/min)
Run
Number
0.4
CR26
0.4
CR26-R
0.3
CR27
15
0.2
CR28
0.1
CR29
0.05
CR30
0.4
CR31
0.3
CR32
0.3
CR32R
20
0.2
CR33
0.1
CR34
0.05
CR35
Note: R indicates a repeated run
Block
Number
6
7
3.5 Flow Loop Wax Deposition Experimental Apparatus
3.5.1 Flow Loop Design
The objectives of these experiments were to investigate the effect of water content,
mixture and coolant temperatures, and wax mixture flow rate (Reynolds number) in two-phase
wax deposition experiments using wax–water–solvent mixtures. A bench-scale flow-loop
apparatus was designed and fabricated to conduct the two-phase deposition experiments under
turbulent flow conditions. The flow-loop apparatus consisted of a temperature-regulated cooling
bath with a submersible pump for circulating the coolant water and a temperature-regulated
heating bath holding a 24-L waxy mixture reservoir. Three submersible pumps, each having a
flow rate of 0.037L/s were placed in the heating bath to aid circulation in the bath. Each of the
temperature-regulated baths was used in conjunction with another temperature-regulated
69
recirculating bath. Other components of the flow loop design include a centrifugal pump for
circulating the waxy mixture in the flow loop; a variable speed 4-blade disc turbine stirrer driven
by air pressure; a flow sensor and ratemeter; calibrated T-type thermocouples; a temperature data
acquisition system; 1” ID copper flow line; an air vent valve; a sample drain valve, a flowregulating valve, and a deposition section.
Unlike the wax deposition study by Parthasarathi and Mehrotra (2005), the fabricated
flow loop apparatus was not of a submerged pump design. In this design, a hole was drilled on
one side of the heating bath as well as the bottom of the wax reservoir. Both were connected
together using a 6 x 1.25 inch (L x ID) flanged stainless steel pipe. The other end of the stainless
steel pipe was joined to a 1.25 x 0.75 x 1.25 inch copper Tee using reinforced rubber and metal
clips, this enabled the draining of the wax reservoir, using a valve on the smaller opening of the
copper Tee, without having to remove the wax mixture reservoir from the heating bath. The
other end of the copper Tee was also connected to 1.5" male NPT connection leading into the
inlet of the wax mixture pump. A 1" female NPT connection from the outlet of the pump was
attached to a 1" brass union through a 1" ID copper pipe 2 inches in length, the other end of the
brass union was attached to 1" ID copper pipe, which was attached to a 1" 45o copper elbow. The
elbow was attached to a 1" ID copper pipe 6.5 inches in length, which was attached to another 1"
45o copper elbow. The second 45o copper elbow was attached to a 1" ID copper pipe, 2.5 inches
in length, the copper pipe was attached to a third 45o copper elbow, which was attached to
another 1" ID copper pipe, 2.5 inches in length. This copper pipe was attached to a fourth 45o
copper elbow, which was attached to a 1" ID copper pipe, 24.5 inches in length. The 24.5 inch
long copper pipe was attached to a second 1" ID brass union, which was attached to 1" ID copper
pipe, 8.5 inches long and flanged on one end. The flange on the 8.5 inch long copper pipe was
70
used as an attachment to the plexiglass of the deposition section. Attached to the other end of the
deposition section was another fanged 1" ID copper pipe, 2 inches in length, and was attached to
a third 1" ID brass union. This brass union was attached to 2 inch long 1" ID copper pipe, which
was attached to a fifth 45o copper elbow, which was in turn attached to a 2.5 inch long 1" ID
copper pipe. This copper pipe was attached to a sixth 45o copper elbow, which was attached to a
fourth 1" ID brass union through a 2 inch long 1" ID copper pipe. The other end of the fourth
brass union was attached to a 4.25 inch long, 1" ID copper pipe, which was attached to a 1" brass
ball valve used for regulating flow rate in the flow loop. The ball valve was attached to a 5.5 inch
long, 1" ID copper pipe, which was attached to a seventh 45o copper elbow.
The succeeding sections of the flow loop consisted of the following fittings attached in
series: a 2.5 inch copper pipe (1" ID), 45ocopper elbow, 2.25" copper pipe (1" ID), 1" brass
union, 1.5 inch copper pipe (1" ID), 1"–0.75" copper reducer, 4 inch copper pipe (0.75" ID),
0.75" threaded brass union, flow sensor, 0.75" threaded brass union, 1.5 inch copper pipe (0.75"
ID), 0.75"–1" copper reducer (to which a 0.25" tube toggle valve was attached for sample drain),
1.5 inch copper pipe (1" ID), 1" brass union, 1.5 inch copper pipe (1" ID), 45o copper elbow, 2
inch copper pipe (1" ID), 45o copper elbow, and a Tygon® discharge line, 8 inches in length.
This flow loop design had so many components and fittings because of the limitations of
the available components and desired geometry. For example, an inclined deposition section was
desired to aid drainage of the deposition section after each experiment, less pressure drop due to
fittings was desired, thus the use of 45o elbows instead of 90o elbows, available flow sensor had a
0.75" inlet and outlet, while the flow line was 1" in diameter, amongst other considerations.
In this flow loop, circulation of the waxsolvent and waxsolventwater mixtures was
accomplished by using the centrifugal pump that was placed outside the reservoir and connected
71
to it.
Downstream from the pump was a deposition section, a valve used for regulating flow
rate, a flow sensor connected to a ratemeter used for measuring flow rate. Solids deposition took
place on the inner surface of a co-current double-pipe heat exchange deposition section,
described in Section 3.5.8. All parts of this flow loop were insulated to minimize heat loss to the
surrounding. Figure 3.7 shows a schematic of the flow loop setup while Figure 3.8 shows a
picture of the flow loop apparatus.
Air Valve
Deposition
Section
TC
TC
TC
Coolant Out
Coolant In
Coolant Bath
Flow Regulating Valve
Stirrer
Sample
Drain
Wax Mixture
Reservoir
Pump
Figure 3.7
Flow meter
Heating
Bath
Schematic of bench-scale apparatus for flow loop wax deposition experiments.
72
Figure 3.8
Bench-scale setup for flow loop wax deposition experiments.
73
3.5.2 Heating Bath and Associated Apparatus
The Wax mixture reservoir was placed in a Precision Model 270 (Category # 51221036)
Circulating Water Bath from VWR International (Cat. No. 13491-010). The bath has a built in
heating element, electronic temperature controller, and an internal circulating pump. The internal
dimensions of the bath are 36 x 18 x 9.5 inch (L x W x H). The bath also has a bottom tray
protecting the heating element, with the bottom tray in place, the internal bath dimensions are 36
x 18 x 8.25 inch (L x W x H). To turn on the heating some hours before the start of the
experiment, a power bar with a built in timer was used. As mentioned earlier, to aid the internal
circulation of the heating bath and increase heat transfer and uniformity of water temperature in
the bath during experiments, three additional pumps, (Model PE-A-PW) obtained from The
Little Giant Pump Company (Oklahoma, USA), were used in the bath. To further help control
the temperature of the heating bath, a VWR heated/refrigerated recirculating chiller (Model
1179, 230 volts) with an internal pump was used. The inlet and outlet of the heated/refrigerated
recirculating chiller were fitted with 75 x 0.375 x 0.25 inch Nylaflow® nylon pressure tubing
(GE Polymershapes Plastic, Calgary, AB) and placed in the heated bath to form a closed loop of
recirculation of the heating fluid.
3.5.3 Cooling Bath and Associated Apparatus
A Haake D8 Immersion Circulator with built-in heating element, which was immersed in
a Haake DC1-V Refrigerated Bath, both obtained from Fisher Scientific were used in
conjunction with a Polyscience heating/cooling bath (Model No. 1187) with an internal pump,
for cooling the water pumped to the annulus of the wax deposition section. Two Tygon® tubings
measuring 14 x 0.75 x 0.5 inch (L x OD x ID) were connected to an annealed copper tubing,
coiled in a 10 inch diameter section measuring 140 x 0.375 x 0.25 inch (L x OD x ID) (Acklands,
74
Calgary, AB, Cat. No. FAR-CTG6), the other ends of the Tygon® tubings were then connected to
the recirculator inlet and outlet. The annealed copper tubing was used as the heat transfer
medium in the coolant bath to prevent the water in the recirculator from mixing with the water in
the coolant bath. A submersible pump, (Model PE-2F-PW) The Little Giant Pump Company
(Oklahoma, USA), was used to pump the coolant water at a rate of 0.0082 L/s. A Swagelok®
female connector (B-400-7-8) fitting was used to connect a 49 x 0.25 x 0.1562 inches (L x OD x
ID) Nylaflow® nylon pressure tubing to the coolant pump. The Nylaflow® nylon pressure tubing
lead to the inlet of the annulus of the deposition section, a similar pressure tubing connected to
the outlet of the deposition lead back to the coolant bath. Figure 3.9 shows the coolant bath with
the annealed copper tubing connected to the coolant bath recirculator.
75
Figure 3.9
Coolant bath with the annealed copper tubing connected to coolant
bath recirculator.
76
3.5.4 Wax Mixture Reservoir
It was necessary for the wax reservoir to be made of a high thermal conductivity material
and be large enough to contain a sufficient amount of wax mixture. The wax mixture reservoir
was an aluminum container, 11.25 inches in diameter and 15.5 inches high. Since the stirrer was
held at the center of the container, the lid of the container was cut across from the center to the
circumference to enable it slide around the stirrer and still be used to cover the wax mixture
during the experiments. A semi-circular cut about 1.2 inches in diameter and 2 inches deep was
made from the top of the wax reservoir as a support for the copper pipe discharging wax mixture
back into the reservoir at the end of the flow loop.
To ensure adequate mixing and prevent formation a vortex during the two-phase
experiments with wax–solvent–water mixtures, the wax reservoir was fitted with four baffles,
each with a width of 0.94 inch.
3.5.5 Wax Mixture Stirrer
Stirring was done with a 4-blade disc turbine mounted on a threaded stainless steel rod.
The diameter of the turbine was 3.75 inches while each rectangular blade had dimensions of 0.94
x 0.75 inch (L x W). The stirring unit was connected to a straight-in-line drill and powered by
compressed air. The compressed air was fed to the drill through a combined filter-regulator­
lubricator (FRL) unit. The FRL unit and the straight-in-line drill were obtained from AcklandsGrainger, Richmond Hill ON, Canada. The regulator on the FRL unit was pre-calibrated and had
a pressure range of 10–150 psig (70–1050 kPag).
The height of disc turbine was adjusted to be 0.33 times the height of the liquid in the
reservoir during experiments.
77
3.5.6 Photo/Contact Tachometer
A photo/contact tachometer obtained from ITM Instruments Inc. was used to measure the
rotational speed of the stirrer used for mixing the waxsolventwater mixtures during the
experiments. It was used in the photo mode and it measured the rotational speed in rotations per
minute (rpm).
3.5.7 Wax Mixture Centrifugal Pump
The pump used for circulating the wax mixtures through the flow loop was a centrifugal
pump Model # COMSV33 obtained from Cole Palmer Instrument Inc (Chicago IL, USA). The
pump head was made of 316 SS and had a maximum allowable operating temperature of 250°F.
The pump was placed in a position that made the pump inlet the same vertical level as the bottom
of the wax mixture reservoir to enable priming by gravity. The flowrate supplied by the pump
was controlled with a valve located downstream from the pump outlet after the deposition
section. Figure 3.10 shows the position of the pump.
78
Figure 3.10
Position of Wax mixture centrifugal pump.
3.5.8 Wax Deposition Section
As mentioned earlier, the deposition section was a co-current double pipe heat exchanger
under co-current flow conditions, such that the coolant flowed in the annulus of the deposition
section. Wax deposition occurred on the inside surface of the heat exchanger that was similar to
the one used by Fong and Mehrotra (2007). The deposition section consisted of a machined
(6061 grade) aluminum tube, 1.0  1.3  4.0 inch (ID x OD x L), which formed the inner-tube of
the double-pipe heat exchanger. Figure 3.11 shows the dimensions of the aluminum tube.
79
.125”
.15”
1.5”
1”
4”
Figure 3.11
Cross-section of Aluminum deposition tube (Fong, 2007).
The outer-tube of the heat exchanger was a flanged plexiglass section with dimensions,
1.5  1.8  4.0 inch (ID x OD x L). The entrance flange measured 3.5 x 0.865 inches (OD x
Thickness). The center hole on the outside the flange (copper pipe connection) was machined
1.132 x 0.4 inch (OD x Depth) with an inset groove for an O-ring. On the inside of this flange,
the center hole was machined with two holes, one was 1.5 x 0.125 inch (OD x Depth) while the
other, an inner hole, was machined 1 x 0.335 inch (OD x Depth). The entrance flange to the wax
deposition section was sealed with 3 O-rings, sizes 1.125 x 1.3125 x 0.0937 inch (ID x OD x
Thickness, #122) and 2.0 x 2.1875 x .0937 inch (ID x OD x Thickness, #136). The first O-ring
(#122) was used in an inset groove to seal the entrance pipe to the wax deposition section, while
the second O-ring, of the same size was used to seal, and hold in place, the wax deposition tube.
The third O-ring (#136) was used to seal the annulus of the deposition section. A 0.125 inch
FNPT threaded hole was drilled on the top of the entrance flange, in which a Swagelok ® 1/16”
tube – 1/8” male connector (Cat. No. B-100-1-2) fitted with a thermocouple was attached. Four
0.266 inch diameter holes were drilled approximately 0.3 inch (edge to center,) from the edge of
80
the entrance flange. These were used to connect the entrance flange the body of the heat
exchanger section. The inlet cooper pipe was attached using stainless steel socket head cap
screws. The design of the exit flange was similar to that of the entrance flange except that the top
hole was used for a pressurized air inlet (5 psig). The pressurized air inlet was regulated using a
Swagelok® plug valve (Cat. No. B-4TA-1-2) in conjunction with ¼” tube – 1/8” NPT male
adapter (Cat. No. B-4TA-1-2). Figure 3.12 shows the outside and the inside of the entrance
flange while Figure 3.13 shows the plexiglass body of the wax deposition section.
a
Figure 3.12
b
Picture of entrance flange. a) inner side, b) outer side (Fong, 2007)
81
a
b
Figure 3.13 Plexiglass body of wax deposition section.
a) Side view, b) Front view: entrance section (Fong, 2007).
The outside surface of the plexiglass tube was insulated with 2-cm thick styrofoam
insulation to minimize heat exchange (qgain) with the surroundings. Figure 3.14 shows a cross
sectional view of the wax deposition section without the end flanges.
82
Coolant Outlet
Coolant Inlet
Foam Insulation
Coolant Flow
Aluminum Tube
1.76" 1.5"
Wax-Solvent Flow
1" 1.3" 3.5"
Center Line
Aluminum Tube
Coolant Flow
Foam Insulation
2.75"
Plexiglass Shell
4.00"
Figure 3.14
Plexiglass body of wax deposition section (Fong, 2007)
3.5.9 Wax Mixture Flow Regulator
The wax mixture flow regulator was a 1" ball valve. A ball valve was chosen because its
internal configuration provided the least obstruction to flow, and therefore minimum pressure
drop resulting from the valve fitting. The valve was placed between the wax deposition section
and the flow sensor.
83
3.5.10 Flow Sensor and Rate Meter
The flow sensor (Model No. PS612BN40) was a pulsed output type flow sensor and was
as used in conjunction with a Florite 700 series ratemeter (Part No. M750B1A1A) to measure
and display the flow rate of the wax mixture. Both were obtained from Proteus Industries
(Mountainview, California, USA). The ratemeter was purchased already pre-calibrated with
water, however, Fong (2007) calibrated it with a 10% wax mixture and the measured flow rate
was found to follow equation 3.1 as follows:
Ah  0.770 Oh  3.025
3.1
where Ah is the flow rate in gal min–1 and Oh is the ratemeter reading in gal min–1.
The entrance and exit of the flow sensor were connected to 0.75" ID threaded brass
unions, which were connected to 0.75" ID copper pipes.
3.5.11 Wax Mixture Sample Drain
For experiments performed with transient emulsions, it was important to make sure that
the composition of the mixture in the wax mixture reservoir was the same as that flowing in the
flow loop. The sample drain was thus used to collect samples from the flow loop. The samples
were centrifuged and the water content of the samples were compared to the water content of the
mixture in the wax mixture reservoir. The sample drain was a 0.25" tube toggle valve and was
located at the end of the flow loop just before re-entry into the wax mixture reservoir.
84
3.6 Associated Equipment and Measurements
3.6.1 Centrifuge
The centrifuge used for wax mixture samples was the VWR Centrifuge Clinical 200 (# C­
0200-A-VWR). It was capable of centrifuging at speeds in the range of 250-600 rpm and had a
timer mode that could be preset up to 30 min. An imbalance sensor is incorporated into the
control loop to stop operation of the centrifuge in the case of an improperly loaded rotor. At the
end of a run, dynamic braking brings the rotor to a quick and turbulence-free stop. 50 mL
graduated conical plastic bottles were used in the centrifuge.
3.6.2 Temperature Measurements
The thermocouple temperature data acquisition system is described in detail in section
3.3.6. All temperature measurements were done using 6-inch T-type thermocouples,
thermocouples (Cat. No. TMQSS-062G-6) obtained from Omega (Stamford, Connecticut, USA).
For the flow loop wax deposition experiments, four thermocouples were used to record
temperatures at different locations throughout the deposition process. These temperatures were
those of the waxy mixture inlet (Thi), coolant inlet (Tci), and coolant outlet (Tco), and the room
(Troom). The outlet temperature of the waxy mixture (Tho,) exiting the deposition section, could
not be measured reliably due to the existence of a radial temperature gradient (Fong and
Mehrotra, 2007; Bidmus and Mehrotra, 2009; Tiwary and Mehrotra, 2009); hence, it was
estimated from the energy balance given by equation 5.1 (included in Chapter 5).
The thermocouple measuring the wax-solvent inlet temperature was attached using a
Swagelok® male connector (Cat. No. B-100-1-2) while those measuring the coolant temperatures
were attached using Swagelok® nylon male run tees (Cat. No. NY-200-3TMT) and Swagelok®
reducing unions (Cat. No. NY-200-6-1).
85
3.6.3 Density Measurements
A 25-mL pycnometer, was used to determine the densities of the wax and wax deposits.
After collecting the wax deposit sample, it was homogenized by melting with a heat gun. Normal
pycnometer procedure was used in wax deposit density measurement except that the wax deposit
was melted to the bottom of the pycnometer to ensure that it did not float to the top when water
was added. The densities of the wax–solvent mixtures were measured at different temperatures
between WAT and about 65 °C using a 100 mL volumetric flask.
3.6.4 Viscosity Measurements
The viscometer used in measuring the viscosities of the solvent and wax–solvent
mixtures was a Haake rotational-type concentric cylinder viscometer, Model RotoVisco 1,
obtained from ThermoFisher Scientific (Nepean ON, Canada). The viscosity measurements of
the different wax solvent mixtures were done at atmospheric pressure, and at temperatures above
their respective WAT. A temperature-regulated bath was connected to the viscometer for
controlling the wax–solvent mixture temperatures during measurements. Tiwary (2002) showed
that, for the range of temperature and at the shear rate used in this study, these waxy mixtures
behave as Newtonian fluids. These measurements were done at a constant shear rate.
3.6.5 Titrator
For all two-phase experiments performed with wax–solvent–water mixtures, the water
content of the deposits was determined using a C20 Compact Karl Fischer Coulometer utilizing a
generator cell without diaphragm. The Karl Fischer method is a chemical analysis procedure
which is based on the oxidation of sulphur dioxide by iodine in a methanolic hydroxide solution.
In the coulometric procedure, the iodine participating in the reaction is generated directly in the
86
titration cell by electrochemical oxidation of iodide until again a trace of unreacted iodine is
detected. Faraday's law is used to calculate the amount of iodine generated from the quantity of
electricity required.
3.6.6 GC Analysis of Samples
Compositional analyses were carried out on the waxes, solvents, different compositions
of mixtures of wax dissolved in solvent, and some deposit samples. These were performed in the
In-Situ Combustion Laboratory of the Department of Chemical and Petroleum Engineering at the
University of Calgary (Calgary, AB). The characterization was performed using a HP 6890
series Gas Chromatography (GC) system that used a simulated distillation method. The system
was equipped with a fused-silica non-polar column measuring 10 m x 0.53 mm x 0.88 μm film
(Separation Systems Inc., Florida, USA). A flame ionization detector (FID) was used to detect
the hydrocarbon contents and HP ChemStation software was used to collect data. This method of
analysis utilized a capillary column that was used to elute the hydrocarbons components in order
of increasing boiling point. SimDist Expert V6.3 software was used in analyzing the GC results.
Before each set of analysis, an n-alkane standard (C5-C66) SD-SS3E-5, obtained from Separation
Systems, was used for calibrating the GC using ASTM D2887 extended method. The sample was
prepared by dissolving it in carbon disulphide to produce an approximate 2% sample solution.
87
3.7 Flow Loop Experiments
3.7.1 Experimental Procedure for Flow Loop Experiments
After assembling the flow-loop apparatus, the 24-L mixture reservoir was filled with the
waxy mixture heated to about 65 oC and allowed to remain at this temperature for one hour,
while stirring continuously to ensure homogeneity and to erase any thermal history. The
temperatures of the heating, cooling and recirculating baths were set to the desired temperatures
for each experiment. During trial experiments, it was observed that the temperature of the wax
mixture was increased by energy input from the centrifugal pump. Similarly, the temperature of
the coolant water was increased slightly as it flowed from the coolant bath to the inlet of the
deposition section, thus these were accounted for in the temperature settings of the heating and
coolant baths. The deposition tube was weighed with a precision of ±0.1 mg before inserting into
the wax deposition section. Because the WAT of the used wax mixture was higher than the room
temperature, the deposition tube was heated to a temperature above the WAT of wax mixture, to
prevent premature wax deposition prior to turning on the coolant water pump. After attaining the
desired heating bath and cooling bath temperatures, the wax-solvent pump and the temperature
data acquisition system were turned on and the flow-regulating valve was adjusted to achieve the
desired flow rate.
The deposition process was commenced by turning on the coolant water pump to
circulate the coolant water from the refrigerated-bath, through the annular-side of the heat
exchanger. A timer was also started at the same time as the coolant water pump. During each
deposition experiment, the readings of Troom, Thi, Tci and Tco were recorded using the temperature
data acquisition system described in section 3.3.6. The wax mixture flow rate was also measured
and recorded using the device described in section 3.5.10. The flow line downstream of the pump
88
was sufficiently long to provide fully-developed hydrodynamic flow conditions, leading into the
removable deposition section.
After a predetermined duration, the deposition experiment was terminated by stopping
the wax mixture pump, followed by quickly draining the wax mixture from the deposition
section (by opening the air-vent valve). It is noted here that previous deposition studies from our
laboratory (Fong and Mehrotra, 2007; Tiwary and Mehrotra, 2009) have reported the likelihood
of continued deposition unless the deposition tube is drained quickly. The draining process was
aided by quickly opening the air-vent to a pressure of about 5 psig after each run, as well as an
upward inclination of the heat-exchanger assembly. The coolant circulation was then
