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Fouling from sour heavy oil under incipient coking conditions Wang, Wei 2016

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FOULING FROM SOUR HEAVY OIL UNDER INCIPIENT COKING CONDITIONS  by  Wei Wang  B.A.Sc., China University of Petroleum, 2006 M.A.Sc., China University of Petroleum, 2009  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in The Faculty of Graduate and Postdoctoral Studies (Chemical and Biological Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  March 2016  © Wei Wang, 2016  ii Abstract Fouling is a long-standing and major issue in the oil processing industry. At elevated temperatures in refineries, heavy and sour feedstocks promote fouling due to both corrosion product formation and carbonaceous species deposition. An isothermal batch reactor was built to study this complex process with a bitumen (ATB) sample which contains 4.1 wt% sulphur. Metal rings of five surface materials with Cr contents of 0-100% were mounted on a cylinder and were rotated in the ATB in a pressurized reactor. Experiments were carried out at bulk temperature of 380°C to 410°C at different rotational speeds for 6-24 hours. A microscopy method was developed to determine the thickness, density and porosity of deposit. The organic and inorganic components of the deposit, which represent coke deposition and sulphide corrosion respectively, were determined. An iron-rich transitional zone was found between metal surfaces and bulk deposit. Radial elemental profiles in the transitional zone were analyzed. The transfer of trace inorganic elements during experiments was investigated. The effects of chemical composition of the metal surface, temperature and wall shear stress on deposit growth were discussed. Based on the research, physicochemical and mathematical models of deposition growth involving sulphide corrosion and coke deposition were proposed. Corrosion was markedly reduced in the presence of coking. An mathematical model was developed to describe sulphide corrosion and deposition under the restricted diffusion of dissolved H2S through the deposit film of increasing thickness. Short and long term corrosion and deposition behaviors were predicted with the model. To describe the coking process, parameters of the phase separation model for the ATB iii were determined. The assumption that surface coking is related to dissolved asphaltene cores was proposed and verified. Wall shear stress was demonstrated to have significant effects on coke deposition on the metal surface, but little effect on growth of inorganic films. A non-isothermal fouling unit was built to study the fouling process on a hot surface with lower bulk temperature. Preliminary experiments were done for carbon steel and Incoloy 800 surfaces.   iv Preface The dissertation is original, independent work by the author, Wei Wang. Chapter 2. Part of content is included in three papers. W. Wang, A.P. Watkinson, "Iron Sulphide and Coke Fouling from Sour Oils: Review and Initial Experiments," in: International Conference on Heat Exchanger Fouling and Cleaning - 2011, Eurotherm, Crete Island, Greece, 2011, pp. 23-30, W. Wang, A.P. Watkinson, "Deposition From a Sour Heavy Oil Under Incipient Coking Conditions: Effect of Surface Materials and Temperature," Heat Transfer Engineering 2015, 36, and W. Wang, A.P. Watkinson, "Deposition from a Sour Heavy Oil under Incipient Coking Conditions: Wall Shear Stress Effects and Mechanism," in: International Conference on Heat Exchanger Fouling and Cleaning XI, Eurotherm, Enfield, Dublin, 2015. Chapter 3. Part of content is included in two papers. W. Wang, A.P. Watkinson, "Deposition From a Sour Heavy Oil Under Incipient Coking Conditions: Effect of Surface Materials and Temperature," Heat Transfer Engineering 2015, 36. W. Wang, A.P. Watkinson, "Deposition from a Sour Heavy Oil under Incipient Coking Conditions: Wall Shear Stress Effects and Mechanism," in: International Conference on Heat Exchanger Fouling and Cleaning XI, Eurotherm, Enfield, Dublin, 2015. Chapter 4 and 5. Part of content was included in one paper. W. Wang, A.P. Watkinson, "Deposition From a Sour Heavy Oil Under Incipient Coking Conditions: Effect of Surface Materials and Temperature," Heat Transfer Engineering 2015, 36. v Chapter 6, 7, 9 and Section 8.4. Part of content was included in one paper. W. Wang, A.P. Watkinson, "Deposition from a Sour Heavy Oil under Incipient Coking Conditions: Wall Shear Stress Effects and Mechanism," in: International Conference on Heat Exchanger Fouling and Cleaning XI, Eurotherm, Enfield, Dublin, 2015. vi Table of Contents Abstract .......................................................................................................................... ii Preface .......................................................................................................................... iv Table of Contents ......................................................................................................... vi List of Tables .............................................................................................................. xvi List of Figures ............................................................................................................ xix List of Symbols ....................................................................................................... xxvii List of Abbreviations ............................................................................................. xxxvii Acknowledgements ................................................................................................ xxxix Chapter 1: Introduction ................................................................................................. 1 Chapter 2: Literature Review ........................................................................................ 4 2.1 Vacuum Distillation and Vacuum Tower furnace ............................................... 4 2.1.1 Vacuum Distillation .................................................................................... 4 2.1.2 Vacuum Distillation Unit Furnace ............................................................... 5 2.2 Oil Sand Processing ......................................................................................... 6 2.2.1 Oil Sands ................................................................................................... 6 vii 2.2.2 Processing of Oil Sands ............................................................................. 8 2.2.2.1 Upgrading of Bitumen ............................................................................. 9 2.3 Fouling in Petroleum Refining ........................................................................... 9 2.3.1 Fouling in VDU Furnaces ......................................................................... 10 2.4 Corrosion in Refineries ................................................................................... 12 2.4.1 Sulphur Species in Petroleum and Their Properties ................................ 12 2.4.2 Three Fundamental Rate laws for Sulphide Corrosion ............................ 14 2.4.2.1 Linear Rate Law ................................................................................... 14 2.4.2.2 Logarithmic Rate Law ........................................................................... 15 2.4.2.3 Parabolic Rate Law .............................................................................. 15 2.4.3 Corrosion Model during Oil and Gas Production and Transportation ....... 15 2.4.4 High Temperature Sulphide Corrosion..................................................... 16 2.4.5 Sulphide Corrosion with H2S ................................................................... 18 2.5 Fouling Involving Iron Sulphide ....................................................................... 19 2.6 Fouling with Coking ......................................................................................... 21 2.6.1 The Phase Separation Mechanism for Coke Formation .......................... 22 viii 2.6.2 Other Mechanisms for Coke Formation ................................................... 24 2.7 Hydrodynamic Effects on Fouling ................................................................... 25 2.8 Summary......................................................................................................... 26 Chapter 3: Experimental Materials, Apparatus and Procedures ............................. 27 3.1 Test Oil Sample .............................................................................................. 27 3.2 Test Metal Surfaces ........................................................................................ 29 3.3 Experimental Apparatus .................................................................................. 30 3.3.1 Batch Fouling Reactor ............................................................................. 31 3.3.2 Dual Signals Temperature Control System .............................................. 34 3.3.3 Data Acquisition ....................................................................................... 35 3.4 Experimental Procedures ................................................................................ 35 3.4.1 Proper Experiment Duration .................................................................... 35 3.4.2 Pre-experimental Procedure .................................................................... 36 3.4.2.1 Preparation of Oil Sample .................................................................... 36 3.4.2.2 Preparation of Test Metal Ring ............................................................. 36 3.4.2.3 Unit Assembly ...................................................................................... 37 ix 3.4.3 Experimental Procedures ......................................................................... 38 3.4.3.1 Air Elimination ...................................................................................... 39 3.4.3.2 Heat-up Period ..................................................................................... 39 3.4.3.3 Cooling Period ...................................................................................... 40 3.4.4 Post Experimental Procedure .................................................................. 40 Chapter 4: The Deposition Build-Up Rate ................................................................. 41 4.1 Determination of Deposit Thickness, Density and Mass ................................. 41 4.1.1 Features of Fouling Deposit ..................................................................... 41 4.1.2 Determination of Deposit Thickness ........................................................ 43 4.1.3 Determination of Density and Mass of Deposit ........................................ 45 4.2 Fouling Rate of Five Metal Surfaces with Bulk Temperature .......................... 46 4.3 Summary......................................................................................................... 48 Chapter 5: Composition and Structure of Deposit ................................................... 50 5.1 Basic Components of Deposit – Thermogravimetric Analysis ......................... 50 5.2 Carbonaceous Material and Ash in Deposit for Different Metal Surfaces ....... 53 5.2.1 Overall Composition of Deposits .............................................................. 53 x 5.2.2 Mass of Ash and Carbonaceous Materials .............................................. 54 5.2.3 Two Fouling Regimes .............................................................................. 57 5.3 Radial Deposit Composition Profiles ............................................................... 57 5.3.1 SEM-EDX Analysis of Deposit Cross Section .......................................... 57 5.3.2 Element Mapping of Iron and Sulphur on Deposit Cross-Section ............ 61 5.3.3 Elements Radial Profiles in Deposit ......................................................... 62 5.4 Crystal Structure of Fe Compounds in the Oil and Deposit ............................. 68 5.5 Summary......................................................................................................... 71 Chapter 6: Hydrodynamic Effects on Fouling .......................................................... 73 6.1 Shear Stress and Reynolds Number Determination ....................................... 73 6.1.1 Shear Stress in Rotating Cylinder System ............................................... 73 6.1.2 Density of ATB at High Temperatures ..................................................... 73 6.1.3 Viscosity of ATB at High Temperatures ................................................... 75 6.1.3.1 Viscosity Measurement – Rheometer Method ...................................... 76 6.1.3.2 Correlation of Viscosity with Temperature ............................................ 76 6.1.4 Shear Stress and Reynolds Number with Rotating Speeds ..................... 79 xi 6.2 Effects of Shear Stress ................................................................................... 80 6.2.1 Effect of Shear Stress on Deposition Rate and Properties ...................... 80 6.2.2 Porosity of Deposit ................................................................................... 84 6.3 Summary......................................................................................................... 86 Chapter 7: Sulphide Corrosion .................................................................................. 88 7.1 Active Sulphur Species in the ATB ................................................................. 88 7.2 Sulphide Corrosion Model ............................................................................... 89 7.3 Corrosion Reaction Analysis ........................................................................... 91 7.4 Effect of Additional Organic Sulphur ............................................................... 96 7.5 Threshold Chromium Content for Sulphide Corrosion Resistance .................. 98 7.6 Summary....................................................................................................... 100 Chapter 8: Carbonaceous Material Deposition ....................................................... 102 8.1 The Phase Separation Mechanism for Coke Formation ............................... 102 8.2 Determination of Asphaltene and Heptane Solubles Concentration ............. 103 8.3 Coke Formation Kinetic Model Based the Phase Separation Mechanism .... 104 8.4 Activation Energy of Coking Reaction ........................................................... 111 xii 8.4.1 Bulk Coking and Heptane Solubles Conversion .................................... 111 8.4.2 Surface Coking ...................................................................................... 112 8.5 Summary....................................................................................................... 113 Chapter 9: Trace Inorganic Elements in the Oil and Products .............................. 115 9.1 Trace Inorganic Elements Transfer during Fouling Experiments .................. 115 9.1.1 Elemental Analysis – ICP-AES .............................................................. 116 9.1.2 Mass Balance of Trace Inorganic Elements ........................................... 116 9.2 Addition of Iron Oxide Particulates ................................................................ 121 9.3 Summary....................................................................................................... 122 Chapter 10: Non-isothermal Fouling Research ...................................................... 124 10.1 Non-isothermal Fouling System .................................................................... 124 10.1.1 Reactor .................................................................................................. 124 10.1.2 Cartridge Heater Probe .......................................................................... 128 10.1.3 Design of Impeller .................................................................................. 130 10.1.4 Temperature Control .............................................................................. 131 10.1.5 Power Supply ......................................................................................... 131 xiii 10.2 Experiment Procedures ................................................................................ 131 10.2.1 Pre-experimental Procedure .................................................................. 131 10.2.2 Experimental Procedure ........................................................................ 132 10.2.3 Post Experimental Procedure ................................................................ 133 10.3 Preliminary Experiments ............................................................................... 133 10.3.1 Thermal Fouling Resistance and Fouling Rate ...................................... 134 10.3.2 Experiments with Carbon Steel Cartridge Heater Probe ........................ 135 10.3.3 Experiment with Incoloy 800 Cartridge Heater Probe ............................ 141 10.4 Summary....................................................................................................... 146 Chapter 11: Mathematical Model.............................................................................. 148 11.1 Physicochemical Model ................................................................................ 148 11.2 Mathematical Model for Sulphide Corrosion ................................................. 150 11.2.1 Development of the Expanding Scale Model ......................................... 150 11.2.2 Parameters in Equation (11-17) ............................................................. 158 11.2.2.1 Porosity of Deposit .......................................................................... 158 11.2.2.2 Effective Diffusion Coefficient ......................................................... 158 xiv 11.2.2.3 Initial Concentration of Active Sulphur Species in the ATB ............. 159 11.2.2.4 Thermal Decomposition Rate Constant of Active Sulphur Species 159 11.2.2.5 Mass Fraction of FeS in Deposit ..................................................... 160 11.2.3 Discussion of the Model ......................................................................... 161 11.2.3.1 Concentration of H2S in the Bulk Oil ............................................... 162 11.2.3.2 Temperature Effects on the Corrosion Rate ................................... 162 11.2.3.3 Thickness of the Deposit ................................................................ 165 11.2.3.4 Effects of Initial Sulphur Species Concentration on Corrosion rate 167 11.2.3.5 Shear Stress Effects on Corroded Metal Thickness ....................... 168 11.3 Thermal Coking Mechanism Based on the Phase Separation Model ........... 170 11.3.1 Asphaltene Cores and Coke Accumulation Rates ................................. 170 11.3.2 Model Development and the Application................................................ 176 11.4 Summary....................................................................................................... 179 Chapter 12: Conclusions and Recommendations .................................................. 180 12.1 Conclusions .................................................................................................. 180 12.2 Recommendations for Further Study ............................................................ 183 xv References ................................................................................................................. 185 Appendices ................................................................................................................ 206 Appendix A Properties of Syncrude ATB ................................................................. 206 A.1 Special Distillation of Syncrude ATB (ASTM D86)* ................................... 206 A.2 Trace Inorganic Elements in Syncrude ATB* ............................................ 207 Appendix B Metal Chemical Composition Ranges of Tested Metals ....................... 208 Appendix C Temperature Control System ............................................................... 209 C.1 Single Temperature Control: Pros and Cons ............................................. 209 C.2 Dual Temperature Control System ............................................................ 210 Appendix D Derivation of Equations for the Phase Separation Kinetic Model [89] .. 212 Appendix E Determination of Asphaltene Concentration in the ATB and the Spend Oil – Detailed Procedure ............................................................................................... 214 Appendix F Typical Heat Transfer Coefficients [165] ............................................... 216 Appendix G Integration of Equation (11-16) in Wolfram Mathematica 10.0 ............. 217 Appendix H Porosity of FeS, Coke and Deposit ...................................................... 218 xvi List of Tables Table 2-1 Some Parameters of Vacuum Distillation Unit Furnaces ................................. 5 Table 2-2 Maximum Working Temperature for Furnace Materials[21, 22] ...................... 6 Table 2-3 Properties of Bitumen and Conventional Crude Oil [25] .................................. 8 Table 2-4 Sulphur Species in Crude Oil and Properties ................................................ 13 Table 3-1 Properties and Ultimate Analysis of ATB (from Syncrude Canada Ltd.) ....... 27 Table 3-2 Partial Trace Inorganic Elements Concentration (ICP) .................................. 28 Table 3-3 TGA Analysis of ATB .................................................................................... 28 Table 3-4 Specifications of Alloy Rings ......................................................................... 30 Table 3-5 Specifications of Parr Model 4563 Reactor ................................................... 31 Table 3-6 Operational Condition of Isothermal Batch Fouling Experiments .................. 38 Table 5-1 Temperature Programming for Thermogravimetric Analysis of Deposit Samples ........................................................................................................................ 51 Table 5-2 Average Iron and Sulphur Concentration and Atomic Fe/S Ratio in Transitional zone ........................................................................................................... 66 Table 5-3 Atomic Ratio of Nickel and Vanadium to Iron in the ATB, Metal and Deposit 68 Table 5-4 Operating Parameters of XRD Analysis ........................................................ 69 xvii Table 5-5 Deposit Samples for XRD Analysis ............................................................... 69 Table 6-1 Types of Petroleum Oil and Corresponding API Gravities [138].................... 74 Table 6-2 ATB Density at Experimental Temperatures ................................................. 75 Table 6-3 Fitting Quality for Different Numbers of Points .............................................. 77 Table 6-4 Calculated Viscosity of ATB at Experimental Temperatures ......................... 78 Table 7-1 Effects of Additional DMS.............................................................................. 96 Table 8-1 Values of Coefficients in the Phase Separation Model for ATB Experiments .................................................................................................................................... 106 Table 8-2 Comparison of Measured and Calculated Mass of Coke after 24-Hour Experiment .................................................................................................................. 109 Table 9-1 Mass Balance of the ATB and Post Experimental Products ........................ 118 Table 9-2 Elements in the ATB and Products (Cr-CS, 390°C, 24h, 300rpm, 315.9g ATB) .................................................................................................................................... 118 Table 9-3 Elements in the ATB and Products (CS, 400°C, 24h, 300rpm, 338.4g ATB) .................................................................................................................................... 118 Table 9-4 Transfer of Trace Inorganic Elements after Experiments ............................ 119 Table 9-5 Change of Asphaltene Amount before and after Experiments .................... 120 Table 9-6 Effects of Addition of Iron Oxide Particulates .............................................. 122 xviii Table 10-1 Specification of Cartridge Heater Probe .................................................... 128 Table 10-2 Operating Conditions of Two Non-isothermal Experiments ....................... 134 Table 10-3 Summary of Main Results of the Two Experiments ................................... 146 Table 11-1 Parameters in the Mathematical Model ..................................................... 157 Table 11-2 Ds and De at 380-410°C for the Deposit Porosity of 0.5 ............................ 159 Table 11-3 kS for 24-Hour Experiments at 370°C and 380°C ...................................... 160 Table 11-4 Mass Fraction of FeS in Deposit ............................................................... 161 Table 11-5 Corrosion Rate Determined from the Deposition Model and from McConomy Curves ......................................................................................................................... 165 Table 11-6 Comparison of Calculated and Measured Mass of Coke (390°C, 600rpm, CS) .............................................................................................................................. 175   xix List of Figures Figure 2-1 Typical Flow Scheme for the Atmospheric and Vacuum Distillation ............... 5 Figure 2-2 Vacuum Distillation Unit Furnace ................................................................... 6 Figure 2-3 Typical Composition of Oil Sand Particles ..................................................... 7 Figure 2-4 Generalized Scheme for Oil Sands Processing ............................................. 9 Figure 2-5 Temperature Gradient in Clean Tube Compared to Coked Tube in a Fired Furnace [34] .................................................................................................................. 11 Figure 2-6 Three Basic Rate Laws of Oxidation ............................................................ 14 Figure 2-7 Modified McConomy Curves [70] ................................................................. 17 Figure 2-8 Corrosion Rate Multiplier for McConomy Curves [70] .................................. 17 Figure 2-9 Calculated Scale Retention versus Time (P = 0.1MPa, 10% H2S, 80°C) [75] ...................................................................................................................................... 18 Figure 2-10 Adhesion of Coke to Stainless Steel Requires Sulphiding for the Carbonaceous Mesophase ........................................................................................... 20 Figure 2-11 The Phase Separation Model for Coke Formation [89] .............................. 23 Figure 3-1 TGA Analysis of Syncrude ATB Sample ...................................................... 29 Figure 3-2 Isothermal Batch Fouling Unit ...................................................................... 31 xx Figure 3-3 Structure and Flow Scheme of Model 4563 Stirred Batch Reactor .............. 32 Figure 3-4 Typical Experimental Procedure .................................................................. 38 Figure 4-1 Deposit on the Ring Surface (Carbon Steel, Tb = 380°C, ω = 300rpm, t = 24h) ............................................................................................................................... 41 Figure 4-2 Deposit on the Ring Surface (Carbon Steel, Tb = 400°C, ω = 600rpm, t = 24h) ............................................................................................................................... 42 Figure 4-3 Microscopic Images of Deposit for Experiments of 24h at 300rpm .............. 44 Figure 4-4 Microscopic Image of a Standard 0.1mm Gap ............................................. 45 Figure 4-5 Photograph of Deposit Pieces and Vernier Caliper ...................................... 46 Figure 4-6 Fouling Rate of Different Ring Surfaces Materials (600rpm, 24 hours) ........ 47 Figure 4-7 Fouling Rate on Carbon Steel with Different Rotational Speeds .................. 48 Figure 5-1 A Typical TGA Graph of Deposit .................................................................. 51 Figure 5-2 Effect of Bulk Oil Temperature on Weight Fraction of Carbonaceous Matter of Deposit (24h, 600rpm) ............................................................................................... 54 Figure 5-3 Effect of Bulk Oil Temperature on the Mass of Ash in Deposit (24h, 300rpm) ...................................................................................................................................... 55 Figure 5-4 Effect of Oil Temperature on the Mass of Carbonaceous Matter in Deposit (24h, 300rpm) ................................................................................................................ 56 xxi Figure 5-5 Incoloy 825 Ring Cross Section after Being Polished with 200-1000 Grit Emery Papers and Diamond Papers ............................................................................. 59 Figure 5-6 SEM Image of Deposit on Cr-CS Surface after a 24-Hour Experiment at 390°C and 300rpm (WD15.0mm, 20.0kV, ×350) ........................................................... 60 Figure 5-7 SEM Image of Deposit on CS Surface after a 24-Hour Experiment at 390°C and 300rpm (WD15.0mm, 20.0kV, ×2000) .................................................................... 60 Figure 5-8 Element Mapping of Cross Section of the Deposit ....................................... 62 Figure 5-9 Locations for EDX Analysis .......................................................................... 63 Figure 5-10 Radial Distribution of Iron in Deposit after a 24h Experiment at 390°C and 300rpm .......................................................................................................................... 64 Figure 5-11 Radial Distribution of Sulphur in Deposit after a 24h Experiment at 390°C and 300rpm ................................................................................................................... 64 Figure 5-12 Atomic Ratio of Fe/S in Transitional zone .................................................. 66 Figure 6-1 Specific Gravity – Temperature Relationship for Petroleum Oils and Cuts .. 74 Figure 6-2 Walther and McCoull Correlation of Viscosity – Temperature ...................... 78 Figure 6-3 Shear Stress with Rotating Speeds ............................................................. 79 Figure 6-4 Reynolds Number with Rotating Speeds ..................................................... 80 xxii Figure 6-5 Deposition Rate on Carbon Steel Rings versus Wall Shear Stress at 380°C and 390°C ..................................................................................................................... 81 Figure 6-6 Deposit Density versus Wall Shear Stress at 380°C and 390°C .................. 82 Figure 6-7 Mass of Carbonaceous Matter and Ash for Corrosion Controlled Regime (380°C) .......................................................................................................................... 83 Figure 6-8 Mass of Carbonaceous Matter and Ash in Deposits for Incipient Coking Regime (390°C) ............................................................................................................ 84 Figure 6-9 Wall Shear Stress Effects on Porosity of Deposit of 380-390°C Experiments ...................................................................................................................................... 86 Figure 7-1 Corrosion Rate Multiplier Curve Fitting ........................................................ 