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Deposition of sodium carbonate and sodium sulfate in supercritical water oxidation systems and its mitigation Khan, Mohammad Sultan 2005

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DEPOSITION OF SODIUM CARBONATE AND SODIUM SULFATE IN SUPERCRITICAL WATER OXIDATION SYSTEMS AND ITS MITIGATION by  M O H A M M A D SULTAN K H A N B.Sc, University of Engineering and Technology Lahore, 1990 M.Sc, King Fahd University of Petroleum and Minerals, 1996  A THESIS SUBMITTED IN PARTIAL F U L F I L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF  DOCTOR OF PHILOSOPHY in T H E F A C U L T Y OF G R A D U A T E STUDIES ( M E C H A N I C A L ENGINEERING*)  T H E UNIVERSITY OF BRITISH COLUMBIA  March 2005 © M o h a m m a d Sultan Khan, 2005  Abstract Supercritical water oxidation ( S C W O ) is a technique to destroy wet organic waste. T h e oxidation reaction takes place at high temperature ( T > 374°C) and pressure (P > 22 M P a ) . Organics are miscible w i t h water at these conditions but inorganic salts, such as Na2SC>4 and Na2C03, are not soluble and crystallize on the reactor surface leading to the problem of heat exchanger fouling. Solubility and deposition of these salts on a tubular heat exchanger (reactor) surface have been studied i n this work. Experiments were performed to determine solubility of these salts i n binary phase and i n ternary phase systems, for a wide range of temperatures. A rapid decrease in the salt solubility was observed just above the pseudo-critical temperature. For supercritical conditions, the solubility of each salt i n the form of a mixture was quite close to the solubility of pure salt. In order to reduce the net salt deposition, particulate instead of crystalline deposition was encouraged. In the presence of particulate fouling, the deposit buildup was not steady. T h e flowing fluid partially removed the deposited layer, once it reached a certain thickness, and then the deposition process continued over a number of cycles. Compared to pure crystalline fouling, combined particulate-crystalline fouling resulted in a three times longer operating period, before the system had to be shut down for removing salt deposits. Salt solution leaving the reactor was four times higher than the saturation l i m i t . T h e structure of the deposits, b o t h pure crystalline and combined particulate-crystalline, were analyzed using Scanning Electron Microscope ( S E M ) and Energy Dispersive X - r a y ( E D X ) . T h e crystalline scale structure was found to be dense and tenacious, whereas the combined particulate-crystalline deposit was relatively less dense and easy to remove. A computer program has been developed, i n M A T L A B , to simulate heat and salt mass transfer i n order to determine the salt deposition at various reactor locations. T h e model predicts the clean tube surface temperature quite accurately. T h e surface temperature change after the salt deposition is also i n good agreement w i t h the actual experimental measurements. T h e calculated location of the peak surface temperature change, due to fouling resistance, was found to be quite close to the experimental data.  ii  Acknowledgements A l l praise to the merciful G o d , who bestowed me the strength and patience to accomplish m y goals. I consider myself fortunate to work under the supervision of D r . Rogak and would like to thank h i m for his guidance and cooperation. It is due to his competence and expertise that m y research work progressed smoothly. I am indebted to his expert suggestions and advice. I also wish to thank D r . B r a n i o n for his enthusiastic and thoughtful comments and discussions during our group meetings. T h a n k s are due to D r . Watkinson for his expert and valuable advice. I am grateful for the time he spared for my research from his busy schedule. I am thankful to D r . Bushe for his guidance and discussions we had regarding my research work and other heat transfer issues. I have had the pleasure of meeting many bright and interesting people during my studies at U B C . It has been wonderful knowing my colleagues D a v o o d Faraji, Ivette Vera-Perez, Biilent G i i z e l , T i m o t h y Wang, Heather Jones, E d u a r d Asselin, Conner Reynolds and G r e g B r o w n . I a m grateful to D a v o o d Faraji for not only helping me in virtually a l l my experiments but also for his positive and encouraging attitude. I appreciate his assistance during experiments on weekends & late nights and his eagerness to r u n the experiments. I certainly owe my success to my wife M a r i a m , who always gave priority to m y academic goals. I am grateful for her encouragement and support during tough times. I appreciate her patience and understanding. T h a n k s are due to m y parents for their prayers that enabled me to see this work to its completion. Finally, financial support provided by N S E R C and N O R A M is acknowledged.  iii  Contents Abstract  ii  Acknowledgements  iii  List of Tables  viii  List of Figures  xvi  Nomenclature  xvii  1 Introduction 1.1 1.2 1.3  1  Supercritical water oxidation ( S C W O ) Problems associated w i t h S C W O Current status of S C W O technology  1 2 3  2 Literature Review on Salt Deposition and Fouling Mitigation  7  2.1 2.2  Salt deposition studies Fouling mitigation techniques 2.2.1 On-line cleaning 2.2.2 Other fouling mitigation techniques reported i n S C W O systems  7 11 12 15  2.3  Objectives of this work  19  3 Experimental Facility Description 3.1 3.2 3.3 3.4 3.5 3.6  22  Process equipment Pressure measurement and calibration Temperature measurement and calibration Heat flux measurement Salt concentration measurement D a t a acquisition  22 23 23 27 28 28  4 Solubility of Na S0 , N a C 0 and Na S04-Na C03 mixture in Supercritical Water 30 2  4.1 4.2  4  2  3  2  Introduction Salt concentration measurement  2  30 31 iv  4.3 4.4 4.5  E x p e r i m e n t a l procedure Solubility reporting temperature M o d e l i n g the effect of heat and mass transfer on measurements  4.6  Results and discussion 4.6.1 N a C 0 solubility 4.6.2 N a S 0 solubility 4.6.3 Solubility of N a C 0 - N a S 0 mixture Conclusion 2  3  2  4  2  4.7  3  2  32 34 34  . . . .  40 40 41 42 43  4  5 Salt Deposition and its Mitigation 5.1 5.2  5.3  5.4  46  Introduction E x p e r i m e n t a l procedures 5.2.1 Heterogeneous nucleation experiments 5.2.2 C o m b i n e d heterogeneous and homogeneous nucleation experiments (heated test section) 5.2.3 C o m b i n e d heterogeneous and homogeneous nucleation experiments (unheated test section)  46 47 47  Results and discussion 5.3.1 Heterogeneous nucleation 5.3.2 C o m b i n e d heterogeneous and homogeneous nucleation (heated test section) 5.3.3 C o m b i n e d heterogeneous and homogeneous nucleation experiments (unheated test section) Conclusion  50 50  47 49  51 53 54  6 Collection and Analysis of N a C 0 and N a S 0 Deposits 2  6.1 6.2  3  2  57  4  Salt-deposit preservation procedure S E M and E D X analysis of N a C 0 and N a S 0 deposits 6.2.1 P u r e crystalline fouling deposits of N a C 0 6.2.2 C o m b i n e d crystalline and particulate fouling deposits of N a C 0  3  57 59 60 63  6.2.3 6.2.4  4  65 68  2  3  2  4  2  3  2  Pure crystalline fouling deposits of N a S 0 C o m b i n e d crystalline and particulate fouling deposits of N a S 0 2  2  6.3  T h e r m a l conductivity of the N a C 0  6.4  Conclusion  2  3  deposit  7.3 7.4  69 74  7 Modeling: Mixing, Heat and Mass Transfer 7.1 7.2  4  Introduction Salt particle nucleation 7.2.1 G r o w t h of nucleated particles 7.2.2 Coagulation of the particles M o d e l i n g of the m i x i n g process Heat transfer calculation  v  76 76 76 78 79 79 82  7.5  7.6 7.7 7.8 7.9  Salt deposition 7.5.1 Molecule deposition 7.5.2 Particle deposition Conservation equations Results of model simulation 7.7.1 Comparison of model simulation and experimental data Effect of parameters on the model results Conclusion  8 Summary of Conclusions and Future Work Recommendations 8.1 8.2 8.3  Thesis overview and conclusions Implications for S C W O system design Future work  105  A Discussion of the N a C 0 Fouling Mitigation Experiments 2  3  A.l  Homogeneous & heterogeneous nucleation experiments A . 1.1 Experiment: 1 A . l . 2 Experiments: 2 & 3 A . 1.3 Experiment: 6 A . 1.4 Experiment: 7 A . 1.5 Experiment: 11 A . 2 Homogeneous & heterogeneous nucleation unheated test section experiments A.2.1 Experiment: 8 A.2.2 Experiment: 10 A . 3 Heterogeneous nucleation runs: Solubility type experiments A.3.1 Experiment: 9 A . 3.2 Experiment: 12  B S E M photographs of N a C 0 and N a S 0 deposits 2  B. 2  3  2  C.2  4  106 108 108 109 Ill 113 114 114 114 116 118 119 120  121  N a C 0 deposits B . l . l N a C 0 crystalline scale B . l . 2 N a C 0 combined crystalline and particulate deposits  122 123 137  N a S 0 deposits B.2.1 N a S 0 crystalline scale B . 2.2 N a S 0 combined crystalline and particulate deposits  155 156 166  2  2  3  2  3  2  3  4  2  4  2  4  C Computer Codes C. l  101 101 103 104  Appendices  B. l  84 84 84 86 90 90 92 95  168  N a C 0 solubility codes C. l . l M a i n Code: m o l . m N a S 0 solubility codes 2  3  2  4  168 168 173 vi  C.3 C.4  C.2.1 M a i n Code: m o l N a 2 S 0 4 . m Figure Code: N a C 0 - N a S 0 4 mixture (graphmixture.m) M a i n Code: M i x i n g , heat and mass transfer ( M i x H t M a s s C o d e . m ) . . . C.4.1 Figures Code: M i x i n g , heat and mass transfer (Depositfigs.m) . 2  3  2  Bibliography  173 178 181 192  196  vii  List of Tables 1.1  C o m m e r c i a l l y designed S C W O facilities currently i n existence [16] . . .  2.1  C o m m e r c i a l l y developed approaches to S C W O salt precipitation control [16]  5  16  3.1  Distance of thermocouples (measured from the electric power connection) 26  4.1 4.2 4.3  Details of N a C 0 3 solubility experiments Details of N a S 0 solubility experiments Details of N a C 0 - N a S 0 mixture solubility experiments  39 40 45  5.1  C o m p a r i s o n of the three types of N a C 0 3 nucleation experiments, ColC at is the ratio of effluent salt concentration to saturation concentration  56  2  2  4  2  3  2  4  2  S  6.1 6.2 6.3 6.4  Thermocouple and tube-insert-section locations Details of experiments performed to collect salt deposits Details of N a C 0 scale thickness and surface temperature rise due to deposition for the heterogeneous nucleation experiment (Experiment S E M - 4 ) Details of N a C 0 3 deposit thickness and surface temperature rise due to deposition for the combined homogeneous-heterogeneous nucleation experiment (Experiment S E M - 3 ) 2  3  Details of N a C 0  B. l  S u m m a r y of N a C 0  B.3 B.4  72  2  A. l  B.2  59 61  2  3  deposition experiments  2  3  73 107  pure crystalline deposit characteristics (Experi-  ment S E M - 4 ) S u m m a r y of N a C 0 3 combined crystalline and particulate deposit characteristics (Experiment S E M - 3 ) S u m m a r y of N a S 0 pure crystalline deposit characteristics (Experiment S E M - 7 ) S u m m a r y of N a S 0 combined crystalline and particulate deposit characteristics (Experiment S E M - 6 )  122  2  2  2  122  4  155  4  viii  155  List of Figures 1.1  1.2  Physical properties of water at a pressure of 24 M P a versus temperature. Dielectric constants of typical organic solvents at room temperature are indicated [2] Conventional S C W O process and reaction leading to problems i n the particular parts of the plant [2]  2 4  2.1  Reactor concepts for S C W O [50,52]  17  3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8  U B C - N O R A M S C W O pilot plant Reynolds number versus fluid temperature Schematic of electric heating for pre-heaters and test section Electric heating schematic of the heated tube sections L o c a t i o n of thermocouples i n the test section Thermocouple spot welded to the test section surface C o n d u c t i v i t y meter calibration for N a C 0 3 C o n d u c t i v i t y meter calibration for N a S 0  24 25 25 27 27 27 29 29  4.1 4.2 4.3  Concept of salt solubility experiments 32 Effluent conductivity vs. time (a) run " S I " , (b) run "S2" and (c) run "S3" 33 Modeled salt concentration along test section for run "S6" 38  4.4  Na C03 solubility vs. temperature  41  4.5  Na C03 solubility vs. density  42  4.6  Na S04 solubility vs. temperature  43  4.7 4.8  N a S 0 solubility vs. density Solubility of mixture of N a C 0  44 45  5.1 5.2 5.3 5.4  Modified process equipment for homogeneous salt nucleation Metering p u m p calibration at 24.7 M P a Temperature and pressure behavior for the heterogeneous nucleation run Temperature and pressure behavior for the combined homogeneous and heterogeneous nucleation run (heated test section) Temperature and pressure behavior for the combined heterogeneous and homogeneous nucleation run (unheated test section)  48 49 51  Schematic of the tube-insert  58  5.5  6.1  2  2  4  2  2  2  2  4  2  3  and N a S 0 2  . ., ix  4  53 55  6.2  L o c a t i o n of tube-insert sections w i t h respect to the thermocouples location 58  6.3 6.4  Elemental composition analysis of standard N a C 0 3 salt S E M photograph of the N a C 0 3 deposition on test section wall due to heterogeneous nucleation (Experiment S E M - 1 ) 6.5 Elemental composition analysis of Na CC>3 deposit for the heterogeneous nucleation (Experiment S E M - 1 ) 6.6 S E M photograph of the N a C 0 deposition on test section wall due to heterogeneous nucleation at 79 cm location (Experiment S E M - 4 ) . . . . 6.7 S E M photograph of the Na CC>3 deposition on test section wall due to heterogeneous nucleation at 139 cm location (Experiment S E M - 4 ) . . . 6.8 S E M photograph of the N a C 0 3 deposition on test section wall due to heterogeneous nucleation at 139 cm location (Experiment S E M - 4 ) . . . 6.9 Elemental composition analysis of N a C 0 deposit for the combined homogeneous & heterogeneous nucleation (Experiment S E M - 3 ) 6.10 S E M photograph of the N a C 0 3 deposit due to combined homogeneousheterogeneous nucleation at 109 cm location (Experiment S E M - 3 ) . . . 6.11 S E M photograph of the N a C 0 3 deposit due to combined homogeneousheterogeneous nucleation at 109 cm location (Experiment S E M - 3 ) . . . 6.12 S E M photograph of the N a S 0 4 deposit due to heterogeneous nucleation at 154 c m location (Experiment S E M - 7 ) 6.13 S E M photograph of the Na SC>4 deposit due to heterogeneous nucleation at 127 c m location (Experiment S E M - 7 ) 6.14 S E M photograph of the N a S 0 4 deposit due to heterogeneous nucleation at 97 c m location (Experiment S E M - 7 ) 6.15 Elemental composition analysis of Na SC>4 deposit for the combined homogeneous-heterogeneous nucleation experiment (Experiment S E M - 6 ) 6.16 S E M photograph of the N a S 0 deposit due to combined homogeneousheterogeneous nucleation at 154 cm location (Experiment S E M - 6 ) . . . 6.17 S E M photograph of the N a S 0 4 deposit due to combined homogeneousheterogeneous nucleation at 154 c m location, mostly crystalline (Experiment S E M - 6 ) 6.18 S E M photograph of the N a S 0 deposit due to combined homogeneousheterogeneous nucleation at 154 cm location, mostly particulate (Experiment S E M - 6 ) 6.19 S E M photograph of the N a S 0 deposit due to combined homogeneousheterogeneous nucleation at 64 cm location, mostly particulate (Experiment S E M - 6 ) 6.20 N a C 0 deposit thickness and surface temperature rise along the test section for the heterogeneous nucleation (Experiment S E M - 4 ) 2  60  2  62  2  2  62  3  63  2  64  2  2  64  3  65  2  66  2  66  2  67  2  67  2  68  2  2  69  4  70  2  2  2  2  4  71  4  72  3  6.21 N a C 0 deposit thickness and surface temperature rise along the test section for the combined homogeneous-heterogeneous nucleation (Experiment S E M - 3 ) 2  70  73  3  x  74  7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18 7.19  Salt particle nucleation rate, mass fraction and fluid temperature as a function of mixture fraction Schematic of the salt solution (fluid A) cells and pure water (fluid B) cells at the beginning of the mixing process Temperature and radii schematic for the test section Salt particle deposition velocity vs particle radius Temperature profiles at various axial locations Salt mass fraction at various axial locations Comparison of clean surface temperature experiment data w i t h the model results (heated test section case) N u m b e r of nucleated particles and their average size at various test section locations (heated test section case) Mass of salt molecules and particles deposited per unit length at various test section locations (heated test section case) Surface temperature rise due to salt deposit: experiment data vs model results (heated test section case) Comparison of clean surface temperature experiment data w i t h the model results (unheated test section case) Surface temperature drop due to salt deposit: experiment data vs model results (unheated test section case) Effect of surface tension on the number of nucleated particles Effect of surface tension on particle size Effect of surface tension on particle deposition Effect of surface tension on molecule deposition Effect of surface tension on salt layer thickness Effect of segment length on tube outer surface temperature Effect of number of fluid parcels on salt deposition  A.l  Temperature homogeneous A . 2 Temperature homogeneous A . 3 Temperature homogeneous A . 4 Temperature homogeneous A . 5 Temperature A.6 A.7  homogeneous Temperature homogeneous Temperature homogeneous  and pressure behavior for the combined nucleation run (Experiment 3) and pressure behavior for the combined nucleation run (Experiment 3) and pressure behavior for the combined nucleation run (Experiment 6) and pressure behavior for the combined nucleation r u n (Experiment 7) and pressure behavior for the combined  80 83 86 91 92 93 94 95 96 96 97 97 98 98 99 99 100 100  heterogeneous & 110 heterogeneous & Ill heterogeneous & 112 heterogeneous & 113 heterogeneous &  nucleation run (Experiment 7) and pressure behavior for the combined heterogeneous & nucleation run (Experiment 11) and pressure behavior for the combined heterogeneous and nucleation unheated test section run (Experiment 8) . . .  xi  78  115 116 117  A.8  Temperature and pressure behavior for the combined heterogeneous and homogeneous nucleation unheated test section run (Experiment 8) . . . A . 9 Temperature and pressure behavior for the heterogeneous nucleation run (Experiment 9) B. l B.2 B.3 B.4 B.5 B.6 B.7 B.8 B.9 B.10 B.ll B.12 B.13 B.14 B.15 B.16  S E M photograph of the N a 2 C 0 3 deposition due to heterogeneous nucleation at 139 c m location (Experiment S E M - 4 ) S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 139 c m location (Experiment S E M - 4 ) S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 139 c m location (Experiment S E M - 4 ) S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 139 c m location (Experiment S E M - 4 ) S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 109 c m location (Experiment S E M - 4 ) S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 109 c m location (Experiment S E M - 4 ) S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 109 c m location (Experiment S E M - 4 ) S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 109 c m location (Experiment S E M - 4 ) S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 109 c m location (Experiment S E M - 4 ) S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 109 c m location (Experiment S E M - 4 ) S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 109 c m location (Experiment S E M - 4 ) S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 79 c m location (Experiment S E M - 4 ) S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 79 cm location (Experiment S E M - 4 ) S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 79 c m location (Experiment S E M - 4 ) S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 79 cm location (Experiment S E M - 4 ) S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 64 cm location (Experiment S E M - 4 )  B . l 7 S E M photograph of the ation at 64 c m location B.18 S E M photograph of the ation at 64 c m location  118 119  123  2  123  2  124  2  2  124  3  125  2  125  2  126  2  2  126  3  127  2  127  2  2  128  3  128  2  129  2  129  2  2  130  3  N a C 0 3 deposition due to heterogeneous nucle(Experiment S E M - 4 ) N a C 0 deposition due to heterogeneous nucle(Experiment S E M - 4 )  130  2  2  131  3  xii  131  B.19 S E M photograph of the Na CC>3 deposition due to heterogeneous nucleation at 64 c m location (Experiment S E M - 4 ) 132 B.20 S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 64 c m location (Experiment S E M - 4 ) 132 B.21 S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 64 c m location (Experiment S E M - 4 ) 133 B.22 S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 64 cm location (Experiment S E M - 4 ) 133 B.23 S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 49 cm location (Experiment S E M - 4 ) 134 B.24 S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 49 c m location (Experiment S E M - 4 ) 134 B.25 S E M photograph of the N a C 0 3 deposition due to heterogeneous nucleation at 19 c m location (Experiment S E M - 4 ) 135 B.26 S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 19 c m location (Experiment S E M - 4 ) 135 B.27 S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 19 c m location (Experiment S E M - 4 ) 136 B.28 S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 154 c m location (Experiment S E M - 3 ) 137 B.29 S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 154 cm location (Experiment S E M - 3 ) 137 B.30 S E M photograph of the Na CC>3 deposition due to combined homogeneous & heterogeneous nucleation at 154 cm location (Experiment S E M - 3 ) 138 B.31 S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 154 c m location (Experiment S E M - 3 ) 138 B.32 S E M photograph of the Na CC>3 deposition due to combined homogeneous & heterogeneous nucleation at 154 c m location (Experiment S E M - 3 ) 139 B.33 S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 154 c m location (Experiment S E M - 3 ) 139 2  2  2  3  2  2  3  2  2  2  3  2  3  2  3  2  3  2  3  2  3  2  2  B.34 S E M photograph of the N a C 0 3 neous & heterogeneous nucleation B.35 S E M photograph of the N a C 0 neous & heterogeneous nucleation B.36 S E M photograph of the Na CC>3 neous & heterogeneous nucleation 2  2  3  2  deposition due to combined homogeat 154 cm location (Experiment S E M - 3 ) 140 deposition due to combined homogeat 154 cm location (Experiment S E M - 3 ) 140 deposition due to combined homogeat 154 c m location (Experiment S E M - 3 ) 141  B.37 S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 154 c m location (Experiment S E M - 3 ) 141 2  3  B.38 S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 139 cm location (Experiment S E M - 3 ) 142 2  3  B.39 S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 139 c m location (Experiment S E M - 3 ) 142 2  3  xiii  B.40 S E M photograph of the N a C 0 3 deposition due to combined homogeneous & heterogeneous nucleation at 139 c m location (Experiment S E M - 3 ) 143 B.41 S E M photograph of the N a C 0 3 deposition due to combined homogeneous & heterogeneous nucleation at 139 cm location (Experiment S E M - 3 ) 143 B.42 S E M photograph of the N a C 0 3 deposition due to combined homogeneous & heterogeneous nucleation at 139 c m location (Experiment S E M - 3 ) 144 B.43 S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 139 cm location (Experiment S E M - 3 ) 144 B.44 S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 139 cm location (Experiment S E M - 3 ) 145 B.45 S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 109 c m location (Experiment S E M - 3 ) 145 B.46 S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 109 cm location (Experiment S E M - 3 ) 146 B.47 S E M photograph of the N a C 0 3 deposition due to combined homogeneous & heterogeneous nucleation at 109 cm location (Experiment S E M - 3 ) 146 B.48 S E M photograph of the N a C 0 3 deposition due to combined homogeneous & heterogeneous nucleation at 109 c m location (Experiment S E M - 3 ) 147 B.49 S E M photograph of the N a C 0 3 deposition due to combined homogeneous & heterogeneous nucleation at 109 c m location (Experiment S E M - 3 ) 147 B.50 S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 109 cm location (Experiment S E M - 3 ) 148 B.51 S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 79 c m location (Experiment S E M - 3 ) 148 B.52 S E M photograph of the N a C 0 3 deposition due to combined homogeneous & heterogeneous nucleation at 79 cm location (Experiment S E M - 3 ) 149 B.53 S E M photograph of the N a C 0 3 deposition due to combined homogeneous & heterogeneous nucleation at 79 c m location (Experiment S E M - 3 ) 149 B.54 S E M photograph of the N a C 0 3 deposition due to combined homogeneous & heterogeneous nucleation at 79 c m location (Experiment S E M - 3 ) 150 B.55 S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 79 cm location (Experiment S E M - 3 ) 150 B.56 S E M photograph of the N a C 0 3 deposition due to combined homogeneous & heterogeneous nucleation at 79 cm location (Experiment S E M - 3 ) 151 B.57 S E M photograph of the N a C 0 3 deposition due to combined homogeneous & heterogeneous nucleation at 49 c m location (Experiment S E M - 3 ) 151 B.58 S E M photograph of the N a C 0 3 deposition due to combined homogeneous & heterogeneous nucleation at 49 cm location (Experiment S E M - 3 ) 152 B.59 S E M photograph of the N a C 0 3 deposition due to combined homogeneous & heterogeneous nucleation at 49 cm location (Experiment S E M - 3 ) 152 B.60 S E M photograph of the N a C 0 3 deposition due to combined homogeneous & heterogeneous nucleation at 49 c m location (Experiment S E M - 3 ) 153 2  2  2  2  3  2  3  2  3  2  3  2  2  2  2  3  2  3  2  2  2  2  3  2  2  2  2  2  xiv  B.61 S E M photograph of the Na2CC>3 deposition due to combined homogeneous & heterogeneous nucleation at 49 cm location (Experiment S E M - 3 ) B.62 S E M photograph of the Na CC>3 deposition due to combined homogeneous & heterogeneous nucleation at 49 c m location (Experiment S E M - 3 ) B.63 S E M photograph of the Na SC>4 deposition due to heterogeneous nucleation at 154 c m location (Experiment S E M - 7 ) B.64 S E M photograph of the Na SC>4 deposition due to heterogeneous nucleation at 154 c m location (Experiment S E M - 7 ) B.65 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 154 c m location (Experiment S E M - 7 ) B.66 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 124 c m location (Experiment S E M - 7 ) B.67 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 124 c m location (Experiment S E M - 7 ) B.68 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 94 c m location (Experiment S E M - 7 ) B.69 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 94 c m location (Experiment S E M - 7 ) B.70 S E M photograph of the N a S 0 4 deposition due to heterogeneous nucleation at 94 cm location (Experiment S E M - 7 ) B.71 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 49 c m location (Experiment S E M - 7 ) B.72 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 49 c m location (Experiment S E M - 7 ) B.73 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 49 cm location (Experiment S E M - 7 ) B.74 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 19 c m location (Experiment S E M - 7 ) B.75 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 19 c m location (Experiment S E M - 7 ) B.76 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 19 c m location (Experiment S E M - 7 ) B.77 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 19 c m location (Experiment S E M - 7 ) B.78 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 4 c m location (Experiment S E M - 7 )  153  2  154  2  156  2  2  156  4  2  4  2  4  2  157 157 158  4  2  158  4  159  2  2  4  2  4  2  2  2  2  2  2  159 160 160  4  161  4  161  4  162  4  162  4  163  4  163  B.79 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 4 c m location (Experiment S E M - 7 ) B.80 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 4 c m location (Experiment S E M - 7 )  164  B.81 S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 4 c m location (Experiment S E M - 7 )  165  2  2  2  4  164  4  4  xv  B.82 S E M photograph of the N a S 0 deposition due to combined homogeneous h heterogeneous nucleation at 154 cm location (Experiment S E M - 6 ) B.83 S E M photograph of the N a S 0 4 deposition due to combined homogeneous & heterogeneous nucleation at 79 cm location (Experiment S E M - 6 ) B.84 S E M photograph of the N a S 0 deposition due to combined homogeneous & heterogeneous nucleation at 79 c m location (Experiment S E M - 6 ) B.85 S E M photograph of the N a S 0 deposition due to combined homogeneous & heterogeneous nucleation at 79 c m location (Experiment S E M - 6 ) 2  4  166  2  2  2  166  4  167  4  xvi  167  Nomenclature A h  c  c  Cp Co d dl d p  v  m  V dx T  f  H h J  Jm  kd k t  #12  L Le m m rh m. m-pi rripo n m  p  cell cross-sectional area B o l t z m a n n constant dissolved salt concentration specific heat at constant pressure total salt concentration salt concentration i n the effluent tube diameter m i x i n g step length salt particle diameter molecule diffusion coefficient turbulent diffusivity integration step length friction factor fluid enthalpy convective heat transfer coefficient mass transfer coefficient salt particle nucleation rate per unit volume salt molecule condensation rate thermal conductivity of the deposit layer thermal conductivity of the tube salt particle coagulation coefficient length Lewis number number of cells i n pure water fluid mass flow rate molecule deposition rate mass of nucleated salt particle mass of grown salt particle mass of average sized salt particle number of cells i n salt solution  xvii  0  m  J/K  kg/rr? J/kgK  kg/vr? kg/rr? m m m m /sec m jsec m 2  2  J/kg  W/m K m/sec 2  W/mK W/mK m /sec m 3  kg/sec kg/sec kg kg kg  N  m  N  p  Nu P Pr Q Q r  r* R Re R' f r r  p  S Sc Sh SLSI t T vl V  v  d  V  m  molecule concentration particle concentration Nusselt number system pressure P r a n d t l number heat supplied heat flux tube radius salt particle critical radius average number of fluid parcels in a cell Reynolds number actual number of fluid parcels in a cell final particle radius particle radius degree of salt saturation Schmidt number Sherwood number salt layer solution interface time temperature velocity fluctuation fluid mean velocity . salt particle deposition velocity volume of salt molecule  MPa W W/m  2  m m  m m  sec,  hr  °C ml  sec  m/sec ml  sec  m  3  Greek symbols Ad Az e i 7 [i VT p r T T D  P  W  cell height distance moved by the fluid parcels kinetic energy dissipation rate tube surface roughness surface tension fluid dynamic viscosity turbulent viscosity density characteristic time for turbulent diffusion particle relaxation time wall shear stress  xviii  m m m /sec 2  3  m iV/ra N.s/m m /sec kg/m  3  2  3  N/m  2  Subscripts A B b e ep f i m 0  P pc s sat sp w  salt solution pure water bulk fluid conditions conditions i n cell at the edge of S L S I particle concentration i n the cell at the edge of S L S I fluid inner surface molecule outer surface particle pseudo-critical salt layer solution interface saturated condition particle concentration at S L S I at tube wall condition  xix  Chapter 1 Introduction 1.1  Supercritical water oxidation (SCWO)  Supercritical Water O x i d a t i o n is a process for the destruction of aqueous organics (waste), which is made possible due to special properties of supercritical water. For pure water, the critical point corresponds to 22.09 M P a and 374.14°C [1]. W h e n exceeding its critical point, the values of density, dielectric constant, and ionic product of water decrease, so supercritical water acts as a non-polar solvent of high diffusivity and excellent transport properties (see F i g 1.1 [2]). A t supercritical conditions, the reactants consist of a homogeneous single-phase mixture facilitating complete reaction i.e., organics and oxygen are completely miscible which allows oxidation of organics without any interphase mass transfer resistance. A s a medium of chemical reactions, depending on its density, supercritical water has b o t h gas-like and liquid-like properties. T h e gaslike low viscosity promotes mass transfer. T h e liquid-like density promotes solvation. T h e low dielectric constant promotes dissolution of non polar organic materials and the high temperature increases the thermal reaction rates [3]. S C W O is a non-polluting alternative to other waste-disposal techniques such as incineration and biological treatment when the others are inefficient or potentially hazardous to the environment. Furthermore, S C W O is a compact, energy-efficient process, which can be integrated into a closed cycle chemical plant since its effluent components can be separated. T h e process is totally enclosed up to the point of final discharge to the environment. T h i s feature is very useful when treating highly toxic or radioactive wastes. T h e operating temperatures are much lower than incineration, so nitrogen oxides are not formed. T h e S C W O process involves pressurizing aqueous waste and oxidant to the working pressure. T h i s is followed by mixing the pressurized streams; preheating to the temperature at which reaction is initiated; oxidation reaction w i t h subsequent cooling. Finally, the system is depressurized and the gaseous, liquid and solid products separated. In a typical S C W O waste treatment system, dilute aqueous organic waste is combined w i t h an oxidizer at elevated pressure and temperature i n a reactor for res-  1  2  1.2. Problems associated with SCWO 1400 1200 •  to c  tl cn o u  "  £•  1000 1 800 H 600  u •— •= « la c u eg « Q 0)  400 200  100  200  300  400  500  600  Temperature [°C]  1.1: Physical properties of water at a pressure of 24 M P a versus temperature.  Figure  Dielectric constants of typical organic solvents at r o o m temperature are indicated [2] idence times on the order of 30 to 90 seconds which strongly depends on the reaction temperature. T y p i c a l l y S C W O is carried out at reaction temperatures of 500-700°C and pressures of 24-50 M P a . T h e products of the reaction are C O 2 , H 0 and for some wastes inorganic salts also. T h e salt may be present i n the waste itself or could be a product of the oxidation reaction. Water at room temperature is an excellent solvent for most salts, w i t h solubility at typically 100 g/1. However, whereas the organics are totally miscible at S C W O conditions, the inorganic compounds are not soluble. In low-density supercritical water, the solubility of most salts is low, typically 1-100 p p m [4-7]. T h i s results i n the precipitation of salts when a sub-critical salt containing solution is heated to supercritical temperature. C o m m o n examples of such compounds are N a S 0 , N a C 0 and C a S 0 . 2  2  1.2  4  2  3  4  Problems associated with SCWO  T h e reason why S C W O has not yet become a current waste treatment technology can be seen in three reasons [2]: • Severe reactor corrosion caused by acids, which are formed during the waste treatment process. • Serious plugging of the reactors caused by precipitating salts at supercritical temperatures and low densities. • D u e to lack of experimental data, cost evaluations, especially for the scale-up of S C W O plants to an industrial scale, are unreliable.  1.3. Current status of SCWO technology  3  T h e problems hindering the commercialization of S C W O are corrosion, due to acids produced during the reaction and salt deposition due to the undissolved salts. Solid salts tend to agglomerate and coat internal surfaces thereby inhibiting heat transfer to/from exterior surfaces. W h e n scale buildup is not controlled, plugging of transport lines and/or the reactor can occur. It then becomes necessary to remove the plugs by flushing them out w i t h cold water, by mechanical means or by chemical means (acid wash) [8]. Often, this results i n substantial and costly downtime i n the S C W O process. D u r i n g the heat-up i n the absence of oxidant, polymerization of certain organics may also lead to scale buildup i n the form of char or tar [8]. Plugging of reactors caused by precipitating salts at supercritical temperature and low densities is one of the major reasons for S C W O not being a current waste treatment technology so far. It is not yet clear i f S C W O w i l l really become competitive process to classical incineration because technical problems related to corrosion and plugging need to be solved [9].  1.3  Current status of SCWO technology  In 1966 Connolly [10] published data on hydrocarbon solubilities i n water at high temperature and pressure. It was reported that, i n some regions of the phase diagram, hydrocarbons and water are miscible i n a l l proportions. R a p i d development of experimental techniques made this work possible and speculations began about the consequences of the observations [3]. For example, i n 1970 Schneider [11] suggested the extension of wet air oxidation to higher temperatures for disposal of organic wastes. After the experiments done by M o d e l l and A m i n [12] to convert carbohydrates in supercritical water i n the m i d 1970s, the potential of the supercritical water oxidation process was recognized. A c t i v e chemical and engineering R & D began i n the 1980s at national laboratories and universities i n the U S A [13]. A simplified flow sheet of the process is shown i n F i g . 1.2. There are at least three broad categories of feeds or wastes for S C W O treatments applications [14]: 1. M i l i t a r y wastes - chemical agents, munitions, energetics, smokes and dyes which typically contain high concentrations of salt and corrosive species. 2. Sludges w i t h "inert" solids such as oxides and lower salt content than halogenated waste streams. 