discontinued and, after draining the coolant, the deposition section was dismantled to carefully
recover the aluminum tube. The tube was then weighed on a Sartorius BP 210S balance with a
precision of ±0.1 mg. The mass of the deposition tube was subtracted from the mass of the
deposition tube with deposit to obtain the deposit mass.
For all experiments performed with wax mixtures containing water, it was considered
important to provide sufficient agitation to ensure the homogeneity of the mixture throughout the
apparatus. For these experiments, the wax–solvent–water mixture in the wax reservoir was
stirred with the stirrer described in section 3.5.5 and the rotational speed of the stirrer was
measured with the photo/contact tachometer, described in Section 3.5.6. Stirring was done for
about 15 minutes at a rate of 500 rpm at the beginning of each experiment to ensure complete
dispersion of the water phase in the oil phase. The stirring was continued throughout the duration
of the experiments. It was also important to ensure that the composition of the two-phase
mixture in the wax mixture was the same as that flowing through the deposition section, thus
samples of the waxy mixture were taken using the sample valve located at the end of flow loop
89
just before the mixture exited into the reservoir. The samples of wax mixture flowing through the
deposition tube and held in the reservoir were centrifuged to measure their water contents. The
water contents of the two samples were compared to confirm that the water fraction in the wax
mixture flowing through the flow loop was the same as that in the reservoir. Results of this
comparison are presented in Chapter 5. Another set of batch experiments was conducted to study
the stability of the oil–water wax mixtures by observing phase separation in the suspension,
under gravity, with time. These experiments indicated that the time required for a significant
extent of phase separation was in the order of minutes and much more than about 1-2 second
residence time in the flow loop.
Wax deposits obtained from the two-phase experiments had water globules attached to
them. The water content of the deposit was determined by dissolving the complete deposit in the
Tetrahydrofuran and titrating the solution in a C20 Coulometric KF Titrator, already described in
section 3.6.5.
3.7.2 Experimental Design for Flow Loop Experiments
The factors that were studied in the two-phase flow loop wax deposition experiments
were the inlet wax solvent temperature (Thi), inlet coolant temperature (Tci), the water content of
the mixture and the wax mixture flow rate (Fh) or Reynolds number. A total of 43 flow loop wax
deposition experiments, including 6 repeat experiments, were performed according to a design of
experiments summarized in Table 3.6. The values of Thi were (WAT+7 °C) and (WAT+15 °C)
while the values of Tci were (WAT–10 °C) and (WAT–20 °C). The wax concentration was 6
mass% , the water contents used were 0, 5, 10, 15, 20, 25, and 30 volume%, while the flow rate
of wax mixtures was varied over 0.50–1.05 L/s (corresponding to 5600 < Re < 25300). A
90
constant coolant flow rate of 0.0082 L/s was used in all experiments, which produced a high
enough heat transfer coefficient, hc.
From the 6 repeated experiments, the average variability in the deposit mass was
estimated to be 4.1% for the total deposit mass (including water) and 8.1% for the deposit
mass on a water-free basis. Each deposition experiment was run for 1 hour. To ensure that
steady state was achieved within the 1-h duration, four extended experiments were conducted
over durations of 2 and 4 hours of deposition time. These extended experiments were performed
at Re ≈ 10000, with Th = (WAT+7 °C) and Tc = (WAT–10 °C). Results, presented in Chapter 5,
indicated that a deposition time of 1 hour was sufficient to achieve a thermal steady state and a
relatively constant deposit mass.
To avoid any significant compositional changes of the wax mixture in the reservoir
between experiments, each prepared batch of waxy mixtures was used for up to 6 deposition
experiments. It was estimated that the wax depletion from the wax mixture reservoir was not
more than 3.5% of the original concentration.
91
Table 3.6
Conditions of flow loop wax deposition experiments (Wax concentration
= 6 mass%, WAT = 28 °C )
variable
number of
levels
values of each variable tested
wax concentration, mass%
1
6
water content (total volume basis),
vol%
7
0, 5, 10, 15, 20, 25, 30
inlet temperature of waxy mixture
(Thi), ºC
2
WAT+7 and WAT+15
inlet temperature of coolant (Tci), ºC
2
WAT–10 and WAT–20
Reynolds number of
3
5600 < Re < 25300
waxy mixture (Re)
(plus 1 repeat)
time for deposition, h
all experiments
1
1h
extended experiments
2
2 and 4 h at Th = WAT+7,
Tc = WAT–10, Re = 10000
92
3.8 Cold Finger Wax Deposition Experimental Apparatus
All the heating, cooling and recirculation baths, wax mixture reservoir, wax mixture
stirrer and photo/contact tachometer used for the flow loop wax deposition experiments were
used for the cold finger wax deposition experiments. Other associated apparatuses such as the
temperature data acquisition system, centrifuge, coulometric titrator and GC analysis equipment
used for the cold finger wax disposition experiments were also the same as those used for the
flow loop wax deposition experiments.
3.8.1 Cold Finger Design
The cold finger was designed and fabricated to enable the study of the effects of water
content on wax deposition, and to investigate the effects of shear rate and time (aging) on the
wax deposits. The design of the finger was such that the coolant flowed within a pipe that was
inserted in the reservoir of sheared wax mixture kept at constant temperature above the WAT of
wax mixture. With this configuration, the wax deposition took place on the outside of the pipe
wall, with heat being transferred from the outside of the pipe wall, across the pipe wall, and into
the coolant flowing in the pipe.
The cold finger apparatus consisted of a 0.375" OD Aluminum rod (used for clamping),
8.25 inches in length attached to a 0.375"–0.25" NPT copper reducer, which was connected to a
copper tee (tee #1) having one 0.25" NPT and two 0.25" tube fittings. One of the 0.25" tube
fittings on tee #1 was connected to a 0.25" OD stainless steel tube, 1 inch long. The 1 inch long
stainless steel tube was used as a link for connecting another tee (tee #2) having one 0.25" NPT
and two 0.25" tube fittings. The 0.25" NPT on tee #2 was connected to a 0.0625" tube used to
hold a thermocouple in place for measuring the inlet coolant water to the cold finger apparatus,
while the second 0.25" tube on tee #2 was the inlet of the coolant water. The second 0.25" tube
93
fitting on tee #1 was connected 0.25" OD stainless steel tube, 8.75 inch in length, which was the
inner tube of the cold finger apparatus through which the coolant water flowed into the annulus
of the cold finger. A 0.25"–0.375" tube male insert was attached to the stainless steel tube 0.32"
below tee #1, the 0.375" connection of the tube male insert was connected to a 0.375" copper tee
(tee #3), having three 0.375" tube fittings. One of the 0.375" tube fittings was attached to a
0.375" tube male insert, which was in turn attached to 0.25" stainless steel tube fitting. This tube
fitting was attached to a 0.25" stainless steel tube, 0.875 inch long, which was connected to
another tee (tee #4) having one 0.25" NPT and two 0.25" tube fittings. The 0.25" NPT was
connected to a 0.063" tube fitting used to hold the thermocouple measuring the outlet coolant
water temperature. The second 0.25" tube fitting on tee #4 was used as the coolant water outlet
for the cold finger apparatus.
The third 0.375" tube fitting on tee #3 was connected to a 0.375" OD copper tube, 5.75
inches long, which served as the wax deposition section. Only 3 inches of the total length of the
copper tube was exposed as the deposition section, 2.125 inches of the length at the top and
0.325 inch of the length at the bottom were covered with 0.625" OD teflon. Teflon was used because of its insulating properties and very low affinity to wax. Figure 3.15 shows the schematic of the cold finger apparatus, while Figure 3.16 and Figure 3.17
are photographs of the cold finger apparatus in assembled and dismantled positions, respectively.
94
Coolant inlet
Coolant outlet
Stainless steel tube
Copper tube
Teflon insulator
Figure 3.15
Schematic of cold finger apparatus.
95
Figure 3.16
Assembled cold finger apparatus.
96
Figure 3.17
Dismantled cold finger apparatus.
97
3.9 Associated Equipment and Measurements
3.9.1 Microscopy
For the effect of deposit aging with time, samples of the wax deposits from experiments
period for different period of time were studied under the microscope and pictures of the wax
crystals were taken. A Carl Zeiss Axiovert S100 inverted optical microscope equipped with an
Axiocam video camera was used to capture the images at 20X magnification. AxioVision
software was used for image analysis. The microscope was connected directly to a computer on
which the images of the wax crystals from the deposit samples were captured. The pictures taken
were in .zvi format, but they were converted to jpeg format using the AxioVision LE software.
3.10 Cold Finger Experiments
3.10.1 Experimental Procedure for Cold Finger Experiments
The experimental procedure used for the cold finger experiments was similar to the one
used for the flow loop experiments, the difference being that the wax mixture was not being
pumped by any pump, rather the cold finger assembly was inserted into the stirred wax mixture
kept at a constant temperature in the heating bath. It was ensured that the cold finger was inserted
into the wax mixture at the same position in the wax mixture reservoir as much as possible, for
all experiments, and that the stirrer was at the same position as much as possible. However, the
height of the stirrer was adjusted according to the height of the fluid in the reservoir. This was
done to reproduce the similar hydrodynamic and shearing conditions for all experiments.
After the wax mixture and coolant had attained the desired set temperatures, the
deposition process was commenced by turning on the coolant water pump to circulate the coolant
water from the refrigerated-bath, through the stainless steel tube and then filling up the annular
region between the stainless steel tube and the copper tube, such that the inside of the copper
98
tube was constantly at a temperature lower than the WAT of the wax mixture. A timer was also
started at the same time as the coolant water pump to determine the duration of the each
experiment. During each cold finger deposition experiment, four thermocouples were used to
record the temperature of the wax mixture above its WAT, Th, the inlet and outlet temperatures
of the coolant, Tci and Tco respectively, and the temperature of the room, Troom, using the
temperature data acquisition system described in section 3.3.6.
At the end of the predetermined duration of the experiment, the deposition experiment
was terminated by removing the cold finger from the wax mixture reservoir. The mass of the
deposited wax was determined by scraping the deposit off the cold finger into a pre-weighed
sample bottle with a spatula, while passing warm water through the cold finger. The sample
bottle with the deposit in it was then weighed on a Sartorius BP 210S balance with a precision of
±0.1 mg.
For all experiments performed with wax mixtures containing water, to ensure adequate
dispersion of water in the oil–water dispersion, samples of the wax mixture in the reservoir were
withdrawn at depths similar to that of the exposed surface of the cold finger (while stirring),
these samples were centrifuged to determine the water content of the samples. The water content
in the samples were compared to those of that of the wax mixture in the reservoir. Stirring was
done at a rate of 500 rpm at the beginning of each experiment to ensure adequate dispersion of
the water phase in the oil phase. The stirring was continued throughout the duration of the
experiments. Results of this comparison are presented in Chapter 6. Determination of the water
content of wax deposits from two-phase cold finger experiments was done the same way as was
done for deposits from flow loop experiments.
99
3.10.2 Experimental Design for Cold Finger Experiments
The factors that were studied in the 2-phase cold flow wax deposition experiments were
the effect of time (aging), water content of the mixture, and the stirring rate of the wax mixture.
Apart from the preliminary experiments, a total of 43 cold finger wax deposition experiments,
including 7 repeat experiments, were performed according to a design of experiments
summarized in Table 3.7. The values of Th was (WAT+3 °C) while the value of Tci was (WAT–
15 °C). The wax concentration was 10 mass% while the water contents used were 0, 10, 20, and
30 volume%. Two stirring rates of 250 and 500 rpm were used and experiments were done for
different durations ranging from 5 min to 24 h. Two very short duration experiments were
performed for 30 s and 2 min. The short duration experiments were performed at a stirring speed
of 250 rpm. A constant coolant flow rate of 0.0303 L/s was used in all experiments, which
allowed for a high enough heat transfer coefficient, hc.
Again, to avoid any significant compositional changes of the wax mixture in the reservoir
between experiments, each prepared batch of waxy mixtures was used for up to 6 deposition
experiments. It was estimated that the wax depletion from the wax mixture reservoir was not
more than 1.5% of the original.
100
Table 3.7
Conditions of cold finger wax deposition experiments (Wax concentration = 10
mass%, WAT = 32 °C)
variable
number of levels
values of each variable tested
wax concentration, mass%
1
10
water content (total volume basis),
vol%
4
0, 10, 20, 30
inlet temperature of waxy mixture
(Th), ºC
1
WAT+3
inlet temperature of coolant (Tci), ºC
1
WAT–15
stirring speed
2
250, 500 rpm
all experiments
9
0.1, 0.2, 0.5, 1, 2, 4, 8, 12, 24 h
short duration experiments
2
0.01 and 0.03 h, 250 rpm stirring speed
(0% water content)
time for deposition, h
101
Chapter Four: Results of WPT–Cooling Rate Experiments
The results presented in this chapter have been published in Fuel by Kasumu et al.
(2013). As suggested by Paso et al. (2009), the term WPT has been used in this study to define
the temperature for the onset of solid formation under a constant cooling rate, which
distinguishes it from the WAT, that is measured using a stepwise cooling (and at an uncontrolled
rate) as in the ASTM method. The main objective of the WPT–Cooling Rate experiments was to
investigate the effect of cooling rate and wax concentration on WPT. As described earlier,
experiments were carried out using mixtures of seven different wax concentrations and at five
different cooling rates. The effects of cooling rate and wax concentration in the wax mixture are
discussed in this chapter.
Tiwary and Mehrotra (2004) reported WAT measurements on six prepared wax–solvent
mixtures using a modified ASTM D 2500-09 visual method and found the results to compare
well with those obtained from other methods, including CPM, DSC and viscometry.
The
average absolute differences between the WAT measurements from the visual method and the
other methods were reported to vary from 0.3% to 5.8%, with an overall average absolute
difference of 1.7%.
As mentioned previously, the WAT measurements are performed typically without
taking into consideration the cooling rate during the cooling process. For example, the visual
method prescribed in ASTM Standard D 2500-09 does not specify any specific cooling rate to be
used. However, the effect of cooling rate on the crystallization process and the phase
transformation temperature has been reported for pure paraffins and mixtures (Hammami and
Mehrotra, 1995).
102
4.1 Effect of Cooling Rate
Figure 4.1 shows the variation of experimental and predicted WPT values for different
compositions of the prepared Conros Parowax–Norpar13 mixtures using the modified visual
method at constant cooling rates in the range of 0.05–0.4 oC/min. The effect of cooling rate on
the measured WPT values is nearly linear such that the WPT is higher at a lower cooling rate.
Figure 4.1 also shows values of WAT for all of the seven compositions, using a 1oC stepwise
cooling process in which the cooling rate was not controlled or measured (Fong and Mehrotra,
2007; Bidmus and Mehrotra, 2008b; Bidmus and Mehrotra, 2009). It is observed that the WAT
values match the WPT values at cooling rates varying between 0.2 and 0.4 oC/min.
103
45
20%
15%
40
8%
o
WPT ( C)
10%
35
6%
4%
30
2%
WAT
25
0.0
0.1
0.2
0.3
0.4
0.5
Cooling rate (o C/min)
Figure 4.1
Variation of WPT with cooling rate for different Conros Parowax–
Norpar13 mixture compositions.
104
All of the WPT data obtained in this study were fitted to several correlations and
Equation 4.1 was found to be the best fit. It relates WPT to the cooling rate and the wax
concentration.
WPT = f1 + f2x + f3lny
4.1
In Equation 4.1, WPT is in oC, x is cooling rate in oC/min, and y is wax concentration in mass %.
The regressed values of parameters f1, f2 and f3 were 24.17±0.21, –4.155±0.494 and 6.684±0.087,
respectively. The t-values for parameters f1, f2 and f3 were 114.2, –8.40 and 76.9, respectively.
For the data used, Equation 4.1 was found to have a coefficient of determination, r2, of >0.99 and
a standard error of 0.37. The average absolute difference between experimental and calculated
WPT values was less than 0.3 oC.
Calculations were made using Equation 4.1 to obtain the variation of WPT with cooling
rate and composition. Figure 4.2 is a scatter plot of the experimental and calculated values of
WPT, which shows that except for one data point all data are fitted by Equation 4.1 within 95%
confidence limits.
4.1.1 Significance of Cooling Rate
Recently, Arumugam et al. (2013) used the relationship between WPT, x and y in
Equation 4.1 to achieve the transition from the 'hot flow' to the 'cold flow' regime in a wax
mixture flowing in a cylindrical pipeline. The significance of the cooling rate in transitioning
from the 'hot flow' to the 'cold flow' regime is illustrated in Figure 4.3. The solid line in Figure
4.3 represents the WPT predictions from Equation 4.1 as the cooling rate is varied for a 6 mass
% wax–solvent mixture. The area above the WPT line is the one-phase liquid region
(corresponding to the „hot flow‟ regime) whereas the area below the WPT line is the two-phase
liquid–solid region (corresponding to the „cold flow‟ regime). The points a, b and c in Figure 4.3
105
represent the different states for the 6 mass% mixture at 35 oC, when cooled at different cooling
rates of 0.4, 0.27 and 0.1 oC min–1. Between points a and b, the mixture would be one-phase
liquid; however, from points b to c, the mixture would exist in the two-phase (liquid + solid)
state. That is, starting from point a, when the cooling rate decreases to approximately 0.27 oC
min–1 (at point b), Equation 4.1 predicts the transition from one liquid phase to two (liquid and
solid) phases. Line d–e–f in Figure 4.3 illustrates the cooling of the same mixture from 36.5 oC to
35.5 oC at a constant cooling rate of 0.1 oC min–1, for which the solid phase is predicted to
precipitate at a temperature of 35.7 oC (at point e). Line g–h–i in Figure 4.3 corresponds to the
cooling of the same mixture from 34.8 oC to 33.8 oC but at a higher constant cooling rate of 0.4
C min–1, for which the solid phase is predicted to precipitate at a temperature of 34.5 oC (at
o
point h). Thus, for the same 6 mass% wax–solvent mixture, an increase in the cooling rate from
0.1 oC min–1 to 0.4 oC min–1 is predicted to decrease the WPT from 35.7 oC to 34.5 oC. It is
pointed out that the wax precipitation process illustrated by Line a–b–c in Figure 4.3 is more
relevant for the transition from the hot flow regime to the cold flow regime of the waxy mixture
used in this study, flowing in a pipeline under cooling conditions.
106
45
o
Calculated WPT ( C)
40
35
30
25
25
30
35
40
45
Experimental WPT (oC)
Figure 4.2
Comparison of calculated and experimental WPT values for Conros Parowax–
Norpar13 mixtures (dotted curves show 95% confidence limits).
107
37
one phase region
(liquid)
temperature (T), oC
d
36
e
f
b
a
35
c
g
h
34
two phase region
(liquid+solid)
33
0.0
0.1
i
0.2
0.3
0.4
0.5
cooling rate (|dT/dt|), oC min-1
Figure 4.3. The effect of cooling rate on the wax precipitation temperature and liquid-to-solid
phase transformation for w29 = 6 mass%.
108
4.2 Effect of Composition
Figure 4.4 shows the variation of WPT with the mixture composition, where the effect of
Conros Parowax concentration on WPT, for all cooling rates, is seen to be more pronounced at
lower wax concentrations. The WPT values increased with increasing concentration of Conros
Parowax in Norpar13. This is an expected trend that has been reported previously in literature
(Hammami and Mehrotra, 1995; Guo et al., 2006; Paso et al., 2009).
109
50
0.1 oC/min
0.2 oC/min
WPT (oC)
45
0.3 oC/min
0.4 oC/min
40
35
30
25
0
5
10
15
20
parowax concentration (mass%)
Figure 4.4
Variation of WPT with Parowax–Norpar13 mixture composition at different
cooling rates as predicted by Equation 4.1.
With the WPT being dependent on the cooling rate, it may not correctly represent the
thermodynamic liquidus temperature for the liquid-to-solid phase transformation process. It is
emphasized that Equation 4.1 is based on experimental results for prepared waxy mixtures over a
110
cooling rate range of 0.05–0.40 oC/min and a wax concentration range of 2–20 mass %. Since
Equation 4.1 was obtained by fitting the WPT data, its extrapolation to other waxy mixtures or
“waxy” crude oils, at wax concentrations or cooling rates outside the range of the experimental
measurements of this study, should be done with caution.
111
Chapter Five: Results of Two-Phase Flow Loop Wax Deposition Experiments
In this chapter, results are presented from the 2-phase wax deposition experiments using
the flow loop apparatus. This study extends the single-phase laminar (Bidmus and Mehrotra,
2004; Parthasarathi and Mehrotra, 2005) and turbulent flow (Fong and Mehrotra, 2007; Tiwary
and Mehrotra, 2009) deposition studies from our laboratory into the two-phase regime. The
experimental program investigated the effects of water content, waxy mixture temperature
(above the WAT), coolant temperature (below the WAT), and Reynolds number (or shear rate).
Since all experiments were performed with the waxy mixture temperature held above the
corresponding WAT, the liquid phase did not contain any solid phase; that is, all of the
experiments were performed under the “hot flow” conditions.
Also presented is the steady-state heat transfer model that was used to analyze the results
from the flow loop wax deposition experiments. This model has been successfully utilized to
analyze experimental results from "hot flow" wax deposition under laminar and turbulent flow
conditions (Bidmus and Mehrotra, 2004; Parthasarathi, 2005; Fong and Mehrotra, 2007; Tiwary
and Mehrotra, 2008; Bidmus and Mehrotra, 2009).
5.1 Steady State Heat Transfer Model
In the steady-state heat-transfer model used for the flow loop experiments, the „hot‟ waxy
mixture (comprising wax, solvent and water), held at a temperature higher than its WAT (Th >
WAT) and flowing through a tube, is cooled by a coolant, held at a temperature below its WAT
(Tc < WAT) and flowing through an annular region. Heat transfer from the waxy mixture to the
coolant results in a radial temperature gradient, which leads to the formation of a deposit-layer,
provided the inside tube-wall temperature, Twi, is less than the WAT. The rate of heat transfer is
112
decreased because of the additional thermal resistance offered by the deposit-layer. The depositlayer continues to grow in thickness until a thermal steady-state is attained, when all thermal
resistances become constant. At thermal steady-state, the rate of heat transfer across the waxy
mixture, the deposit layer, the tube wall, and the coolant will be equal.
The temperature profile across the four thermal resistance in series, during the wax
deposition process, is shown schematically in Figure 5.1. For the double-pipe heat exchanger
configuration, used co-currently in the flow loop apparatus, the rate of heat transfer at steadystate is equal to the rate of thermal energy released by the waxy mixture and the rate of thermal
energy accepted by the coolant, as follows:
 Thi  Tci   Tho  Tco  
 h C h (Thi  Tho )  m
 c C c (Tco  Tci )  q gain  U i Ai 
qm