93 Figure 7-2 Arrhenius-Type Plot of the Sulphide Corrosion Rate According to McConomy Curves ........................................................................................................................... 94 Figure 7-3 Arrhenius-Type Plot of the Sulphide Corrosion Rate in Presence of Fouling (mm/year) ...................................................................................................................... 95 Figure 7-4 Effect of Weight Percentage of Cr in the Metal Rings on the Weight Percentage of Fe in Deposit at Different Distances from the Metal Surface after a 24-Hour Experiment at 390°C and 300rpm ........................................................................ 99 Figure 7-5 Effect of Weight Percentage of Cr in the Metal Rings on the Mass of Ash in Deposit at Different Temperatures after a 24-Hour Experiment at 300rpm ................. 100 xxiii Figure 8-1 Apparatus for Asphaltene Content Determination ...................................... 104 Figure 8-2 Evaluation of Rate Constant for Disappearance of Unreacted Asphaltenes .................................................................................................................................... 105 Figure 8-3 Evaluation of Rate Constant for Disappearance of Unreacted Heptane Solubles ...................................................................................................................... 105 Figure 8-4 Projected Formation of Toluene Insoluble Coke with Time ........................ 107 Figure 8-5 Calculated Formation of Toluene Insoluble Coke in the First 48 Hours ..... 108 Figure 8-6 Four Major Products from ATB versus Time at 380°C ............................... 110 Figure 8-7 Four Major Products from ATB versus Time at 390°C ............................... 110 Figure 8-8 Four Major Products from ATB versus Time at 400°C ............................... 111 Figure 8-9 Determination of Activation Energy for Bulk Coking and Heptane Solubles Conversion .................................................................................................................. 112 Figure 8-10 Arrhenius-Type Plot for Coke Deposit Rate (mg/day) for Experiments at 380-400°C and at 600rpm ........................................................................................... 113 Figure 9-1 Fouling Products after Experiments ........................................................... 115 Figure 9-2 Ni+V Content in the Oil Products versus Asphaltene Content [88] ............ 121 Figure 10-1 Schematic Diagram of Non-isothermal Fouling Unit ................................ 125 Figure 10-2 Non-isothermal Reactor ........................................................................... 126 xxiv Figure 10-3 Bolted Flange of the Non-isothermal Reactor .......................................... 126 Figure 10-4 AutoCAD Design of the Cooling Coil ........................................................ 127 Figure 10-5 Cartridge Heater Probe ............................................................................ 128 Figure 10-6 Structure of Cartridge Heating Probe ....................................................... 129 Figure 10-7 Temperature Change from the Cartridge Probe Heater to the Bulk Oil .... 129 Figure 10-8 Location of the Cartridge Heating Probe .................................................. 130 Figure 10-9 Temperature Data Recording of a Non-isothermal Experiment ............... 132 Figure 10-10 Probe Power and Electrical Resistance Recording of a Non-isothermal Experiment .................................................................................................................. 133 Figure 10-11 80-Hour Carbon Steel Probe Experiment............................................... 135 Figure 10-12 Partial Enlarged Probe Surface Temperature (Carbon Steel) ................ 136 Figure 10-13 Fouling Resistance of 80-Hour Carbon Steel Probe Experiment ........... 137 Figure 10-14 Fouling Rate Calculation for CS Experiments (64-74 Hours) ................. 138 Figure 10-15 Fouling Rate Calculation for CS Experiments (Last Hour of the Experiment) ................................................................................................................. 139 Figure 10-16 Overall Heat Transfer Coefficient of 80-Hour Carbon Steel Probe Experiment .................................................................................................................. 140 xxv Figure 10-17 TGA Analysis of Carbon Steel Probe Deposit ........................................ 141 Figure 10-18 250-Hour Incoloy 800 Probe Experiment ............................................... 142 Figure 10-19 Partial Enlarged Probe Surface Temperature (Incoloy 800)................... 143 Figure 10-20 Fouling Resistance of 250-Hour Incoloy 800 Probe Experiment ............ 144 Figure 10-21 Fouling Rate Calculation (60-230 Hours) ............................................... 144 Figure 10-22 Overall Heat Transfer Coefficient of the Experiment with Incoloy 800 Probe ........................................................................................................................... 145 Figure 10-23 TGA Analysis of Incoloy 800 Probe Deposit .......................................... 146 Figure 11-1 Sulphide Corrosion and Coking Involved Fouling on a Metal Ring .......... 152 Figure 11-2 Change of Dissolved H2S Concentration in Bulk Oil ................................ 162 Figure 11-3 Calculated Corroded Fe Thickness Details for the First 24 Hours (600rpm) .................................................................................................................................... 163 Figure 11-4 Power Curve Fitting of Corrosion Fe Thickness vs Time (One Year, 600rpm) ....................................................................................................................... 164 Figure 11-5 Change of Thickness of Deposit with Time (24 hours) ............................. 166 Figure 11-6 Change of Thickness of Deposit with Time (One Year) ........................... 166 Figure 11-7 Calculated Corroded Fe Thickness Change with Additional DMS (600rpm) .................................................................................................................................... 167 xxvi Figure 11-8 Calculated an Measured Corroded Metal Thickness for Experiments at 380°C .......................................................................................................................... 168 Figure 11-9 Calculated an Measured Corroded Metal Thickness for Experiments at 390°C .......................................................................................................................... 169 Figure 11-10 Coke Generation on the Surface with Time (380°C, 600rpm) ................ 171 Figure 11-11 Concentration of Asphaltene Cores in the ATB versus Time (380°C and 390°C) ......................................................................................................................... 171 Figure 11-12 Coke Generation Rate on the Surface vs Asphaltene Cores Concentration .................................................................................................................................... 172 Figure 11-13 Calculated Dissolved Asphaltene Cores (A*) in the ATB solution (390°C) .................................................................................................................................... 174 Figure 11-14 Coke Generation with Time (390°C, 600rpm) ........................................ 175 Figure 11-15 Coke Generation on Metal Surface versus Time ................................... 178 Figure 11-16 Projected Coke Generation on Metal Surface versus Time in the First 140 Hours ........................................................................................................................... 178   xxvii List of Symbols a stoichiometric coefficient in the phase separation coke formation model, dimensionless A heat transfer area, m2 Ac lumped pre-exponential factor for corrosion of carbon steel in Modified McConomy curves, m/s AM corrosion rate multiplier for Modified McConomy curves, dimensionless AL logarithmic rate law coefficient, dimensionless AS pre-exponential factor of Arrhenius equation for thermal decomposition of active sulphur species, dimensionless A+ concentration of unreacted asphaltenes, wt% A* concentration of asphaltene cores, wt% A*d concentration of dissolved asphaltene A*Ex excess asphaltene cores beyond the solubility limit, wt% A*max maximum asphaltene cores that can be held in solution, wt% b stoichiometric coefficient in the phase separation coke formation model, dimensionless xxviii c asphaltene concentration in the oil, g/L cA H2S concentration, mol/m3 cAb H2S concentration in bulk ATB, mol/m3 cAs H2S concentration on deposit outer surface, mol/m3 cb bulk concentration of active sulphur species, kg/m3 Cp parabolic rate law constant, dimensionless cs oil sulphur concentration in Modified McConomy curves, mol/L csi,d concentration of Si in deposit, wt% csi,e concentration of Si in bulk coke, wt% csi,f concentration of Si in feed ATB, wt% csi,h concentration of Si in spent oil, wt% ct asphaltene concentration in the oil at time t, mol/L cw concentration of active sulphur species adjacent to the surface, kg/m3 c0 asphaltene concentration in feedstock oil, mol/L c2 asphaltene concentration on metal surfaces c’A*  concentration of asphaltene cores in bulk oil, wt%; xxix dcyl diameter of cylinder, m De effective diffusion coefficient of dissolved H2S, m2/s Df diffusion coefficient for active sulphur species through the FeS layer or the deposit, m2/s Ds diffusion coefficient of dissolved H2S, m2/s e Walther and McCoull correlation coefficient, dimensionless Ea activation energy, J/mol Eac activation energy of carbon steel corrosion in Modified McConomy curves, J/mol Ea2 activation energy of coking on metal surfaces, J/mol EaA  activation energy for the bulk asphaltene disappearance, J/mol EaM activation energy for the bulk heptane solubles disappearance, J/mol EaS activation energy for thermal decomposition of active sulphur species, J/mol F rotation speed of cylinder, rpm k reaction rate constant, mol1−n·Ln−1·s−1 ka reaction rate constant of asphaltene, mol1−n·Ln−1·s−1 xxx kA first order rate constant for the thermolysis of asphaltenes, min-1 kc sulphide corrosion reaction rate constant in Modified McConomy curves, mol1−n·Ln−1·s−1 k’c rate constant of coke generation, g·m-2·h-1 kd thermal conductivity of deposit, W/m•K kf thermal conductivity, W/m•K kl linear rate law rate constant, m/s kL logarithmic rate law rate constant, dimensionless km convective mass transfer coefficient, m/s kM first order rate constant for the thermolysis of heptane solubles, min-1 kp parabolic rate law rate constant, m2/s kr rate constant for the reaction of the active sulphur species with the metal, m3n-2kg1-n s-1 kS rate constant of thermal decomposition of active sulphur species, s-1 k2 rate constant of coking on metal surface, s-1 m stoichiometric coefficient in the phase separation coke formation model, dimensionless xxxi mC mass of FeS in deposit, g md mass of deposit on metal ring surfaces, g mD mass of deposit on metal ring surfaces, g me mass of bulk coke, g mf mass of feed ATB, g mg mass of oil gas and vapour, g mh mass of spent oil, g mfc mass of fixed carbon, mg ms mass of spent oil after experiments, g MB molar mass of Fe, kg/mol MC molar mass of FeS, kg/mol Mf average molecular weight of feed ATB oil, g/mol M+ unreacted heptane solubles, wt% M* heptane soluble cores, wt% n reaction order, dimensionless NA mole of diffusing H2S, mol xxxii p Walther and McCoull correlation coefficient, dimensionless q Walther and McCoull correlation coefficient, dimensionless Q heat transferred per unit time, W QA  diffusion flux of H2S at any location, and metal surface, mol/(m2·s) QAo  diffusion flux of H2S at deposit surface, mol/(m2·s) QAi diffusion flux of H2S at metal surface, mol/(m2·s) r distance from a certain location in deposit layer to the centre of the carbon steel ring, m rc sulphide corrosion rate of carbon steel in the Modified McConomy curves, m/s rcyl radius of cylinder, m r’c coke generation rate, g·m-2·h-1 r2 coke formation rate on metal surfaces, mg/day R gas constant, 8.3145 J/(mol·K) Ri radius of carbon steel rings after being corroded, m Ro total radius of carbon steel rings with outer deposit layer, m Rr original radius of carbon steel rings xxxiii Rf thermal fouling resistance, m2·K/W Re Reynolds number, dimensionless SG specific gravity of oils at 15.6/15.6°C, dimensionless SL solubility limit, dimensionless t time, s ta mean boiling point, °C T absolute bulk temperature, K Tb bulk oil temperature, °C Tc cartridge probe heater core temperature, °C Tf film temperature, °C Th heating temperature, °C TI toluene insoluble coke, wt% Ts cartridge probe heater surface temperature, °C Ts,0 initial cartridge probe heater surface temperature, °C ΔT temperature difference between hot and cold medium, K ucyl rotation speed of cylinder, m/s xxxiv U overall heat transfer coefficient, W/m2·K V volatiles, wt% VA molar volume of H2S at boiling point, m3/kmol VB volume of corroded iron, m3 VD volume of deposit, m3 w weight of deposit, kg wC mass fraction of FeS in the deposit, dimensionless ws mass fraction of sulphur in the oil, dimensionless ws,f mass fraction of active sulphur species in the ATB, dimensionless Wa weight of ash (FeS) in the oil sample in TGA test, g Wc weight of carbonaceous material (volatile + fixed carbon), g Wfc weight of fixed carbon, g Wv weight of volatile fraction, g W1 weight of sample at the end of stage 1 in TGA test, g W2 weight of sample at the end of stage 2 in TGA test, g W3 weight of sample at the end of stage 3 in TGA test, g xxxv x thickness, m xB corroded Fe thickness, m xD deposit thickness, m y stoichiometric coefficient in the phase separation coke formation model, dimensionless yf thickness of corrosion layer, m  Greek Symbols  ε porosity of deposit, dimensionless µ dynamic viscosity of oil, Pa·s ν kinematic viscosity of fluid, mm2/s or cSt ρ density of oil, kg/m3 ρB density of carbon steel, kg/m3 ρc density of corrosion products, kg/m3 ρD bulk density of deposit, kg/m3 ρf density of corrosion product (FeS) layer, kg/m3 ρr,C real density of FeS without pores, kg/m3 ρr,D real density of deposit without pores, kg/m3 xxxvi ρr,E real density of coke without pores, kg/m3 τ tortuosity, dimensionless τw  wall shear stress, Pa φ association parameter of the solvent, dimensionless Φ thermal fouling rate, m2K/kJ Φc gross corrosion flux, kg/(m2·s) Φd thermal fouling deposition term, m2K/kJ Φr thermal fouling removal term, m2K/kJ ω rotational speed, rad/s   xxxvii List of Abbreviations AC alternating current API American Petroleum Institute ATB atmospheric topped bitumen BDL below detection limit Cr-CS chrome-plated type 1018 low carbon steel CS carbon steel DC direct current DMS dimethyl sulphide EDX energy-dispersive x-ray spectroscopy HVGO heavy vacuum gas oil ICP-AES inductively coupled plasma atomic emission spectrometry IWT inner wall temperature LVGO light vacuum gas oil MCR micro carbon residue MVGO medium vacuum gas oil xxxviii NAC naphthenic acid corrosion OWT outer wall temperature PID proportional integral derivative PSV primary separation vessels SS stainless steel SEM scanning electron microscope TAN total acid number TGA thermogravimetric analysis VABP  volume average boiling point VDU Vacuum distillation unit VR vacuum residue VTB vacuum topped bitumen WD working distance XRD x-ray diffraction 9-Cr 9Cr-1Mo steel  xxxix Acknowledgements I wish to express my sincere gratitude to Dr. A. Paul Watkinson for the incredible amount of support and guidance he has provided throughout this study. I am also truly grateful to my committee members for all support and contributions to this work. I would like to show my special thanks to Craig A. McKnight of Syncrude Canada Ltd. for his valuable technical input and feedback. My thanks are due to all members of the Department of Chemical & Biological Engineering, particularly to Dr. Yong Hua Li, B. Petkovic, G. Feiz and Dr. B. Ehsan for their kind help in the research, and staff from the department office, workshop and stores for their assistance and advice. Assistance from K. Jacob, L. Kato and ALS on oil and deposit characterization is highly appreciated. The research funding and oil sample from Syncrude Canada Ltd., and financial support from the University of British Columbia are gratefully acknowledged. This thesis is dedicated to my family for their love and support.1 Chapter 1: Introduction Fouling refers to the formation of unwanted deposit on equipment surfaces. It has significant effects on the thermal efficiency of oil processing [1], and leads to increased CO2 emissions. Vacuum tower furnaces are used for preheating high boiling point fractions for vacuum distillation in refinery and in oil sand upgrading processes. Typical vacuum tower furnace outlet temperatures are in the range 390°C to 450°C [2]. Atmospheric topped bitumens (ATB) are highly viscous and polar heavy oil fractions which contains high concentrations of sulphur compounds and asphaltenes. The former can lead to serious sulphide corrosion, while the latter can lead to coke formation under vacuum tower furnace operating conditions [3]. Two types of fouling predominate in crude oil pre-heat trains down-stream of the de-salter in refineries, and on the tube-side of furnaces which treat heavy fractions. Inorganic fouling, in which deposits mainly consist of FeS and salts, and carbonaceous material fouling due to asphaltenes which ultimately result in coke deposits, may occur together, or separately, depending on circumstances. Sulphide corrosion is widely observed in oil processing especially above temperatures of 260°C. In sour oils, concentrated sulphur compounds or hydrogen sulphide will react with iron in oil or on the internal surface of the furnace tubes to generate iron sulphide. Thus iron sulphide has been a key component of deposition in heat exchangers [4] and furnaces [5], as suggested by Wiehe [6]. Carbonaceous species also deposit from oils, leading to a complex mechanism of fouling where both coking and sulphidation may 2 contribute to deposition. Stephenson et al. [7] studied corrosion of 316 stainless and pure iron wires in atmospheric bottoms fraction of a crude oil, and proposed a pitch - coke - iron sulphide structure of deposit.  Flow past a surface is widely known to affect the build-up of fouling layers. At fixed temperature, fouling rates may be correlated by a flow parameter such as bulk velocity, flow Reynolds number or wall shear stress. Much literature shows that fouling rates of oils decrease with increasing flow velocity [8, 9]. Effects of flow are captured in models of the fouling process, such as that of Epstein [10], where the deposition process is viewed as mass transport of foulants in series with an n-th order chemical reaction attachment step. In this model, the rate of fouling goes through a maximum with increasing flow parameter, as transport increases with velocity, and attachment is inversely proportional to wall shear stress. Joshi et al. [11] found that in crude oil pre-heat trains, fouling rate varied as τw-1.6, presumably because of a suppression or removal effect. Corrosion rates are also reported to increase with velocity, or wall shear stress [12] and knowledge of wall shear stress is required to make corrosion rate measurements meaningful. However, the effect of fluid shear on the fouling buildup rate or composition of foulant is not yet well understood. The objectives of this research were to explore the connection between rates of iron sulphide and carbonaceous matter film formation and properties of oil, types of surface materials, temperature, and wall shear stress, find out the probable interrelationship between sulphide corrosion and carbonaceous accumulation when both processes occur in fouling, and understand the mechanism of sulphide corrosion and coke deposition under incipient coking conditions. Focusing on deposit composition can 3 simplify the problem by elucidating the relative roles of iron sulphide and coke deposition at temperatures where incipient coking occurred in the bulk fluid. Temperatures used in the work are typical oil temperatures in the tubes of vacuum tower furnaces. Metal surfaces studied included carbon steel and chrome-containing alloys which can be used in vacuum tower furnaces. To simplify the problem, most work focused on isothermal experiments. A rotating cylinder apparatus was constructed such that wall shear stress effects could be studied. Multiple characterization methods were introduced to aid in establishing mechanisms of the deposition process. Physicochemical and mathematical models were developed to describe the probable mechanism of sulphide corrosion and coke deposition on the metal surface. 4 Chapter 2: Literature Review 2.1 Vacuum Distillation and Vacuum Tower furnace 2.1.1 Vacuum Distillation Crude oil contains many different components which must be separated into several cuts first for further processing. This separation initially occurs via atmospheric pressure distillation, to separate the oil into a number of fractions with boiling point below about 380°C in order to prevent the thermal cracking of high molecular weight components at high temperatures [13]. The residue from the bottom of the atmospheric distillation tower, ATB, with boiling point higher than 380°C is then processed with vacuum distillation to extract more middle distillate cuts from the atmospheric residue. Reduced pressure in vacuum distillation permits vaporization at reduced temperatures, and accordingly minimizes thermal cracking and coking. A similar approach may be applied in upgrading of bitumen. A general flow scheme for atmospheric and vacuum distillation is shown in Figure 2-1. In vacuum distillation, ATB is firstly preheated with a series of exchangers. Then it goes through the vacuum tower furnace for a final heating to 380-415°C [14], and is then charged to the vacuum distillation tower to be separated into light, medium and heavy vacuum gas oil as well as vacuum residue. Pressure in vacuum distillation tower is typically 3.3-5.3 kPa (25-40mmHg) [15].  5  Figure 2-1 Typical Flow Scheme for the Atmospheric and Vacuum Distillation 2.1.2 Vacuum Distillation Unit Furnace A VDU furnace (Figure 2-2) is used to heat feed oil to the desired temperature before the oil is sent to the vacuum distillation tower [16]. In a VDU furnace, heat generated from combustion of fuels is transferred to oil fluid which is circulating in the tubes located along the wall and roof. Some typical values for the parameters of vacuum tower furnaces are shown in Table 2-1. Table 2-1 Some Parameters of Vacuum Distillation Unit Furnaces Parameter Typical Value Radiant Fluxes 24-27 kW/m2 [17] Outlet Temperatures up to 415-425°C [18] Furnace Tube Inside Diameter 136-249mm [19] Outlet Fluid Velocity 55m/s (180ft/s) [20]  6  Figure 2-2 Vacuum Distillation Unit Furnace In construction of vacuum tower furnaces, different alloys are required for different working temperature zones. Maximum working temperatures of some common alloys used in a vacuum tower furnace are listed in Table 2-2. Table 2-2 Maximum Working Temperature for Furnace Materials[21, 22] Material Maximum Working Temperature (°C) Carbon Steel 480 9-Cr (9% Cr – 1% Mo) 700 Stainless Steel 317 870 Incoloy 800 985  2.2 Oil Sand Processing 2.2.1 Oil Sands Oil sands are mixtures of bitumen, water, quartz/clay particles and other mineral matter[23]. A typical composition of oil sand particles is seen in Figure 2-3. Oil sands 7 mainly occur in Canada, Venezuela, the United States and Russia. In Canada, most oil sands are found in Alberta, including three deposits: Athabasca, Cold Lake and Peace River, which totally cover 141,000 km2 of land.  Figure 2-3 Typical Composition of Oil Sand Particles Bitumen is the desired part of oil sands. It is an extremely viscous oil based substance which contains thousands of carbon atoms in its molecules. Compared to conventional crude oil, higher concentrations of sulphur, nitrogen and metal elements are found in bitumen. Generally, it is a very heavy petroleum substance with an American Petroleum Institute (API) gravity of 6°-10° [24], which corresponds to specific gravities of 1.00-1.03. A comparison of properties between bitumen and conventional crude oil is listed in Table 2-3 [25]. 8 Table 2-3 Properties of Bitumen and Conventional Crude Oil [25] Property Bitumen Conventional Crude Oil Gravity, °API 8 35 Elemental Analysis (wt%)    C 83 86  H 10.6 13.5  S 4.8 0.1  N 0.4 0.2  O 1 0.2 Fractional Composition (wt%)    Asphaltenes 19 5  Resins 32 10  Aromatics 30 25  Saturates 19 60 Metals (mg/kg or ppm)    Vanadium 250 10  Nickel 100 5  The bitumen content in oil sands is typically between 1% and 18%. When bitumen content is over 12%, the oil sands will be considered rich. On average, one barrel (159 litres) of synthetic crude oil can be produced from 2 tonnes of mined oil sand. 2.2.2 Processing of Oil Sands In oil sands, bitumen is mixed with sand and water. Thus the processing of oil sand is very different from that of conventional crude oils. Typically, it contains several procedures including mining, extraction and upgrading [26, 27], as shown in Figure 2-4. Bitumen is separated from the sands in extraction before upgrading. 9  Figure 2-4 Generalized Scheme for Oil Sands Processing 2.2.2.1 Upgrading of Bitumen Bitumen is converted to high quality, light, low sulphur crude oil with upgrading. Firstly, the light gas oil fraction naturally in bitumen is removed and diluent naphtha is recovered, via a process similar to atmospheric distillation in a conventional refinery, where ATB is obtained.  ATB is then fed to the VDU to remove the remaining light and heavy gas oils, and is finally fed to the conversion units. The light gas oil is then conveyed to the hydrotreating units for final clean-up. 2.3 Fouling in Petroleum Refining Fouling usually refers to the generation and accumulation of undesirable matter on the surface of facilities. The presence of these deposits causes a resistance to heat 10 transfer, which may require an increase in pumping power, therefore reducing the efficiency of heat transfer equipment. The rate of the fouling process may be described in terms of mass per unit area, mD, thickness, x, or thermal fouling resistance of deposit, Rf, as: 𝒅𝒎𝑫𝒅𝒅= 𝝆𝒅 𝒅𝒅𝒅𝒅 = 𝝆𝒅𝒌𝒇 𝒅𝑹𝒇𝒅𝒅        (2-1) where kf is thermal conductivity of the deposit (W/m•K). The unit of Rf is (m2•K/W). Fouling rates are functions of many variables, including chemical and physical properties of fluid, temperature, fluid flow regime, surface material and morphology, impurities in fluid, and so on.  Fouling is a prevalent phenomenon in many industrial processes. In petroleum refining, it is estimated that the total fouling related expenses of refineries in the United States were more than $1.3 billion/year in 1981 [28], and over $4.4 billion/year in recent years [29]. Two thirds of the expenses were incurred in crude units [28]. Expenses mainly come from excessive energy, maintenance, shortage of capacity, inactivation of catalysts, and loss of production when units are shut down [30-32]. For a preheat train processing 100,000 bbl/day, an additional $50,000 CAD and $24,000 CAD will be spent every day for a 1°C temperature drop and a 10% loss of production, respectively [33]. 2.3.1 Fouling in VDU Furnaces Coke formation on the internal surfaces of the tubes in fired furnaces will thermally insulate the process fluids from the inside tube surfaces, and therefore requires a higher 11 outside surface temperature to maintain the same fluid temperature (Figure 2-5) [34]. Flame temperature is raised until the temperature limit of the tube metal is reached. Coking not only decreases the thermal efficiency, but also raises safety issues.   Figure 2-5 Temperature Gradient in Clean Tube Compared to Coked Tube in a Fired Furnace [34] The temperature of the flame or flue gas is much higher than the tube metal temperature. Typically, if the tube skin temperature was elevated from the design temperature of 525°C to 635°C, the tube strength will decrease by 80% from the strength at 525°C [35]. Besides, uneven coke deposition may cause a more significant expansion of one side of the tube, leading to a bulge or rupture. 12 2.4 Corrosion in Refineries Corrosion due to naphthenic acid and active sulphur in oil fractions has been widely discussed [36-39]. Naphthenic acid corrosion (NAC) is believed to start at about 216°C (420  °F), and reach a maximum in the range of 260-288°C (500-550°F) [40]. In the range of 370-400°C (700-750°F), NAC is negligible due to the thermal decomposition of naphthenic acid [41, 42].  Total acid number (TAN) is widely used as a measurement of acidity due to naphthenic acid in petroleum products [43]. TAN is determined by ASTM D664 [44]. According to the standard methods, the number of milligrams of potassium hydroxide required to neutralize 1 g of oil is measured by titration.  Usually the TAN is between 0.1 and 3.5 mg KOH/g [45]. Oils with TAN values higher than 0.5 mg KOH/g are believed to be corrosive to a refinery plant [46]. The onset of significant corrosion due to active sulphur species is at 260°C [40] and corrosion rate increases at higher temperatures. Corrosion caused from sulphur compounds is more evident at elevated temperatures. For bitumen derived from oil sands, sulphide corrosion is concluded to be the predominant type of corrosion [20]. 2.4.1 Sulphur Species in Petroleum and Their Properties Sulphur is one of the principal corrodents in the oil processing industry. Sulphur compounds in crude oil have been studied for decades [47-51] since they cause corrosion directly in both crude oils and their fractions. As well, they must be removed from most refinery products for environmental reasons. The main sulphur species in petroleum are listed in Table 2-4.  13 Table 2-4 Sulphur Species in Crude Oil and Properties Sulphur Species Concentration/ Distribution Corrosivity Stability at High Temperature S Rarely present in crude oils [52] High  H2S Very low in crude oil, <250°C cut High  Thiols/Mercaptans (R-S-H) Lowest concentration organic S in crude, <250°C cut. Zero concentration in >370°C cut [52] High Least stable in organic S. Decompose to H2S and alkene at 280-290°C [53]. Disulphide (R-S-S-R) Low in crude oil, <250°C High  Thioether (R-S-R) Highest in low BP distillation, especially 120-250°C Low Between thiol and thiophene, stable at 300°C, Decompose to thiol, H2S, alkene and thiophene Thiophene Most important in the ATB and VTB, very low  when <250°C Low Stable at temperatures up to 450°C, at high temperature, thiophene derivatives decompose to smaller molecules, but the thiophene core is very stable. Large derivatives polymerize and go to coke. Benzothiophene Low Dibenzothiophene Low Naphtho Benzothiophene Low  Although hydrogen sulphide concentration is originally very low in crude oil and even negligible in heavy cuts, however it is still the main corrosive species during oil refining because at processing temperatures the thermal decomposition of organic sulphur species mainly produce hydrocarbons and hydrogen sulphide [54]. Thus the sulphidation mechanism with organic sulphides is linked to hydrogen sulphide [55]. The corrosivity of different sulphur species depends on the concentration of the sulphur species in the fraction and their thermal stability at processing temperatures. 14 2.4.2 Three Fundamental Rate laws for Sulphide Corrosion Sulphide corrosion is basically a series of reduction-oxidation reactions. Extensive research has been conducted to study sulphide corrosion [56, 57]. Three basic rate laws which describe the oxidation rates were proposed [58], in terms of the thickness of oxide, as illustrated in Figure 2-6.   Oxide ThicknessTime Linear Parabolic Logarithmic LinearParabolicLogarithmic Figure 2-6 Three Basic Rate Laws of Oxidation 2.4.2.1 Linear Rate Law The linear rate law describes the corrosion rate when the oxide scale is non-protective, or falls off after reaching a critical thickness [59]. In this situation, the oxidation is reaction controlled. The oxidation scale growth rate is independent of the scale thickness. 