3. Specific chemical wastes and sludges from variety of industrial sources. M i l i t a r y wastes are extremely challenging w i t h respect to corrosion and salt plugging. Commercial industrial wastes, including waste water sludge, are relatively benign w i t h respect to corrosion and salt plugging. T h e more challenging feeds require  1.3. Current status of SCWO  Waste Pre heater TCC) Reactions Agressive species Main Problem  4  technology  25 Pyrolysis may occur Salts, (HCI) no 0 , Slight corrosion  Oxidant Preheater 380  No problem  Reactor  Heat exchanger  600  600 -» 25  Oxidation  Formed acids dissociate  HCI; 0  H*; C.I-; 0  2  Salt precipitation  2  Severe corrosion  F i g u r e 1.2: Conventional S C W O process and reaction leading to problems i n the particular parts of the plant [2] more elaborate S C W O designs or operating techniques to manage the associated corrosion and salt plugging problem [15]. Some examples of companies pursuing the former include General Atomics ( U S A ) and Foster Wheeler Development Corporation ( U S A ) , while examples of companies pursuing the latter are Chematur Engineering Group (Sweden), HydroProcessing ( U S A ) and N O R A M Engineers and Constructors (Canada). W h i l e m i l i t a r y applications are most challenging and currently driving the development of S C W O , the wider and long term market for S C W O is i n the private sector handling the less challenging feeds. Table 1.1 contains a list of full-scale facilities of the S C W O processes developed by several companies, along w i t h recent feed materials that have been processed [16]. State of S C W O technology is now summarized by regions.  United States and Canada A commercial plant for civic waste treatment has been i n operation i n Texas since 1994 by the H u n t s m a n Corporation [3,17]. T h e plant was designed and constructed by E C O Waste Technology ( E W T ) supported by the comprehensive development work done at the University of Texas [18]. T h e tubular reactor made of a non-specified alloy is 200 m long and is usually operated at 25-28 M P a and between 540-600°C. T h e normal throughput amounts to 1100 k g / h r . T y p i c a l organic concentration is about 10 wt.%. T h e plant is not suitable for processing waste w i t h high chlorine content and  1.3. Current status of SCWO technology  5  T a b l e 1.1: C o m m e r c i a l l y designed S C W O facilities currently i n existence [16] Applications Company Large scale plants Semiconductor manufacture waste MODAR Organo, Japan Pharmaceutical wastes,pulp and paMODEC None per m i l l waste, sewage sludge B u l k V X nerve agent hydrolysate, exU S A r m y Newport, I N General plosives, shipboard waste, rocket proAtomics pellant Smokes and dyes, shipboard wastes FosterU S A r m y P i n e Bluff, A R Wheeler EcoWaste Huntsman Chemical, Oxygenated and nitrogen-containing Austin, T X hydrocarbons Technology M u n i c i p a l sludge Chematur Japan Harlingen Wastewater M i x e d m u n i c i p a l and industrial Hydrowastewater sludge Treatment, Harlingen, T X Processing salt containing waste. However, E W T operates a pilot plant, where such material has been successfully treated [12]. Currently, the m a i n activities i n the U S A are directed toward hazardous wastes from the defense sector. Such wastes include propellants, explosives, dyes, poisons, and nuclear waste. T h e programs are executed i n a close collaboration between the institutions of the U S Forces and national laboratories, universities and industry [3]. General Atomics has three pilot (or demonstration) systems now operable. A t Los Alamos N a t i o n a l Laboratory, research is being carried out to treat radioactive and explosive wastes. General Atomics, E C O Waste Technologies and University of Texas are partners of the A i r Force waste treatment program. A t Sandia N a t i o n a l Laboratories, a consortium led by Foster Wheeler C o r p o r a t i o n has treated U S A r m y smoke and dye wastes (polyaromatics, salts) i n the transpiring wall reactor. U S N a v y as a part of their "environmentally sound ships" program, has commissioned S C W O reactors for disposal of sewage, paint, solvents, fuel and o i l , etc. T w o units are in test: a down-flow tubular design by General Atomics and a transpiring wall by Foster W h e e l e r / A e r o jet [3]. M O D A R developed a reactor to treat wastes from the pharmaceutical plant i n 1986 and had a successful demonstration operating 50-500 gal/day. A change i n environmental regulations removed the need for this plant and it is not i n operation [3]. In 1995, M O D A R was acquired by General Atomics. In Canada, University of B r i t i s h C o l u m b i a ( U B C ) i n collaboration w i t h N O R A M E n gineers and Constructors have built a S C W O pilot plant at U B C . A m o n g other hazardous wastes, "red water" and 2,4 Di-nitrophenol destruction has been successfully carried out. Research is focused on heat and mass transfer i n S C W , salt solubility, salt  1.3. Current status of SCWO technology  6  deposition & mitigation, and corrosion of the reactor tubes [7,19-24].  Europe M o s t of the E u r o p e a n development work i n S C W O is done i n Germany at Forschungszentrum K a r l s r u h e ( F Z K ) [12]. A film-cooled two-zone reactor (porous inner pipe rinsed w i t h cold water to avoid salt deposits) is i n testing since 1998 [25]. T h e Fraunhofer Institute developed a tubular reactor for the treatment of electronic scrap i n collaboration w i t h Daimler Chrysler and built a mobile plant (20 1/hr) to treat hazardous waste at the source of generation [26]. T h e Swedish company Chematur started experimental work w i t h an industrial scaled plant ( " A q u a C r i t o x " ) licensed from E c o Waste Technologies ( E W T ) , U S A , in 1997 [27]. T h e plant consists of a tubular nickelbase alloy 625 reactor and has a capacity of 250 k g aqueous organic waste per hour [24]. A variety of waste-streams have been successfully treated. A m o n g these were wastes from the amine production, de-inking sludge from paper recycling, and cutting liquid. However, none of these waste streams contains the acid-forming hetero-atoms chlorine, sulfur, or phosphorus which are usually present i n the organic wastes, and corrosion has not been a critical item for that plant so far. B u i l d i n g of a larger plant to treat electronic scrap is under consideration [12].  Japan Organo C o r p o r a t i o n i n Tokyo has acquired licenses of M O D A R (acquired by General Atomics i n 1995) and M O D E C built the first plant i n Japan. Japanese companies Hitachi and N G K are also licensees of M O D E C . T h e Shinko Pantec C o m p a n y in K o b e has signed a cooperative agreement w i t h E W T to develop the technology for the Japanese market. T h e companies K o m a t s u and K u r i t a have an agreement concerning technical support by General Atomics [12]. The present status of salt deposition and mitigation research w i t h emphasis on S C W O related conditions is reviewed i n the next chapter. T h e objective of this study is also discussed i n Chapter 2.  Chapter 2 Literature Review on Salt Deposition and Fouling Mitigation 2.1  Salt deposition studies  The problem of salt precipitation is multivariant, dependent on at least the following parameters [14]: 1. Temperature - affects density and solid salt behavior. 2. Pressure - affects density. 3. Density - affects water properties and interaction of water and salts. 4. C o m p o s i t i o n - different salts have dramatically different behaviors, e.g. N a C l vs N a S 0 , N a C 0 , or C a S 0 . 2  4  2  3  4  5. T i m e - salt morphology can be affected by time b o t h i n the initial precipitation as well as i n the aging of salt deposits. Salt deposition is frequently localized to a region where a rapid drop i n salt solubility occurs. 6. Geometry - reactor geometry, diameter expansions and contractions, and condition of surfaces can play a significant role in the accumulation of salt deposit. 7. F l u i d dynamics - velocity and flow patterns play a significant role in the accumulation of salt deposits. For example, rapid changes i n velocity in sudden expansions or contractions can be important i n increasing susceptibility to both scaling and erosion. In general, the deposition of unwanted solids on the heat transfer surface is defined as fouling. T h e deposition may be crystalline, biological material, products of chemical reactions or particulate matter [28]. In the initiation of the fouling process, the interaction is between the heat transfer surface and the foulant. Subsequently, the interaction 7  2.1. Salt deposition studies  8  is between the foulant material clinging to the surface and the fresh foulant arriving at the fluid/solid interface. L o n g range attraction forces serve to b r i n g the foulant to the surface and to provide the basis of contact. T h e forces involved may include van der Waals forces and electrostatic forces [28]. Due to fouling, the thermal-hydraulic performance of the heat transfer equipment is affected. Considering the consequence of fouling, much concern has developed among scientists and engineers regarding the importance of fouling related research. It is necessary to understand its nature, to formulate methods for its elimination, (or at least control). Three basic processes may be visualized i n relation to deposition of solids on surfaces from a moving fluid. T h e y are [28]: • T h e diffusional transport of the foulant across the boundary layers adjacent to the solid surface w i t h i n the flowing fluid. T h e transport of the foulant could be in the form of b o t h ions and salt particles nucleated i n the bulk. • T h e adhesion of the deposit to the surface itself. • T h e transport of the material away from the surface. Salt deposition kinetics depends on whether or not particles of salt form i n the bulk fluid. If the salt solution i n a heated tube is rapidly taken above the critical temperature, a super-saturated solution may result. E i t h e r nucleation of salt particles, or diffusion of salt ions to the walls, w i t h subsequent nucleation, may reduce the super-saturation. Particulate salt, depending on the particle size and flow Reynolds number may be transferred to the wall at a greater or lesser rate than individual salt ions, which result in crystalline fouling. According to homogeneous nucleation theory, whether or not particles form depends on the super-saturation of the solution, the particle surface tension and diffusional parameters. A r m e l l i n i [29] studied some aspects of N a S 0 4 nucleation i n supercritical and near-critical water. A r m e l l i n i and Tester [5] have presented results of an experimental study of the solubility of sodium chloride and sulfate i n supercritical and near-critical water. T h e objective of the study was to obtain solubilities of the two common salts, sodium chloride and sodium sulfate, at conditions prevalent in the supercritical water oxidation process. 2  LaJeunesse et al. [30] conducted experiments on Sandia's S C W flow reactor w i t h alloy-625 tubing of 0.47 c m I D . A 0.5 wt.% solution of N a S 0 , at 2-5 k g / h r , was heated to approximately 400°C to quantify the deposition rate of N a S 0 over a range of pressures, flow rates and heating rates. Pressure transducers were placed at different locations of the reactor to monitor the pressure during the tests such that the development of a constriction or plug could be detected. A s the plug was formed a pressure differential occurred. The test was then terminated and reactor cooled down. T h e plug was re-dissolved by passing pure water and all effluent was collected. Evaluation of effluent by ion specific electrode yields a deposition rate. T h e results 2  4  2  4  2.1. Salt deposition studies  9  suggested that at lower flow rates, the rate the plug formed is proportional to the rate that salt is injected into the reactor. It took longer for the tubes to be plugged at higher flow rates. T h e pressure range studied was about 25-26 M P a and it was reported that the higher-pressure conditions produced the plugging slightly faster than the lower pressure. C h a n et al. [31], at Sandia National Laboratories ( U S A ) , conducted experiments to study salt solubility and deposition kinetics in the N a 2 S 0 4 - H 0 system at conditions relevant to S C W O . A 50-cm long, alloy-625 tube served as a tubular reactor. T h e O D and ID of the reactor were 14.3 and 4.7 m m respectively. T h e reactor had a m a x i m u m operating temperature of 650°C and pressure of 51 M P a . In the deposition experiments a 0.5 wt.% salt solution was pumped through the reactor and the fluid temperature at the exit of the reactor was near 400°C. R a p i d precipitation was reported due to an extreme drop in salt solubility concentration that occurred as the feed stream became supercritical. Flow rate at ambient condition feed (25°C) could be varied from 0.2 to 1.5 m l / s (1.1 to 8.4 cm/sec). T h e reactor section was heated w i t h six 375 W cable heaters used to maintain isothermal conditions along the reactor. Pressure transducers were placed at three locations and their readings were recorded continuously such that the development of plug could be detected as pressure differential from one transducer to the next. T h e reactor got plugged in about 30 minutes i n the majority of the test runs. T h e concentration of the N a S 0 salt i n the solution was obtained experimentally by varying the fluid temperature and measuring salt effluent concentration. A t a given pressure, the salt concentration is a function of fluid temperature. It was assumed that the undissolved salt precipitates as a solid and the deposition occurs at the place of precipitation. A model was thus developed from the principle of mass conservation. T h e concentration gradient was obtained by determining the solubility as a function of temperature and combining the solubility information w i t h the temperature profile of the fluid as a function of axial position w i t h i n the reactor. 2  2  4  Ffodes et al. [32] presented the results of their study of salt deposition rates from a near supercritical aqueous sodium sulfate solution to a heated cylinder. T h e purpose of the study was to develop an understanding of salt deposition kinetics and nucleation phenomenon i n S C W O reactors. Experimental deposition rate data have been provided for sodium sulfate containing S C W and a predictive model based on the data was developed. Teshima [33] carried out an experimental study on U B C - N O R A M S C W O pilot plant to study the deposition of N a S 0 4 - T h e deposition experiments were done w i t h a m a x i m u m salt concentration of about 1 wt.% and the 6.2 m m I D reactor was plugged w i t h i n 20 minutes of operation. Since the tube walls were heated and hence at a higher temperature compared to the bulk fluid, salt molecules were crystallizing at 2  10  2.1. Salt deposition studies  the wall. T h e outer surface temperature of the fouled-heated tube was examined for inferring Na2SO"4 thickness profiles. Models were developed for predicting deposition of N a S 0 and compared molecular deposition to particulate fouling. T h e fouling rates predicted by the model were fairly close to the actual experimental values but the axial location of the deposit, w i t h m a x i m u m thickness (peak of the scale deposit) could not be predicted accurately. Experiments were also conducted to determine the solubility of N a S 0 i n water at 25 M P a and for a temperature range of 370-500°C. It was reported that the solubility decreases rapidly at the pseudo-critical temperature (385°C and 25 M P a ) and then less rapidly once the critical temperature is exceeded. (The pseudo-critical temperature is defined as that corresponding to m a x i m u m isobaric heat capacity). Furthermore, it was observed that the salt deposition profiles were influenced by mass transfer limitations and wall temperature i n addition to the solubility. It was also reported that the fouling rates are most affected by how quickly the solubility l i m i t is decreasing. T h e solubility l i m i t is a strong function of temperature and it was recommended to have small temperature gradients especially near the critical region where the solubility limit is decreasing quite rapidly. It was also observed that the monitoring of outer tube temperature appears to give a good indication of extent of fouling and i n conjunction w i t h the differential pressure measurement would be useful to predict the location of the deposition peak. Rogak and Teshima [7] presented the results of a heat and mass transfer model for the tubular reactor, developed and tested experimentally for N a S 0 4 deposition at 25 M P a . It was observed that the salt deposition profiles were influenced by mass transfer limitation i n addition to the solubility. T h e model uses empirical heat transfer relations to estimate mass transfer rates. T h e diffusion coefficient of the salt is calculated from the StokesEinstein relation using a hydrodynamic diameter of 2-6 A . T h e solubility was found to reduce by a factor of 1000 as the temperature increases from 380-400°C. T h e bulk solution never became supersaturated, therefore salt particle nucleation was not modeled. 2  4  2  4  2  Filipovic [34] investigated N a C l deposition i n the U B C - N O R A M S C W O pilot plant. Solubility measurements were made for various pressure and temperature ranges. It was reported that the solubility of N a C l decreased w i t h temperature and increased w i t h pressure. N a C l - w a t e r solution i n the bulk was passed through the two-phase vaporliquid region before the transition to vapor-solid region. D u r i n g the experimental study two distinct regions of depositions were observed: the vapor-liquid region, and the vapor-solid region. It was reported that the deposition rates d i d not change w i t h time. It was observed that the heat transfer coefficient increased by 20-75% when salt solution was introduced into the system. T h e salt thickness profiles were inferred from the tube outer surface temperature. Models were developed for heat and mass transfer.  2.2. Fouling mitigation techniques  11  2.2 Fouling mitigation techniques A broad range of solids deposition control methods have been tested i n S C W O reactors [14]: • C o n t r o l precipitation/reaction zone, e.g., keep precipitation away from the wall. • Utilize inert solids as nucleation sites to avoid wall deposition. • Utilize inert solids to scour wall deposits. • Take advantage of favorable regions of phase equilibrium, e.g., use high pressure or relatively low temperature to keep salt i n the solution. • C a r r y out continuous (e.g. transpiring wall) or intermittent flushing. • C o n t r o l feed chemistry to yield transportable solids. • Use high velocity to reduce deposition. • Use acid washing for occasional descaling. • Use quenching to redissolve salts at the reactor exit or brine zone. • C o n t r o l temperature profile to have higher salt solubility at reactor wall. • Filter hot solids mechanically. • Use mechanical devices for periodic or continuous removal of scale buildup. Investigation of anti-fouling methods has received much attention i n the past and a variety of chemical and mechanical methods have been suggested to reduce the formation of deposits on heat transfer surfaces. One way of overcoming, or at least reducing the problem, is i n some way to interfere w i t h the fouling process by the addition of chemicals to the flowing fluid. T h e use of such an additive technique for reducing or eliminating the deposition of the foulant on heat exchanger surface during the operation of the heat exchanger may be regarded i n broad terms, as on-line cleaning. Other on-line techniques are used that depend on physical and mechanical mechanisms and do not involve the use of chemicals. However, these techniques involve additional equipment needed at the design stage. A n alternative to on-line cleaning is to stop the operations and clean the heat exchanger either chemically or mechanically.  2.2. Fouling mitigation techniques  12  2.2.1 On-line cleaning Brush and cage systems T h e principle of the brush and cage system is that a brush, fabricated from suitable wires, is passed through the tubes by the liquid flow. A t either end of the tube there is a cage located so as to arrest the brush projectile. Cleaning takes place by running a wire brush through the system while it is operating. T h e brush is pulled or pushed through the reactor by a pigging mechanism. However, such a system cannot be used for any thing other than straight tubes. In the oil industry, pipelines are frequently cleaned by "pigs" transported w i t h the bulk flow, w i t h the object of scraping away deposits on the pipe wall. Conco [35] developed an air gun that fires small "pigs" through the fluid i n tubes to clean them in regularintervals. T h i s technique could be a good tool for scale removal in the S C W O systems. However, there are some problems associated w i t h the pigging system. T h e tubes to be cleaned should be of uniform diameter without any weld protrusions i n the inner side of the tube. T h e brushes attached to the pig would produce some drag and thus the pig must develop a sufficient pressure drop so as to provide enough thrust to not only move itself through the tubes but also to push (or pull) the cleaning brush itself. Online removal of the scale i n S C W O systems using this technique has also been suggested in [36] & [19].  Magnetic devices T h e use of magnetic fields to reduce or eliminate scale formation i n pipes has been attempted for many years [28]. It could be supposed that slightly soluble compounds such as C a C 0 3 existing i n solution as charged ions, would be affected by the application of an electric field, and this could form the basis of the technique to alleviate fouling. Duffy [37] reported that magnetic devices had not been used extensively for industrial applications due to the strong criticism, which they have received from engineers. He described work that demonstrated no influence of magnetic fields on the precipitation of C a C O s . T h e skepticism is still apparent i n the industry, despite the fact that successful applications have been reported. Donaldson [38] for instance, reports a successful use of a magnetic device. T h e use of the magnetic device resulted in the removal of calcium phosphate scale that had formed on a plate heat exchanger. T h e other examples of scale reduction are reported by Nordell [39], Donaldson & Grimes [40] and Donaldson & Grimes [41]. T h e evidence of these examples cannot be ignored. Donaldson [38] reports carefully controlled laboratory tests where a pipe badly scaled w i t h calcite gradually became clean over prolonged exposure to a magnetic field under flowing water conditions. Donaldson [38] attributes the beneficial effects of magnetic devices to a number of closely related changes brought about by the application of  2.2. Fouling mitigation techniques  13  magnetic fields. • C r y s t a l size is increased w i t h less opportunity for the incorporation i n a scale structure. • Evidence from research w i t h zinc phosphate solutions suggests an increase in solubility i n the presence of a magnetic field. It would appear that the technique shows promise but more work need to be done on the use of magnetic devices for the reduction of the scaling problems before the technology can be used w i t h confidence. Furthermore the possibility of inducing electric currents in metallic structures, that could result i n enhanced corrosion, must be considered.  Use of inserts Inserts have been used for many years to improve heat transfer, particularly from viscous liquids. T h e principle involved is to disturb the viscous sub-layer near to the heat transfer surface thereby reducing the resistance to heat flow. Since the problem of fouling is very concerned w i t h the transport of foulants across the viscous sub-layer it is expected that any attempt to reduce the resistance to heat flow w i l l also effect the propensity toward fouling. Hewitt et al. [42] have given some backgrounds to the use of heat transfer enhancement techniques. T h e inserts are usually twisted tapes or wire matrices. It has been reported that inserts can reduce fouling problems where reactions are involved [43] and where wax and other organic precipitates arise [44, 45]. Some inserts are primarily designed to reduce fouling e.g. wire spring-like configurations that are free to oscillate and move under the influence of the flow conditions. T h e movement of the insert against the wall knocks or rub off, any deposit as it is formed. A more robust design is when the insert is held tightly w i t h i n the tube by a "push fit" or anchored at the end of the tube. Gough and Rogers [43] report the use of m a t r i x tubulators inside the tubes of a shell and tube heat exchanger for heating tar o i l . W i t h o u t the inserts, a reduction of 50% in the heat transfer coefficient was encountered over a period of four months. T h e heat transfer coefficient fell about 4% only over the same period when inserts were installed. Crittenden et al. [46] conclude that the disturbance of the hydrodynamics by the tubulators is largely responsible for the beneficial effects on fouling. It is not clear if these devices would be effective i n reducing the salt deposition i n S C W O systems, where the flow conditions are already highly turbulent.  Surface treatments From the point of view of surface science, the formation of deposits on a metal surface may be considered as an interaction between the deposits and the heat transfer surface. Forster et al. [47] carried out an experimental study for fouling mitigation by using  2.2. Fouling mitigation techniques  14  different reactor materials i n order to increase the induction period. T h e approach was to change the interface crystal/heat transfer surface so that an increase i n removal rate may be achieved by decreasing the adhesive strength due to modification of inter-facial characteristics. Various surface materials were deployed i n the fouling test runs w i t h an aqueous C a S 0 4 solution. T h e solution was passed through the heat transfer surface w i t h initial wall temperature at 75°C, heat flux of 31.8 k W / m , velocity of 0.2 m / s and salt concentration of 2.5 g/1. A new surface, known as diamond like carbon D L C , proved to be a good choice to increase the duration of the induction period significantly. T h e performance of D L C material was found much better then copper, a l u m i n u m , steel and brass. 2  Low energy surfaces are likely to reduce the tendency of particles to attach. Changes in the surface characteristics therefore, have the potential to reduce the incidence of fouling. In addition to reducing fouling the surface also prevent corrosion. Muller-Steinhagen and Zhao [48] investigated low fouling surface alloys made by ion implantation technology. Fouling experiments during pool boiling of C a S 0 4 solutions demonstrate that fouling is significantly reduced for all investigated conditions of heat flux and C a S 0 concentration. It may be concluded that the pre-requisite condition for a surface to posses low fouling behavior is that the surface has a low surface energy [48]. 4  Ion implantation is the introduction of atoms into the surface layer of a solid with ions in the k e V to M e V energy range [49]. T h e environment of particles on the surface of a solid differs from that i n the interior. In the interior, a particle is evenly acted on by forces exerted by the particles around it. O n the surface, where the coordination number is reduced, an unsaturated force field exists. There is a tendency for the particle to be pulled into the m a i n b o d y i n order to reduce the surface area to a m i n i m u m ; hence surface tension is produced. Surface free energy is a function of internal energy, temperature and surface entropy (surface energy = U - T S ) . E n t r o p y increases when foreign particles are implanted i n the surface. Therefore, the surface energy would decrease w i t h an increase of entropy. L o w fouling surface alloys produced by ion implantation w i l l have unique advantages: • A l l o y elements implanted exist i n a solid state so there is no interface and the alloy layer is not easily removed. • A d d i t i o n a l heat transfer resistance is negligible. • A l l o y surface is weldable. T h e majority of the techniques to mitigate fouling can only increase the duration of induction period. Thus changing the material, implanting ions on the tube surface etc., are all temporary measures, which may be adopted to prolong the induction period. Thus the above mentioned techniques would only increase the interval between the  2.2. Fouling mitigation techniques  15  actual cleaning process. A regular cleaning procedure is thus required after a certain period of plant operation.  2.2.2  Other fouling mitigation techniques reported in SCWO systems  In the early 1980s, S C W O was claimed to be the technology to solve every waste treatment problem. T h e boundless optimism of the inventors covering up the serious problems, which might never be solved for all kinds of wastes, hindered (and still hinders) an industrial application and thus a broader distribution of the technology. It must be pointed out that S C W O can only become an alternative to incineration in special - l i m i t e d cases [2]. Salt-free waste streams can easily be oxidized in tube reactors. For wastes containing only C , Ff, O , and N , no special reactor design is necessary. For wastes containing salts, the precipitating salts lead to plugging of reactor tubes and to overcome this problem various techniques have been suggested recently. M a n y of the companies that have attempted to commercialize the S C W O technology over the past two decades have developed innovative approaches to dealing w i t h the salt deposition problems. Table 2.1 summarizes the commercially designed approaches that have been developed for precipitation control, mostly w i t h i n the last decade. T h e y are arbitrarily divided into two categories: those that involve unique system or component designs and those that employ specific operating techniques [16]. Some studies [2] suggest increasing the system pressure and thus increase solubility of some salts. However, at higher pressure corrosion problems are also enhanced. Other studies present special reactor designs to prevent settling-down at wall surface. Such concepts include simple tank reactors i n which the salts sink down to the zones of low subcritical temperature where they are dissolved again [2] & [50]. However, in such designs, the low settling speed and high vertical turbulence present a problem. Alternatively, salts precipitating i n the reactor zone have to be dissolved before the deposition at the wall. Crooker et al. [51] implemented a transpiring wall reactor to address the technical problems of corrosion and salt plugging i n S C W O systems. T h e reactor pressure boundary was exposed to controlled-temperature deionized water, resulting i n a safer design. T h e transpiring platelet liner flows supercritical water that forms a film barrier from undissolved salt. T h e salts formed d u r i n g the oxidation were carried out of the reactor. T h e plant has been designed to destroy U S N a v y excess hazardous materials. Salt-producing solutions have been processed at feed rates of 45 and 95 k g / h r . Tests were conducted at a pressure of 24.1 M P a and reactor temperatures between 594 and 816°C. Post-test inspections have not revealed any obvious reactor liner corrosion or salt deposition. However, it should be evaluated, if a salt separation as a first step (e.g. by filtration) followed by S C W O i n a tube reactor  2.2. Fouling mitigation techniques  16  T a b l e 2.1: Commercially developed approaches to S C W O salt precipitation control [16]  Approach  Method  Companies using the method  Reactor designs  Reverse flow, tank reactor Transpiring wall reactor Adsorption/reaction on solid phase  MODAR Foster Wheeler S R I International  Reversible  Abitibi-Price  Specific techniques  flow,  tubular  reactor H i g h velocity flow Mechanical brushing R o t a t i n g scraper Reactor flushing Additives L o w turbulence, homogeneous precipitation Crossflow filtration Density separation Extreme pressure tions  opera-  M O D E C , Chematur, Organo MODEC M O D A R , General atomics General atomics, Abiti-Price, Chematur EcoWaste Technologies, General Atomics HydroProcessing University of Texas, A u s t i n Oxidyne, General Atomics, H y droprocessing Los A l a m o s N a t i o n a l Laboratory, EcoWaste Technologies  may be a cheaper way of treatment. A fundamental problem of this k i n d of treatment might be a simultaneous separation of the organics leading to another contaminated waste. Essentially three reactor concepts (see F i g . 2.1 [50,52]) have been developed and studied: tubular reactor, tank reactor w i t h the reaction zone i n the upper part and a cool zone i n the lower part of the tank to dissolve the salts [50], and the "transpiring wall reactor" w i t h an inner porous pipe which is rinsed w i t h water to prevent salt deposits at the wall [52]. Tubular reactors are the most common. A technique, using the control of operating conditions, such that salts precipitate only in the bulk fluid has been patented by HydroProcessing i n their S C W O process [53]. It is claimed that salts which have nucleated i n the bulk fluid tend not to adhere to surfaces. One way to minimize salt buildup i n a solid wall S C W O reactor is to ensure that the particles are well suspended i n a high speed flow. T h e particles must remain suspended u n t i l they redissolve once the effluent is cooled, or until they can be otherwise removed [16]. T h i s approach has been utilized by M o d e l l et al. [54], and is primarily applicable to feeds w i t h a relatively high proportion of nonsticky to sticky salts. T h e downside to this approach is that the reactor length must be  17  2.2. Fouling mitigation techniques Tube reactor  — « - Efflueni  I  Cooling water  ^  Film-cooled hydrothermal burner  Pressure containment Transpiring  Feed -  —  I ..[  Effluent  wall \ - - Splash ring  600 °C Mixing and  'V  v  Transpiring flow  Porous ! - — liner  vj ^. Transpiring i^" flow Cooling water M O D A R tank reactor  Transpiring wall reactor a) Platelet principle b) Porous inner pipe  Figure 2.1: Reactor concepts for S C W O [50,52] correspondingly increased i n order to maintain the residence time. Aymonier et al. [55] developed a hydrothermal-sonochemical reactor to degrade acetic acid. I n order to avoid plugging of the heat exchanger, a new reactor concept, has been introduced based on the use of ultrasonics under cavitation conditions. T h e ultrasound activation increased the yield of acetic acid oxidation reaction by 40%. T h e influence of the horn v i b r a t i o n amplitude on acetic acid conversion was studied. Furthermore, tests w i t h an industrial waste containing salts and halogens showed the performance of the t i t a n i u m liner of the reactor for overcoming salt precipitation a n d corrosion. Tests, to study the salt precipitation, were carried out for pressures of 2.8 M P a a n d at a temperature of 220°C. It was reported that the ultrasound considerably improved the salt recovery at the reactor outlet. L o n g time tests to prove the suitability of these reactor concepts for an industrial application have not yet been performed w i t h any of these new designs. In a review study, K r i t z e r a n d Dinjus [2] concluded, that the new reactor concepts seem to be too susceptible to fail i n long term application. Corrosion is a serious problem for treating chlorinated wastes by S C W O because of the formation of hydrochloric acid. M u t h u k u m a r a n and G u p t a [56] proposed addition of sodium carbonate to reduce the corrosion related to S C W O treatment of chlorinated  2.2. Fouling mitigation techniques  18  wastes because of the formation of hydrochloric acid. D a t a were provided to show the enhancement of oxidation, by addition of sodium carbonate. It was reported that the improvement of oxidation might be due to a combination of the catalytic effects of N a C 0 3 and removal of H C I by N a C 0 . A d d i t i o n of N a C 0 3 was said to play a key role on reducing corrosion on reactor walls by neutralizing the acid. However, it was reported that N a C 0 3 is insoluble under supercritical conditions because of low dielectric constant of supercritical water and thus presented a problem. N o plugging of reactor tube was reported for their conditions of experiment (30 M P a and 400°C). It was mentioned that the concentration of N a C 0 was kept low enough to avoid plugging and about 1 m m or smaller size N a C 0 3 particles were expected during the S C W O process. After the product mixture was cooled down later, N a C 0 3 re-dissolved into the fluid and thus avoided any plugging problems i n the back-pressure regulator. 2  2  3  2  2  2  3  2  2  T h e reactor flushing technique involves rinsing of the S C W O reactor periodically during operation w i t h a fluid that w i l l dissolve accumulated salts scale. T h e most common flushing fluid is cool (subcritical temperature) pressurized water. Ravich [57] presents some data for the solubility of N a C 0 3 at various pressure and temperature levels. T h e solubility reported at 24.8 M P a and fluid temperature of 400°C is almost zero. B u t at lower temperature i.e., at 300°C, the solubility increases to about 15 % (weight). Therefore rinsing technique can be employed i n order to remove plugging of the tube. D u r i n g the test, when plugging of tubes occurs, the heaters can be turned off to decrease the fluid temperature. T h e plug may thus be removed due to higher salt solubility. T h i s technique has been tried by C h a n et al. [31] for CaS04 deposit removal. B y reducing the fluid temperature to 320°C at 25 M P a (corresponding to 20 wt.% of CaS04 solubility), the accumulated salt re-dissolved i n the bulk fluid. Thus by reducing the temperature of effected portion of the reactor by 100°C, the salt can be re-dissolved and removed as a brine stream. T h e y suggested that if the location and time profile of the deposit is known, the affected portion can be isolated by valves and pure water feed can be substituted and the reagent feed is diverted to a parallel tube for continuous processing. T h i s technique seems to be useful for laboratory experiments to remove the plug. B u t using a similar technique on a commercial plant would require a complicated system of valves and monitoring devices for automatic switching to remove the plugging and processing the influent i n parallel. 