 lnThi  Tci  / Tho  Tco 
5.1
where m
 h and m c are mass flow rates of the wax mixture and coolant streams respectively, Ch
and Cc are the average specific heat capacities of the mixture and coolant streams respectively,
Thi and Tho are the inlet and outlet wax mixture temperatures respectively, Tci and Tco are the inlet
and outlet temperatures of the coolant respectively, Ui is the inside overall heat-transfer
coefficient, and Ai is the inside pipe surface area. The term qgain accounts for the rate of thermal
energy gained by the coolant from the ambient. From the heat transfer calculations, qgain was
estimated to be less than 2% of the rate of heat transfer, q.
113
C
wax deposit
Th
pipe wall
Td
Two
Twi
Tc
xd
ri
ro
Figure 5.1
Temperature profile during wax deposition.
114
The combined thermal resistance can be expressed as a sum of four individual thermal
resistances in series, i.e.
ln( ri /( ri  x d )) ln( ro /ri )
1
1
1




= Rh + Rd + Rm + Rc
2πk d L
2πk m L 2ro Lhc
U i Ai 2 (ri  x d ) Lh h
5.2
where, Rh = [2π(ri–xd)Lhh]–1, Rd = [(2πLkd)/ln{ri/(ri–xd)}]–1, Rm = [(2πLkm)/ln{ro/ri}]–1 and Rc =
[2πroLhc]–1. Next, the following equalities are obtained by equating the heat flux through each of
the four thermal resistances included in UiAi:
k d (Td  Twi )
k (T  Two ) hc (Two  Tc )
q hh (Th  Td )