15 𝒅 = 𝒌𝒍𝒅           (2-2)  2.4.2.2 Logarithmic Rate Law The logarithmic rate law was first proposed by Tammann and Koster in 1922 [60, 61], and is usually used when oxidation occurs in thin oxide scale [62], or with other rate determining steps [59]. One of the most important assumptions for the logarithmic rate law is that the oxidation rate depends on the uncovered surface area [57]. This rate law includes a rapid growth of oxide thickness in the beginning and an asymptotic value afterwards. 𝒅 = 𝒌𝑳𝒍𝒍𝒍(𝑨𝑳𝒅 + 𝟏)          (2-3) 2.4.2.3 Parabolic Rate Law This model was suggested by Tammann in 1920 [63], and is the most common mechanism in high temperature oxidation of engineering alloys. In this oxidation mechanism, the oxide scale thickness grows with a decreasing oxidation reaction rate [64]. The restrictive diffusion of reactant through the growing oxide scale is the rate determining steps. 𝒅𝟐 = 𝒌𝒑𝒅 + 𝑪𝒑          (2-4) 2.4.3 Corrosion Model during Oil and Gas Production and Transportation Corrosion by H2S/CO2 under oil and gas production and transportation conditions has been studied extensively with different models proposed [58, 65-67]. These studies mainly focused on low temperature H2S/CO2 corrosion. 16 Sun and Nesic proposed a model for mild steel corrosion in a 1 wt% NaCl solution with dissolved H2S at 25-80°C, with the formation and growth of FeS scale. The diffusion effect of H2S from outer FeS scale to the metal surface was considered during the development of the mathematical model.  2.4.4 High Temperature Sulphide Corrosion Modified McConomy curves [68-71], which show sulphide corrosion rates in oils versus temperature on the basis of industrial experience, are widely used to estimate the corrosion rate at different operating temperatures when hydrogen is absent or hydrogen pressure is less than 345 kPa (50 psi). The curves (Figure 2-7) are based on a sulphur content of 0.6 wt% in oil. For different sulphur contents, the corrosion rates have to be calibrated with the corrosion rate multiplier in Figure 2-8. For convenience, corrosion rate are expressed in mm/year of metal consumed. It can be concluded from the curves that corrosion resistance increases with increasing chromium content in alloys. It can be concluded from the curves that for a given type of metal, temperature and sulphur content, the corrosion rate is constant, which means the curves are based on the linear rate law discussed in Section 2.4.2. Thus the corrosion reaction is the rate determining step and diffusion effects are not considered. McConomy curves are more accurate in estimating corrosion rate based on sulphur content only, or with a lower TAN rather than for high TAN fractions [72]. For instance, laboratory and industrial data indicate that the corrosion rate of carbon steel was close to that of ASTM A387 grade 5 alloy (5% chromium in alloy) [73], which is not in accordance with the curves.  17 240 260 280 300 320 340 360 380 4001E-30.010.111018/812Cr9Cr7Cr4-6Cr  Corrosion Rate (mm/year)Temperature (°C)Carbon Steel1-3CrSulfur content: 0.6 wt% Figure 2-7 Modified McConomy Curves [70] 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.010.1110  Sulphur Content (wt%)Corrosion Rate Multiplier  Figure 2-8 Corrosion Rate Multiplier for McConomy Curves [70] 18 Sulphide corrosion in the absence of carbonaceous fouling will lead to the outward growth of an iron sulphide film, according to the relative molar volumes of FeS and Fe. For each millimeter of Fe reacted, the thickness of the FeS film will be 2.56mm. For sulphide corrosion with hydrogen present, modified Couper-Gorman curves are often used to predict corrosion rates [74]. 2.4.5 Sulphide Corrosion with H2S Sun and Nesic [75] studied the H2S corrosion on carbon steel and developed a mechanistic model to predict the corrosion with the inhibition effect due to the Mackinawite scale (FeS). Figure 2-9 shows a curve fitting of one group of scale retention data from the work.  0 5 10 15 20 250.000.020.040.060.080.10  Scale Retention (mol/m2 )Time (hour)Model Allometric1Equation y = a*x^bReduced Chi-Sqr 2.772E-6Adj. R-Square 0.99677Value Standard ErrorScale Retentiona 0.01685 3.0677E-4b 0.51618 0.00654 Figure 2-9 Calculated Scale Retention versus Time (P = 0.1MPa, 10% H2S, 80°C) [75] 19 Results show that a power fitting correlation with the power value of 0.519 is in good agreement with the data, indicating a pseudo parabolic rate law discussed in Section 2.4.2. Kane and Cayard [45] put carbon steel coupons in a high H2S/oil environment at 345°C for 30 days and obtained a sulphide film with the thickness of 84µm, which means around 1mm of FeS layer would be generated each year. 2.5 Fouling Involving Iron Sulphide Fouling usually occurs via several sequential events including initiation, transport, attachment, removal and ageing [32]. Initiation is a crucial step of fouling which may involve formation and build-up of fouling precursors. Iron sulphide has been determined not only as one of the most common species in deposits from refinery heat exchangers and furnaces but also to be an initiator of fouling. Deposit analyses from various parts of refining and upgrading processes consistently show high concentration of iron and sulphur [76, 77]. The sulphur originates from the oil [1], however the iron may arise from the oil (dissolved iron species or suspended corrosion products) as implied by the work of Lemke and Stephenson [1], or from the metal. Taylor [78] found that the deposition rate in deoxygenated jet fuel significantly increased with addition of different types of sulphur compounds except thiophene did not promote the deposition process. Pareek et al. [55] studied sulphidation corrosion of 4130 steel in vapour phase CH3SH and found two rate-determining steps of surface reaction. A linear kinetics at temperatures below 370°C indicated a reaction control mechanism, while a 20 parabolic kinetics at temperatures over 370°C represented a diffusion control mechanism. Cosultchi et al. [79] claimed non-stoichiometric iron sulphide helped alkyl chains to adsorb non-dissociatively on tube surfaces. Similarly, Wiehe [80] concluded the adherence between carbonaceous mesophase and an oxide metallic surface is weak, whereas hydrogen sulphide reacts with metal surfaces and forms iron sulphide, which makes the adherence much more powerful, as shown in Figure 2-9. This model is also supported by Laursen and Frandsen [81], who claimed molten FeS will form a sticky surface and lead to a quick build-up of deposit at high temperatures.   Figure 2-10 Adhesion of Coke to Stainless Steel Requires Sulphiding for the Carbonaceous Mesophase  Adams [82] reported that asphaltene adsorption capacities of surfaces has a strong relationship with surface acidity. FeS has higher acidity than Fe2O3 and NiO, making it a better adsorbent surface than the other two materials. 21 Panchal et al. [83] believed deposition in sulphur-containing oils is probably induced with iron sulphide, which is generated from iron naphthenates and reaction with sulphur species. Thus a threshold temperature for the decomposition of iron salts was discussed.  Parker and McFarlane [30] proposed a probable sequence of events for deposition in furnaces, which included the following steps: formation of iron sulphide in bulk oil, accumulation of part of the iron sulphide on inner tube surface, attachment of coke precursors to the iron sulphide layer, and formation of coke from these precursors at high skin temperatures. For preheating of heavy petroleum fractions such as atmospheric distillation residue, sulphide corrosion should attract special attention since sulphur species have been found predominantly in heavy oil fractions. 2.6 Fouling with Coking Research indicates that insoluble carbonaceous matter is mainly derived from asphaltene present in oil [3, 84, 85]. There are two common reasons for asphaltene to precipitate from the oil: blending of oils which can be predicted with the oil compatibility model [86, 87], or high temperatures, particularly when the temperature is over 380°C, and the oil stability drops rapidly [88]. Barletta [34] proposed three most important factors that may lead to rapid coke formation, including temperature, oil residence time and instability. Refiners’ experience indicates that at the high temperature end of the preheat train (crude/HVGO and crude/vacuum residue) asphaltene precipitation is the major fouling mechanism, whereas at lower temperatures in the preheat train iron sulphide formation is the major fouling mechanism [28].  22 Gentzis et al.[77] studied the fouling in oil sands bitumens delayed coker furnace by pigging deposit of different layers, and identified the types of coke with microscopy research. Results indicate that pyrolytic carbon gathers around the metal skin; while semicoke is common in bulk deposit. 2.6.1 The Phase Separation Mechanism for Coke Formation Oils may be characterized by solvent fractionation. A common approach defines “maltenes” as the fraction of oil which is soluble in heptane, “asphaltene” as soluble in toluene but insoluble in heptane, and “coke” as insoluble in toluene. The phase separation mechanism was developed by Wiehe [84] based on a series of experiments which gave the following common features of thermal conversion kinetics of residual oils. (1) Maltene or heptane soluble fraction inhibits the formation of coke from the asphaltenes. (2) Maltene or heptane soluble fraction reacts to form asphaltenes, which form coke. (3) There is a solubility limit for asphaltenes to convert to coke in a given oil mixture. (4) Unconverted asphaltenes are the most thermal reactive fraction of heavy oil cuts such as vacuum residue. The mechanism is shown in Figure 2-10. Asphaltenes are comprised of thermally stable, polynuclear aromatic cores with saturate and aromatic pendants. These pendants are thermally cracked with high reactivity to form free radicals. It is hypothesized that the 23 residual oils contains natural hydrogen donors, saturated rings adjacent to aromatic rings, which can donate hydrogen and terminate free radicals. However, the solubility of the asphaltenes decreases as they lose pendants and approach the reaction limit of the asphaltene aromatic core.   (A* = thermally stable asphaltene cores; a = small ring aromatic pendant group or molecule; s = saturated pendant group or molecule; M+ = unreacted maltenes;) Figure 2-11 The Phase Separation Model for Coke Formation [89] At some point, asphaltenes become insoluble during reactions and undergo a liquid–liquid phase separation to form a phase lean in hydrogen donors. In this heavy phase, asphaltene free radicals combine with addition and recombination reactions to form 24 high-molecular weight coke. Phase separation can occur both before and after asphaltene is thermally cracked [90]. In the phase separation model, the generation of asphaltene cores and their precipitation are key steps for coke formation. It is believed [91] that the production of aromatic cores due to the breaking of labile bonds, rather than the polymerization of aromatic species, arises in the initial stages of coking. It was suggested that the main associative force for aggregation of asphaltene cores might be π – π stacking [92]. Savage and Klein [93] also concluded that the pyrolysis of asphaltene produced aromatic cores, maltene and gas products, which is in agreement with the statement in the phase separation model. The application of the phase separation model in the present research is discussed in Chapter 8. It was concluded by Wiehe [84] that the coking reaction is first order in the reactant asphaltene, for both closed tube or open tube reactor. The coking reaction rate constant for the closed tube reactor is 0.026 min-1 at 400°C.  2.6.2 Other Mechanisms for Coke Formation Reyniers and Froment [94] believed there are three mechanisms contributing to deposition of coke layers  in the thermal cracking of hydrocarbons, including heterogeneous catalytic, heterogeneous non-catalytic and homogeneous non-catalytic mechanisms. These generally apply to components of lower molecular mass than asphaltene in vacuum residue. The latter two mechanisms were also investigated by Wauters and Marin [95]. Albright and Marek [96] verified three coking models of in high temperature hydrocarbon pyrolysis, involving metal catalyzed reaction, aromatics as 25 intermediates and the reactions of micro-species with the free radicals on the coke surfaces, respectively. In addition, Wiehe also believed there are at least two other mechanisms for forming coke from oil. These are by polymerization of conjugated olefins, and by insoluble asphaltenes in oil being heated to thermal cracking temperatures, as described in section 2.6.1. 2.7 Hydrodynamic Effects on Fouling Shear stress has been the most effective parameter to link laboratory data to industry applications since poor predictive capabilities were found for fluid flow velocity [41, 97]. Panchal [76] investigated fouling behavior of iron-doped oil with different speed rotating helical impeller. Results showed that fouling rate increased with increase in flow velocity at low Reynolds numbers, indicating diffusion of iron salt into the thermal boundary layer is a controlling step at test conditions; while the experimental result obtained by Watkinson and Li [98] showed that at velocities over 0.7 m/s, fouling rate decreased as velocity was increased, indicating shear stress control.  Flow rate was believed to have a significant effect on asphaltene adsorption. Xie and Karan [99] studied on the kinetics of asphaltene adsorption on a gold surface using a quartz crystal microbalance in a flow-cell system. Results indicated that diffusion of the asphaltene dissolved in the bulk solution to the surface was the rate determining step.  Srinivasan and Watkinson [100] carried out experiments using crude oils where the initial surface and bulk temperatures were held constant. The range of Reynolds number in the experiment was 1100-5600. They found a decrease in the fouling rate as 26 the velocity or Reynolds number was increased. Fouling rate was seen to vary as velocity to the -0.35 power which probably reflects the transition from laminar to turbulent flow. Panchal et al. [101] found that for the threshold crude oil fouling model, the velocity dependence was -0.66 in turbulent flow. Watkinson [102] investigated the influence of flow velocity on fouling rate by testing six oils. Results showed that at fixed surface temperature, the initial fouling rate decreased with increasing velocity, suggesting that the fouling rates in those cases are not controlled by transport step. Wall shear stress values were not reported. 2.8 Summary Fouling in refineries often occurs with two processes, sulphide corrosion and coke formation. In terms of high temperature fouling under incipient coking conditions, H2S is the main corrosive substance. Sulphide corrosion has been widely studied. Early researches mainly focused on the electrochemical principles of corrosion as a type of oxidation reaction. Recent work included mild temperature sulphide corrosion under oil and gas production and transportation conditions and high temperature sulphide corrosion during oil processing. For studies in consideration of restrictive diffusion of sulphide, the iron sulphide scale was discussed extensively as a protective layer. The phase separation model has been accepted as a proper tool to describe coke formation mechanisms from heavy oil fractions under furnace conditions.   27 Chapter 3: Experimental Materials, Apparatus and Procedures 3.1 Test Oil Sample An atmospheric topped bitumen (ATB) oil sample provided by Syncrude Canada Ltd. has been used in the research. ATB is the undistilled bottom fraction from the atmospheric distillation of oil sands bitumen. It is a heavy oil fraction usually with an initial boiling point of 343°C and an atomic C/H ratio of 0.72. The boiling range of Syncrude ATB, which was determined with ASTM D86 [103], is listed in Appendix A.1. The lighter distillation fraction (<343°C) composes 6.84% of the whole ATB sample. Table 3-1 Properties and Ultimate Analysis of ATB (from Syncrude Canada Ltd.) Property Value Density, kg/m3 at 15.6°C 1021.5 Asphaltene, wt% 9.9 Ash, wt% 1.45 MCR, wt% 14.98 API Gravity 7.0 Ultimate Analysis, wt%   C 83.1  H 9.65  S 4.088  N 0.45  In addition, ATB contains much higher concentrations of sulphur, nitrogen and metal elements than crude oils, and asphaltenes are also much more concentrated. The main properties and elemental constituents of the ATB oil sample are listed in Table 3-1. The elemental analysis of metallic constituents was determined from Inductively Coupled Plasma (ICP) using ASTM D5184 [104]. Concentrations of some trace inorganic 28 elements are listed in Table 3-2. A complete elemental analysis for Syncrude ATB is seen in Appendix A.2. Table 3-2 Partial Trace Inorganic Elements Concentration (ICP) Element Concentration, mg/kg Si 775 Fe 744 Al 658 V 142 Ca + Mg 186 K 95 Ti 80 Ni 73  Thermogravimetric analysis (TGA) is widely used to determine the volatile, fixed carbon and ash content of oils and deposits. A detailed introduction of TGA will be discussed in 5.1. Figure 3-1 is the TGA analysis of ATB oil sample. The volatile, fixed carbon and ash content was then determined as shown in Table 3-3. Table 3-3 TGA Analysis of ATB Component Content, wt% Volatiles (<110°C) 0.65 Volatiles (110-900°C) 89.40 Fixed carbon 8.57 Ash 1.38  29 0 20 40 60 80 100 120 14001002003004005006007008009001000 Temperature (°C)Time (s)05101520TGA (mg) Figure 3-1 TGA Analysis of Syncrude ATB Sample 3.2 Test Metal Surfaces Several types of alloy, which are widely used in refinery facilities [105], were investigated, including type 1018 low carbon steel (CS), type 317 stainless steel (SS317), 9Cr-1Mo steel (9-Cr) and Incoloy alloy 825 (Incoloy 825). Carbon steel is the most common material in refinery facilities. 9Cr-1Mo steel is widely used in vacuum furnaces tubes [54]. Type 317 stainless steel and Incoloy 800 or 825 are nickel-based alloys, and are often adopted for return bends and other severe impingement points [20]. Chemical composition ranges of the alloys are shown in Appendix B. Chromium has been recognized as a very effective corrosion resistant element [36, 106, 107]. In order to create a metal surface with minimum corrosion reaction as a reference 30 to the other alloy surfaces, some carbon steel rings were electroplated to deposit a thin layer of chromium onto the rings. This was done by Hudson Plating Company Inc.. The thickness of the chromium layer was determined from a Scanning Electron Microscope to be 0.127mm. Thus the chrome-plated surface was considered as a pure chromium layer without any iron or other elements on the surface. Rings were made from the above alloys to test in the reactor. CS rings were made from type 1018 low carbon steel tubes. 9-Cr rings were made from 9-Cr rods. SS317 and Incoloy 825 rings were made from plate of corresponding materials. The specifications of the rings are seen in Table 3-4. Table 3-4 Specifications of Alloy Rings Specifications Value Outside Diameter, mm 38.1 Wall Thickness, mm 3.05 Height, mm 10  3.3 Experimental Apparatus An isothermal batch fouling unit was established for the research. Constant and uniform temperature can be achieved in an isothermal system for the determination of parameters for a kinetic study. Thus the effect of different alloys to coking and corrosion rates can be determined. Hydrodynamic effects can be studied by changing rotational speeds of the stirred shaft. The whole unit includes a rotating cylinder inside an autoclave, a temperature control system and a data acquisition system, as seen in Figure 3-2. 31  Figure 3-2 Isothermal Batch Fouling Unit 3.3.1 Batch Fouling Reactor The system was based on a 600ml Model 4563 reactor manufactured by Parr Instrument Company. The specifications of the reactor are seen in Table 3-5.  Table 3-5 Specifications of Parr Model 4563 Reactor Cylinder Dimensions  Reactor Size 600mL  Inside Diameter 6.35cm (2.5”)  Inside Depth 20.32cm (8”)  Weight of Cylinder 7.26kg Operating Condition  Maximum Pressure 20.7MPa (3000 psig)  Maximum Temperature 225-500°C (depending on the material of gasket) Electrical Supply  Heater Power 780W  Volts, AC 115V/230V  Maximum Load 10A/5A 32  Figure 3-3 shows the schematic diagram of the reactor. A 600mL reactor made with type 316 stainless steel was surrounded by a 780W mantle heater. A glass liner (2 mm thickness) from Parr Instrument Company which is compatible with the cylinder was used to isolate hot oil from the interior metal wall of the reactor, which otherwise could be subject to corrosion.  Figure 3-3 Structure and Flow Scheme of Model 4563 Stirred Batch Reactor Two type K thermocouples were used to control and record the heating temperature (Th) and bulk temperature (Tb). The former thermocouple is located between the heater and the cylinder and the latter is immersed in the oil within the cylinder close to the test ring surface. The tip of the latter thermocouple was 4mm from the ring surface. Both 33 thermocouple tips and centre of the ring were located approximately at the same level (16.5cm depth from the reactor cap).  The unit was run under high pressure during experiments since the lighter fraction of ATB would otherwise evaporate at experiment temperatures. A Swagelok high pressure proportional relief valve (SS-4R3A1) was used to maintain a uniform system pressure of 2.4 MPa (350 psi) during experiments. Since the maximum working temperature of the relief valve is 121°C while the oil vapour temperature is up to 410°C, the relief valve is connected to the cap of the unit via a 1/4” copper tube of around one meter long. A fan blower is used to cool the oil vapour in the tube before it arrives at the relief valve. The relief valve was open to the atmosphere downstream of a buffer tank filled with sodium carbonate to help remove any acidic gas generated during experiments. In order to seal the unit well at high temperatures, graphite die formed gaskets were used between cap and cylinder. Nitrogen is also connected to the reactor to remove dissolved air from the unit before runs. A magnetic stirrer from Parr Instrument company (Model A1120HC6) with a maximum torque of 1.8 N·m was attached to the top of reactor to drive the shaft. The magnetic stirrer is connected with a stirrer motor which is able to achieve variable rotational speeds of 0 to 1500rpm adjusted with a GKH S-20 speed regulator. The rotation speeds were determined from a REED AT-6 tachometer. Annular rings of different metals are mounted to the shaft by two cylindrical pads of the same diameter as the rings. The two cylindrical pads were made from MACOR® glass ceramic [108]. This ceramic has very stable physical and chemical properties and can 34 be used continuously at 800°C and for short period at 1000°C. To make a rotary cylinder, rings are sandwiched between the two ceramic pads and mounted to a threaded rod (10-24 thread) made of titanium, which has superior corrosion resistance to acid and high strength for long term high temperature rotation. The rod shaft is 21cm in length and 4.83mm in outside diameter. It is mounted in the center of the unit and connected to the magnetic stirrer. 3.3.2 Dual Signals Temperature Control System Temperature control is one of the most crucial factors in fouling research. There are two goals for successful temperature control. The first one is to heat the bulk oil to the desired temperature (380-410°C) in a short time, since extended time at lower temperature (220-350°C) may cause a significant naphthenic acid corrosion on the test metal surface, which should be eliminated in our work. The second one is to maintain a constant bulk oil temperature during the experiment, which is important for repeatable data. The two goals are not easily met with a single signal temperature control. Firstly, the heat demand for a constant Tb is variable during long term experiments due to evaporation of lighter fraction or slight thermal cracking at very high temperatures. Therefore Th may actually change from time to time and constant Th is not able to guarantee a constant Tb. Secondly, controlling the heating with the Tb signal gives hysteresis due to the slow temperature change in the temperature increasing period. It will cause an extremely high Tb and rapid coking of ATB. For these reasons, a dual temperature control circuit was designed to achieve the following functions: 35 • For the increasing temperature procedure, temperature was controlled with the Th signal to limit Tb and heat the ATB to the desired temperature in a short duration (within 1 hour). • When Tb reaches the desired value, the temperature control signal is automatically switched to Tb to achieve a precise control of bulk oil temperature. Temperature control is realized with two Omega CN76000 auto tune process controllers with PID control. More details of the control system are seen in Appendix C. 3.3.3 Data Acquisition Bulk and Heating temperature are measured with two type K thermocouples. System pressure is measured with an Omega PX309-500G5V pressure transducer. Temperature and pressure signals are then recorded with an Omega OMB-DAQ-54 data acquisition module. 3.4 Experimental Procedures 3.4.1 Proper Experiment Duration Proper experiment duration is one of the key considerations in the research. The fouling rate and the corrosion rate are usually expressed in the unit mm/year in the oil industry. However, long term experiments are unpractical in laboratory research. Thus an alternative schedule would be necessary to get reasonable data. Several points need to be considered in decision of proper experiment durations. Firstly, long term experiments will take the risk that properties of the oil sample will have significantly changed during the experiments. Thus shorter experiments are preferred.  36 Secondly, the duration should be long enough for all experiments to get enough deposit for analysis. This is especially important for runs at lower temperature (380°C or lower) since the very small thickness of deposit made it difficult to collect any fouling product from the ring surfaces.  According the preliminary experiments, 24-hour was chosen as the optimum experiment duration. In order to get more details during experiments, 6-18 hours experiments are also adopted when needed. 3.4.2 Pre-experimental Procedure 3.4.2.1 Preparation of Oil Sample ATB is originally stored in large (~170L) steel barrels. Since ATB is highly viscous at room temperature, barrels are slowly heated overnight with two external heating jackets to decrease the oil viscosity. Then the barrels are rolled on the ground for about 30 minutes for a full mixing of the oil to get uniform samples. Samples were then transferred to 4-litre stainless steel pails for convenience in the laboratory. Before an experiment, a pail of oil was slowly heated with a heating pad to about 80°C and well mixed before sampling, and then 300ml oil was transferred to the glass liner. The weight of oil was determined from a Mettler Toledo SB12001 high capacity precision balance. 3.4.2.2 Preparation of Test Metal Ring It is believed that surface roughness contributes to contact angle hysteresis [109], and thus has a significant impact on fouling [110, 111]. Therefore, a consistent surface roughness of the different alloy rings was considered to be crucial to obtain repeatable 37 and convincing data. In order to produce a constant initial surface roughness, all rings were polished in sequence with 4 types of emery paper of 360, 600, 1000 and 1500 grit. Surface polishing also helps to remove probable stains or oxidation layer and exposes fresh surface. The surface roughness was then determined by a Mitutoyo SJ-210 surface roughness tester. Using this procedure, the initial roughness of metal surfaces was maintained in the range of 0.31-0.36μm. Metal rings were then rinsed with water to remove any metal particles generated during polishing, and dried in an oven at 110°C for 30 minutes. 3.4.2.3 Unit Assembly The polished and washed alloy ring was inserted between the two ceramic pads, and mounted to the threaded shaft with two stainless serrated-flange hex locknuts. In order to offset the probable expansion and contraction of metal rings and ceramic pads, stainless steel Belleville disc washers were used between the locknut and ceramic pad. This helped to ensure sufficient tightness of the rotating cylinder during experiments and prevented any slipping. The whole rotating cylinder was then mounted to the reactor lid. The cap and unit are tightened with a pair of clamps with 6 screws. The graphite gasket embedded in the inner track of the cap was carefully checked before closing up the whole unit to ensure a good seal. The whole hermetic unit was weighed and put into the cylindrical heating jacket. Nitrogen, relief valve and thermocouples were connected to the unit. 38 For a leakage test, 0.4 MPa (60 psig) nitrogen was introduced to the unit. All vents were closed up for 30 minutes and the pressure change was monitored. The magnetic stirrer was connected to the rotating shaft after the leakage test. 3.4.3 Experimental Procedures Experiments mainly include air elimination, heat-up period, temperature control period and the cooling period. Pressure and temperature traces during a typical experiment are shown in Figure 3-4. The operating conditions are listed in Table 3-6. 0 5 10 15 20 25050100150200250300350400450500System PressureBulk Temperature Temperature (°C)Time (hour)Heating Temperature050100150200250300350400450500System Pressure (psi) Figure 3-4 Typical Experimental Procedure Table 3-6 Operational Condition of Isothermal Batch Fouling Experiments Operational Condition Value Tb, °C 380-410 F, rpm 150-1200 t, hours 6-24 39 3.4.3.1 Air Elimination Dissolved oxygen in oil has been found to enhance fouling significantly [98, 112]. Preliminary experiments also showed that more coke was found on the wall of glass liner for an ATB sample with dissolved oxygen present than that of a sample without dissolved oxygen at the same experimental conditions. In order to minimize the effect of oxygen and prevent rapid coking during experiments, nitrogen was introduced to the reactor to remove the oxygen dissolved in the ATB. In order to ensure that the oil and nitrogen are well mixed, oil has to be stirred while nitrogen is introduced to the system. Thus the oil should be heated to decrease its viscosity. During this procedure, Th was set to 150°C. The stirring motor was turned on when Tb reached 90°C. The rotational speed is 300rpm. Nitrogen was introduced to the reactor. A vent outlet was opened to allow the mixture of nitrogen and air to be released. This process lasted for 1 hour to remove as much air as possible. Finally the nitrogen flow was stopped and the reactor was sealed with all outlets closed except the relief valve. 