2  Fouling can be a major problem i n evaporators used to concentrate pulping liquor in alkaline pulping mills. T w o types of scales predominate. T h e y are C a C 0 and water soluble N a S 0 4 - N a C 0 scales. T h e term soluble scale refers to water-soluble inorganics which deposits on black liquor evaporators. T h e y form by crystallizing from a saturated solution when their concentrations exceed the solubility limit. For salts whose solubility decreases w i t h temperature, supersaturation may be due to the temperature gradient existing at the hot surface as well as concentration changes. Kraft pulp is obtained from wood and treated w i t h aqueous solutions of N a O H and 3  2  2  3  2.3. Objectives of this work  19  N a S . Kraft spent pulping liquor solids may contain up to 12 wt.% of N a C 0 3 and 10 wt.% of N a C 0 3 [58]. Soluble scales are easily removed from heat transfer surfaces by water washing. There are two approaches to control soluble scales. T h e first is to avoid exceeding the saturation limit of the inorganics, which deposit as scales. T h e second approach is to recirculate product liquor back to the evaporator. Liquor recirculation is beneficial because the recycled liquor contains precipitated solids, which act as nucleation sites to relieve supersaturation. It has been shown that increasing the velocity of the recirculation liquor reduces the fouling rate [58]. 2  2  2  2.3  Objectives of this work  T h e problems associated w i t h S C W O have hindered an industrial scale-up of the process so far. Salt plugging seems to be most severe of them and all attempts to solve it i n a satisfactory way, lead either to new problems, make a long-time solution doubtful or increase the cost. These techniques are yet to be tested in an actual S C W O plant. T h e plugging of the reactors cannot be avoided by variation of the process parameters without simultaneously triggering a new problem [2]. T h e current possible ways of reducing the problem have not been totally effective and seem to be susceptible to failure i n long term application. Thus none of these approaches has achieved any commercial success and scaling of inorganic salts remains a major obstacle i n long term S C W O operation treating organic waste w i t h inorganic compounds. It is to be noted that the techniques discussed above have been used to delay the problem of fouling. T h i s would only prolong the time intervals between the shut down of the equipment, for actual scale removal, and can not totally eliminate the problem of scaling [2]. For an industrial application, it is of minor interest if a destruction rate of a certain organic compound is 99.99 or 99.999% (which seems to be the objective of most of the studies carried out so far). O n the other hand, it is absolutely necessary to prove the long time applicability of an industrial process. Waste streams that contain salts i n too high concentration w i l l sooner or later lead to plugging of every k i n d of reactor. Furthermore, S C W O is not and most probably w i l l never become a "general" technology for a l l kinds of waste-streams. Consequently, the wastes suitable for S C W O have to be found and selected carefully [2]. Benzene, toluene and several other hydrocarbons are nitrated on a large scale by industry mostly as an initial stage i n the manufacture of polymers, dye and insecticides etc. N i t r a t i o n generally occurs i n a mixed acid media containing mostly sulfuric acid (acts as catalyst) and nitric acid (reacts w i t h organics). T h e nitrated products contain inorganic acid (H S04) and nitrated byproducts, which have to be removed. T h e byproducts typically are nitrophenols that have water-soluble salts that can be removed by alkaline wash. Treatment of chemical wastes (e.g. phenol) using N a O H , 2  20  2.3. Objectives of this work  as a base, leads to production of salts ( N a S 0 a n d / o r N a 2 C 0 ) which precipitate at high temperatures and elevated pressure conditions. Schmieder and A b e l n [12] in a review suggested that for better understanding of the salt deposition problem, more salt-water phase diagrams are required. Besides the many salt-water binary phase diagrams determined until now, ternary (saltl-salt2-water) systems have to be determined. T h e determination of the phase diagrams has to be completed w i t h data of the k i n d of the precipitate, e.g., morphology, stickiness etc. 2  4  3  N O R A M Engineers and Constructors is a leading Mononitrobenzene ( M N B ) plant manufacturing engineering firm and is collaborating w i t h University of B r i t i s h C o l u m b i a i n S C W O research projects. Use of S C W O i n M N B plants in the next few years is most likely and requires technical know-how for better understanding of fouling related problems i n this field. N a 2 C 0 and N a 2 S 0 are thus good candidates for determining solubility, studying deposition and fouling mitigation. F r o m the literature reviewed, i t has been noticed that only a few N a S 0 deposition studies have been reported and not much information is available for N a C 0 solubility at S C W O conditions. In the literature, no detailed fouling research has been found for N a C 0 salt deposits i n S C W O systems. So far there have been no results published for N a C 0 deposition i n supercritical water on a heated tube and the fundamental data needed to model the nucleation are not known. T h e analysis of the actual deposits on the reactor surface, under turbulent flow conditions, has never been reported. T h i s analysis is important i n order to study the structure of the scale and to determine deposit layer properties such as thermal conductivity. T h e objective of the present study is to determine the solubility of these salts in supercritical water and thus develop a relation between the solubility and fluid density for estimation purpose. T h e solubility of N a C 0 and N a 2 S 0 in pure form and i n the presence of each other is to be determined, for the temperature range relevant to S C W O . T h e next step is to study the deposition behavior of N a C 0 and develop a m i t i g a t i o n technique to prolong the operating period of the system before the reactor gets plugged due to salt deposition. The salt particles are to be nucleated i n the bulk fluid for fouling mitigation purposes. T h i s would result i n combined particulate and crystalline fouling instead of the usual pure crystalline scale which occurs due to salt molecule deposition. T h e hypothesis of the fouling mitigation technique is that the structure of the combined particulate and crystalline deposit would be weaker than the pure crystalline deposit. Thus removal of deposited salt layer may occur due to the drag force of the flowing fluid. S E M and E D X analysis of b o t h types of deposits, crystalline and particulate, w i l l be carried out to study the deposit structure. Heat and mass transfer models w i l l then be developed, for the two types of fouling phenomena, i n order to simulate the deposition process. 3  4  2  4  2  2  3  3  2  3  2  3  4  2  3  The experimental setup, which includes various components of the U B C - N O R A M S C W O pilot plant, is discussed i n Chapter 3. Heterogeneous-nucleation experiments have been performed to determine the solubility of these salts and salt molecules crys-  2.3. Objectives of this work  21  tallized on the reactor surface. Chapter 4 covers the procedure adapted for determining the solubility of the salts and results of the solubility experiments. A computer code, to simulate these experiments is also discussed i n this chapter. Chapter 5 discusses the fouling mitigation technique adapted to prolong the operation of the S C W O system prior to the plugging of the reactor due to salt deposition. T h e modified experimental setup, to apply this technique, is also discussed i n this chapter. Results of the fouling mitigation runs are compared w i t h the tests carried out following the usual procedure. T h e scale structure and elemental composition analysis are presented i n Chapter 6. A heat and mass transfer model developed to simulate the fouling mitigation experiments is discussed i n Chapter 7. T h e experimental results are compared w i t h the simulation model estimations. F i n a l l y Chapter 8 summarizes the conclusions of the study and recommendations for future research in this field.  Chapter 3 Experimental Facility Description 3.1  Process equipment  T h e U B C - N O R A M S C W O facility was constructed for research and development purposes using a tubular type reactor, for the destruction of wet organic wastes. A wide range of pressures, heat fluxes, temperatures and mass flows can be achieved. Figure 3.1 shows a schematic of the experimental setup. T w o 550-liter cylindrical storage tanks supply the system w i t h water and waste. Water is pressurized w i t h a triplex plunger p u m p ( G I A N T P57) while gas is pressurized using an air pressure operated booster compressor. A pulsation damper (Hydrodynamics Flowguard D S - 1 0 - N B R - A ) is used w i t h the plunger pump to suppress the flow variations. T h e speed of the p u m p and hence the flow rate is controlled by a variable frequency drive (Reliance Electric ISU21002). T h e pump can be operated between flow rates of 0.6 to 2.2 k g / m i n at a m a x i m u m outlet pressure of 45 M P a . For a given tube diameter and fluid mass flow rate, the Reynolds number is a function of the fluid dynamic viscosity only (Re oc p' ), which decreases w i t h temperature. Under typical S C W O conditions, the flow is thus highly turbulent (see F i g . 3.2). T h e liquid flow is measured w i t h a graduated cylinder and stopwatch at the system outlet, when it is cold. 1  T h e m a i n heat transfer elements of the S C W O system are the recuperative heat exchanger, two pre-heaters, the test section, the reactor and the process cooler. T h e heat exchanger is a counter flow double pipe type, w i t h 1.27 c m diameter Schedule 80 pipe (SS 347) on the shell side. T h e fluid coming from the influent tank passes through the tube side of the heat exchanger. T h e recuperative heat exchanger is designed to recover approximately 30 k W of power from the reactor outlet. T h e process cooler is 6.2 m long stainless steel tube. A l l other tubing is made of nickel base alloy-625 high pressure t u b i n g (6.2 m m I D and 9.52 m m O D ) . In the heated tube sections, electrical current is passed through the tube wall. T h e electrical resistance of the wall causes it to heat up as the current passes through the wall. T h e power is supplied from silicon controlled rectifiers ( S C R ) panel directed through two step-down transformers (240/24  22  3.2. Pressure measurement and calibration  23  V A C , H a m m o n d Manufacturing) for each heated section as shown i n F i g . 3.3. Each pair of transformers is wired i n series i n input and parallel i n output and is capable of delivering 24 V at 45 amps. T h e transformers are attached to the heated sections by 2.5 cm thick copper cables that lead to barrel connectors which are attached to stainless steel rods. T h e steel rods are silver-soldered onto the tube. T h e high (max. 24 V A C ) voltage connections are made at the middle of the heated section and the ground wires are attached to the ends, eliminating the possibility of any ground loops in the system. T h e wiring arrangement also provides a balanced load to each half of the heated section. E a c h pre-heater is 4.7 m long. T h e power to pre-heater 1 is adjusted manually on the S C R panel. T h e power to pre-heater 2 can be adjusted w i t h a feedback temperature controller that has a manual and automatic mode. T h e heating for the test section is achieved i n the same way as for the pre-heaters. Power control of the test section is manual. T h e test section is made from four tube sections. T w o shorter sections (0.3 m), placed at the inlet and the outlet of the test section are not heated. T h e other two (1.52 m each) are electrically heated as shown i n F i g . 3.4. Test section is the part of the system where most of the measurements are done. After passing through the test section the fluid enters a 140 m long reactor section w i t h 17 U-shaped bends, which can be heated in the same manner as discussed above. T h e n the fluid enters the recuperative heat exchanger where it heats up the incoming feed from the influent tank. Finally, the fluid is cooled down further in a process cooler. A back-pressure regulator is used to control the system pressure. A gas dome back-pressure regulator is used in the system.  3.2  Pressure measurement and calibration  Pressure transducers, located at the inlet and outlet of the test section, are used to measure the gauge pressure. T h e pressure transducers have been calibrated w i t h a digital calibrator (Cole Parmer 68036 series). T h e uncertainty of the pressure measurement, considering the errors i n the data acquisition system and variation along the test section is approximately 0.1%. Pressure can also be measured at three other locations in the system as shown i n F i g . 3.1 but is not logged during the experiment.  3.3  Temperature measurement and calibration  In the test section, K - t y p e C h r o m e l - A l u m e l thermocouples are used to measure the outer tube surface temperature. A total of 29 thermocouples are spot welded to the test section to measure outer surface temperature as shown i n F i g . 3.5. In the test section, the thermocouples are spot welded to the test section tube as shown i n F i g . 3.6. T h e surface between the two wires acts as a j u n c t i o n for the thermocouple. T h i s is the intrinsic type of thermocouple arrangement and the temperature measured is  3.3. Temperature measurement and calibration  24  Legend salt solution tank  distilled H 0 tank  0 pressure gauge (T^ bulk fluid thermocouple  2  (\f\*  pressure relief valve  booster pump  rp5^ back pressure regulator  Wgas tank  pre-heater 2  pre-heater  &  heat exchanger  "—w  process cooler cooling water in  cooling water  back pressure regulator  Figure 3.1: U B C - N O R A M  conductivity meter effluent tank  S C W O pilot plant  actually the average of the temperatures at the two spots. T h e peripheral temperature variation across the short distance between the two spot welds is infinitely small. Even along the axial direction, where the temperature variations are important, the distance between the spot welds is too small for a noticeable change i n temperature. Insulating ceramic is used to prevent contact between the unshielded thermocouple wire and the tube surface. T w i s t e d shielded wires are used to extend the thermocouple from the junction to the data acquisition system. Surface temperatures are also measured at other sections of the system and some of them are attached to the alarm system. There are three thermocouples i n the test section, which are used to measure the bulk fluid temperature. These are located at the inlet, middle and outlet of the test section at the unheated unions, as shown i n F i g . 3.5. These thermocouples have been inserted in the union fittings and their junction extend to the center of the tube to measure bulk fluid temperature. Since these union fittings are unheated, the fluid passing through them is at uniform temperature. A s mentioned earlier, stainless steel rods were soldered to the test section tube  3.3. Temperature measurement and calibration  25  x 10  50  100  150  200  250  300  350  400  450  500  Fluid temperature (°C)  Figure 3.2: Reynolds number versus fluid temperature for electric power cable connections. On the test section, the distances of all the thermocouples are measured from the downstream edge of the steel connector just after union 2 shown in Fig. 3.3 and is mentioned in Table 3.1. The thermocouples have been calibrated by measuring the saturation temperatures of pure water at known pressures and the calibration procedure is as follows. The fluid temperature and pressure was set above the critical values and then the pressure was decreased below the critical value, without adjusting the heat input to the system. The fluid in the test section would thus be in the saturated state during the calibration procedure. The measured temperatures were then compared with the saturation temperature values from the steam tables. For the surface thermocouples, a similar Heated Sections Union 1 Union 2  /  24 VAC  Union 3  V  Cables  \  /  24 VAC  Union 4  Union 5  Barrel Connectors  Figure 3.3: Schematic of electric heating for pre-heaters and test section  26  3.3. Temperature measurement and calibration  T a b l e 3 . 1 : Distance of thermocouples (measured from the electric power connection) Thermocouples Thermocouples Distance from conat the top sur- at the b o t t o m electric nector (cm) surface face SIO SB9 S9 SB8 S8 SB7 S7 SB6 S6 SB5 S5 SB4 S4 SB3 S3 SB2 S2 SB1 SI SB11 SB12 SB13 SB14 SB15 SB16 SB17 SB18 SB19 SB20  6.1 15 25 34.2 44.3 52 61.3 67.6 75.1 80.7 83.7 90.2 96.8 103.1 111.4 117.7 125.5 132.8 140 157.7 173.8 192.2 209.7 221.6 230 243.7 257.2 271.7 287.4  3.4. Heat Hux  27  measurement Preheater One  Preheater Two  Test Section  SCR  SCR  SCR  F i g u r e 3.4: Electric heating schematic of the heated tube sections First half of the heated length of the test section  S e c o n d half of the heated length of the test section  in  Union SB9 SB1 union from p r e - ^ • • i i • l I I I I I I i i I heater 2 S10 S1  1 1  /  1  Bulk thermocouple  S 1 1  1  1  S  1  1  1  1  1  1  1  1  2  0  1 I M  Union t  /  Electric power connections  Bulk thermocouple  F i g u r e 3.5: L o c a t i o n of thermocouples in the test section procedure was followed assuming the test section to be adiabatic and the condensing heat transfer coefficient to be very high. T h e error i n the temperature is less than 1 K .  Spot Welds  Overbraid.  Ceramic Rod  Tube Top View  Side View  F i g u r e 3.6: Thermocouple spot welded to the test section surface  3.4 Heat flux measurement T h e heat gained by the fluid i n a section can be determined by the heater power input. However, not all electric power generated is transferred to the fluid due to thermal losses. T h e heat lost is a function of tube surface temperature. A simple energy balance  28  3.5. Salt concentration measurement  is done instead, to determine the gain in fluid enthalpy across the test section. T h e increase i n bulk fluid temperature across the heated test section permits the calculation of the heat flux. T h e heat flux q (W/m ) can be determined as: 2  =  m(H - Hi) ndL 2  where TO is the mass flow rate of the fluid and H & H\ are the fluid enthalpies at the outlet and inlet of the test section of inside diameter d and length L. 2  3.5  Salt concentration measurement  Salt concentration was inferred from the effluent conductivity measurement. T h e conductivity meter was first calibrated for various concentrations of salt solutions, prior to the actual solubility experiments. T h e conductivity of the salt solution is a function of the salt concentration. Several solutions were prepared of various salt concentrations ranging from 10~ to 1 wt.% of salt and conductivity of each solution was measured. Several conductivity measurements were taken at each concentration and then averaged. 5  Figure 3.7 shows the calibration graph plotted for conductivity versus Na C03 concentration for the range of our experimental study. A trend line, was then fit to the experimental data giving a R value (coefficient of determination) of 0.9969. T h i s figure shows salt concentration versus conductivity for 15 measurements. In terms of salt concentration (wt.%), about 70% of the data points lie w i t h i n ± 7 % of the fitted equation. A similar calibration was made for Na S04 in order to determine the concentration of salt i n the effluent interpreted from the measured conductivity and is shown i n F i g . 3.8. A fitted curve predicted w i t h i n ± 1 0 % of the measured conductivity w i t h an R value of 0.9989. 2  2  2  2  3.6  Data acquisition  T h e temperature, pressure and conductivity measurements are sent to a high speed data acquisition system (Omega M u l t i S c a n 1200) which has a channel to channel isolation. T h e M u l t i S c a n board can sample data from each channel once every 520 //sec. There are 24 channels on the acquisition system which is connected to a computer for data logging. T e m p V i e w version 4.14 was used as the data acquisition program and was configured to a scan-time of about 5 sec for the 24 channels.  3.6. Data  29  acquisition  0.001  0.01  0.1  N a C 0 weight % in water 2  3  Figure 3.7: Conductivity meter calibration for Na C03 2  Figure 3.8: Conductivity meter calibration for Na S04 2  Chapter 4 Solubility of Na S0 , N a C 0 and Na2S04-Na2CC>3 mixture in Supercritical Water 2  4.1  4  2  3  Introduction  T h e solubility of inorganic salts i n water at high temperature and high pressure is important i n natural hydrothermal systems and some technological systems such as Supercritical Water O x i d a t i o n ( S C W O ) and Wet A i r O x i d a t i o n ( W A O ) . Supercritical water (i.e., water above 22.1 M P a and 374.14°C) has the ability to dissolve organic chemicals but the inorganic compounds are much less soluble at these conditions. These salts precipitate out of the supercritical water, agglomerate and usually stick to the reactor wall. In a tubular reactor a flow restriction is thus produced, in addition to a heat transfer resistance across the reactor wall, thus reducing the thermal-hydraulic performance of the reactor. In order to model the salt deposition, the salt solubility information is needed as a function of fluid temperature (or fluid density). There are, i n general, two types of salt phase behavior depending on whether the solubility curve intersects the critical curve (Type I) or not (Type II) [59]. T y p e I systems are often soluble i n water at ambient conditions: N a C l - H 0 is a typical example. T y p e II salts - N a S 0 , K S 0 , N a C 0 3 , C a S 0 - are generally less soluble; the solubility of N a S 0 i n S C W is about l p p m at 250 bar and 450 ° C and is about 3 orders of magnitude less than that of N a C l . T h e solubility of C a S 0 is only about 1 ppb [4], N o t much information could be found about the phase behavior of N a C 0 3 salt at conditions prevalent to S C W O systems. 2  2  2  4  2  4  2  4  4  4  2  Dell'Orco et al. [60] reported that sodium sulfate, chloride and bicarbonate appeared to be sticky salts. T h e y were removed primarily by heterogeneous precipitation or impingement. T h e reported solubility of N a C 0 3 in supercritical water is 26 p p m at 2  30  31  4.2. Salt concentration measurement 24.1 M P a and 4 5 0 ° C and that of N a H C 0  is 86 p p m at 29.8 M P a and 509°C [61].  3  Measurements of isochoric heat capacity of sodium sulfate and s o d i u m carbonate were made i n a spherical high-temperature, high-pressure adiabatic calorimeter. Valyashko et al. [62] presented data regarding densities of liquid and vapor solutions in three-phase equilibrium for the sodium carbonate and water system data near the critical end point. Densities were reported for fluid mixtures, at around the critical temperature of pure water, for liquid and vapor solutions of sodium carbonate. It was reported that for an aqueous sodium carbonate solution the critical temperature is 6 4 9 ± 0 . 2 K as compared to 6 4 7 . 1 ± 0 . 1 K for pure water. S o d i u m carbonate and sodium sulfate are reported to exhibit Type-2 solid-fluid phase behavior (the solubility of salt starts declining before the critical temperature of the solvent is reached) [62]. T h e solubility of the salts being studied, N a C 0 3 i n particular, was available i n the literature only for a few temperatures at elevated pressures. Several solubility measurements have been reported for sodium sulfate [4, 5, 7, 59]. Shvedov and Tremaine [63] developed a correlation for the solubility of s o d i u m sulfate. For sodium carbonate, at supercritical conditions, L i and G l o y n a [64] reported its solubility for two temperatures. Valyashko [65] presented solubility behavior of sodium carbonate at subcritical and near critical temperature. N o information was available for these salts i n the presence of each other. 2  4.2  Salt concentration measurement  A s mentioned i n the previous chapter the conductivity meter was calibrated for different concentrations of [ N a C 0 3 ] and [Na SC>4]. For the experiments w i t h sulfate and 2  2  carbonate mixture, effluent samples were collected and analyzed for [ N a ] , [ C O g ] , +  -  [ H C 0 ] and [SO^~] to determine the [ N a C 0 ] and [ N a S 0 ] . [ N a ] was measured us+  3  2  3  2  4  ing atomic absorption and t i t r a t i o n was used for [ C O ] and [HCO3] measurement. For 2 -  [ S O ] measurement, the turbidimetric method was used. T h e turbidimetric method, 2 -  to determine the sulfate concentration, is based on the fact that light is scattered by particulate matter i n aqueous solution. B a C l  2  is added to the sample to form milky-  white precipitate and light absorption is then measured using a photometer. Standard procedures were followed to determine the concentrations of the ions and are discussed in Ref. [66]. O n l y the above ions were found i n the effluent samples and no corrosion products were present, although atomic absorption was used to look for chromium and nickel.  32  4.3. Experimental procedure  4.3  Experimental procedure  For the solubility experiments, the salt solution was prepared by dissolving a certain mass of salt i n a known volume (mass) of distilled water. A n electric mixer was used to ensure a well-mixed salt solution. A series of experiments were performed around 24-25 M P a and at various temperatures. Initially distilled water was passed through the system to achieve a steady state condition. It usually took one hour to achieve steady state such that no change i n temperature was observed w i t h respect to time. T h e test section surface temperature was kept at the highest temperature i n the system. Once steady state was reached, the salt solution was introduced into the system. It was assumed that the salt above the solubility limit at test section temperature would precipitate and stick to the tube wall. T h e fluid thus leaving the test section would be at the solubility limit at the test section temperature. T h i s concept is shown in F i g . 4.1. T h e measured conductivity would then be used to determine the solubility. After running w i t h salt solution for 10-15 minutes, distilled water was switched back on again. T h e distilled water would dissolve enough salt, deposited on the wall, to become saturated by the time it exits the "salt bed". T h e effluent would thus again be at the solubility limit. T h e conductivity remained the same during the deposition and dissolution processes until there was no salt left on the tube wall. Therefore, the solubility measurements are not greatly affected by the deposition kinetics and integration resistance of the tube surface is negligible.  heated test section fluid enters at salt concentration above solubility I limit of test section conditions  • ^ ^ ^ ^ ^ ^ ^ ^ fluid exits at undissolved salt solubility limit ^> P CZZf>corresponding heterogeneous to test section ^s>vJ2^ conditions d e  o s i t s  d  u  e t 0  F i g u r e 4.1: Concept of salt solubility experiments Figure 4.2 shows the conductivity measurement for some sample experimental runs corrected for residence time. In all the experimental runs the conductivity increased from that of pure water to initially the conductivity of the salt solution i n the influent tank. A l t h o u g h an initiation period is often exhibited i n fouling systems, based on the literature reviewed, this is the first time it has been observed for the supercritical salt-water system. Unfortunately, the initiation period is very short compared to any reasonable S C W O operation period. After the initiation of the deposition, the conductivity decreased to a uniform value corresponding to the solubility l i m i t . In the experimental  4.3. Experimental  procedure  33  run shown i n F i g . 4.2(a), the salt solution was introduced for about 10 minutes. T h e conductivity of the salt solution i n the influent tank was about 1400 /iS/cm. T h e solubility corresponding to the temperature for that r u n i n terms of conductivity was 1330 pS/cm. W h e n pure water was introduced at the end of the deposition part of the experiment, a l l the salt deposited on the tubes dissolved into the water and the dissolution period (salt bed) was quite short. For such cases only the deposition part was considered. However, it can be observed that the conductivity of the effluent d i d not change much during the deposition and dissolution parts of the experimental r u n until a l l the salt was removed from the tube. Figure 4.2(b) shows a similar r u n but w i t h a longer dissolution duration. For some cases when the salt concentration i n the influent tank was well above the solubility limit, as shown i n F i g . 4.2(c), more salt deposited on the tubes. For such cases the dissolution period was much longer as it took a while for all the deposited salt to dissolve i n the pure water.  F i g u r e 4 . 2 : Effluent conductivity vs. time (a) r u n " S i " , (b) r u n "S2" and (c) r u n "S3"  4.4. Solubility reporting temperature  34  It was noticed that when the salt solution was introduced into the system the test section surface temperature decreased 1 or 2°C from the i n i t i a l clean tube temperature. T h i s decrease could be due to the higher heat transfer coefficient of salt solution as compared to water and i n i t i a l negative resistance at the onset of fouling. T h e salt solution was used only for a short period so that the surface temperature rise was not more than about 3°C from the clean conditions. T h e heat input to the test section was kept low enough to ensure a small rise in the bulk fluid temperature across the test section. T h e bulk fluid inlet and outlet temperatures were also monitored and it was observed that the difference between the bulk inlet and outlet temperature remained almost constant during the experiment. T h i s may indicate that the solid/solution interface temperature was close to the initial clean tube surface temperature. In order to determine the solubility of the salt mixtures, the procedure adopted was the same as i n pure salt experiments except that instead of a pure salt solution, a mixture of N a C 0 3 and N a S 0 was used. 2  4.4  2  4  Solubility reporting temperature  T h e tube inner surface temperature was calculated from the measured outer surface temperature and known heat input to the test section. T h e solubility was reported at a temperature taken to be clean tube average inner surface temperature of the second segment of the test section when the salt solution was introduced. T h i s choice of reporting temperature is justified i n Section 4.5. T h e error range for the reporting temperature was determined i n the following manner. T h e upper limit was taken to be the m a x i m u m surface temperature. Based on experience, 0.2°C was added to the measured temperature i n order to include the effect of noise i n the experimental data. For the lower limit, the m i n i m u m of; average inner surface temperature, fluid bulk outlet temperature and the temperature determined from the model (Section 4.5) was considered. A g a i n , to include the effect of noise, 0.2°C was subtracted from this value.  4.5  Modeling the effect of heat and mass transfer on measurements  Salt deposition i n the heated test section was modeled i n order to understand the relation between an "underlying" solubility-temperature curve and the experimentally accessible parameters (outlet concentration and temperature). A one dimension model was developed by Teshima [33] for salt deposition on a heated tube. T h i s model is reviewed below and extended by considering alternate heat transfer correlations.  4.5. Modeling the effect of heat and mass transfer on measurements  35  Furthermore a more sophisticated method has been developed to estimate the temperature corresponding the salt solubility. Once the solubility is exceeded i n the salt solution, the salt can deposit o n the tube surface due to homogeneous or heterogeneous nucleation. In this model i t is assumed that the salt nucleating o n the tube surface sticks to the wall. Precipitation of salt due to homogeneous nucleation, i.e., salt particles nucleated i n the bulk fluid, has not been considered i n the model. For the heterogeneous mechanism, i.e., crystalline scaling, heat a n d mass transfer relations were programmed i n the M A T L A B environment ( T h e M a t h W o r k s , Inc., Massachusetts, U S A ) . A s a simplification, pure water thermodynamic a n d transport properties were used to model the salt solution. T h e heat transfer coefficient must be known to determine the wall temperature. In order to calculate the heat transfer coefficient, an empirical correlation can be used. T w o Nusselt number correlations, developed by Swenson et a l . [67] a n d Yamagata et a l . [68] have been considered. There are other empirical relations that can be used to calculate the heat transfer coefficient [69], however, the estimated values lie between the heat transfer coefficient values determined by the two considered correlations. T h e details of these correlations are discussed below. The Swenson correlation: [67] 0.613  Nu = 0.00459  (Re f s  T,-T  J k.  h  /  \ 0.231  Pi Pb  923  (4.1)  where Re is the Reynolds number, H is the fluid enthalpy, /i is the fluid dynamic viscosity, k is the fluid thermal conductivity and p is the fluid density. T h e subscripts b and s correspond to conditions i n the bulk and at the fluid/salt deposit surface respectively. The Y a m a g a t a correlation: [68]  Nu = Pr  0  85  b  8  b  (  is the P r a n d t l number of the bulk fluid and  (E>1)  1  I Fc  (4.2)  0Mb3Re° Pr° F  (H -H )/(T -T ) C b  s  b  s  (£< ),  n = 1.44(1 + ^ )  (otherwise),  n j = 0.77 ( l + -p^j + 1.49  0  2  -0.53  Pb  0.67Pr-  0 0 5  (H„-H.y(T -T,) b  c  Pb  (4.3)  in which E = ^ i j ^ , Cp is the specific heat at bulk conditions and pc is for the pseudo-critical conditions. T h e heat transfer coefficient can then be calculated using b  36  4.5. Modeling the effect of heat and mass transfer on measurements the Nusselt number:  h=^  (4.4)  For the heterogeneous nucleation, the similarities for the heat a n d mass transfer were used to determine the deposition rate. T h e deposition rate would depend on the mass transfer coefficient, h and the dissolved salt concentration difference between the bulk and wall conditions: m  fn  m  - h ndL(C m  b  - C)  (4.5)  w  where C is the dissolved salt mass concentration i n the bulk fluid, C is the dissolved salt mass concentration at the fluid/deposit surface or at the tube wall, d is the diameter of the tube, L is the length of the tube, rh is the molecular deposition rate (kg/sec). b  w  m  The mass transfer coefficient was determined as follows. W h e n forced convection dominates transport and mass transfer does not significantly affect the flow field, given a correlation for the heat transfer coefficient, a mass transfer coefficient may be obtained and vice versa. T h i s is accomplished by replacing the Nusselt number w i t h Sherwood number (Sh = h d/V ) and the P r a n d t l number w i t h the Schmidt number (5c = u/V ). V is the molecular diffusion coefficient and can be determined from the Stokes-Einstein relation [70] using the molecule diameter d : m  m  m  m  m  V  m  = ^ r -  (4.6)  where b)~ is B o l t z m a n n constant, \x is the dynamic fluid viscosity. T h e molecular diameter was varied from 3-9 A and negligible change i n T d i was noticed. For the results presented here, it is taken to be 5.1 and 5.3 A for N a 2 C 0 and N a S 0 4 respectively calculated using the Avagrados number, salt density and molar mass. Rogak and Teshima [7] used a similar approach to determine the molecular diameter of sodium sulfate and the calculated diffusion coefficient value appeared acceptable based on the experimental values reported by Hodes et al. [32] mo  e  3  2  T h i s equivalence of correlations is subsequently referred to as the analogy between heat and mass transfer. Rogak and Teshima [7] presented the results of a heat and mass transfer model for the tubular reactor, developed a n d tested experimentally for N a S 0 deposition at 25 M P a . T h e model uses empirical heat transfer relations by Swenson et al. [67] to estimate mass transfer rates. W h e n natural convection is important, the analogy between heat and mass transfer applies only if the Lewis number (a/V ) of the fluids equals 1 i.e., similar temperature and concentration profiles [8]. 2  4  m  T h e heat transfer coefficient is a function of Reynolds number and P r a n d t l number: ™=f(Re,Pr)  (4.7)  4.5. Modeling the effect of heat and mass transfer on measurements  37  and from the Sherwood number, the mass transfer coefficient, h ,  is a function of  m  Reynolds number and Schmidt number:  ^  = f(Re, Sc)  (4.8)  Therefore using the Nusselt number correlation and an analogous equation for Sherwood number, the following relation for the mass transfer coefficient can be derived:  h  - = ^ L ?  <'> 4  9  where a = 0.387 and 0.2 for Nusselt number correlations developed by Swenson et al. [67] and Y a m a g a t a et al. [68] respectively. Using E q . 4.5, for a guessed value of saturated salt concentration i n the bulk, the deposition rate was calculated. T h e experimental solubility curve was then used to determine the saturated salt concentration at the wall. T h e actual concentration of salt in the bulk can thus be calculated using E q . 4.5. T h e test section was then discretized into 0.5-cm segments. A segment length of 0.5 cm was found to be appropriate for numerical analysis. T h e bulk fluid and wall temperatures were then calculated from the energy balance and heat transfer coefficient. T h e saturated salt concentration was estimated from the measured solubility and the salt concentration in the bulk fluid was calculated as  dC "~ = -h ird{C -C ) dL A  b  m  b  (4.10)  w  T h e concentration of salt calculated from the model for a sample experimental run is shown in F i g . 