 m wi

Ai
ri /(ri  xd ) ri ln( ri /(ri  xd ))
ri ln( ro /ri )
ri /ro
5.3
where hh and hc are the individual convective heat-transfer coefficients for the wax mixture and
coolant streams respectively, xd is the average deposit-layer thickness, kd and km are the average
thermal conductivities of the deposit and pipe-wall respectively, and Td is the liquid–deposit
interface temperature. Using the experimental data for q, Ai, Th, Tc, hh, hc, ri, ro, xd and km, the
four equalities in equation 5.3 can be solved simultaneously to obtain Twi, Two, Td and kd. The
two important quantities of interest in the heat-transfer modelling approach are Td and kd. Note
that, at steady-state, xd, kd and Td are assumed to be constant over the entire deposition surface.
Bidmus and Mehrotra (2004) proposed a dimensionless ratio, d, which is the ratio of the
deposit layer thermal resistance to the combined or total thermal resistance under thermal steady
state conditions. It represents the fractional thermal resistance offered by the deposit layer and is
given by the ratio of the temperature drop across the deposit layer to the overall temperature
difference as follows:
d 
Rd
T  Twi
 d
Rh  Rd  Rm  Rc Th  Tc
5.4
115
where Rh, Rd, Rm, and Rc, are the thermal resistances corresponding to the waxy mixture, the
deposit layer, the tube or pipe wall, and the cold stream respectively, and are defined in equation
5.2. Similar  ratios can be obtained for the other three thermal resistances, as follows:
h 
T  Td
Rh
 h
Rh  Rd  Rm  Rc Th  Tc
m 
T  Two
Rm
 wi
R h  Rd  R m  Rc
Th  Tc
5.5
5.6
c 
Rc
T  Tc
 wo
R h  Rd  R m  Rc
Th  Tc
5.7
Note that, at all times, (h +d + m +c) = 1.
Heat transfer calculations were performed over the range of experimental conditions used
in this study, to predict the effect of the deposit layer thickness on h, d, m, andc during the
2-phase deposition process. Figure 5.2 shows a set of predicted results from the calculations
showing the effect of the deposit layer thickness (relative to the inside pipe radius), xd/ri, on each
of the individual fractional thermal resistances. It can be observed that for a small deposit
thickness, the convective thermal resistance due to the wax-solvent mixture (h) is the
predominant thermal resistance.
However, as the deposit layer thickness increases, h decreases while d (due to the
deposit layer) increases sharply until the deposit layer begins to offer the dominant thermal
resistance when xd exceeds about 3% of ri. As shown in Figure 5.1, the largest temperature
gradient at this point would occur across the deposit layer. Figure 5.2 also shows that, for a
typical set of experimental conditions, the thermal resistances due to convection in the coolant
116
(c) and conduction through the pipe walls (m) are negligible, compared to the combined
thermal resistance.
1.0
d
Predicted Fractional Thermal Resistance, 
Re = 20000
0.8
h
0.6
0.4
0.2
c
m
0.0
0.00
0.05
0.10
0.15
0.20
Deposit Thickness, (xd / ri)
Figure 5.2
Predicted effects of deposit-layer thickness on fractional thermal resistances (kd =
–1 –1
0.38 W m K , Re = 10000).
117
5.2
Estimation of Heat Transfer Coefficients, hh and hc
To solve equation 5.3, estimates of the convective heat transfer coefficients for the waxy
mixture and coolant fluid, hh and hc, were required. These were obtained by performing a series
of non-depositing calibration experiments, in which both the waxy mixture and the coolant were
held at temperatures above the WAT of the wax mixture. These calibration experiments were
performed using the same coolant flow rate of 0.0082 L/s used in the actual deposition
experiments, thus hc was assumed to be constant. For the relatively small temperature ranges
involved in the experiment, any variation in the properties of the waxy mixtures was ignored and
it was assumed that hh  Re. These assumptions simplified equation 5.2 for the non-depositing
calibration experiments. Equation 5.2 was simplified as follows:
Ui = ( Re– + )–1
5.8
The calibration experiments were carried out for wax mixtures containing 0 and 10 vol%
water. Data for the average specific heat capacity, Cc, and density of water were obtained from
Perry‟s Handbook (Perry et al., 1997). Using equation 5.1, the experimental Ui was obtained, a
regression analysis with equation 5.8 yielded estimates of the values of  to be 0.8 and  to be
0.00037 and 0.00051 for waxy mixtures containing 0 and 10 vol% water respectively. The
values of  were 0.001 and 0.0007 for waxy mixtures containing 0 and 10 vol% water
respectively. With  = 0.00037 and km = 237.8 W m–1 K–1, hc was estimated to be 2137 W m–2
K–1. Values for hh for all other waxy mixtures containing different amounts of water were
extrapolated and hh varied between approximately 465 W m–2 K–1 and 1900 W m–2 K–1,
depending on the flow rate (or Re) and water content of the waxy mixtures.
Figure 5.3 shows a comparison of the experimental and correlated Ui for all four
compositions of waxy mixtures used. The average relative deviations between the experimental
118
and calculated Ui were 8.0% and 2.9% waxy mixtures containing 0 and 10 vol% respectively. As
shown in Figure 5.2, at xd/ri > 0.02–0.03, the deposit offered the dominant thermal resistance;
hence, the deposition calculations were not affected significantly as a result of any uncertainty in
the estimation of hh or hc.
119
800
Calculated U i (W m-2 K-1 )
700
0% Water
10% Water
600
500
400
300
300
400
500
600
700
800
Experimental U i (W m-2 K-1 )
Figure 5.3
Comparison of experimental and correlated overall heat transfer coefficient, Ui,
for wax mixtures (obtained from experiments performed under non-depositing conditions).
120
5.3 Properties of Wax–Solvent, Wax–Solvent–Water Mixtures and Deposit Samples
5.3.1 Density of Wax–Solvent and Wax–Solvent–Water Mixtures
All flow loop experiments were performed with wax mixtures containing Bernardin
Parowax as the wax and Linpar1416V as the solvent. The density of the Bernardin Parowax–
Linpar 1416V mixtures was required for the determination of flow characteristics, such as the
Reynolds Number at each flow rate. The densities of the Linpar1416V and 6, 10 and 20 mass%
Bernardin Parowax-Linpar1416V mixtures were measured at different temperatures above the
WAT as described previously. The density data were fitted using the following linear correlation
to express density as a function of temperature (with r2 > 0.99):
 so ln  a1  a2Th
5.9
The regression constants a1 and a2 are listed in Table 5.1 while Figure 5.4 shows the variation of
density with temperature for the solvent and wax mixtures.
The density of two-phase wax mixtures containing water was estimated as a weighted
average of those for the wax–solvent mixture and water.
121
Table 5.1
Density regression constants for equation 5.9.
wax concentration,
constants in density correlation
mass %
a1 (kg m-3)
a2 (kg m-3K-1)
0
774.6  0.2
–0.522  0.005
6
779.3  0.1
–0.535  0.003
10
792.6  0.4
–0.533  0.008
122
775
770
soln (kg m-3)
765
760
755
750
10 mass%
6 mass%
APCO 1416V
fitted, eq 5.9
745
740
735
20
30
40
50
60
70
Temperature (oC)
Figure 5.4
Variation of the density of Bernardin Parowax-Linpar1416V mixtures with
Temperature.
123
5.3.2 Specific Heat Capacity of Wax–Solvent and Wax–Solvent–Water Mixtures
Energy balance calculations and estimation of the mixture outlet temperature (Thout)
required the use of the specific heat capacity of Bernardin Parowax-Linpar1416V mixtures. The
average specific heat capacity of each mixture, Ch, was estimated as the weighted-average of the
heat-capacities of the components in the mixture. The component specific heat capacities were
estimated from a group contribution method developed by Jin and Wunderlich (1991). The effect
of temperature on the specific heat capacity of the three mixtures is shown in Figure 5.5. The
following correlation (with r2 ≈ 1.00) was used to fit the estimated specific heat capacities:
Ch = c1 + c2 Th
5.10
The regression constants for equation 5.10 are listed in Table 5.2.
The specific heat capacity of two-phase wax mixtures containing water was estimated as
a weighted average of those for the wax–solvent mixture and water.
124
2420
-1
-1
Specific Heat Capacity, Ch (J kg K )
2410
2400
2390
2380
2370
2360
10 mass%
6 mass%
Linpar1416V
fitted, eq 5.10
2350
2340
10
20
30
40
50
60
70
Temperature (oC)
Figure 5.5
Specific heat capacities of Bernardin Parowax-Linpar1416V mixtures.
125
Table 5.2
Regression constants for equation 5.10, the specific heat capacity of
mixtures of Bernardin Parowax in Linpar1416V.
wax concentration
constants in specific heat capacity correlation
mass %
c1 (J kg-1 K-1)
c2 (J kg-1 K-2)
0
2326
1.313
6
2330
1.305
10
2333
1.300
126
5.3.3 Viscosity of Wax–Solvent and Wax–Solvent–Water Mixtures
The viscosity of Bernardin Parowax–Linpar1416V mixtures was required for the
calculation of Reynolds numbers at different temperatures. The results obtained from viscometer
measurements are shown in Figure 5.6, which presents the variation of the viscosity of the
mixtures with temperature. It is observed that viscosity of the mixture increases with
concentration of wax in the mixture. The viscosity–temperature data for each mixture were fitted
to Equation 5.11 (with r2 > 0.99):
 = 10–3  exp [b1 + b2 / (Th + 273.15)]
5.11
The regression constants b1 and b2 are shown in Table 5.3.
The viscosity of the two-phase waxy mixture was estimated using the Brinkman
correlation (Brinkman, 1952) for the viscosity of dispersions, given in equation 5.12.
m = c (1 – φd) –2.5
5.12
where m is the viscosity of the mixture, c is the viscosity of the continuous phase, and φd is the
volume fraction of the dispersed phase.
127
0.7
0.6
ln (), in mPa s
0.5
0.4
0.3
0.2
10 mass%
6 mass%
Linpar1416V
fitted, eq 5.11
0.1
0.0
2.9
3.0
3.1
3.2
3
3.3
3.4
-1
1/T X 10 (K )
Figure 5.6
Viscosities of various Bernardin Parowax-Linpar1416V mixtures at wax
concentrations from 0-10 mass%.
128
Table 5.3
Viscosity regression constants for viscosity equation 5.11.
wax concentration,
constants in viscosity correlation
mass%
b1
b2
0
–4.25 0.04
1442 12
6
–4.53 0.02
1540 5
10
–6.28 0.03
2129 9
129
5.3.4 Density of Deposit Samples
The deposit density was required for estimating the average deposit-layer thickness, xd,
and for relating the deposit density to the average temperature and the Reynolds number. The
deposit samples used in these measurements were all from the 1-h experiments performed with
wax mixtures containing no water and at Thi = (WAT+7°C) and Tci = (WAT–10°C). A
pycnometer was used to measure the deposit density. The correlation relating deposit density to
the Reynolds number and the average temperature is shown in equation 5.13, which gave the
best overall fit for the data (out of several other forms of correlations tested).
d = d1 + d2 Re–1 + d3 (WAT – Tdavg)
5.13
where Tdavg denotes the average deposit temperature. Regression constants d1, d2 and d3 in
equation 5.13 are 788.1, -358000 and 0.784 respectively.
The extent of deposition was expressed as the mass of deposit per unit inside tube or
deposition surface area, , and it is related to the deposit layer thickness, xd, and the deposit
density, d, as follows:
Ω = d [{ri2 – (ri – xd)2}/2ri]
5.14
Equation 5.14 was used along with the experimental deposit density and deposit mass per unit
area to determine the average deposit thickness.
130
5.4 Thermal Steady State
For the steady heat transfer model to be used in predicting the extent of wax deposition, it
was necessary to ensure that the experiments had attained a thermal pseudo steady state before
stopping the experiments. Previous deposition experiments carried out with similar waxy
mixtures in both the laminar and turbulent flow regimes showed that a thermal steady state was
attained within 30 min (Bidmus and Mehrotra, 2004; Parthasarathi and Mehrotra, 2005; Fong
and Mehrotra, 2007; Tiwary and Mehrotra, 2009).
To ensure that steady state was achieved within the 1-h duration, four extended
experiments were conducted over durations of 2 and 4 hours of deposition time. These extended
experiments were performed at Re ≈ 10000, with Th = (WAT+7 °C) and Tc = (WAT–10 °C).
Results, shown in Figure 5.7, indicated that a deposition time of 1 hour was sufficient to achieve
a thermal steady state and a relatively constant deposit mass.
131
0.40
Deposit Mass with Water (kg m-2)
Deposit Mass without Water (kg m-2)
-2
Deposit Mass/Area,  (kg m )
0.35
0.30
0.25
0.20
0.15
0.10
0
1
2
3
4
5
Time (h)
Figure 5.7
Variation of deposit mass per unit area,  with time for extended experiments.
132
Deposition experiments indicated that the thermal steady-state was attained within 10-20
min. The data for the gain in coolant temperature, (Tco – Tci), versus deposition time are shown
in Figure 5.8 for the experiments at Th = (WAT+7 °C) and Tc = (WAT–10 °C) with 0, 10, 20 and
30 vol% water at three levels of Re. In all experiments, (Tco – Tci) was high initially but it
decreased rapidly to about 1-3 °C within 10 min, and the thermal steady-state was reached in less
than 10-20 min. The temperature profiles in Figure 5.8 are similar to those reported previously
for single-phase deposition studies under laminar (Bidmus and Mehrotra, 2004; Parthasarathi and
Mehrotra, 2005) and turbulent flow (Fong and Mehrotra, 2007; Tiwary and Mehrotra, 2009)
which also showed the deposition process to be relatively fast, requiring less than 10-20 min to
reach the thermal steady-state in the benchscale apparatus.
The temperature profiles in Figure 5.8 also show that (Tco – Tci) is larger at higher Re of
the wax mixture. This is attributed to a decrease in the convective thermal resistance, Rh, and a
corresponding smaller deposit-layer thickness at higher Re. As shown in equation 5.1, (Tco – Tci)
is directly proportional to the rate of heat transfer. Thus, an increase in the Re would yield a
higher rate of heat transfer at steady-state.
133
6
0% Water
Re = 12500
Re = 18900
Re = 25300
5
4
3
2
1
0
10% Water
Re = 10000
Re = 15300
Re = 20100
20% Water
Re = 7600
Re = 11600
Re = 15400
5
o
Gain in Coolant Temperature, [Tco - Tci] ( C)
6
4
3
2
1
0
6
5
4
3
2
1
0
6
30% Water
Re = 5600
Re = 8600
Re = 11500
5
4
3
2
1
0
0
10
20
30
40
50
60
Time (min)
Figure 5.8
Approach to thermal steady-state during deposition shown by the difference in
coolant temperature for 1-hour experiments at Thi = (WAT+7ºC) and Tci = (WAT–10ºC) for wax
mixtures with 0, 10, 20 and 30 vol% water content.
134
5.5 Estimation of Liquid–Deposit Temperature (Td) and Deposit Thermal Conductivity (kd)
The results were analyzed with equations 5.1 and 5.3 to predict the liquid–deposit
interface temperature, Td, and the average deposit thermal conductivity, kd. The four heat-flux
equalities in equation 5.3 were solved to obtain Twi, Two, Td and kd. From the steady-state data of
each experimental run, the measured Tc was used to estimate Two, which was then used to
estimate Twi. The measured Th was then used to estimate Td, which was in turn used to estimate
the average thermal conductivity of the deposit, kd. The ratio ri/(ri – xd) in the first two equalities
of equation 5.3 can be written as (1 – xd/ri)–1. When xd/ri  1, Td estimated from the first
equality of equation 5.3 is less sensitive to xd. The heat flux through the deposit layer, described
by the second equality in equation 5.3, contains Td, kd and xd, which makes the calculated kd
more sensitive to xd. This is because, even though the term (1 – xd/ri) remained close to 1 for
most experiments, the term –ln(1 – xd/ri) in the second equality in equation 5.3 varied with xd/ri.
Thus, a small experimental uncertainty in xd caused a relatively larger variation in the estimated
kd than in Td.
Using the heat transfer calculations for all 1-h deposition experiments, the calculated Td
was found to be 28.5±2.0 oC, which compares very well with the experimentally measured WAT
of 28.0 oC. These results support similar findings from single-phase wax deposition studies by
Bidmus and Mehrotra (2004), Parthasarathi and Mehrotra (2005), Fong and Mehrotra (2007) and
Tiwary and Mehrotra (2009). Note that Bidmus and Mehrotra (2008a, 2008b) also reported the
experimentally measured liquid–deposit interface temperature to be approximately equal to the
WAT of waxy mixtures. The summary of all 1 h experiments is presented in Table 5.4.
135
Table 5.4
Average Reynolds number, Re, estimated average liquid–deposit
interface temperature, Td, and average deposit thermal
conductivity, kd, at different hot and cold stream temperatures .
wax mixture
temperature,
Th
coolant
temperature,
Tc
(oC)
(oC)
WAT+7
WAT-10
WAT+7
measured
average
estimated (Td)
average
deposit
thermal
conductivity,
kd (W m-1 K-1)
8900
28–29
27.8±1.4
0.35±0.11
WAT-10
13400
28–29
28.3±1.0
0.40±0.11
WAT+7
WAT-10
17900
28–29
28.4±1.4
0.42±0.10
WAT+7
WAT-20
9300
28–29
27.4±1.5
0.29±0.12
WAT+15
WAT-10
16200
28–29
30.9±2.9
0.33±0.13
WAT+15
WAT-20
16600
28–29
28.7±3.2
0.47±0.21
28.5±2.0
0.38±0.13
WAT (oC)
Average
Re
All 1 h
experiments
136
As shown in Table 5.4, the average deposit thermal conductivity, kd, was calculated to be
0.38±0.13 W m–1 K–1, which compares well with those reported for single-phase deposition
experiments under turbulent flow (Fong and Mehrotra, 2007; Tiwary and Mehrotra, 2009). The
relatively high standard deviation, indicated by ±0.13 W m–1 K–1, in the calculated average kd,
can be attributed partly to the variations in Re, which resulted from changes in the viscosity of
waxy mixtures because of the addition of water. The results did not show any trend between the
deposit water content and the estimated deposit thermal conductivity.
The average kd of 0.38 W m–1 K–1 is higher than those reported for deposits under laminar
flow (Bidmus and Mehrotra, 2004; Parthasarathi and Mehrotra, 2005). The higher kd values
could be attributed to the higher deposit wax-content due to turbulent flow.
5.6 Effect of Deposit-layer Thickness (xd) on the Rate of Heat Transfer (q) and the Inside
Tube-wall Temperature (Twi)
Calculations were performed with the above heat-transfer model to explore the effects of
deposit-layer thickness (xd) on the rate of heat transfer (q) and the inside tube-wall temperature
(Twi). As shown in Figure 5.9, it was found that, at typical experimental conditions used in this
study, both q and Twi decreased sharply with an increase in xd. For example, for an average
deposit layer thickness of 1 mm (or xd /ri = 0.079), q was predicted to decrease by 67% with a
corresponding lowering of Twi by about 3 oC. These results confirm a recent observation by
Bidmus and Mehrotra (2012) that the average tube-wall temperature, Twi, should not be assumed
to remain constant after the deposition process begins because of the significant thermal
resistance offered by the deposit layer.
137
1.0
4
0.8
o
3
q/q o
0.6
2
0.4
1
0.2
0.0
0.0
[(Twi)o - Twi] ( C)
q/qo
[(Tw i)o - Tw i]
0.1
0.2
0.3
0.4
0
0.5
x d /r i
Figure 5.9
Predicted effect of deposit-layer thickness (xd) on the rate of heat transfer and
inside tube-wall temperature (Twi)
138
5.7 Effect of Process Conditions on Flow Loop Wax Deposition
The results for the mass of the deposit-layer from 1-h experiments performed with waxy
mixtures of different water content, flow rate (or Re) and the temperatures of the waxy mixture
(hot) and coolant water (cold) streams are presented and discussed below.
The deposit mass per unit deposition area is denoted by Ω (in kg m–2). For the deposition
experiments performed in this study, xd varied from about 0.1 mm (Ω  0.075 kg m–2) to about
0.9 mm (Ω  0.639 kg m–2). Thus, for the 2.5-cm diameter deposition tube, the relative deposit
thickness, xd/ri, varied from about 0.008 to 0.068. It is noted that the deposit-layer thickness
values in this study are much smaller than those obtained under single-phase laminar flow
(Bidmus and Mehrotra, 2004; Parthasarathi and Mehrotra, 2005), but are comparable to those
from single-phase turbulent flow (Fong and Mehrotra, 2007; Tiwary and Mehrotra, 2009) of
similar waxy mixtures.
5.7.1 Effect of Water Content on Deposit Mass
For the hot and cold stream temperatures of (WAT+7) and (WAT–10), respectively, Ω
increased as the water content increased from 0 vol%, reaching a peak at 10 vol% water content.
As the water content in the waxy mixture increased further, Ω decreased and remained almost
constant until the water content reached 30 vol%, when another increase was observed. This
same trend was noted for all three average Re. Figure 5.10 is a plot of the ratio (Ω/Ωo), which
relates the deposit masses obtained from waxy mixtures with water and without water. It shows
that increasing the water content in the waxy mixture increases Ω/Ωo at 10 and 30 vol% water
content. It also shows the variation of the average values of Ω/Ωo (at all three Re values) with
water content.
139
1.4
Re=8900, Th=WAT+7, Tc=WAT-10
Re=13400, Th=WAT+7, Tc=WAT-10
Re=17900, Th=WAT+7, Tc=WAT-10
Average for all Three Re Values
1.3
1.2
  
1.1
1.0
0.9
0.8
0.7
0
5
10
15
20
25
30
35
 r(vol%)
Figure 5.10 Effect of the water content in the wax mixtures on the deposit mass
per unit area, Ω.
140
Figure 5.11 presents the results for the variation in the deposit mass with the water
content in the waxy mixture. The three plots in Figure 5.11 show the individual effects of the
waxy mixture temperature, Th, the coolant temperature, Tc, and the Reynolds number, Re. The
specific effects of these parameters on the deposition process and the deposit mass are discussed
in the following sub-sections.
5.7.1.1 Effect of Th on Deposit Mass
For the two-phase wax deposition study, the effect of Th was evaluated relative to the
WAT of each waxy mixture in terms of (Th – WAT). Figure 5.11(a) shows that the deposit mass
increased with decreasing Th. That is, the deposit mass was observed to be higher for a lower (Th
– WAT).
These results are consistent with those reported previously from single-phase
experiments in both laminar (Bidmus and Mehrotra, 2004; Parthasarathi and Mehrotra, 2005) and
turbulent (Fong and Mehrotra, 2007; Tiwary and Mehrotra, 2009) flow regimes as well as the
model predictions (Bhat and Mehrotra, 2005; Bhat and Mehrotra, 2006; Mehrotra and Bhat,
2007; Mehrotra and Bhat, 2010).
Previous experimental investigations (Bidmus and Mehrotra, 2004; Parthasarathi and
Mehrotra, 2005; Fong and Mehrotra, 2007; Tiwary and Mehrotra, 2009; Bidmus and Mehrotra,
2009) have established that the deposit mass is not directly related to the overall thermal driving
force for heat transfer, (Th – Tc); instead, the extent of solid deposition has been shown to depend
on two thermal driving forces, namely (Th – WAT) and (WAT – Tc). As mentioned previously,
in the thermally-controlled wax deposition approach, it is assumed that Td ≈ WAT throughout the
deposition process, which has been verified through batch deposition experiments under static
and sheared cooling (Bidmus and Mehrotra, 2008a; Bidmus and Mehrotra; 2008b).
141
5.7.1.2 Effect of Tc on Deposit Mass
Previous studies on single-phase wax deposition (Bidmus and Mehrotra, 2004;
Parthasarathi and Mehrotra, 2005; Fong and Mehrotra, 2007; Tiwary and Mehrotra, 2009;
Bidmus and Mehrotra, 2009) have shown that the deposit mass increases with a decrease in Tc or
an increase in (WAT – Tc). Again, this observation has been supported by the predictions from a
mathematical model based on the moving boundary problem formulation (Bhat and Mehrotra,
2005; Bhat and Mehrotra, 2006; Mehrotra and Bhat, 2007; Mehrotra and Bhat, 2010).
The effect of Tc in this two-phase wax deposition study was also evaluated relative to the
WAT of each waxy mixture in terms of (WAT – Tc). Figure 5.11(b) shows that the deposit mass
increased with decreasing Tc. That is, the deposit mass was observed to be higher for a higher
(WAT – Tc) or a lower Tc. These results are consistent with those reported previously from the
same single-phase experiments in both laminar and turbulent flow regimes as well as the model
predictions.
5.7.1.3 Effect of Flow Rate or Reynolds Number on Deposit Mass
Figure 5.11(c) shows the variation of Ω with water content at three average Reynolds
numbers. As shown by the three sets of results in Figure 5.11 (c), the deposit mass per unit area,
Ω, decreases with an increase in Re. This is because an increase in Re causes an increase in hh
(and a corresponding decrease in the convective thermal resistance, Rh). For the same Th and Tc,
a lower Rh implies that the deposit thermal resistance, Rd, would also decrease, which implies a
decrease in the deposit-layer thickness, xd, and consequently a lower deposit mass or Ω. The
overall effect of these changes is that the rate of heat transfer is higher at higher Re due to a
lower convective thermal resistance, Rh, as well as a lower conductive thermal resistance, Rd,
offered by the deposit-layer.
142
(a)
Tc=WAT-10
0.6
Th =WAT+7, Re=13400
0.4
Th =WAT+15, Re=16200
0.2
-2
Deposit Mass/Area,  (kg m )
0.0
(b)
Th =WAT+7
0.6
0.4
0.2
Tc=WAT-10, Re=8900
Tc=WAT-20, Re=9300
0.0
(c)
Th =WAT+7
0.6
Tc=WAT-10
0.4
0.2
Re=8900
Re=13400
Re=17900
0.0
0
5
10
15
20
25
30
Water Content of Waxy Mixture (vol%)
Figure 5.11 Variation in the deposit mass at different water contents; (a) Effect of
waxy mixture temperature, Th, (b) Effect of coolant temperature, Tc, and (c) Effect of
Reynolds number, Re.
143
5.7.2 Effect of Wax Mixture Water Content on Deposit Water Content
Figure 5.12 shows a scatter plot of the variation of the measured water content in the
deposit with the water concentration in the waxy mixture. The water content in the deposit is
observed to be consistently lower than that in the waxy mixture; however, a trend or correlation
between the two quantities is not observed. That is, there does not appear to be a relationship
between the water content in the deposit and the water concentration in the waxy mixture. As
shown in Figure 5.12, the water content of several deposit samples was measured to be close to 0
vol%. It is, therefore, likely that the measured water content of the deposit may not be related to
the deposition process but it might represent “wetness” of the deposit surface.
144
Water Content of Deposit (vol%)
30
25
20
15
10
5
0
0
10
20
30
Water Content of Waxy Mixture (vol%)
Figure 5.12
mixture
Comparison of the water content of deposit to the water content of the wax
145
5.7.3 Effect of Reynolds Number on Deposit Water Content
The scatter plot in Figure 5.13 shows the variation of the measured deposit water content
with Re, where no trend is observed between these two quantities. Since the deposit mass is
known to decrease with an increase in Re, the results in Figure 5.13 offer further confirmation
that the measured water content of the deposit may not be related to the deposition process.
146
Water Content of Deposit (vol%)
30
25
20
15
10
5
0
5000
10000
15000
20000
25000
Re
Figure 5.13
Variation of the water content of the deposits with Reynolds Number, Re.
147
5.7.4 Effect of Reynolds Number on Deposit Mass per unit Area
Figure 5.14 shows a scatter plot for the variation of Ω with Re for all deposition
experiments at Th = (WAT+7 ºC) and Tc = (WAT–10 ºC). The results indicate the deposit mass
decreases with an increase in Re; a similar trend has been reported previously from single-phase
deposition experiments under both laminar (Singh, P. et al; 2000; Bidmus and Mehrotra, 2004;
Parthasarathi and Mehrotra, 2005; Bidmus and Mehrotra, 2009) and turbulent flow conditions
(Fong and Mehrotra, 2007; Tiwary and Mehrotra, 2009).
148
Deposit Mass/Area,  (kg m-2 )
0.5
0.4
0.3
0.2
0.1
0.0
5000
10000
15000
20000
25000
Re
Figure 5.14 Variation of water-free deposit mass per unit area, Ω, with Reynolds number, Re,
for all deposition experiments at Th = (WAT+7 ºC) and Tc = (WAT–10 ºC).
149
5.8 Homogeneity and Stability of Wax–Solvent–Water Mixtures in the Flow Loop
For the two-phase transient emulsions, it was considered important to provide sufficient
agitation to ensure the homogeneity of the mixture throughout the apparatus. For the experiments
with two-phase waxy mixtures, samples of the waxy mixture were taken using the sample valve
located at the end of flow loop just before the mixture exited into the reservoir. The samples of
waxy mixture flowing through the deposition tube and held in the reservoir were centrifuged to
measure their water contents. The water contents of the two samples were compared to confirm
that the water fraction in the waxy mixture flowing through the flow loop was the same as that in
the reservoir. Figure 5.15 presents a comparison of the water content in the waxy mixture
flowing in the flow loop versus the water content of the waxy mixture held in the reservoir. For
all experiments performed, the absolute average deviation between the water contents of the two
sets of samples is 3.8%.
Another set of batch experiments was conducted to study the stability of the oil–water
waxy mixtures by observing phase separation in the suspension, under gravity, with time. These
experiments indicated that the time required for a significant extent of phase separation was in
the order of minutes and much more than about 1-2 s residence time in the flow loop.
150
35
 f (vol%)
Th=WAT+7,
Th=WAT+7,
Tc=WAT-10, Re=8900
Tc=WAT-10, Re=13400
30
Th=WAT+7, Tc=WAT-10, Re=17900
Th=WAT+7, Tc=WAT-20, Re=9300
Th=WAT+15, Tc=WAT-10, Re=16200
25
Th=WAT+15, Tc=WAT-20, Re=16600
20
15
10
5
0
0
5
10
15
20
25
30
35
 r(vol%)
Figure 5.15 Comparison of the water content of the waxy mixture in the reservoir with the
water content of the waxy mixture flowing in the flow-loop.
151
Chapter Six: Results of Two-Phase Cold Finger Wax Deposition Experiments
In this chapter, results are presented from the single-phase and two-phase wax deposition
experiments using the cold finger apparatus. The experimental program investigated the effects
of deposition time, stirring speed (shear rate), and water content on two-phase wax deposition
using an experimental apparatus that is different from the flow loop apparatus. Similar to the
flow loop experiments, all experiments were performed with the wax mixture temperature held
above the corresponding WAT (i.e., under the „hot flow‟ conditions) such that the liquid phase
did not contain any solid phase as wax crystals.
The experimental results are evaluated with a steady-state heat-transfer model, similar to
that presented in Chapter 5. In Chapter 7, the time-dependent deposition results will be compared
with the predictions from a transient, or unsteady-state, heat-transfer model, which is based on
the moving boundary problem formulation.
6.1 Steady-State Heat Transfer Model
In the steady-state heat-transfer model developed to simulate the cold finger experiments,
the „hot‟ waxy mixture (comprising wax, solvent and water) is considered to be held in a large
vessel or reservoir, whose temperature was maintained constant and higher than its WAT (i.e., Th
> WAT). This was achieved by placing the reservoir in a water bath set at the desired
temperature. The wax mixture was stirred continuously throughout the deposition experiment.
The cold finger assembly (described previously in Chapter 3, Section 3.8.1) was inserted in the
wax mixture. Cold water at a constant temperature, below the WAT (i.e., Tc < WAT) of the wax
mixture, was allowed to flow through the cold finger at a constant flow rate at all times. Heat
transfer from the wax mixture to the coolant resulted in a radial temperature gradient, which
152
caused the formation of a deposit-layer on the outside of the copper cold finger, provided the
cold finger wall temperature, Tw, was less than the WAT. The rate of heat transfer decreased
because of the additional thermal resistance offered by the deposit-layer. The deposit-layer
continued to grow in thickness until a thermal steady-state was attained, when all thermal
resistances became constant. At the thermal steady-state, the rate of heat transfer across the wax
mixture, the deposit layer and the tube wall would be equal to the rate of heat gained by the
coolant.
Similar to the steady-state heat-transfer model used for the flow loop apparatus, described
in Chapter 5, the steady-state rate of heat transfer for the cold finger apparatus is equal to the rate
of thermal energy accepted by the coolant, as follows:
q  m c C c (Tco  Tci )  U i Ai Th  Tc 
6.1
where m c is the mass flow rate of the coolant streams, Cc is the average specific heat capacity of
the coolant stream, Tci and Tco are the inlet and outlet temperatures of the coolant respectively, Ui
is the inside overall heat-transfer coefficient, Ai is the inside pipe surface area, and Th and Tc are
the average temperatures of the wax mixture and coolant, respectively. The combined thermal
resistance can be expressed as a sum of four individual thermal resistances in series, i.e.
ln(( ro  xd )/ro ) ln( ro /ri )
1
1
1