3.4.3.2 Heat-up Period After eliminating the air, Tb was set to its desired value (380°C in Figure 3-4), Th was usually 70-90°C higher than Tb. Rotational speed was adjusted according to the experimental design. Since Tb was far below the set-point, Th rose rapidly to the set-point and kept stable afterwards, until Tb approached its set-point. Then the Tb value was used for temperature control and the Th value might change slightly, depending on the variable heat needed to keep Tb stable. The relief valve would automatically open, to release excessive gas and vapour if the system pressure was higher than 2.4 MPa 40 (350 psi), the timer was started when Tb reached its set-point. During experiments, temperature and pressure data were recorded with the data acquisition module and saved to a Microsoft Excel file. Eight temperature or pressure values were collected uniformly for each minute, and the average value was calculated and displayed in the file. 3.4.3.3 Cooling Period When the experiment duration met its target value (6-24 hours), power to the cylindrical heating jacket was turned off. The relief valve was closed and the unit was taken out from the heating jacket. A fan blower was used to cool the reactor down to 100°C within around 20 minutes. Data logging was stopped at the end. 3.4.4 Post Experimental Procedure When Tb was decreased to 100°C, the unit pressure was released to atmospheric pressure. The reactor was first weighed before being opened and the rotating cylinder was taken out. All spent oil was preserved in sample jars for future use. Then the whole cylinder was rinsed carefully with toluene, in order to clean the liquid oil on the metal surface and deposit without disturbing the deposit. Metal rings with fouling on the surfaces were dried at room temperature for 6 hours and preserved in sealed bags. The stainless steel cylinder, cap and thermocouple in the bulk oil were carefully cleaned with toluene. The glass liner, ceramic pads and threaded shaft were heated to 500°C with air flow in a muffle furnace for 4-8 hours to burn out all oil and coke attached. Then those parts were rinsed with water and dried for the next run. Procedures for deposit characterization are discussed in the following corresponding chapters. 41 Chapter 4: The Deposition Build-Up Rate 4.1 Determination of Deposit Thickness, Density and Mass 4.1.1 Features of Fouling Deposit Figure 4-1 shows one type of deposit on the metal surface, as well as some deposit on the ceramic pads. Usually there are several notable features for the deposit on the metal surface.   Figure 4-1 Deposit on the Ring Surface (Carbon Steel, Tb = 380°C, ω = 300rpm, t = 24h) • In many cases the deposit was fragile, and had very weak adhesion on the metal surfaces. Some debris was even lost to the oil during the high speed rotation, as seen in Figure 4-2, where a large chunk of deposit is missing. This makes the determination of deposit mass difficult since it is not easy to get a complete 42 fouling scale. This problem was especially common when the deposit contained primarily iron sulphide, and little carbonaceous material.  Figure 4-2 Deposit on the Ring Surface (Carbon Steel, Tb = 400°C, ω = 600rpm, t = 24h) • In some cases the deposit was porous and soft. The apparent thickness could be easily changed if deposit was compressed with a measuring device such as a micrometer. In this circumstance, it is difficult to determine the exact original thickness of the deposit. This usually occurred when the deposit was mostly organic.  • The thickness of deposit on the same metal surface was usually non-uniform in both axial and azimuthal directions. Thus one single piece of deposit cannot represent the properties of the whole deposit. In this situation, an average thickness is calculated from a number of measurements. 43 Figure 4-3 shows microscopic images of deposits on SS317 (Upper) and on CS (middle) and on 9-Cr (lower). The thickness of deposit was roughly 243µm for the SS317, 54µm for the CS, and 92µm for Incoloy 825, which were determined from the methods discussed below in 4.1.2. Figure 4-3 also shows two typical morphologies for the deposit accumulated on metal surfaces. For the SS317 and Incoloy 825 surfaces, the deposit adhered tightly to the surface. For the CS at the lowest temperature tested, a gap appears between a loose, poorly attached layer which surrounds the surface. This layer can easily be dislodged from the surface and drop into the fluid. It was also reported that the FeS scale formed at lower temperatures (e.g. in oil pipeline) was easily removed from the metal surface [65, 113]. 4.1.2 Determination of Deposit Thickness In consideration of the above-mentioned features, indirect methods were developed to determine the thickness, mass and density of deposit without touching or damaging the deposit. The methods were based on photographs, obtained with a microscope. Before measurements, a ring with deposit was rinsed with toluene and dried at room temperature for 6 hours, as mentioned in 3.4.3. The cross section of the ring was cleaned with caution to show the edge of metal and deposit clearly. Then the cross section of the ring was placed under an Olympus BX41 laboratory microscope equipped with an Olympus U-CMAD3 video camera which obtained microscopic images and transmitted the images to a computer. Sample images are shown in Figure 4-3. A gap between the metal surface and deposit was observed for carbon steel experiment at 380°C, which is in accordance with the work of Stephenson et al. [114], who attributed  the separation to the cooling process. 44    Figure 4-3 Microscopic Images of Deposit for Experiments of 24h at 300rpm (Upper: SS317 at 400°C Middle: CS at 380°C Lower: Incoloy at 390°C) Incoloy Deposit 45 In order to determine the real deposit thickness in the microscopic picture, a standard size was needed for comparison. Thus Images were taken via the same microscope, lens and settings for a 0.1mm gap of a Vernier caliper, as seen in Figure 4-4. Then the real thickness of deposit was calculated using the relative lengths of the gap and the deposit in microscopic images. To minimize the influence of non-uniform deposit, eight circumferential locations were measured for each ring to allow calculation of an average thickness and standard deviation. An Eagletac D25A2 flashlight with 453 lumen output was used to provide enough light for taking microscopic images.  Figure 4-4 Microscopic Image of a Standard 0.1mm Gap 4.1.3 Determination of Density and Mass of Deposit The mass of deposit is usually not easily determined directly, if the deposit is not complete. Thus a photographic method is used. Firstly, several pieces of deposit were collected and were weighed together with an analytical balance of 6 decimal places. Then those pieces of deposit were carefully put together under a thin slide glass. 46 Photographs were taken with a Fujifilm F200 camera for the deposit together with a Vernier caliper, which served as a standard scale, as shown in Figure 4-5.   Figure 4-5 Photograph of Deposit Pieces and Vernier Caliper Photographs were processed by MATLAB to convert the pictures to grayscale maps and finally a binary image. Then the total pixel number was calculated to determine the accurate area of deposit scales. The real area of deposit scales can be determined by means of the Vernier caliper in the photo. Since the thickness of deposit was determined in 4.1.2, the volume of the deposit was readily determined. Then the density of deposit and the mass of a “complete” deposit scale were determined. 4.2 Fouling Rate of Five Metal Surfaces with Bulk Temperature A series of experiments has been completed for different ring materials at bulk temperatures from 380°C to 410°C, for 24 hours with a rotational speed of 300rpm. Figure 4-6 shows the effect of bulk oil temperature on the deposition rate at fixed 47 experiment duration and rotation speed. Error bars represent the standard deviation for two parallel experiments.  380 385 390 395 400 405 410050100150200250300350  Fouling Rate (mm/year)Bulk Temperature (°C)CS9-CrCr-CSSS317Incoloy Figure 4-6 Fouling Rate of Different Ring Surfaces Materials (600rpm, 24 hours) Fouling rate increases with bulk oil temperature for all five surfaces. At bulk temperature of 380°C, deposition rate on all surfaces are quite close to each other, and below 30 mm/year. At 390-400°C, the five surfaces can be divided into two groups based on deposition rate. The deposit film growth rate on CS and 9-chrome surfaces is significantly thicker (~100-150 mm/year) than on the other three surfaces (25-75 mm/year). Deposit on CS and Cr-CS surface increased sharply at 410°C, while the amount of deposit for the other three surfaces did not change markedly compared to the values of 400°C. Chromium has been proven effective as a dehydrogenation catalyst [115, 116]; hence it may enhance coke formation at 410°C for the Cr-CS. 48 Figure 4-7 shows the fouling rate of two groups of experiments on carbon steel with different rotational speeds from 380°C to 410°C, which indicates a mild increase of fouling rate with time for 300rpm experiments compared to that of 600rpm experiments. The reason for the difference will be discussed later. 380 385 390 395 400 405 410050100150200250300350CS 300rpm   Fouling Rate (mm/year)Bulk Temperature (°C)CS 600rpm Figure 4-7 Fouling Rate on Carbon Steel with Different Rotational Speeds 4.3 Summary In most circumstances, isothermal fouling on metal surfaces with a heavy and sour oil resulted in fragile, porous, compressible and non-uniform deposits. This increased the difficulties of accurate measurement of thickness and mass of deposit, as well as some physical properties such as density and porosity. Microscopy methods were thus used to provide better measurements. 49 Proper experiment duration was determined to get adequate fouling product for analysis and avoid significant alteration of oil properties in batch operation. Fouling rate increased with bulk temperature. Deposition rates on carbon steel and 9Cr-1Mo steel were similar, and were significantly higher than on the other three surfaces at the same rotational speed of 300rpm. For carbon steel, higher rotational speeds led to lower deposition rate at the same temperature, which was more obvious at higher temperatures.  50 Chapter 5: Composition and Structure of Deposit 5.1 Basic Components of Deposit – Thermogravimetric Analysis Organic material which represents carbonaceous matter or coke and its precursors, and inorganic material which represents corrosion products, are two essential components of the fouling deposits in this work. These two components are also the products of coking and sulphide corrosion, respectively. Thus partitioning of the deposit into organic and inorganic parts is essential to the research. The separation can be realized with thermogravimetric analysis (TGA), which is a method to characterize thermophysical properties of materials [117]. A method based on the TGA test was developed to effectively separate the deposit into these two mentioned parts. Rings had been washed in toluene to remove oil constituents stuck to the deposit surfaces, before the deposit was recovered. A Shimadzu TGA-50 Thermogravimetric Analyzer with a TA-60WS Thermal Analysis Workstation was used to characterize deposits. A typical TGA graph is seen in Figure 5-1. Before a TGA experiment, deposit from one fouling experiment was well mixed to get a uniform sample. Mass of 15-20mg sample was collected to an alumina cell (dia. 6 x 2.5mm). The cell with sample was then loaded to the balance of the analyzer. Grade 5.0 ultra-high purity nitrogen was introduced to the system to protect the sample from being burned at high temperatures. In the nitrogen environment, a temperature programming process was carried out following the order of Table 5-1.  51 0 20 40 60 80 100 120 14001002003004005006007008009001000 Temperature (°C)Time (s)101214161820TGA (mg) Figure 5-1 A Typical TGA Graph of Deposit Table 5-1 Temperature Programming for Thermogravimetric Analysis of Deposit Samples Stage Temperature before Heating Target Temperature Heating Rate Holding Time* Atmosphere Final Mass of Sample 1 Room Temperature 110°C 10°C/min 30min N2 W1 2 110°C 900°C 20°C/min 30min N2 W2 3 900°C 900°C - 30min air W3 * At target temperature In Stage 1, temperature was elevated to 110°C and held for 30 minutes, for drying of samples. Weight loss during this stage is very small (<1 wt%). In Stage 2, temperature was increased to 900°C and then held for 30 minutes. Volatiles, which are mainly liquid oil fractions insoluble in toluene, or products of cracking were removed in this stage, leaving only the solid part of samples which is mainly fixed carbon (coke) and ash (iron 52 sulphide). In Stage 3, temperature is maintained at 900°C, and the atmosphere was switched from nitrogen to air. Fixed carbon was quickly burned out, leaving ash. In this process, the organic and inorganic components of deposit have been precisely separated. The mass of carbonaceous matter (including volatiles and fixed carbon): 𝑾𝒄 = 𝑾𝒗 + 𝒘𝒇𝒄 = (𝑾𝟏 −𝑾𝟐) + (𝑾𝟐 −𝑾𝟑) = 𝑾𝟏 −𝑾𝟑     (5-1) FeS has the following possible reactions with excess O2 at high temperatures [118, 119]: 4FeS + 7O2 = 2Fe2O3 + 4SO2 FeS + 2O2 = FeSO4 FeSO4 will decompose at about 640°C [120]: FeSO4 = FeO + SO3 2FeO+1/2O2 = Fe2O3 Thus the final product of FeS in stage 3 is Fe2O3. Mass of FeS can be determined from Fe2O3 as: 𝑾𝒂 = 𝑾𝟑𝟏𝟏𝟏.𝟔𝟏 ∗ 𝟐 ∗ 𝟖𝟖.𝟏𝟏 = 𝟏.𝟏𝟏𝒘𝟑       (5-2) This equation is based on the hypothesis that the atomic ratio of Fe to S is 1. Actually this has been proved with the work discussed in section 5.4. Laursen et al. also 53 confirmed this conclusion [81]. With Equation (5-1) and (5-2), one can separate the coke formation process and the corrosion process in the fouling process. 5.2 Carbonaceous Material and Ash in Deposit for Different Metal Surfaces 5.2.1 Overall Composition of Deposits With the methods discussed in 5.1, the deposit or film on the metal surfaces in Figure 4-6 can be separated into carbonaceous material and ash. Figure 5-2 shows the effects of bulk oil temperature on weight percentage of carbonaceous matter in deposits. The remainder is ash. For the Cr-CS ring, deposits were over 98% carbonaceous matter at all temperatures investigated. For the CS and 9-chrome, the percentage carbonaceous matter increased sharply with temperature, from about 18-30% at 380°C, to 90% at 410°C. For SS317 and Incoloy 825, deposits were 75-90% carbonaceous matter at low temperature and 95% at 410°C. At 410°C, deposits are 91-99 wt% carbonaceous matter for all metals tested. This reflects the dominance of the coking reactions in forming deposits at high temperatures. As previously mentioned, two different morphologies of deposit have been observed. Actually the loose layer only occurred on CS and 9-chrome surface at bulk oil temperature of 380°C, where the weight percentage of ash in the deposit is higher than 70%. The separation of deposit and metal surface is considered as the result of density change. Thus it usually initiates at the boundaries where the initial sulphide film was weakest [121]. For higher temperatures on these two surface materials and at all temperature of the other three, a tightly adherent layer was obtained. This appears to be due to the composition of deposit. Where there is a significant weight percentage of 54 inorganic ash, the deposit layer has a weak structure and is less cohesive, and is easily dislodged from the metal. However, if most of the deposit is carbonaceous, it attaches rather tightly to all metals. 380 385 390 395 400 405 410102030405060708090100  Weight Fraction of Carbonaceous Matter (wt%)Bulk Temperature (oC) Carbon Steel 317 Stainless Steel 9-Chrome Carbon Steel (Chrome Plated) Incoloy 825 Figure 5-2 Effect of Bulk Oil Temperature on Weight Fraction of Carbonaceous Matter of Deposit (24h, 600rpm) 5.2.2 Mass of Ash and Carbonaceous Materials Figure 5-3 indicates the effect of bulk oil temperature on the mass of ash in the deposits at fixed experiment duration and rotation speed. For chrome-plated CS, the mass of ash in the deposit after 24 hours was very small and increased uniformly from 0.3mg to 6.9mg as temperature was raised. For the other four surface materials, ash levels were higher, and there was a maximum mass of ash at bulk oil temperature of 390°C. Above this temperature, coke formation dominated, as shown in Figure 5-4, and appeared to 55 result in reduced ash accumulations on these surfaces. For the SS317, and Incoloy 825, the ash content was slightly higher than the Cr-CS, and generally below 10 mg. For CS and 9-chrome, the mass of ash on each metal was very similar, and considerably higher (range 30-60 mg), except for a slightly larger difference at 390°C. Given the large differences in ash formation, and the two clusters of data in Figure 5-3, the five metal surfaces can be assigned to two categories. Carbon steel and 9-chrome are surfaces corroded by the ATB, which is also reported by Rebak [122], Farrell and Roberts [123], while stainless steel 317, Incoloy 825 and chrome-plated carbon steel are non-corroded surfaces under the condition of these experiments. 380 385 390 395 400 405 4100102030405060708090100110  Mass of Ash (mg)Temperature (oC) Carbon Steel Stainless Steel 317 9 Chrome Carbon Steel (Chrome Plating) Incoloy 825 Figure 5-3 Effect of Bulk Oil Temperature on the Mass of Ash in Deposit (24h, 300rpm) There are two potential sources of the inorganic ash in the deposits: corrosion products of the metal surface and inorganic compounds in the oil (Table 3-1). Since the mass of 56 ash for CS and 9-chrome is around 5-10 times of that of the other three metal surfaces under identical operational conditions, most of the ash for CS and 9-chrome presumably comes from corrosion products. 380 385 390 395 400 405 4100100200300400500600700  Mass of Carbonaceous Matter (mg)Temperature (oC) Carbon Steel Stainless Steel 317 9 Chrome Carbon Steel (Chrome Plating) Incoloy 825 Figure 5-4 Effect of Oil Temperature on the Mass of Carbonaceous Matter in Deposit (24h, 300rpm) Figure 5-4 shows the effect of bulk oil temperature on the mass of carbonaceous matter in deposits at fixed experiment duration and rotation speed. The trend was similar to the fouling rates with temperature shown in Figure 4-6. It should be noted that at 380°C, both fouling rates and mass of carbonaceous deposit for all five surfaces were similar to each other. At 390°C and 400°C, CS and 9-chrome had remarkably higher values for both fouling rate and mass of carbonaceous deposit than on the other three metal surfaces for a given temperature. Considering the mass of ash in Figure 5-3, the 57 inorganic metal compounds apparently play a key role in this stage in promoting the accumulation of carbonaceous deposits. 5.2.3 Two Fouling Regimes In consideration of the significant change of mass fraction of carbonaceous materials for corroded surfaces including carbon steel and 9-chrome from 380°C to 390°C, as shown in Figure 5-2, two fouling regimes based on the bulk temperature can be defined according to the dominant deposit composition, in order to describe the remarkable difference of fouling rates and deposit compositions.  • Corrosion controlled regime: at temperatures of 380°C or lower, deposits are mainly corrosion products. • Coking regime: at temperatures of 390°C or higher, deposits are mainly carbonaceous matter arising from thermal coking reactions. For non-corroding surfaces, only the latter incipient coking regime occurred at temperatures tested. 5.3 Radial Deposit Composition Profiles 5.3.1 SEM-EDX Analysis of Deposit Cross Section Scanning electron microscopy (SEM) is a powerful technique for observation and characterization of microstructure, which can contribute to a better understanding of laydown pattern of the deposit. In a scanning electron microscope, the sample surface is swept across with a finely collimated beam of mono-energetic electrons. Thus information on the microstructure was obtained from the back scattered or secondary 58 electrons emitted as a result of the interactions between the beam and surface materials [124].  Energy dispersive x-ray spectroscopy (EDX) is an element identification and quantification method with an x-ray detector added to a scanning electron microscope. Atoms on the sample surface are excited by the electron beam from the SEM, as mentioned in the previous paragraph, leading to the emission of x-rays of certain frequency. The atomic structure will be revealed consequently by the x-ray, which can be analyzed with the energy dispersive detector, which discriminates among x-ray energies. In an EDX analysis, only a few cubic micrometers samples were required [125]. The sensitivity of EDX is 0.1-1 % (atomic percentage) [126]. The profiles of key elements in deposits from metal surface to the outermost layer provide essential information on the initiation and development of deposit. Therefore, radial profiles of deposit have been examined with SEM-EDX. Since the deposit is often fragile and easily detaches from the metal surfaces, it has to be protected before SEM-EDX tests. Water soluble epoxy resin has been used in researches [46] and is believed to be an ideal protector used for embedding electron microscope samples. The procedure contains two steps: Firstly, a ring with deposit was immersed in the epoxy resin solution. After about 20 minutes, the solution turned to solid with a large heat release, and the ring with the deposit would be embedded in the solid epoxy resin. Secondly, to get a profile of elements along deposit cross section, the probe has to be moved to different locations in parallel to the cross section of deposit. Thus a constant 59 distance between the probe and cross section is required. To meet this requirement, the cross section was carefully polished sequentially on a series of rotational discs with four emery papers of 200, 400, 600 1000 grit, followed by 6µm and 1µm diamond papers. Each time a switch was made to a more fine paper, the direction of the ring had to be changed so that the new polishing direction was perpendicular to the texture direction already formed. After the last processing with 1µm diamond paper, the cross section was rinsed and loaded for the test after it was completely dry. Figure 5-5 is the photograph of a metal ring cross section after polishing.  Figure 5-5 Incoloy 825 Ring Cross Section after Being Polished with 200-1000 Grit Emery Papers and Diamond Papers Figure 5-6 is an SEM image of the cross-section of a Cr-CS ring with deposit, mounted in epoxy and polished. The thickness of deposit is about 60µm. The layer of chrome plating is about 110µm thick. Deposit 60  Figure 5-6 SEM Image of Deposit on Cr-CS Surface after a 24-Hour Experiment at 390°C and 300rpm (WD15.0mm, 20.0kV, ×350)  Figure 5-7 SEM Image of Deposit on CS Surface after a 24-Hour Experiment at 390°C and 300rpm (WD15.0mm, 20.0kV, ×2000) 61 Figure 5-7 shows the cross-section of a carbon steel ring with deposit, taken at higher magnification. Due to the large thickness and magnification, the deposit thickness cannot be determined in the image. Fragmentation is observed at the border of CS. 5.3.2 Element Mapping of Iron and Sulphur on Deposit Cross-Section One of the most useful features of SEM-EDX is element mapping [127], which shows the spatial distribution of elements on sample surfaces. It is a useful method for showing compositional zonation. The map is generated by progressively rastering the electron beam over an area of interest point by point [125], to provide a 2D image of chemical zonation. It usually needs 0.5-12 hours to achieve a satisfactory resolution and noise performance [126]. A carbon steel ring with deposit was obtained from an experiment at bulk temperature of 410°C for 24 hours, with a rotational speed of 600rpm. The ring was then protected with epoxy resin and the cross section was polished, as described in Section 5.3.1. The sample was coated in ~20nm of carbon for conductivity. The scanning time is 1.5 hours.  Figure 5-8 shows the element mappings of Fe and S along the deposit cross section. Epoxy resin is on top of the image. Deposit is beneath the resin. The metal is at the bottom of the image. Thickness of deposit, which is measured from the metal edge (Line 1) to the deposit edge (Line 2), is 340 µm.  For sulphur and iron mapping, a transitional zone was found between the metal edge and deposit (immediately above Line 1 in Figure 5-8). The width of the region is around 17-26 µm. The element concentrations of iron and sulphur in this region were significantly different from that in the deposit, which displayed a uniform distribution of 62 the two elements, from the transitional zone to the resin edge (line 2). Thus the bulk of the deposit shows a uniform composition which is different from the near-metal region. Since the sulphur concentration in the transitional zone is even higher than the outer deposit, we may conclude that it was formed mainly before the outer layer covered the surface, which means there was a delay for coking reaction before it started. This is in accordance with the phase separation model for thermal coking [84]. The delay is the induction period in which asphaltene is well dissolved in heptane soluble fractions (maltenes).   (1) S Mapping         (2) Fe Mapping Figure 5-8 Element Mapping of Cross Section of the Deposit 5.3.3 Elements Radial Profiles in Deposit Due to the different profile of sulphur and iron in the transitional zone mentioned in Section 5.3.2, the element distribution in the transitional zone is of interest. For the other parts of deposit, a bulk element analysis will be satisfactory due to the uniform distribution. Therefore, EDX was done for the transitional zone. Several lines were Line 2 Line 1 Epoxy Resin  Bulk deposit  Metal Surface Transitional Zone 63 marked for different locations on cross section, as seen in Figure 5-9. EDX analysis was completed for these locations to get a profile of elements.  Figure 5-9 Locations for EDX Analysis Figure 5-10 and Figure 5-11 are radial profiles of iron and sulphur, respectively, from the surfaces to a 20µm thick outer layer for different surfaces. All experiments are run at 390°C with a rotational speed of 300rpm for 24 hours. The zero value on the X-axis refers to a position just inside of the metal. Thus the weight fraction of Fe is in accordance with the metal composition. Four additional reference lines with different distances from the metal surface were taken to measure the weight percentage of key elements, including iron, sulphur, carbon, chromium, nickel, etc.  64 0 5 10 15 200102030405060708090100  Weight Fraction of Iron (wt %)Distance from Metal Surface (mm) CS SS317 9-Cr Cr-CS INC825 Figure 5-10 Radial Distribution of Iron in Deposit after a 24h Experiment at 390°C and 300rpm 0 5 10 15 200123456789  Weight Percentage of Sulphur (wt %)Distance from Metal Surface (mm) CS SS317 9-Cr Cr-CS INC825 Figure 5-11 Radial Distribution of Sulphur in Deposit after a 24h Experiment at 390°C and 300rpm 65 Figure 5-10 shows that, with the exception of the Cr-CS surface, the weight percentage of iron in deposits decreased significantly (~45%) in a very small distance (~5µm) from the surface. For CS and 9-chrome, the iron concentration values kept decreasing gradually with distance after 5µm, while for the other three surfaces, a relative constant value was achieved after 5-10µm. For Cr-CS, there is virtually no gradient in iron mass fraction, which is at about 10%. Iron mass fraction of Incoloy 825 is similar to that of Cr-CS except that the iron on the Incoloy 825 surface is 2 times higher. In Figure 5-11, the sulphur weight percentage was highest (5-8 wt%) in the zone very close (~2.5µm) to the metal, for Incoloy 825, SS317 and Cr-CS. It then dropped sharply to about 3 wt%. For CS and 9-chrome, beyond a few µm the weight percentage of sulphur gradually decreased with distance in a longer scale. The sulphur includes organic and inorganic sulphur. The atomic ratio of Fe/S can be calculated from Figure 5-10 and Figure 5-11. As shown in Figure 5-12, for locations of different distance from the surface of a given metal, atomic ratio of Fe/S is similar. However, the ratio varies for different metals. For CS, 9-Cr and SS317, the ratio is roughly 3-6. That is, deposits were iron-rich, in comparison to FeS. In contrast, the ratio is 1-2 for Incoloy 825 and Cr-CS. The atomic ratio of Fe/S for the bulk deposit will be discussed in Section 5.4. 66 0 5 10 15 20012345678910   CS SS317 9-Cr Cr-CS INC825Atomic Ratio of Fe/SDistance from Metal Surface (mm)  Figure 5-12 Atomic Ratio of Fe/S in Transitional zone Since the radial profile of Fe in the deposit was measured, it is not difficult to estimate the total iron content in the deposit by integrating the radial profile curve with distance from the metal surface (Figure 5-10 and Figure 5-11). The fitting results are seen in Table 5-2. Table 5-2 Average Iron and Sulphur Concentration and Atomic Fe/S Ratio in Transitional zone Metal Surface Average Fe Concentration, wt% Average S Concentration, wt% Average Atomic Fe/S Ratio CS 46.0 5.9 4.5 9-Cr 50.0 5.1 5.6 SS317 22.8 3.2 4.1 Incoloy 825 10.0 3.6 1.6 Cr-CS 9.3 3.1 1.7   67 The following conclusions can be obtained from Table 5-2: For corroded surfaces such as CS and 9-Cr in the transitional layer, the deposit is about 50% Fe. In fact, the most probable structure of iron compound is FeS, which will be concluded from x-ray diffraction analysis of bulk deposit in Section 5.4. However, the atomic ratio of Fe/S is 1.6-5.6 in the transitional zone, which may indicate an excessive element Fe. Thus the deposit in the transitional zone on corroded surface is very likely to be a mixture of FeS and Fe. Hucinska [54] reported an elemental analysis result of the corrosion layer on a 9-Cr steel tube in vacuum distillation furnace, which indicated that the Fe and S in the corrosion products were 61 wt% and 7 wt%, respectively. This equals to an atomic Fe/S ratio of 5.00, which is very close to the data in Figure 5-12 and Table 5-2. For a non-corroded surface such as Cr-CS and Incoloy 825, the Fe concentration in transitional zone is around 10 wt%, indicating that Fe is still diffusing out of the metal surface into the transitional zone, even for Cr-CS, which has a chromium coating layer over 100μm. The atomic Fe/S ratio is closer to 1 with slightly excessive Fe, compared with the value for corroded surface. Further information may be gained from examining ratios of key metals in the system to indicate transport of iron and other metals transfer from the fluid into the deposit. Nickel and vanadium mainly accumulate in similar oil components (such as porphyrins). The atomic ratios of nickel and vanadium to iron were calculated for feed oil, metal, and deposit, with ICP elemental analysis results, and are shown in Table 5-3. 68 Table 5-3 Atomic Ratio of Nickel and Vanadium to Iron in the ATB, Metal and Deposit  Ni/Fe V/Fe SS317    ATB 0.093 0.209  Metal Surface 0.191 0  Deposit 0.189-0.191 0.007-0.009 Cr-CS    ATB 0.093 0.209  Metal Surface 0 0  Deposit 0.101 0.178  Romeo et al. [128] found nickel in the outer layer of the scale formed when nickel-chrome alloys are sulphided at 700°C in hydrogen sulphide-hydrogen atmospheres. For the SS317, the Ni/Fe in the deposit is similar to that in the metal (Ni/Fe ≈ 0.19), which is over twice that in the ATB. Hence the deposit inorganic content appears to originate from the metal. The V/Fe ratio in the ATB (V/Fe ≈ 0.21) is much larger than that in the deposit (V/Fe ≈ 0.01), which supports the argument that the deposit inorganic material (mainly iron) is from the metal. For the Cr-CS, both the Ni/Fe and V/Fe ratios in the deposits are similar to the respective values in the ATB. Hence for the Cr-CS the deposits appear to originate in the ATB and corrosion of the metal does not play a significant role. This confirms what was found from TGA analysis. 5.4 Crystal Structure of Fe Compounds in the Oil and Deposit Probable forms of iron sulphides from corrosion of mild steel in the petroleum industry include mackinawite (FeS), Troilite (FeS), pyrrhotite (Fe1-xS, x=0 to 0.17), greigite (Fe3S4), pyrite (FeS2) and marcasite (FeS2) [129, 130].  X-ray diffraction (XRD) is used to determine the most probable forms in the present system. XRD is a technique for 69 identification and characterization of compounds based on their diffraction pattern [131]. XRD was used to determine the crystal structure of Fe compounds in the oil and deposit. The method and operation condition are listed in Table 5-4.  Table 5-4 Operating Parameters of XRD Analysis Parameter Value Start Angle 3° Stop Angle 80° Step Size 0.03565° Time/Step 0.5s Total Time 18min Spin Speed 50rpm Voltage 35kV Current 40mA  Deposit samples selected for XRD analysis are listed in Table 5-5. All experiments were carried out at rotational speed of 300rpm, 24 hours. It was of interest to investigate whether insoluble corrosion products suspended in the oil would be incorporated in deposits. Therefore iron oxide particles were added to the oil in two runs, one of which was selected for XRD analysis. For ATB with Fe2O3, 0.319g Fe2O3 (<5 μm) was added to 300ml oil, to double the total (dissolved plus suspended) Fe concentration in the oil.  