4.3. T h e bulk fluid temperature increases from 388.7°C to 396.6°C in the test section. T h e salt concentration in the bulk fluid, C , calculated from the program is compared to the saturation concentration i n the bulk, C ( ), and saturation concentration at wall conditions, C ( ). b  b  w  sat  sat  T h e use of this heat and mass transfer model to interpret measurements is discussed below. T h e test section is not perfectly isothermal, so it is not obvious which temperature should be used as the "reporting temperature" for the measured concentration in the effluent. P r o v i d e d that the fluid leaving the test section is not supersaturated or laden w i t h particles, the reporting temperature should be greater than the bulk exit temperature. Considering that there is some mass-transfer limitation, the reporting temperature should be less than the m a x i m u m surface temperature. A simple approach is to take the average surface temperature as the reporting temperature. N o r m a l l y this average is close to the bulk temperature anyway. Near the critical temperature, density and solubility vary dramatically w i t h temperature, so a 2°C error in reporting temperature has a significant effect. For this reason, a more sophisticated model of the  4.5. Modeling the effect of heat and mass transfer on measurements  3  1  388  .  390  .  .  38  >-  392 394 Bulk fluid temperature (°C)  396  Figure 4.3: Modeled salt concentration along test section for run "S6" experimental apparatus has been developed. The actual "reporting" temperature from model, T d i should be some weighted average of surface and bulk temperatures: mo  e  Tmodel =  X (T  Tb,exit +  s  —  Tfi)  (4-11)  where £ is a weighting factor. Average wall and bulk temperatures are used in the second term to minimize experimental noise. The weighting factor x should mainly be a function of the mass transfer characteristics of the flow, and secondarily, the variation of solubility with temperature. The heat and mass transfer model was used to estimate x for each experimental run. In the model, it has been assumed that there is some underlying solubility function C ( T ) which is to be estimated from the bulk outlet concentration C , by choosing a temperature T such that C = C ( T ) . The model uses the actual measured bulk temperatures to determine the heat flux and wall surface temperatures. The modeled wall temperatures T are not exactly the same as the actual wall temperatures T , due to errors in the heat transfer model, but the modeled temperatures are not used directly. Instead, the model is used only to estimate x from: s a t  0  b  s  a  t  s  s  x =  f  -  T b  f -f s  b  '  e x U  (4.12)  4.5. Modeling the effect of heat and mass transfer on measurements T a b l e 4 . 1 : Details of N a C 0 2  Experiment Code Influent Gauge salt pressure reference no. & concen- (MPa) Data File tration (wt.%)  Average surface temperature  Mass Bulk fluid flow temperature rate (°C) (kg/ min)  3  39  solubility experiments  Error range f o r , temperature corresponding to the solubility PC)  (°C)  Temperature calculated from the Swenson  Solubility Run type Temperature (wt.%) calculated from the Yamagata a  min  max  model (°C) model (°C)  May 10, 2002 C1 MAY10.2002.xls  0.19  24.5  0.66  398.3 408.2 409.5  407.2  411.6  407.3  407.2  0.0120  deposition & salt bed  May 06, 2002-03 C2 MAY06.2002.xls  0.56  24.5  0.68  382.2 383.1 384.2  382.9  386.1  383.5  383.1  0.1010  deposition & salt bed  May 06, 2002-02 C3 MAY06.2002.xls  0.56  24.4  0.68  378.1 380.7 380.1  379.9  381.0  380.5  380.6  0.3900  deposition & salt bed  May 06, 2002-01 C4 MAY06.2002.xls  0.56  24.2  0.68  373.4 378.6 378.3  378.0  379.5  378.0  378.1  0.5280  deposition & salt bed  May 03, 2002-01 C5 MAY03.2002.xls  0.56  24.3  0.70  385.4 390.0 390.2  389.8  391.3  390.6  390.4  0.0270  deposition & salt bed  May 03, 2002-02 C6 MAY03.2002.xls  0.1  24.3  0.70  380.8 384.9 384.7  384.5  385.7  385.6  385.6  0.0730  deposition & salt bed  C7 Mar 12'02-NL MAR12'02NL.xls  0.1  24.9  0.18  388.2 390.6 391.8  390.4  393.2  391.2  390.6  0.0220  deposition only  Mar 12, 2002-02 C8 MAR12'02N.xls  0.1  25.0  0.70  391.9 397.9 398.3  397.5  401.1  397.5  397.5  0.0160  deposition only  Mar 12, 2002-03 C9 MAR12'02N.xls  0.1  25.0  0.70  395.2 403.2 403.5  401.9  407.1  401.9  402.8  0.0120  deposition only  Mar 12, 2002-04 C10 MAR12'02N.xls  0.1  25.0  0.70  399.9 410.0 410.3  409.1  414.3  409.1  409.6  0.0090  deposition only  Mar 12, 2002-05 C11 MAR12'02N.xls  0.1  25.0  0.70  403.0 416.0 415.7  415.5  420.0  416.3  416.7  0.0079  deposition only  Mar 12, 2002-06 C12 MAR12'02N.xls  0.1  25.0  0.70  407.0 423.3 422.0  421.3  427.2  421.3  421.4  0.0057  deposition only  Mar 12, 2002-07 C13 MAR12'02N.xls  0.1  25.0  0.70  412.5 431.3 429.3  426.2  435.3  426.2  426.5  0.0043  deposition only  Mar 12, 2002-08 C14 MAR12'02N.xls  0.1  25.0  0.70  420.6 440.0 437.7  434.9  441.1  434.9  438.0  0.0038  deposition only  inlet  a  outlet  1 wt.% is about 10,000 mg/L  T h e T dei was then calculated for each experimental run. Tables 4.1 & 4.2 compare this temperature w i t h various temperatures measured i n the test section for N a C 0 and N a S 0 experiments. For the N a C 0 runs, the difference between T d i and average test section temperature was less than 1°C for majority of cases. T h e r u n "C13" has the m a x i m u m difference i.e., 3.1°C. For the Na SG"4 runs, this difference was less than 1.4°C for a l l cases. It was therefore concluded, as a simple approach, that the average surface temperature of the test section should be the appropriate reporting temperature. However, as mentioned earlier i n Section 4.4, this T dei was considered in determining the error range for the reporting temperatures. mo  2  2  4  2  3  mo  2  mo  e  3  40  4.6. Results and discussion T a b l e 4 . 2 : Details of N a S 0 2  Experiment reference no. (Data file: May24.2002.xls)  Code Influent Gauge salt pressure concen- (MPa) tration (wt.%)  Mass Bulk fluid flow temperature rate (°c) (kg/ min)  inlet  Average surface temperature  outlet (°C)  solubility experiments  4  Error range for temperature corresponding to the solubility f C ) •: :  Temperature calculated from the Swenson  Solubility Run type Temperature (wt.%) calculated from the Yamagata a  model (°C) model (°C)  May 24, 2002-01  S1  0.1  24.4  0.66 379.6 383.1  382.2  382.0  383.4  383.2  383.2  0.0850  deposition only  May 24, 2002-02  S2  0.1  24.4  0.66 379.7 382.4  382.3  382.1  383.2  382.4  382.4  0.0670  deposition & salt bed  May 24, 2002-03  S3  0.1  24.5  0.66 382.3 383.6  383.6  383.4  384.4  383.7  383.7  0.0400  deposition & salt bed  May 24, 2002-04  S4  0.1  24.6  0.66 383.7 384.9  384.5  384.3  385.4  384.9  384.9  0.0220  deposition & salt bed  May 24, 2002-05  S5  0.1  24.4  0.66  385.4 388.4  388.7  388.2  389.6  388.4  388.4  0.0010  deposition & salt bed  May 24, 2002-06  S6  0.1  24.3  0.66  388.7 396.6  397.0  395.6  398.4  395.6  395.8  0.0004  deposition & salt bed  ' 1 wt.% is about 10,000 mg/L  4.6 Results and discussion 4.6.1  Na C0 solubility 2  3  Figure 4.4 shows the solubility data for N a C 0 for the temperature range of interest. A similar behavior of solubility versus water density is shown i n F i g . 4.5. A t h i r d order polynomial has been fit to the experimental data. T h e empirical relation to predict the N a C 0 solubility concentration (wt.%), as a function of fluid density, p ( k g / m ) is as follows: 2  3  3  2  3  log {C co } Na2  3  = 6.24 x 1 0 ~ y - 8.48 x 1 0 ~ p + 0.046p - 9.74 5  2  (4.13)  Information available from the literature is also shown. T h e subcritical data were reported by Valyashko [65]. A t supercritical conditions the solubility data were found at two temperatures [64] and are also shown i n Figs. 4.4 & 4.5. In order to test the assumption that the test section was long enough such that the undissolved salt deposits on the test section wall, r u n " C 7 " was done at 24.5 M P a and at a lower flow rate of 0.18 k g / m i n . If the assumption were false then a higher salt concentration should have been observed i n the effluent for the higher flow rate, as compared to the lower flow rate run. T h e experimental results seem to be i n good agreement w i t h the existing information i n the literature. A s mentioned earlier, the average surface temperatures are considered to be the actual temperatures corresponding to the solubility limit. These temperatures are found to be quite close to the reporting temperatures calculated from the model program. T h e details of the operating parameters for the N a C 0 experiments are shown i n Table 4.1. 2  3  41  4.6. Results and discussion 1  1  +  r  + + +  <  -  A A  1  1  :  Valyashko, 1973 (24.5 MPa) : C2-C4 C5-C6 C7 C8-C14 C1 : Li etal., 1999(24.1 MPa)  + A O •  X  A-  e  %  *X  •3 |  320  ,  ,  ,  Ii  Ii  I1  1  340  360  380  400  420  440  460  Temperature (°C)  F i g u r e 4.4: N a C 0 2  4.6.2  Na S0 2  4  3  solubility vs. temperature  solubility  T h e solubility behavior for N a S 0 versus temperature and density is shown in Figs. 4.6 & 4.7 respectively. A second order polynomial was fitted to calculate the N a S 0 4 solubility concentration (wt.%), as a function of fluid density, p ( k g / m ) . T h e relation is as follows: log [C so ] = - 2 . 1 6 x 1 0 - y + 0.037p - 13.11 (4.14) 2  4  2  3  Na2  4  Figures 4.6 & 4.7 also show the solubility measurements reported by A r m e l l i n i & Tester [5] and Rogak & Teshima [7]. T h e thermocouples used to measure temperatures reported by Rogak & Teshima [7] were later found to have an offset of 2°C. T h e data shown here have been corrected for the offset. Furthermore, it is worth mentioning that the solubility data reported by Rogak & Teshima [7] correspond to the fluid temperature at the test section outlet. However, for this study, a more sophisticated procedure has been followed to determine the solubility reporting temperature. A correlation developed for N a S 0 solubility by Shvedov & Tremaine [63] is also shown in Figs. 4.6 & 4.7. T h e correlation gives a good indication of the solubility up to a fluid density of 200 k g / m and after that it underestimates the solubility. For example at 100 k g / m the correlation underestimates the solubility by almost a factor of 3, compared to other measurements. T h e operating parameters and other details for N a S 0 experiments are shown i n Table 4.2. T h e average surface temperatures were found to be quite close to the reporting temperatures calculated, using the model. For the range of flow rates and heat input to the test section considered i n this study, it was observed that the bulk fluid temperature at the outlet of the test section is a 2  3  3  2  4  4  42  4.6. Results and discussion  Figure  4.5: N a C 0 3 2  solubility vs. density  good estimate for the actual temperature corresponding to the solubility limit. B u t for higher heat input or flow rate the wall-bulk temperature difference w i l l be higher and for those cases the bulk fluid outlet temperature may not be a correct temperature corresponding to the solubility limit.  4.6.3  Solubility of Na C03-Na S04 mixture 2  2  For the solubility experiments i n which a mixture of salts was used, chemical analysis of samples was done to determine the salt concentration. It was noticed from the chemical analysis that the [ N a ] content was not always the exact amount of what was required to make N a C 0 3 and Na SC>4 from measured [ C O 3 ] , [HCO3] and [SO4 ]. Therefore N a C 0 and Na SC>4 concentrations i n the solution were determined using two methods. [ N a ] required to make N a C 0 3 and N a S 0 from the measured [ C 0 ] , [HCO3] and [ S O ^ ] was calculated and then the concentrations of N a C 0 and N a S 0 were calculated. Thus, i n this method, the [ C O 3 ] and [SO4 ] measurements were assumed to be accurate. In the other procedure, the concentrations of these salts were calculated based on measured [ N a ] and [SO4 ]. T h i r t e e n experiments were performed w i t h a mixture of salts. For these experiments, the percentage difference i n [Na+] calculated, based on [ C O 3 ] , [ H C 0 ] & [SO|~] and [ N a ] detected ranged from -8.3% to 12.5%, w i t h 70% of the data having less than ± 5 % difference. It was decided to report the results based on the former procedure, i.e., salt concentration calculated based on [ C O 3 ] , [ H C 0 ] and [SO4 ] measurements. T h e solubility behavior +  -  2  2  -  2  3  2  +  2  -  2  4  -  3  2  -  2  -  4  +  -  +  -  3  -  -  3  3  4.7. Conclusion 10  1  10°  i !5 _3 « 10"  3  10"  4  10"  5  340  360  380  400  420  440  460  480  500  520  Temperature (°C)  F i g u r e 4.6: N a S 0 4 solubility vs. temperature 2  of N a C 0 3 and N a S 0 i n a mixture is shown i n F i g . 4.8. It is interesting to note that at low fluid density, the solubility of each salt when present in a mixture is almost same as that of i n d i v i d u a l binary salt-water system. However, at a density of about 470 k g / m , N a S 0 was found to be less soluble i n the presence of N a C 0 3 . T h i s could be due to the common-ion effect i.e., the shift i n an equilibrium position caused by the presence of an ion involved i n the equilibrium reaction. Thus the solubility of less soluble N a S 0 can decrease due to the presence of N a , i.e., the common ion. T h e details of parameters for salt-mixture experiments are shown i n Table 4.3. 2  2  4  3  2  4  2  +  2  4.7  4  Conclusion  Salt solubility information is needed to predict the deposition of these salts on the heat transfer surface. T h e pressure and temperature conditions focused were those which are usually encountered i n S C W O systems. T h e solubility data reported cover a wide range of temperatures and fill the gap in the information available in the literature. Very few previous measurements i n the critical region were found for N a C 0 . Furthermore, solubility of these salts, when present i n the solution in the form of a mixture, has also been determined for the first time at S C W O conditions. It was noticed that the solubility of the salts studied i n the form of a mixture, above supercritical conditions, was quite close to the solubility of the pure salt. However, at near critical conditions, the presence of N a C 0 3 reduced the solubility of N a S 0 , 2  3  2  2  4  44  4.7. Conclusion  Figure 4.7: Na SC>4 solubility vs. density 2  presumably due to the common-ion effect. For b o t h salts considered in this study, there was a rapid decrease i n solubility just above the pseudo-critical temperature. Furthermore the results show that a lower order polynomial i n log of solubility l i m i t versus density can be used to interpolate data. T h e reported temperatures were confirmed by developing a heat and mass transfer model to determine the temperature corresponding to the solubility l i m i t . T h e experimental procedure adapted to measure the solubility seems to be quite reasonable given the fact that the measured values agreed well w i t h the data existing i n the literature.  45  4.7. Conclusion 10  10  cf*  i S  1  F  .2 0  = 10  Na C0 , CS9-CS13 Eq. 4.13 for pure Na C0 Na S0 , CS1 Na S0 , CS2-CS3 Na S0 , CS4-CS6 Na S0 , CS7-CS8 Na^SO,, CS9-CS13 4 for pure Na SO _ _ Eq.2 4.14  3  2  3  2  4  2  4  2  4  2  4  2  o  10  10 500  450  400  350  3  300  AA  \  250  200  150  100  50  Fluid density (kg/m ) 3  F i g u r e 4.8: Solubility of mixture of N a C 0 2  T a b l e 4.3: Details of N a C 0 - N a S 0 2  3  2  4  Gauge Mass Bulk fluid pressure flow temperature (MPa) rate (°C) (kg/ min) inlet outlet Na C0 Na S0 0.66 373.6 377.0 Aug 07, 2002-01 CS1 1.053 1.077 24.6 AUG07, 2002.xls 0.66 380.7 382.4 Aug 08, 2002-01 CS2 0.140 0.131 24.5 AUG08, 2002.xls 0.66 384.2 385.9 Aug 08, 2002-02 CS3 0.140 0.131 24.3 AUG08, 2002.xls 0.66 385.4 388.0 Aug 14, 2002-01 CS4 0.051 0.006 24.7 AUG14, 2002.xls 0.66 401.5 407.0 Aug 14, 2002-03 CS5 0.051 0.006 24.5 AUG14, 2002.xls 0.66 396.3 400.3 Aug 14, 2002-04 CS6 0.051 0.006 24.4 AUG14, 2002.xls 0.66 391.1 394.8 Aug 16, 2002-01 CS7 0.051 0.006 24.6 AUG14, 2002.xls 0.66 398.2 403.2 Aug 16, 2002-02 CS8 0.051 0.006 24.6 AUG 14, 2002.xls 0.66 375.4 378.7 Dec 11,2002-01 CS9 0.829 0.427 24.6 DEC11, 2002.xls 0.66 375.4 378.7 Dec 11,2002-01 CS10 0.829 0.427 24.6 DEC 11, 2002.xls 0.66 378.1 380.1 Dec 11,2002-02 CS11 0.829 0.427 24.6 DEC11, 2002.xls 0.66 381.9 382.2 Dec 11,2002-03 CS12 0.829 0.427 24.6 DEC 11, 2002.xls 0.66 381.9 382.2 Dec 11,2002-03 CS13 0.829 0.427 24.6 DEC11, 2002.xls " 1 wt.% is about 10,000 mg/L  Experiment reference no. & data file  Code Influent salt concentration (wt. %)  2  3  2  3  and N a S 0 2  4  mixture solubility experiments Average surface temperture. (°C)  Error range for Solubility (wt.%) Run type temperature corresponding 1 ° solubility (°C) min max Na C0 Na S0 376.8 378.5 0.6320 0.2707 deposition & salt bed 381.7 383.2 0.1253 0.0899 deposition & salt bed 385.3 386.5 0.0611 0.0033 deposition & salt bed 387.8 391.2 0.0442 0.0031 deposition & salt bed 406.4 408.1 0.0142 0.0004 deposition & salt bed 400.1 402.1 0.0172 0.0004 deposition & salt bed 393.8 395.0 0.0255 0.0004 deposition only 402.8 405.1 0.0152 0.0003 salt bed only 378.1 379.5 0.5661 0.1509 deposition & salt bed 378.1 379.5 0.5815 0.2189 deposition & salt bed 379.8 381.2 0.4332 0.1509 deposition only 381.7 382.9 0.3033 0.0541 deposition & salt bed 381.7 382.9 0.2212 0.1130 deposition & salt bed a  t n e  2  4  377.3 381.9 385.5 389.3 406.6 400.6 394.0 403.0 378.29 378.29 380.02 381.89 381.89  3  2  4  Chapter 5 Salt Deposition and its Mitigation 5.1  Introduction  A s discussed i n the last chapter, it was observed that the solubility of inorganic salts decreases drastically around the pseudo-critical temperature. T h e heated reactor tube surface is at a higher temperature compared to the bulk fluid, hence salt molecules crystallize at the tube surface. T h i s type of nucleation is known as heterogeneous nucleation and results i n crystalline scale on the tube wall. O n the other hand if the salt becomes supersaturated i n the bulk fluid, salt particles nucleate i n the fluid and this type of nucleation is known as homogeneous nucleation. Precipitation of salt particles lead to particulate deposit. Hodes [71] studied N a S 0 4 deposition on a heated cylinder. Salt concentration and time i n the deposition experiments were varied between 2 & 8 w t . % and 6 & 12 minutes. T h e salt solution was preheated to about 5 ° C below the solubility temperature corresponding to the concentration in the bulk solution surrounding a cylinder. T h e cylinder was heated beyond the solubility temperature to drive deposition. N o homogeneous nucleation was observed through the visually accessible test cell during the experimental run. T h e purpose of the study was to develop an understanding of salt deposition kinetics and nucleation phenomenon i n S C W O reactors. T h e results of the deposition study were presented by Hodes et al. [32]. E x p e r i m e n t a l deposition rate data have been provided for sodium sulfate and a predictive model based on the data was developed. S m i t h et al. [72] developed a model to predict whether or not homogeneous nucleation would occur i n a natural convection boundary layer around a cylinder heated beyond the solubility temperature corresponding to the concentration of salt i n the surrounding aqueous salt solution. Lewis number was found to be a critical property i n this regard. T h e model was applied to the experiments r u n by Hodes [71] and yielded consistent results, i.e., homogeneous nucleation was absent. 2  T h i s chapter discusses the deposition behavior of N a C 0 3 due to heterogeneous nucleation. A s a possible fouling mitigation technique, the salt was made to nucleate i n the 2  46  5.2. Experimental procedures  47  bulk fluid just before the test section. T h e salt particles nucleating i n the bulk fluid should agglomerate and are more likely to flow w i t h the fluid, through the system, due to their larger size. T h e experimental procedure for this m i t i g a t i o n technique is discussed in this chapter. T h e deposition behaviors of b o t h heterogeneous and combined homogeneous & heterogeneous type nucleations have also been compared.  5.2 5.2.1  Experimental procedures Heterogeneous nucleation experiments  A s mentioned i n the last chapter, experiments were initially carried out to determine the salt solubility at S C W O conditions. T h e experimental method was to pass the salt solution through a near isothermal test section and the salt above the solubility limit was assumed to be depositing on the tube surface. T h e solution leaving the test section would thus be at its saturation limit. T h e test section was set to be the hottest section in the system such that the concentration of salt in the effluent should be the saturation limit corresponding to the test section temperature. T h e tube surface temperature was higher than the fluid temperature and thus the salt was nucleated on the tube surface and homogeneous nucleation was unlikely. T h e salt solution was passed for a short period of time (less than 20 minutes), i n order to avoid plugging or excessive tube surface temperature rise. T h e flow was switched to pure water afterwards to dissolve the deposited salt. T h e fluid was heated i n the pre-heaters to achieve temperatures above the pseudo-critical temperature. D u r i n g the experiments it was noticed that the pre-heaters were most susceptible to plugging and/or overheating. D u e to this reason, the system had to be shut down and thus these experiments could not be run for a longer period. These experiments are similar to those performed by Teshima [33] and later modeling work carried out by Rogak and Teshima [7] indicated only heterogeneous nucleation was occurring.  5.2.2  Combined heterogeneous and homogeneous nucleation experiments (heated test section)  In order to check the hypothesis that larger homogeneously nucleated particles are less likely to stick to the tube surface, the experiment set up was modified as shown i n F i g . 5.1. Instead of the salt solution, only pure water was passed through the pre-heaters such that no salt deposition occurred before the test section. Salt solution was then injected into this stream of water, using a metering p u m p , at the test section inlet. A B r a n + L u e b b e metering p u m p (model N - K 3 1 ) , shown as p u m p # 2 in F i g . 5.1 was used for this purpose. T h e m a x i m u m discharge rate of the metering p u m p is about 0.2 k g / m i n and is adjusted by varying the stroke length of the plunger. T h e metering pump calibration was done at a system pressure of 24.7 M P a by measuring pump discharge  48  5.2. Experimental procedures  Legend solution  distilled  pressure gauge (T^) bulk fluid thermocouple f\f\*  pressure relief valve  booster pump  back pressure regulator  f^igas tank  A  heat exchanger  *—w  process cooler  cooling water  back pressure regulator  cooling water in  conductivity meter  Figure 5.1: Modified process equipment for homogeneous salt nucleation at various stroke length settings of the pump. T h e discharge and stroke length relation is shown i n F i g . 5.2. A pulsation damper (Hydrodynamics Flowguard D S - 1 0 - N B R - A ) was used to suppress the flow variations. T h e flow rate of the metering p u m p was set to 10% of the m a i n pump's flow rate. T h e pure water stream was heated such that the temperature after m i x i n g was beyond the solubility temperature corresponding to the salt concentration i n the mixed streams. T h e temperatue of the salt solution was measured using a bulk temperature thermocouple just before it mixed into the m a i n stream coming from pre-heater 2. Thus the salt particles were expected to nucleate in the bulk fluid. Since the test section was heated i n these runs, therefore heterogeneous nucleation may also be expected. T h e heat input to the test section was kept low, usually about 1.25 k W , which corresponds to a nearly adiabatic condition. T h e experiment  49  5.2. Experimental procedures  was terminated when the test section was plugged due to the salt deposition and the pressure relief valve, just after the m a i n pump, opened due to excessive pressure. Pure water was then pumped through the metering p u m p to dissolve the salt deposited on the tube walls. D u r i n g the experiment, due to the salt deposition, a pressure increase at the inlet of the test section was noticed. T h e reactors were set to a temperature of about 5-10°C lower than the test section temperature. T h e pressure at the outlet of the test section remained constant thus indicating that nearly a l l the deposition was taking place i n the test section. 0.22  0.17 O) (U D)  ro o w  sz  0.12  T3  ex  E  3 Q.  0.07  discharge (kg/min) = 0.0081 x stroke length (mm) - 0.0332  0.02 5  15  25  35  stroke length (mm) F i g u r e 5.2: Metering pump calibration at 24.7 M P a  5.2.3 Combined heterogeneous and homogeneous nucleation experiments (unheated test section) For this type of experiments, a similar procedure was followed as mentioned in the last section. However, i n order to reduce heterogeneous nucleation, the test section was not heated in these experiments. T h i s set of experiments was carried out to check if the net salt deposition could be further reduced by reducing heterogeneous nucleation. Some sample experiments from each of the above three types of experiments are discussed below.  5.3. Results and discussion  5.3  50  Results and discussion  Results of salt deposition experiments performed are discussed below. T h e test section outer surface temperature was measured during the deposition process. T h e temperature measurement locations discussed i n this chapter are of thermocouple locations mentioned in Table 3.1.  5.3.1  Heterogeneous nucleation  A s mentioned earlier, such experiments could not be run for more than 30 minutes and the experiments had to be terminated due to excessive pre-heater surface temperature and/or pressure. T h e salt deposition rate, among other parameters, depended on the salt solution concentration and how fast the solubility was decreasing along the length of the tube. T h e surface temperature i n the pre-heaters, which were at higher power input compared to the test section, increased quite rapidly due to the deposition of salt. However, there are not many thermocouples on the surface of pre-heaters and the temperatures over their entire length could not be measured. T h e test section surface temperature rise for a sample experiment (Experiment C I , see Table 4.1 for details) is shown i n F i g . 5.3. T h e flow rate in this run was 0.66 k g / m i n w i t h a N a C 0 3 concentration of 0.19 wt.% i n the influent tank. Thus the salt delivery rate at the system inlet was 1.25 g / m i n . 2  Based on the assumption that the salt solution leaving every section is at its saturation limit corresponding to the section temperature, the fluid entering the test section would be at the saturation limit corresponding to the pre-heater 2 temperature. T h e fluid salt concentration entering the test section was thus 0.018 wt.% and the actual salt delivery rate at the inlet of the test section would have been 0.12 g / m i n . After operating for 15 minutes, a pressure increase of about 70 k P a was noticed at the inlet of the test section. However, it is to be noted that for this type of experiment, major deposition was taking place i n the pre-heaters and the pressure at the inlet of the pre-heaters was not logged during the experiment. A monotonic increase i n test section surface temperature was observed which indicated a steady buildup of salt on the tube surface. T h e concentration of salt leaving the system was also constant and thus a l l salt above the solubility limit was depositing on the heat transfer surface. Thus the ratio of salt concentration i n the effluent to the saturation limit was 1.  51  5.3. Results and discussion  420  1.5 m top 2.8 m bottom Average surface temperature  24.9  415  410  <bd«*b  y+ ^+ + +  +  .  405  h + +  % ^+^+  +  + 4  4-  +  +  . .  rf-.  *  + + ^  +  +  +  +  24.7  + +  +  + +  ++ +  +  Pressure 400 11:10  11:15  11:20  24.5 11:25  Time  F i g u r e 5 . 3 : Temperature and pressure behavior for the heterogeneous nucleation run  5.3.2  Combined heterogeneous and homogeneous nucleation (heated test section)  These experiments were carried out to reduce the net salt deposition rate i n order to increase the duration before the experiment had to be terminated due to either excessive surface temperature and/or pressure. In other words a higher ratio of salt concentration i n the effluent to the saturation limit, compared to the experiments discussed i n the last section, was desired. A sample experiment (Experiment 11, see Table A . l for details) is shown i n F i g . 5.4. T h e flow rate of pure water from the main p u m p was 1.2 k g / m i n . T h e metering pump was set to 10% of this flow rate and was injecting salt solution in the pure water stream. T h u s the total flow rate i n the test section was 1.32 k g / m i n w i t h a salt concentration of 0.1 wt.% at the test section inlet. T h e salt delivery rate at the inlet of the test section would thus be 1.32 g / m i n . T h e temperature of pure water at the outlet of pre-heater 2 was maintained at 415°C. T h e system was operated for about 90 minutes before the r u n was terminated, due to excessive pressure at the inlet of the test section. However, pressure at the outlet of the test section remained con-  5.3. Results and discussion  52  stant through out the run, indicating all deposition was taking place i n the test section. It can be observed that the temperature rise (due to the salt deposition) was not continuous. T h e average clean test section inner-surface temperature was about 396°C. A temperature rise of about 12°C was noticed at the 0.15 m location i n about fifteen minutes and then the surface temperature decreased suddenly. T h i s indicated that the deposited salt layer was removed at the end of the cycle. T h i s cycle was repeated nine or ten times during the 90-minute run. It seems that the salt was depositing and then at the end of the cycle the salt layer was removed due to excessive upstream pressure. D u r i n g the period when pressure was increasing, the fluid temperature at the exit of pre-heater 2 also increased thus indicating a plug-like condition. D u r i n g the run, the effluent conductivity fluctuated, indicating the salt deposition and removal were taking place i n the system. A t the 0.61 m location, three such cycles were observed but at the end of each cycle the temperature d i d not drop a l l the way to the clean surface condition, thus the salt layer was only partially removed. There was a steady temperature rise noticed at locations after 1.5 m and no sudden removal of deposit occurred. T h e thermocouple at the 1.5 m location showed a temperature increase of about 18°C over the 90 minutes of operation. Similarly at the 2.8 m location the temperature increased steadily by about 8 ° C . T h e system pressure relief valves were set to a pressure of about 29 M P a and the experiment was terminated when the pressure relief valve opened. T h e heaters were then turned off and the flow from the metering pump was then switched to pure water, to dissolve the salt deposit, i n order to clean the system. T h e deposition-removal cycles were studied by observing temperatures at different locations. In a l l of these cycles, the temperature at the 0.15 m location showed a different trend as compared to temperatures at downstream locations. W h e n it was close to plugging the pressure and the pre-heater 2 temperature increased very quickly and only the thermocouple at 0.15 m behaved in the same manner. T h e temperatures at later locations either remained the same or reduced until the plug was removed and then a sudden increase i n surface temperature was noticed. T h u s the location of the plug was just after the 0.15 m location. Another observation was that after the salt was removed from the 0.15 m location, no sudden temperature increase was noticed at the downstream locations. Thus the removed salt layer was not sticking at downstream locations i n the test section. D u r i n g the time when salt solution was being passed through the system, the effluent was collected i n a tank. T h e salt concentration in the effluent tank was 0.075 wt.%. T h e saturation limit corresponding to the test section temperature was 0.018 wt.%. T h e ratio of effluent concentration and saturation limit is thus 4.2, which is four times higher as compared to the pure heterogeneous case. Thus due to homogeneous nucleation more salt was able to flow through the system and resulted i n longer running time before  53  5.3. Results and discussion  Time  Figure 5.4: Temperature and pressure behavior for the combined homogeneous and heterogeneous nucleation run (heated test section) the experiment had to be terminated.  5.3.3 Combined heterogeneous and homogeneous nucleation experiments (unheated test section) These runs were made to further reduce the salt deposition such that more salt flowed through the system. T h e test section was not heated i n these runs. Details of a sample experiment (Experiment 10, see Table A . l for details) from this set of experiments are discussed below. The total flow rate for this r u n was 1.32 k g / m i n . T h e salt delivery rate at the inlet of the test section would thus be 1.32 g / m i n . T h e average clean test section inner-surface  54  5.4. Conclusion  temperature was about 396°C and bulk fluid temperature leaving the test section was 394°C. T h e bulk fluid temperature at the end of the long reactor sections, which were also not heated, was 383°C. Thus a temperature drop of about 11°C was noticed due to heat losses. W h i l e the salt was being deposited, the surface temperature dropped due to the insulating salt layer. T h i s is different compared to the other runs i n which the surface temperature increased since the test section was being heated i n those cases. A number of deposition-removal cycles were noticed as shown i n F i g . 5.5. A t the 0.15 m location, there were about 10 of these cycles and at the 0.6 m location three such cycles occurred w i t h temperature reducing back to clean surface conditions, thus indicating that a l l of the deposit was being removed. Furthermore, a small pressure increase was enough to remove the deposit, as observed from the pressure behavior i n F i g . 5.5. One such cycle was observed at the 0.96 m location. D u r i n g the 90 minute run the temperature at the 2.8 m location remained constant thus there was no deposition at that location. There was a pressure drop of only 138 k P a over the test section and pressure at the end of the test section remained constant. D u e to this small pressure drop across the deposit, the bulk fluid temperature at pre-heater 2 outlet d i d not i n crease during the deposition process. It can therefore be concluded that no major plug was occurring i n the test section. T h e run was terminated after running for 75 minutes. T h e salt concentration at the inlet of the test section was 0.1 wt.%. D u r i n g the time when salt solution was being passed through the system, the effluent was collected in a tank and the effluent salt concentration was 0.09 wt.%. T h e saturation limit corresponding to the average clean test section inner-surface temperature was 0.018 wt.%. For this type of experiments w i t h unheated test secion, the surface temperature was calculated as the average surface temperatures at the first few locations in the test section. T h e ratio of concentration i n tank and saturation limit for this run was 5, which is even higher than the last type of experiments. T h u s more salt was able to flow through the system thereby increasing the time before the system plugged. Table 5.1 shows a comparison of these three types of N a C 0 3 nucleation experiments. 2  5.4  Conclusion  Three types of N a C 0 3 deposition, on the heat transfer surface at S C W O conditions, have been studied i n this chapter. In the presence of pure crystalline fouling (due to heterogeneous nucleation) of salt on the tube surface, the fluid leaving the tube was at the saturation l i m i t corresponding to the surface temperature and a l l the undissolved salt stuck to the tube wall. T h e system could not be run for more than 30 minutes for typical S C W O conditions and periodic removal of deposition needed to be done to operate the system. However if the salt was made to nucleate i n the bulk fluid, the 2  55  5.4. Conclusion 26.8  Time  + °  0.96 m top 2.8 m top  395  26.8 26.3  03  CL  25.8 2 3 0) U)  f25.3  OL  Pressure 385 — 12:30 1  13:00  14:00  '24.8 14:30  Figure 5.5: Temperature and pressure behavior for the combined heterogeneous and homogeneous nucleation run (unheated test section) net deposition rate of the salt on the tube surface was reduced and the S C W O system could operate for a longer period of time. For a run in which b o t h heterogeneous and homogeneous nucleation of salt was occurring the heated test section plugged after 90 minutes of operation. Salt concentration leaving the test section was four times higher than the saturation limit. T h e net deposition rate was further reduced when combined heterogeneous and homogeneous nucleation was occurring in unheated test section. For an actual S C W O plant, this means that the waste treatment could be carried out for a longer period of time. T h e fouling of pre-heaters could be eliminated in this manner, since only water (and oxygen) would be flowing through them. Once the required fluid temperature was achieved at the end of the pre-heater sections, the waste could then be injected thereby encouraging homogeneous nucleation. T h e inor-  56  5.4. Conclusion  Table 5.1: Comparison of the three types of N a C 0 nucleation experiments, C /C is the ratio of effluent salt concentration to saturation concentration C / C t Comments Salt Experiment type delivery rate (g/min) E x p e c t e d time to termi1 1.25 Heterogeneous nucleation only nate experiment about 2030 minutes. Plugged after 90 minutes. 4.2 1.32 Homogeneous and heterogeneous 2  3  0  nucleation (heated test section) Homogeneous and heterogeneous nucleation (unheated test section)  1.32  5.0  0  sat  s a  N o sign of plugging after 75 minutes.  ganics nucleated i n this manner are thus more likely to flow through the tubular reactor. T h e t h i r d type of experiment discussed i n this chapter showed that the net deposition rate is further reduced if the section after mixing chamber was not heated. It is worth mentioning that the fouling mitigation method used is irrespective of the salt. It was noticed that almost all of the salt deposited w i t h i n the test section w i t h most of it immediately after the point of injection. T h u s i f the problem of plugging occurs during the process, the deposited salt has to be removed from only this short length of the reactor tube. T h i s can be achieved online by mechanical means [19] & [36]. In this type of experiment a temperature drop of less than 15°C was noticed over the 140-m long unheated reactor. D u r i n g the treatment of actual waste, which is an exothermic reaction, this temperature drop will be further reduced; thus the reaction should be selfsustaining. Otherwise, some fuel may be added, i n the aqueous waste, which oxidizes and produces heat enabling the reaction to be self-sustainable. Since the reactor wall may not be heated i n this case, therefore heterogeneous nucleation would be reduced.  