= Rh + Rd + Rm + Rc
U i Ai 2 (ro  xd ) Lh h
2πk d L
2πk m L 2ro Lh c
6.2
where, Rh = [2π(ri–xd)Lhh]–1, Rd = [(2πLkd)/ln{ri/(ri–xd)}]–1, Rm = [(2πLkm)/ln{ro/ri}]–1 and Rc =
[2πroLhc]–1. Next, the following equalities are obtained by equating the heat flux through each of
the four thermal resistances included in UiAi:
k d (Td  Two )
k (T  Twi ) hc (Twi  Tc )
q hh (Th  Td )


 m wo

Ai
ri /(ro  xd ) ri ln(( ro  xd )/ ro )
ri ln( ro /ri )
ri /ro
153
6.3
where hh and hc are the average individual convective heat-transfer coefficients for the wax
mixture and coolant streams respectively, xd is the average deposit-layer thickness, kd and km are
the average thermal conductivities of the deposit and pipe-wall respectively, and Td is the
average liquid–deposit interface temperature.
With a relatively high flow rate of the coolant through a small cross-sectional area in the
cold finger, its convective heat transfer coefficient would be large and this convective resistance
can be neglected. Since the cold finger wall was made of copper, with a high thermal
conductivity and small wall thickness (~ 0.9 mm), its thermal resistance can be neglected. With
these two simplifying assumptions, the temperature of the cold water flowing inside the cold
finger (Tc) would be equal to the temperatures at the inner and outer walls of the cold finger,
such that Tc = Twi = Two = Tw, where Tw denotes the average wall temperature of the cold finger.
Similarly, with a relatively small thickness of the copper tube wall, the inner tube radius is
assumed to be equal to the outer radius, such that ri = ro = rw.
With the above simplifications, the combined thermal resistance in equation 6.2 can
therefore be expressed as a sum of only two individual thermal resistances in series, i.e.
ln(( rw  xd )/ rw )
1
1


UAw 2 (rw  xd ) Lh h
2πk d L
= Rh + Rd
6.4
where, Rh = [2π(rw+xd)Lhh]–1 and Rd = [(2πLkd)/ln{rw+xd/(rw)}]–1. Next, the following equalities
are obtained by equating the heat flux through the two thermal resistances included in UAw:
h (T  Td )
k d (Td  Tc )
q
 h h

Aw rw /(rw  xd ) rw ln((rw  xd )/rw d )
6.5
Note that the two unknowns in equation 6.5 are xd and kd, which can be estimated by solving the
two equalities using experimental measurements.
154
From the experimental data, the average difference in coolant temperature between the
inlet and the outlet was typically of the order of 0.1–0.2 oC, which is of the same order of
magnitude as the error associated with the thermocouple measurements. It was thus not possible
to estimate q in equation 6.5 with a reasonable degree of accuracy, which resulted in only one
equality in equation 6.5. Previous laboratory studies (Bidmus and Mehrotra, 2004; Parthasarathi
and Mehrotra, 2005; Fong and Mehrotra, 2007; Tiwary and Mehrotra, 2009) as well as the
results in Chapter 5 have shown conclusively that the liquid–deposit interface temperature, Td, is
equal to the WAT. For the steady-state calculations, therefore, Td in equation 6.5 was taken to be
equal to the WAT of the mixture, leaving kd as the only unknown. Using the experimental data
for Aw, Th, Tc, hh, rw, and xd, the equality in equation 6.5 was solved to obtain kd. As explained
previously in Chapter 5, xd, kd and Td were assumed to be constant over the entire deposition
surface. It is important to note that, for the estimation of kd using equation 6.5, the steady-state
model was applied only to experimental data from the 12-h and 24-h experiments, where a
thermal steady-state had already been achieved.
The dimensionless ratio, d, for the cold finger set up is the ratio of the deposit layer
thermal resistance to the combined or total thermal resistance under thermal steady state
conditions. In this case, it is given by the ratio of the temperature drop across the deposit layer to
the overall temperature difference as follows:
d 
Rd
T  Tc
 d
Rh  Rd Th  Tc
6.6
where, similar to the flow loop steady-state analysis, Rh and Rd are the thermal resistances
corresponding to the wax mixture and the deposit layer, respectively, and are defined in equation
6.4 A similar h ratio can be obtained for the convective thermal resistance as:
155
h 
T  Td
Rh
 h
Rh  Rd Th  Tc
6.7
Heat transfer calculations were performed within the range of experimental conditions
used in this study, to predict the effect of the deposit layer thickness on hand d for the onephase and two-phase cold finger deposition process. Figure 6.1 presents a set of predicted results
from the calculations showing the effect of the deposit layer thickness (relative to the cold finger
outer radius), xd/rw, on hand d for the single-phase deposition process. At a stirring rate of 500
rpm, it can be observed that, for a small deposit thickness, the convective thermal resistance due
to the wax-solvent mixture (h) is the predominant resistance. However, as the deposit layer
thickness increases, h decreases while d increases sharply until the deposit layer begins to offer
the dominant thermal resistance when xd exceeds about 4% of rw. As shown in Figure 6.1, the
largest temperature gradient at this point would occur across the deposit layer.
When a lower stirring rate of 250 rpm was used, corresponding to a lower heat transfer
co-efficient in the wax mixture, similar trends are observed, but the deposit layer begins to offer
the dominant thermal resistance when xd exceeds about 6% of rw.
156
Predicted fractional thermal resistance, 
1.0
500 rpm
250 rpm
0.8
d
0.6
0.4
h
0.2
0.0
0.0
0.1
0.2
0.3
0.4
0.5
Deposit thickness, xd/rw
Figure 6.1
Predicted effects of deposit-layer thickness on fractional thermal resistances (0%
water content).
157
6.2 Estimation of Heat Transfer Coefficient, hh
To solve equation 6.5, an estimate of the convective heat transfer coefficient for the waxy
mixture, hh, was required. This was obtained by performing a series of non-depositing calibration
experiments, in which both the wax mixture and the coolant were held at temperatures above the
WAT of the wax mixture. These calibration experiments were performed using the same coolant
flow rate of 0.0303 L/s that was used in the actual deposition experiments. With the thermal
resistances of the coolant water and copper pipe-wall assumed to be negligible, and without any
deposit layer, the heat transfer coefficient of the wax mixture became equal to the overall heat
transfer coefficient as follows:
U ≈ hh = q/[Aw*(Th - Tc)]
6.8
The calibration experiments were carried out for wax mixtures containing 0% water only.
Using equation 6.8, the experimental U was obtained from the calibration experiments to be
610±200 W m–2 K–1 at the 250-rpm stirring rate and 980±205 W m–2 K–1 at the 500-rpm stirring
rate. The relatively high average deviations are attributed to the error margin in the temperature
measurements relative to the difference between the inlet and outlet coolant water temperatures.
6.3 Density of Deposit Samples
The deposit density was required for estimating the average deposit-layer thickness, xd,
and for relating the deposit density to the deposition time. The deposit samples used in these
measurements were from experiments performed with wax mixtures containing no water. A
pycnometer was used to measure the deposit density. The deposit density data were fitted using a
natural logarithm regression and the correlation relating deposit density to deposition time is
shown in equation 6.9.
158
d = e1lnt + e2
6.9
where t denotes the deposition time in hour. Regression constants e1 and e2 in equation 6.9 are
shown in Table 6.1.
The extent of deposition was expressed as the mass of deposit per unit deposition surface
area, , and it is related to the deposit layer thickness, xd, and the deposit density, d, as follows:
Ω = d/[2r (xd2 +2rxd)]
6.10
Equation 6.10, along with the experimental deposit density and deposit mass per unit area, was
used to estimate the average deposit thickness, xd.
159
Table 6.1
Density regression constants for equation 6.9.
Stirring rate,
constants in the density correlation, Eq 6.9
rpm
e1
e2
250
4.85  0.37
756.3  0.7
500
13.38  1.03
761.9  2.0
160
6.4 Estimation of Deposit Thermal Conductivity (kd)
Since there was no increase in the deposit mass after 12 h of deposition time, the results
of the 12 h and 24 h experiments were analyzed with equation 6.5 to predict the average deposit
thermal conductivity, kd. As mentioned previously, with q in equation 6.5 being subject to a
significant error, Td was assumed to be equal to WAT and the heat-flux equality in equation 6.5
was solved to obtain kd. From the steady-state data of each experimental run for the 12 h and 24
h runs, and with Td being equal to WAT, the second term in equation 6.5 could be estimated
easily, which was in turn used to estimate the average thermal conductivity of the deposit, kd.
Using the steady state heat transfer calculations for all 12 h and 24 h deposition
experiments, the overall average deposit thermal conductivity, kd, was calculated to be 0.18±0.02
W m–1 K–1. As shown in Table 6.2, unlike the average thermal conductivity estimated for the
flow loop experiments, which was comparable to those reported for single-phase flow loop
experiments in the turbulent flow regime, the overall average thermal conductivity estimated for
the cold finger experiments is comparable to values reported for single-phase flow loop
experiments in the laminar flow regime. Table 6.2 also shows that the average thermal
conductivity for single-phase experiments performed with at a stirring rate of 250 rpm is 0.15 W
m–1 K–1, while the average value for experiments performed with a stirring rate of 500 rpm is
0.19 W m–1 K–1. Furthermore, it is observed from Table 6.2 that the average estimated thermal
conductivity of deposits from the two-phase experiments performed with wax mixtures
containing water (0.20 W m–1 K–1) is higher than that of deposits from single-phase experiments
(0.17 W m–1 K–1). This may be due to the presence of water droplets attached to the deposits
from the two-phase experiments.
161
Table 6.2
Average estimated deposit thermal conductivities for deposits from 12 h
and 24 h experiments.
deposition
time
stirring speed
water content
deposit thermal
conductivity, kd
h
rpm
% vol water
W m-1 K-1
CF8
12
250
0
0.16
CF9
24
250
0
0.15
CF17
12
500
0
0.20
CF18
24
500
0
0.18
CF23
24
500
10
0.21
CF27
12
500
20
0.18
CF28
24
500
20
0.20
CF33
24
500
30
0.19
run no.
162
6.5 Effect of Deposit-layer Thickness (xd) on the Rate of Heat Transfer (q)
Calculations were performed with the above heat-transfer model to explore the effects of
deposit-layer thickness (xd) on the rate of heat transfer (q). As shown in Figure 6.2, it was found
that, at typical experimental conditions used in this study, q decreased sharply with an increase in
xd. For example, for an average deposit layer thickness of 0.3 mm (or xd/rw = 0.063), q was
predicted to decrease by 60%.
163
1.0
0.8
q/qo
0.6
0.4
0.2
0.0
0.0
0.1
0.2
0.3
0.4
0.5
xd/rw
Figure 6.2
Predicted effect of deposit-layer thickness (xd) on the rate of heat transfer, q, for
Th = (WAT+3) oC, (Tc = WAT–15) oC, and hh = 980 W m-1 K-1.
164
6.6 Effect of Process Conditions on Cold Finger Wax Deposition
The results for the mass of the deposit-layer from all experiments performed with wax
mixtures of different water contents, and at different stirring rates and deposition times are
presented and discussed in the following sub-sections. Selected results from 5 min, 12 h and 24
h experiments are shown in Table 6.3.
The deposit mass per unit deposition area is denoted by Ω (in kg m–2). For the deposition
experiments performed in this study, xd varied from about 0.5 mm (Ω  0.37 kg m–2) to about 1.1
mm (Ω  0.97 kg m–2). Thus, for the 0.95-cm outer diameter deposition tube, the relative deposit
thickness, xd/rw, varied from about 0.100 to 0.238.
165
Table 6.3
Deposit mass per unit area, Ω, for 5 min, 12 h and 24 h experiments.
deposition
time
stirring speed
wax mixture
water content
deposit water
content
deposit mass per
unit area, Ω
h
rpm
% vol water
% vol water
kg m-2
CF1
0.1
250
0
0
0.637
CF1R
0.1
250
0
0
0.584
CF8
12.0
250
0
0
0.973
CF9
24.0
250
0
0
0.933
CF10
0.1
500
0
0
0.395
CF10R
0.1
500
0
0
0.391
CF17
12.0
500
0
0
0.779
CF18
24.0
500
0
0
0.733
CF19
0.1
500
10
7.8
0.378
CF19R
0.1
500
10
1.8
0.412
CF23
24.0
500
10
0.5
0.859
CF27
12.0
500
20
9.5
0.751
CF28
24.0
500
20
1.3
0.812
CF29
0.1
500
30
24.1
0.366
CF33
24.0
500
30
1.0
0.773
run no.
R indicates repeat experiments
166
6.6.1 Effect of Water Content on Deposit Mass
For the hot and cold stream temperatures of (WAT+3) and (WAT–15), respectively, Ω
increased with water content for up to 4 h, then decreased for up 12 h and then increased after 12
h. However, the increase or decrease in Ω with water content was not found to depend on the
water content of the waxy mixture. Figure 6.3 is a plot of the ratio (Ω/Ωo), which relates the
deposit masses obtained from wax mixtures with water and without water at different times. It
shows that increasing the water content in the wax mixture increases Ω/Ωo up to 4 h and after 8 h
for wax mixtures containing 10 and 30 vol% water content. For wax mixtures having 20 vol%
water content, Ω/Ωo decreased initially up to 2 h, increased up to 4 h, decreased up to 12 h, and
then increased up to 24 h.
167
1.4