Table 5-5 Deposit Samples for XRD Analysis Run Bulk Temperature Oil Ring Material 1 380°C ATB Carbon Steel 2 390°C ATB Carbon Steel 3 380°C ATB with 0.319g Fe2O3 added Carbon Steel 4 370°C ATB with Fe2O3 added Ceramic 5 370°C ATB Ceramic  70 Test results indicated the following facts: For Run 1 and 2, the most probable structure is FeS; others are Fe0.99S, Fe0.98S. By contrast, Fe7S8 structure ranks 49 for probability. Thus it is considered that Fe7S8 does not form in the deposit. This conclusion is in accordance with Laursen and Frandsen’s research, which indicated the chemical composition of iron sulphides is equivalent to FeS [81]. For Run 3 and 4 with Fe2O3 added to the oil, both FeS and Fe2O3 are detected in the deposit. The ratio of FeS to Fe2O3 is roughly 1:7.3 and 1:12.7, respectively. This suggests that particulates from the oil contribute little (~10%) to the inorganics in the deposit and also indicates that more Fe2O3 was converted to FeS during 380°C experiments rather than that of 370°C runs. In consideration of atomic Fe/S ratios in the transitional zone discussed in Section 5.3.3, especially for corroding surfaces such as CS and 9-Cr, which are much higher than 1, one can conclude that the transitional zone deposit is very likely to attach to the metal surface rather than to the bulk deposit. Compared to sulphur, the deposit in transitional zone contains excessive iron diffusing from the metal surface, which was also concluded by Pareek [55], who discussed the diffusion of Fe cation through corrosion products (FeS) layer. For non-corroded surfaces such as Cr-CS and Incoloy 825, the atomic Fe/S ratios in the transitional zone are similar to those in the bulk deposit. 71 5.5 Summary Fouling from sour heavy oil under incipient coking conditions involves sulphide corrosion and thermal conversion of carbonaceous material. Thermogravimetric analysis provided the means of measurement for inorganic and organic components in deposit, which represent the two processes mentioned above. Five surfaces were divided into two groups. Corroded surfaces include carbon steel and 9Cr-1Mo steel. Non-corroded surfaces include type 317 stainless steel, Incoloy 825 and chrome plated carbon steel. For corroded surfaces, deposits are mostly corrosion products at temperatures of 380°C and below, and carbonaceous material at temperatures over 390°C. The ash content in deposits on corroded surfaces is roughly 5-10 times that of the non-corroded surfaces.  The radial deposit composition profiles were studied by scanning the cross section of the deposit with an SEM-EDX method. For an experiment with carbon steel at 410°C, element mapping indicated that there was a transitional zone of around 20µm close to the carbon steel edge, which had significantly higher concentration of sulphur and iron. According to the Fe/S ratio, this transitional zone is iron-rich. This zone indicates that there is a period in the early stage of the experiment in which corrosion rather than coking is the main reaction.  XRD results indicated that the chemical composition of the corrosion product of Fe is equivalent to FeS rather than Fe7S8. Particulates from the oil contribute little to the inorganics in the deposit. Atomic ratios of nickel and vanadium also suggested that the 72 deposit inorganic material (mainly iron) originates from the metal surface rather than from the bulk oil.   73 Chapter 6: Hydrodynamic Effects on Fouling 6.1 Shear Stress and Reynolds Number Determination 6.1.1 Shear Stress in Rotating Cylinder System For the present geometry, the shear stress at the surface of the rotating cylinder can be calculated from the rotational speed as [132-134]: 𝝉𝒘 = 𝟏.𝟏𝟖𝟏𝟏𝝆𝑹𝑹−𝟏.𝟑𝒖𝒄𝒄𝒍𝟐          (6-1) In which, 𝑹𝑹 = 𝒅𝒄𝒄𝒍𝒖𝒄𝒄𝒍𝝆𝝁         (6-2) 𝒖𝒄𝒄𝒍 = 𝝎𝒓𝒄𝒄𝒍 = 𝝅𝒅𝒄𝒄𝒍𝑭𝟔𝟏         (6-3) 6.1.2 Density of ATB at High Temperatures A widely used petroleum oil density – temperature relationship chart was developed by Crane Co. [135, 136]. Part of the chart is shown in Figure 6-1. The density of petroleum oils at specific temperatures can be determined if API gravity at 15.6°C (60°F) is known. API gravity is the abbreviation of the American Petroleum Institute gravity, which is a measurement of oil density. It is generally defined as [137]: 𝑨𝑨𝑨 𝒍𝒓𝒂𝒗𝒈𝒅𝒄 =  𝟏𝟏𝟏.𝟏𝑺𝑺− 𝟏𝟑𝟏.𝟏       (6-4) 74 In which SG is the specific gravity of oils @ 15.6°C.  0 50 100 150 200 250 300 350 400 450 5000.20.30.40.50.60.70.80.91.00.3780.5840.70.70.80.91.0  Specific Gravity @ 15.6°CTemperature (°C)1.04 Figure 6-1 Specific Gravity – Temperature Relationship for Petroleum Oils and Cuts  Thus petroleum oils can be classified as light or heavy oil according to the API gravity, as shown in Table 6-1. The specific gravity of the ATB at 15.6/15.6°C is 1.0215, according to Table 3-1. Thus the API gravity of the ATB oil sample can be calculated as 7.0, indicating the oil is very heavy. Table 6-1 Types of Petroleum Oil and Corresponding API Gravities [138] Type of Oil API Gravity Condensates 50-60 Lighter Crudes 30-50 Medium Crudes 20-30 Conventional Heavy Crude 10-20 Unconventional Extra Heavy Crude/Bitumen <10 Vacuum Resid <5  75 Figure 6-1 indicates the correlation of oil specific gravity with temperature is approximately linear for oils with API grade below 19 at temperatures below 538°C (1000°F). The correlation for the ATB density with temperature can be obtained by fitting of selected data in Figure 6-1. R-squared value (0.99997) indicates the linear fitting describes the original data (for oil with API gravity of 7.1) very well. Assuming the slope of the linear fitting for ATB (API gravity of 7.0) is the same value, the ATB density can be determined from the following correlation with a corrected intercept with the specific gravity of the ATB at 15.6/15.6°C: 𝝆 = 𝟏.𝟏𝟑 − 𝟏.𝟏𝟑𝟔𝟏𝟏× 𝟏𝟏−𝟏𝑻(℃)       (6-5) The calculated ATB density for the temperature range of the work is listed in Table 6-2. Table 6-2 ATB Density at Experimental Temperatures Temperature, °C Density, kg/m3 380 823.4 390 818.0 400 812.6 410 807.1  6.1.3 Viscosity of ATB at High Temperatures ATB is a high viscosity oil fraction. Besides, its viscosity is strongly dependent on temperature, especially at temperatures of 200°C and lower. Thus the viscosity of ATB at high temperatures (around 400°C) will be a key parameter for determination of the shear stress. However, it is impractical to measure the viscosity at such temperatures. Thus correlations are developed to estimate the value at high temperature. To achieve a better accuracy, a series of viscosity data at lower temperatures is necessary. 76 6.1.3.1 Viscosity Measurement – Rheometer Method A rheometer is an apparatus applied to measure how a liquid responds to applied forces. Viscosity is a measure of the resistance of a fluid deformed by shear stress, which can be measured by a rheometer. In this research, the viscosity of ATB was determined with a Malvern Kinexus Pro rheometer. This apparatus is a rotational rheometer system, which measures the flow properties and dynamic material properties of the test sample which is under controlled shear deformation. A series of dynamic viscosity values were obtained for temperatures from 20°C up to 180°C. For each temperature, the shear rate is roughly 0.1-8.3 s-1, except at 20°C, for which the shear rate is 0.1-3.9 s-1. 6.1.3.2 Correlation of Viscosity with Temperature Various viscosity-temperature correlations have been proposed since the 19th century [139]. Of those models, the loglog form of correlation was generally accepted as a more accurate correlation type for petroleum oil viscosity prediction. The most widely used correlation for petroleum mixtures is the Walther and McCoull equation, which is also the basis of the ASTM viscosity versus temperature chart [140]. The correlation is expressed as: 𝐥𝐥𝐥(𝐥𝐥𝐥(𝒗+ 𝑹)) = 𝒑 − 𝒒 ∗ 𝐥𝐥𝐥 (𝑻(𝑲))       (6-6) The parameter ν is kinematic viscosity with the unit mm2/s or cSt. T is temperature with the unit K. Coefficients “p” and “q” are constants related to the oil properties. Coefficient 77 “q” is usually referred to as the viscosity-temperature coefficient [141]. Coefficient “e” is equal to 0.7 when  v > 2 cSt [142].  Since it is difficult to obtain the viscosity data of petroleum oil at temperature over 200°C, a long extrapolation is required for the high temperatures in the present work (370-410°C). Thus the fitting quality is of particular importance. Though the viscosity data of ATB at 20-180°C was available, some low temperature data were omitted for a better curve fitting since lower temperature (such as 20 and 40°C) ATB samples were approximately a solid state with very high viscosities over 60000 cSt, which may lead to serious errors for viscosity measurement. In order to determine the proper number of data points, fitting was done for 4-9 points with the Levenberg–Marquardt algorithm. Fitting results and the chi-square of each fit were recorded, as listed in Table 6-3.  Table 6-3 Fitting Quality for Different Numbers of Points Number of Points p q Chi Square Number of Iterations 9 9.00844 3.33003 1.143 x 108 5000 8 9.03206 3.34481 2.971 x 105 5000 7 9.03804 3.35039 15.709 212 6 8.9265 3.30666 1.040 5000 5 8.85069 3.27722 0.276 349 4 8.75718 3.24129 0.005 364  According to the table, seven points fitting may be a proper choice with enough data and satisfactory fitting quality. The data for 20 and 40°C were then excluded for the fitting. Values “p” and “q” are finally determined as 9.03804 with a standard error of 4.86297×10-4 and 3.35039 with a standard error of 5.26772×10-4. Therefore, the Walther and McCoull equation can be expressed as: 78 𝐥𝐥𝐥(𝐥𝐥𝐥(𝒗+ 𝟏.𝟖)) = 𝟏.𝟏𝟑𝟖𝟏𝟏 − 𝟑.𝟑𝟏𝟏𝟑𝟏 ∗ 𝐥𝐥𝐥 (𝑻(𝑲))     (6-7) The measured values with the rheometer and the calculated values with the Walther and McCoull equation are shown in Figure 6-2. Thus the viscosity values of ATB at experimental temperatures (380-410°C) are listed in Table 6-4. 0 100 200 300 4001101001000100001000001000000   Measured Value Calculated ValueKinematic Viscosity (cSt)Temperature (°C)  Figure 6-2 Walther and McCoull Correlation of Viscosity – Temperature Table 6-4 Calculated Viscosity of ATB at Experimental Temperatures T, °C Kinetic Viscosity, cSt Dynamic Viscosity, mPa·s 380 1.84 1.51 390 1.72 1.41 400 1.62 1.32 410 1.53 1.23  79 6.1.4 Shear Stress and Reynolds Number with Rotating Speeds Shear stress at the rotating surface and Reynolds number under the present experimental conditions can be determined from the equations in 6.1.1, as seen in Figure 6-3 and Figure 6-4. 0 300 600 900 1200 1500048121620  Shear Stress (Pa)Rotating Speed (RPM) 380°C 390°C 400°C 410°C Figure 6-3 Shear Stress with Rotating Speeds It can be concluded in Figure 6-3 and Figure 6-4 that shear stress and Reynolds number increase with increasing rotational speed. Both shear stress and Reynolds number have slight variations at different temperature, mainly due to the change of oil viscosity. For rotational speeds used in the present work, the minimum Reynolds number is around 6000 (150rpm at 380°C). Thus turbulent flow patterns are expected for all experiments. 80 0 300 600 900 1200 150001020304050607080  Reynolds Number (x103)Rotating Speed (RPM) 380°C 390°C 400°C 410°C Figure 6-4 Reynolds Number with Rotating Speeds 6.2 Effects of Shear Stress 6.2.1 Effect of Shear Stress on Deposition Rate and Properties Two fouling regimes designated as the corrosion controlled regime and the incipient coking regime have been discussed in Section 5.2. In the present chapter, the effect of wall shear stress was studied with carbon steel rings and Syncrude ATB under the two regimes, at rotational speeds of 150-1200rpm. Experiment duration was 24 hours and the pressure was set at 2.4MPa (350 psi). After each run, deposit thickness was determined. Fouling rate and deposit density at different wall shear stress values under both the corrosion controlled regime and the incipient coking regime are seen in Figure 6-5 and Figure 6-6.  81 0 2 4 6 8 10 12 1420406080100120140  Fouling Rate (mm/year)Wall Shear Stress (Pa) 380°C 390°C Figure 6-5 Deposition Rate on Carbon Steel Rings versus Wall Shear Stress at 380°C and 390°C As shown in Figure 6-5, fouling rate is 10-30 mm/year and 40-130 mm/year for the corrosion controlled regime (380°C) and the incipient coking regime (390°C), respectively. For the corrosion controlled regime, fouling rate declined significantly as wall shear stress increased to 1Pa, and then remained constant at wall shear stress to 14Pa. For the incipient coking regime, the fouling rate was about four times higher at shear stress of 0.5 to 2 Pa, and then dropped sharply as wall shear stress was raised above 3 Pa. Deposit rate is very sensitive to wall shear stress in this range.  82 0 2 4 6 8 10 12 14 160.60.81.01.21.41.61.82.02.2   380 °C 390 °CDensity (g/cm3 )Shear Stress (Pa)  Figure 6-6 Deposit Density versus Wall Shear Stress at 380°C and 390°C Figure 6-6 indicates that deposit density increases with increasing wall shear stress at both temperatures, i.e. at a given temperature, higher wall shear stress resulted in more compact deposits. For the 390°C experiments, deposit density is 700-1400 kg/m3 which is close to 700-1100 kg/m3 reported for petroleum coke by Edwards et al. [143]. For 380°C, the deposit density (1200-2100 kg/m3) is higher than at 390°C, as the deposit contains more FeS. As mentioned previously, TGA was adopted to determine the weight of carbonaceous matter and ash in the deposits. Results are seen in Figure 6-7 and Figure 6-8. At 380°C (Figure 6-7), the mass of ash is about 5 times the mass of carbonaceous material in the deposit, and both components are independent of the wall shear stress. Deposits averaged 83 wt% ash and 17 wt% carbonaceous content. At 390°C (Figure 6-8), the 83 carbonaceous deposition rate increased with increasing shear stress in the low shear stress region (0-3 Pa), presumably because larger shear stress enhanced the mass transfer of asphaltene in the liquid oil. A transitional shear stress region (3-4 Pa) was found in which deposit composition changed markedly, from being predominantly carbonaceous to a uniform ash-carbonaceous content of 53 wt% ash and 47 wt% carbonaceous contents at higher shear stresses. Hau [144] also reported that increasing fluid velocity didn’t evidently change the corrosion rate. 0 2 4 6 8 10 12 14 16050100150200250300   Carbonaceous AshMass (mg)Shear Stress (Pa)  Figure 6-7 Mass of Carbonaceous Matter and Ash for Corrosion Controlled Regime (380°C) 84 0 2 4 6 8 10 12 14 1650100150200250300  Mass (mg)Shear Stress (Pa) Carbonaceous Ash Figure 6-8 Mass of Carbonaceous Matter and Ash in Deposits for Incipient Coking Regime (390°C) The effect of wall shear stress appears to be limited to carbonaceous deposition which requires adhesion of the organic deposit to the surface. When corrosion is involved, inorganic deposits result which are not affected by wall shear stress over the range tested.  6.2.2 Porosity of Deposit Porosity of the deposit is an important parameter since it has a great effect on diffusion of H2S from the outer deposit layer to the metal surface. The porosity can be calculated with the bulk density and real density of the deposit. Typically, the real density is roughly 2110 kg/m3 (2080-2140 kg/m3) for petroleum coke [145, 146], and 4840 kg/m3 for FeS [147]. These density values, when compared to bulk values in Figure 6-6, indicate that 85 the deposit is porous, and the porosity will change under different wall shear stress. The porosity can be determined from the following equation: 𝜺 = 𝟏 − 𝝆𝑫𝝆𝒓,𝑫          (6-8) where ε is porosity of deposit, ρD is bulk density of deposit, kg/m3; ρr,D is real density of deposit without pores, kg/m3.  The porosity is shown in Figure 6-9. It is interesting that even though the composition of deposit differs greatly, the porosity is close for similar wall shear stress for the two temperatures. This may indicate that the porosity of FeS and coke can be treated roughly as a function of wall shear stress in a narrow temperature range. In fact, experiments with Incoloy 825 for 360rpm at 390°C and 410°C showed very close densities of deposit (715 and 702 kg/m3). Since the deposit can be treated as pure coke (no corrosion product), it may indicate that the porosity of coke is independent of bulk temperature. With this assumption, it can be proved that the porosity of deposit is a function of shear stress and composition (i.e. mass fraction of FeS), as seen on Figure 6-9. Thus a generalized correlation of porosity with wall shear stress can be estimated as: 𝜺 = 𝟏.𝟑𝟏𝟖𝟖𝑹− 𝝉𝒘𝟏.𝟖𝟐𝟏𝟏 + 𝟏.𝟑𝟏𝟏𝟏       (6-9) where τw is wall shear stress, Pa. Detailed calculations are seen in Appendix H. 86 0 2 4 6 8 10 12 14 160.400.450.500.550.600.650.70  PorosityWall Shear Stress (Pa)  Figure 6-9 Wall Shear Stress Effects on Porosity of Deposit of 380-390°C Experiments 6.3 Summary Shear stress, which is a function of fluid properties and flow velocity, is an essential parameter to describe the hydrodynamic effects on fouling behaviour. In order to determine the shear stress on the metal surface at high temperatures and different rotational speeds, density and viscosity of oil at high temperatures was estimated. Thus the shear stress and Reynolds number can be obtained with proper correlations. The effects of shear stress on fouling rate on carbon steel surfaces were significantly different for 380°C and 390°C experiments. A sharp decrease of fouling rate was found when the shear stress was raised above about 3 Pa for 390°C experiments. This change is mainly because of the decreasing rate of carbonaceous material 87 accumulation. The mass of ash content in the deposit was independent of the wall shear stress at 380°C and 390°C. Porosity of deposit is a key parameter in sulphide corrosion. Higher wall shear stress resulted in more compact deposits (higher density), which corresponds to lower porosity of deposit. The porosity of deposit can be treated roughly as a function of wall shear stress in the temperature range of the present work.    88 Chapter 7: Sulphide Corrosion Fouling with iron sulphide formation includes two processes: corrosion of the metal and coking on metal surfaces. These two types of reaction were analyzed respectively for a better understanding of the entire fouling mechanism. First the corrosion process is considered. As mentioned in Section 2.4.2, sulphide corrosion in the absence of carbonaceous fouling will lead to the outward growth of an iron sulphide film, according to the relative molar volumes of FeS and Fe. For each millimeter of Fe reacted, the thickness of FeS film will be 2.56mm. The coking process will be discussed in the last section of this chapter. 7.1 Active Sulphur Species in the ATB Sulphur species in crude oil and its distillates have been studied for decades. Key information was summarized in Section 2.4.1. The following statements apply to heavy oils such as ATB: • Elemental sulphur and hydrogen sulphide concentrations are negligible in heavy oil. Thiol is the lowest concentration organic sulphur species in heavy oil, especially in 300°C+ fractions. Disulphides only exist at significant levels in <250°C fractions. • Most (70-80%) sulphur species in heavy oil are thiophene derivatives and other thioethers (20-30%) [148-150]. More than half of thiophene occurs with 5+ ringed species. Thiophene derivatives are so stable at high temperatures that they can 89 only decompose to small thiophene derivatives. Thiophene cores are very difficult to destroy to release active sulphur (H2S) without catalysts. • Although thioether is stable, it is still able to decompose to thiol, H2S, alkene and thiophene [151]. Then thiol rapidly decomposes to H2S and alkene. Therefore, the H2S in our oil is very likely to come from thioether. 7.2 Sulphide Corrosion Model A brief introduction to generic linear and parabolic corrosion models was provided in Section 2.4.2. For in situ sulphide corrosion, the corrosion reaction occurs on the metal surface, thus the corrosion rate is considered to involve three processes including transport of sulphur species from bulk fluid to deposit edge, diffusion of sulphur species through the deposit or corrosion film to the metal surface, and corrosion reaction on the metal surface. Therefore, the corrosion rate, with the unit of kg/(m2·s), can be expressed as [152]: ∅𝒄 = 𝝆𝒄 𝒅𝒄𝒇𝒅𝒅 = 𝟏𝑨 𝒅𝒘𝒅𝒅 = 𝒄𝒃𝟏𝒌𝒎+𝒄𝒇𝑫𝒇+𝟏𝒌𝒓𝒄𝒘𝒏−𝟏       (7-1) For the present case, cb is bulk concentration of active sulphur species; km is the mass transfer coefficient; yf is the thickness of the corrosion layer (FeS); Df is the diffusion coefficient for active sulphur species through the FeS layer; kr is the rate constant for the n-th order reaction of the active sulphur species with the metal; cw is the concentration of active sulphur species adjacent to the metal wall. As is evident from 90 Equation (7-1), the corrosion rate, Φc, can be also expressed in terms of the thickness of deposit, yf. Where exernal mass transfer is rate controlling, the corrosion process occurs at a constant rate. ∅𝒄 = 𝝆𝒄 𝒅𝒄𝒇𝒅𝒅 = 𝒌𝒎𝒄𝒃         (7-2) and yf increases linearly with time: 𝒄𝒇 = 𝒌𝒎𝒄𝒃𝝆𝒄 𝒅          (7-3) If diffusion of active sulphur species through the corrosion product layer is the rate determining step, Equation (7-1) can be simplified as: ∅𝒄 = 𝝆𝒄 𝒅𝒄𝒇𝒅𝒅 = 𝒄𝒃𝑫𝒇𝒄𝒇           (7-4) 𝒄𝒇𝒅𝒄𝒇 = 𝒄𝒃𝑫𝒇𝝆𝒄 𝒅𝒅         (7-5) Integration of Equation (7-5) gives the parabolic corrosion equation. 𝒄𝒇𝟐𝟐+ 𝒄 = 𝒄𝒃𝑫𝒇𝝆𝒄𝒅          (7-6) When t = 0, yf = 0. Thus c = 0. 91 Equation (7-6) can be rewritten as: 𝒄𝒇𝟐 = 𝟐 𝒄𝒃𝑫𝒇𝝆𝒄𝒅          (7-7) If resistance to transport or diffusion of active sulphur species can be neglected, then cb = cw, and the following equation can be obtained for chemical reaction control: 𝒄𝒇 = 𝒌𝒓𝒄𝒃𝒏𝝆𝒄 𝒅          (7-8) Thus a parabolic rate law Equation (7-7) will be observed for diffusion controlled corrosion, which was discussed a lot for high temperature oxidation and corrosion [153-157], and liner rate laws result when either external mass transport controls (equation (7-3)), or corrosion reaction controls (Equation (7-8)) [158]. 7.3 Corrosion Reaction Analysis According to modified McConomy curves discussed in Section 2.4.2, corrosion rates of carbon steel at 380°C and 390°C for oils of 0.6 wt% sulphur content, which are determined from the disappearance of iron layer, are expected to be 1.48 and 1.65 mm/year, respectively. Since the sulphur content in Syncrude ATB is 4.1 wt%, the corrosion rate multiplier is around 2.0. Thus in the absence of coking, the expected corrosion rates in the present work are 2.96 and 3.30 mm/year, respectively, and increases by 11.5% from 380°C to 390°C. By comparison, the average measured corrosion rates, which were determined from the ash formation rate from TGA results (Figure 6-7 and Figure 6-8) with Equation (5-2), are 2.72 and 2.35 mm/year, 92 respectively. The measured corrosion rate, in the presence of carbonaceous deposition, decreases by 13.6% from 380°C to 390°C. The corrosion rate for the metals in modified McConomy curves can be expressed as: 𝒓𝒄 = ∅𝒄𝝆𝒅 = 𝒅𝒄𝒇𝒅𝒅 = 𝒌𝒄𝒄𝒔𝒏 = 𝑨𝒄𝒄𝒔𝒏𝑹𝒅𝒑 �− 𝑬𝒂𝒄𝑹𝑻�     (7-9) where the unit of rc is m/s. The lumped constant Ac contains an alloy factor to account for the corrosion rate of different alloys; cs is the sulphur concentration on the surface where corrosion occurs; and csn is proportional to the corrosion rate multiplier. Eac is the activation energy of carbon steel corrosion, J/mol. The expression of the multiplier can be obtained by curve-fitting of data on the corrosion rate multiplier in Figure 2-8 with a power form correlation. As determined from Figure 7-1, n is roughly 0.37. 93 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.0400.20.40.60.81.01.21.41.61.82.02.2  Corrosion Rate MultiplierMass Fraction of S  Figure 7-1 Corrosion Rate Multiplier Curve Fitting Thus the multiplier, AM can be expressed as: 𝑨𝑴 = 𝟔.𝟏𝟐𝟑𝟏𝟖𝒘𝒔𝟏.𝟑𝟔𝟏𝟔𝟏         (7-10) where ws is mass fraction of sulphur. The temperature dependence can be expressed via Arrhenius form as: 𝒍𝒏(𝑹𝒄) = 𝒍𝒏(𝑨𝒄𝒄𝒔𝒏) − 𝑬𝒂𝒄𝑹 �𝟏𝑻�       (7-11) With assumed constant cs, activation energy Eac can be obtained by plotting ln(Rc) versus (1/T) in the range of 380-400°C, as shown in Figure 7-2, where the activation energy is calculated as 32.1 kJ/mol. 94 1.48 1.49 1.50 1.51 1.52 1.530.350.400.450.500.550.60  ln(Rc)1/T (103K-1)Equation y = a + b*xWeight No WeightingResidual Sum of Squares3.48304E-4Pearson's r -0.9961Adj. R-Square 0.99144Value Standard Errorln(r)Intercept 6.32928 0.16319Slope -3.86506 0.10822 Figure 7-2 Arrhenius-Type Plot of the Sulphide Corrosion Rate According to McConomy Curves The same calculation procedure was used to determine the activation energy in the same range of temperature for the rate of corrosion (measured by ash content) in this work, as shown in Figure 7-3. For experiments in the temperature range of 380-400°C and at 300 rpm, in the presence of carbonaceous deposition as the temperature increased, the growth rate decreased, corresponding to an activation energy of corrosion of -99.2 kJ/mol. Therefore, when fouling accumulates on the surface, the temperature affects the film growth rate in the opposite direction compared to the circumstance when there is no fouling on the surface. 95 1.48 1.49 1.50 1.51 1.52 1.530.20.30.40.50.60.70.80.9  ln(r)1/T (103K-1)Equation y = a + b*xWeight No WeightingResidual Sum of Squares4.57701E-5Pearson's r 0.99984Adj. R-Square 0.99938Value Standard Errorln(r)Intercept -17.46152 0.31723Slope 11.9305 0.21032 Figure 7-3 Arrhenius-Type Plot of the Sulphide Corrosion Rate in Presence of Fouling (mm/year) According to McConomy curves and the multiplier, the corrosion rates of 380°C and 390°C are 3.08 mm/year and 3.40 mm/year, respectively, in the absence of fouling. This compares to the average value of 2.81 mm/year and 2.46 mm/year in the present experiments with fouling. This suggests that at 380°C, the deposit thickness rate decreases by 8.8%, and at 390°C, it decreases by 27.6%, due to the fouling on the surface. Thus the fouling process appears to inhibit the corrosion, which was also supported with the positive sloped mass of ash versus temperature shown in Figure 5-3, for T≥ 390°C.  96 7.4 Effect of Additional Organic Sulphur Experiments were carried out with 28ml dimethyl sulphide (DMS) added to 300g oil to double the organic sulphur content in the ATB, at the bulk temperatures of 380 and 390°C, and 600 rpm at 2.4 MPa (350 psi). Table 7-1 shows the change of deposit thickness with additional organic sulphur species. Increasing sulphur content resulted in increased deposit thickness in both experiments.  Table 7-1 Effects of Additional DMS Bulk temperature, °C 380 390 Deposit Thickness    Without DMS, µm 55.0 287.4  With DMS, µm 82.8 322.2  Change, % 51 12 Mass of Ash    Without DMS, mg 81.6 123.0  With DMS, mg 133.1 142.3  Change, % 63 16 Mass of Carbonaceous Matter    Without DMS, mg 30.9 259.2  With DMS, mg 44.3 269.9  Change, % 43 4  The sulphur content of the original ATB sample is 4.088 wt%. The new added DMS concentration is also 4.088 wt% (1302 mol/m3). Thus the sulphur content of the sample with DMS added is 8.2 wt%. The corrosion rate multiplier, which can be determined from Equation (7-8), is 2.0 for the original ATB sample and 2.6 for the sample with DMS added, Therefore, a 30% higher corrosion rate (FeS formation rate) with adding DMS is expected. For comparison, the mass of ash increase in Table 7-1 was 63% for 380°C, 97 where deposits are typically 70 wt% ash, and 16% for 390°C, where deposits are typically 30 wt% ash. The fact that corrosion rate increased significantly for 380°C (much higher than 30%) can be explained as follows. The active sulphur species are only a part of the total sulphur species in the ATB. Thus when the total sulphur content is doubled with DMS, the change of active sulphur species is even larger. Assuming 380°C experiments are completely corrosion controlled (no diffusion resistance), the active sulphur content after adding DMS would be 3.8 times that of the oil without adding DMS, according to the multiplier. Thus the active sulphur content of ATB can be estimated with the following equation: 𝟏.𝟏𝟏𝟏𝟖𝟖+ 𝒘𝒔,𝒇 = 𝟑.𝟖𝒘𝒔,𝒇         (7-12) where ws,f is the mass fraction of active sulphur species in the ATB, and is 0.0146 according to the above equation. Thus only about 36 wt% of total sulphur species contributes to corrosion. For the 390°C experiment, the mass of ash increased only by 16%. Apparently coke on the ring surface hindered the corrosion reaction. For the 380°C experiment, carbonaceous matter increased by 43% after adding DMS, indicating more corrosion product brings more coke. This fact agrees with Wiehe’s model, which assumes the FeS layer assists the adherence of asphaltene. For the 390°C experiment, the FeS layer is completely covered with thick coke deposit, leading to a very low FeS concentration on deposit outer surface. Thus the amount of carbonaceous matter was almost constant, rather than being affected by the FeS layer. 98 7.5 Threshold Chromium Content for Sulphide Corrosion Resistance Chromium has been proven to be an effective corrosion resistance element [106]. It is proposed that a multi-layered scale forms due to the sulphide corrosion in hydrogen free environments. The scale includes a mixed Fe1-xS and FeCr2S4 layer inside and a Fe1-xS layer outside. With the increase of Cr content in the alloy, a single layer of FeCr2S4 is expected, which is believed to be more stable and protective than Fe1-xS [159]. Figure 7-4 shows the influence of the nominal chromium contents in metals on the weight percentage of iron at locations of different distance from surfaces. For Cr-CS, the chrome plating is assumed thick enough that the surface behaves as 100 % chromium. Sudden changes in iron content of deposits were seen when weight percentages of chromium in metals were 15-20 wt%. When chromium content was 20 wt% or higher, the Fe contents in deposit was decreased to around 1/5 of the value when chromium content was lower than 15 wt%.. The effect of chromium on corrosion performance has been widely studied in other systems. Mrowec et al. [13] proposed three different mechanisms of formation of sulphide scales corresponding to chromium content, i.e. low chromium content (up to 2 at% or 1.9 wt%), intermediate (2-40 at% or 1.9-38.3 wt%) and high (above 40 at% or 38.3 wt%) in sulphur vapour at 700-1000°C. Corrosion tests in 1 N HCL by Naka et al. [23] indicated addition of up to 20 at% (18.9 wt%) of chromium to boron-bearing alloys doesn’t affect the corrosion resistance; while the addition of 30 at% (28.5 wt%) or more chromium significantly decreases the corrosion rate. Delabrouille et al. [24] believed that in 360°C water, continuous and compact layers of chromium oxide formed for alloys which contain more than 10 wt% chromium. This layer would cover the metal surface, and protect the alloy from corrosion. 99 0 20 40 60 80 100010203040506070  Mass Fraction of Fe in Deposit (wt %)Mass Fraction of Cr in Metal (wt %) 2.5um from surface 5um from surface 10um from surface 20um from surface Figure 7-4 Effect of Weight Percentage of Cr in the Metal Rings on the Weight Percentage of Fe in Deposit at Different Distances from the Metal Surface after a 24-Hour Experiment at 390°C and 300rpm Figure 7-5 illustrates the influence of chromium content in the metals on the mass of ash in deposit at different temperatures, which reveals the corrosion resistance performance of the different alloys. In this figure, the mass of ash in deposit is shown to be significantly affected by temperature, and is much higher when the mass fraction Cr in the metal was less than about 15-20 wt%. However, for the alloys containing more than 15-20 wt% chromium, the mass of ash is evidently lower than that on the low chromium content alloys, and is not very dependent on bulk temperatures. This also demonstrates that 15-20 wt%. of Cr content is a boundary for metals which perform differently in high temperature sulphide corrosion. Past research [22] also showed that the corrosion rates of H2S on metals with 18% and 11-13% Cr are significantly different. 