Chapter 6 Collection and Analysis of Na CC>3 and Na S04 Deposits 2  2  6.1  Salt-deposit preservation procedure  Pure crystalline deposits and combined crystalline & particulate deposits have been collected for Scanning Electron Microscope ( S E M ) and Energy Dispersive X - r a y ( E D X ) analysis. T h e sample collection of the deposits has been made possible using the nitrogen purging technique. T h e problem encountered i n preserving a salt deposit on a tube surface is that the salt dissolves back into the fluid, when the heaters are shut off to cool down the system. T h i s is due to the solubility characteristics of the salts. A nitrogen purge procedure, to preserve the sample for examination, was thus developed. A s mentioned earlier, the inner diameter of the test section tube is 6.2 m m . A stainless steel tube of 6 m m outer diameter and 1 m m thickness was inserted into the first half of the test section. The tube-insert was used to collect salt deposits and was weighed before and after the salt deposition experiment. T h e schematic of the tube-insert is shown i n F i g . 6.1. T h e inner radius of the tube-insert is r and the inner radius of the salt deposit is r\. c  T h e salt deposit collection procedure is discussed below. Homogeneous or heterogeneous nucleation experiments were performed following the procedures discussed i n Section 5.2. T h e surface temperature of the test section was monitored while salt deposition was occurring on the inner surface of the tube-insert. T h e outer surface of the tube-insert was i n contact w i t h the inner surface of the test section tube. Once enough deposition had occurred, nitrogen gas at high pressure was inserted using the gas booster pump shown in Figs. 3.1 & 5.1. A back pressure regulator at the outlet of the booster pump was set to a pressure 1-3 M P a higher than the system pressure. T h e flow from the main pump into the system was reduced gradually using the by-pass mechanism while the gas flow rate was being increased. In case of the homogeneous nucleation type experiments, the metering pump was shut off. After a short time the fluid from the  57  6.1. Salt-deposit preservation procedure  alloy 625 test section  58  s t a j n | e s s  ^  salt deposit thickness, 5  t u b e  .  j n s e r t  S  F i g u r e 6 . 1 : Schematic of the tube-insert surface thermocouples  tube-insert section number  flow i—\ direction 4 cm  19" cm  ''  34 cm  124' ' cm  cm  |-» all locations from electric cable connector  cm  A  S2  139 \ 1541 c  cm  S1  cm  157 cm  F i g u r e 6.2: L o c a t i o n of tube-insert sections w i t h respect to the thermocouples location main pump was fully diverted back to the influent tank and only nitrogen gas flowed through the system. T h i s procedure took about 20-30 sec to complete and after the liquid was completely purged from the system, the nitrogen flow rate was gradually reduced. T h e system was then de-pressurized and the test section dismantled to remove the tube-insert. T h e orientation of the insert i n the test section was noted and it was again weighed to determine the weight of the salt deposit i n the tube-insert. T h e insert was then cut into 15 c m long sections for S E M and E D X analysis of the deposits. Figure 6.2 shows the schematic of the sections of the tube-insert and details of their location with respect to the thermocouples are mentioned i n Table 6.1. T h e section numbers of the tube-insert start from the end of the tube-insert and the first section is the most downstream. A s mentioned earlier, stainless steel rods were soldered to the test section tube for electric power cable connections as shown i n F i g . 3.3. T h e thermocouple and section number locations are shown in F i g . 6.2 and the distances shown are from the downstream edge of the steel connector. T h e edge of the tube insert extends about 3 cm further to the left (upstream) from this reference.  6.2. SEM and EDX analysis of Na^COz and NffcSCk deposits  59  T a b l e 6 . 1 : Thermocouple and tube-insert-section locations Thermocouple Thermocouple Tube insert Tube insert section num- section localocation (cm) number tion (cm) ber  6.2  S B 9 , top S9, b o t t o m  15 25  S7, b o t t o m  61  S B 4 , top S B 3 , top S2, b o t t o m S B 1 , top S i , bottom  90 103 125 132 140  4 19 34 49 64 79 94 109 124 139 154  11 10 9 8 7 6 5 4 3 2 1  SEM and EDX analysis of N a C 0 and Na S0 deposits 2  3  2  4  Scanning electron microscope (Hitachi 2000N) was used to study the structure of the deposits and elemental composition analysis of the deposit was carried out using an E D X spectrometer system. T h e E D X is able to distinguish between different elements present i n a sample by analyzing the energy of the X - r a y s given off. T h e technique is atomic weight sensitive. Samples of the tube-insert sections were mounted in the desired orientation and placed under vacuum i n the S E M for analysis. It is worth mentioning that whereas E D X is quite reliable for qualitative analysis, the concentrations of the elements can not be measured w i t h high accuracy. T h e error i n measured concentration could be as high as 10 wt.% even for a well prepared sample. T h e E D X analysis of the deposit samples were basically carried out to determine the elements present i n the deposits. T h e elemental analysis of standard N a C 0 3 salt is shown i n F i g . 6.3. E x periments have been performed to collect and analyze N a C 0 and N a S 0 deposits. Details of sample experiments are mentioned i n Table 6.2. T h e details include the bulk fluid temperatures at the inlet and outlet of the test section. For the combined homogeneous k, heterogeneous nucleation experiments the test section inlet temperature was the temperature of the pure water before the salt solution was injected into this stream. In order to determine the heat input, the fluid enthalpies at the test section inlet and outlet were used. For the combined heterogeneous & homogeneous nucleation experiments the fluid enthalpy at the inlet of the test section was determined from an experiment performed on M a y 26, 2003. T h e system was operated without fluid injected into the mixing-tee. T h e test section inlet temperature was set to the required 2  2  3  2  4  60  6.2. SEM and EDX analysis of NaQ,COz and N^SO* deposits Counts Na  Concentration 47.17 wt% 30.78 wt% 22.07 wt%  Species Oxygen Sodium Carbon  3000 J  2000  1000 .  i  r r v i "i  i  11  2  Figure 6.3:  4  'i—i—i—i—i—i—r 6  keV  8  Elemental composition analysis of standard N a C 0 3 salt 2  mixed stream temperature and flow rate. T h e fluid enthalpy at the end of test section was then determined for certain heat inputs to the test section. T h e S E M photographs and results of elemental analysis for the two different types of deposits are discussed below.  6.2.1 Pure crystalline fouling deposits of  Na2CC>3  The first salt-deposit collection run was performed without the tube-insert to confirm that deposits can be preserved on the tube surface using the nitrogen purging technique. In a l l the later salt-deposit collection experiments, a tube-insert was used. In this experiment the system pressure was 24.8 M P a and was the heterogeneous type nucleation experiment w i t h N a 2 C 0 3 . T h e flow rate was set to 0.74 k g / m i n and a 0.035 wt.% N a C 0 solution was used. F l u i d temperatures at the inlet and outlet of the test section were 393 and 4 3 8 ° C respectively and remained almost constant during the experiment. T h e m a x i m u m test section surface temperature was about 461°C. T h e test section was dismantled after the experiment and a small sample of deposit was scraped off the tube surface for analysis. T h e scraped sample was weighed. The remaining deposits on the first half of the test section were dissolved by passing distilled water through the tube and the salt concentration i n the collected wash was measured to calculate the mass of salt deposited i n the first half of the test section. Figure 6.4 shows the S E M image of N a C 0 3 scraped from the test section after a heterogeneous nucleation experiment (Experiment S E M - 1 ) and its elemental analysis is shown i n F i g . 2  3  2  6.2. SEM and EDX analysis of NaqC0  3  and Na^SO^ deposits  61  Table 6.2: Details of experiments performed to collect salt deposits Salt concentration at test section inlet (wt.%)  Heat input to the first half of the test section (kW)  Salt collected in the first half of the test section (g)  438  0.021  0.3  4  395  0.1  0.29  9.8  445  0.017  2.2  9.5  395  0.1  0.29  8.6  412  0.001  2.3  3.5  Experiment Experiment Salt and type of Bulk fluid temperatures reference nucleation date (°C) Test Test section section outlet inlet 393  March 11, 2003  SEM-1  Na C0 , heterogeneous  March 31, 2003  SEM-3  Na C0 , 415 homogeneous & heterogeneous  April 12, 2003  SEM-4  Na C0 , heterogeneous  July 23, 2004  SEM-6  Na S0 , 415 homogeneous & heterogeneous  August 06, 2004  SEM-7  Na S0 , heterogeneous  2  2  2  2  2  3  a  3  3  397  4  4  388  a  for the combined nucleation experiments, this is the temperature of pure water before mixing with the salt solution  6.5. The major elements found are sodium, carbon and oxygen. Long Na2C03 crystals can be seen from the S E M photograph. The scale analysis of another heterogeneous nucleation type experiment, S E M - 4 is discussed now. This was performed with a tube-insert in the first half of test section on which the Na C03 scale was collected for analysis. The flow rate was set to 0.78 kg/min and 0.035 wt.% solution of N a C 0 was passed through the system at a pressure of 24.5 M P a . The tube-insert was weighed after the experiment and the mass of deposit collected on the tube-insert was found to be 9.5 g. The tube-insert was cut into 15 cm long sections for scale analysis. Fig. 6.6 shows the photograph taken from insertsection 6 which was about 79 cm from the inlet of the tube-insert. A small portion of the tube can be seen on the top of the photograph and long crystals of Na C03 are also visible. These crystals seem to be nucleating from the tube surface (heterogeneous nucleation) and grew toward the center of the tube during the fouling process, resulting in a crystalline scale. A larger view of insert-section 2, showing almost the full cross section of the tube can be seen in Fig. 6.7. The location of this section was further downstream to the section shown in Fig. 6.6. The scale deposit can be seen on the inner surface of the tube and is of almost uniform thickness. Figure 6.8 shows a magnified view of the deposit. Again long salt crystals are observed, which nucleated from the tube surface and grew towards the center of the tube quite similar to the crystals seen 2  2  3  2  6.2. SEM and EDX analysis of Na C0 2  3  and Na^SO^ deposits  02  Figure 6.4: SEM photograph of the N a C 0 deposition on test section wall due to heterogeneous nucleation (Experiment SEM-1) 2  3  Counts  600 J  Species  Concentration  Oxygen Sodium Carbon  55.94 wt% 22.19 wt% 21.88 wt%  400 J  200  f  f  2  rt  •f"'" |""t' ll  4  •TTT*' —^""1— — ~^ — 6 8 keV 1  1  r  ]  Figure 6.5: Elemental composition analysis of N a C 0 deposit for the heterogeneous nucleation (Experiment SEM-1) 2  3  6.2. SEM and EDX analysis of Na^C0  3  Figure  6.6:  63  and Na^SO^ deposits  SEM photograph of the N a C 0 deposition on test section wall due to heterogeneous nucleation at 79 cm location (Experiment SEM-4) 2  3  in the insert-section 6. Photographs of other sections showing deposits of Na CC>3 are shown in Appendix B . l . 2  6.2.2  Combined crystalline and particulate fouling deposits of Na C0 2  3  In this experiment (SEM-3), salt solution was injected into the supercritical water just before the beginning of the test section. The total flow rate was 1 kg/min with the main pump set to 0.9 kg/min. The system pressure was 24.6 MPa. About 9.8 g of deposits were collected after purging the system. Results of Na CC>3 deposit analysis of a combined homogeneous-heterogeneous type nucleation experiment performed on March 31, 2003 are discussed below. The elemental concentration analysis carried out with the EDX is shown in Fig. 6.9. Sodium, carbon and oxygen are the major constituents with concentration quite similar to that found in the deposits of experiments discussed in Section 6.2.1. Figure 6.10 shows the cross section of the insert-section 4 located at about 109 cm from the inlet of the tube-insert. Again the deposition is quite uniform all over the inner surface of the tube. However instead of long crystals, the deposit consisted of small particles. It seems that these salt particles nucleated in the bulk fluid (homogeneous nucleation) and deposited on the tube surface. The structure of this particulate fouling deposit was thus found to be different from that of crystalline 2  6.2. SEM and EDX analysis of NaaC0  3  and Na^SO^ deposits  64  F i g u r e 6.7: S E M photograph of the N a C 0 deposition on test section wall due to heterogeneous nucleation at 139 c m location (Experiment S E M - 4 ) 2  3  F i g u r e 6.8: S E M photograph of the N a C 0 deposition on test section wall due to heterogeneous nucleation at 139 cm location (Experiment S E M - 4 ) 2  3  6.2. SEM and EDX analysis of Na^C0  3  and IV^SC^ deposits  65  Counts 600.  Species Oxygen Sodium Carbon  Concentration 53.63 wt% 33.55 wt% 12.82 wt%  400.  200.  keV  F i g u r e 6.9: Elemental composition analysis of Na2C03 deposit for the combined homogeneous & heterogeneous nucleation (Experiment S E M - 3 ) fouling deposits discussed i n Section 6.2.1. It is worth mentioning that the magnification of this photograph is same as that of Figs. 6.6 & 6.8. Since the test section was heated, at some insert sections heterogeneous nucleation deposits were also observed with particle deposition. T h e photographs of the other sections are shown in A p p e n d i x B.l.  6.2.3  Pure crystalline fouling deposits of Na S04 2  Some of the S E M photographs of S E M - 7 experiment, performed to study crystalline fouling structure are discussed below. T h e flow rate was 0.76 k g / m i n and 0.02 wt.% Na2S04 salt solution was used. T h e system pressure was set at 24.6 M P a . A b o u t 3.5 g of salt deposits were collected on the tube insert. Figures 6.12-6.14 show the Na S04 crystals on the tube-insert surface. These crystal shapes are quite similar to those of the N a C 0 crystals seen i n F i g . 6.6. A t some locations, these crystals formed a solid-fused layer as seen i n Figs 6.13 & 6.14. A t tube-insert section location of 154 c m some needle shaped crystals were observed grown out of the solid deposit as shown i n F i g . 6.12. However, it can be observed that heterogeneous nucleation leads to crystal-deposition, which has a very dense structure and is quite different from the particulate fouling deposits of N a S 0 particles as shown i n F i g . 6.18. 2  2  3  2  4  66  6.2. SEM and EDX analysis of NaqCO^ and Na^SO^ deposits  Figure 6.10: SEM photograph of the N a C 0 deposit due to combined homogeneousheterogeneous nucleation at 109 cm location (Experiment SEM-3) 2  SE  3  WD36.8mm 5.OOkV x300  lOOum  Figure 6.11: SEM photograph of the N a C 0 deposit due to combined homogeneousheterogeneous nucleation at 109 cm location (Experiment SEM-3) 2  3  6.2. SEM and EDX analysis ofNa^CO^ and Na^SO^ deposits  67  Figure 6.12: SEM photograph of the N a S 0 deposit due to heterogeneous nucleation at 154 cm location (Experiment SEM-7) 2  4  Figure 6.13: SEM photograph of the Na S0 deposit due to heterogeneous nucleation at 127 cm location (Experiment SEM-7) 2  4  68  6.2. SEM and EDX analysis ofNa^COz and Na^SO^ deposits  F i g u r e 6.14: S E M photograph of the N a S 0 deposit due to heterogeneous nucleation at 97 c m location (Experiment S E M - 7 ) 2  6.2.4  4  Combined crystalline and particulate fouling deposits of Na S0 2  4  Results of a combined homogeneous & heterogeneous type nucleation experiment (SEM-6) are discussed i n this section. T h e main pump flow rate was 0.85 k g / m i n and the total flow rate, including that of the metering pump, was 0.94 k g / m i n . T h e system pressure was set at 24.4 M P a . T h e weight of salt collected on the tube-insert was 8.9 g. T h e E D X analysis of the deposit sample is shown i n F i g . 6.15. T h e major elements are sodium, sulfur and oxygen. Some of S E M photographs of experiments performed on J u l y 23, 2003 are discussed i n this section. T h e rest of S E M photographs of N a S 0 deposits are included i n A p p e n d i x B . T h i s run (SEM-6) was performed following the procedure of the N a C 0 3 homogeneous & heterogeneous type nucleation experiments. However, when the test section was dismantled, it was noticed that the N a S 0 deposits were weaker than the N a C 0 3 deposits. A t some regions the salt-deposit was washed off m a k i n g the tube inner surface visible. Some of the deposits d i d not cling on to the tube surface and fell off when the sections of the tube-insert were being cut. Thus some of the insert sections d i d not have a uniformly thick deposit layer. T h e test section i n the experiment was heated and combined crystalline and particulate fouling deposits were expected and are observed i n Figs. 6.16 &; 6.17. These photographs are of the insert-section 1 which is the last section of the tube-insert. A t the same location N a S 0 particulate deposition was also observed and is shown in F i g . 6.18. 2  2  2  2  2  4  4  4  6.3. Thermal conductivity of the Na^COs deposit  69  kCts Na  Species  Concentration  Oxygen Sodium Sulfur Iron  50.47 wt% 31.47 wt% 16.49 wt% 0.74 wt%  20  10'  Fe -1 15  r-  F i g u r e 6 . 1 5 : E l e m e n t a l composition analysis of Na S04 deposit for the combined homogeneous-heterogeneous nucleation experiment (Experiment S E M 2  6) Some of these deposited particles are hollow and their shape is quite different from the Na C03 particles deposits discussed above. Such particles, among other sections, were also noticed at the insert-section 7 and can be observed i n F i g . 6.19. 2  6.3  Thermal conductivity of the  Na2CC>3  deposit  The thermal conductivity of the Na CC>3 deposit was determined using the known heat input, thickness of the salt deposit and the measured temperature difference across the deposit layer. T h e bulk fluid temperature at the outlet of the test section remained constant during the deposition process. Therefore, it can be assumed that the salt-deposit inner surface temperature was very close to the clean tube inner surface temperature. T h e increase i n the surface temperature due to deposition is thus the temperature difference across the deposit layer, AT . T h e following relation was then used to determine the thermal conductivity of the salt-deposit, kd (W/mK) [73]. 2  S  The details of these salt-deposit analysis experiments are mentioned i n Tables 6.2, 6.3 & 6.4. T h e deposit layer thickness was measured from the S E M photographs at each  6.3. Thermal conductivity  of the Na^CO^ deposit  70  Figure  6.16: SEM photograph of the N a S 0 deposit due to combined homogeneousheterogeneous nucleation at 154 cm location (Experiment SEM-6)  Figure  6.17: SEM photograph of the N a S 0 deposit due to combined homogeneousheterogeneous nucleation at 154 cm location, mostly crystalline (Experiment SEM-6)  2  2  4  4  71  6.3. Thermal conductivity of the Na COz deposit 2  !  Figure 6.18: SEM photograph of the Na S04 deposit due to combined homogeneousheterogeneous nucleation at 154 cm location, mostly particulate (Experiment SEM-6) 2  tube-insert section. However, the thermocouple locations did not coincide with the tube-insert section locations. The deposit layer thickness, at each thermocouple location, was thus interpolated using the layer thicknesses at section locations. Thus inner radius of deposit layer, r\ at each thermocouple location could be inferred. Thermal conductivity of the Na C03 deposits, at various locations, was then calculated using Eq. 6.1 and is tabulated for different locations for both heterogeneous and combined heterogeneous & homogeneous type nucleation experiments. The deposition rate for the heterogeneous nucleation type experiment was found to be quite steady. However, for the combined heterogeneous & homogeneous type experiments, instead of a steady scale growth, deposition and removal of salt-deposit was noticed. Thus the thickness of deposit observed in the combined heterogeneous & homogeneous experiments might not necessarily correspond to the temperature rise before the liquid was purged from the system. Therefore, the thermal conductivity values of the heterogeneous nucleation type experiments should be relatively more accurate. 2  For Na S04, since the salt deposit was partially washed off the tube and some later fell off while cutting the sections, the actual deposit layer thickness could not be measured. Therefore, thermal conductivity of the Na SC-4 deposit was not calculated. 2  2  6.3. Thermal conductivity of the Na^C0  3  deposit  72  Figure 6.19: SEM photograph of the Na S0 deposit due to combined homogeneousheterogeneous nucleation at 64 cm location, mostly particulate (Experiment SEM-6) 2  4  Table 6.3: Details of N a C 0 scale thickness and surface temperature rise due to deposition for the heterogeneous nucleation experiment (Experiment SEM4) 2  3  Section Section Measured Thermo- Interpolated couple salt deposit number location salt location thickness at deposit thermocouple thickness location 10 8 7 6 4 2  (cm)  (mm)  (cm)  (mm)  19 49 64 79 109 139  0 0.364 0.406 0.361 0.305 0.296  15 25 61 90.2 103 132.8  0 0.182 0.406 0.333 0.305 0.296  Test section clean outer surface temperature  Test section Surface outer surface temperature temperature rise with salt deposit  (°C) 466 469.4 488.05 490.39 475.7 509.76  (°C) 488.21 510.2 549.05 546.89 550.64 550.46  (°C) 22.21 40.8 61 56.5 74.94 40.7  Thermal conductivity of N a C 0 deposit 2  (W/mK) 0.44 0.69 0.60 0.41 0.73  3  73  6.3. Thermal conductivity of the Na^CCs deposit  T a b l e 6.4: Details of N a C 0 3 deposit thickness and surface temperature rise due to 2  deposition for the combined homogeneous-heterogeneous nucleation experiment (Experiment S E M - 3 ) Section Section Measured Thermo- Interpolated number location salt couple salt deposit location thickness at deposit thermocouple thickness location (mm) (mm) (cm) (cm)  Test section clean outer surface temperature  Test section Surface outer surface temperature temperature rise with salt deposit  Thermal conductivity of N a C 0 deposit  (°C)  (°C)  (°C)  (W/mK)  10 8 6 4 2 1  402.01 402.9 405.45 410.19 403.52 407.96  413.91 412.6 420.65 434.69 435.62 438.46  11.9 9.7 15.2 24.5 32.1 30.5  0.07 0.14 0.28 0.36 0.30  19 49 79 109 139 154  15 25 61 90.2 103 132.8  0 0.1 0.218 0.716 0.59 0.66  0 0.05 0.159 0.467 0.716 0.59  2  3  Distance along test section (cm) F i g u r e 6.20: N a C 0 2  3  deposit thickness and surface temperature rise along the test  section for the heterogeneous nucleation (Experiment S E M - 4 )  6.4. Conclusion  74  0.8  Distance along test section (cm)  Figure 6.21: N a C 0 3 deposit thickness and surface temperature rise along the test 2  section for the combined homogeneous-heterogeneous nucleation (Experiment S E M - 3 )  6.4  Conclusion  A novel procedure has been developed to preserve salt deposits on the heat transfer surface for analysis. T h e N a C 0 3 fouling deposits were harder to remove compared to the N a S 0 deposits. It was noticed, at some locations of the tube insert, the cross section of the N a S 0 deposits was not uniform. Furthermore, some of these deposits fell off the insert tube later, during sectioning of the tube insert. 2  2  4  2  4  For both N a C 0 3 and N a S 0 , heterogeneous nucleation experiments led to pure crystalline scale. L o n g salt crystals were seen i n the S E M photographs, which nucleated on the insert-tube surface and grew i n the direction of the center of the tube. These deposits were found to be very dense and hard to remove. O n the other hand, instead of long crystals, salt particles were seen i n the combined crystalline-particulate fouling experiments. These particulate deposits were relatively less dense but at some locations deposits were quite similar to the pure crystalline scale. Since the pure crystalline deposits were found to be dense and strong, a steady increase i n surface temperature was noticed i n the heterogeneous type experiments. T h i s was due to the steady growth of salt-scale layer on the tube surface. O n the other hand, for the combined heterogeneous-homogeneous nucleation experiments the tube surface temperature, near the salt solution injection location, increased gradually and then 2  2  4  6.4. Conclusion  75  decreased suddenly. Thus b o t h salt deposition and removal processes were occurring i n the combined homogeneous type experiments. T h i s was due to the less dense and easy to remove particulate-crystalline fouling deposits, which washed off when a certain deposit-layer thickness was achieved. T h e deposit buildup of the combined crystalline-particulate fouling deposits was unsteady compared to a steady growth of pure crystalline scale. Therefore the thickness of salt deposit layer determined from the S E M photographs of pure crystalline scale is likely to be more accurate compared to the combined deposits. T h e r m a l conductivity of the deposits has been inferred from the thickness of the deposit layer. Hence the thermal conductivity values calculated for the pure crystalline scale is more accurate compared to the other type of deposits. Elemental analysis of the scale was carried out using the E D X . M a j o r elements found i n Na2C03 deposits were sodium, carbon and oxygen. Sodium, sulfur and oxygen were the major components of Na2S04 deposits with less than 1 wt.% of iron.  Chapter 7 Modeling: Mixing, Heat and Mass Transfer 7.1  Introduction  In Chapter 5 experiments were discussed, i n which a w a r m salt solution stream was mixed i n a stream of supercritical water. W h e n the salt solution is exposed to the hot supercritical water i n the mixing-tee section, depending on the salt concentration and temperature, the solution may become supersaturated and homogeneous nucleation of salt particles m a y occur. T h e salt depositing on the tube surface would thus be due to the precipitation of the salt particles nucleated i n the bulk fluid and salt molecules crystallizing on the tube surface. T h i s chapter discusses the modeling of the mixing process, heat and mass transfer, to determine the salt deposition at various test section locations. Homogeneous nucleation of salt particles, their growth and coagulation, deposition of salt particles and salt molecules on the tube surface have been modeled. Pure water thermodynamic properties [74] were used. Similarly pure water transport properties were used to model the salt solution.  7.2  Salt particle nucleation  Formation of salt particles i n the bulk fluid can be described as a homogeneous nucleation process. Salt enters the mixing-tee dissolved i n a w a r m liquid stream and mixes w i t h supercritical water. D u r i n g the mixing process, r a p i d heating of the salt solution occurs and the salt solubility falls orders of magnitude leading to a high supersaturation values, causing rapid nucleation and growth of salt particles in the supercritical water. T h e number of salt particles nucleated can be determined by the classical theory of nucleation. There are other complicated theories which involve the direct generation of nuclei from ions [75]. However, they provide qualitatively similar results, and required information on the liquid-solid surface energy is still 76  77  7.2. Salt particle nucleation  unavailable [76]. Therefore, the desirability of selecting such sophisticated theories for modeling practical problems m a y be questioned, thus favoring the selection of classical theory. In the classical theory of nucleation, the free energy required to form a cluster of molecules from the liquid (dissolved) phase is first determined. B o t h the energy from the phase change due to crystallization and energy required to form the surface of the cluster are considered. Once the energy for the formation of the surface is overcome, the nucleus w i l l form, but it may redissolve. T h e free energy increases from zero to a m a x i m u m value at which the nucleus w i l l not redissolve. So i f the radii of a nucleus is less than r*, it w i l l have to either continue to grow toward a critical radius or to dissociate into its component molecules. T h i s w i l l continue u n t i l the size of the nucleus (or the number of molecules i n the nucleus) reaches a critical value [77]. T h e nucleation rate per unit volume per unit time is then given by the following relation [78]: -167T7 V 3  J = A exp  (7.1)  r  3o T (In S) 2  2  2  in which A is the m a x i m u m number of particles that can nucleate and is usually taken to be 1 0 ^ 3 ^ [78], 7 is the surface tension, V is the volume of the salt molecule, bk is the B o l t z m a n n ' s constant (1.3805 x 1 0 J/K), T is the temperature and S is the degree of salt saturation. T h e fluid temperature, T and dissolved salt mass fraction, C are used to calculate the degree of saturation i.e., S = -pf-. T h e saturation limit, C is determined from the correlations developed for N a C 0 3 and N a S 0 (Eqs. 4.13 & 4.14). 30 P  S  m  - 2 3  sat  2  2  4  The effect of supersaturation on the nucleation rate is highly dependent on the interfacial energy or surface tension. T h e difficulty of obtaining a value of this energy by direct measurement is a major problem w i t h the homogeneous theory of nucleation. For the majority of salts the value of surface tension reported is between 6 0 x l 0 and 1 5 0 x l 0 ~ N / m [78]. If homogeneous nucleation occurs, many sub-micron particles are formed. Nucleation rate is highly dependent on temperature and supersaturation. T h e critical radius of nucleated particles can be determined as: [78] & [77]. - 3  3  V  b TlnS  [  L  Z  )  k  If a warm salt solution stream, w i t h salt mass fraction CA at temperature TA, is mixed w i t h a pure hot water stream at temperature T  B  then the mixture fraction Z may  be defined as Z = 0, for pure water stream and Z = 1, for salt solution stream. For typical experimental conditions the salt particle nucleation rate can be determined as a function of mixture fraction Z and is shown i n F i g . 7.1 for N a C 0 . T h e total salt mass 2  3  fraction, CT and salt mass fraction at saturated conditions, C t sa  are also shown as a  function of mixture fraction. For the conditions shown, the pseudo-critical temperature is about 3 8 4 ° C a n d for higher temperatures, there is a sudden drop i n salt solubility.  7.2. Salt particle nucleation  78  T h e critical mixture fraction Z i.e., corresponding to the pseudo-critical temperature is about 0.28. Salt particle nucleation occurs for supersaturated conditions and the rate of particles nucleated is m a x i m u m around mixture fraction value of about 0.14. crit  Mixture fraction, Z F i g u r e 7.1: Salt particle nucleation rate, mass fraction and fluid temperature as a function of mixture fraction  7.2.1  Growth of nucleated particles  The nucleated particles grow by condensation of additional molecules from the fluid to solid phase, or by collision and coagulation w i t h other particles. Diffusion limited growth is considered in this section. The rate at which the additional molecules diffuse towards the salt particle is given by the M a x w e l l equation [79]:  J  m  = 2nV d m  (N  p  m  - N  m  (sat))  (7.3)  where N is the number of molecules per unit volume, N (sat) is at saturation conditions and d is the diameter of the salt particle. V is the molecular diffusion coefficient and can be determined from the Stokes-Einstein relation [70] using the molecule diameter d . m  m  p  m  m  V  m  =  (7-4)  7.3. Modeling of the mixing process  7.2.2  79  Coagulation of the particles  Brownian coagulation is considered i n this study and turbulent induced coagulation has been neglected. T h e coagulation coefficient, K\ (m /sec) is calculated for two equal-sized particles and is given by: [79] 3  2  K  12  =  —  (7.5)  F r o m the discrete coagulation equation, the change i n particles concentration w i t h time is given by: [79]  ^  = -iff„A?«)  (7.6)  If /Yp(O) = N , then the solution of E q . 7.6 is: 0  - rrk  (77)  where T = 2/KuNoC  7.3  Modeling of the mixing process  T h e modeling of the m i x i n g process of two streams along the test section is discussed in this section. A w a r m stream of salt solution, stream A was injected i n the stream of pure supercritical water, stream B, i n the mixing-tee. F l o w rates of salt solution and pure water streams are fn^ and m g respectively. T h e exact location of the salt solution jet is not of interest here a n d transport of heat and mass to the wall is modeled using empirical transfer coefficients. W i t h i n the turbulent core of the pipe flow, some sort of closure model is needed to take into account the turbulent fluctuation correlations of concentrations a n d temperature. Due to this reason, commercially available C F D packages were not used for which it is hard to put a good closure model for turbulent fluctuations for temperature and salt concentration. T o this end, a stochastic mixing process is developed that w i l l approximate the length and timescale of turbulent flow. Recognizing that the initial trajectory of the salt solution is not to be modeled and the interest is only i n closing the C and T fluctuations, the simulation treats the core flow as 1-D m i x i n g process. Schematically, it can be shown as a flow between parallel plates, which is divided into slabs (cells). It is assumed that the salt solution is initially at the center of the tube surrounded by pure water. T h e salt solution has to move a distance equal to the tube radius, i n the radial direction, to reach the tube surface. In order to determine the tube inner surface temperature a n d particle concentration at various test section locations, it is assumed that the fluid streams are flowing between  7.3. Modeling of the mixing process  80  two parallel plates. The distance between the plates is equal to the test section inner diameter, d. Thus, if initially, the salt solution is in the center of the plates, it again has to move a distance equal to d/2, in the vertical direction, to reach the tube surface. The assumed flow in parallel plates is considered only to determine concentration of particles nucleated per unit time at each segment, the temperature and salt mass concentration in the cell at the edge of the salt deposition surface. The later modeling for that segment is carried out considering the actual circular tube geometry. The test section length, L is discretized into X number of segments such that each segment length A L = J£. The height of each segment is also discretized such that there are m + n number of cells, each of height Ad and length A L . At the beginning of the mixing process, the salt solution is assumed to be sandwiched by the pure water cells as shown in Fig. 7.2. The number of cells in streams A and B are n and m respectively. The m:n ratio is determined from the desired m :mA- The total number of cells in each segment are: B  m  (7.8)  + n = -^Ad  CD  o  CG -q  CD CD  Fluid B  Fluid A cells  K * W J &  CD  o  E 03 TD CD X! 3  \f  test section length, L  Fluid A F i g u r e 7.2:  Schematic of the salt solution (fluid A) cells and pure water (fluid cells at the beginning of the mixing process  B)  In each segment the fluid is assumed to comprise R(m + n) number of fluid parcels such that there are R number of fluid parcels in each cell. The salt mass fraction and temperature of the fluid parcels are initialized with respect to their cell conditions. All fluid parcels move a vertical distance Az in each AL. The cell height Ad is chosen such that while the fluid is moving through A L , each fluid parcel lands in another cell after moving a distance of Az.  81  7.3. Modeling of the mixing process  T h e radial distance Az traveled by the fluid parcels is determined from the average dissipation rate of turbulent kinetic energy. For a circular tube geometry, the turbulent kinetic energy dissipation rate, e = [80] i n which V is the mean fluid velocity and / is the friction factor, calculated from the following relation [81]. -2  (7.9) where Re  is the Reynolds number corresponding to wall conditions and e is the tube  w  surface roughness. Using L = d/2 as the characteristic length, the velocity fluctuation can be calculated: u = ( e L ) / [82]. T h e kinetic energy would thus be, KE = | u . T h e time taken by a fluid parcel to move a distance of L , i n the radial direction, is the characteristic time. T h e characteristic time for turbulent diffusion is: [82] 0  x  3  2  0  D  (7.10) where V  T  i.e., V  T  =  is the average turbulent diffusivity and is determined from the n-e model [83]. Sc  T  is the turbulent Schmidt number and is taken to be = 0.7 [80].  T h e turbulent viscosity, v  T  is calculated as v  T  =  0 0 9  k e 2 £  [82]. T h u s the radial distance  a fluid parcel moves i n each segment A L is: (7.11) T h e height of each cell, Ad is chosen such that the fluid parcel can land in a neighboring cell after moving a distance of Az. Once Ad is computed, the total number of cells, m + n, can be determined from E q . 7.8. In order to include the effects of fluctuations i n cell temperature and salt concentration, due to turbulence, the fluid parcels move i n a random direction, upward or downward. For each fluid parcel a randomly generated sign (+ or —) determines the direction in which the fluid parcel moves a distance of Az. After each mixing step, the cell temperature, dissolved salt mass fraction and particulate salt mass deposition are updated using the mean salt mass fraction and temperature of the new parcels. T h e dissolved salt mass fraction and temperature at each cell can be used to determine the concentration of salt particles nucleated in each cell, as discussed i n Section 7.2. T h e mass fractions of dissolved salt and particulate salt are required to determine the dissolved salt deposition rate (i.e., crystallization fouling) and salt particle deposition rate (i.e., particulate fouling) as discussed i n Sections 7.5.1 and 7.5.2. T h e characteristic time for turbulent diffusion is determined using E q . 