1.2
1.0
0.8
10 vol% water
20 vol% water
30 vol% water
0.6
0
5
10
15
20
25
Time (h)
Figure 6.3
Effect of the water content in the wax mixtures on the deposit mass
per unit area, Ω, at different deposition times.
168
6.6.2 Effect of Deposition Time on Deposit Mass
Deposition experiments were carried out at nine different deposition times (5 min, 10
min, 30 min, 1 h, 2 h, 4 h, 8 h, 12 h and 24 h). For the single-phase cold finger wax deposition
experiments, the effect of time is shown in Figure 6.4(a). For the single-phase experiments, it is
observed from Figure 6.4(a) that the deposit mass per unit area stopped increasing after
approximately 12 h. This observation applies to both sets of experiments performed at 250 rpm
stirring and 500 rpm stirring rate. It was observed that the deposit samples from the shorterduration experiments were softer (and less dense). On the other hand, the deposits from the
longer-duration experiments were harder (and more dense). This is attributed to a higher fraction
of solid wax in the longer-duration deposits as a result of aging effects, where with time, the
lower carbon number wax components are "squeezed" out of the deposit, leaving a higher
fraction of higher carbon number wax components, as explained by Mehrotra and Bhat (2007),
Bhat and Mehrotra (2008), and Tiwary and Mehrotra (2009).
Figure 6.4(b) shows the effect of time on the deposit mass per unit area for the two-phase
experiments. It is observed that, unlike the results of the single-phase experiments, the deposit
mass per unit for the wax mixture containing 20 vol% water increases slightly after 12 h. The 12­
h experiment was not conducted for the two-phase wax mixture containing 10 vol% water.
6.6.3 Effect of Stirring Rate on Deposit Mass
To investigate the effects of stirring rate on wax deposition, experiments were performed
at two different stirring speeds of 250 rpm and 500 rpm. The effect of stirring rate is also shown
in Figure 6.4(a), where deposits from experiments performed at a stirring rate of 250 rpm have a
higher deposit mass per unit area than the corresponding deposits from experiments performed at
a stirring rate of 500 rpm. This is expected because of the higher heat transfer coefficient of the
169
wax mixture, hh, (and a corresponding decrease in the convective thermal resistance, Rh) at the
higher stirring rate. For the same Th and Tc, a lower Rh implies that the deposit thermal
resistance, Rd, would also decrease, which implies a decrease in the deposit-layer thickness, xd,
and consequently a lower deposit mass or Ω.
170
1.2
(a)
1.0
-2
deposit mass per unit area, (kg m )
0.8
0.6
0.4
250 rpm
500 rpm
0.2
0.0
1.2
(b)
1.0
0.8
0.6
0.4
500 rpm, 0 vol% water
500 rpm, 10 vol% water
500 rpm, 20 vol% water
500 rpm, 30 vol% water
0.2
0.0
0
5
10
15
20
25
Time (h)
Figure 6.4
Variation of deposit mass per unit area, Ω with deposition time, t. (a)
single phase mixtures at stirring rates of 250 and 500 rpm; (b) two-phase mixtures at a
constant stirring rate of 500 rpm.
171
6.6.4 Effect of Wax Mixture Water-Content on Deposit Water-Content
Figure 6.5 shows a scatter plot for the variation of the measured water content in the
deposit with the water concentration in the wax mixture for different deposition times. Similar to
the results of the two-phase flow loop experiments (in Section 5.7.2), the water content in the
deposit is observed to be consistently lower than that in the wax mixture; however, a trend or
correlation between the two quantities is not observed. That is, there does not appear to be a
relationship between the water-content in the deposit and the water-content in the wax mixture.
Again, as shown in Figure 6.5, the water content of several deposit samples was measured to be
close to 0 vol%, which supports the postulation from the flow loop experiments that the
measured water content of the deposit is not related to the deposition process but it might
represent a random “wetness” of the deposit surface or physical attachment of water droplets to
the deposit surface or entrapment of water droplets with the deposit matrix.
172
30
0.1 h
0.2 h
0.5 h
1.0 h
2.0 h
4.0 h
8.0 h
12.0 h
24.0 h
water content of deposit (vol%)
25
20
15
10
5
0
0
10
20
30
water content of waxy mixture (vol%)
Figure 6.5
Comparison of the water content of deposit to the water content of the wax
mixture for different deposition times.
173
6.6.5 Effect of Time on Deposit Water-Content
The scatter plot in Figure 6.6 shows the variation of the measured deposit water content
with time for different water content of the wax mixture. Again, no apparent trend is observed
between these two quantities. It is also observed that deposits from the 24 h experiments have
consistently low water content for all three wax mixture water content of 10, 20 and 30 vol%.
Again, since the deposit mass is known to increase with time (up to 12 h), the results in
Figure 3.15 offers further confirmation that the measured water content of the deposit
may not be related to the deposition process.
174
30
10% water
20% water
30% water
water content of deposit (vol%)
25
20
15
10
5
0
0
5
10
15
20
25
water content of waxy mixture (vol%)
Figure 6.6
Variation of the water content of the deposits with time, for different wax mixture
water content.
175
6.7 Short-Duration Experiments
Apart from the objective of using a different experimental apparatus, with a different
geometrical arrangement, to study the wax deposition process, the most important reason that the
cold finger apparatus was used in addition to the flow loop experimental apparatus was to be able
to investigate the rate of the deposition process by performing experiments over different
deposition times. Two very short duration wax deposition cold finger experiments were
performed with very short deposition times of 30 s and 2 min. Table 6.4 presents the results of
these short-duration experiments. It was observed that more than half of the deposit was actually
formed within a deposition time of 30 s, and almost two-thirds of the deposition process was
completed within the first 2 min! Assuming that it takes 12 h to reach steady-state, 56% of the
deposition process was completed in 0.07% of the time for the deposit to stop growing, while
62% of the deposition process was completed in 0.28% of the time.
The results in Table 6.4 further confirm that the wax deposition is a very fast process. It
is well known that, when exposing a system to a change in thermal and compositional state
conditions (i.e., a system under unsteady-state), the thermal equilibrium is accomplished much
faster than the diffusional equilibrium. The experimental evidence of a relative fast deposition
process further supports the wax deposition process to be primarily thermally-driven. In some
ways, we believe that it is similar to the solidification or freezing processes encountered in the
metallurgical industry, which have been modelled successfully as thermally-driven liquid-to­
solid phase transformation processes (Bhat and Mehrotra, 2005, 2006; Mehrotra and Bhat, 2010;
Arumugam et al. 2012, 2013).
176
Table 6.4
Deposit mass per unit area for short-duration experiments of 30 s and 2 min, in comparison to the deposit mass per unit area at 12 h.
Deposition Time
Deposit mass per unit
area, 
min
kg m-2
0.5
0.546
56
2.0
0.608
62
720.0
0.973
100
177
% of 12-h deposit mass
per unit area
6.8 Homogeneity of Wax–Solvent–Water Mixtures During Cold Finger Experiments
Just as it was considered important to provide sufficient agitation to ensure the
homogeneity of the mixture throughout the apparatus during flow loop experiments, it was also
desirable to have a well-mixed transient emulsion in the wax reservoir during the cold finger
experiments. For the experiments with two-phase wax mixtures, samples of the wax mixture
were taken using a syringe at depths of the deposition surface during the cold finger experiments.
These samples of were centrifuged and their water content was measured. The water content of
the samples were compared to that of the reservoir wax mixtures to ensure that the wax mixture
in the reservoir was well mixed and that cold finger deposition surface was actually exposed to a
homogeneous and desired composition.
Figure 6.7 presents a comparison of the water content in the reservoir wax mixture versus
the water content of the samples taken. For all experiments performed, the absolute average
deviation between the water contents of the two sets of samples is 3.4%.
178
water fraction during cold finger experiments (vol%)
30
20
10
0
0
10
20
30
reservoir water content of waxy mixture (vol%)
Figure 6.7
Comparison of the water content of the waxy mixture in the reservoir with the
water content of samples taken.
179
6.9 Aging of Deposit Samples
"Deposit aging" has been used to describe the change in deposit composition with time.
To investigate the effect of time, through aging of deposit samples from the cold finger
experiments, two methods were used; microscopy and GC analysis. Samples from the 5 min and
12 h experiments performed with water-free wax mixtures at both 250 and 500 rpm stirring
speeds were selected for analysis. The equipment and procedures employed have been described
previously in Chapter 3. The results of the both methods are discussed in the following sub­
sections.
6.9.1 Deposit Sample Microscopy
Visual microscopy sample analysis using the equipment previously described was done at
20X magnification. Figure 6.8 and Figure 6.9 show microscopy pictures from samples of 5 min
and 12 h cold finger deposition experiments performed at a stirring rate of 500 rpm. Figure 6.10
and Figure 6.11 show microscopy pictures from samples of 5 min and 12 h cold finger
deposition experiments performed with at a stirring rate of 250 rpm. It is observed that, at both
stirring rates, pictures of samples from 5 min experiments show a much lower wax crystal
density, indicating a lower fraction of solid wax crystals, than those from the 12 h experiments.
Figure 6.9 and Figure 6.11 also show a higher wax crystal density for the sample from the 250
rpm stirring rate experiment than that of the sample from the 500 rpm stirring rate experiment.
Fong and Mehrotra (2007) reported that, for extended single-phase flow loop experiments
performed in the turbulent flow region for up to 8 h, deposit aging was evident in the results at a
lower Re of 11400, but that there was a relatively lower extent of deposit aging at a higher Re of
27600. It was further reported that for extended experiments (8 h), unlike 1-h duration
180
experiments, the effects of deposit aging diminish as the Reynolds number is increased. A
similar trend is observed here, where an increase in the stirring rate for the cold finger apparatus
can be compared to an increase in Re in the flow loop apparatus. Thus the observed higher wax
crystal density for the 250 rpm stirring rate experiment when compared to that from the 500 rpm
stirring rate experiment demonstrates an increased extent of deposit aging in the deposit from the
250 rpm stirring rate experiment.
181
Figure 6.8
rate.
Microscopy pictures of deposit sample from 5 min experiment at 500 rpm stirring
182
Figure 6.9
rate.
Microscopy pictures of deposit sample from 12 h experiment at 500 rpm stirring
183
Figure 6.10 Microscopy pictures of deposit sample from 5 min experiment at 250 rpm stirring
rate. Scale is the same as that of Figure 6.8
184
Figure 6.11 Microscopy pictures of deposit sample from 12 h experiment at 250 rpm stirring
rate. Scale is the same as that of Figure 6.8
185
6.9.2 Deposit Sample GC Analysis
The same deposit samples that were used for microscopy were also used for the GC
analysis. In addition to the GC analysis of the deposit samples from the 5 min and 12 h
experiments, GC analysis was also done for the 10 mass% wax mixture used for the cold finger
experiments. The results of the compositional analysis for the samples from the experiments
performed at 500 rpm and 250 rpm are shown in Figure 6.12 and Figure 6.13, respectively.
Figure 6.12 and Figure 6.13 show that for both the 500 and 250 rpm experiment deposit samples,
the composition of the deposit sample from the 5 min experiment was almost the same as that of
the 10 mass% wax mixture. However, the composition of the deposit sample from the 12 h
experiment was very different, having a lower solvent fraction and a much higher wax fraction,
indicative of a decrease in the solvent fraction and an increase in the wax fraction from 5 min to
12 h. However, the deposit sample from the experiment performed at 250 rpm is seen to have
more solid wax fraction than the deposit sample form the experiment performed at 500 rpm. This
confirms observations from the microscopy analyses.
186
60
5
500 rpm
waxy mixture
5 min deposit
12 h deposit
50
40
3
30
2
20
wax composition (mass%)
solvent composition (mass%)
4
1
10
0
10
20
30
40
0
50
carbon number
Figure 6.12 GC analyses of 10 mass% wax mixture and deposit samples from 5
min experiment and 12 h experiments at 500 rpm stirring rate.
187
60
5
250 rpm
waxy mixture
5 min deposit
12 h deposit
50
40
3
30
2
20
wax composition (mass%)
solvent composition (mass%)
4
1
10
0
10
20
30
40
0
50
carbon number
Figure 6.13 GC analyses of 10 mass% wax mixture and deposit samples from 5
min experiment and 12 h experiments at 250 rpm stirring rate.
188
Chapter Seven: Predictions from Transient Heat-Transfer Model
Bhat and Mehrotra (2005) presented a mathematical model for solids deposition from
“waxy” mixtures under static conditions. The model utilized the moving boundary problem
formulation and was used to describe the growth of the deposit layer from a binary eutectic
mixture in a circular pipe, with time, under non-flowing or static conditions. Their model
considered heat transfer in the liquid phase to be by conduction and ignored any convection
effects in the liquid region. Predictions from the model of Bhat and Mehrotra (2005) showed a
temperature profile in the liquid region with the liquid temperature decreasing from the pipe
center to the liquid-deposit interface temperatures, held at the WAT of the liquid mixture, within
a few minutes. However, cooling experimental results from Bidmus and Mehrotra (2008a,
2008b) showed that the temperature throughout the liquid phase remained uniform while the
liquid cooled from an initial temperature above the WAT, until reaching the WAT of the liquid
phase. That is, there was no radial temperature gradient during the deposition process, until the
bulk liquid temperature had decreased to WAT of the liquid. Bidmus (2008) and Mehrotra et al.
(2012) modified the model of Bhat and Mehrotra (2005) by using an effective liquid thermal
conductivity of the liquid much higher than that used by Bhat and Mehrotra (2005), to account
for the convective effects in the liquid region, resulting in model predictions that gave a
reasonable match with the experimental liquid-region temperature profiles.
The moving boundary formulation was also used to predict the extent of wax deposition
under laminar flow conditions (Bhat and Mehrotra, 2005, Bhat and Mehrotra, 2006) and
turbulent flow conditions (Mehrotra and Bhat, 2010). More recently, the moving boundary
problem formulation was used by Arumugam et al. (2013) to successfully model the deposition
of solids in a cylindrical pipeline under both "hot flow" conditions and "cold flow" conditions of
189
a "waxy" mixture flowing in the turbulent flow regime. In their model, Arumugam et al. (2013)
also considered heat transfer in the liquid region during "hot flow" (with no solid wax particles
present) to be governed by convection, instead of conduction.
The heat-transfer based model developed by the researchers mentioned previously has
been modified and used to predict the deposition of wax on the outside of the cold finger used in
this study. For the cold finger wax deposition experiments, the results presented in Chapter 6
showed that the deposit mass per unit area continued to increase till about 12 h. A transient heat
transfer model was therefore required to model the growth of the deposit thickness with time.
The calculations were performed with a pseudo-binary mixture, comprising n-C14H30 (denoted
by C14) and n-C30H62 (denoted by C30), to represent the lighter and the heavier fractions of the
wax mixture, respectively.
The model predictions are presented for the effects of deposition time and heat transfer
coefficient. The trends in the model predictions are compared with the experimental results of
the single-phase cold finger experiments performed at both 250 and 500 rpm stirring rates, and
the two-phase cold finger experiments performed at 500 rpm.
7.1 Moving Boundary Problem Formulation
As mentioned previously, the transient heat transfer model is based on the moving
boundary problem formulation. The moving boundary problem approach deals with problems
involving transient heat transfer during phase transformations, such as in melting and
solidification processes. Numerous applications of the moving boundary formulation have been
reported, especially in studies related to metallurgical systems that involve melting and
solidification of metals and alloys. These processes are typically characterized by the presence of
a solid–liquid interface where the liquid-solid phase transformation occurs. The location of the
190
interface changes with heat transfer during phase transformation; however, the interface location
is not known a priori, which makes the numerical solution procedure challenging. The phase
transformation associated with the solidification of the liquid layer adjacent to the deposit layer
has been assumed to be an equilibrium process controlled primarily by the rate of heat transfer.
Furthermore, the small difference in the densities of the liquid and solid phases can be neglected
in the moving boundary approach; however, this density difference typically causes a small
movement of the liquid during solidification at the interface (Boley, 1978). In order to simplify
the calculations, the model developed by Bhat and Mehrotra (2005) assumes that the densities of
the liquid and solid to be the same.
7.2 Model Development for Transient (Unsteady-State) Wax Deposition
In the development of the unsteady state heat transfer mathematical model, as is done in
the moving boundary problems, any mass transfer resistance, due to molecular diffusion within
the deposit or convective diffusion across the liquid–deposit interface, was not taken into
consideration. It was also assumed that the liquid–deposit interface is hydrodynamically smooth
and the liquid-to-solid phase transformation is instantaneous and governed only by
thermodynamic considerations.
7.2.1 Energy Balance Equations and Heat Transfer Considerations
In the one-dimensional problem considered by Bhat and Mehrotra (2005), a liquid
mixture at an initial temperature Th, (> WAT) was held statically inside a circular pipe of radius,
R. Following the lowering of the pipe-wall temperature to Tw < WAT (or Td), deposition was
commenced due to an outward radial heat transfer. The deposition occurred as a result of the
liquid temperature adjacent to the pipe wall decreasing below the WAT (or Td). With the liquid­
191
deposit interface assumed to be at Td, at all times during the deposition process, continued solids
deposition would increase the deposit-layer thickness. The liquid–deposit interface would divide
the pipe cross-section into regions, with 0 < r < s as the domain of the liquid region and s < r < R
as the domain of the deposit region.
The relationship for unsteady-state heat transfer by conduction in the liquid region was
expressed as:
1   Tl  1 Tl
,
r

r r  r   l t
0r s
7.1
where s is the radial location of the liquid–deposit interface and αl is the liquid region thermal
diffusivity. Note that any natural convection effects in the liquid region were ignored in the
model by Bhat and Mehrotra (2005). The actual temperature for liquid-to-solid phase
transformation of waxy mixtures was observed to be lower than the thermodynamic liquidus
temperature, which was attributed to the supercooling effects involved during crystallization
(Bhat and Mehrotra, 2004). It was assumed that the temperature at the liquid–deposit interface
(Td) is equal to the WAT, which is lower than the liquidus temperature, TL (Bidmus and
Mehrotra, 2004; Parthasarathi and Mehrotra, 2005). The two-phase deposit region would consist
of a solid phase mass fraction (f ) and a liquid-phase mass fraction, (1 - f), with f as a function of
temperature and mixture composition, which was estimated from the equilibrium calculations.
The unsteady state heat transfer relationship for the deposit layer was obtained by
combining the conduction and energy balance terms as follows (Bhat and Mehrotra, 2005):
1   Tδ
r
r r  r
 1 Tδ

   t
ρλ df
,
k  dt
s rR
192
7.2
In equation 7.2, the term ρλ(df/dt) accounts for the heat released in the liquid–solid two-phase
region due to the increased solid-phase fraction in the deposit-layer. Equation 7.2 was re-written
in the following form (Bhat and Mehrotra, 2005):
1   Tδ
r
r r  r
 1 Tδ
, s rR

   t
7.3
where   represents a modified thermal diffusivity value for the deposit-layer, as follows:
1
1  f


   k  Tδ
7.4
The energy balance at the liquid–deposit interface was given by equation 7.5:
k
ds
Tδ
T
 k l l  f s
, rs
r
r
dt
7.5
where fs was used to represent the equilibrium solid-phase fraction at the liquid-deposit interface
(i.e., at r = s) corresponding to the interface temperature (Td).
The transient heat transfer model modified for the cold finger apparatus is thus given in
the following section.
7.3 Model for Transient Heat Transfer during Cold Finger Wax Deposition
When a cold finger assembly is inserted into a wax mixture or crude oil, and the inside of
the cold finger is exposed to cooler temperatures lower than the WAT of the wax mixture or
crude oil, a solid layer would start to deposit, via a partial freezing process, on the outer cold
finger surface. The deposit layer thickness would increase with time as thermal energy (including
both the sensible heat and the latent heat of phase change) is transferred radially inwards. Thus,
the deposition in the cold finger would occur on the outer cylindrical surface, as opposed to the
deposition on the inner surface of a pipe considered in previous studies.
193
The wax mixture, stirred continuously in the wax reservoir is held at a constant
temperature, Th (> WAT of the wax–solvent mixture), while the cooler cold finger surface is held
at a constant temperature, Tc (< WAT of the wax–solvent mixture) throughout the deposition
process. The deposit-layer growth, which takes place is predicted with time until a steady state
deposit thickness is attained. Figure 7.1 shows a cross-sectional view of wax deposition on the
cold finger with the different phases accounted for in the model development.
In addition to the assumptions previously stated for the transient heat transfer model, the
one-dimensional model for the wax deposition using the cold finger apparatus did not account
for the effect of shear stress on the wax deposit formation and growth, and did not account for
any shear stripping of the deposit layer due to stirring of the wax mixture. Furthermore, any
deposit aging effects were not considered. Other assumptions in the cold finger transient heat
transfer model are as follows:

Wax mixture temperature remains at a constant average value throughout the deposition
process

The temperature of the cold pipe-wall is a constant average value throughout the
deposition process