100 0 20 40 60 80 100020406080100  Mass of Ash in Deposit (mg)Mass Fraction of Cr in Metal (wt %) 380oC 390oC 400oC 410oC Figure 7-5 Effect of Weight Percentage of Cr in the Metal Rings on the Mass of Ash in Deposit at Different Temperatures after a 24-Hour Experiment at 300rpm According to the Modified McConomy curves, the corrosion rate of carbon steel is around 8.6 times that of 9-chrome and 27 times of that of 18/8 stainless steel, indicating a significant change of corrosion rate when chromium content is increased from 9 wt% to 18 wt%, which is consistent with the present results at 380°C for carbon steel. The mass of ash is about 40mg for 15 wt% Cr, and 5mg for 20 wt% Cr. 7.6 Summary In processing of heavy oil cuts such as ATB, sulphide corrosion mainly comes from H2S generated from thermal decomposition of thioethers. The active sulphur was estimated to comprise around 36 wt% of the total sulphur in the ATB. 101 Sulphide corrosion usually occurs in three steps, namely transport of sulphur species from bulk fluid to the deposit edge, diffusion of sulphur species through the deposit or corrosion film to the metal surface, and the corrosion reaction on the metal surface. For diffusion controlled corrosion, a parabolic rate law will be observed. Modified McConomy curves from the literature show the effects of temperature and sulphur content in oil on sulphide corrosion rates in the absence of coke deposition, and were used to assist the analysis of sulphide corrosion in the present work. An activation energy was calculated for the sulphide corrosion for experiments with coking, which indicated an inhibition effect of the carbonaceous deposit layer on sulphide corrosion. Dimethyl sulphide was added to ATB to investigate the effect of increased sulphur content on sulphide corrosion. Results indicated that the promoting effect of higher sulphur content was more evident at 380°C where coke deposition is minimal than at 390°C where coking rates are higher.  Chromium was proved to be a key element to slow down the sulphide corrosion. The threshold chromium content for sulphide corrosion resistance is 15-20 wt%.   102 Chapter 8: Carbonaceous Material Deposition Coking is an important source of fouling, especially at higher temperatures (>390°C). This reaction occurs both in the bulk oil and on the ring surfaces. In this chapter, the coking process will be described with the phase separation model, which was proposed by Wiehe [89]  and has been proven to be a successful coking reaction model.  8.1 The Phase Separation Mechanism for Coke Formation The phase separation kinetic model can be described as follows [89]: 𝑴+𝒌𝑴� 𝒎𝑨∗ + (𝟏 −𝒎)𝑽 𝑨+𝒌𝑨� 𝒂𝑨∗ + 𝒃𝑴∗ + (𝟏 − 𝒂 − 𝒃)𝑽 Solubility Limit:    𝑨𝒎𝒂𝒅∗ = 𝑺𝑳(𝑴+ + 𝑴∗) 𝑨𝑬𝒅∗ = 𝑨∗ − 𝑨𝒎𝒂𝒅∗  𝑨𝑬𝒅∗ ∞→ 𝒄𝑯∗ + (𝟏 − 𝒄)𝑻𝑨 where: M+ is unreacted heptane solubles (maltenes), wt%; M* is heptane soluble cores, wt%; A+ is unreacted asphaltenes, wt%; A* is asphaltene cores, wt%; V is volatiles, wt%; TI is toluene insoluble coke, wt%; SL is solubility limit. A*max is maximum asphaltene cores that can be held in solution; A*Ex is excess asphaltene cores beyond the solubility limit; kM is first order rate constant for the thermolysis of heptane solubles, min-1; kA is first order rate constant for the thermolysis of asphaltenes, min-1; m, a, b and 103 y are stoichiometric coefficients. Note that two reactions which produce A* occur in parallel. A series reaction model has also been proposed [89]. Wiehe [89] developed the following equation to describe the yield of coke (toluene insolubles) as a function of time and temperature, assuming that coking reaction is first order in the concentration of asphaltenes: 𝑻𝑨 = 𝟏−𝒄𝟏+𝒄𝑺𝑳�𝒎(𝟏𝟏𝟏 − 𝑨𝟏)− (𝒎 + 𝑺𝑳)(𝟏𝟏𝟏 − 𝑨𝟏)𝑹−𝒌𝑴𝒅 + 𝑨𝟏(𝒂 − 𝒃𝑺𝑳)�𝟏 − 𝑹−𝒌𝑨𝒅��   (8-1) where TI is the weight fraction of toluene insoluble fraction, which refers to coke, wt%. TI is positive only after the induction period ends. The steps of derivation are shown in Appendix D. 8.2 Determination of Asphaltene and Heptane Solubles Concentration Concentrations of asphaltenes and heptane soluble fractions in ATB after different experiment durations were key parameters in the phase separation kinetic model. In this work, they were determined using ASTM methods. The sediment extraction apparatus described under ASTM D473-07 is seen in Figure 8-1. The whole protocol used was designed also with reference to ASTM D6560-12. Whatman Grade 42 (110mm diameter) filter paper of pore size 2.5μm is used for asphaltene collection. 0.5-1g oil was sampled to the dried cone-shape filter paper. The filter paper was then mounted to the bracket and put into the flask with n-heptane in it. The whole apparatus was heated on a heating station to keep n-heptane or toluene boiling (98.4°C-110.6°C). Cooling water flows through the cooling coil near the top of the flask, to condense the n-heptane vapour, forming drops, which fall off the bottom end of the cooling coil to the cone-104 shape filter paper to wash out all oil components except asphaltene, coke and ash. Then the bracket with filter paper was dried in oven for 1 hour and weighed. Then the same procedure was used with toluene as was done with heptane to determine the asphaltene content. A detailed procedure of this method is shown in Appendix E.  Figure 8-1 Apparatus for Asphaltene Content Determination 8.3 Coke Formation Kinetic Model Based the Phase Separation Mechanism Since there is very little hydrogen in asphaltene cores, coefficient y is usually very small and thus can be neglected. Parameter b is also negligible [160]. First order reaction rate constant kA and kM can be calculated from Figure 8-2 and Figure 8-3. The data at higher temperature deviate from a straight line, suggesting that there may be more than one reaction in sequence. 105 0 200 400 600 800 1000 1200 14001.41.61.82.02.22.4   380°C 390°C 400°Cln(A+)Time (min)Equation y = a + b*xWeight No WeightingResidual Sum of Squares5.74854E-4 0.00118 0.04511Pearson's r -0.98088 -0.99496 -0.94107Adj. R-Square 0.94318 0.98493 0.82842Value Standard Errorln(A+)Intercept 2.30342 0.01313Slope -1.13467E-4 1.59205E-5Intercept 2.27091 0.01885Slope -3.20857E-4 2.28554E-5Intercept 2.16661 0.11633Slope -5.54949E-4 1.41028E-4 Figure 8-2 Evaluation of Rate Constant for Disappearance of Unreacted Asphaltenes 0 200 400 600 800 1000 1200 14003.83.94.04.14.24.34.44.54.6   380°C 390°C 400°Cln(M+)Time (min)Equation y = a + b*xWeight No WeightingResidual Sum of Squares6.32618E-5 0.00205 0.01993Pearson's r -0.99403 -0.98187 -0.95375Adj. R-Square 0.98214 0.9461 0.86446Value Standard Errorln(M+)Intercept 4.5004 0.00436Slope -6.80433E-5 5.2814E-6Intercept 4.48036 0.02479Slope -2.20105E-4 3.00483E-5Intercept 4.41675 0.07733Slope -4.20657E-4 9.37472E-5 Figure 8-3 Evaluation of Rate Constant for Disappearance of Unreacted Heptane Solubles 106 Coefficients m and a can be determined by substituting the amount of bulk coke of 24-hour experiment at 390°C and 400°C for TI into Equation (8-1). The coefficients are listed in Table 8-1.  Table 8-1 Values of Coefficients in the Phase Separation Model for ATB Experiments Tb, °C kA, 10-4min-1 kM, 10-4min-1 SL A0 m a 380 1.13 0.68 0.107 9.9 0.619 0.842 390 3.21 2.20 0.101 9.9 400 5.55 4.21 0.093 9.9  Thus the correlation of coke formation (also the mass of asphaltene cores precipitating from the solution) with time for different temperatures can be determined by substituting values in Table 8-1 for the corresponding coefficients into Equation (8-1). The values of solubility limit in the present work are around 0.1, which is very different from that of the open reactor (0.49) [89], but similar to the values for the closed reactor (0.137) [160]. This significant difference has been explained [160]. In a closed reactor, volatiles generated in thermal cracking have the chance to stay in the liquid with the other heavier fractions as the solvent for asphaltenes. Those volatiles negatively affect the quality of the solvent since they are more saturated and have poor solubility for asphaltenes. While in an open reactor, volatiles are released from the system immediately, leaving the heavier fractions, which are much better solvents for asphaltenes compared to volatiles. These facts indicate that the solubility limit reveals the quality of the solvent. 107 Solubility limit is expected to increase with increasing temperatures [160]. However the opposite direction is observed in the present work. This can also be explained by the quality of the solvents. More volatiles are obtained at higher temperatures. In the reactor for the present work, which can be treated approximately as a closed reactor, most volatiles still stay in the solvent. Thus the solvent qualities are worse at higher temperatures, leading to slightly lower SL values. Since parameters of Equation (8-1) for 380-400°C have been obtained, toluene insoluble coke can now be determined. Figure 8-4 and Figure 8-5 illustrates the formation of toluene insoluble coke versus time.  0 200 400 600 800 1000 1200 1400-10010203040506070  Weight Fraction of Products (wt%)Time (h) TI (380°C) TI (390°C) TI (400°C) Figure 8-4 Projected Formation of Toluene Insoluble Coke with Time 108 Figure 8-4 indicates that after a long time of heating, 64 wt% of ATB will be converted to coke at all three temperatures, though different durations may be needed from 200 hours to 1500hours. 0 5 10 15 20 25 30 35 40 45-10010203040  Weight Fraction of Products (wt%)Time (h) TI (380°C) TI (390°C) TI (400°C) Figure 8-5 Calculated Formation of Toluene Insoluble Coke in the First 48 Hours Applying Equation (8-1) over short times leads to negative values of mass of coke precipitated as in Figure 8-5. These values indicate that the asphaltene concentration for those experiments didn’t reach the solubility limit, which means the experiments are still in the coke induction period and no coke is expected. These results (for TI ≥ 0) are in good agreement with the finding in experiments. In the 380°C experiments, for instance, no notable bulk coke was observed after 24 hours. The induction period can be estimated from Figure 8-5. For 380°C, the period is around 32 hours, whereas it is 10 and 5 hours for 390°C and 400°C, respectively. However, carbonaceous matter 109 (coke) is still found in the metal rings surface deposit, which indicated that the metal surface or FeS layer can still attract asphaltene cores, even under conditions when they did not precipitate from the solution. Another way to verify the phase separation model parameters is to check if mass of bulk coke after experiments is in good agreement with calculated values from the model. The mass of bulk coke can be determined from a mass balance method to be discussed in Chapter 9. The comparison results between calculated and measured mass of bulk coke are shown in Table 8-2. Measured data come from Table 9-1. Table 8-2 Comparison of Measured and Calculated Mass of Coke after 24-Hour Experiment Tb, °C Mass of ATB, g TI (24h), wt% Mass of Coke, g Deviation Measured Calculated 390 315.9 11.61 39.6 36.7 7.3% 400 338.4 25.35 79.8 85.8 7.5%  Four major products from ATB at different bulk temperatures, including heptane solubles (maltene), asphaltenes, toluene solubles (coke) and volatiles, can be consequently predicted by the phase separation model, as shown in Figure 8-6, Figure 8-7 and Figure 8-8. Asphaltenes include asphaltene cores and unreacted asphaltenes dissolved in the solution. For all three temperatures, weight fractions of dissolved asphaltene reach their maximum value during the experiments and decreases afterwards. The Induction periods end when the maximum value is reached, and toluene insolubles (bulk coke) start to generated. The induction periods are different for different temperatures. 110 0 10 20 30 40 50 60 70 80 90020406080100  VolatilesToluene InsolublesAsphaltenesWeight Fraction of Products (wt%)Time (h)Heptane Solubles Figure 8-6 Four Major Products from ATB versus Time at 380°C 0 10 20 30 40 50 60 70 80 90020406080100VolatilesAsphaltenesToluene InsolublesHeptane Solubles  Weight Fraction of Products (wt%)Time (h)  Figure 8-7 Four Major Products from ATB versus Time at 390°C 111 0 10 20 30 40 50 60 70 80 90020406080100VolatilesAsphaltenesToluene Insolubles  Weight Fraction of Products (wt%)Time (h)Heptane Solubles Figure 8-8 Four Major Products from ATB versus Time at 400°C 8.4 Activation Energy of Coking Reaction 8.4.1 Bulk Coking and Heptane Solubles Conversion The activation energy for the bulk asphaltene and heptane solubles disappearance, EaA and EaM, can be obtained from the Arrhenius plot using kA and kM in Table 8-1, as shown in Figure 8-9, EaA = 291 kJ/mol, EaM = 333 kJ/mol. 112 0.00148 0.00149 0.00150 0.00151 0.00152 0.00153-9.5-9.0-8.5-8.0-7.5  ln(k)1/T (1/K) Asphaltene Heptane SolublesEquation y = a + b*xWeight No WeightingResidual Sum of Squares0.03645 0.04146Pearson's r -0.98588 -0.98777Adj. R-Square 0.94393 0.95138Value Standard Erroln(k)Intercept 44.49859 8.95208Slope -34947.3285 5935.2241Intercept 51.88386 9.54762Slope -40101.6809 6330.06216 Figure 8-9 Determination of Activation Energy for Bulk Coking and Heptane Solubles Conversion 8.4.2 Surface Coking The rate of coke formation in the bulk liquid is related directly to the rate of asphaltene disappearance. However, only a small fraction of the coke forms on the ring. The coke formed on the surface can be calculated however, from the analysis of the deposit. The rate of deposit mass accumulation for coke on the surface of the metal ring is given by dwfc/dt, and was determined thermo-gravimetrically from the mass of fixed carbon in the deposit, after 24 hours. Its temperature dependence follows an Arrhenius plot (Figure 8-10), from which an activation energy of 394 kJ/mol was calculated. The coke deposition process appears to have a stronger temperature dependence than does the asphaltene disappearance reaction. 113 1.48 1.49 1.50 1.51 1.52 1.532.02.53.03.54.04.55.0  ln(r)1/T (103K-1)Equation y = a + b*xWeight No WeightingResidual Sum of Squares0.00539Pearson's r -0.99884Adj. R-Square 0.99537Value Standard Errorln(r)Intercept 75.22673 3.44372Slope -47.38431 2.28318 Figure 8-10 Arrhenius-Type Plot for Coke Deposit Rate (mg/day) for Experiments at 380-400°C and at 600rpm Note that the surface of the metal ring is small compared to the volume of the fluid in the reactor (0.04 cm2/cm3 liquid), and generally the coke formed on the ring surface is a very small fraction of what is formed in the bulk liquid, as will be discussed in Chapter 9. 8.5 Summary The phase separation model successfully described the thermal coking in this work. The model considers the conversion between maltenes and asphaltenes in oil, and treats the oil as a solution system, in which asphaltene cores are the solute and maltenes are the solvent. Concepts of solubility limit and induction period account for the precipitation of asphaltene cores and coke formation. 114 A method was developed based on ASTM standards to measure the concentration of asphaltenes and maltenes in the ATB and spent oil for different experiment durations, and the parameters of the phase separation model were determined from these data to obtain expressions of the model for the ATB in the present work. According to the model, after very long time, the mass fraction of ATB converted to coke would be the same (around 64 wt%) for all temperatures from 380°C to 400°C, though different times were required to reach this condition. Induction period varies with temperature from 5 hours for 400°C to 32 hours for 380°C. Experiment results indicated the phase separation model works well in prediction of the mass of coke formation in the present work. Activation energies for coke deposition in the bulk oil and on the metal surface were calculated. Coking on metal surface had a stronger temperature dependence than in bulk oil.   115 Chapter 9: Trace Inorganic Elements in the Oil and Products 9.1 Trace Inorganic Elements Transfer during Fouling Experiments Knowing how trace inorganic elements transfer among ATB, metal ring surfaces, bulk coke, and other products will facilitate the understanding of fouling mechanisms. As illustrated in Figure 9-1, products after each run were divided into four parts, namely deposit on the rotating cylinder, spent oil, bulk coke and gas. Deposit refers to the foulant attached to metal surfaces. Spent oil is the liquid oil in the reactor after each run. Bulk coke is the coke floating in spent oil and that attached to the wall of liner and Macor® ceramic pads. Gas refers to vapour products released from the system.  Figure 9-1 Fouling Products after Experiments Gas 116 9.1.1 Elemental Analysis – ICP-AES Inductively coupled plasma atomic emission spectrometry (ICP-AES) is a powerful technique for detecting and analyzing trace inorganic elements. It is widely used for analysis of petroleum and the products due to its capability to detect metallic species in organic and aqueous solutions [161].  In ICP-AES, a liquid sample is sprayed into an argon plasma, and electronically excited. Photons are emitted with the retuning of excited atoms to the ground states. The wavelengths of the photons represent unique elements. A polychromator is then used to analyze the emitted photons [162]. ICP-AES was carried out for ATB and collected spent oil, bulk coke and deposit to determine trace inorganic elements content in each part. The analysis was completed by ALS Global. 9.1.2 Mass Balance of Trace Inorganic Elements The vapour is assumed to be light hydrocarbon and H2S, thus the trace inorganic elements only exist in the deposit, spent oil and bulk coke. The amount of deposit can be easily determined from the method described in Section 4.1. The mass of vapour can be determined by the weight loss of the whole reactor before and after each experiment. The exact amount of bulk coke and spent oil are not easily determined directly since they are always mixed together. However, the total amount of spent oil and bulk coke was known. The mass balance can be done if the concentration of elements in each of them were known. As an example, the mass balance equation for 117 silicon, an element associated with clays present in small quantities in bitumen, can be expressed as: 𝒎𝒇𝒄𝒔𝒈,𝒇 = 𝒎𝒉𝒄𝒔𝒈,𝒉 + 𝒎𝑹𝒄𝒔𝒈,𝑹 + 𝒎𝒅𝒄𝒔𝒈,𝒅       (9-1) 𝒎𝑭 = 𝒎𝒅 + 𝒎𝑹 + 𝒎𝒍 + 𝒎𝒉        (9-2) where subscripts d, e, f, g, h represent deposit, coke, feed ATB, gas and spent oil. For the equations above, all parameters were known except me and mh, thus these two parameters can be solved with the two equations. In fact, for the four of the metallic elements of high concentration in the ATB other than iron (Si, Al, V, Ca), the source of metal ring can be neglected since the metal surface area to mass of oil ratio is very small, as mentioned previously, and the content of each element in the metal ring is very low. Iron is excluded since it’s the main element in the metal surface. To determine me and mh, a 198 × 198 wear-resistant nylon mesh with 88.9μm (0.0035”) opening was used to separate part of the spent oil from bulk coke, and also to collect bulk coke floating in spent oil. As well coke sticking to the liner wall was collected. The bulk coke was washed with toluene to remove attached spent oil and dried at 120°C for 24 hours. The spent oil, coke and deposit samples were analyzed with ICP-AES. Mass balances were done for the above four elements respectively to obtain values for me and mh, from two representative experiments. Results indicate that the standard deviations for me and mh of the two experiments are 4.4% and 1.2%, which are considered acceptable. Mass balance results are listed in Table 9-1. Both experiments 118 were run with a rotational speed of 300 RPM for 24 hours. Then the amounts of all elements in each part were calculated. As shown in Table 9-2 and Table 9-3. Table 9-1 Mass Balance of the ATB and Post Experimental Products Tb, °C Surface Mass of ATB, g Mass of Products, g Gas Liquid Coke Deposit 390 Cr-CS 315.9 50.3 225.9 39.6 0.12875 400 CS 338.4 83 175.6 79.8 0.2041  Table 9-2 Elements in the ATB and Products (Cr-CS, 390°C, 24h, 300rpm, 315.9g ATB) Element Si Fe Al V Ni Weight (mg) ATB 244.8 235.0 207.8 44.9 23.1 Coke 229.9 233.9 218.0 27.7 7.9 Spent oil 0 6.1 2.3 15.8 7.5 Deposit 0 0.03 0 0.08 0.01 Concentration (wppm) ATB 775 744 658 142 73 Coke 5800 5900 5500 700 200 Spent oil 0 27 10 70 33 Deposit 0 200 0 600 100  Table 9-3 Elements in the ATB and Products (CS, 400°C, 24h, 300rpm, 338.4g ATB) Element Si Fe Al V Ni Weight (mg) ATB 262.3 251.8 222.7 48.1 24.7 Coke 239.4 247.3 223.4 39.9 8.0 Spent oil 0 4.2 0.7 12.6 4.2 Deposit 0 4.3 0 0.1 0 Concentration (wppm) ATB 775 744 658 142 73 Coke 3000 3100 2800 500 100 Spent oil 0 24 4 72 24 Deposit 0 21300 100 400 100  119 A detailed reporting of trace inorganic elements before and the distribution after experiments is seen in Table 9-4. Si and Al arise mainly from clay in the ATB from the mining process used by Syncrude. For both bulk temperature experiments (Table 9-2 and Table 9-3), nearly all Si and Al are concentrated in bulk coke after runs. None was detected in the deposits, and in the spent oil. Table 9-4 Transfer of Trace Inorganic Elements after Experiments Element Concentration In Feed ATB, mg/kg Source Distribution after Experiments (Approximate) Oil Coke Deposit Silicon 775 Feed 0 100% 0 Iron 744 Mainly metal surface See Paragraph Below Aluminum 658 Feed 1% 99%  Vanadium 142 Feed 30% 70% 0 Calcium 131 Feed 10% 90% 0 Gold 105 Feed 80% 20% 0 Potassium 95 Feed 0 100% 0 Titanium 80 Feed 6% 94% 0 Nickel 73 Feed 30% 70% 0 Magnesium 55 Feed 4% 96% 0 Tin 49 Feed 30% 70% 0 Manganese 25 Feed 3% 97% 0 Barium 8 Very Small Amount Copper 8 Cadmium 4 Chromium BDL* Lead BDL Molybdenum BDL Phosphorus BDL Sodium BDL Zinc BDL *BDL: Below detection limit 120 Most Fe (97%) transfers from the ATB (744 mg/kg) to the bulk coke, while a very small part remains in spent oil. Results showed only 200wppm Fe was found in the deposit of chrome-plated carbon steel rings. This is a considerably (factor of 107) lower concentration compared to the concentration of iron in the deposit on carbon steel rings. This suggests that nearly all iron in the deposit comes from the metal surface rather than ATB. Results indicated chromium is below the detection limit in either spent oil or bulk coke. No chromium is observed even in the deposit. This means that chromium is an excellent isolator which ensures no iron in spent oil, bulk coke and deposit are derived from the ring surface. Laursen and Frandsen also deduced that the pyrrhotites are crystals, which grew in the deposit around ash particles, rather than being deposited [81]. V and Ni mainly exist in resin and asphaltene. Most of these elements transferred to coke and a small part remained in spent oil. Table 9-5 Change of Asphaltene Amount before and after Experiments Experiment Asphaltene in the ATB, g V+Ni in Spent Oil, ppm Asphaltene in Spent Oil, wt% Asphaltene in Spent Oil, g Change 390°C Cr-CS 31.6 103 5.8 13.1 59% 400°C, CS 33.8 96 5.5 9.7 71%  The concentration of nickel and vanadium was found to have a clear correlation with the asphaltene content in oil products [88]. Figure 9-2 shows the relationship between the total amount of Ni and V and the asphaltene content. The data with asphaltene less than 8 wt% are from the work by Bartholdy and Andersen [88], while the point with 121 asphaltene content of around 10 wt%, which fit the curve very well, is from ICP-AES analysis of the ATB in present work. Thus the asphaltene content in spent oils can be estimated with Figure 9-2, and the change of asphaltene before and after two experiments were determined, as seen in Table 9-5. Apparently the reduced asphaltene was converted to bulk coke and deposit. 0 2 4 6 8 10020406080100120140160180200220  Ni + V Concentration in Oil (ppm)Asphaltene Content in  Oil (wt %)Present ATB Figure 9-2 Ni+V Content in the Oil Products versus Asphaltene Content [88] 9.2 Addition of Iron Oxide Particulates  It has been considered that upstream corrosion may lead to insoluble iron products which then deposit in downstream equipment. In order to study the fouling performance with suspended particulates in the oil, 0.316g Fe2O3 particles (<5 μm) was added to 300ml ATB, to give 744ppm suspended particulate. Experiments were carried out for 24 122 hours at bulk temperature of 380 and 390°C, with the rotating speed of 600 rpm and 2.4 MPa (350 psi). Results listed in Table 9-6 showed no significant change in deposit growth rate. The experiments suggest that suspended particulates play a minor role in fouling under test conditions. Table 9-6 Effects of Addition of Iron Oxide Particulates Bulk Temperature 380°C 390°C Deposit Thickness without Addition of Iron Particles 55.0µm 104.9µm Deposit Thickness with Addition of Iron Particles 66.4µm 90.2µm Growth Rate Change +21% -14%  9.3 Summary The products after fouling experiments include gas, spent oil, bulk coke and deposit on the metal surface. In order to study the transfer of trace inorganic elements during experiments, all post experimental products except gas were analyzed with ICP-AES, mass of each product was determined, and mass balances were completed on four elements with the highest concentration in the ATB. Results indicate that iron in the deposit comes from the metal surface rather than the ATB. Concentration of V + Ni has strong relationship with asphaltene content and thus can be used to estimate asphaltene concentration in the oil. 123 The mass of coke formed in the bulk oil greatly exceeds that deposited on the metal ring. The mass of bulk coke determined from the mass balance method is in good agreement with the value calculated from the phase separation model. Experiments with additional Fe2O3 particles in the ATB indicated that the impact of suspended particles on fouling rate was weak.   124 Chapter 10: Non-isothermal Fouling Research The isothermal measurements have shown the importance of metal composition, oil bulk temperature and wall shear stress on the rate of fouling in rotary cylinder experiments and the composition of deposits. However the vacuum tower furnace is obviously a non-isothermal unit with hot surfaces (460°C) and the oil is relatively cooler (<300°C). Bulk coking is avoided. Thus non-isothermal deposition is an important topic that requires detailed time-consuming studies, and is largely beyond the scope of this thesis.  Nevertheless, a non-isothermal apparatus was constructed, and initial experiments are reported for two metal surfaces. 10.1 Non-isothermal Fouling System The new non-isothermal fouling unit is constituted of four parts, namely a stirred reactor, temperature and rotational speed control, probe heating and data acquisition. A schematic diagram of the fouling unit is shown in Figure 10-1. 10.1.1 Reactor The reactor is a 7.56L bolted pressure vessel assembled by Parker Autoclave Engineers. The reactor material is type 316 stainless steel. It utilizes a solid metal seal in a bolted flange that relies on bolting force to produce a seal. The inside diameter of the reactor cylinder is 16.51cm (6.5”). The height is around 35cm. The reactor was heated with a ceramic band heater. The whole reactor is shown in Figure 10-2. 125  Figure 10-1 Schematic Diagram of Non-isothermal Fouling Unit In order to increase the resistance to leakage, a bolted flange with thickness of 7.62cm (3”) was supplied. The layout of the flange is seen in Figure 10-3. The flange was tightened on the reactor with 10 bolts.  This type of closure permits a working pressure of up to 41 MPa (6000 psig) and temperature of up to 650°C.  126  Figure 10-2 Non-isothermal Reactor  Figure 10-3 Bolted Flange of the Non-isothermal Reactor During experiments, a large amount of heat is released from the cartridge heater to the bulk oil. In order to maintain a constant bulk oil temperature, a cooling coil was designed to take the excessive heat from the system. The tube diameter of the cooling coil should 127 be small to minimize the influence of cooling coil to the fluid flow. However, a diameter that is too small will increase the water flow resistance, especially when there is vaporization of water due to higher bulk temperature. The inside diameter of cooling coil was finally determined as 3.0mm with a thickness of 0.9mm. The design of cooling coil is shown in Figure 10-4.  Figure 10-4 AutoCAD Design of the Cooling Coil A Series 1.50-02 MagneDrive II was assembled to actuate the rotational shaft. High speed rotation is obtained via internal magnets connected to the shaft. The internal magnets are driven by external magnets which were connected to a high speed motor with a transmission belt. 128 10.1.2 Cartridge Heater Probe The cartridge heater probe (Figure 10-5) was used to create a hot surface in experiments. Probes are manufactured by Nordic Sensors Inc. The specifications are listed in Table 10-1.  Figure 10-5 Cartridge Heater Probe Table 10-1 Specification of Cartridge Heater Probe Specification Value Power Rating 1000W Voltage Rating 120V Metal Shell Thickness 0.9mm Outside Diameter 0.95cm Length 11.4cm Material Carbon Steel or Incoloy 800 Heating Coil Wire Diameter 0.3mm  The cartridge heater probe included a metal tube of carbon steel or Incoloy 800, a heating coil and thermocouple located in the center both axially and radially. The rest 129 space of the tube was filled with MgO for insulation. Figure 10-6 shows the structure of probes.  Figure 10-6 Structure of Cartridge Heating Probe  Figure 10-7 Temperature Change from the Cartridge Probe Heater to the Bulk Oil Due to the thermal resistance of different materials in the probe, there is a difference between the measured core temperature Tc and the calculated surface temperature Ts, as shown in Figure 10-7. Zone 1 and 3 are MgO packing. Zone 2 is heating coil. Zone 4 is metal shell. Zone 5 is fouling deposit on the surface. Petkovic [163] calculated the 130 temperature difference between Tc and Ts for the same type of probe at core temperature of 469-482°C and bulk temperature of 320°C, and found the temperature difference between Tc and Ts is consistently between 31.12-31.55°C, with the average value of 31.4°C, at Q=700W. 10.1.3 Design of Impeller A 4-leaf impeller was fabricated in order to create a uniform flow over the whole axial length of the probe. The shape of each leaf or blade was rectangular (18 x 110mm). Leaves are mounted on a type 316 stainless steel tube. The length, outside diameter and inside diameter of the tube is 110mm, 22.2mm (7/8”) and 16.1mm (0.635”), as seen in Figure 10-8. The flat-leaf design helps to create concentric circular flow and avoid axial mixing. The distance between the axis of the impeller and cartridge heating probe is 50.8mm.  Figure 10-8 Location of the Cartridge Heating Probe 131 10.1.4 Temperature Control Temperature control is similar to the method used in 3.3.2. Two dual element thermocouples (SCASS-062U-6-DUAL and CASS-14U-18-DUAL) were used in the heating jacket and reactor thermal well, respectively. One connector of each thermocouple was connected to Omega DAQ-54 data acquisition module for temperature record. The other connectors were connected to the control box to achieve the dual temperature control, as shown in Figure 10-1. 10.1.5 Power Supply The cartridge heater probe was powered by a BK Precision Model VSP12010 programmable PFC DC Supply with 120V/10A output. Constant voltage mode was adopted in the experiment. A Tenma 72-1020 multimeter was used in the circuit for a precise adjustment of voltage during experiments. 10.2 Experiment Procedures 10.2.1 Pre-experimental Procedure Before experiments, a probe was tested to inspect the electrical resistance, and then fixed into the correct position. Power wires of the probe were connected to the power supply. The thermocouple wire was connected to the data acquisition module. Then 3.2-L of ATB at about 60°C was added to the reactor. The oil depth was around 15cm, to completely submerge the cartridge heater probe. Finally the whole reactor was closed and sealed with 10 bolts. 