7.10. T h e axial length AL, is then calculated for this time and known flow velocity. Based on the  82  7.4. Heat transfer calculation  ratio of mass flow rates of streams A & B, m i n i m u m number of cells (m + n) are determined. For a k n o w n tube inner diameter, the height of each cell Ad is calculated, which should be equal to the distance dz, moved by the fluid parcels i n each mixing time step. T h u s for a given turbulent diffusivity, V the axial distance moved by the fluid dl is determined by the following relation: T  dl = dz ^-  (7.12)  2  A m i x i n g step occurs after every dl length along the test section.  7.4  Heat transfer calculation  A s mentioned earlier two fluid streams are mixed i n a mixing-tee at the test section inlet. T h e temperature of stream B, TB is set such that supersaturation is achieved when stream A at temperature TA and w i t h salt concentration CA is mixed i n it. T h e enthalpy of the mixed stream and hence the mixed stream temperature can be determined for known mass flow rates of the streams. T h e heat input to the test section is determined experimentally from the change in fluid enthalpy across the test section. A flow rate rn is set w i t h the injection port of the mixing-tee closed and test section fluid inlet temperature near the desired mixed stream temperature, T\. T h e mass flow rate m is chosen such that: m = riiA + mB  (7-13)  T h e heat supplied (W) to the test section would then be: Q = m(H  2  where H (J/kg)  is the enthalpy of the  - H)  (7.14)  x  fluid.  T h e schematic of the test section tube is shown i n F i g . 7.3. U s i n g Nusselt number correlations as discussed i n Section 4.5, the heat transfer coefficient h can be determined. T h e heat transfer between the surface and the fluid occurs i n the cell at the salt layer-solution interface (SLSI) surface. T h e S L S I surface temperature, T  S  can be  determined from the following relation: rh ^-=hird(T -T )^ dx e  where T  E  S  E  R  (7.15)  is the average fluid temperature of the cell at the S L S I surface, R is the  actual number of fluid parcels i n that cell, R is the average number of fluid parcels in each cell and m  e  is the fluid mass fluid rate through the cell next to the salt deposit  83  7.4. Heat transfer calculation  F i g u r e 7.3: Temperature and radii schematic for the test section surface. T h e actual number of parcels i n each cell is not fixed. In E q . 7.15, the mass flow rate is calculated from the actual mass of fluid parcels at the S L S I and a factor ^ is multiplied w i t h the heat transfer rate to accommodate the fluctuations in the number of fluid parcels at S L S I . If m is the mass of salt present at the tube inner surface and assuming the density of deposit same as that of the salt, p , the thickness of the deposit layer, c5 = r - r can be calculated by determining r\ as follows: saU  salt  r  s  i = i i ~ r  , „  {  1 ;  (7-16)  For a known S L S I surface temperature, the tube surface temperatures are modeled using the radial heat conduction through the wall. U s i n g the thermal conductivity of the salt deposit, k^ the tube inner surface temperature, Tj can be calculated from the following relation.  T, = T + 9^tH  . )  (7  5  17  T h e differential equation for the heat conduction through the tube wall w i t h internal heat generation q (W/m ) z  "  is: [73]  ( 8)  Since the thermal conductivity of alloy 625 (tube material), k is a weak function of temperature, it can be assumed to be constant over the wall thickness. It is also assumed that the tube is perfectly insulated and the outer surface temperature is T . In order to solve the above second order differential equation, the two boundary conditions are; at the tube inner surface i.e., r = r^, T = Tj and at the tube outer surface i.e., r = r , t  0  0  84  7.5. Salt deposition  Salt deposition  7.5  T h e salt has to transport from the bulk fluid before it can get deposited on the tube walls. T h e salt can reach the wall surface by deposition of salt molecules and/or by deposition of salt particles, which have nucleated i n the bulk fluid.  7.5.1  Molecule deposition  T h e similarities of heat a n d mass transfer can be used to determine the mass transfer coefficient, h as discussed i n Section 4.5. T h e molecular deposition rate is given by: m  "dim — h nddxpf m  {C — C (sat)) s  (7.20)  where C (sat) is the saturated dissolved salt mass concentration at the fluid/deposit surface conditions, m (kg/sec) is the molecular deposition rate, C is the average dissolved salt mass fraction i n the bulk fluid and is determined semi-implicitly as: s  m  C=  7.5.2  (7.21)  2  Particle deposition  In order to calculate the deposition of particles that nucleated i n the bulk fluid, the deposition velocity has to be determined. Papavergos a n d Hedley [84] studied the deposition of particles from a turbulent flow stream t o adjacent surface. T h e y d i d a comprehensive review of previous experiments mainly involving aerosol droplets entrained i n duct air streams. D a t a for particle deposition i n liquid streams would be more accurate but due to convenience and low cost, experiments are conducted for aerosol droplets. Furthermore, the data reviewed d i d not cover the variation i n bulk and wall properties. Kostoglou and Karabelas [76] have reported using this deposition velocity for modeling deposition of lead sulfide particles i n geothermal fluids. In the absence of data for deposition of particles i n supercritical fluids, the results of the review were implemented i n the current model. T h e proposed empirical relation to calculate the particle deposition velocity is: [84]  v = v *u* d  d  (7.22)  7.5. Salt deposition  85  V * is the dimensionless salt deposition velocity determined as: d  { 0.0655c3.5 x 1 0 " V + 0.18  (r+ < 0.2) (0.2 < r+ < 20) (r+ > 20)  0 6 6 7  v;  (7.23)  where r+ is the dimensionless particle relaxation time and is given by: *\2  (7.24) m to/wc/i r is the particle relaxation time which can be determined from the following relation using salt density p u and particle diameter d . p  sa  p  T  P  dip.salt  =  (7.25)  18//  Also U* is the wall friction velocity and is determined from the following relation: 1/2  u* =  (7.26)  where T is the wall shear stress and is given by: T = W  p V (-). 2  w  w  For T+ < 0.2, it is diffusion regime and the deposition velocity is considered as the mass transfer coefficient. For 0.2 < T+ < 20, it is inertia regime and the large particles have sufficient inertia to move through the viscous sub-layer. Finally for > 20, particle velocity toward the wall attains a similar magnitude to U*. Stopping distance becomes the same order as the tube diameter. Effect of turbulent fluctuations on the particles is limited such that V becomes v i r t u a l l y constant. T h e particle deposition velocity, V can then be calculated using E q . 7.22. Figure 7.4 shows the salt particle deposition velocity as a function of particle diameter for typical experimental conditions. T h e deposition velocity is determined for a fluid flow rate of 1.3 k g / m i n and salt deposition surface temperature of 4 0 0 ° C at a system pressure of 24.5 M P a . T h e three regimes for calculating the deposition velocity are also shown. For the condition shown, the diffusion regime is for particle radius up to about 0.2 pm and the inertia regime extends to a particle radius of about 2 pm. d  d  If C is the available mass concentration of particles i n the bulk fluid for deposition and assuming the mass concentration of particles in fluid at the deposition surface is zero, the mass deposition rate of salt particles i n a segment can be determined using the following relation: Pi  m  p  = V nddxp d  f  (  C  p  '  +  1  + 2  C  p  i  )  (7.27)  86  7.6. Conservation equations  o to  0.04  Ts =400°C  0.03  rh = 1.3 kg/min P = 24.5 MPa  o  _g >  0.02  g '53 o o. CD "O _Q)  0.01  o  •c CO Q. ^—'  V*=3.5E-4T d p +  V d=0.065 ScT  ro CO 10  10  1(T  lo '  10"  -  10"°  V d=0.18  10"  Salt particle radius (m) F i g u r e 7.4: Salt particle deposition velocity vs particle radius where C , the concentration of particles i n the bulk after particle deposition can be determined as: Vi+l  C „ . . , , = C  w  - ^ f ^ ± i ± ^ ' |  (7.28)  m  7.6 Conservation equations A s mentioned earlier, heat transfer between the S L S I surface and the fluid occurs in the fluid cells at the surface. E q u a t i o n 7.15 (mentioned again for completeness) was used to calculate the change i n enthalpy. m  e  ^  = h7rd(T -T )^ s  (7.29)  e  After each m i x i n g step, the mass of salt molecules and particulate salt deposited on the tube is removed from the cells at the fluid/salt deposit surface. C o n s e r v a t i o n equations o f salt mass f r a c t i o n  For cells at the SLSI surface: dC  7  m -^e  R  = -h -Kdp (C m  f  e  - C )— - V irdp (C s  d  f  ep  -  R  C )^ sp  (7.30)  87  7.6. Conservation equations  T h e two terms on the right hand side of the above equation are for salt mass transfer due to molecule a n d particle deposition respectively. A s mentioned earlier, the mass of salt deposited is removed from the cells next to the S L S I surface only i n each integration step.  For bulk cells: = 0 (7.31) dx where h is the molecules mass transfer coefficient, Vd is the salt particle mass deposition coefficient, p / is the cell fluid density, C & C are the average dissolved salt and particulate salt mass fraction i n the cell at the S L S I surface respectively. C and C are the dissolved salt a n d particulate salt mass concentration at the salt deposit surface conditions. T h e particulate salt mass fraction at the salt deposition surface C , is assumed to be zero. m and rh are the fluid mass flow rate through the cells at the edge and the total fluid mass flow rate respectively. m  e  ep  s  sp  sp  e  Conservation equations of particulate salt mass fraction For cells at the SLSI surface: ^cKTp  da;  =  —_  R j +  +  ri  x> (C  mplNp2n  - C  m  s a  *)—  p it  (7.32)  sa  For bulk cells: ra^JL  = j  m  A + m iN 2irV {C c  p  p  m  - C ) —  (7.33)  aat  where J is the rate of salt particles generated per unit volume and A is the cell cross sectional area. C a n d C t are the dissolved salt mass fraction and saturated salt mass fraction respectively. m * a n d m i are the mass of a nucleated particle a n d a grown particle respectively. T h e terms on the right hand side of the above equation are for the increase i n particulate mass of salt due to salt particle nucleation and salt molecule condensation o n salt particles respectively. c  sa  p  p  T h e number of particles nucleated a n d their size are determined as follows. Particle nucleation occurs i n a l l cells w i t h supersaturated conditions. T h e segment length dl is first determined as discussed i n Section 7.3 and is divided into intermediate integration steps each d x long. Residence time dt, for the integration step is then determined using the fluid velocity. T h u s the number of particles nucleated per unit volume i n each integration step is: N = Jdt (7.34) p  T h e size of nucleated particles is determined using E q . 7.2. In order to determine the increase i n the size of the particle due to diffusion of salt molecules, the degree of  88  7.6. Conservation equations reaction a is first defined: [85]  N - N ~ N - N (sat)  a  m  m  a varies from 0—>1, corresponding to time 0—>oo. N is the dissolved salt molecule concentration i n the cell and corresponds to a for an i n i t i a l dissolved salt concentration of N . T h e growth of particle radius w i t h time, r(t) is assumed to be: [85] m  m  r(t) = r a  (7.36)  l / z  s  T h i s equation is valid for particles w i t h morphologies close to spherical. > / is the final particle radius a n d can be determined as: [85]  (N -  N (sat))V ]  1/3  m  f  m  m  =  r  where N is the number of particles per unit volume. For bulk diffusion limited growth, the linear growth of the particle can be written as: [29] & [85] p  dr  VV  p  m  m  (N - N (sat)) m  dt  m  (7.38)  r  p  Solving Eqs. 7.36-7.38: f dt = K I D  Jo  (7.39)  D  where K  = [i8n V N 2  D  (N  2  m  - N  m  (sat))} "  m  1 / 3  V  (7.40)  l m  and I  d  =  i/3  r  ^  ( ' 7  4 1  )  Jo « - «) Equation 7.39 can be solved, for a given residence time, to determine the extent of reaction, a. T h e growth of particle can then be calculated using Eqs. 7.36 & 7.37. Also the dissolved salt concentration after the growth of salt particles, N can be determined using E q . 7.35 for known a. These particles grow w i t h time a n d the particle size is determined using E q . 7.36. Some of these particles deposit a n d the rest remain suspended i n the fluid. T h e undeposited particles are considered to coagulate i n the next segment length. T h e number of particles after coagulation is determined as discussed i n Section 7.2.2. T h e diameter of the particles for deposition is determined to be the weighted average of the coagulated undeposited particles and the new particles nucleated & grown i n the current segment. Assuming the concentration of particulate salt at S L S I is zero, the mass deposition of salt particles is determined as: m  m = V nddx p  d  Pf  ^  ^  2  ^  (7.42)  89  7.6. Conservation equations  Conservation equations for the dissolved salt mass fraction For the cells at the SLSI surface: rhe^- = -h irdp {C OX For the bulk cells: m  f  - C ) ^ - Jm *A ti  e  s  rn^-  p  = -Jm .A p  c  - m i N 2nV (C p  p  Pl  sat  (7.43)  sa  - m N 2TrV (C  c  - C )-^p it  m  p  - C  m  s a f  )—  dX  (7.44)  Psalt  T h e molecule mass deposition rate is assumed to be based on salt concentration gradient at S L S I surface conditions and the cell next to this surface. For the known initial dissolved salt concentration, C ; , the dissolved salt mass fraction of the cell near the S L S I surface at the end of the step after molecule deposition is: h irddx  (9i±^£i ^ -  m  O+i = Q  - C)  |  s  —  (7.45)  J  where R is the actual number of fluid parcels in the cell next to the salt deposit surface, R is the average number of fluid parcels in each cell and rh is the fluid mass flow rate through the cell next to the salt deposit surface. e  T h e molecular mass deposition rate fn  m  rh  is thus:  = h nddxp  m  m  f  ^> (C - C ) —  (7.46)  s  Conservation equations for number of particles per unit volume For the cells at the SLSI surface: . dN m —± dx p  e  =  -V Trdp} d  (CT - C ) R -l- + J A mo R P  sp v  Pf  1 - -K N p A 2 2  c  p  12  p  A r f  2 c  7.47  The first term on the right hand side of the above equation is for the deposition of particles on the S L S I surface. T h e second term is for the increase i n the particle concentration due to nucleation of new particles and the last term is for the change in the number of particles due to coagulation. For the cells in the bulk: .dN m dx n  p  ,  - JA  Pf c r j  .  1  - -K N A " 2 2  l2  p  cPf  (7.48)  where m o is the mass of a salt particle. p  T h i s procedure is repeated for all integration steps and then the next mixing step occurs.  7.7. Results of model simulation  90  7.7 Results of model simulation T h e model was run for conditions simulating the experimental conditions of N a C 0 deposition experiments. T h e simulated model results have been compared to the experimental data and are discussed i n this section. 2  7.7.1  3  Comparison of model simulation and experimental data  T h e m i x i n g step length dl and the intermediate integration step length dx are determined first as discussed above. Figure 7.5 shows the fluid temperature at various radial locations (cell locations) for the conditions mentioned i n the figure. For these conditions, AL was 0.1 m and dl was found to be about 0.003 m . T h e number of cells (m + n) are 11 and the number of fluid parcels were taken to be 10000, i.e., R = 909. T h e fluid temperature profiles have been drawn at different axial locations as the two fluid streams are being mixed. A t the beginning of the m i x i n g process T% is at 688.15 K and T is at 495.15 K . M i x i n g occurs along the length of the test section and at 500 m m location the fluid temperature attains an almost uniform temperature of about 670 K . A similar behavior can be observed for the salt mass fraction as shown in F i g . 7.6. A t the beginning of the mixing process, salt mass fraction i n stream A is 0.01, while stream B is pure water. T h e salt mass fraction profiles i n various cells at different axial locations are shown i n F i g . 7.6. A  Figure 7.7 shows the results of model simulation of clean surface temperature profile. D a t a of three experiments performed at similar conditions are also shown for comparison. T h e details of these experiments are mentioned i n Table A . l . For this particular case, the integration step is taken to be 0.036 m m and the surface tension is 8 8 x l 0 N / m . T h e surface temperature at clean conditions at the inlet of the test section is almost the same as the temperature of stream B, i.e., pure water from the pre-heater 2. T h e surface temperature decreases along the test section as it mixes w i t h the injected fluid which is at a lower temperature. Later, the surface temperature of the heated test section starts to increase along the test section. - 3  W h e n the fluid injected i n the m i x i n g tee is switched to salt solution, deposition of salt particles and salt molecules occurs. Figure 7.8 shows the number of particles nucleated at different location of the test section. For the conditions considered in this high particle nucleation rate is seen at the inlet of test section which drops quickly along the test section length. T h e salt particle size increases due to diffusion limited growth and coagulation of particles. T h e size of the salt particle increases along the test section length and reaches a m a x i m u m diameter of about 0.16 /xm at the test section outlet. Figure 7.9 shows the mass of salt molecules and particles deposited per unit length at different test section locations. T h e mass of salt deposited increases  7.7. Results  of model  91  simulation  480  0 mm 50 mm 500 mm  500 h 520  q = 7.30 kW/m* P = 24.5 MPa T = 415 C T = 222 °C  540  d  B  560 £  .A  m = 1.2 kg/min rh = 0.12 kg/min salt m.f. in A = 0.01 dx = 0.000036 m B  580  A  CD  S. 600 620 640 660 680 0  2  3  4  5  Location along tube diameter (mm)  Figure 7.5: Temperature profiles at various axial locations very quickly close to the test section inlet. After reaching its peak, it then decreases gradually along the length of the test section. T h e surface temperature of the heated test section thus increases due to the fouling resistance. T h e thermal conductivity of the salt deposit layer is taken to be 0.48 W / m K based on the thermal conductivity values determined experimentally as discussed i n Section 6.3. T h e increase i n surface temperature after salt deposition is shown i n F i g . 7.10. T h e results are plotted after 16 minutes of operation w i t h salt deposition. A s discussed i n Chapter 5, the plug-like conditions were noticed after the thermocouple located at 0.15 m from the test section inlet. T h e model results show a m a x i m u m temperature rise slightly earlier than the 0.15 m location. Figure 7.11 shows test section tube surface temperature simulation at clean conditions of experiments i n which the test section was not heated. T h e data of two experiments performed and the experimental parameters are also shown i n the figure. A bulk fluid temperature drop of about 1.5°C was observed across the unheated test section during this experiment. Due to the salt deposit layer a thermal resistance resulted in a drop of test section surface temperature and is shown i n F i g . 7.12. For these model runs, the predicted particle size and particle deposit mass were much lower than those observed. In the next section the model sensitivity to various param-  7.8. Effect of parameters on the model results  0 mm 50 mm 500 mm  0.01 r 0.009 c •B 0.008 ro **= 0.007  w w c  0.006  ™ 0.005 J 0.004 o w 0.003  92  q = 7.30 kW/m' P = 24.5 MPa T = 415X T = 222 °C m = 1.2 kg/min m = 0.12 kg/min B  B  salt m.f. in A = 0.01 dx = 0.000036 m  0.002 0.001 0  "0  1  2 3 4 5 Location along tube diameter (mm)  Figure 7.6: Salt mass fraction at various axial locations eters is discussed in order to understand the cause of these errors.  7.8 Effect of parameters on the model results Some parameter values were assumed in the model. The effect of these parameters are discussed in this section. Surface tension: 7 The surface tension has a substantial effect on the number of nucleated salt particles and its exact value is not known for Na2C03. The number of particles nucleated in an integration step was determined using Eq. 7.34, and thus the mass fraction of particles nucleated was used to update the mass fraction of dissolved salt after nucleation for a known initial dissolved salt mass fraction. For very low values of surface tension, the mass fraction of nucleated particles was found to be more than the dissolved salt mass fraction available for nucleation. The minimum value of surface tension was thus chosen such that the mass of salt nucleated was less than the available mass fraction of dissolved salt. The surface tension was varied from 88xlCT to 100 x l O " N/m. The model showed a larger number of nucleated particle for lower values of surface tension. Figure 7.13 shows the effect of surface tension on the number of particles nucleated per unit volume at different locations of the test section. It can 3  3  7.8. Effect of parameters on the model results 420  o ° 415  93  — O * •  q = 7.30 kW/m* P = 24.5 MPa T = 415 C T = 222 °C d  Model simulation Expt: Sep. 26, 2002 Expt: Sep. 30, 2002 Expt: Nov. 04, 2002  B  CD 3  2 CD  410  Q.  E  0) <D o  A  m = 1.2 kg/min rh = 0.12 kg/min y = 0.088 N/m salt m.f. in A = 0.01 dx = 0.000036 m B  A  405  •g 3  CO  O  c  S> 395  O 390  500  1000  1500  2000  2500  3000  Test section location (mm) Figure 7.7: Comparison of clean surface temperature experiment data w i t h the model results (heated test section case) be observed that the number of particles nucleated decrease along the length of the test section a n d is m a x i m u m for lowest value of the surface tension. T h e particle radii at various test section locations for different surface tension values are shown i n F i g . 7.14. Higher number of salt particles result i n larger particle size due to coagulation of salt particles. T h e m a x i m u m particle diameter varied from 0.04 to 0.16 fxm for the considered values of surface tension. Figure 7.15 shows the mass of particles deposited per unit length for various surface tension values. T h e mass of particles deposited decreases w i t h an increase i n surface tension and is comparatively negligible for surface tension value of l O O x l O N / m . However, more molecule mass is deposited for higher surface tension values as shown in F i g . 7.16. It should be noted that the actual salt particle size, from the S E M photographs, was more than 112m. A l s o based on the model results, lower values of surface tension resulted i n larger particle size. Therefore the lower values of surface tension are more likely to determine the actual mass of particles deposited. F i g u r e 7.17 shows the salt layer thickness after 16 minutes of operation for various values of surface tension. - 3  Integration step length: da; T h e test section was divided into a number of integration steps. T h e model was r u n for integration step lengths of 0.03 m m to 0.96 m m i n order to determine the effect of  7.8. Effect of parameters on the model results  94  Test section location (mm) F i g u r e 7 . 8 : Number of nucleated particles and their average size at various test section locations (heated test section case) step length on the mass of salt deposited and hence the change i n surface temperature. Figures 7.18 shows the effect of segment length on the tube surface temperature after salt deposition. T h e surface temperature rise is almost the same for a l l step sizes. N u m b e r o f fluid p a r c e l s i n e a c h c e l l : R E a c h cell comprised R number of fluid parcels. A s mentioned earlier, during the simulated mixing process, the fluid parcels move i n a vertical direction, either upwards or downwards and the number of fluid parcels in a cell was not fixed. T h e direction in which the fluid parcels move was determined by generating random signs (+ or —). Therefore, the higher the number of parcels, the higher the probability that exactly half of them move i n either direction. T h e model was r u n for various number of fluid parcels and F i g . 7.19 shows the effect of number of fluid parcels on the mass of deposited salt. For the conditions shown i n the figure there were 11 cells. T h e model was run considering 100, 1000 and 10000 fluid parcels and therefore fluid parcels per cell were 9, 91 and 909 respectively. T h e simulation w i t h highest number of fluid parcels produced a relatively smooth curve for the deposited mass of salt. T h e mass of salt deposited, for the runs i n which 100 and 1000 fluid parcels were considered, fluctuated about the mass deposition curve for the 10,000 fluid-parcel run.  95  7.9. Conclusion  3.5  x 10 -.3.5  x 10 r  JtD  q = 7.30 kW/nT P = 24.5 MPa T„ = 4 1 5 C 222 °C 1.2 kg/min ; 0.12 kg/min  CD  6  :  y = 0.088 N/m salt m.f. in A = 0.01 dx = 0.000036 m  2  1.5  D)  co £ o  O)  "Si  as  T3 O  £> w  CD «^ 0.5  1000  1500  2000  Test section location (mm)  0 3000  Figure 7.9: Mass of salt molecules and particles deposited per unit length at various test section locations (heated test section case)  7.9  Conclusion  M i x i n g of two fluid streams, heat transfer and salt deposition on the tube surface have been modeled. Salt particle nucleation, growth and coagulation have been considered to determine the mass of salt particles and molecules deposited on the tube surface. T h e change i n tube outer surface temperature, due to the fouling resistance, has been calculated and compared w i t h the experimental results. T h e model results have been compared w i t h data from two types of experiments i.e., heated and unheated test section. T h e model estimates the tube surface temperature profile along the length of the quite well, d u r i n g the mixing of the two fluid streams occurs at clean surface conditions. T h e location of the peak surface temperature change i n the test section, calculated from the model, was in a good agreement w i t h the experimental data. T h e model seems to estimate the peak surface temperature increase for the heated test section case quite well. It should be noted that the density of the deposit layer is assumed to be the same as that of the salt and effect of porosity has not been considered in the model. T h e modeled salt particle size was also found to be less than the size of the particles observed from the S E M analysis of the deposit structure. A possible reason could be the agglomeration of salt particles at the tube surface which has not been modeled.  7.9. Conclusion  96  Test section location (mm)  Figure 7.10: Surface temperature rise due to salt deposit: experiment data vs model results (heated test section case) 415  . . 410 3  TO mp  CD  405  o  CD  o tro 400  q = -6.21 kW/m* P = 24.75 MPa T = 413X T = 220 °C  — • *  Model simulation Expt: Oct. 31, 2002 Expt: Oct. 02, 2002  B  .A  m = 1.2 kg/min rfi = 0.12 kg/min y = 0.085 N/m salt m.f. in A = 0.01 dx = 0.000036 m B  3 CO  aj  3 o c 395 0 ! CD  O 390  500  1000 1500 2000 Test section location (mm)  2500  3000  Figure 7.11: Comparison of clean surface temperature experiment data with the model results (unheated test section case)  97  7.9. Conclusion  Test section location (mm) F i g u r e 7 . 1 2 : Surface temperature drop due to salt deposit: experiment data vs model results (unheated test section case)  i  1  i  i  700  Test section location (mm) F i g u r e 7 . 1 3 : Effect of surface tension on the number of nucleated particles  7.9.  98  Conclusion  x 10 —  q = 7.30 k W / m ' P = 24.5 M P a T = 415' C S  B  w 1.6 O t CO CL  Y = 0.088 N/m y = 0.095 N/m y = 0.100 N/m  T = 222 °C ,A m = 1.2 kg/min B  m = 0.12 kg/min salt m.f. in A = 0.01 dx = 0.000036 m A  C/>  (D 0.8 E CO T3 QJ O) CO  CD > <  0.4  500  1000 1500 2000 Test section location (mm)  2500  3000  Figure 7.14: Effect of surface tension on particle size  q = 7.30 k W / m " P = 24.5 M P a T = 415 C  Y = 0.088 N/m Y = 0.095 N/m Y = 0.100 N/m  < 5  B  T = 222 °C .A 1.2 kg/min :  %  0.12 kg/min A salt m.f. in A = 0.01 dx = 0.000036 m M  500  ;  1000 1500 2000 Test section location (mm)  2500  3000  Figure 7.15: Effect of surface tension on particle deposition  7.9. Conclusion  4I  1  1  1  1  i  3000  Test section location (mm) F i g u r e 7.16: Effect of surface tension on molecule deposition  0.9  3000  Test section location (mm) F i g u r e 7.17: Effect of surface tension on salt layer thickness  7.9. Conclusion  3000  Test section location (mm) F i g u r e 7 . 1 8 : Effect of segment length on tube outer surface temperature  ......  —  0  i  0  1  .  '  500  1000  1500  ^  '  2000  >  R=9 R  =  9  1  R= 909  "  2500  •  1  3000  Test section location (mm) F i g u r e 7 . 1 9 : Effect of number of fluid parcels on salt deposition  Chapter 8 S u m m a r y of Conclusions a n d Future W o r k Recommendations 8.1  Thesis overview and conclusions  The supercritical water oxidation (SCWO) has the potential of being a viable technology for processing organic waste. However, its commercial application has not been successfully possible due to the problems of corrosion and salt precipitation on the heat transfer surfaces. Inorganic salts, which might be present in the waste feed or formed during the process have very low solubility at S C W O conditions. These salts are usually accumulate on the reactor surface. Due to the steady buildup of these salt deposits, the tubular reactors are ultimately plugged. The precipitation of salt on the reactor wall not only wastes energy, due to its thermal resistance, but also leads to even more cost associated system shutdowns. Several approaches have been suggested by companies trying to commercialize this technology to overcome this problem. In order to control the buildup of salt deposits, attempts have been made to develop specific reactor designs and to modify the operating techniques. All of these attempts have been successful to some extent but none of them has been able to eradicate the problem of fouling in the SCWO reactors. Some techniques are better suited for certain types of wastes only and none of them has proved to be superior than others. Due to this reason, importance of continued fundamental research in the phase behavior (particularly in ternary component systems), precipitation of salts, deposition dynamics and morphology of the deposits is evident. The objective of this work was to study the deposition of Na2C03 and Na2S04 at high pressure and elevated pressure conditions associated with the SCWO process. These salts are encountered in wastes of mononitrobenzene plants, among several other organic wastes which are good candidates for S C W O treatment. Since the solubility of these salts ( N a C 0 3 in particular), at high pressure and a range of temperatures encountered in SCWO process was not known, an experimental study 2  101  8.1. Thesis overview and conclusions  102  was carried out to measure the solubility of these salts i n binary (salt-water) and ternary (salt-salt-water) system. Experiments were performed i n which heterogeneous nucleation of salt molecules (crystalline fouling) on the reactor surface occurred. T w o heat and mass transfer correlation have been used to simulate the salt deposition process and a sophisticated model has been developed to verify the solubility reporting temperature. It was found that the solubility of these salts decreases rapidly after the pseudo-critical temperature. T h e solubility of these salts i n the form of a mixture was quite close to that of pure salts. However, possibly due to the common ion effect, the solubility of Na2S04 i n the presence of Na2CC>3 was found to be further reduced at near critical conditions. T h e solubility of these salts was presented i n the form of correlations as a function of fluid density, which can be used to estimate the m a x i m u m amount of dissolved salt for a given fluid density. A heat and mass transfer model was also developed to confirm the solubility reporting temperature. D u r i n g this experimental study, it was observed that the tubular reactor plugged due to the salt deposits i n a very short time. T h e system had to be shut down, sometimes, w i t h i n five minutes due to either high system pressure or excessive surface temperature of the heated sections. Three types of experiments were performed i n order to study the effect of type of fouling (crystalline and particulate) on the net salt deposition. C o m b i n e d crystalline and particulate deposit runs were found to be longer than the pure crystalline deposit experiments. In order to make the salt particles nucleate i n the bulk fluid, salt solution was injected i n pure supercritical water such that supersaturation conditions were achieved. T h i s was carried out at the inlet of the heated test section and resulted i n combined crystalline and particulate deposition. In some experiments the test section was kept unheated to further reduce the crystalline deposition. T h e net salt deposition was found to be reduced for the combined crystalline and particulate runs compared to the pure crystalline deposition experiments. Four times more salt passed through the system when the salt particles nucleated i n the bulk fluid. T h i s resulted i n longer runs before system shut down. T h e other observation for the pure crystalline type deposition experiments was that the surface temperature increased steadily w i t h the steady growth of the deposits i n the heated test section experiments. However, for the combined crystalline-particulate deposition experiments, the surface temperature initially increased gradually and then suddenly decreased, thus indicating unsteady buildup of the deposit layer. T h e location of the plug was found to be near the point where salt solution was injected and for the conditions studied, and a l l of the salt deposition occurred w i t h i n the 3 m long test section. Similar unsteady growth of deposits was noticed i n the experiments in which the test section was unheated. Thus for wastes w i t h inorganic salt content, more salt is likely to flow through the system, if it is made to nucleate i n the bulk fluid. A novel procedure was developed to preserve the salt deposited, under  turbulent  8.2. Implications for SCWO system design  103  conditions, on the heat transfer surface for studying the structure of the deposits. T h e system was purged w i t h nitrogen after enough salt deposition occurred on a tube inserted i n the test section to collect deposit samples for S E M analysis. In this manner the salt deposit thickness profile along the test section was measured. Based on the measured surface temperature rise due to deposition, the thermal conductivity was calculated. N a C 0 3 deposits were found to be stronger then the Na S04 deposits. T h e Na SC>4 deposits (combined crystalline-particulate i n particular) were weaker and partially washed off during the purging process. T h e pure crystalline deposits were found to be different from the combined crystalline-particulate deposits. T h e S E M photographs revealed long salt crystals which nucleated at the tube inner surface and grew towards the center of the tube i n case of pure crystalline deposition. These deposits were very dense. O n the other hand for the combined crystalline-particulate deposition, salt particles were seen and the deposits were comparatively less dense and easy to remove. It is due to this reason a steady salt deposit layer buildup was observed for pure crystalline deposition experiments. For the combined crystalline-particulate deposition, the deposit layer was periodically removed (partially), because of the weaker deposit. 2  2  2  Finally, a computer code was written to model the deposition of combined crystallineparticulate deposition and heat transfer i n the tubular reactor. In the model, simulation of m i x i n g of two fluid streams was carried out. Homogeneous nucleation of salt particles, their growth, coagulation and deposition on the reactor tube was modeled i n conjunction w i t h the deposition of salt molecules nucleating on the tube. T h i s model can thus be used to estimate the mass of salt deposited on the tube surface and hence the change i n tube surface temperature due to the fouling resistance. T h e model results were compared to experimental data. It was noticed that the model predicts the heat transfer between the fluid and tube quite accurately and the surface temperature profile, as the two fluid streams were m i x i n g along the test section length, was i n good agreement w i t h the experimentally measurements for clean surface conditions. T h e estimated increase i n surface temperature due to fouling resistance agreed well w i t h the experimental data. T h e location of the peak surface temperature change due to the fouling resistance was also estimated quite well. However, the calculated size of the particles was found to be smaller than the actual salt particle size observed i n the S E M photographs.  