The deposit thermal conductivity is a constant average value
194
liquid-deposit interface
at Td = TWAT
liquid phase at Th > TWAT
T
wax deposit (solid +
liquid) at Tc < T <
TWAT
coolant at Tc < TWAT
cold wall at Twall =
Tc < TWAT
T
Figure 7.1
Cross-sectional view of wax deposition on cold finger with
different phases and their relative temperatures.
195
As stated previously, for the cold finger experimental apparatus used in the current study, since
the liquid wax mixture was held at a constant temperature throughout the deposition process by a
water bath, no calculations were performed for the liquid wax mixture i.e., Th = Constant. Also,
the deposition occurred on the outside of the cold finger tube-wall, rather than on the inside
surface of the pipe, as in previous studies.
The one-dimensional energy balance equation for unsteady state radial heat transfer by
conduction in the deposit layer is given as:
1   Tδ  1 Tδ
,
r

r r  r   δ' t
rw < r < rw+s
7.6
where, rw is the location of the cold finger wall and s is the location of the liquid-deposit
interface, and the modified thermal diffusivity in the deposit phase,  δ is given as:
'
1
1  f δ
 
,
'
 δ  δ kδ Tδ
7.7
In equation 7.7, fβ is the mass fraction of solid phase in the deposit, λ is the latent heat of
fusion, and kβ is the thermal conductivity of the deposit at Tβ.
The energy balance at the liquid–deposit interface is given as:
kδ
Tδ
ds
,
 h(Th  Td )   f s
dt
r
r=s
7.8
where, fs is the equilibrium solid phase fraction at the liquid–deposit interface, at r = s,
corresponding to the interface temperature, Td.
7.3.1 Boundary and Initial Conditions
The following boundary and initial conditions were used for solving equations 7.6 and
7.8, which constitute the moving boundary formulation.
196
At t > 0, the pipe wall temperature is maintained at a constant temperature, Tw = Tc <
WAT. The liquid–deposit interface temperature, Td, was set at the WAT of the wax mixture at
all times during the deposition process. Thus the boundary conditions for equations 7.6 and 7.8
are as follows:
Tβ = Tw = Tc
r = rw,
t>0
7.9a
Tβ = Td = WAT
r = rw+s,
t>0
7.9b
Prior to starting the coolant flow in the cold finger and without any deposit formation, the initial
condition for the cold finger deposition process is given as:
s = rw,
7.3.1
t=0
7.9c
Thermodynamic Considerations
The wax and solvent used in this cold finger experiments had average carbon numbers of
14 and 30, respectively. To keep the thermodynamic calculations simple, the wax–solvent
mixture was treated as a pseudo binary mixture comprising C14 (representing the liquid or
solvent fraction) and C30 (representing the wax fraction). It was assumed that the C14–C30 binary
mixture is an ideal eutectic mixture, i.e. with no heat of mixing and no change in volume. The
temperature–composition phase diagram for an ideal binary eutectic system can be obtained from
the freezing point depression equation as follows:
ln xi  
(H m ) i  1
1 

 , i  1, 2

R
 (TL ) i (Tm ) i 
7.10
where (Tm)i, (TL)i and (H m ) i are the melting-point temperature, the liquidus temperature and
the enthalpy of melting (or fusion) of component i, respectively. The values of Tm and
H m
for
C14 and C30 were taken to be 272.8 K and 337.8 K, and 45.3 MJ/kmol and 111.2 MJ/kmol,
197
respectively. The solid-phase mass fraction, f, in an equilibrium mixture held at Tβ was obtained
*
by applying the lever-rule between w30 and w30 = 1.0, as follows:
f  ( w30  w30* ) /(1.0  w30* )
7.11
*
where w30 is the corresponding liquid-phase mass fraction of C30 at Tβ.
7.3.2
Simulation Procedure
The input quantities for the numerical calculations were the mixture composition (w30),
the constant mixture temperature (Th), the constant cold finger wall temperature (Tw), the cold
finger radius (r), and the deposition time (t). The density and viscosity values were obtained
from the property estimation methods reported by Bhat and Mehrotra, (2005, 2006). The solution
methodology involved discretization of the computational domain in the radial direction. The
equations in the moving boundary formulation were solved simultaneously and then used to
predict the deposit thickness (s) with time. These results yielded the profiles for the depositthickness and temperature in the radial direction.
As mentioned previously, at time t = 0, there is no deposition initially anywhere on the
cold finger surface. At time, t > 0, while the wax mixture temperature = Th, the temperature of
the pipe wall, at r = rw, is held at Tw = Tc < WAT. This would cause the wax mixture temperature
near the cold finger wall to decrease below the WAT, thereby initiating the deposition process.
The first deposit layer, adjacent to the cold finger wall corresponds to a radial location (r+Δr).
The movement of the liquid–deposit interface would cause changes in the boundary between the
liquid region and the deposit region.
Equation 7.6 along with equations 7.8, 7.9a, 7.9b and 7.9c, were solved numerically
using the finite difference method to obtain the deposit region temperature profile and the
198
location of the liquid–deposit interface as the deposition time progressed. The discretized
equations were solved simultaneously and MATLAB™ was used for performing the
computations.
7.3.3 Estimation of Liquid and Solid Phase Properties
The required physical, thermal and thermodynamic properties were estimated in solving
equations 7.6 and 7.8, particularly the thermal diffusivity ( = k/ρCp) and the thermal
conductivity of the liquid and deposit phases. The thermal conductivity of the deposit, kd, was
calculated by assuming the thermal resistances of the solid and liquid phases in the deposit to be
in parallel. Different values of heat transfer coefficient of the liquid wax mixture were tried,
starting with values obtained from the calibration experiments. Furthermore, as previously
mentioned, the small density change that could result from a partial solidification of the liquid at
the interface was neglected, i.e.  l
mix
  f    . The liquid and deposit specific heat capacities
(Cp,l and Cp,) were calculated as a weighted average of the individual components. All liquidphase properties were estimated at the constant temperature of the liquid wax mixture.
7.3.4 Numerical Solution Methodology
The set of equations was solved numerically, using Matlab™, to obtain the temperature
profile in the deposit and the radial movement of the liquid–deposit interface with time, for each
axial element. Equations were discretized using an explicit scheme, where the dependant
variables were estimated from the known values at the previous time interval. The time
increment, Δt, and the radial increment, Δr, were chosen such that to satisfy the following
stability criterion (Bhat and Mehrotra, 2005; Bhat and Mehrotra, 2006):
199
t / r 2  1 / 2
7.6
Several sets of preliminary calculations were used to select the number of radial grids as
2001. A larger number of radial grids could yield "smoother" deposit thickness profiles,
especially when the deposit thickness became small, but the computational time increased
significantly; however, the numerical results did not change appreciably. With 2001 radial grids,
one complete simulation typically required about 3 hours of computation time on a desktop
computer with 8 GB of RAM and a quad core processor with a processing speed of 3.30 GHz.
7.4
Model Predictions
7.4.1 Predicted WAT Values
The predicted values of WAT for C14–C30 binary mixtures corresponding to 2, 4, 6, 8, 10,
15 and 20 mass% wax in the solvent, and the experimentally measured WAT values for the same
wax–compositions are shown in Figure 7.2. A good agreement between the predicted and the
experimental WAT values was observed, especially for the 10 mass% composition (used in this
study) and lower compositions. At compositions above 10 mass%, the predicted WAT values
were slightly lower than the experimental WAT values.
200
40
temperature (oC)
35
30
measured WAT
predicted WAT
25
20
15
0
5
10
15
20
25
wax concentration (mass%)
Figure 7.2
Predicted and experimental values of WAT for Bernardin Parowax–
Linpar1416V mixtures.
201
7.4.2 Deposit Thickness Profiles
As stated previously, results from heat transfer calibration experiments performed with
the coolant temperature above the WAT of the wax mixture yielded heat transfer coefficients of
610 and 980 W m-2 K-1 at 250 and 500 rpm, respectively. Figure 7.3 shows an increase in the
predicted deposit thickness with time, for the single-phase cold finger wax deposition from the
transient model. It also shows the values of calculated deposit thickness from experimental data
at stirring rates of 250 and 500 rpm. It is observed that deposit thickness profile from the
transient model compares well with the experimental deposit thickness values. For experimental
deposit thickness values from the 250 rpm stirring rate experiments, the transient model deposit
thickness profile fits the experimental data when the heat transfer coefficient of the wax mixture
is between 750 and 850 W m-2 K-1. For experimental deposit thickness values from the 500 rpm
stirring rate experiments, the transient model deposit thickness profile fits the experimental data
when the heat transfer coefficient of the wax mixture is between 900 and 1100 W m-2 K-1. It is
emphasized that, despite the error that could be associated with the temperature measurements
used in estimating the heat gained by the coolant, which was used for estimating the
experimental heat transfer coefficients, the experimental heat transfer coefficients values of 610
and 980 W m–2 K–1 (as reported in Section 6.2) are of the same order of magnitude, and actually
close to the heat transfer coefficients predicted by the model, in developing the deposit thickness
profiles.
According to equation 7.8, the first term on the L.H.S. of the equation, which corresponds
to the heat transfer across the deposit is initially much higher than the second term on the L.H.S.
which corresponds to the heat transfer across the liquid, providing the thermal driving force for
deposition to occur. The deposit thickness will continue to increase until the values for these two
terms become equal, i.e. until the heat transfer across the deposit and the liquid phases balances
202
out. Thus having a higher heat transfer coefficient, h, (as a result of the higher stirring rate)
means that the value of the term corresponding to the heat transfer across the liquid is set to be
higher, and will thus become equal to the heat transfer across the deposit faster, thereby leading
to a lower deposit thickness.
The experimental deposit thickness of the deposits from the two-phase experiments,
along with the deposit profile from the transient model at using heat transfer coefficients between
900 and 1100 W m-2 K-1 is presented in Figure 7.4. Again, there is a good agreement between the
experimental and predicted results from the transient model. Having set the interface temperature
in the transient model to be equal to the WAT of the wax mixture, and getting values of heat
transfer coefficients close to the experimentally determined heat transfer coefficient of the wax
mixture at the stirring rates, is an indication of the validity of the constant interface temperature
assumption.
203
0.0014
deposit thickness (m)
0.0012
0.0010
0.0008
250 rpm
500 rpm
750 W m-2 K-1
800 W m-2 K-1
850 W m-2 K-1
900 W m-2 K-1
1000 W m-2 K-1
1100 W m-2 K-1
0.0006
0.0004
0.0002
0
5
10
15
20
25
time (h)
Figure 7.3
Deposit thickness profile from transient heat transfer model
compared to deposit thickness from experimental data for single-phase
experiments at 250 and 500 rpm.
204
0.0014
500 rpm
deposit thickness (m)
0.0012
0.0010
0.0008
10 vol% water
20 vol% water
30 vol% water
900 W m-2 K-1
1000 W m-2 K-1
1100 W m-2 K-1
0.0006
0.0004
0.0002
0
5
10
15
20
25
time (h)
Figure 7.4
Deposit thickness profile from transient heat transfer model
compared to deposit thickness from experimental data for two-phase experiments
500 rpm.
205
7.4.3 Deposit Temperature Profiles
Figure 7.5 shows the predictions of the temperature profile of the deposit-layer at
different times, ranging from 5 min to 24 h from the cold wall temperature to the deposit
interface temperature. The predictions were made using a heat transfer coefficient of 750 W m-2
K-1. As expected, the temperature across the deposit layer increases from the cold wall
temperature value to the deposit interface temperature value, with the temperature gradient
decreasing with deposition time. Figure 7.5 also shows that the rate of change of temperature
gradient decrease as the deposition time increases.
206
34
32
30
temperature (oC)
28
26
24
5 min
30 min
2h
4h
8h
12 h
24 h
22
20
18
16
0.00
0.05
0.10
0.15
0.20
0.25
0.30
/rw
Figure 7.5
Predictions of temperature profile across the deposit layer at
different deposition times, ranging from 5 min to 24 h.
207
Chapter Eight: Conclusions and Recommendations
8.1 Conclusions
Novel experimental procedures were developed to study the effects of cooling rate and
composition on the wax precipitation temperature of well-defined wax–solvent mixtures; to
study the deposition of wax from two-phase wax–solvent–water mixtures in a flow loop
experimental apparatus under turbulent flow conditions; and to study the deposition of wax from
single-phase wax mixtures and two-phase wax–solvent–water mixtures using the cold finger
experimental apparatus. The effects of different process variables on the deposition process were
investigated. Furthermore, the results were used to validate the predictions from steady-state and
transient heat transfer calculations.
A procedure was developed to investigate the effects of cooling rate and composition on
the wax precipitation temperature (WPT) of seven compositions of a multicomponent waxy
mixture of Conros Parowax in Norpar13. A modified visual method was used to measure the
WPT of the waxy mixtures at five controlled cooling rates. A comparison of the measured WPT
values with WAT values published by other researchers showed that the WAT values match the
WPT values at cooling rates varying between 0.2 and 0.4 oC/min. The measured WPT values
were found to decrease with an increase in the cooling rate and increase with an increase in the
wax concentration of the waxy mixture. A relationship was proposed to describe the dependence
of WPT on cooling rate and composition. The effect of wax concentration on WPT, for all
cooling rates, was observed to be more pronounced at lower wax concentrations. With the WPT
being dependent on the cooling rate, WPT and WAT may not correctly represent the
thermodynamic liquidus temperature for the liquid-to-solid phase transformation process.
208
A benchscale flow loop experimental apparatus was fabricated to study wax deposition
from two-phase wax–solvent–water mixtures under turbulent flow conditions. The effects of
water content, wax mixture temperature, coolant temperature, and flow rate (or Re) on the
deposition process were investigated. The deposition experiments were performed with a wax
concentration of 6 mass%, with seven water fractions of 0, 5, 10, 15, 20, 25 and 30 vol% (total
volume basis), at three levels of Reynolds number, two levels of wax mixture temperature, and
two levels of coolant temperature. Extended experiments, lasting up to 4 h, were performed to
ascertain that steady state was achieved within the 1-h duration of the deposition experiments.
Similar to the previous single-phase deposition experimental studies under laminar and turbulent
flow, the deposition process in the two-phase experiments under turbulent flow was found to be
relatively fast, attaining a thermal steady-state in less than 10-20 min.
For a wax mixture temperature of Th = (WAT+7 ºC) and coolant temperature of Tc =
(WAT–10 ºC), it was observed that, as the water content of the waxy mixture was increased from
0 vol%, the mass of the deposited solid increased, with a maximum at 10 vol% water content. As
the water content in the mixture increased further, the deposit mass per unit area decreased and
remained fairly constant thereafter. A decrease in the temperature of both the waxy mixture and
the coolant, relative to the WAT, resulted in an increase in the mass of deposited solid, while
increasing the flow rate of the waxy mixture resulted in a decrease in the mass of deposited solid.
The liquid–deposit interface temperature, Td, for all experiments was found to be approximately
equal to the experimentally measured WAT. The average deposit thermal conductivity was
estimated to be 0.38 W m–1 K–1. The deposition data were analyzed with a steady-state heattransfer model. Overall, the results of this study confirmed the solids deposition from waxy
mixtures to be primarily a thermal process that can be explained by heat-transfer considerations.
209
In order to study the wax deposition process using a different experimental apparatus, and
more importantly, to study the effects of time, a benchscale cold finger experimental apparatus
and procedure were developed. The cold finger apparatus was used to study the effects of
deposition time and stirring rate in one-phase waxy mixtures, and the effects of deposition time
and water content in two-phase waxy mixtures. The deposition experiments were performed with
a wax concentration of 10 mass%, with four water fractions of 0, 10, 20, and 30 vol% (total
volume basis), at two levels of stirring rate (250 and 500 rpm), and seven levels of time ranging
from 30 min to 24 h. The growth of the deposit layer was observed to have stopped at about 12 h
for all the single-phase experiments, while a slight increase was observed for the 20% water
content two-phase experiment after 12 h. The deposit mass per unit area from the single-phase
experiments performed at 500 rpm stirring rate were found to be consistently lower than those
from single-phase experiments performed at 250 rpm.
The effect of water on the amount wax deposit during the cold finger experiments were
found to vary at different deposition times. No definite relationship was observed between the
waxy mixture water content and the deposit mass per unit area. Similar to results from the flow
loop experiments, the water content of the waxy mixture was found to be not related to the
deposit water content. The deposit water content was also found to be not related to the
deposition time, even though deposits from the 24 h two-phase experiments had extremely low
water contents for all waxy mixture water content of 10, 20 and 30 vol%.
To further investigate the rate of the deposition process, two short-duration experiments
of 30 s and 2 min were performed. It was observed that more than half of the deposition process
actually occurred within a deposition time of 30 s, and almost two-thirds of the deposition
process was completed within the first 2 min! If steady state was attained in about 12 h, 56% of
210
the deposition process was completed in 0.07% of the time for steady state, while 62% of the
deposition process was completed in 0.28% of the time for steady state. This further confirms
that wax deposition is a very fast process. Because thermal equilibrium is known to be
accomplished much faster than diffusional equilibrium, this provides even further support for the
wax deposition process to be primarily thermally-driven.
The 12-h and 24-h deposition data were analyzed with a steady-state heat-transfer model,
and the overall average thermal conductivity of the was found to be 0.18 W m–1 K–1, which is
comparable to values reported for wax deposits from single-phase flow loop experiments in the
laminar flow regime. The moving boundary problem formulation of Bhat and Mehrotra (2005)
was modified and used to predict the transient results from the cold finger experiments. With the
interface temperature set at the WAT of the wax mixture, the transient heat-transfer model
predictions matched well the experimental results The experimental heat transfer coefficients
values were close to the values estimated from the transient model. This is another confirmation
of the validity of the constant interface temperature assumption of the heat transfer model.
The results of this study consistently showed that the liquid–deposit interface
temperature, Td, at all times during wax deposition in both single and two-phase wax deposition,
under steady state and unsteady state modeling, is equal to the WAT of the liquid phase. This
supports the constant-interface-temperature assumption in the heat-transfer approach for
modeling solids deposition. The results did not show any indication of an increase in the
interface temperature, Td from an initial value close to the wall (or coolant) temperature, to the
WAT, at the interface, which is an important assumption in the molecular diffusion approach for
modeling wax deposition.
211
The major contributions of this research work are as follows:

Quantitatively expressing the dependence of WPT on cooling rate and composition for
waxy mixtures

Establishing that the presence of water is not related to the extent of wax deposition,
using two different experimental apparatuses

Quantitatively establishing that the wax deposition process is a relatively very fast
process