132 10.2.2 Experimental Procedure The heating temperature was firstly set to 150°C to decrease the viscosity of ATB. Then nitrogen was sent through the reactor at a rotational speed of 300rpm for one hour, in order to remove the oxygen from the oil and the free-board gas space. Then the system was sealed, and bulk temperature was elevated to 300°C. When the bulk temperature achieved steady state, the power of the cartridge heater probe was turned on. Required probe surface temperature was reached by adjusting the output voltage. Then a steady probe surface temperature and bulk temperature was reached. Excessive heat was taken by the cooling water in cooling coil, which was also controlled with the control box. Figure 10-9 and Figure 10-10 show an experiment with carbon steel probe at a bulk temperature of 180°C, and an initial probe core temperature of 450°C. Probe input power is 550-600W. 0 10 20 300100200300400500  Temperature (�℃)Time (h)Probe TBulk THeating Jacket T Figure 10-9 Temperature Data Recording of a Non-isothermal Experiment 133 -5 0 5 10 15 20 25 30 35 400100200300400500600Time (h)Power (W)151617181920 Electrical Resistance (Ohm)Probe PowerElectrical Resistance Figure 10-10 Probe Power and Electrical Resistance Recording of a Non-isothermal Experiment 10.2.3 Post Experimental Procedure After experiments, power to the heating probe and the heating jacket were turned off. When the bulk oil temperature was below 120°C, the oil was flushed out with nitrogen. Then the reactor was opened and the cartridge heater probe was taken out for thickness measurement and composition analysis. 10.3 Preliminary Experiments As the representatives of corroded and non-corroded surfaces, cartridge heater probes of carbon steel and Incoloy 800 alloy were tested in experiments. Operational conditions are listed in Table 10-2. Tf in the table is film temperature, which is defined as: 134 𝑻𝒇 = 𝑻𝒔+𝑻𝒃𝟐           (10-1) In fouling caused by chemical reactions, the film temperature is often used to characterize the temperature at which the fouling reaction occurs in the narrow zone or film near the hot surface. Table 10-2 Operating Conditions of Two Non-isothermal Experiments Probe Surface Material Carbon Steel Incoloy 800 Ts,0 (°C) 490* 470** Tb (°C) 230 300 Tf (°C) 360* 385** Power (W) 630 500 Rotational Speed (rpm) 300 300 Duration (h) 80 250 * Start from 30 hours ** Start from 50 hours 10.3.1 Thermal Fouling Resistance and Fouling Rate Thermal fouling rate can be determined by the following equation, ∅ = 𝒅𝑹𝒇𝒅𝒅= ∅𝒅 − ∅𝒓        (10-2) Φd and Φr are deposition term and removal term with the unit of m2K/kJ. Rf is thermal fouling resistance, which can be calculated as: 𝑹𝒇(𝒅) = 𝟏𝑼(𝒅) − 𝟏𝑼(𝟏) = 𝑨�𝑻𝒔(𝒅)−𝑻𝒃(𝒅)�𝑸 − 𝑨�𝑻𝒔(𝟏)−𝑻𝒃(𝟏)�𝑸    (10-3) where Rf is in m2K/kW. Thermal fouling rate is related to mass deposition rate and deposit thickness growth rate via: 135 𝒅𝑹𝒇𝒅𝒅= 𝟏𝒌𝒅𝒅𝒅𝒅𝒅= 𝟏𝒌𝒅𝝆𝒅𝒅𝒎𝒅𝒅𝒅       (10-4) 10.3.2 Experiments with Carbon Steel Cartridge Heater Probe Figure 10-11 shows a non-isothermal experiment with the carbon steel probe. The bulk temperature was initially set to 180°C, and elevated to 230°C after 30 hours. Probe power was 500-640W. Initial film temperature is 265-360°C. Final film temperature is 770°C. The entire experiment ran for 80 hours. Figure 10-11 indicates probe surface temperature first increased and then decreased following each rise in probe power, especially at about 33-hour, when probe power was increased to 630W in the first a period of different probe power inputs.  0 20 40 60 800200400600800100012001400Time (h)Temperature (�℃)Bulk T0100200300400500600700 Power (W)Probe PowerProbe Surface T Figure 10-11 80-Hour Carbon Steel Probe Experiment 136 In order to see it clearly, a partial enlarged figure of probe surface temperature is shown in Figure 10-12, which clearly illustrates the decreasing of temperature in each time period. The most significant decrease of probe surface temperature was seen in the experimental period of 33-64 hours. During this 12 hours period, probe surface temperature decreased by 72°C from 493°C to 421°C. In the period 64-72 hours, surface temperature slowly increased from 421°C to 451°C and then rapidly increased to 1340°C until the experiment was shut down automatically. 0 20 40 60 80300320340360380400420440460480500   Probe Surface TTemperature (�℃)Time (h)  Figure 10-12 Partial Enlarged Probe Surface Temperature (Carbon Steel) Figure 10-13 shows the fouling resistance of this experiment. The following observations can be made from Figure 10-13: 137 1) In 2-32 hours period, bulk temperature was constant at 180°C. The fouling resistance gradually decreased from 0 to -0.2 m2K/kW, though probe surface temperature was elevated twice in this section. 2) Fouling resistance had a significant change at the 32-33 hours period, apparently due to the unsteady state of increasing bulk temperature.  3) A substantial decrease of fouling resistance occurred again in the period 33-64 hours. Then it increased sharply, indicating accelerated fouling towards the end of the experiment. 0 20 40 60 80-101234  Rf (m2 K/kW)Time (h)  Figure 10-13 Fouling Resistance of 80-Hour Carbon Steel Probe Experiment Negative values of fouling resistance have been discussed by Watkinson and Li [98] and many other authors. They are usually attributed to enhanced heat transfer due to 138 the roughness change which is induced by corrosion, or deposition of high thermal conductivity crystals. The accelerated fouling at the end of the run suggests a possible boiling on the surface, followed by drying out which would reduce the heat transfer coefficient drastically. Fouling rates can be calculated from the slope of Rf versus time, as shown in Figure 10-14 and Figure 10-15.  64 66 68 70 72 74-0.10-0.050.000.050.10  Rf (m2 K/kW)Time (h)  Figure 10-14 Fouling Rate Calculation for CS Experiments (64-74 Hours) The whole experiment can be divided into 3 periods based on the fouling rate. The first period (0-64 hours) is fouling induction time and no significant fouling is observed. In the second period (64-74 hours), fouling occurred mildly with a fouling rate of 5.60×10-6 m2K/kJ. In the last period (74-80.5 hours), fouling became significantly faster, especially 139 in the last one hour of the experiment, which had a fouling rate of 6.26×10-4 m2K/kJ, more than 110 times the fouling rate in the second period, leading to a sharp rise of the probe core temperature to 1340°C. 79.6 79.8 80.0 80.2 80.4 80.61.01.52.02.53.03.54.0  Rf (m2 K/kW)Time (h)  Figure 10-15 Fouling Rate Calculation for CS Experiments (Last Hour of the Experiment) Heat transfer across a surface can be expressed as [164]: 𝑸 = 𝑼𝑨∆𝑻 = 𝑼𝑨(𝑻𝑺 − 𝑻𝒃)        (10-5) where Q is the heat flow, W. U is defined as the overall heat transfer coefficient, W/m2·K. A is heat transfer area, m2. ΔT is the temperature difference between hot and cold medium, K. In the present work, ΔT is the temperature difference between probe metal surface temperature and bulk oil temperature. Some typical heat transfer 140 coefficients are listed in Appendix F [165]. Figure 10-16 shows the heat transfer coefficient versus time.  The following facts can be observed from the figure: 1) Heat transfer coefficient in most of experiment periods are around 1000 W/m2·K, which is in accordance with the values of light organic liquids (viscosity of oil is low due to high bulk temperatures). 2) At the end of the experiment, heat transfer coefficient decreased sharply and finally to around 200 W/m2·K, which fits the values of high pressure gases. This may be evidence that the oil around the probe wall was fully film boiling at the final stage. 0 20 40 60 80200400600800100012001400  Overall Heat Transfer Coefficient (W/m2 K)Time (h)  Figure 10-16 Overall Heat Transfer Coefficient of 80-Hour Carbon Steel Probe Experiment The average thickness of deposit was 396.8μm based on the measurement with a micrometer, with a standard deviation of 62.5 μm. TGA analysis was carried out for the 141 deposit, as seen in Figure 10-17. Results indicate carbonaceous material takes 51.7 wt%. of deposit, in comparison with 48.3 wt%. of ash. 0 1000 2000 3000 4000 5000 6000 7000 800001002003004005006007008009001000 Temperature (°C)Time (s)101214161820TGA (mg) Figure 10-17 TGA Analysis of Carbon Steel Probe Deposit 10.3.3 Experiment with Incoloy 800 Cartridge Heater Probe Figure 10-18 shows a non-isothermal experiment with an Incoloy 800 alloy probe. The bulk temperature was initially set to 300°C. Probe power was 400-500W. The initial film temperature is 365-385°C, and the final film temperature is 400°C. The entire experiment ran for 250 hours. Figure 10-18 shows a slowly increasing probe surface temperature from 470°C to 500°C, while the probe power and bulk temperature were constant. In order to compare the probe temperature change with that of carbon steel in 10.3.2, the partially enlarged 142 Figure 10-19 was plotted with the same scale used in Figure 10-12. Compared to the carbon steel probe, no large temperature decreases (~70°C) were seen for the Incoloy 800 probe, where decreases were <10°C. This may indicate that the surface roughness didn’t change significantly during these periods. 0 50 100 150 200 250050100150200250300350400450500550Time (h)Temperature (�℃)0100200300400500600700 Power (W)Probe PowerProbe Surface TBulk T Figure 10-18 250-Hour Incoloy 800 Probe Experiment Figure 10-18 shows a slowly increasing probe surface temperature from 470°C to 500°C, while the probe power and bulk temperature were constant. In order to compare the probe temperature change with that of carbon steel in 10.3.2, the partially enlarged Figure 10-19 was plotted with the same scale used in Figure 10-12. Compared to carbon steel probe, no large temperature decreases (~70°C) were seen for the Incoloy 800 probe, where decreases were <10°C. This may indicate that the surface roughness didn’t change significantly during these periods. 143 0 20 40 60 80300320340360380400420440460480500   Probe Surface TTemperature (�℃)Time (h)  Figure 10-19 Partial Enlarged Probe Surface Temperature (Incoloy 800) Figure 10-20 shows the fouling resistance in the Incoloy 800 experiment. The fouling resistance gradually increased from 0 to 0.2 m2K/kW. The fouling rate was calculated from the slope of fouling resistance versus the time, as shown in Figure 10-21. The experiment was also divided into 3 periods. The first period (0-60 hours) is the fouling induction time. In the second period (60-230 hours), the fouling rate was 2.67×10-7 m2K/kJ. In the last period (230-250 hours), the fouling achieved an equilibrium. Figure 10-22 showed the overall heat transfer coefficient of the Incoloy 800 experiment. The heat transfer coefficient is gradually decreasing due to the fouling accumulation from roughly 1100 to 900 W/m2·K, which indicates boiling may have occurred for part of the oil after 150 hours, according to Appendix F. 144 0 50 100 150 200 2500.000.050.100.150.20  Rf (m2 K/kW)Time (h)  Figure 10-20 Fouling Resistance of 250-Hour Incoloy 800 Probe Experiment 50 100 150 200 2500.000.050.100.150.20  Rf (m2 K/kW)Time (h)  Figure 10-21 Fouling Rate Calculation (60-230 Hours) 145 0 50 100 150 200 250850900950100010501100  Overall Heat Transfer Coefficient (W/m2 K)Time (h)  Figure 10-22 Overall Heat Transfer Coefficient of the Experiment with Incoloy 800 Probe The deposit has a thickness of 84.4μm with a standard deviation of 12.7μm. TGA was also used to analyze the Incoloy 800 Deposit, as seen in Figure 10-23. The carbonaceous matter occupies 74.1 wt% of deposit, whereas the ash content is 25.9 wt%. Ash contents in deposit of the carbon steel probe and the Incoloy 800 probe are both higher than typical value for carbon steel and Incoloy 825. This might be because of the effect of naphthenic acid, since in the bulk temperature of these two experiments, naphthenic acid corrosion should not be neglected. 146 0 20 40 60 80 100 120 14001002003004005006007008009001000 Temperature (°C)Time (min)468101214161820TGA (mg) Figure 10-23 TGA Analysis of Incoloy 800 Probe Deposit 10.4 Summary The main results of the two experiments are listed in Table 10-3. For both experiments, very little coke was found in the bulk oil or on the reactor wall. This was expected for the low bulk temperature chosen. Table 10-3 Summary of Main Results of the Two Experiments Probe Surface Material Carbon Steel Incoloy 800 Ts,0 (°C) 490* 470** Tb (°C) 230 300 Tf (°C) 360* 385** Duration (h) 80 250 Fouling Rate     dx/dt () 69.52mm/year (190.5μm/day) 4.35mm/year (11.9μm/day)  dRf/dt (m2K/kJ) 5.60×10-6 - 6.26×10-4 2.67×10-7 * Start from 30 hours ** Start from 50 hours 147 The fouling rates for carbon steel and Incoloy 800 in Table 10-3 expressed on an annual basis are 69.52 mm/year and 4.35 mm/year, respectively. For isothermal experiments, the bulk temperatures, at which similar fouling rates were obtained, are roughly 385°C for carbon steel, and 377°C for Incoloy 825, respectively, according to Figure 4-6. This might indicate that different weight of Ts and Tb should be put in calculation of Tf, since fouling rate is more sensitive to Ts rather than Tb.   148 Chapter 11: Mathematical Model Based on the experimental work, a physicochemical and mathematical model can be proposed to describe the fouling involving iron sulphide and coke. 11.1 Physicochemical Model Based on the facts in the present work, a physicochemical model can be described with the following key information: 1) Active sulphur species (mainly thioethers) in the ATB decomposed at high temperatures (380-400°C) to generate H2S. H2S dissolved in the feed ATB at high temperatures (380-400°C) and pressures (up to 2.4 MPa). 2) The ATB can be treated as a solution system with asphaltene (heptane insoluble but toluene soluble) as solute and maltenes (heptane soluble) as solvent. For a specific amount of maltenes, only a limited amount of asphaltene can disperse readily in it, which defined the solubility limit of heptane soluble, a parameter depending on the composition of the maltenes. 3) In the initial stage of heating of ATB, asphaltene is well dissolved in the heptane soluble fraction of ATB. In this stage, dissolved H2S reacted with the metal surface to form FeS. No asphaltene cores form coke and precipitate in the bulk oil. Thus the deposit is mainly constituted of corrosion product. 4) As corrosion proceeds, thickness of the surface metal is reduced and an  FeS layer (with a small part of coke) is formed and becomes thicker, leading to 149 greater diffusion resistance for the transfer of H2S from the liquid oil to the metal surface. 5) Meanwhile, the asphaltene cores are more attracted to the acidic FeS layer  than to the fresh metal surface.   A small amount of asphaltene cores adheres to the FeS layer and finally forms coke, even if the solubility limit is not reached and asphaltene cores are well dissolved in the maltenes. The rate of adherence on metal surface depends on both the concentration of dissolved asphaltene cores and surface properties. 6) Along with the heating of ATB, part of the maltenes in the ATB decomposes, to release asphaltene cores and volatiles, leading to the decrease of maltenes and increase of asphaltene cores. Meanwhile, asphaltenes also release cores and volatiles at high temperatures. This is the coke induction period. When the amount of asphaltene cores reaches the solubility limit due to the decomposition of maltenes and asphaltenes, the induction period ends and excessive asphaltene cores start to combine to form coke or precursors, which precipitate from ATB. Part of the precipitated coke or precursors may adsorb to the metal surface at low wall shear stress. Most form coke in bulk oil. At higher wall shear stress, the adherence of precipitated coke or precursors on metal surface is very difficult and can be neglected, due to the weak force between coke or precursors and metal surface. 7) Diffusion resistance of H2S from bulk oil to the metal surface increases due to the growth of the deposit (FeS and coke). Finally the corrosion rate is decreased to a very low level. 150 8) For the present work, the induction period mainly depends on the bulk temperature and duration. For 24-hour experiments at 380°C, all experiments are within the induction period. At 390°C, roughly the first 9.6-hours are in the induction period, and then the rapid coking in bulk oil occurs. Higher temperatures reduce the induction periods. 11.2 Mathematical Model for Sulphide Corrosion 11.2.1 Development of the Expanding Scale Model Sulphide corrosion and thermal coking are two main processes in the physicochemical model which was discussed above in Section 11.1. In this section, a mathematical model is proposed to describe the sulphide corrosion. The coking mechanism will be discussed in Section 11.3. Equation (7-1) indicated that there may be three steps during sulphide corrosion. 1) Convective mass transfer, which is the transfer of active Sulphur (H2S) from bulk oil to deposit surface. Due to high Reynolds numbers in industry furnace tubes, as well as in the present research, the resistance in this step is insignificant for both circumstances. Note that this resistance is not time-dependent (except for secondary effects such as roughening of the corrosion layer). 2) H2S diffusion in deposit, which is the transfer of H2S from deposit surface to metal surface through the pores in deposit. Resistance to transport through the deposit layer increases with deposit thickness and time. It is usually the dominating resistance. It has been proved that for most experiments in the 151 present work, significant resistance occurred in a short time (24 hours), as the typical operating duration in a refinery, which may last for 1 year or longer. 3) Corrosion reaction, which is a pure chemical process involving H2S and metal on the ring surfaces. This is a critical step only in the very initial stage of the experiment when the ring surface hasn’t been covered by fouling deposit. For the case of negligible resistance to convective mass transfer, the surface concentration will equal the bulk concentration during this initial period. As the resistance to H2S diffusion in the deposit grows, the concentration of H2S at the metal/deposit interface decreases, approaching zero in the limiting situation where diffusion controls the rate, as all H2S will be consumed once they reach the metal surface due to the much faster corrosion rate compared to the diffusion rate. Since one of the aims of the work is to develop a model which can be simple and accurate enough for prediction of long term behaviors of heavy oil at high temperatures, the chemical reaction step will not be treated as the rate determination step in the following development of the mathematical model for sulphide corrosion. Thus the in-deposit transport of sulphide will be assumed to be rate determining in the model discussed below. 152  Figure 11-1 Sulphide Corrosion and Coking Involved Fouling on a Metal Ring Figure 11-1 illustrates the situation in which the diffusion of H2S through the deposit layer controls the rate of corrosion. The corrosion rate can be expressed as a relation between time and radius of metal ring, Ri. The relation is developed based on the unreacted core model for particle reactions [166], applied to a cylindrical shape. As the reaction proceeds, the unreacted meatal cylinder is shrinking, while the outer edge of deposit is expanding, leaving the deposit to remain around the cylinder. This bidirectional expansion assumption is different with unreacted core model, in which the unreacted sphere is shrinking while the outer edge of the sphere doesn’t change during reaction. In the present work, if there is no coke formation on the metal surface, the corrosion reaction is assumed to occur as: 153 𝐹𝐹 + 𝐻2𝑆 → 𝐹𝐹𝑆 + 𝐻2 The metal ring shrinks due to the corrosion, and FeS accumulates on the surface, which is similar to the unreacted core model. However, in the present situation, the size of the ring with deposit is actually not constant, due to the difference of density between the metal and FeS. If the FeS does not adhere to the metal, the cylinder radius would decrease from Rr to Ri. If the FeS adheres to the metal, the corroded ring would increase in radius to Ro, as the metal thickness decreases. Furthermore, the deposit is not pure FeS since there will be coke in it at the temperatures used in the present research. Both changing cylindrical size and the formation of coke are dealt with in the model developed below. For convenience, A, B, C, D, E are used as the subscripts to represent H2S, Fe, FeS, deposit (mixture of FeS and coke) and coke, respectively. The real density of a non-porous mixture of FeS and coke can be determined as: 𝝆𝒓,𝑫 = 𝟏𝒘𝑪𝝆𝒓,𝑪+𝟏−𝒘𝑪𝝆𝒓,𝑬 = 𝟏𝒘𝑪𝟏𝟖𝟏𝟏+𝟏−𝒘𝑪𝟐𝟏𝟏𝟏 = 𝟏𝟏𝟐𝟏𝟐.𝟏𝟏.𝟖𝟏−𝟐.𝟖𝟑𝒘𝑪     (11-1) where ρr,C, ρr,D, and ρr,E, are real density of FeS, deposit and coke without pores, kg/m3. ρr,C = 4840kg/m3,  ρr,E = 2110 kg/m3. wC is the mass fraction of FeS in the deposit. Thus the bulk density of a deposit of porosity, ε, can be determined according to Equation (6-8) as: 𝝆𝑫 = (𝟏 − 𝜺)𝝆𝒓,𝑫          (11-2) 154 The ratio of deposit thickness increase to the metal thickness decrease due to corrosion referring to Figure 11-1 can be calculated as: 𝑹𝒍−𝑹𝒈𝑹𝒓−𝑹𝒈= 𝒅𝑫𝒅𝑩= 𝑽𝑫𝑽𝑩         (11-3) 𝑽𝑫 = 𝒎𝑫𝝆𝑫 = 𝒎𝑪 𝒘𝑪⁄𝝆𝑫 = 𝑽𝑩𝝆𝑩𝑴𝑪𝑴𝑩𝒘𝑪 𝟏.𝟖𝟏−𝟐.𝟖𝟑𝒘𝑪𝟏𝟏𝟐𝟏𝟐.𝟏(𝟏−𝜺)      (11-4) where VB and VD are volumes of Fe consumed and deposit generated, m3. MB is the molar mass of Fe, 0.055845 kg/mol. MC is the molar mass of FeS, 0.08791 kg/mol, and ρB is density of carbon steel, 7850 kg/m3. Thus Equation (11-3) and (11-4) can be rewritten as: 𝑽𝑫𝑽𝑩= 𝟏.𝟐𝟏(𝟏.𝟖𝟏−𝟐.𝟖𝟑𝒘𝑪)𝒘𝑪(𝟏−𝜺)          (11-5) From Equation (11-3) and (11-5), for example at ε = 0.5, for wC = 1.0 (pure FeS), xD/xB = 5.1, i.e. for every 1-mm of corroded metal thickness, the FeS deposit is 5.1 mm thick. At any instant, diffusion rate of H2S at different radial locations can be expressed as: −𝒅𝑵𝑨𝒅𝒅= 𝟐𝝅𝒓𝒉𝑸𝑨 = 𝟐𝝅𝑹𝒍𝒉𝑸𝑨𝒍 = 𝟐𝝅𝑹𝒈𝒉𝑸𝑨𝒈 = 𝒄𝒍𝒏𝒔𝒅𝒂𝒏𝒅    (11-6) where h is the height of metal ring, h = 1cm. NA is the mole of diffusing H2S, mol. QA, QAo and QAi are diffusion flux of H2S at a given location, deposit surface and metal surface, respectively, mol/(m2·s). According to Fick’s law [167], molecular diffusion can be described as: 155 𝑸𝑨 = −𝑫𝑹 𝒅𝒄𝑨𝒅𝒓           (11-7) where cA is the concentration of H2S, De is effective diffusion coefficient of dissolved H2S, m2/s.  For any r, combining Equation (11-6) and (11-7), −𝒅𝑵𝑨𝒅𝒅= −𝟐𝝅𝒓𝒉𝑫𝑹 𝒅𝒄𝑨𝒅𝒓         (11-8) Since the diffusion rate of H2S is much faster than the deposit growth rate, H2S diffusion can be assumed to be in the steady state. Integrating from surface of deposit layer, Ro, to the metal surface, Ri, −𝒅𝑵𝑨𝒅𝒅∫𝟏𝒓𝑹𝒈𝑹𝒍𝒅𝒓 = −𝟐𝝅𝒉𝑫𝑹 ∫ 𝒅𝒄𝑨𝟏𝒄𝑨,𝒔       (11-9) −𝒅𝑵𝑨𝒅𝒅𝒍𝒏 �𝑹𝒈𝑹𝒍� = 𝟐𝝅𝒉𝑫𝑹𝒄𝑨,𝒔       (11-10) The radius after deposit formation from equation (11-5) is 𝑹𝒍 = 𝑹𝒈 + (𝑹𝒓 − 𝑹𝒈) 𝟏.𝟐𝟏(𝟏.𝟖𝟏−𝟐.𝟖𝟑𝒘𝑪)𝒘𝑪(𝟏−𝜺)       (11-11) Rr is the original radius of metal ring, Rr = 1.905cm. −𝒅𝑵𝑨 = −𝒅𝑵𝑩 = −𝝆𝑩𝒅𝑽 = −𝟐𝝅𝒉𝝆𝑩𝑹𝒈𝒅𝑹𝒈     (11-12) Thus, 156 −𝟐𝝅𝒉𝝆𝑩 ∫ 𝑹𝒈𝒍𝒏 �𝑹𝒈𝑹𝒍� 𝒅𝑹𝒈𝑹𝒈𝑹𝒍= 𝟐𝝅𝒉𝑫𝑹𝒄𝑨𝒔 ∫ 𝒅𝒅𝒅𝟏     (11-13) The equation linking Ro and Ri as function of time is then ∫ 𝑹𝒈𝒍𝒏 �𝑹𝒈𝑹𝒍� 𝒅𝑹𝒈𝑹𝒈𝑹𝒍= −𝑫𝑹𝒄𝑨𝒔𝝆𝑩∫ 𝒅𝒅𝒅𝟏      (11-14) It is reported that the thermal decomposition of DMS can be treated as a first order reaction from which the concentration of H2S in the liquid is given by: 𝒄𝑨𝒔(𝒅) = 𝒄𝑨𝒃(𝒅) = 𝒄𝑨𝒃(𝟏)�𝟏 − 𝑹−𝒌𝑺𝒅�      (11-15) where kS is the rate constant of thermal decomposition of active sulphur species, s-1. Thus Equation (11-14) can be expressed as: ∫ 𝑹𝒈𝒍𝒏 �𝑹𝒈𝑹𝒍� 𝒅𝑹𝒈𝑹𝒈𝑹𝒍= −𝑫𝑹𝒄𝑨𝒃(𝟏)𝝆𝑩∫ �𝟏 − 𝑹−𝒌𝑺𝒅�𝒅𝒅𝒅𝟏    (11-16) Equation (11-16) cannot be simply integrated analytically, therefore it was integrated using Wolfram Mathematica with Ri, which usually provides better symbolic integration than Matlab, and combining with Equation (11-11) yields: 𝑺(𝒅) = 𝑭𝟏(𝑹𝒍) + 𝑭𝟐(𝑹𝒍) + 𝑭𝟑(𝑹𝒍) − 𝑭𝟏(𝑹𝒈) − 𝑭𝟐(𝑹𝒈) − 𝑭𝟑(𝑹𝒈)    (11-17) where 𝑺(𝒅) = 𝑫𝑹𝒄𝑨𝒃(𝟏)𝝆𝑩�𝑹−𝒌𝑺𝒅−𝟏𝒌𝑺+ 𝒅�        (11-18) 157 𝑭𝟏(𝒓) = 𝒓(𝟏.𝟏𝟏𝟏𝟖𝟖𝟐𝟐−𝟏.𝟏𝟑𝟏𝟏𝟔𝟑𝟏𝒘𝑪)𝟏.𝟖𝟏𝟔𝟏+(𝜺−𝟏.𝟑𝟏𝟑𝟑)𝒘𝑪         (11-19) 𝑭𝟐(𝒓) = 𝟏.𝟏𝟏𝟏𝟏𝟖𝟏𝟏𝟔(𝟏.𝟖𝟖𝟐𝟖𝟏−𝒘𝑪)𝟐𝑳𝒏[𝟏.𝟏𝟏𝟏𝟏𝟔𝟏−𝟏.𝟏𝟔𝟐𝟏𝟐𝟖𝟏𝒘𝑪+𝒓(𝒘𝑪(𝟏.𝟑𝟏𝟑𝟑−𝜺)−𝟏.𝟖𝟏𝟔𝟏)][𝟏.𝟖𝟏𝟔𝟏+𝒘𝑪(𝜺−𝟏.𝟑𝟏𝟑𝟑)]𝟐    (11-20) 𝑭𝟑(𝒓) = 𝟏.𝟏𝒓𝟐𝑳𝒏 � 𝒓(𝜺−𝟏)𝒘𝑪𝟏.𝟏𝟔𝟐𝟏𝟐𝟖𝟏𝒘𝑪+𝒓(𝒘𝑪(𝜺−𝟏.𝟑𝟏𝟑𝟑)+𝟏.𝟖𝟏𝟔𝟏)−𝟏.𝟏𝟏𝟏𝟏𝟔𝟏�   (11-21) Integration are shown in Appendix G. Parameters in the model are listed in Table 11-1. Table 11-1 Parameters in the Mathematical Model Parameter Definition Comments t (s) Time Independent variable Ri (m) Radius of rings after being corroded Dependent variable Ro (m) Radius of rings with deposit Ro can be express by Ri with Equation (11-11). De (m2/s) Effective diffusion coefficient De of H2S depends on the oil properties, deposit structure and temperature. cAb(0) (mol/m3) Initial active sulphur concentration in the ATB Roughly 36 wt% of total sulphur is active in the present work. ρB (kg/m3) density of the ring metal 7850 kg/m3 for carbon steel kS (s-1) Rate constant of thermal decomposition of active sulphur species kS is obtained with Equation (11-17) if several groups of t and Ri are known. wC Mass fraction of FeS in deposit Mass fraction of coke is (1-wC). ε Porosity of the deposit The porosity of coke and FeS may be significantly different.  158 11.2.2 Parameters in Equation (11-17) 11.2.2.1 Porosity of Deposit According to Appendix H, the porosity of deposit is roughly a function of wall shear stress and mass fraction of FeS; however, the influence of mass fraction is much weaker than shear stress. For the coke induction period, the deposit is mostly FeS. Thus for FeS, the porosity of deposit can be treated as a function of only wall shear stress. The function can be determined from Equation (6-9): 𝜺 = 𝟏.𝟑𝟏𝟖𝟖𝑹− 𝝉𝒘𝟏.𝟖𝟐𝟏𝟏 + 𝟏.𝟑𝟏𝟏𝟏        (6-9) 11.2.2.2 Effective Diffusion Coefficient Since the ratio of H2S size to the deposit pore size is very small [168], De can be expressed as [169]: 𝑫𝑹 = 𝑫𝒔 𝜺𝝉          (11-22) In which ε and τ are the porosity and tortuosity factor of the outer deposit layer, respectively. For deposit layers mainly constituted of FeS, the tortuosity can be estimated as high as 333 [75], due to the layered structure of FeS [170]. Ds is the diffusion coefficient of H2S in the ATB. For smaller solute molar volumes, the Wilke-Chang correlation is recommended to estimate the diffusion coefficient [171].  𝑫𝒔 = 𝟏.𝟏𝟖𝟑 × 𝟏𝟏−𝟏𝟔�𝝋𝑴𝒇 𝑻𝝁𝑶𝑽𝑨𝟏.𝟔      (11-23)  159 where T is the absolute temperature, K. μO is the dynamic viscosity of oil, Pa·s. φ is an “association parameter” of the solvent. For the present work, φ = 1 [171]. VA is the molar volume of H2S at boiling point, m3/kmol. VA = 0.0329 m3/kmol. Mf is the average molecular weight of ATB oil, g/mol. It can be determined from the formula of Voinov [172]: 𝑴𝒇 = 𝟔𝟏+ 𝟏.𝟑𝒅𝒂 + 𝟏.𝟏𝟏𝟏𝒅𝒂𝟐        (11-24) where ta is mean boiling point, °C. For ATB, ta = 560°C. Thus Mf = 541.6 g/mol. For a typical deposit porosity of 0.5, Ds and De values of H2S are listed in Table 11-2. Table 11-2 Ds and De at 380-410°C for the Deposit Porosity of 0.5 Bulk Temperature, °C Ds, ×108 m2/s De, ×1011 m2/s 380 0.915 1.373 390 0.997 1.497 400 1.083 1.626 410 1.173 1.762 11.2.2.3 Initial Concentration of Active Sulphur Species in the ATB As discussed in Section 7.4, only about 36% of sulphur compounds in the ATB contribute to corrosion. Assuming that one active sulphur compound molecule contains one sulphur atom, the concentration of active sulphur in the ATB can be determined as: 𝒄𝑨𝒃(𝟏) = 𝟏𝟏𝟔 ∗ 𝟏.𝟏𝟖𝟖∗ 𝟏.𝟑𝟔𝟑𝟐.𝟏𝟔𝟏𝟏𝟏𝟏𝟏.𝟏𝟐𝟏𝟏 𝒎𝒍𝒍𝒎𝟑 = 𝟏𝟔𝟏 𝒎𝒍𝒍/𝒎𝟑   (11-25) 11.2.2.4 Thermal Decomposition Rate Constant of Active Sulphur Species  If bulk temperature and rotational speed (wall shear stress) are known, ε and De can be determined. For experiments of fixed bulk temperature and rotational speed for different 160 durations, wC and Ri can be calculated with TGA data. Thus all parameters except kS are known for Equation (11-17). Thus kS values are obtained from 24-hour experiments at 370°C and 380°C, as seen in Table 11-2. Table 11-3 kS for 24-Hour Experiments at 370°C and 380°C Bulk Temperature, °C kS, ×106 s-1  370 1.146 380 2.191  Activation energy, EaS, and the pre-exponential factor, AS, can be determined from the Arrhenius equation: 𝒍𝒏�𝒌𝑺(𝟑𝟖𝟏°𝐂)� = 𝒍𝒏(𝑨𝑺) − 𝑬𝒂𝑺𝑹 𝟏𝟔𝟏𝟑.𝟏𝟏𝑲     (11-26) 𝒍𝒏�𝒌𝑺(𝟑𝟖𝟏°𝐂)� = 𝒍𝒏(𝑨𝑺) − 𝑬𝒂𝑺𝑹 𝟏𝟔𝟏𝟑.𝟏𝟏𝑲     (11-27) Thus EaS =226.3 kJ/mol; AS = 2.780×1012. The rate constant kS can be expressed as: 𝒌𝑺 = 𝟐.𝟖𝟖 × 𝟏𝟏𝟏𝟐𝑹−𝟐𝟐𝟔𝟑𝟖𝟑𝑹𝑻        (11-28) 11.2.2.5 Mass Fraction of FeS in Deposit The mass fraction of FeS in deposit for 6-24 hours experiments at 380°C and 390°C, determined from TGA results, are listed in Table 11-3.  At 380°C, the mass fraction of FeS is nearly constant with experiment durations, and most (90 wt%) deposit is ash (corrosion product). At 390°C, the mass fraction of FeS in 161 the 6 hours experiment is close to that for 12-24 hours experiments at 380°C (around 0.9); however it decreased significantly with 18 or 24 hours experiment. According to the facts in Section 8.3, it takes about 31 hours and 10 hours for the asphaltene cores to reach the solubility limit at 380°C and 390°C, respectively. Table 11-4 Mass Fraction of FeS in Deposit Duration, Hours wC 370°C 380°C 390°C 6  - 0.872 12  0.911  18  0.896 0.637 24 0.906 0.839 0.572  These facts may indicate two circumstances: 1) Before the limit was reached, only a very small part of asphaltene cores attached to metal surface and formed coke, where wC is close to 1. Apparently FeS deposit or layer promotes this attachment significantly. 2) Extensive coke deposition on ring surfaces occurs approximately after the solubility limits of asphaltene cores are reached and huge amount of asphaltene core precipitates from ATB, where the mass fraction of FeS, wC, is close to zero.  11.2.3 Discussion of the Model Determination of parameters has been discussed in Section 11.2.2. The model is now ready for calculations. 162 11.2.3.1 Concentration of H2S in the Bulk Oil Dissolved H2S in bulk oil comes from the decomposition of sulphur species (mainly thioethers). Assuming that all H2S is dissolved in the oil during the experiments, the concentration can be determined from Equation (11-15), as shown in Figure 11-2. As shown in Figure 11-2, after 24-hour experiments, about 16%, 26% and 41% of active sulphur compounds were decomposed to release H2S, for experiments at 370°C, 380°C and 390°C, respectively. The H2S concentration is 75-190 mol/m3 after 24 hours. 0 5 10 15 20 25020406080100120140160180200  Concentration of Hydrogen Sulphide (mol/m3 )Time (hours) 370°C 380°C 390°C Figure 11-2 Change of Dissolved H2S Concentration in Bulk Oil 11.2.3.2 Temperature Effects on the Corrosion Rate Temperature effects on corrosion rates were predicted with Equation (11-17), as shown in Figure 11-3 and Figure 11-4. In the first 24 hours, the changes of metal thickness are 163 almost linear. The corrosion rate at 390°C is evidently higher than at 370°C and 380°C, as shown in Figure 11-3. However, Figure 11-4 shows that the expected corrosion rate would slow down over extended time periods, due to the thicker deposit layer. It is interesting that highest corroded metal thickness after a year occurred at 370°C rather than 390°C. It should be noted that the predictions are based on an average wC when the deposit is mostly FeS rather than coke, and thus is only applicable within the induction period. If rapid coking occurred, the corroded thickness value will be much lower due to the large diffusion resistance brought about by the rapid growth of coke. 0 5 10 15 200.0000.0020.0040.0060.0080.010  Corroded Fe Thickness (mm)Time (hours) 370°C 380°C 390°C Figure 11-3 Calculated Corroded Fe Thickness Details for the First 24 Hours (600rpm) 164 -50 0 50 100 150 200 250 300 350 4000.00.10.20.30.40.5   370°C 380°C 390°CCorroded Fe Thickness (mm)Time (day)Model Allometric1Equation y = a*x^bReduced Chi-Sq 1.93766E- 1.07539E- 1.29187E-4Adj. R-Square 0.99333 0.99335 0.99448Value Standard ErroCorroded Fe Thicknessa 0.01929 0.00235b 0.55429 0.0224a 0.01785 0.00195b 0.51795 0.02029a 0.02381 0.00224b 0.5012 0.01757 Figure 11-4 Power Curve Fitting of Corrosion Fe Thickness vs Time (One Year, 600rpm) Power curve fittings of corrosion Fe thickness with time is shown in Figure 11-4. The power of rate laws for 370°C, 380°C and 390°C is 0.554, 0.518 and 0.501, respectively, indicating that the parabolic rate law, as discussed in Section 2.4.2, well describes the corrosion kinetics. Thus the rate determining step is diffusion of H2S through the deposit. In addition, power values indicate how strong the restrictive diffusion affects the corrosion. Thus the most significant influence occurs at 390°C, which is logical since more coke is obtained at higher temperature.  