8.2  Implications for S C W O system design  For wastes w i t h inorganic salt content, more salt is likely to flow through the system, if it is made to nucleate in the bulk fluid. T h i s can be achieved by heating pure water (and oxygen) only, to supercritical conditions i n the pre-heaters and then injecting  8.3. Future work  104  the waste feed into it. In this manner, the S C W O system w i l l be able to run for longer periods of time and also the problem of salt deposition w i l l be restricted over a short length of the reactor. T h e salt deposits i n this short length can be flushed/quenched by passing subcritical water through it. O r the deposits can be removed by mechanical means. D u r i n g the salt removal process, the waste can be passed through a reactor parallel to the one being cleaned. Thus two short length reactors are needed such that while the feed is being treated i n one, salt removal takes place i n the alternate reactor. D u r i n g the exothermal S C W O reaction, it may not be necessary to heat the surface of the reactors. Possible addition of fuel i n the waste itself may ensure the process be self-sustaining. A s a possible fouling mitigation measure, use of additives to provide nucleation sites in the bulk fluid may be studied. A d d i t i o n of solid, inert particles (e.g., silica) in the feed itself may provide the salt to adhere to a mobile surface instead of sticking to the reactor surface. If the particles are rough, they may scour the tube inner surface thereby removing the deposits on the wall. Since the combined crystalline-particulate deposits are easier to remove, even if the inert particles accumulate on the tube surface, they are more likely to result in a weaker deposit. In the U B C - N O R A M pilot plant the injection of particles may be carried out at the inlet of the test section. However, consideration is required to design a system to collect these particles before the fluid pressure is reduced, in order to eliminate any erosion and choking problems at the back pressure regulator. For some applications w i t h high heating value wastes, it might be unnecessary to preheat past the critical temperature, in which cases, subcritical salty wastes can be injected into supercritical water, forming homogeneous particles. T h i s i n fact happens in the vessel and platelet reactors, and the results here show that only a modest force should be needed to remove deposits, at least initially. For other applications, salt solution could be injected prior to the cool down section. For example, i n S C W O of chlorinated waste, H C I causes extreme corrosion at cool-down side unless neutralizers are added. N a C 0 3 should be added to increase the p H without risking N a O H melt corrosion and apparently, w i t h no risk of fouling. 2  8.3  Future work  It was concluded that combined crystalline-particulate fouling deposits are weaker than the crystalline deposits. For N a C 0 3 , a number of experiments were performed and it was observed that more salt was able to pass through the system, instead of depositing on the tube, when homogeneous nucleation occurred. T h i s was because both deposition and removal processes occur simultaneously due to the weak deposit characteristics. For the experiments i n which salt particles were made to nucleate 2  8.3. Future work  105  in the bulk fluid, the net salt deposit was less not necessarily because those salt particles did not deposit on the reactor surface at a l l and instead passed through the system. T h u s flow conditions (preferably low turbulent) should be studied for which the particles are more likely to pass through the tubular reactor instead of depositing on the reactor wall. However, it might be tricky to have conditions where the fluid velocity is high, but still low turbulence, such that the particles remain suspended in the fluid. D u r i n g the process of preservation of the salt deposit layer for S E M analysis, it was noticed that the N a C 0 3 deposits were easier to preserve by nitrogen purging technique. However, it was found that Na S04 deposits were weaker and were partially washed off during the purging process. In order to confirm this, combined crystalline-particulate deposition experimental study, similar to that performed w i t h N a C C - 3 salt should be carried out for Na S04 also. In case Na S04 deposit is found to be weak, the homogeneous nucleation may be more effective as a fouling mitigation technique for Na S04. 2  2  2  2  2  2  The S E M analysis of the salt deposits was carried out to study the structure of the deposit layer and its thickness along the test section length. T h e thermal conductivity of the salt deposit layer was then inferred from the measured increase i n surface temperature. T h e deposits seemed to be quite dense, but further analysis may be carried out to determine the porosity of the deposited layer. T h i s can be done if the size of the tube is larger then the one used as the insert i n this study. In that case the system can be run for longer period of time and thus thicker deposit layer maybe preserved for analysis. T h e effect of aging of the deposit layer has not been studied. S E M analysis of deposits preserved at different time intervals may be carried out to determine of the change i n deposit structure w i t h time. The simulation model developed for estimating combined crystalline-particulate deposition comprises salt particle nucleation, growth and coagulation of particles and their deposition on heat transfer surface, which occurs in parallel w i t h deposition of salt molecules. It does not simulate the salt removal process of salt after a certain salt layer thickness is achieved as indicated from the experimental data. T h e model can thus be modified to simulate the actual fouling phenomenon during which both salt deposition and removal processes occur simultaneously. T h e model may thus be optimized to determine values of operating parameters i n order to reduce net salt deposit rate on the heat transfer surface.  Appendix A Discussion of the Na2CC>3 F o u l i n g Mitigation Experiments Three types of salt deposition experiments have been performed. In the first type, the salt solution was heated in the pre-heaters before entering the test section. The objective of these experiments was to determine the solubility of Na2C03 and Na2S04 at different fluid temperatures. The bulk fluid temperature at the outlet of pre-heater 2 was set such that minimum salt deposition occurred in the pre-heaters. The test section heat input was kept low in order to have a near-isothermal condition in the test section. Heterogeneous nucleation of salt molecules resulted in crystalline scale on the test section in this type of experiment. The details of these experiments have already been discussed in Chapter 4 and the operating parameters are mentioned in Tables 4.1-4.3. These experiments will not be discussed in this chapter. However, two N a C 0 3 heterogeneous nucleation experiments were later performed in which instead of heating the salt solution, pure water was passed through the pre-heaters. Salt solution was then injected into the supercritical water. The objective of these experiments was to compare the behavior of pure crystalline scale with combined crystalline-particulate deposits. These experiments will be discussed in Appendix A.3. 2  In the second type of experiments, N a C 0 solution was injected in a stream of supercritical water just before the test section, for fouling mitigation purposes. The fluid temperature after mixing of the two streams was above the N a C 0 3 saturation temperature and thus salt particles were expected to nucleate in the bulk fluid. In this type of experiments the test section was heated and thus combined crystalline-particulate fouling was expected. A sample experiment of this type has already been discussed in Chapter 5. Other experiments, of this type, are discussed in the next section. The third type of experiment was similar to the second type, but the test section was unheated, in order to further reduce crystalline scale. For the second and third type of experiments, the experimental procedures have been discussed in Section 5.2 and details of experimental parameters are mentioned in Table A . l . 2  3  2  106  107  T a b l e A . l : Details of N a C 0 2  3  Salt concPressure Fluid Experi-Data file Date flow rate entration performed (MPa) ment (kg/min) at test No. section nlet (wt.%) 0.055 (0.8+0.1) 24.61 SEP13.xls Sept. 13, 1 2002  deposition experiments Salt  Comments Time to terminate concentration in experiment collection tank (wt.%) no plugging Perhaps the salt concnot done entration at test section inlet was quite low 60 minutes Test section was not not done actually plugged, but the heating was reduced when PH2 outlet temperature was seen to be increasing  2  SEP17.xls Sept. 17, 2002  24.54  (0.84+0.1)  0.1  3  SEP17.xls Sept. 17, 2002  24.54  (0.84+0.1)  0.1  4  SEP20.xls Sept. 20, 2002  (1.2+0.12)  5  SEP23.xls Sept. 23, 2002  (1.2+0.12)  0.1  0.065  6  SEP26.xls Sept. 26, 2002  24.48  (1.2+0.12)  0.1  0.06  7  SEP30.xls Sept. 30, 2002  24.82  (1.2+0.12)  0.1  0.088  8  0CT02.xls Oct. 02, 2002  24.65  (1.2+0.12)  0.1  0.08  9  0CT31.xls Oct. 31, 2002  24.72  (0.84+0.1)  0.1  0.018  10  0CT31.xls Oct. 31, 2002  24.72  (1.2+0.12)  0.1  0.09  11  NOV04.xls Nov. 04, 2002  24.75  (1.2+0.12)  0.1  0.075  12  NOV8.txt  24.46  (1.2+0.12)  0.1  not done  Nov. 08, 2002  not done  not done  75 minutes  Experiment was stopped when relief valves opened slightly Could not achieve a steady pressure, using the spring loaded BPR stopped after Pressure was continuously 40 minutes increasing due to a leak in the BPR 50 minutes Experiment stopped when pressure relief valve opened slightly 66 minutes Experiment stopped when pressure relief valve opened fully 55 minutes Unheated test section, experiment stopped when pressure relief valve opened fully, plugged at the middle thermocouple 50 minutes Surface temperature rise of about 170°C, experiment terminated 75 minutes Unheated test section, parameters same as Experiment No. 8 but without middle thermocouple, no sign of plugging in 75 minutes 90 minutes Same as last run but with heated test section, plugged in 90 minutes 25 minutes Due to the high heat input to the test section, a 10°C difference was observed between top and bottom thermocouples  108  A.l. Homogeneous & heterogeneous nucleation experiments  A.l  Homogeneous h heterogeneous nucleation experiments  A. 1.1 Experiment: 1 T h i s was the first r u n of the second type of N a 2 C 0 3 deposition experiments. Salt solution was injected into the supercritical water at the inlet of the test section. T h e salt concentration, entering the test section was about 0.055 wt.%. T h e temperatures at 0.15 m ( S B 9 , thermocouple at the top surface) and 0.25 m (S9, thermocouple at the b o t t o m surface) were noted before and after the metering pump was started. The temperatures at these locations were very close to each other, before water was injected from the metering pump. However, when water was injected through the metering pump, the thermocouples at these locations showed temperatures different from each other. T h u s around the 0.25 m location, the two fluids streams were not fully mixed. After the metering pump was started the S B 9 (top surface thermocouple) showed about 4 ° C higher than S9 (bottom surface thermocouple). However at 1.03 m (SB3, thermocouple at the top surface) and 1.1 m (S3, thermocouple at the bottom surface) locations the thermocouples showed temperatures very close to each other, before and after water injection from the metering pump. T h e thermocouples S7 (at 0.61 m bottom) was also showing almost the same temperature as S B 7 (at 0.52 m top surface). T h u s the two streams were almost mixed around 0.6 m location. Salt solution was injected at 13:02 w i t h pre-heater 2 bulk fluid outlet temperature set at 403°C. T h e pre-heater 2 outlet temperature started increasing immediately after that and at 13:20 the power input to the pre-heater 2 was reduced to maintain the output at 416°C. Over the 50 minute salt deposition period, the temperature rise was as follows:  Location (m) Temperature rise (°C)  0.15 4  0.61 7  0.96 7  1.1 1.25 8 7  1.4  1.5 1.7 6 4 4  2.3 2  2.8 2  A steady increase i n surface temperature was noticed, but the system pressure remained constant during the 50 minute period. A t 14:12 the flow from the metering pump was switched to pure water to redissolve the salt deposits. T h e time taken to reduce temperature back to clean surface conditions at 0.15 m location i.e., about 400°C was about 15 minutes. A l l thermocouples up to the 1.4 m location showed a reduction in temperature w i t h i n 30 minutes of switching back to water. D u r i n g this period, the temperature of thermocouples located at 1.5 to 2.8 m stayed almost the same, so either salt deposit was not being dissolved or there was no deposition at a l l i n that area. T h e average clean surface temperature was about 399°C. B u l k fluid temperature at the test  A.l. Homogeneous & heterogeneous nucleation experiments  109  section outlet was about 396°C. T h e solubility limit at 399°C is about 0.015 wt.%. However effluent conductivity fluctuated around 500 / / S / c m corresponding to N a C 0 3 solubility of 0.025 wt.% which actually corresponds to a fluid temperature of 390°C. Since the surface temperature and pressure rise during the 50-minute run were not high, it was decided that the next experiment would be carried out at double the salt concentration. 2  A.1.2  Experiments: 2 & 3  T h e salt concentration at the test section inlet for Experiment 2 was 0.1 wt.%. W h e n the salt solution was injected, due to salt depostion i n the test section, a sudden increase i n pressure at the test section inlet was noticed. T h e bulk fluid temperature, at pre-heater 2 outlet, increased rapidly too, after salt solution was injected into the supercritical water stream. T h e experiment was thus terminated. It was then decided to do the experiment again and not to terminate the run until the pressure relief valve, located just after the m a i n p u m p opened. In Experiment 3, salt solution was injected at 15:50 and the run was terminated when the pressure relief valve opened slightly at 17:08 i.e., after about 75 minutes of operation. T h e test section average-inner surface temperature was about 397-398°C under clean conditions. F l u i d temperature at the exit of pre-heater 2 was maintained at 416°C. Due to the salt deposition, in ten minutes, a temperature rise of about 15°C was noticed at the 0.15 m location. T h e surface temperature then dropped to the clean surface condition suddenly. T h i s 10 minute cycle was repeated seven times during the 75 minute r u n as shown in F i g . A . l . It seems that salt deposited i n the test section, resulting i n an increase of system pressure at the test section inlet. T h e bulk fluid temperature, at the exit of pre-heater 2, also increased w i t h the increase i n pressure at the test section inlet, thus indicating a plug-like condition. T h e pressure increased from 24.47 to 26.8 M P a , at the inlet of test section, which cleared the plug after the deposit layer reached a certain thickness. T h e system pressure at the outlet of the test section remained constant, thus the location of the plug was i n the test section. A t the 0.61 m location, three such cycles were observed but at the end of each cycle the temperature d i d not drop a l l the way to the clean surface condition thus the deposit layer was only partially removed. A t the 0.96 m location, two deposition-removal cycles were observed. T h e thermocouple at 1.1 m location showed a steady temperature increase of about 14°C. After 75 minutes of operation, the temperature increase at various locations i n the test section was as follows:  Location (m) Temperature rise (°C)  0.15 15  0.61 14  0.96 13  1.1 14  1.5 10  1.7 7  2.3 3  2.8 3  D u r i n g the experiment the effluent conductivity kept on fluctuating thus indicating  110  A.l. Homogeneous & heterogeneous nucleation experiments  415  34.8  1.5 m top 2.8 m top  32.8 ro  30.8 p_ 28.8 £  3 (0  26.8 2 24.8 '22.8 17:15  Pressure 385 15:45  16:00  16:15  16:30 Time  16:45  17:00  F i g u r e A . l : Temperature and pressure behavior for the combined heterogeneous h homogeneous nucleation run (Experiment 3) that salt deposition and removal were taking place i n the system. M o s t of the time it was around 650 pS/cm, but increased to a m a x i m u m of 4 m S / c m . It was therefore decided that for the next run, the effluent would be collected, for salt concentration measurement. T h e surface temperature behavior at the 0.15 m location was found to be different from the downstream surface temperatures. A deposition-removal cycle is shown in F i g . A . 2 . T h e pressure behavior shown in the figure is at the test section inlet. T h e pressure at the test section outlet remained constant. T h e surface temperature at that location increased w i t h an increase i n pressure and fluid temperature at pre-heaters 2 outlet. Thus indicating the location of the plug was just after this location. T h e temperature at other location d i d not increase w i t h an increase i n pre-heater 2 outlet temperature  111  A.l. Homogeneous & heterogeneous nucleation experiments  and pressure. However, at other locations surface temperature increased for a short time, after the removal of the plug and then reduced back to initial condition. Thus the surface temperature increase was due to the fluid which started flowing again after the plug was removed. Another observation was that after the salt was removed from the 0.15 m location, no sudden temperature increase was noticed at the later locations. Thus the removed salt layer d i d not deposit at other locations i n the test section.  425  o  34.8  + 0.15 m top o 0.6 m bottom  32.8  415  30.8  o  , o O o  o o °  -§ 405  0  °  0  0  ° o ° o  0  0  0  °  0  0  n  ooo„°°°"  o o o  0  oo  °  28.8 S>  i_  CD  co co  Q.  26.8 2> o.  E  CD I-  Q-  D  J24.8  395  Pressure  385 16:35  415  16:37  16:36  +  Time  16:38  16:39  34.8  1.5 m top 2.8 m top  o  22.8 16:40  32.8  O  30.8  o  sT 405  28.8 £  •*—>  =J CO CO  CD  k.  CD  0  Q.  0  0  o  0  o O o  0  o o o o o  0  o O o  0  ° o  0  0  0  0  o°  ° ° ° o °  E £ 395 385'— 16:35  S.  0  °  0  °  °o°°°  26.8 9> Q.  H24.8 16:36  16:37  16:38  Pressure —'22.8 16:40 16:39  Time  F i g u r e A . 2 : Temperature and pressure behavior for the combined heterogeneous & homogeneous nucleation run (Experiment 3)  A. 1.3  Experiment: 6  T h e effluent was collected i n this run. Salt solution was injected at 10:54 and switched to pure water at 11:43. F i v e or six deposition-removal cycles were observed at the 0.15  A.l. Homogeneous & heterogeneous nucleation experiments  112  m location during the 50 minute run as shown i n Figure A . 3 . T h e surface temperature at this location increased gradually by more than 10°C and then dropped suddenly to almost the clean surface temperature. A t the 0.61 m location, the surface temperature increase was about 30°C i n 40 minutes and then the salt layer washed off. T h e experiment was terminated when the pressure increased to 26.8 M P a and the pressure relief valve, located just after the m a i n pump, opened slightly. It was decided, for the next experiment, the run would be terminated only when the pressure relief valve remained open for some time.  415  + o  1.5 m top 2.8 m top  27.8 (0  CD  25.8 jg  Pressure 385 10:50  11:00  11:10  11:20 Time  11:30  11:40  23.8 11:50  F i g u r e A . 3 : Temperature and pressure behavior for the combined heterogeneous & homogeneous nucleation run (Experiment 6)  113  A.l. Homogeneous & heterogeneous nucleation experiments  A. 1.4 Experiment: 7 T h i s run was terminated only when the pressure relief valve opened fully (the pressure at the inlet of the test section increased to 28.2 M P a ) . It lasted for 66 minutes. A g a i n five or six deposition-removal cycles were noticed i n this run at the 0.15 m location as shown i n F i g . A . 4 . T h e temperature at this location increased gradually by about 12°C and then dropped suddenly to the clean surface condition. Three such cycles were noticed at the 0.61 m location and two at 0.96 m . A steady increase of surface temperature was noticed at later test section locations.  Time 32.8 415  + °  0.96 m top 2.8 m top  30.8 28.8 I—  26.8  jjj CD 1—  D_  Pressure 385 12:15  12:30  12:45  13:00  13:15  24.8 22.8 13:30  Time F i g u r e A . 4 : Temperature and pressure behavior for the combined heterogeneous & homogeneous nucleation run (Experiment 7) After 66 minutes of operation, the temperature increase at various locations in the test section was as follows:  A.2. Homogeneous & heterogeneous nucleation unheated test section experiments 114  Location (m) Temperature rise (°C)  0.15 0.61 0.96 20 15 13  1.1 13  1.25 11  1.4 11  1.5 8  1.7 7  2.3 2.8 6 6  Pressure at the outlet of the test section remained constant. N o sudden deposition occurred i n the later parts of the test section when salt was washed away from the 0.15 m location. A g a i n during the deposition-removal cycle, at 0.15 m the surface temperature behavior was different from the downstream locations. T w o sample cycles are shown i n F i g . A . 5 . W h e n i t was close to plugging the pressure a n d pre-heater 2 outlet temperature increased very quickly a n d only the thermocouple at 0.15 m behaved i n the same manner. A sudden increase i n temperature was noticed at later locations after the plug was removed. Thus the location of the plug was just after the 0.15 m location. T h i s r u n was slightly longer then Experiment 6, because it was terminated only after the pressure relief valve opened fully and constant fluid flow was observed through it for few seconds. T h e average clean inner-surface test section temperature was about 397°C. Na2C0 solubility at this condition is 0.018 wt.%. T h e effluent salt concentration was 0.088 wt.%. T h e ratio of effluent salt concentration to saturation limit was thus 4.8 and it took around 66 minutes to plug the test section. 3  A. 1.5 Experiment: 11 For this experiment, the ratio of effluent salt concentration to saturation limit was found to be 4.2. T h e test section got plugged after 90 minutes of operation. Figure A.6 shows the behavior of the thermocouple at the 0.15 m location compared to other downstream surface temperatures, during a deposition-removal cycle. A s usual, the plug occurred after the 0.15 m location. T h i s experiment has already been discussed in detail i n Section 5.3.2.  A.2  Homogeneous & heterogeneous nucleation unheated test section experiments  A.2.1  Experiment: 8  The test section was not heated i n this r u n . T h e clean test section inner-surface temperature was about 394°C. Four deposition-removal cycles were observed at the 0.15 m location as shown i n F i g . A . 7 . W h i l e the salt was being deposited, the surface temperature decreased due to thermal resistance of the deposit layer. In the experiments w i t h a heated test section, the test section surface temperature increased  A.2. Homogeneous & heterogeneous nucleation unheated test section experiments 115 440  Pressure 390 12:40 1  ' 13:00  1  12:50  '22.8 13:10  Time F i g u r e A . 5 : Temperature and pressure behavior for the combined heterogeneous & homogeneous nucleation run (Experiment 7) due to salt deposition. It was noticed that the surface thermocouples upstream of the bulk fluid thermocouple at the middle of the test section showed an increase in temperature w i t h an increase in pressure and fluid temperature of pre-heater 2 outlet. T h i s experiment was terminated when the pressure increased to 28.9 M P a after 55 minutes of operation w i t h salt solution. Pressure at the end of the test section remained constant during the run. T h e salt deposition-removal cycle at 15:32 & 15:44 are shown i n F i g . A . 8 . In b o t h the cycles, the surface thermocouples upstream of the 1.4 m location showed an increase in temperature w i t h an increase i n pre-heater 2 outlet temperature and pressure. T h e thermocouples measuring the fluid temperature at the middle of the test section and the later portion of the test section showed either the same temperature or reduced a bit until the plug was washed away. Thus the plug could possibly be due to the thermocouple protruding i n the fluid flow area, at  A.2. Homogeneous & heterogeneous nucleation unheated test section experiments 116 34.8 0.15 m top 0.96 m top  415  32.8  •N,+t+  + +  o o  130.8 CL  CD  3 405 i_  1  + + +A' +  H+  128.8 £ 3  CD  E  in 126.8 2  395  Q.  124.8 Pressure 385 11:15  22.8 11:25 J  11:20 Time  34.8 + o  1.5 m top 2.8 m top  > 32.8  +  O o 400  30.8  S.  CD  3  o  "S  o 4Wj  0  1—  28.8 £ 3  in in 26.8 2>  CD Q.  E I-  0.  24.8 — 390 11:15  1  11:20 Time  Pressure 22.8 11:25  F i g u r e A . 6 : Temperature and pressure behavior for the combined heterogeneous &; homogeneous nucleation run (Experiment 11) the middle of the test section, causing salt particle accumulation at this location. It was therefore decided to remove the bulk fluid thermocouple at the middle of the test section for the next experiment. T h e N a C 0 3 solubility under test section conditions was 0.02 wt.% and the salt concentration the effluent tank was 0.0817 wt.%. T h e ratio of effluent salt concentration to saturation limit was thus 4.2. T h e experiment was terminated after 55 minutes due to plugging. 2  A.2.2  Experiment: 10  T h i s experiment was carried out after removing the bulk fluid thermocouple at the middle of the test section. Other experimental conditions were kept the same as those  A.2. Homogeneous & heterogeneous nucleation unheated test section experiments 117  400  Time  F i g u r e A . 7 : Temperature and pressure behavior for the combined heterogeneous and homogeneous nucleation unheated test section run (Experiment 8) of Experiment 11, for comparison purposes. It was noticed that the bulk fluid thermocouple had actually been plugging the test section earlier and no major sign of plugging was noticed i n this experiment after running for 75 minutes. Salt concentration at the inlet of the test section was 0.1 wt.% and i n the effluent tank the concentration was 0.09 wt.%. Therefore almost all of the salt was flowing through the system. T h e saturation limit for the test section temperature was 0.018 wt.%. For the r u n i n which the test section is not heated the inner surface temperature was calculated as the average of the first few test section inner surface temperatures. T h e ratio of effluent salt concentration and saturation limit was 5 i.e., higher than Experiment 11. T h i s experiment has been discussed i n detail i n Section 5.3.3. It is worth mentioning that a relatively small pressure increase, at the test section inlet, was enough to remove the salt deposit in this experiment as shown i n F i g . 5.5. Therefore the bulk fluid temperature at pre-heater 2  A.3. Heterogeneous nucleation runs: Solubility type experiments 440 430  118  + 1.4 m bottom - PH-2 out  31.8 a c  <s>o *  o  29.8  <^ 420 CD  ! 410  S  h  (D  27.8 =j  | 400  \  *»  390 Pressure  380 15:30  440 430 O 0  S.  o  i  i  15:35  15:40  Time  1.9 m top PH-2 out  25.8  23.8 15:45  32 30 £  420  | 410 CD CL  E 400 390 380' 15:30  15:35  15:40 Time  F i g u r e A . 8 : Temperature and pressure behavior for the combined heterogeneous and homogeneous nucleation unheated test section run (Experiment 8) outlet d i d not increase much during the deposition process as observed i n Experiment 8 and the combined heterogeneous-homogeneous nucleation experiments. It can therefore be concluded that no major plug was occuring i n the test section, therefore the data was not analyzed to determine its location.  A.3  Heterogeneous nucleation runs: Solubility type experiments  The heat input to the test section i n these experiments was higher than the typical experiments carried out to determine the salt solubility. A l s o pure water was passed through the pre-heaters and salt solution was injected before the test section. How-  A.3. Heterogeneous nucleation runs: Solubility type experiments  119  ever, the bulk fluid temperature after mixing was such that the salt solution remained subsaturated.  A.3.1  Experiment: 9  The hot fluid bulk temperature at pre-heater 2 outlet was set such that no salt homogeneous nucleation occurred when salt solution was injected at the test section inlet. H i g h heat input (~7.5 k W ) to the test section was thus required to achieve supersaturation conditions within the test section length. Salt solution was injected at 11:12. N o cleaning cycles were observed (as seen i n the homogeneous case) and the test section temperature (& pressure) increased steadily along the test section as shown i n F i g . A . 9 . T h e pressure increased by about 172 k P a during the 40-minute run, which had to be terminated because of excessive surface temperature. A t some test section locations the surface temperature increased i n excess of 160°C, due to the salt deposit layer. T h e test section fluid outlet temperature d i d not increase much during this period. T h e conductivity was not constant and was around 380 /iS/cm most of the time ( N a C 0 3 concentration of 0.018 wt.%) which is also the saturation limit corresponding to the clean test section inner-surface temperature i.e., 397°C. Thus this r u n was almost like the solubility experiment. 2  28.5  ]27.5 CO Q_  26.5 2>  3 10  CD  25.5  24.5  F i g u r e A . 9 : Temperature and pressure behavior for the heterogeneous nucleation run (Experiment 9)  A.3. Heterogeneous nucleation runs: Solubility type experiments  A. 3.2  120  Experiment: 12  T h i s experiment was performed under conditions similar to E x p e r i m e n t 10 but w i t h a lower pre-heater 2 fluid exit temperature to ensure no homogeneous salt nucleation when salt solution was mixed i n supercritical water. A high heat input (~15 k W ) to the test section was thus required to achieve supersaturation i n the test section and to have bulk fluid test section outlet temperature the same as that in Experiment 10. T h e high heating resulted in a temperature difference of about 10°C, between the adjacent top and b o t t o m surface thermocouples. T h e experiment was therefore terminated and the data were not analyzed.  Appendix B SEM photographs of Na2CC>3 and Na2SC>4 deposits  121  B.l. NavCOs deposits  B.l  122  N a C 0 deposits 2  3  T a b l e B . l : S u m m a r y of N a C 0 3 pure crystalline deposit characteristics (Experiment SEM-4) Crystal Comments SEM Deposit Deposit length location thickness figure number (cm) (mm) (mm) B.1-B.4 0.008-0.3 crystals of various lengths 139 0.3 long and irregularly shaped crystals B.5-B.11 0.03-0.3 109 0.3 long and irregularly shaped crystals 79 0.36 0.01-0.36 B.12-B.15 crystals and needle shaped dendrites B.16-B.22 64 0.4 0.01-0.4 dense crystalline deposit B.13-B.24 0.36 49 dense deposits, non uniform thickB.25-B.27 0.1 19 ness 2  T a b l e B . 2 : S u m m a r y of N a C 0 combined crystalline and particulate deposit characteristics (Experiment S E M - 3 ) SEM Deposit Deposit Particle size Comments location thickness (mm) figure (cm) (mm) number irregularly shaped particles and B.28-B.37 154 0.7 0.005-0.01 crystals irregularly shaped salt particles B.38-B.44 139 0.59 crystals and particles 0.004-0.01 109 0.7 B.45-B.50 0.001-0.004 particles and long crystals 0.21 79 B.51-B.56 particles and long crystals B.57-B.62 0.001-0.015 49 0.1 2  3  123  B.l. Na^CO^ deposits  B.l.l  Na C0 crystalline scale 2  3  IP  •  Figure B . l :  SEM photograph of the N a C 0 deposition due to heterogeneous nucleation at 139 cm location (Experiment SEM-4) 2  F i g u r e B . 2 : SEM  3  photograph of the N a C 0 deposition due to heterogeneous nucleation at 139 cm location (Experiment SEM-4) 2  3  124  B.l. NaaCOz deposits  F i g u r e B.4: S E M photograph of the N a C 0 2  3  deposition due to heterogeneous nucle-  ation at 139 c m location (Experiment S E M - 4 )  B.l. Na^C0  3  125  deposits  F i g u r e B . 6 : S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 109 c m location (Experiment S E M - 4 ) 2  3  126  B.l. NaqCOs deposits  '  •  SF.  0  ,  WD34.6mm 2 0 . 0 k V  V  x880—  .  SOwn  F i g u r e B . 8 : S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 109 c m location (Experiment S E M - 4 ) 2  3  B.l. NaaCO  s  127  deposits  F i g u r e B.10: S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 109 c m location (Experiment S E M - 4 ) 2  3  B.l.  Na^CO?, deposits  128  F i g u r e B.12: S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 79 c m location (Experiment S E M - 4 ) 2  3  129  B.l. NaaCO?, deposits  F i g u r e B . 1 4 : SEM photograph of the N a C 0 deposition due to heterogeneous nu2  3  cleation at 79 cm location (Experiment SEM-4)  B.l. NaaC0  3  deposits  130  F i g u r e B . 1 6 : S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 64 c m location (Experiment S E M - 4 ) 2  3  131  B.l. N&2CO3 deposits  Figure B.17: SEM photograph of the N a C 0 deposition due to heterogeneous nucleation at 64 cm location (Experiment SEM-4) 2  3  WD35.7mm 2 0 , 0 k V x300  lOOum  Figure B.18: SEM photograph of the N a C 0 deposition due to heterogeneous nucleation at 64 cm location (Experiment SEM-4) 2  3  B.l. Nar,C0  3  132  deposits  F i g u r e B . 2 0 : S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 64 c m location (Experiment S E M - 4 ) 2  3  B.l. NaaCO  z  133  deposits  Figure  B.21: SEM photograph of the N a C 0 deposition due to heterogeneous nucleation at 64 cm location (Experiment SEM-4)  Figure  B.22: SEM photograph of the Na C03 deposition due to heterogeneous nucleation at 64 cm location (Experiment SEM-4)  2  2  3  B.l. NaqC0  3  deposits  134  F i g u r e B . 2 4 : S E M photograph of the Na2C03 deposition due to heterogeneous nucleation at 49 cm location (Experiment S E M - 4 )  135  B.l. Na^COs deposits  F i g u r e B . 2 6 : S E M photograph of the N a C 0 deposition due to heterogeneous nucleation at 19 c m location (Experiment S E M - 4 ) 2  3  B.l. Nar,C0 deposits  136  3  Figure  B.27: SEM photograph of the N a C 0 deposition due to heterogeneous nucleation at 19 cm location (Experiment SEM-4) 2  3  B.l. NaaCOz deposits  B.l.2  137  N a C 0 combined crystalline and particulate deposits 2  3  Figure B.28:  SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 154 cm location (Experiment SEM-3)  Figure B.29:  SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 154 cm location (Experiment SEM-3)  2  2  3  3  B.l. NaqC0  3  138  deposits  F i g u r e B . 3 1 : S E M photograph of the N a C 0 2  3  deposition due to combined homo-  geneous & heterogeneous nucleation at 154 cm location (Experiment SEM-3)  B.l.  Na^C0  3  139  deposits  F i g u r e B . 3 2 : S E M photograph of the N a C 0 2  3  deposition due to combined homo-  geneous & heterogeneous nucleation at 154 c m location (Experiment SEM-3)  F i g u r e B . 3 3 : S E M photograph of the N a C 0 2  3  deposition due to combined homo-  geneous & heterogeneous nucleation at 154 cm location (Experiment SEM-3)  B.l. NaaC0  3  deposits  140  F i g u r e B . 3 4 : S E M photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 154 c m location (Experiment SEM-3) 2  F i g u r e B.35: S E M photograph of the N a C 0 2  3  3  deposition due to combined homo-  geneous & heterogeneous nucleation at 154 cm location (Experiment  SEM-3)  141  B.l. Na^CCs deposits  Figure B.36: SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 154 cm location (Experiment SEM-3) 2  3  Figure B.37: SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 154 cm location (Experiment SEM-3) 2  3  142  B.l. Na^COz deposits  Figure B.38: SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 139 cm location (Experiment SEM-3) 2  3  •WB3b-.6sam S . OOkV  x40  Figure B.39: SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 139 cm location (Experiment SEM-3) 2  3  143  B.l. NaaCO?, deposits  W D 3 5 . 8mm  F i g u r e B . 4 0 : SEM  5 . 0 0 k V  x350,  lOOum  photograph of the Na C03 deposition due to combined homogeneous & heterogeneous nucleation at 139 cm location (Experiment SEM-3) 2  WD35.8mm  Figure B.41:  5.OOkV  x80  500um  SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 139 cm location (Experiment SEM-3) 2  3  144  B.l. NavCOz deposits  Figure B.42: SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 139 cm location (Experiment SEM-3) 2  SE  3  WD36.2mm 5. OOkV  x300  lOOum  Figure B.43: SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 139 cm location (Experiment SEM-3) 2  3  B.l. N&2CO?, deposits  SE  145  WD36.3mm  5.6okv"x80O ' 50wn  Figure B.44: SEM photograph of the Na C03 deposition due to combined homogeneous & heterogeneous nucleation at 139 cm location (Experiment SEM-3) 2  SE  WD36.7mm  5.o6kv'x30o'  "  lOOum  Figure B.45: SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 109 cm location (Experiment SEM-3) 2  3  146  B.l. Neu2C0 deposits 3  SE  Figure B.46:  5 . 0 0 k V * x 8 0 0  *  °50um*  SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 109 cm location (Experiment SEM-3) 2  SE  Figure B.47:  WD36.7mm  'S_  -  3  . x * W D 3 6 ..8mm  5 . bo'kV  xl20  300um  SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 109 cm location (Experiment SEM-3) 2  3  147  B.l. NaaCOj, deposits  V  SE  WD36.8rmti  5. O O k V  x300  TOOum  Figure B.48: SEM photograph of the Na C03 deposition due to combined homogeneous & heterogeneous nucleation at 109 cm location (Experiment SEM-3) 2  SE  WD36.9mm  5 . 0 0 k V  x800  50um  Figure B.49: SEM photograph of the Na C03 deposition due to combined homogeneous & heterogeneous nucleation at 109 cm location (Experiment SEM-3) 2  B . J . NaiCOz deposits  SE  148  WD36.8ram  F i g u r e B . 5 0 : SEM  b.OOKV  x5QQ  10 Gum  photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 109 cm location (Experiment SEM-3)  Figure B.51:  2  3  SEM photograph of the Na C03 deposition due to combined homogeneous & heterogeneous nucleation at 79 cm location (Experiment SEM3) 2  149  B.l. NaaCOz deposits  SE  TO37.5mm  S.OOkV x300  lOOum  Figure B.52: SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 79 cm location (Experiment SEM3) 2  3  Figure B.53: SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 79 cm location (Experiment SEM3) 2  3  B.l. NaaC0  3  deposits  150  Figure B.55: SEM photograph of the Na C03 deposition due to combined homogeneous & heterogeneous nucleation at 79 cm location (Experiment SEM3) 2  151  B.l. NavCOs deposits  Figure B.57: SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 49 cm location (Experiment SEM3) 2  3  152  B.l. NaaCOs deposits  SE  WD3b .'4m»  5 .OOkV  x30C  1 OQum  Figure B.58: SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 49 cm location (Experiment SEM2  3  3)  SE  WD35.6mm  5.Q0kV x800  50um  Figure B.59: SEM photograph of the N a C 0 deposition due to combined homogeneous & heterogeneous nucleation at 49 cm location (Experiment SEM2  3)  3  B.l.  