Modelling the transient wax deposition process using a cold finger experimental
apparatus.
8.2 Recommendations
This study provided an experimental framework for the investigation of the deposition of
wax under steady and transient state conditions. It has established that heat transfer is the
controlling mechanism during wax deposition, and has improved the understanding of the effect
of water on wax deposition in two-phase wax mixtures. It has also established that the wax
deposition process is a relatively very fast one, compared to other transfer processes.
For the two-phase flow loop and cold finger experiments, transient emulsions, and not
stable emulsions, were formed by the addition of water to the wax mixtures, the use of
emulsifiers in forming stable emulsions for the experiments can be done. Emulsion
characterization can be done, and the effects of emulsion properties on the deposition process
could be investigated.
The moving boundary approach for modeling the cold finger transient deposition process
can be improved upon. Some of the modifications may include accounting for the effects of
212
shear stress on the wax deposit formation and growth as a result of stirring of the wax mixture,
and accounting for deposit aging.
The use of a longer deposition section may be considered in the flow loop apparatus, this
will increase the length to pipe diameter ratio, and decrease the disparity between the values of
this ratio for the flow loop apparatus, and what obtains in the industry. Deposition experiments
were done with simple well-defined mixtures of wax dissolved in paraffinic solvents, however,
crude oil is a complex mixture of many components. The understanding of the influence of other
components (such as asphaltenes) in crude oil, if any, may be achieved by replicating
experiments with mixtures containing other crude oil components, or by using actual crude oil
samples, although the increased cost might be a detriment.
Currently, relatively few studies have been conducted on two-phase wax deposition
involving oil–water mixtures or emulsions. Additional studies are needed to improve the
understanding of wax deposition from two-phase mixtures.
Available software used by flow assurance groups for modeling and predicting wax
deposition are based on the molecular diffusion approach, perhaps a review of the mechanism of
wax deposition used in these software is needed.
213
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APPENDIX A: WAX PRECIPITATION TEMPERATURE MEASUREMENT DATA 227
Table A1. Measured WPT values and published WAT values for various concentrations of
Conros Parowax in Norpar13.
WPT
Wax
Concentration
WAT
o
o
o
o
o
o
o
o
o
0.4 C/min 0.3 C/min 0.2 C/min 0.1 C/min 0.05 C/min
mass%
C
2
27.0
4
31.8
6
34.6
8
36.2
10
37.8
15
40.8
20
42.9
* Bidmus and Mehrotra (2008b, 2009)
C
27.7
32.5
35.5
36.6
38.1
41.0
43.2
C
28.0
32.5
34.9
36.9
38.4
41.2
43.4
** Fong and Mehrotra (2007)
228
C
28.5
32.5
35.1
37.5
38.9
41.7
43.9
o
C
29.0
32.9
37.2
37.7
40.0
42.0
44.1
o
C
28.0*
32.0*
35.0*
38.0**
41.0**
43.0**
APPENDIX B: HEAT TRANSFER COEFFICIENT DATA
229
Table B1. Overall heat transfer coefficient calibration data for flow loop apparatus (6 mass% waxy mixture, 0% water content).
Trial
No.
H1
H2
H3
H4
H5
H6
H7
H8
H9
H10
H11
H12
Waxy Mixture Inlet Coolant Inlet Coolant Outlet Mass flowrate Mass flowrate
Temperature
Temperature Temperature
Coolant
Wax-Norpar
°C
45.76
45.17
45.03
50.44
50.00
50.00
54.57
54.44
54.46
54.24
53.85
53.79
°C
31.82
34.19
36.38
39.27
41.66
44.02
35.13
38.01
40.78
30.22
30.21
30.22
°C
33.08
35.52
37.69
40.41
42.78
44.98
36.85
39.87
42.66
32.28
32.77
33.15
kg/s
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
230
kg/s
0.371
0.576
0.790
0.372
0.587
0.794
0.380
0.569
0.789
0.380
0.588
0.791
qgain
J/s
qc
J/s
Thout
Tlm
Watt
0.307
0.406
0.498
0.624
0.725
0.824
0.436
0.557
0.673
0.216
0.215
0.216
Watt
43.55
46.06
45.46
39.56
39.00
33.68
59.52
64.32
65.34
70.86
88.43
100.72
°C
45.71
45.14
45.00
50.39
49.97
49.98
54.50
54.39
54.42
54.16
53.79
53.73
°C W/m °C
13.27 383
10.28 523
7.96
666
10.56 437
7.75
587
5.48
717
18.52 375
15.45 486
12.70 600
22.94 360
22.30 463
22.04 533
Ui
Reynolds
Number
2
15533
23741
32441
17666
27564
37320
20279
30255
41970
20107
30732
41275
Table B2. Overall heat transfer coefficient calibration data for flow loop apparatus (6 mass% waxy mixture, 0% water content).
Trial Waxy Mixture Inlet Coolant Inlet Coolant Outlet Mass flowrate Mass flowrate
No.
Temperature
Temperature Temperature
Coolant
Wax-Norpar
H1
H2
H3
H4
H5
H6
H7
H8
H9
H10
H11
H12
°C
56.51
56.45
56.51
52.91
52.80
52.80
48.52
48.46
48.60
42.53
42.47
42.51
°C
30.13
30.22
30.13
33.04
33.06
33.06
37.12
38.01
39.09
30.09
30.12
30.10
°C
33.30
34.18
34.49
35.09
35.77
36.31
38.33
39.51
40.75
31.44
31.94
32.20
kg/s
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
0.0082
231
kg/s
0.385
0.618
0.844
0.344
0.566
0.818
0.351
0.558
0.843
0.389
0.643
0.848
qgain
J/s
qc
J/s
Thout
Tlm
Watt
0.211
0.215
0.211
0.316
0.316
0.316
0.482
0.520
0.565
0.188
0.190
0.189
Watt
109.06
136.19
149.82
70.52
93.53
112.11
42.15
52.03
57.51
46.75
62.80
72.35
°C
56.39
56.36
56.44
52.83
52.73
52.75
48.47
48.42
48.57
42.48
42.42
42.47
°C W/m °C
24.70 515
24.15 658
24.10 725
18.78 438
18.32 596
18.04 725
10.76 457
9.66 628
8.64 777
11.72 465
11.39 643
11.31 747
Ui
Reynolds
Number
2
16614
26682
36501
13418
22000
31811
12140
19285
29204
11457
18932
24981
Table B3. Overall heat transfer coefficient calibration data for cold finger apparatus (10 mass% waxy mixture, 0% water content).
Trial
No.
Waxy Mixture
Temperature
CFH1
CFH2
CFH3
CFH4
CFH5
CFH6
CFH7
CFH8
CFH9
CFH10
CFH11
CFH12
CFH13
CFH14
CFH15
CFH16
CFH17
CFH18
CFH19
CFH20
°C
37.40
37.28
37.24
37.22
37.19
39.07
39.06
39.03
39.03
39.05
37.06
37.10
37.16
37.12
37.16
39.17
39.10
39.07
39.06
39.06
Coolant Inlet Coolant Outlet Temperature
Temperature Temperature
Difference
°C
33.14
33.10
33.08
33.07
33.09
34.04
34.07
34.05
34.07
34.10
33.10
33.11
33.13
33.10
33.12
34.10
34.09
34.08
34.08
34.09
°C
33.22
33.16
33.13
33.13
33.14
34.10
34.10
34.09
34.10
34.13
33.15
33.16
33.20
33.16
33.17
34.22
34.19
34.19
34.17
34.20
°C
0.08
0.06
0.05
0.06
0.05
0.06
0.03
0.04
0.03
0.03
0.05
0.05
0.07
0.06
0.05
0.12
0.10
0.11
0.09
0.11
232
Impeller Mass flowrate
Speed
Coolant
rpm
250
250
250
250
250
250
250
250
250
250
500
500
500
500
500
500
500
500
500
500
kg/s
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
0.0301
qc
J/s
Th - Tc
Ui
Watt
10.12
7.59
6.33
7.59
6.33
7.59
3.79
5.06
3.79
3.79
6.33
6.33
8.86
7.59
6.33
15.18
12.65
13.91
11.38
13.91
°C
4.22
4.15
4.14
4.12
4.08
5.00
4.98
4.96
4.95
4.94
3.94
3.97
3.99
3.99
4.02
5.01
4.96
4.94
4.94
4.92
W/m2 °C
1317
1004
840
1012
852
833
419
560
421
422
883
876
1217
1045
865
1663
1400
1548
1267
1554
APPENDIX C: PHYSICAL PROPERTIES DATA
233
Table C1. Bernardin Parowax-Linpar1416V solution density data.
Wax mass %
APCO1416V
Displayed
Corrected Mass of Volume of
Temperature Temperature Liquid
Liquid
o
o
g
mL
C
C
25.85
25.94
60.889
80.0
35.13
35.16
60.861
80.5
44.75
44.72
60.860
81.0
53.18
53.09
60.767
81.4
63.49
63.33
60.724
81.9
Density of
Liquid
g/mL
0.761
0.756
0.751
0.747
0.741
6
33.84
36.54
39.81
43.36
48.50
53.17
62.32
67.00
33.62
36.30
39.53
43.04
48.13
52.75
61.81
66.44
73.573
74.548
72.067
71.858
72.504
73.169
71.787
70.692
96.7
98.1
95.1
95.0
96.2
97.4
96.2
95.1
0.761
0.760
0.758
0.756
0.754
0.751
0.746
0.744
10
37.25
41.57
49.29
56.92
61.06
37.27
41.56
49.22
56.80
60.92
65.416
65.509
65.768
65.855
65.939
84.7
85.1
85.8
86.4
86.8
0.773
0.770
0.767
0.762
0.760
234
Table C2. Bernardin Parowax-Linpar1416V viscosity data.
Wax mass % Temperature of Liquid
C
24.75
29.69
34.69
39.69
44.68
49.68
Viscosity of Liquid
(mPas)
1.8569
1.6303
1.5036
1.4096
1.3274
1.2643
6
29.70
34.69
39.69
44.69
50.45
1.7721
1.6191
1.4844
1.3766
1.2816
10
34.72
39.74
44.70
49.70
56.00
61.00
1.8754
1.7387
1.5204
1.3598
1.1901
1.1204
o
APCO1416V
235
APPENDIX D: FLOW LOOP EXPERIMENTAL DATA
236
Table D1. Data for experiments with 6 mass% solution with WAT = 28°C (1 h deposition time).
Run
No.
F1
F2
F3
F4
F5
F6
F7
F8
F9
F10
F11
F12
F13
F14
F15
F16
F17
F18
F19
F20
F21
F22
F23
F24
F25
F26
F27
F28
F29
F30
F31
F32
F33
T hi
T ci
o
o
C
C
WAT + 7 WAT – 10
WAT + 7 WAT – 10
WAT + 7 WAT – 10
WAT + 7 WAT – 20
WAT + 15 WAT – 10
WAT + 15 WAT – 20
Average
Waxy Mixture
Volumetric
Flowrate
gpm
8.09
8.11
8.04
8.19
8.06
8.09
7.98
12.32
12.23
12.43
12.07
12.33
12.28
12.41
16.56
16.47
16.46
16.52
16.54
16.03
16.60
8.07
8.09
8.19
8.13
12.31
12.31
12.32
12.35
12.26
12.32
12.34
12.35
Total
Deposit
Mass
Water in
Deposit
Wax
Deposit
Mass
g
2.655
2.805
3.537
2.632
2.715
2.870
2.840
2.253
2.168
3.176
2.242
2.507
2.241
2.997
1.786
1.464
2.412
1.808
1.957
1.819
2.694
4.778
5.537
4.781
4.600
1.124
0.858
1.249
1.992
3.008
2.763
2.138
3.109
vol%
0.0
0.6
6.6
2.8
0.0
13.5
0.4
0.0
1.1
8.2
3.9
0.1
9.9
15.3
0.0
0.1
13.6
6.5
13.3
12.2
15.8
0.0
1.1
0.4
6.7
0.0
24.9
4.3
14.5
0.0
8.2
5.1
10.6
g
2.655
2.787
3.304
2.557
2.715
2.483
2.829
2.253
2.145
2.915
2.154
2.505
2.019
2.540
1.786
1.463
2.084
1.691
1.697
1.597
2.268
4.778
5.477
4.761
4.294
1.124
0.644
1.195
1.703
3.008
2.536
2.029
2.779
237
Reynolds
Number

Water-free
12526
11269
9965
8850
7611
6548
5587
18912
16776
15303
12952
11643
9839
8622
25289
22423
20085
17633
15399
12798
11484
12982
10338
7980
5807
22590
18015
13874
10300
23412
18329
14060
10495
kg/m2
0.310
0.325
0.386
0.298
0.317
0.290
0.330
0.263
0.250
0.340
0.251
0.292
0.236
0.296
0.208
0.171
0.243
0.197
0.198
0.186
0.265
0.557
0.639
0.555
0.501
0.131
0.075
0.139
0.199
0.351
0.296
0.237
0.324
Table D2. Data for experiments with 6 mass% solution with WAT = 28°C (extended
experiments), Thi = (WAT+7) oC, Tci = (WAT-10) oC.
Run
Time
Average
Total
Water in
Wax
Reynolds

Deposit
Mass
Deposit
Deposit
Mass
Number
Water-free
h
1
2
2
4
4
Waxy Mixture
Volumetric
Flowrate
gpm
12.32
12.30
12.32
12.34
12.36
9929
9874
9899
10034
9992
kg/m
0.279
0.256
0.254
0.263
0.273
No.
RE3
RE1
RE1R
RE2
RE2R
g
2.489
2.274
2.346
2.338
2.415
238
vol%
4.1
3.3
7.1
3.4
3.3
g
2.387
2.198
2.179
2.258
2.336
2
APPENDIX E: COLD FINGER EXPERIMENTAL DATA
239
Table E1. Data for single-phase experiments using 10 mass% of wax solution with WAT =
32°C.
Run No.
Time
Stirring
Speed
h
CF1

Water-free
rpm
Total
Deposit
Mass
g
Wax
Deposit
Mass
g
0.1
250
1.4522
1.452
kg/m2
0.637
CF1R
0.1
250
1.3325
1.333
0.584
CF2
0.2
250
1.4512
1.451
0.636
CF3
0.5
250
1.6361
1.636
0.718
CF4
1.0
250
1.8631
1.863
0.817
CF5
2.0
250
1.8176
1.818
0.797
CF5R
2.0
250
1.827
1.827
0.801
CF6
4.0
250
1.874
1.874
0.822
CF7
8.0
250
2.1403
2.140
0.939
CF8
12.0
250
2.2189
2.219
0.973
CF9
24.0
250
2.1276
2.128
0.933
CF10
0.1
500
0.8996
0.900
0.395
CF10R
0.1
500
0.8907
0.891
0.391
CF11
0.2
500
1.0155
1.016
0.445
CF12
0.5
500
1.0219
1.022
0.448
CF13
1.0
500
1.2447
1.245
0.546
CF14
2.0
500
1.2441
1.244
0.546
CF14R
2.0
500
1.305
1.305
0.572
CF15
4.0
500
1.4252
1.425
0.625
CF16
8.0
500
1.668
1.668
0.732
CF17
12.0
500
1.777
1.777
0.779
CF18
24.0
500
1.671
1.671
0.733
240
Table E2. Data for two-phase experiments using 10 mass% wax solution with WAT = 32°C at
Run No.
Time
Stirring
Speed
h
CF19

Water-free
Total
Deposit
Mass
g
Water in
Deposit
rpm
Waxy mixture
water
content
vol%
vol%
Wax
Deposit
Mass
g
0.1
500
10
0.935
7.8
0.863
kg/m
0.378
CF19R
0.1
500
10
0.956
1.8
0.939
0.412
CF20
0.5
500
10
1.080
0.2
1.078
0.473
CF21
2.0
500
10
1.432
1.2
1.414
0.620
CF22
8.0
500
10
1.602
8.3
1.469
0.644
CF23
24.0
500
10
1.967
0.5
1.958
0.859
CF24
0.2
500
20
1.006
8.5
0.920
0.403
CF25
1.0
500
20
1.278
12.3
1.121
0.492
CF25R
1.0
500
20
1.406
18.2
1.150
0.505
CF26
4.0
500
20
1.597
10.1
1.435
0.629
CF27
12.0
500
20
1.891
9.5
1.711
0.751
CF28
24.0
500
20
1.875
1.3
1.850
0.812
CF29
0.1
500
30
1.101
24.1
0.835
0.366
CF30
0.5
500
30
1.263
23.5
0.966
0.424
CF30R
0.5
500
30
1.270
24.3
0.961
0.421
CF31
2.0
500
30
1.282
2.7
1.248
0.547
CF32
8.0
500
30
1.676
15.2
1.422
0.623
CF33
24.0
500
30
1.781
1.0
1.764
0.773
241
2
Table E3. Data for single-phase short-duration experiments using 10 mass% of wax solution
with WAT = 32°C.
Run No.
Time
Stirring
Speed
h
CF34

Water-free
rpm
Total
Deposit
Mass
g
Wax
Deposit
Mass
g
0.01
250
1.245
1.245
kg/m2
0.546
CF35
0.03
250
1.387
1.387
0.608
CF36
48.0
250
2.202
2.202
0.966
242
APPENDIX F: ESTIMATION OF LIQUID MIXTURE AND DEPOSIT PHASE
PROPERTIES IN TRANSIENT MODEL
F1 - Liquid Phase Properties
243
Thermal Conductivity:
The thermal conductivity of liquid mixtures was calculated using the Li correlation (Li,
1976). The correlation can be applied for liquid mixtures containing N number of components.
The mixture thermal conductivity (k) was correlated as a function of the mixture volume
fractions  i :
N
N
k  i j
i 1 j 1
i 
2k i k j
F.1
ki  k j
xi  l,i1
n
x
j 1
j

F.2
1
l, j
where,  i , xi, and ρl,i are the volume fraction, mole fraction and the pure component density of
component i, respectively. The thermal conductivity of liquid C14 was obtained from a
correlation provided by Wada et al. (1985). Wada et al. (1985) expressed the thermal
conductivity of paraffins up to C16 as a function of their carbon number (n) and temperature as
follows:
(kl)14 = An2 + Bn + C – [D(1/n)2 + E(1/n) + F]T
F.3
where, k is the thermal conductivity (W m–1 K–1), A–F are constants, n is carbon number, and T
is temperature (range: 20– 90 °C).
The correlation for the thermal conductivity of liquid C30 (Perry and Green, 1984):
(kl) = 0.00012(1392.4 – T)
F.4
where, T is the temperature in K.
Density:
244
The liquid mixture density was calculated as a volume weighted average (Bhat and Mehrotra,
2005):

mix
l


   w i (l ) i 
 i

1
F.5
The liquid phase density (API Research Project 42, 1966) for C14 and C30 were fitted as:
(ρl)14 = 770.4 – 0.7T
F.6
(ρl)30 = 821.9 – 0.6T
F.7
where, T is the temperature in °C.
Specific Heat Capacity:
The liquid mixture specific heat capacity was calculated as a weighted average (Bhat and
Mehrotra, 2005):


C pmix
, l    w i (C p , l ) i 
 i

F.8
The pure component specific heat capacities were obtained from a group contribution
method (Jin and Wunderlich, 1991).
CH 2
3
Cp,l  2CCH
p,l  (n  2)Cp,l
F.9
2
CCH
p,l = 17.33+0.04551T
F.10
3
CCH
p,l = 30.41 + 0.01479 T
F.11
where, n is the carbon number and T is the temperature in K.
The predicted solid phase specific heat capacity (DIPPR® 801) in J kmol–1 K–1:
Cp,f = 7750T0.79
F.12
245
where, T is the temperature in K.
F2 - Deposit Phase Properties
Thermal Conductivity:
The thermal conductivity of the deposit was obtained as (Bhat and Mehrotra, 2005):
k  klmix l  k f  f
F.13
where, kf, , and  l and  f denote the thermal conductivity of solid, volume fraction of liquid
and volume fraction of solid phase, respectively.
Density
The small variation in densities of the liquid, solid and the deposit phases are neglected
mix
(i.e.  l   f   )
Specific Heat Capacity
The deposit specific heat capacity was obtained as a weighted average of those for the liquid and
the solid phases (Bhat and Mehrotra, 2005):
C p,  (1  f )C pmix,l  fCp, f
F.14
246
APPENDIX G: COPYRIGHT PERMISSIONS
247