For the first 24, the linear corrosion rate law indicates that chemical reaction is the rate determining step in the initial stage of experiments, when deposit scale can be neglected. 165 Table 11-4 also indicates the hindering effect of deposits. It can be concluded from the table that if hindered diffusion through deposit layer is not considered, the model calculated corrosion rate is around 2.4-4 mm/year at 370-390°C, which is close to the value from the McConomy curves. However, when the influence of deposit is considered, the corrosion rate is only around 1/5 - 1/10 of the values without deposit. Table 11-5 Corrosion Rate Determined from the Deposition Model and from McConomy Curves  Corrosion Rate, mm/year Tb, °C With Deposit Layer Without Deposit Layer McConomy Curves 370 0.492 2.428 2.599 380 0.368 2.571 2.956 390 0.446 4.036 3.289  11.2.3.3 Thickness of the Deposit Thickness of the deposit after 24 hours and one year are predicted with the model, as shown in Figure 11-5 and Figure 11-6.  For 24 hours, the average deposition rate is increasing with elevated temperatures, while for a period of one year, the average corrosion rates at 380°C and 390°C are roughly the same, and are higher than the corrosion rate at 370°C. This prediction applies within the induction period for all temperatures and is not applicable if rapid coking occurs.  166 0 5 10 15 200.000.010.020.030.040.050.060.07  Thickness of Deposit (mm)Time (hours) 370°C 380°C 390°C Figure 11-5 Change of Thickness of Deposit with Time (24 hours) 0 50 100 150 200 250 300 350 4000.00.51.01.52.02.53.0  Thickness of Deposit (mm)Time (day) 370°C 380°C 390°C Figure 11-6 Change of Thickness of Deposit with Time (One Year) 167 11.2.3.4 Effects of Initial Sulphur Species Concentration on Corrosion rate  As discussed in Section 7.4, DMS was added to the ATB to increase the initial sulphur compounds concentration. The initial concentration of active sulphur compounds of ATB itself was determined in Section 11.2.2.3 as 465 mol/m3. Addition of DMS, according to Section 7.4, contributed active sulphur of 1302 mol/m3. Thus the total active sulphur species would be 1767 mol/m3. The corrosion rates for ATB with and without additional DMS were determined, as seen in Figure 11-7. The corroded Fe thickness with additional DMS in the ATB is around 1.6-2 times of the values without additional DMS. 0 50 100 150 200 250 300-0.10.00.10.20.30.40.50.60.7   380°C 390°C 380°C with DMS 390°C with DMSCorroded Fe Thickness (mm)Time (day)  Figure 11-7 Calculated Corroded Fe Thickness Change with Additional DMS (600rpm) The corroded metal thickness for the 24-hour experiment, which can be determined from the model, is 13.4 μm for 380°C and 20.7 μm for 390°C. However, according to Section 7.4, the mass of ash in deposit after addition of DMS was 133.1mg for 380°C, 168 which equals to 9.9 μm of corroded metal thickness, and 142.3 mg for 390°C, which equals to 10.6 μm. Two probable reasons may account for the difference. Firstly, the rate constant of DMS decomposition is different from the reaction of actual active sulphur species in the ATB. Secondly, H2S may be saturated in the ATB due to the addition of DMS. In this case, excessive H2S will not be dissolved in the ATB and diffuse to the metal surface. 11.2.3.5 Shear Stress Effects on Corroded Metal Thickness Shear stress effects on corroded metal thickness is also calculated with the model and compared with measured values, as shown in Figure 11-8 and Figure 11-9.  0 2 4 6 8 10 12 14 160.0000.0010.0020.0030.0040.0050.0060.0070.0080.0090.010  Corroded Metal Thickness (mm)Shear Stress (Pa) 380°C Calculated (24 hours) 380°C Measured (24 hours) Figure 11-8 Calculated an Measured Corroded Metal Thickness for Experiments at 380°C 169 At both temperatures of 380°C and 390°C, the calculated corrosion rate are slightly increasing with shear stress, which is a comprehensive effect of lower thickness and porosity (higher density) at high wall shear stress. For the 380°C experiments, the predicted corrosion rate is close to the measured values. For the 390°C experiments, the corroded metal thickness is based on 9.6-hours experiments. This duration is the time of induction period for the ATB at 390°C, according to the phase separation model of coking discussed in Section 8.3. It indicates that around 75% of corrosion occurred in the induction period, though the time of this period is only 40% of total 24 hours. 0 2 4 6 8 10 12 14 160.0000.0010.0020.0030.0040.0050.0060.0070.0080.0090.010  Corroded Metal Thickness (mm)Shear Stress (Pa) 390°C Calculated (9.6 hours) 390°C Measured (24 hours) Figure 11-9 Calculated an Measured Corroded Metal Thickness for Experiments at 390°C 170 11.3 Thermal Coking Mechanism Based on the Phase Separation Model The phase separation model discussed in Chapter 8 is a proper method to describe thermal coking behaviour. In this section, efforts were made to find the relationship between the phase separation model and the coking deposition rate on the ring surface. Then the change of coking behaviour with time at different temperatures and shear stress can be discussed. 11.3.1 Asphaltene Cores and Coke Accumulation Rates According to Figure 5-2, most deposit on the carbon steel ring surface after the 24-hour experiment at 380°C was corrosion products, whereas for experiments with the same duration at temperatures higher than 400°C, carbonaceous material prevails. At 380°C, the whole experiment was in the coking induction period, and rapid coking occurred at higher temperatures. These facts are accordance with the explanation from the phase separation model, which concluded the induction period is 32.2 hours at 380°C, 9.6 hours at 390°C and 4.7 hours at 400°C. The coke deposition on the carbon steel ring surface is illustrated in Figure 11-10. Interpolation was made from 0 to 24 hours, and then the coke generation rate on the surface was obtained by the first derivative of the mass of coke per unit surface area. Meanwhile, the concentrations of asphaltene cores (A*) for any time has been determined from the phase separation model (Appendix D) over extended times, as shown in Figure 11-11. Thus the relationship between coke accumulation rate and concentration of asphaltene cores can be obtained, as shown in Figure 11-12. 171 0 5 10 15 20 25024681012141618  Mass of Coke per Unit Surface Area, (g/m2 )Time (h)  Figure 11-10 Coke Generation on the Surface with Time (380°C, 600rpm) 0 200 400 600 800 1000 1200 1400010203040506070   380°C 390°CConcentration of Asphaltene Cores (A*) (wt%)Time (h)Model Asymptotic1Equation y = a-b*c^xReduced Chi-Sqr 0.00978 0.00311Adj. R-Square 0.99999 1Value Standard ErrorConcentration of Asphaltene Cores (A*)a 64.05184 0.04619b 63.961 0.06318c 0.99565 1.47397E-5a 64.08452 0.0223b 64.00979 0.04015c 0.98625 2.66142E-5 Figure 11-11 Concentration of Asphaltene Cores in the ATB versus Time (380°C and 390°C) 172 0 1 2 3 4 5 6 70.00.20.40.60.81.01.21.41.6  Generation  Rate of Coke (g/(m2 ·h))Concentration of Asphaltene Cores (A*) (wt%)  Figure 11-12 Coke Generation Rate on the Surface vs Asphaltene Cores Concentration The rate of coke generation can be expressed as a function of concentration of asphaltene cores as follows: 𝒓𝒄′ = 𝒌𝒄′ (𝒄𝑨∗′ )𝒏          (11-29) where r’c is coke generation rate, g·m-2·h-1; k’c is rate constant, g·m-2·h-1; c’A* is the concentration of asphaltene cores in bulk oil, wt%; n is the reaction order. The parameters k’c and n can be determined by fitting the data in Figure 11-12 as: 𝒓𝒄′ (𝟑𝟖𝟏°𝑪) = 𝟏.𝟏𝟐𝟔𝟏𝟏(𝒄𝑨∗′ )𝟏.𝟑𝟏𝟏𝟏𝟏       (11-30) The mass of coke per unit surface area for 24-hour experiment at 380°C, calculated with the above correlation is 16.5 g/m2, which is in good agreement with the measured value, 16.4 g/m3. 173 According to Figure 6-7 and Figure 6-8, for 24-hour experiments at different conditions of shear stress, the mass of carbonaceous deposit is independent of shear stress at 380°C, but significantly different at 390°C at lower shear tress zone. This may indicate that the coke generation rate in the coke induction period is similar at both temperatures. Assuming the reaction order is the same for 390°C in coke induction period (0-9.6 hours) as at 380°C, the following equation with a new rate constant can be obtained: 𝒓𝒄′ (𝟑𝟏𝟏°𝑪) = 𝟏.𝟏𝟏𝟔𝟏𝟐(𝒄𝑨∗′ )𝟏.𝟑𝟏𝟏𝟏𝟏        (11-31) Similarly, the mass of coke per unit surface area for 24-hour experiment at 390°C calculated with the above correlation is 106.9 g/m2, which is much higher than the measured value (49.9 g/m3). This indicates Equation (11-31) may be only applied for coke induction period. Since the asphaltene cores (A*) are well dissolved in maltene-asphaltene solution during the coke induction period, whereas they precipitate during the rapid coking period, the coke deposition rate, in this situation, may be related to the dissolved asphaltene cores rather than total asphaltene cores. To verify this hypothesis, the dissolved asphaltene, A*d, was determined for 24-hour experiments, as shown in Figure 11-13. The experiment was divided into two stages with the moment at which the solubility limit of asphaltene cores is reached (9.6 hours). The dissolved asphaltene cores is actually the total generated asphaltene cores before 9.6 hours, and the maximum asphaltene cores that can be held in solution (i.e. the solubility limit), A*max, after 9.6 hours. Data are calculated with the phase separation model.  174 0 2 4 6 8 10 12 14 16 18 20 22 24012345678   390°CDissolved Asphaltene Cores in ATB solution (wt%)Time (h)quick coking periodcoke inductionperiod Figure 11-13 Calculated Dissolved Asphaltene Cores (A*) in the ATB solution (390°C) The solubility limit is slowly decreasing because maltene keeps converting to asphaltenes and volatiles. Thus the coke formation rate can be obtained with Equation (11-31). Then the mass of coke per unit surface area can be determined by integrating the coke formation rate data with time, as shown in Figure 11-14. Table 11-5 lists the predicted value from Figure 11-14 and measured value.  175 0 5 10 15 20 250102030405060   390°CMass of Coke per Unit Surface Area, (g/m2 )Time (h)coke inductionperiodfast coke period Figure 11-14 Coke Generation with Time (390°C, 600rpm) Table 11-6 Comparison of Calculated and Measured Mass of Coke (390°C, 600rpm, CS) Time, h Mass of Coke per Unit Surface Area, g/m2 Calculated Measured 6 4.77 4.99 18 39.08 38.68 24 54.95 49.84  Table 11-5 shows the experiment results are in good agreement with calculated values. Thus this model applies to high shear stress situation (τw > 3-3.5 Pa). In fact, asphaltene cores can be well dispersed in the ATB only because they can get enough donor hydrogen from the heptane solubles (maltene) to terminate asphaltene-free radicals [89]. When the donor hydrogen is not sufficient as the conversion proceeds, the 176 asphaltene radicals will have a strong tendency to recombine to form coke and precipitate from the solution. Therefore, it may be concluded that the metal surface (especially with FeS) will attract the dissolved asphaltene cores, which form coke precursors and finally coke on the surface since they cannot get sufficient donor hydrogen after leaving the solution. This process is not significantly affected by shear stress. When the solubility limit is reached, the asphaltene radicals combine and form coke precursors in the bulk oil. Those coke precursors are still deficient in hydrogen. They have two routes after formation. The first route is combining with the coke precursors on the metal surface to form coke. This step is strongly influenced by the shear stress. Large shear stress (> 3-3.5 Pa) makes it very difficult for precursors to adsorb to the precursors on the metal surface. Under these circumstances, all precursors will combine with each other in bulk oil to form large coke particles, which is the second route. Once coke particles are formed in bulk oil, there is no chance for them to adsorb to the metal surface. 11.3.2 Model Development and the Application Based on the above discussion, the model for thermal coking with concentration of dissolved asphaltene cores, A*d, can be developed from the data obtained via the phase separation model with parameters determined in Section 8.3, as shown in Table 8-1. At 380°C, 𝑨∗(𝟑𝟖𝟏°𝐂) = 𝟔𝟏.𝟏𝟏𝟏𝟖𝟏 − 𝟔𝟑.𝟏𝟔𝟏 ∗ 𝟏.𝟏𝟏𝟏𝟔𝟏𝒅(𝒉)    (11-32) 𝑨𝒎𝒂𝒅∗ (𝟑𝟖𝟏°𝐂) = 𝟏.𝟔𝟏𝟏𝟖 ∗ 𝟏.𝟏𝟏𝟏𝟏𝟑𝒅(𝒉)      (11-33) 177 The solubility limit is reached when 𝑨∗(𝟑𝟖𝟏°𝐂) = 𝑨𝒎𝒂𝒅∗ (𝟑𝟖𝟏°𝐂)         (11-34) Thus t = 32.1515h. The dissolved asphaltene cores, A*d, can be expressed as: 𝑨𝒅∗ (𝟑𝟖𝟏°𝐂) = �𝟔𝟏.𝟏𝟏𝟏𝟖𝟏 − 𝟔𝟑.𝟏𝟔𝟏 ∗ 𝟏.𝟏𝟏𝟏𝟔𝟏𝒅(𝒉) (𝒅 ≤ 𝟑𝟐.𝟏𝟏𝟏𝟏𝒉)𝟏.𝟔𝟏𝟏𝟖 ∗ 𝟏.𝟏𝟏𝟏𝟏𝟑𝒅(𝒉) (𝒅 > 𝟑𝟐.𝟏𝟏𝟏𝟏𝒉)    (11-35) Similarly, the dissolved asphaltene cores, A*d, for 390°C is : 𝑨𝒅∗ (𝟑𝟏𝟏°𝐂) = �𝟔𝟏.𝟏𝟖𝟏𝟏𝟑 − 𝟔𝟏.𝟏𝟏𝟏𝟏𝟐 ∗ 𝟏.𝟏𝟖𝟔𝟐𝟏𝒅(𝒉) (𝒅 ≤ 𝟏.𝟏𝟖𝟏𝟏𝒉)𝟏.𝟏𝟏𝟏𝟏 ∗ 𝟏.𝟏𝟖𝟔𝟖𝟖𝒅(𝒉) (𝒅 > 𝟏.𝟏𝟖𝟏𝟏𝒉)    (11-36) Replacing c’A* in Equation (11-30) and (11-31) with A*d, the coking rate on metal surface can be determined. Then the mass of coke per unit surface area can be obtained by integrating coking rate on metal surface with time. Thus the accumulation of coke with time can be plotted, as shown in Figure 11-15 and Figure 11-16. In the first about 105 hours, the coke generating rate at 390°C is higher than that at 380°C; however, after 105 hours, the mass of coke on the metal surface is higher at 380°C. After a long time, the mass of coke on metal surface at 380°C is over twice that at 390°C. For a limited mass of ATB, the amount of asphaltene cores which can be eventually generated is the same for 380°C and 390°C. If bulk coke consumes more asphaltene cores, there will be fewer cores left for the metal surface. At 600rpm and 390°C, the precipitated asphaltene cores, which are the precursors of coke, cannot as easily adhere to the metal surface. Thus more asphaltene cores are converted to bulk coke than at 380°C. This is the explanation for Figure 11-16. 178 0 200 400 600 800 1000 1200 14000100200300400500  Mass of Coke per Unit Surface Area, (g/m2 )Time (h) 380°C 390°C Figure 11-15 Coke Generation on Metal Surface versus Time 0 20 40 60 80 100 120 140 160 180050100150200250300  Mass of Coke per Unit Surface Area, (g/m2 )Time (h) 380°C 390°C9.6h24h32.1h105h Figure 11-16 Projected Coke Generation on Metal Surface versus Time in the First 140 Hours 179 11.4 Summary A physicochemical model is proposed to describe the probable mechanism for fouling in sour oils under incipient coking conditions, which involves sulphide corrosion of the equipment metal and coke formation on metal surfaces. Sulphide corrosion and coke formation proceeds simultaneously and the products (FeS and coke) are mixed together during the fouling process, which makes the problem more complicated. Thermal coking can be predicted with the phase separation model. Bulk coke forms when the solubility limit is reached and asphaltene cores combine and precipitate. For low wall shear stress, bulk coke may adhere to metal surfaces and lead to a rapid coking. At high wall shear stress, surface coke mainly comes from the adherence of dissolved asphaltene cores. A mathematical model is developed with an expanding scale assumption. H2S diffuses through the pores in the deposit scale to the metal surface, which is the rate determining step, especially when the scale gets thicker. The corrosion kinetics obtained with this model approximates a parabolic law. This model can be used to predict the corrosion rate and fouling accumulation rate in oil processing.   180 Chapter 12: Conclusions and Recommendations 12.1 Conclusions 1. An extensive study of the growth of fouling layers on various metal alloys has shown that fouling in sour heavy oil at elevated temperatures is a complex process in which both inorganic and carbonaceous materials accumulate in deposits. Inorganic material in deposits is mainly from corrosion. Temperature significantly affects the build-up of deposits mainly by the formation of coke. Fouling mainly includes three steps: corrosion of the exposed surface, adherence of asphaltenes to the corroded surface and coke formation from the asphaltenes. 2. Sulphide corrosion is the principal type of corrosion since the naphthenic acid corrosion is negligible in the temperature range of present work (370-410°C). Active sulphur species (mainly thioethers) comprise about 36 wt% of the total sulphur species in the ATB. Active sulphur species decompose at high temperatures (380-400°C) to generate H2S, which dissolves in the feed ATB, and reacts with the metal. Additional active sulphur enhances the sulphide corrosion significantly at 380°C, whereas the effect is much weaker at 390°C, where a coke layer formed. 3. Results showed that the most probable atomic ratio of Fe and S in the sulphide corrosion product is 1:1. Corrosion product was shown to promote the adherence of asphaltene to the surface. Coking on metal surfaces was shown to have a higher activation energy compared to coking in the bulk oil, which means that at 181 higher temperatures, the coking reaction tends to occur preferentially on metal surfaces. 4. The coke formation on both the metal surface and in the bulk oil can be described with the phase separation model. In the induction period, a small part of asphaltene cores adsorb on the metal surface and finally form coke. FeS layers promote this process. After the solubility limit of asphaltene is reached, excessive asphaltene precipitates from the solution to eventually form coke in the bulk liquid. At lower wall shear stress, precursors have a chance to adhere to the rotating metal surfaces to form coke on them, while at larger shear stress, adherence is suppressed, leading all precipitate asphaltene cores to the bulk coke. Under this circumstance, dissolved asphaltene cores contribute most coke deposit on the metal surface. 5. Surfaces tested can be divided into corroding and non-corroding alloys, depending on Cr content. Alloys between 15-20 wt%. Cr, serve as the boundary between low % Cr corroding surfaces where fouling layers contain significant inorganic content, and high % Cr non-corroding surfaces where deposits are essentially organic matter. 6. For corroded surfaces such as carbon steel, there is a transitional layer between the metal surface and coke, which is constituted of an iron-rich FeS. This layer forms in the initial stages of the experiment, when the concentration of asphaltene cores is low in bulk oil and very little asphaltene adheres to the metal surface. Most sulphide corrosion occurs in this period. Subsequently, more and more asphaltene cores adhere to the surface and form coke, which makes the 182 diffusion of H2S to the metal much more difficult. At temperatures higher than 390°C, large amounts of asphaltene cores are generated in a short time, leading to a rapid formation of a coke film on the surface. Thus most deposit (>90 wt%) is carbonaceous matter for both corroded and non-corroded surfaces. 7. Coke deposits are porous with a porosity around 0.35-0.65. These pores are filled with liquid oil during the experiments, which would allow H2S to diffuse from the outer deposit surface to the metal surface. The porosity is significantly affected by shear stress. 8. Trace inorganic element analysis with ICP-AES indicates that most of the Fe in the deposit arises from corrosion of the metal surfaces. Most dissolved iron in the ATB is consumed during the forming of bulk coke, while a small part remains in the spent oil. 9. For carbon steel, the effect of shear stress on deposition is significantly different for corrosion controlled conditions (380°C) than for incipient coking conditions (390°C). At 380°C, the deposition rate and composition of deposit is not largely affected by shear stress. At 390°C, and at lower shear stresses, fouling rate is high and deposits are mostly carbonaceous matter. At higher shear stress, fouling rate drops off sharply and becomes insensitive to shear stress. The significant difference in performance at similar temperatures can be explained with the phase separation model. At 380°C, the induction period is about 32 hours. Thus the whole 24-hour experiment is within this period, where the adherence of asphaltene cores on metal surface is weak; whereas at 390°C or higher temperatures, only a part of the 24-hour experiment is in the induction 183 period. Asphaltene cores start to precipitate when the solubility limit is reached. Part of the cores may attach to the metal surfaces at lower shear stress. At high shear stress, precipitated asphaltene cores cannot adhere to the metal surface and thus form bulk coke instead. Therefore carbonaceous matter in the deposit decreased sharply at higher shear stress. 10. A mathematical model was developed which captures the essential features of the growth of fouling films on corroded metal surfaces. Parameters of the model were discussed. Predictions were made with the model under the circumstances of present work. 12.2 Recommendations for Further Study 1. The mass fraction of FeS in deposit, porosity and effective diffusion coefficient were treated as constants in the mathematical model of diffusion controlled sulphide corrosion. Actually the mass fraction of FeS will change during experiment due to quicker coking reaction and slower sulphide formation. 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Baboian, "9.4.15 Austenitic Stainless Steels - Composition, %," NACE Corrosion Engineer's Reference Book (3rd Edition), NACE International,  2002. 206 Appendices Appendix A  Properties of Syncrude ATB  A.1 Special Distillation of Syncrude ATB (ASTM D86)* Weight Percentage of Evaporated Fraction, wt% Boiling Point, °C IBP 105 2 289 4 318 6 337 8 352 10 365 20 417 30 460 40 505 50 547 60 591 70 642 80 701 90 785 95  FBP  Volume Average Boiling Point (VABP) 560 * Data come from Syncrude Canada Ltd..  207 A.2 Trace Inorganic Elements in Syncrude ATB* Element Concentration, wppm Aluminum 658 Barium 8 Cadmium 4 Calcium 131 Chromium <1 Copper 8 Iron 744 Lead <1 Magnesium 55 Manganese 25 Molybdenum <1 Nickel 73 Phosphorus <1 Potassium 95 Silicon 775 Silver 105 Sodium <1 Tin 49 Titanium 80 Vanadium 142 Zinc <1 * Data come from ICP-AES test.208 Appendix B  Metal Chemical Composition Ranges of Tested Metals Chemical Composition Ranges of Tested Metals (wt%) [173-176] UNS Name Chemical Composition*, wt%, C Cr Cu Mn Mo Ni P S Si Al Ti G10180 1018 CS [173] 0.15-0.2   0.6-0.9   0.04 0.05    N08825 Incoloy 825 [174] 0.05 19.5-23.5 1.5-3 1 2.5-3.5 38-46  0.03 0.5 0.2 0.6-1.2 K90941 9-Cr** [175] 0.15 8-10  0.3-0.6 0.9-1.1  0.03 0.03 0.5-1   S31700 317 SS [176] 0.08 18-20  2 3-4 11-15 0.045 0.03 1   * Max value unless otherwise specified; Fe balanced ** 9-Cr is the abbreviation of 9Cr-1Mo steel  209 Appendix C  Temperature Control System C.1 Single Temperature Control: Pros and Cons Heating Procedure Pros Cons Temperature control with thermocouple in the heating jacket Jacket temperature is limited to prevent a super high temperature. 1. Heating temperature has to be estimated to achieve a certain bulk temperature, therefore not very accurate.   2. Heating temperature has to be adjusted manually and frequently according to the bulk temperature, which is especially inconvenient when energy consumption changes a lot (phase change or cracking at high temperature).  3. It’s difficult to do duplicate experiments since the inaccurate and frequent and random external interference.  Temperature control with thermocouple in the reactor 1. The control is more accurate. 2. Heating temperature can be adjusted automatically when needed. 1. This method cannot be used when the temperature starts to elevate. Temperature increases with different rate for the reactor and heating jacket, which makes the temperature of heating jacket super high.  2. In special cases (rotating stop working or coking due to oxygen), the jacket temperature will continuously increase without limit to maintain a constant reactor temperature, which makes things worse and may cause serious problems.    210 C.2 Dual Temperature Control System In order to solve the problem of the single temperature control system, a new circuit scheme was designed with two identical relays in series for temperature control, as follows.  Thus the problems were solved with this control mode which has the following features: • At first, both relay 1 and relay 2 are on since the heating temperature and bulk temperature are below the setting values. The jacket temperature can be set to a proper value to make the bulk temperature increasing to required temperature rapidly. Meanwhile, a temperature limit is also guaranteed to prevent over heating. 211 • When the bulk temperature approaches the required value, relay 1 turns off and the system is disconnected so that the excessive heat in the jacket can be released to prevent the overheating. • During experiments, Relay 1 is on and off to help adjusting the bulk temperature. Relay 2 is always on since the heating temperature is below the set value. • When huge energy consumption occurs due to a phase change or a minor thermal cracking, the jacket temperature can be adjusted automatically to maintain a constant bulk temperature. • In special cases (stop rotating or coke on the wall), the jacket temperature will be limited below the heating temperature, which ensures a safe operation of the reactor. There are several advantages for dual temperature control mode: • Temperature control is very accurate (389 ~ 391°C for 390°C). • Temperatures set for the jacket will not influence the accuracy of bulk temperature.  • The control method makes sure the fast increasing of bulk temperature as well as prevents coking near the liner wall, which makes the control more reliable.  • This method ensures identical heating time if the jacket and bulk temperature are set to the same value for each experiment.   212 Appendix D  Derivation of Equations for the Phase Separation Kinetic Model [89] The thermolysis of asphaltenes and heptane solubles are first order reactions: AdA k Adt++=  MdM k Mdt++=  Integrating these equations yields: 0Ak tA A e−+ =  ( )0100 Mk tM A e−+ = −  ( )( )( ) ( ) ( )0 01 100 1 1 1M Ak t k tV m A e a b A e− −= − − − + − − −  During the coke induction period: ( )( ) ( )* 0 0100 1 1M Ak t k tA m A e aA e− −= − − + −  *A A A+= +  ( )* 0 1 Ak tM bA e−= −  *M M M+= +  0TI =  213 The coke induction period ends when ( )* *LA S M M+= +  Thereafter, A* is given by the preceding solubility equation, and ( )* 0 11Ak tyTIM bA ey−= + −− [ ] ( )( ) ( ) ( )*0 01 100 1 1M Ak t k t LTI y m A e aA e S M M− − + = − − − + − − +   Substituting for M* and solving for TI: [ ] ( ) ( )( ) ( ) ( )0 0 01100 100 11M Ak t k tL LLyTI m A m S A e a bS A eyS− −−  = − − + − + − − +   214 Appendix E  Determination of Asphaltene Concentration in the ATB and the Spend Oil – Detailed Procedure 1. Separation of Oil and deposit: a. Separate the spent oil from large chunks of coke with wear-resistant 61x61 Nylon mesh (opening size: 300 µm) and measure the weight of oil W(oil) b. Calculate the weight loss of whole set before and after run. This weight loss indicates the mass of gas phase which gets out of the system during experiments, W(gas) c. The weight of deposit including those on the wall, shaft and thermocouple, Macor ceramic pads and rings are calculated as: W(deposit1) = W(feed) - W(oil) - W(gas). 2. Determination of the amount of Coke in liquid oil/deposit a. Fold up the Whatman grade 41 ashless filter paper (20 µm in pore diameter) to form a funnel shape filter and weigh it b. Well mix the oil/deposit in Step 1) and sample about 1 g in the funnel paper filter, record the weight of sample c. Put 50 ml toluene (HPLC grade) in the flask and suspend the filter in the flask d. Start the cooling water circulation e. Set the heating temperature to 115-120°C to evaporate the toluene f. Extract the sample with hot toluene for 30 minutes after the solvent dripping from the sandpaper becomes colorless 215 g. Stop heating and dry the filter paper in an oven at 120°C for 1 hour h. Measure the weight of filter paper 3. Determination of the amount of asphaltene in the oil/deposit a. Fold up the Whatman grade 42 ashless filter paper (2.5 µm in pore diameter) to form a funnel shape filter and weigh it b. Well mix the oil/deposit in Step 1) and sample about 1 g in the funnel paper filter, record the weight of sample c. Put 50 ml n-heptane (HPLC grade) in the flask. Suspend the filter in the flask d. Start the cooling water circulation e. Set the heating temperature to 105-110°C to evaporate the toluene f. Extract the sample with hot n-heptane for 30 minutes after the solvent dripping from the sandpaper becomes colorless g. Stop heating and dry the filter paper in an oven at 120°C for 1 hour h. Measure the weight of filter paper   216 Appendix F  Typical Heat Transfer Coefficients [165] Fluid U, W/m2·K Gases   Gases, Low Pressure 20-80  Gases, High Pressure 100-300  Hydrogen-Rich Gases 80-150 Liquid   Water, Turbulent Regime 1500-3000  Dilute Aqueous 1000-2000 Solution   Light Organic Liquids 1000-1500  Viscous Organic Liquids 500-800  Heavy-Ends 200-500  Brines 800-1000  Molten Salts 500-700 Boiling Liquids   Boiling Water 1500-2000  Boiling Organics 800-1300 Condensing Vapor   Condensing Steam 4000-5000  Thermal Fluids 2000-3000  Organics 800-2000  Organics with NC* 500-1500  Refrigerants 1500 * NC: noncondensables   217 Appendix G  Integration of Equation (11-16) in Wolfram Mathematica 10.0 In[1]:= Integrate[Ri*Log[Ri/(Ri+(0.01905-Ri)*1.21*(4.84-2.73*wC)/wC/(1-epsilon))],Ri] Out[1]= (Ri (0.0557822 -0.0314639 wC))/(5.8564 +(-4.3033+epsilon) wC)+(0.00197996 (1.77289 -1. wC)^2 Log[0.111564 -0.0629279 wC+Ri (-5.8564+(4.3033 -1. epsilon) wC)])/(5.8564 +(-4.3033+epsilon) wC)^2+0.5 Ri^2 Log[((-1.+epsilon) Ri wC)/(-0.111564+0.0629279 wC+Ri (5.8564 +(-4.3033+epsilon) wC))] In[2]:= FullSimplify[%1] Out[2]= (Ri (0.0557822 -0.0314639 wC))/(5.8564 +(-4.3033+epsilon) wC)+(0.00197996 (1.77289 -1. wC)^2 Log[0.111564 -0.0629279 wC+Ri (-5.8564+(4.3033 -1. epsilon) wC)])/(5.8564 +(-4.3033+epsilon) wC)^2+0.5 Ri^2 Log[((-1.+epsilon) Ri wC)/(-0.111564+0.0629279 wC+Ri (5.8564 +(-4.3033+epsilon) wC))] In[3]:= Integrate[1-Exp[-kS*t],t] Out[3]= e^(-kS t)/kS+t   218 Appendix H  Porosity of FeS, Coke and Deposit The porosity of deposit can be expressed in terms of mass of FeS, wC, and the porosity of coke and FeS, εC and εE as: 𝜀𝐷 = 1 − 𝜌𝐷𝜌𝑟 = 1 − 𝑚𝐷𝑉𝐷𝑚𝐷𝑉𝑟 = 1 − 𝑉𝑟𝑉𝐷 = 𝑤𝐶𝜌𝑟,𝐶+1−𝑤𝐶𝜌𝑟,𝐸𝑤𝐶�1−𝜀𝐶�𝜌𝑟,𝐶+ 1−𝑤𝐶�1−𝜀𝐸�𝜌𝑟,𝐸  (A.1) where ρr,C = 4840 kg/m3, ρr,E = 2110 kg/m3 Assuming the porosities of FeS and coke are constant for the same shear stress at 380°C and 390°C. Thus for each wall shear stress value, two equations were obtained for Equation (A.1), for the two bulk temperatures. Thus the unknowns, εC and εE can be determined from the two equations. Wall Shear Stress, Pa 380°C 390°C εC εE  wC εD wC εD   0.414 0.818 0.652 0.345 0.701 0.607 0.716 1.344 0.878 0.569 0.292 0.655 0.522 0.672 4.367 0.839 0.479 0.572 0.531 0.419 0.578 8.701 0.816 0.423 0.507 0.446 0.398 0.465  Correlations can be obtained by fitting the data of εC and εE versus wall shear stress. 𝜀𝑐 = 0.2665 × 𝐹�− 𝜏1.79484� + 0.39578        (A.2) 𝜀𝑐 = 0.55024 × 𝐹�− 𝜏13.31987� + 0.17953        (A.3) The R-Squares for Equation (A.2) and (A.3) are 0.99998 and 0.99617, respectively. 219 Thus the correlation of deposit porosity and wall shear stress can be determined by combining Equation (A.1) (A.2) and (A.3). The plot can be obtained with Matlab (wC: 0-1; τw: 0-10Pa) >> x=0:0.01:1; >> y=0:0.01:10; >> [X,Y]=meshgrid(x,y); >> Z=1-(X./4840+(1-X)./2110)./(X./(1-(0.2665.*exp(-Y./1.79484)+0.39578))./4840+(1-X)./(1-(0.55024.*exp(-Y./13.31987)+0.17953))./2110); >> mesh(X,Y,Z)  It was concluded from the plot that the porosity is slightly influenced with mass fraction of FeS but significantly influenced by wall shear stress. 

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