NaQC0  3  deposits  153  Figure B.61: SEM photograph of the Na C03 deposition due to combined homogeneous & heterogeneous nucleation at 49 cm location (Experiment SEM2  3)  B.l. Neu2C0 deposits 3  154  B.2. N&2SO4 deposits  B.2  155  N a S 0 deposits 2  4  Table B.3: S u m m a r y of N a S 0 4 pure crystalline deposit characteristics (Experiment 2  SEM-7) Deposit location (cm) 154 B.63-B.65  SEM figure number  B.66-B.67 B.68-B.70 B.71-B.73 B.74-B.77 B.78-B.81  124 94 49 19 4  Deposit thickness (mm)  Crystal length (mm)  Comments  0.1  0.1  0.04 0.2 0.2 0.3 0.15  0.04  deposits of non uniform thickness and needle shaped dendrites dense deposits of non uniform thickness dense deposits of non uniform thickness dense deposits of non uniform thickness dense deposits of non uniform thickness dense deposits of non uniform thickness  Table B.4: S u m m a r y of N a S 0 combined crystalline and particulate deposit charac2  SEM figure number  4  teristics (Experiment S E M - 6 ) Deposit Deposit Particle location thickness size (mm) (cm) (mm)  B.82  154  B.83-B.85  79  1  Comments  hollow particles and dense crystalline deposit portions of deposits broken off from upstream location  B.2. NaaS0  4  B.2.1  deposits  Na2S0  Figure B.64:  4  156  crystalline scale  S E M photograph of the N a S 0 4 deposition due to heterogeneous nucleation at 154 c m location (Experiment S E M - 7 ) 2  B.2.  Nar>S0  4  157  deposits  Figure B.66: S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 124 c m location (Experiment S E M - 7 ) 2  4  B.2. NaqS04 deposits  Figure B.68:  158  SEM photograph of the Na2SC>4 deposition due to heterogeneous nucleation at 94 cm location (Experiment SEM-7)  B.2. NaaS0  4  deposits  159  F i g u r e B . 7 0 : S E M photograph of the Na2S04 deposition due to heterogeneous nucleation at 94 cm location (Experiment S E M - 7 )  B.2. NaaS0  4  160  deposits  Figure B.72: SEM photograph of the Na2S0 deposition due to heterogeneous nucleation at 49 cm location (Experiment SEM-7) 4  B.2.  NSQSOA  161  deposits  Figure B.74: SEM photograph of the N a S 0 deposition due to heterogeneous nucleation at 19 cm location (Experiment SEM-7) 2  4  162  B.2. NaqSOi deposits  F i g u r e B . 7 6 : S E M photograph of the Na S04 deposition due to heterogeneous nucleation at 19 c m location (Experiment S E M - 7 ) 2  163  B.2. NavSOt deposits  Figure B.77:  SEM photograph of the N a S 0 deposition due to heterogeneous nucleation at 19 cm location (Experiment SEM-7)  Figure B.78:  SEM photograph of the N a S 0 deposition due to heterogeneous nucleation at 4 cm location (Experiment SEM-7)  2  2  4  4  B.2. NavSO deposits  164  A  F i g u r e B . 8 0 : S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 4 c m location (Experiment S E M - 7 ) 2  4  B.2. Ne^SO^ deposits  165  F i g u r e B . 8 1 : S E M photograph of the N a S 0 deposition due to heterogeneous nucleation at 4 c m location (Experiment S E M - 7 ) 2  4  B.2. NavSO  A  B.2.2  deposits  Na2SC>4  166  combined crystalline and particulate deposits  Figure B.82: SEM photograph of the Na S0 deposition due to combined homogeneous & heterogeneous nucleation at 154 cm location (Experiment 2  4  SEM-6)  Figure B.83: SEM photograph of the Na S04 deposition due to combined homogeneous & heterogeneous nucleation at 79 cm location (Experiment SEM2  Figure B.85: SEM photograph of the N a S 0 deposition due to combined homogeneous & heterogeneous nucleation at 79 cm location (Experiment SEM2  6)  4  Appendix C Computer Codes Na2C03 solubility codes  c.i C.l.l  M a i n Code: mol.m  clear '/this program c a l c u l a t e s the s o l u b i l i t y f o r a c a l c u l a t e d b u l k f l u i d temperature, '/.using the expt. s o l u b i l i t y data at w a l l c o n d i t i o n s . I t uses t h e MOLCALC and .. '/ LOOKUP f i l e s . Pressure=25; '/pressure i n MPa Tb=391.9+273;'/Bulk Temperature at t e s t s e c t i o n i n l e t i n K Q=22.4;'/Heat input i n kW/m2 m=0.0116; /flow r a t e i n kg/s D=0.0062; '/tube diameter i n m ,  moldia=5.1E-10;'/molecular d i a i n m, f o r sodium carbonate rhos=2530;°/salt d e n s i t y i n kg/m3 Tw=Tb+.5;°/ guessed w a l l temperature DZ=0.05;'/segment l e n g t h i n m [rhob,rhow,Hb,Hw,Cpb,Cpw,viscb,viscw,Kb,Kw,Prb,Prw,Reb,Rew]=... molcalc(Pressure,Tb,Tw,Q,m,D,moldia,rhos,DZ);  Subroutine: molcalc.m function  [rhob,rhow,Hb,Hw,Cpb,Cpw,viscb,viscw,Kb,Kw,Prb,Prw,Reb,Rew]...  =molcalc(Pressure,Tb,Tw,Q,m,D,moldia,rhos,DZ); length=0; '/load a l l t h e p r o p e r t y  tables  l o a d dens.txt; l o a d K.txt; load cp.txt; load enth.txt; load prand.txt; load v i s . t x t ; '/, get f i l e s i z e s from dens, but other f i l e s must have same s i z e [nT,nP]=size(dens); '/ the f i r s t row c o n t a i n s the p r e s s u r e s i n MPa  168  C.l. Na-iCOz solubility codes P=dens(l,2:nP); '/, the f i r s t column contains the Temperatures i n K T=dens(2:nT,l); A=cp(2:nT,2:nP); Cp=interp2(P,T,A,Pressure,T); [Tsort,i]=sort(T); Cpsort=Cp(i); [maxCp,imax]=max(Cp); Tpc=T(imax) A=prand(2:nT,2:nP); Pr=interp2(P,T,A,Pressure,T); Prpc=Pr(imax); A=dens(2:nT,2:nP); rhob=interp2(P,T,A,Pressure,Tb); CB=.04; CW=CB; '/.number of segments NZ=3/DZ; for j=l:NZ '/, other than the f i r s t rows and columns, we have actual property values A=dens(2:nT,2:nP); rhob=interp2(P,T,A,Pressure,Tb); A=K(2:nT,2:nP); Kb=interp2(P,T,A,Pressure,Tb); A=enth(2:nT,2:nP); Hb=interp2(P,T,A,Pressure,Tb); A=cp(2:nT,2:nP); Cpb=interp2(P,T,A,Pressure,Tb); A=vis(2:nT,2:nP); viscb=interp2(P,T,A,Pressure,Tb); A=prand(2:nT,2:nP); Prb=interp2(P,T,A,Pressure,Tb); A=vis(2:nT,2:nP); viscb=interp2(P,T,A,Pressure,Tb); Reb=4*m/(pi*D*viscb); '/.Fluid properties at wall °/,Guess wall temperature for i=l:10 A=dens(2:nT,2:nP); rhow=interp2(P,T,A,Pressure,Tw); A=K(2:nT,2:nP); Kw=interp2(P,T,A,Pressure,Tw); A=enth(2:nT,2:nP); Hw=interp2(P,T,A,Pressure,Tw); A=cp(2:nT,2:nP); Cpw=interp2(P,T,A,Pressure,Tw); A=vis(2:nT,2:nP); viscw=interp2(P,T,A,Pressure,Tw); A=prand(2:nT,2:nP); Prw=interp2(P,T,A,Pressure,Tw); Rew=4*m/(pi*D*viscw);  C . J . N&2CO3 solubility codes  170  °/,Nusselt number from Swenson c o r r e l a t i o n °/,Nu=0.00459* (Rew) "0.923*((Hw-Hb) *viscw/ ((Tw-Tb) *Kw)) "0.613* (rhow/(rhob)) "0.231; 7, Calculation of Nusselt number from Yamagata c o r r e l a t i o n . E=(Tpc-Tb)/(Tw-Tb); i f E>1 Fc=l; else i f E<0 n2=l.44*(1+1/Prpc)-0.53; Fc=((Hb-Hw)/(Tb-Tw)/Cpb)~n2; else nl=-.77*(l+l/Prpc)+1.49; Fc=0.67*Prpc"(-.05)*((Hb-Hw)/(Tb-Tw)/Cpb)~nl; end end Nu=0.0135*Reb~.85*Prb~.8*Fc; Tw=Tb+Q*D/(Nu*Kw)*1000; end Tw; Tb; [CW]= lookup(rhow); [Cl]=lookup(rhob); Rew; Nu; Prw; Reb=4*m/(pi*D*viscb); kviscw=viscw/rhow; kviscb=viscb/rhob; diff=1.38e-23*(Tw)*1/(3*pi*viscb*moldia); Sc=kviscw/diff; h=Nu*(Kb)/D; Le=Sc/Prw; '/, Le"0.387 f o r Swenson c o r r e l a t i o n and Le"0.2 f o r Yamagata c o r r e l a t i o n •/.Hm=h/(rhow*Cpw*Le~0.387); Hm=h/(rhow*Cpw*Le~0.2); Flowmass=Hm*DZ*pi*D*rhow*(CB-CW)/100; DIFF=Flowmass/m*100; length=length+DZ; results(j,l)=length; results(j,2)=Tb-273; results(j,3)=Tw-273; results(j,4)=CB; results(j,5)=CW; results(j,6)=DIFF; results(j,7)=C1; save c:\matlabrll\work\results.txt r e s u l t s - a s c i i figure(1) hold on plot(Tb-273,results(j,4),'k.',Tb-273,results(j,5),'k+',Tb-273,results(j,7),'k*') t i t l e ( [ ' P = ',num2str(Pressure),' MPa',', Q= ',num2str(Q),' kW/m"2',', m= .. num2str(m),' kg/s'],'Fontsize',12)  C.l. Na CC>3 solubility codes 2  171  legendCCB, wt'/„','CW (SAT), vt'/.',' CB(SAT), wt'/.') xlabeK['Bulk f l u i d temperature (C)'], 'FontSize', 16) '/.calculate the bulk f l u i d temperature and s o l u b i l i t y f o r the next step Tb=Tb+Q*1000*pi*D*DZ/(m*Cpb); CB=CB-Flowmass/m*100; Tw; end load r e s u l t s . t x t aveTw=mean(results(1:NZ,3)) '/.figure (2) '/.hold on '/.plot(resuits(DZ:DZ:NZ,l) ,results(DZ:DZ:NZ,4) ,results(DZ:DZ:NZ, 1),results(DZ:DZ: . . . 7. NZ.5)) '/.legend(' CB, vt'/.' ,'CSATW, wt'/.')  '/.xlabeK ['length  along TS (m)'], 'FontSize', 12)  Subroutine: lookup.m '/.this f i l e can be used to calculate the s o l u b i l i t y at a given density function [C]= lookup(rho) '/.load the s o l u b i l i t y table load s o l s o r t 2 . t x t ; [nA.nB]=size(solsort2); •/. the second column contains the wt'/, Y=solsort2(l:nA,2); '/, the f i r s t column contains the density i n kg/m3 X=solsort2(l:nA,l); C=interpl(X,Y,rho);  Figure Code: graphNa2C03.m clear '/, This program graphs the Na2C03 s o l u b i l i t y vs density and temperature. ... '/. I t uses finddens.txt '/, and solsortnew.txt f i l e s . load s o l s o r t . t x t ; load solsortnew.txt; nT=20; nP=20; '/, the f i r s t column contains the Temperatures i n C T=solsortnew(l:nT,1); '/, we measure gauge pressure from the transducer and the tables. . . '/are i n absolute pressure i . e , a d i f f of 0.1 MPa P=solsortnew(1:nT,3)+0.1; [rho]=finddens(P,T+273.15); '/, info f o r error bars Pnew=solsortnew(5:18,3)+0.1; Tlow=solsortnew(5:18,4); Thigh=solsortnew(5:18,5); wt=solsortnew(5:18,2) ;  C.l. Na CC>3 solubility codes 2  [Dlow]=f inddens(Pnew,Tlow+273.15); [Dhigh]=finddens(Pnew,Thigh+273.15); wtl=solsortnew(l:4,2); wt2=solsortnew(5:7,2); wt3=solsortnew(8:9,2); wt4=solsortnew(10,2); wt5=solsortnew(ll:12,2); wt6=solsortnew(13,2); wt5new=solsort(14:18,2); wt7=solsortnew(19:20,2); density=rho; figure(l) semilogy(T(l:4),wtl,'k+', T(5:7),wt2,'k*', T(8:9), wt3, 'ko', T(10),wt4... ,'ks',T(11:12),wt5,'kp', T(13),wt6, 'k<>,T(19:20),wt7, 'kx',T(14:18),... wt5new,'kp',Tlow(l:14),wt(l:14), 'k.',Thigh(l:14),wt(l:14),'k.') hold on semilogyOTlowU) : .l:Thigh(l) , wt(l), >k-',Tlow(2): .l:Thigh(2), wt(2),'k-',... Tlow(3):.l:Thigh(3), wt(3),'k-',Tlow(4):.l:Thigh(4), wt(4),'k-',... Tlow(5):.l:Thigh(5), wt(5),'k-',Tlow(6):.1:Thigh(6), wt(6),'k->,... 'LineWidth', 1) hold on semilogy(Tlow(7):.l:Thigh(7), wt(7),'k-',Tlow(8):.l:Thigh(8), wt(8),'k-',... Tlow(9):.l:Thigh(9), wt(9),'k-',Tlow(10):.l:Thigh(10), wt(10),'k-',... T l o w ( l l ) : . l : T h i g h ( l l ) , wt(ll),'k->,Tlow(12):.l:Thigh(12), wt(12),'k-',... 'LineWidth', 1) hold on semilogy(Tlow(13):.l:Thigh(13), wt(13),'k-',Tlow(14):.l:Thigh(14), ... wt(14),'k-','LineWidth', 1) t i t l e ( [ ' F i g . 5: Sodium carbonate s o l u b i l i t y vs temperature'],'Fontsize',16) '/.axis( [0.006 0.05 0.005 0.68]) legendCRef. 7 (24.5 MPa)', 'C2-C4', 'C5-C6','C7',. . . 'C8-C14', 'CI', 'Ref. 6 (24.1 MPa)') xlabeK['temperature (~oC)'],'FontSize',14) y l a b e l ( [ ' S o l u b i l i t y l i m i t (wt '/.)'] , 'FontSize', 14) hold off x=rho; y=solsortnew(1:20,2); wtnew=solsort(5:18,2); xnew=x; ynew=log(y); pl=polyfit(xnew,ynew,3); xnew=x(l):-10:100; fl=polyval(pl,xnew); fl=exp(f1); '/,plot(x,y, 'o' ,x,f,'-' ,xnew,f 1,'-') '/.set (gca,' XDir',' reverse' ,' YDir',' normal'); figure(2) '/.hold on semilogy(rho(l:4),wtl,'k+', rho(5:7),wt2,'k*', rho(8:9),... wt3, 'ko', rho(10),wt4,'ks',rho(ll:12),wt5,... 'kp', rho(13),wt6, 'k<',rho(19:20),wt7, 'kx',xnew,f1,'k-',...  172  C.2. NaqSOi solubility codes rho(14:18),wt5new,'kp',Dlow(l:14),... wt(l:14),'k.',Dhigh(l:14),wt(l:14),'k.') set(gca,'XDir','reverse','YDir','normal'); Dhigh(l) Dlow(l) wt(l) hold on semilogy(Dhigh(l):l:Dlow(l), wt(l),'k-',Dhigh(2):l:Dlow(2), wt(2),'k-',. Dhigh(3):l:Dlow(3), wt(3),'k-',Dhigh(4):1:Dlow(4), wt(4),'k-',... Dhigh(5):l:Dlow(5), wt(5),... 'k-',Dhigh(6):l:Dlow(6), wt(6),'k-','LineWidth', 1) hold on semilogy(Dhigh(7):l:Dlow(7), wt(7),'k-',Dhigh(8):l:Dlow(8), wt(8),'k-',. DhighO) :l:Dlow(9), wt(9), 'k-',Dhigh(10):1:Dlow(10), wt(10), 'k-', . . . D h i g h ( l l ) : l : D l o w ( l l ) , wt(ll),'k-',Dhigh(12):1:Dlow(12), wt(12),'k-',... 'LineWidth', 1) hold on semilogy(Dhigh(13):l:Dlow(13), wt(13),'k-',Dhigh(14):1:Dlow(14), wt(14), •k-','LineWidth', 1) hold on t i t l e ( [ ' F i g . 6: Sodium carbonate s o l u b i l i t y vs density'],'Fontsize',16) '/.axis( [0.006 0.05 0.005 0.68]) legendCRef. 7 (24.5 MPa)', 'C2-C4', 'C5-C6','C7', 'C8-C14', 'CI', ... 'Ref. 6 (24.1 MPa)', 'Eq. 7 (curve f i t ) ' ) xlabel(['density (kg/m~3)'],'FontSize',14) y l a b e K [ ' S o l u b i l i t y l i m i t (wt '/.)'],'FontSize', 14)  C.2 C.2.1  Na S04 solubility codes 2  Main Code: molNa2S04.m  clear '/.this program calculates the s o l u b i l i t y f o r a calculated bulk f l u i d '/.temperature using the expt. s o l u b i l i t y data at wall conditions. '/.It uses the M0LCALCS04 and L00KUPS04 f i l e s . Pressure=24.4;'/.pressure i n MPa Tb=379.6+273;Bulk Temperature at test section i n l e t i n K Q=43.3;'/,Heat input i n kW/m2 m=0.011; '/.flow rate i n kg/s D=0.0062;'/.tube diameter i n m '/.molecular d i a i n m, 5.1E-10 f o r sod. carb. and 5.27E-10 f o r sod. s u l f a t '/,moldia=5.1E-10; moldia=5.27E-10; rhos=2530;°/,salt density i n kg/m3 Tw=Tb+.5;7, guessed wall temperature DZ=0.05;'/.segment length i n m [rhob,rhow,Hb,Hw,Cpb,Cpw,viscb,viscw,Kb,Kw,Prb,Prw,Reb,Rew]=molcalcS04.. (Pressure,Tb,Tw,Q,m,D,moldia,rhos,DZ);  C.2. Na^SO^ solubility codes  Subroutine: molcalcS04.m function [rhob,rhow,Hb,Hw,Cpb,Cpw,viscb,viscw,Kb,Kw,Prb,Prw,Reb,Rew]... =molcalc(Pressure,Tb,Tw,Q,m,D,moldia,rhos,DZ); length=0; '/.load a l l the p r o p e r t y t a b l e s '/.all must have the same s i z e and the same T,P s p a c i n g l o a d dens.txt; load K.txt; load cp.txt; load enth.txt; load prand.txt; load v i s . t x t ; '/, get f i l e s i z e s from dens, but other f i l e s must have same s i z e [nT,nP]=size(dens); '/, the f i r s t row c o n t a i n s the p r e s s u r e s i n MPa P=dens(l,2:nP); '/, the f i r s t column c o n t a i n s the Temperatures i n K T=dens(2:nT,l); A=cp(2:nT,2:nP); Cp=interp2(P,T,A,Pressure,T); [Tsort,i]=sort(T); Cpsort=Cp(i); [maxCp,imax]=max(Cp); Tpc=T(imax) A=prand(2:nT,2:nP); Pr=interp2(P,T,A,Pressure,T); Prpc=Pr(imax); A=dens(2:nT,2:nP); rhob=interp2(P,T,A,Pressure,Tb); CB=.27; CW=CB; "/.number of segments NZ=3/DZ; f o r j=l:NZ '/, other than the f i r s t A=dens(2:nT,2:nP);  rows and columns, we have a c t u a l p r o p e r t y v a l u e s  rhob=interp2(P,T,A,Pressure,Tb); A=K(2:nT,2:nP); Kb=interp2(P,T,A,Pressure,Tb); A=enth(2:nT,2:nP); Hb=interp2(P,T,A,Pressure,Tb); A=cp(2:nT,2:nP); Cpb=interp2(P,T,A,Pressure,Tb); A=vis(2:nT,2:nP); viscb=interp2(P,T,A,Pressure,Tb); A=prand(2:nT,2:nP); Prb=interp2(P,T,A,Pressure,Tb); A=vis(2:nT,2:nP); viscb=interp2(P,T,A,Pressure,Tb); Reb=4*m/(pi*D*viscb);  C.2. Na^SO^ solubility codes '/.Fluid properties at wall '/.Guess wall temperature for i=l:5 A=dens(2:nT,2:nP); rhow=interp2(P,T,A,Pressure,Tw); A=K(2:nT,2:nP); Kw=interp2(P,T,A,Pressure,Tw); A=enth(2:nT,2:nP); Hw=interp2(P,T,A,Pressure,Tw); A=cp(2:nT,2:nP); Cpw=interp2(P,T,A,Pressure,Tw); A=vis(2:nT,2:nP); viscw=interp2(P,T,A,Pressure,Tw); A=prand(2:nT,2:nP); Prw=interp2(P,T,A,Pressure,Tw); Rew=4*m/(pi*D*viscw); '/.Nusselt number from Swenson correlation •/.Nu=0.00459* (Rew) "0.923* ((Hw-Hb) *viscw/ ((Tw-Tb) *Kw)) "0.613* (rhow/ (rhob). 51) "0.231; '/. Calculation of Nusselt Number from Yamagata c o r r e l a t i o n . E=(Tpc-Tb)/(Tw-Tb); i f E>1 Fc=l; else i f E<0 n2=l.44*(1+1/Prpc)-0.53; Fc=((Hb-Hw)/(Tb-Tw)/Cpb)~n2; else nl=-.77*(l+l/Prpc)+1.49; Fc=0.67*Prpc*(-.05)*((Hb-Hw)/(Tb-Tw)/Cpb)"nl; end end Nu=0.0135*Reb*.85*Prb".8*Fc; Tw=Tb+Q*D/(Nu*Kw)*1000; end Tw; [CW]= lookupS04(rhow); [Cl]=lookupS04(rhob); Rew; Nu; Prw; Reb=4*m/(pi*D*viscb); kviscw=viscw/rhow; kviscb=viscb/rhob; diff=1.38e-23*(Tw)*1/(3*pi*viscb*moldia); Sc=kviscw/diff; h=Nu*(Kb)/D; Le=Sc/Prw; 7. f o r Swenson Le~0.387 '/.Hm=h/(rhow*Cpw*Le-0.387); 7. f o r Yamagata Le'0.2  C.2. Na2S0 solubility codes 4  176  Hm=h/(rhow*Cpw*Le~0. 2); Flowmass=Hm*DZ*pi*D*rhow*(CB-CW)/lOO; DIFF=Flowmass/m*100; length=length+DZ; resultsS04(j,l)=length; resultsS04(j,2)=Tb-273; resultsS04(j,3)=Tw-273; resultsS04(j,4)=CB; resultsS04(j,5)=CW; resultsSD4(j,6)=DIFF; resultsS04(j,7)=C1; save c:\matlabrll\work\resultsS04.txt resultsS04 - a s c i i figure(1) hold on plot(Tb-273,resultsS04(j,4),'k.',Tb-273,resultsS04(j,5),'k+',Tb-273,... resultsS04(j,7),'k*') title(['P= ',num2str(Pressure),' MPa',', Q= ',num2str(Q),' kW/nT2',>, m= num2str(m),' kg/s'],'Fontsize',12) legend('C_B, (wt'/)', 'C_{W(SAT)>, (wt'/)' , 'C_{B(SAT)>, (wt'/)') '/title(['Fig. 4: Modeled salt concentration along test section for run "S6"'],... '/'Fontsize' ,14) xlabel(['bulk fluid temperature (*oC)'], 'FontSize', 14) ylabeK ['salt concentration (wt. 7,)'], 'FontSize', 14) '/calculate the bulk fluid temperature and solubility for the next step Tb=Tb+Q*1000*pi*D*DZ/(m*Cpb); CB=CB-Flowmass/m*100; Tw; end load resultsS04.txt aveTw=mean(resultsS04(1:NZ,3)) '/figure (2) '/hold on */plot(resultsS04(DZ:DZ:NZ,l),resultsS04(DZ:DZ:NZ,4),resultsS04(DZ:DZ:NZ,1),... '/. resultsS04(DZ:DZ:NZ,5)) '/legend (' CB, wt'/' ,' CSATW, wt'/') '/xlabeK ['length along TS (m)'], 'FontSize', 12)  Subroutine: lookupS04.m '/this f i l e can be used to calculate the s o l u b i l i t y at a given density function [C]= lookupS04(rho) '/load the s o l u b i l i t y table load solsortS04.txt; [nA,nB]=size(solsortS04); '/ the second column contains the wt'/ Y=solsortSD4(l:nA,2); '/ the f i r s t column contains the density i n kg/m3 X=solsortS04(l:nA,l); C=interpl(X,Y,rho);  C.2. JVa S04 solubility codes 2  Figure Code: graphNa2S04 clear '/.function [CSATW.rhow]= graph(CSATW.rhow) '/.load a l l the property tables '/.all must have the same size and the same T,P spacing load paulsdata.txt; load May242002.txt; load May242002new.txt; load Shvtre.txt; '/, get f i l e sizes from dens, but other f i l e s must have same size [nT,nP]=size(paulsdata); '/.the f i r s t row contains the pressures i n MPa PPaul=paulsdata(l:nT,2)+0.1; TPaul=paulsdata(l:nT,l); wtPaul=paulsdata(l:nT,3); '/, we measure gauge pressure from the transducer and the tables '/.are i n absolute pressure i . e , a d i f f of 0.1 MPa PMay=May242002(1:6,2)+0.1; TMay=May242002(1:6,1); wtMay=May242002(l:6,3); Tlow=May242002(1:6,4); Thigh=May242002(1:6,5); [rholow]=finddens(PMay,Tlow+273.15) ; [rhohigh]=finddens(PMay,Thigh+273.15); '/.Shvedov and Tremaine model (1997) rhomod=Shvtre(1:15,1); Wtmod=Shvtre(1:15,2); Tmod=Shvtre(l:15,3); [rhoPaul]=finddens(PPaul,TPaul+273.15); [rhoMay]=finddens(PMay,TMay+273.15); PMayl=May242002new(1:12,2)+0.1; TMayl=May242002new(l:12,l); wtMayl=May242002new(l:12,3); [rhoMayl]=finddens(PMayl,TMay1+273.15); xnew=rhoMayl(1:12); ynew=log(wtMayl) ; pl=polyfit(xnew,ynew,2); xnew=xnew(l):-10:80; fl=polyval(pl,xnew); fl=exp(f1); figure(1) '/.hold on semilogy(TPaul(1:22),wtPaul(1:22),'k+', TMay(1:6),wtMay(1:6),'kx',Tmod(1:15), Wtmod(l:15),'k-',500,le-4,'k*',Tlow(l:6),wtMay(1:6),'k.',Thigh(l:6),... wtMay(l:6),'k.','MarkerSize',7) hold on semilogy(Tlow(l):0.1:Thigh(l), wtMay(l),'k-', Tlow(2):0.1:Thigh(2), wtMay(2). ,'k-',Tlow(3):0.1:Thigh(3), wtMay(3),'k-', Tlow(4):0.1:Thigh(4), ... wtMay(4),'k-',Tlow(5):0.1:Thigh(5), wtMay(5),'k-', Tlow(6):0.1:Thigh(6),.. wtMay(6),'k-','LineWidth',1)  C.3. Figure Code: Na^C03-Na>2S04 mixture (graphmixture.m)  178  '/.errorbar (T(1),wt 1,0.005,0.019) t i t l e ( [ ' F i g . 7: Sodium sulfate s o l u b i l i t y vs temperature'],'Fontsize16) •/.axis([0.006 0.05 0.005 0.68]) •/.legend('Rogak and Teshima corrected data, 1999 (25 MPa)', 'May 24, 2002 . . . 7.(24.3-24.6 MPa)' '/,,'Shvedov and Tremaine, 2000 (25 MPa)','Armellini and Tester, 1993 (25 MPa)') legend('Ref. 4 corrected data (25 MPa)', 'S1-S6','Ref. 5 (25 MPa)','Ref. 3 . . . 7.(25 MPa)') xlabel(['temperature (~oC)'],'FontSize',14) ylabeK ['Solubility l i m i t (wt7.)'],'FontSize', 14) figure(2) '/.hold on °/.set(gca, 'XDir' , 'reverse' , ' Y D i r ' , 'reverse'); semilogy(rhoPaul(l:22),wtPaul(l:22),'k+', rhoMay(l:6),wtMay(l:6),'kx'... ,rhomod(l:15),Wtmod(l:15),'k-',89.74,le-4,>k"',xnew,f1,'k-.',rholow(l:6)... ,wtMay(l:6),'k.',rhohigh(l:6),wtMay(l:6),'k.','MarkerSize',7) set(gca,'XDir','reverse','YDir','normal'); '/.errorbar (rho (1) , wt 1,0.005,0.019) hold on semilogy(rhohigh(l):1:rholow(l), wtMay(l),'k-', rhohigh(2):1:rholow(2), . . . wtMay(2),'k-',rhohigh(3):l:rholow(3), wtMay(3),'k-', rhohigh(4):l:rholow(4)... , wtMay(4),'k-',rhohigh(5):l:rholow(5), wtMay(5),'k-', rhohigh(6):l:rholow... (6), wtMay(6),'k-','LineWidth',1) t i t l e ( [ ' F i g . 8: Sodium sulfate s o l u b i l i t y vs density'],'Fontsize',16) '/.axis([0.006 0.05 0.005 0.68]) legend('Ref. 4 corrected data (25 MPa)', 'S1-S6','Ref. 5 (25 MPa)','Ref 3 (25 MPa)','Eq. 8 (curve f i t ) ' ) •/.legend('Rogak and Teshima corrected data, 1999 (25 MPa)', 'May 24, 2002 •/.(24.3-24.6 MPa)' ,'Shvedov and Tremaine, 2000 (25 MPa)','Armellini and Tester, •/.1993 (25 MPa)','2nd order f i t t e d polynomial') xlabeK['density (kg/m"3)'],'FontSize',14) ylabeK ['Solubility l i m i t (wt'/.)'],'FontSize', 14)  C.3  F i g u r e C o d e : N a 2 C 0 - N a S 0 4 m i x t u r e (graphmixture.m) 3  2  clear load mixturesol.txt; load May242002new.txt; load solsortnew.txt; [nT.nP]=size(mixturesol); '/, we measure gauge pressure from the transducer and . . . '/, the tables are i n absolute pressure i . e , a difference P=mixturesol(1:nT,2)+0.1; T=mixturesol(1:nT,1); wtna2co3=mixturesol(1:nT,3); wtna2so4=mixturesol(1:nT,4); Tlow=mixturesol(l:13,5);  of 0.1 MPa  C.3. Figure Code: Na^COz-NaqSO^  mixture (graphmixture.m)  Thigh=mixturesol(l:13,6); [rholow]=finddens(P,Tlow+273.15); [rhohigh]=finddens(P,Thigh+273.15); [rho]=finddens(P,T+273.15); PMayl=May242002new(2:12,2)+0.1; TMayl=May242002new(2:12,l); wtMayl=May242002new(2:12,3); [rhoMayl]=finddens(PMay1,TMay1+273.15); xnew=rhoMayl; ynew=log(wtMay1); pl=polyfit(xnew,ynew,2); xnew=xnew(l):-10:80; fl=polyval(pl,xnew); fl=exp(f1); PC03=solsortnew(1:20,3)+0.1; TC03=solsortnew(l:20,l); [DC03]=f inddens(PC03,TC03+273.15); xc=DC03; °/.xc=solsort (1:20,3) ; /.yc=solsort (1:20,2); yc=solsortnew(l:20,2); xnewc=xc; ynewc=log(yc); p2=polyfit(xnewc,ynewc,3); xnewc=xnew(l):-10:80; f2=polyval(p2,xnewc); f2=exp(f2); •/.figure (1) •/.hold on y „ s e m i l o g y ( T ( l ) , w t n a 2 c o 3 ( l ) , ' k + ' , T(2:3),wtna2co3(2:3),'kx',T(4:6).... */. wtna2co3(4:6), 'k*',T(7:8) ,wtna2co3(7:8), 'kp' ,T(1) ,wtna2so4(l), 'ko' '/. T(2:3) ,wtna2so4(2:3) , 'ks' ,T(4:6) ,wtna2so4(4: 6) , 'k~' ,T(7:8) ,wtna2so4(7:8) '/. , 'kv' ,Tlow(l:8) ,wtna2so4(l:8), ' k . ' ,Thigh(l:8) ,wtna2so4(l :8) , ' k . ' , . . . 7. Tlow(l:8),wtna2co3(l:8),'k.',Thigh(l:8),wtna2co3(l:8),'k.') '/.errorbar (T(1),wt 1,0.005,0.019) '/.title(['Fig. 9: S o l u b i l i t y of mixture of sodium carbonate and sodium... '/„ sulfate'] ,'Fontsize',15) '/.axis([0.006 0.05 0.005 0.68]) •/.legendCNa_2C0_3, Aug07, 2002', 'Na_2C0_3, Aug08, 2002','Na_2C0_3,. . . •/. Augl4, 2002','Na_2C0_3, Augl6, 2002', 'Na_2S0_4, Aug07, 2002', . . . •/. 'Na_2S0_4, Aug08, 2002','Na_2S0_4, Augl4, 2002','Na_2S0_4, Augl6, 2002') '/.xlabeK ['temperature (~oC) '] , 'FontSize', 14) •/.ylabel ( [' S o l u b i l i t y l i m i t (wt*/,) ' ] , ' FontSize', 14) figure(2) '/.hold on '/,set(gca, ' X D i r ' , 'reverse', ' Y D i r ' , 'reverse'); semilogy(rho(1),wtna2co3(l),'k+', rho(3),wtna2co3(3),'kx',rho(4:6)... ,wtna2co3(4:6),'k*',rho(7:8),wtna2co3(7:8),'kp',rho(9:13),wtna2co3(9:13) ,'kh',xnewc,f2,'k-',rho(l),wtna2so4(l),'ko', r h o ( 2 : 3 ) . . . . wtna2so4(2:3),'ks',rho(4:6),wtna2so4(4:6),'k~',rho(7:8),wtna2so4(7:8),. 'kv',rho(9:13),wtna2so4(9:13),'kd',xnew,f1,'k-.',rholow(l:13).... 5  C.3. Figure Code: Na^COz-Na^SOi  mixture (graphmixture.m)  wtna2so4(l:13),'k.',rhohigh(l:13),wtna2so4(l:13),'k.',rholow(l)... ,wtna2co3(l),'k.',rholow(3:13),wtna2co3(3:13),'k.') hold on semilogy(rhohigh(l),wtna2co3(l),'k.',rhohigh(3:13),wtna2co3(3:13),'k.'); hold on semilogy(rhohigh(l):1:rholow(l), wtna2so4(l), 'k-',rhohigh(2):l:rholow(2)... , wtna2so4(2),'k-',rhohigh(3):l:rholow(3), wtna2so4(3),'k-',rhohigh(4)... :l:rholow(4), wtna2so4(4), 'k-',rhohigh(5):1:rholow(5), wtna2so4(5),... 'k-',rhohigh(6):l:rholow(6), wtna2so4(6),'k-','LineWidth', 1) hold on semilogy(rhohigh(7):l:rholow(7), wtna2so4(7),'k-',rhohigh(8):l:rholow(8)... , wtna2so4(8),'k-',rhohigh(9):1:rholow(9), wtna2so4(9),'k-'.rhohigh... (10):l:rholow(10), wtna2so4(10),'k-',rhohigh(11):1:rholow(ll), . . . wtna2so4(ll),'k-',rhohigh(12):1:rholow(12), wtna2so4(12),'k-',... rhohigh(13):1:rholow(13), wtna2so4(13),'k-','LineWidth', 1) hold on semilogy(rhohigh(l):l:rholow(l), w tn a 2 co 3 (l), 'k -', . . . rhohigh(3):l:rholow(3), wtna2co3(3),'k-'.rhohigh(4):l:rholow(4), . . . wtna2co3(4),'k-'.rhohigh(5):l:rholow(5), wtna2co3(5).... 'k-',rhohigh(6):l:rholow(6), wtna2co3(6),'k-','LineWidth', 1) hold on semilogy(rhohigh(7):l:rholow(7), wtna2co3(7),'k-',rhohigh(8):l:rholow(8)... , wtna2co3(8),'k-',rhohigh(9):l:rholow(9), wtna2co3(9),'k-',rhohigh(10)... :l:rholow(10), wtna2co3(10),'k-'.rhohigh(ll):l:rholow(ll), wtna2co3(ll),.. 'k-',rhohigh(12):l:rholow(12), wtna2co3(12),*k-',... rhohigh(13):l:rholow(13), wtna2co3(13),'k-','LineWidth', 1) •/„semilogy(rho(l) ,wtna2co3(l), 'k+', rho(3) ,wtna2co3(3), 'kx' ,rho(4:6) '/. wtna2co3(4:6) , 'k*' ,rho(7:8) ,wtna2co3(7:8), 'kp' ,xnewc,f2, ' k - ' ,rho(l) . . . . '/. wtna2so4(l) , 'ko' , rho(2:3) ,wtna2so4(2:3), 'ks' ,rho(4:6) ,wtna2so4(4:6), ' k * ' , '/. rho(7:8) ,wtna2so4(7:8), 'kv' ,xnew,f 1, ' k - . ' ,rholow(l: 11) ,wtna2so4(l: 11), 'k. ' '/. , r h o h i g h ( l : l l ) ,wtna2so4(l: 11), ' k . ' ,rholow(l) ,wtna2co3(l), ' k . ' ,rholow(3:11) '/, ,wtna2co3(3:ll), 'k. ' ,rhohigh(l) ,wtna2co3(l), 'k. ' ,rhohigh(3:11) . . . . '/. wtna2co3(3:ll), 'k. ') set(gca,'XDir','reverse','YDir','normal'); '/.errorbar (rho (1) , wt 1,0.005,0.019) t i t l e ( [ ' F i g . 9: S o l u b i l i t y of mixture of sodium carbonate and sodium sulfate ],'Fontsize',15) '/.axis([0.006 0.05 0.005 0.68]) legend('Na_2C0_3, C S 1 \ 'Na_2C0_3, CS2-CS3','Na_2C0_3, CS4-CS6',.. . 'Na_2C0_3, CS7-CS8','Na_2C0_3, CS9-CS13', 'Eq. 7 for pure Na_2C0_3',... 'Na_2S0_4, CS1', 'Na_2S0_4, CS2-CS3','Na_2S0_4, CS4-CS6',.. . 'Na_2S0_4, CS7-CS8','Na_2S0_4, CS9-CS13',' Eq. 8 for pure Na_2S0_4') xlabel(['density (kg/m"3)'],'FontSize',14) ylabel ([' S o l u b i l i t y l i m i t (wt'/.) ' ] , ' FontSize', 14)  CA. Main Code: Mixing, heat and mass transfer (MixHtMassCode.m)  181  C.4 Main Code: Mixing, heat and mass transfer (MixHtMassCode.m) y. 7, THIS CODE CALCULATES: (1) salt molecule deposition, (2) p a r t i c l e nucleation... 7. & (3) p a r t i c l e deposition rate. FILES REQUIRED TO RUN THE CODE: dens.txt . . . 7, cp.txt K.txt enth.txt prand.txt v i s . t x t finddens.m depositfigs.m DATA SAVED . . 7. IN FILES: depositinput.dat, depositoutl.dat and depositout2.dat  7.  clear XYZ=0; rcoag=0; partradius=0; warning off MATLAB:divideByZero Pressure=24.5;7. pressure, MPa MassA=0.12/60;7. flow rate of salt solution stream, kg/sec MassB=1.2/60;7. flow rate of the hot water stream, kg/sec MFA=0.01;7. mass fraction of salt in stream A MFB=0;7. mass fraction of salt in stream B TB=415+273.15; 7. temperature of stream B, K TA=222+273.15;7. temperature of stream A, K Gam=88E-3;7. surface tension, t y p i c a l l y 60xl0~-3 to 150xl0~-3 N/m RunTime=10;7. time the experiment is run, minutes dia=0.0062;7. tube inner diameter, m L=3;7. length of the test section, m molmass=0.106;7. molar mass of sodium carbonate, kg/mole moldia=5.1E-10;7. sodium carbonate molecular diameter, m rhos=2530;7. sodium carbonate density, kg/m*3 inter=80; DZ=2.9037/(inter*1000) ;*/. segment length m (time step), this is denoted by . . . 7. . . . "X" in the thesis Ktube=19;7, thermal conductivity of the test section tube, W/mK Ksalt=0.48;7. thermal conductivity of salt layer, W/mK Rin=dia/2;7. tube inner radius, m Rout=0.009/2;7. tube outer radius, m loca=[250,780,1000,1600,2900];7. temp, vs time profiles drawn at these locations, mm [ET.nloca] =size(loca); numtime=l;7. number of times a segment is exposed to flowing f l u i d N=l;7.number of c e l l s in the salt solution i . e . , stream A 7.1t is important to choose the correct c e l l height i . e . , the number of cells 7„The height should be such that the f l u i d parcel lands in a different c e l l every time '/,it moves a distance (calculated from the energy dissipation rate) NZ=round(round(1000*L/DZ)/1000) ;'/. number of segments DZ=L/NZ;'/. calculated again after rounding of the NZ jump(l:NZ)=0; for kj=l:inter:NZ jump(kj)=l; end jump(l:NZ);  CA. Main Code: Mixing, heat and mass transfer (MixHtMassCode.m)  182  '/, calculate heat transfer from the f l u i d enthalpy gain in the test section 7,T1 and T2 are used to calculate the heat input from enthalpy gain. These '/.temperatures are of f l u i d entering and leaving the test section without '/.any f l u i d being injected at the mixing tee. These should not be confused by f l u i d '/.stream temperatures TA and TB which are for the two f l u i d streams entering the '/.mixing tee. However, the flow rate should be equal to MassA+MassB Tl=399+273.15;'/. bulk temperature at test section i n l e t , K T2=401+273.15;'/, bulk temperature at the test section outlet, K DelT=T2-Tl; load dens.txt;'/, f l u i d density, kg/m~3 [nT,nP]=size(dens);'/, get f i l e sizes from dens P=dens(l,2:nP);'/. the f i r s t row contains the pressures, MPa T=dens (2 :nT, 1) ;'/. the f i r s t column contains the temperatures, K A=dens(2:nT,2:nP); rhol=interp2(P,T,A,Pressure,T1); load cp.txt;'/. specific heat capacity, J/kgK A=cp(2:nT,2:nP); Cpl=interp2(P,T,A,Pressure,TI); Cp2=interp2(P,T,A,Pressure,T2); AvCp=(Cpl+Cp2)/2; Q=(MassA+MassB)*AvCp*DelT;'/. heat supplied, Watts q=Q/(pi*(dia+Rout*2)/2*L) ;'/. heat flux, W/m~2 qprime=Q/L;7, heat supplied per unit length, W/m A=dens(2:nT,2:nP); rhoA=interp2(P,T,A,Pressure,TA); rhoB=interp2(P,T,A,Pressure,TB); M=N*MassB/MassA;7, number of c e l l s in the main flow i . e . , M=round(M);  stream B  fid = fopenCdepositinput.dat','w'); fs = [Pressure; MassA; MassB;MFA;MFB;TB;TA;Ksalt;Ktube;Gam;RunTime;Rin;Rout;... qprime;q;numtime;nloca;DZ;rhos;M;N;L] ; fprintf ( f i d , '7,2.2f 7.1.3f 7.1.3f 7.1.3f 7.1.3f 7.3.2f 7.3.2f 7.2.2f 7.2.If 7.2.3f 7.3.If . . . ...7.2.5f 7.2.5f 7.5.2f 7.5.2f 7.3.Of 7.1.Of 7.1.6f 7.4.2f 7.5.Of 7.2.Of 7,2.2f',fs); ff = [loca(l:nloca)]; fprintf ( f i d , 7,5. Of 7,5.Of 7,5.Of 7.5.Of 7.2. Of \ n ' , f f ) ; fclose(fid); daa = fopen('profile.dat','w'); MFN(1 :M+N)=0;7, mass fraction of nucleated salt R=round(10000/(M+N)); NP=R*(M+N);'/, t o t a l number of f l u i d parcels PMFN(1 :NP)=0;7. mass fraction of nucleated salt in a parcel PMFP(1:NP)=0;7. mass fraction of salt particles in a parcel CMFP(1:M+N)=0;7, mass fraction of salt partciles in a c e l l CNP(1 :M+N)=0;7. number of salt particles in a c e l l PNP(1 :NP)=0;7. number of salt particles in a parcel PNPN(1:NP)=0;7, number of nucleated particles in a parcel CNPN(1:M+N)=0;7. number of nucleated particles in a c e l l Mass=MassA+MassB;7. t o t a l mass flow rate, kg/sec D(l :NZ)=dia;7. i n i t i a l / c l e a n tube inside diameter  CA. Main Code: Mixing, heat and mass transfer  (MixHtMassCode.m)  183  A=dens(2:nT,2:nP); rhoA=interp2(P,T,A,Pressure,TA); rhoB=interp2(P,T,A,Pressure,TB); veloc=(MassA/rhoA+MassB/rhoB)/(pi*dia*2/4) ;'/, f l u i d velocity, m/sec PM=(Mass/veloc)*DZ/NP;y, mass of each parcel in a segment, kg massstar=PM*NP;7, t o t a l mass of f l u i d in a segment, kg DD=dia/(M+N)*1000;% height of each c e l l , mm CLoc(l:M+N) = (l:M+N)*DD;°/, location of the c e l l s , mm CNum(l:M+N)=1:M+N;V. position of each c e l l starting from bottom surface Ts(l:NZ)=TB;% Ts i s required to find properties at wall load K.txt;'/, f l u i d thermal conductivity, W/mK load enth.txt;'/. enthalpy, J/kg load prand.txt;'/, prandtl number load vis.txt;'/, dynamic viscosity, N.s/m~2 massdeptotal(1:NZ)=0; f i d = fopenCdepositout2.dat','w') ;V. leave this for z>l and append later even i f z=l '/, MAIN L00P(i.e., calculation for each time f l u i d passes a segment DZ) for z=l:numtime partradold=0; partgrowth=0; mpart=0; segment=0; mmol=0; BalMFN=0; moldep=0; partdep=0; TotMFN(l:NZ)=0; MFNB(1:NZ)=0; BalMFN(l:NZ)=0; j=0; '/, I n i t i a l i z e c e l l temperatures CT(1:M/2)=TB; CT(M/2+N+l:M+N)=TB; CT(M/2+l:M/2+N)=TA; TMC=mean(CT);% mixed cup temperature, K '/, This calculation is for the Yamagata correlation A=cp(2:nT,2:nP); Cplist=interp2(P,T,A,Pressure,T); [Tsort,i]=sort(T); Cpsort=Cplist(i); [maxCp,imax]=max(Cplist); Tpc=T(imax); A=prand(2:nT,2:nP); Pr=interp2(P,T,A,Pressure,TMC); Prlist=interp2(P,T,A,Pressure,T); Prpc=Prlist(imax); CMF(l:M/2)=MFB;7o i n i t i a l i z i n g for the c e l l salt mass fraction CMF(M/2+N+1:M+N)=MFB; CMF(M/2+1:M/2+N)=MFA;  CA. Main Code: Mixing, heat and mass transfer  (MixHtMassCode.m)  184  das = f o p e n ( ' p r o f i l e l . d a t ' , ' w ' ) ; dad = [CLoc;CMF;CT]; fprintf (das, "/„2.4f '/1.5f '/3.4f\n' ,dad); fclose(das); Saltkg=sum(CMF)*massstar;°/ mass of salt present i n a segment, kg for i=0:1:M+N-1°/ i n i t i a l i z i n g for the f l u i d parcel temperature and salt content PLoc(i*R+l: (i+l)*R)=CLoc(i+l);'/ f l u i d parcel location from the bottom surface, mm PCNum(i*R+l: (i+1) *R)=CNum(i+l);'/ f l u i d parcel location (in terms of c e l l number) '/ from the bottom surface PT(i*R+l: (i+l)*R)=CT(i+l) ;'/ f l u i d parcel temperature PMF(i*R+l: (i+l)*R)=CMF(i+l);'/ salt mass fraction i n each f l u i d parcel end figure (1) subplot(4,1,1) massfrac=plot(CMF,CLoc) ;'/ plots the c e l l salt mass fraction axis([0 .011 -0.5 6.5]); set(massfrac,'EraseMode','xor'); xlabel(['dissolved salt mass fraction']) ylabeK ['tube dia (mm)']) subplot(4,1,2) temp=plot(CT-273.15,CLoc) ;'/ plots c e l l temperatures axis([325 425 -0.5 6.5]); set(temp,'EraseMode','xor'); xlabel(['temperature (~oC)']) ylabeK ['tube dia (mm)']) subplot(4,1,3) Nucl=plot(MFN,CLoc);'/ plots nucleated salt mass fraction at c e l l locations axis([0 1 -0.5 6.5]); set(Nucl,'EraseMode','xor'); xlabel(['mass fraction of nucleated s a l t ' ] ) ylabeK ['tube dia (mm)']) '/.subplot (3,2,4) °/.pplot=plot (segment, p a r t d e p , ' . ' ) ; ' / plots salt p a r t i c l e deposition, kg 7.axis([0 3000 0 0.002E-11]); '/set (pplot,' EraseMode' , ' xor') ; '/ylabeK ['salt p a r t i c l e deposition (kg)']) '/xlabeK ['distance (mm)']) '/subplot (3,2,5) '/mplot=plot( segment, moldep,'.');'/ plots molecule deposition, kg '/axis([0 3000 0 0.006E-9]); ° / s e t ( m p l o t , ' E r a s e M o d e ' , ' x o r ' , 'MarkerSize',12); '/ylabeK ['molecule deposition (kg)']) '/xlabeK ['distance (mm)']) record=hist(PLoc,CLoc); subplot(4,1,4) histogram=plot(record,CLoc);'/ plots histogram of the number of f l u i d parcels axis([0 1860 -0.5 6.5]); set(histogram,'EraseMode','xor'); ylabeK ['tube dia (mm)']) xlabeK ['# of f l u i d parcels']) for j=l:NZ  CA. Main Code: Mixing, heat and mass transfer  (MixHtMassCode.m)  185  drawnow segment=segment+DZ*1000;/, length, mm '/.pro=round(segment*10000000000); i f j==30 daa = f o p e n ( ' p r o f i l e . d a t ' , ' a ' ) ; da = [CLoc;CMF;CT]; fprintf (daa, 7,2.4f '/.1.5f °/.3.4f \ n ' ,da) ; fclose(daa); ttt=-l; end i f j==130 daa = f o p e n ( ' p r o f i l e . d a t ' , ' a ' ) ; da = [CLoc;CMF;CT]; f p r i n t f (daa, 7,2.4f */,1.5f */,3.4f \ n ' , d a ) ; fclose(daa); qqq=-l; end i f j==1400 daa = f o p e n C p r o f i l e . d a t ' , ' a ' ) ; da = [CLoc;CMF;CT]; fprintf (daa, 7.2.4f '/.1.5f '/.3.4f \ n ' , d a ) ; fclose(daa); fff=-l; end i f j==14000 ggg=3; daa = f o p e n C p r o f i l e . d a t ' , ' a ' ) ; da = [CLoc;CMF;CT]; fprintf (daa, 7.2.4f '/.1.5f '/.3.4f \ n ' ,da); fclose(daa); end A=dens(2:nT,2:nP); rhob=interp2(P,T,A,Pressure,TMC) ;°/ f l u i d density at bulk conditions A=K(2:nT,2:nP); Kb=interp2(P,T,A,Pressure,TMC);'/. f l u i d thermal conductivity at bulk conditions A=enth(2:nT,2:nP); Hb=interp2(P,T,A,Pressure,TMC) ;'/, f l u i d enthalpy at bulk conditions A=cp(2:nT,2:nP); Cpb=interp2(P,T,A,Pressure,TMC);'/. specific heat at bulk conditions A=prand(2:nT,2:nP); Prb=interp2(P,T,A,Pressure,TMC) ;'/. Prandtl number at bulk conditions A=vis(2:nT,2:nP); viscb=interp2(P,T,A,Pressure,TMC);'/. dynamic viscosity at bulk conditions A=dens(2:nT,2:nP); rhow=interp2(P,T,A,Pressure,Ts(j));'/, f l u i d density at wall conditions A=K(2:nT,2:nP); K w = i n t e r p 2 ( P , T , A , P r e s s u r e , T s ( j ) ) ; ° / , f l u i d thermal conductivity at wall conditions A=enth(2:nT,2:nP); Hw=interp2(P,T,A,Pressure,Ts(j));'/, f l u i d enthalpy at wall conditions A=cp(2:nT,2:nP); Cpw=interp2(P,T,A,Pressure,Ts(j)) ;*/, specific heat at wall conditions /  0  CA. Main Code: Mixing, heat and mass transfer  (MixHtMassCode.m)  186  A=vis(2:nT,2:nP); viscw=interp2(P,T,A,Pressure,Ts(j));'/, dynamic viscosity at wall conditions A=prand(2:nT,2:nP); Prw=interp2(P,T,A,Pressure,Ts(j)) ;*/, Prandtl number at wall conditions Reb=4*Mass/(pi*D(j) .*viscb);'/, Reynolds number at bulk conditions Rew=4*Mass/(pi*D(j) .*viscw);'/, Reynolds number at wall conditions kviscw=viscw/rhow;% kinematic viscosity at wall conditions kviscb=viscb/rhob;°/. kinematic viscosity at bulk conditions '/, Calculate Nusselt number from Swenson correlation or Yamagata correlation '/, Also change expression for Hm (molecular d i f f u s i v i t y ) accordingly '/, Calculation of Nusselt number from Swenson correlation */.Nu=0.00459* (Rew) "0.923* ((Hw-Hb) *viscw/((Ts(j)-TMC) *Kw)) "0.613* (rhow/(rhob)). . . T O . 231; '/, Calculation of Nusselt number from Yamagata correlation. E=(Tpc-TMC)/(Ts(j)-TMC); i f E>1; Fc=l; else i f E<0; n2=1.44*(l+l/Prpc)-0.53; Fc=((Hb-Hw)/(TMC-Ts(j))/Cpb)~n2; else nl=-.77*(l+l/Prpc)+1.49; Fc=0.67*Prpc"(-.05)*((Hb-Hw)/(TMC-Ts(j))/Cpb)~nl; end end Nu=0.0135*Reb" .85*Prb~.8*Fc;'/, Nusselt number correlation V=Mass/(rhob*pi*D(j)~2/4) ;'/„ f l u i d velocity, m/s '/, Calculation for salt p a r t i c l e deposition rate (kg/sec) dt=DZ/V;% f l u i d residence time i n each segment DZ, sec F=(1.8*logl0(6.9/Rew+(0.002/(3.7*D(j)*1000))"l. ll))~(-2) ;'/. f r i c t i o n factor Epsln=2*F*V~3/D(j);'/, dissipation rate uprime=(Epsln*D(j)/2)~(l/3); KE=(D(j)/2*Epsln)"(2/3); turbvisc=0.09*KE"2/Epsln;'/. turbulent viscosity Xvel=(turbvisc/0.9)/(D(j)/2);'/, charateristic f l u i d parcel velocity Deltime=(D(j)/2)/Xvel;'/, time taken by f l u i d parcel to move a distance of D/2 i . e . , '/, characteristic length Ldash=Deltime*V;'/. the f l u i d parcel moves one X - t i c length while f l u i d move this '/, length along test section, m DZRad=(((turbvisc/0.71)*Deltime)~0.5)*1000;'/, mm distance CH=6.02/11; DZRad=CH; TotCel=6.02/CH;'/, t o t a l number of c e l l s , M+N DX=(6.02/(1000*(M+N)))~2*V/turbvisc*0.71*1000; Vmol=4/3*(pi)*(moldia/2) ~3;'/, volume of salt molecules, m~3 i f jump(j)==l '/.Calculate the distance a f l u i d parcel would move using turbulent characteristic '/.velocity. DIST=(DZRad) .*sign(-l+2.*rand(l,NP));'/. random +/- signs are multiplied by maximum '/, distance a f l u i d parcel can move Move=DIST./DD;'/, the distance moved i n terms of # of c e l l locations numbers=hist(PLoc,CLoc); nuu=numbers(1);  CA. Main Code: Mixing, heat and mass transfer  (MixHtMassCode.m)  187  PCNum=round(PCNum+Move) ; u p d a t e f l u i d parcel position after moving nuulast=numbers (M+N); for r=l:NP i f PCNum(r)<l; PCNum(r)=l; e l s e i f PCNum(r)>M+N; PCNum(r)=M+N; else PCNum(r)=PCNum(r); end end PLoc=PCNum.*DD; histo=hist(PLoc,CLoc); [rho(l:M+N)]=finddens(Pressure,CT(l:M+N)) ;'/, f l u i d density i n each c e l l for b=l:M+N CT(b)=mean(PT(f ind(PCNum==b)));'/, update c e l l temperature PT(: , f ind(PCNum==b))=CT(b) ;'/. update f l u i d parcel temperature CMF(b)=mean(PMF(f ind(PCNum==b))) ;'/, mass fraction of dissolved salt in each c e l l CM(b) = (histo(b)) .*PM;7. mass of f l u i d in each c e l l , kg i f j>l CMFP(b)=mean (PMFP(find(PCNum==b)));'/. m. f. of particulate salt in a c e l l PMFP(: , f ind(PCNum==b))=CMFP(b) ;'/. m. f. of particulate salt i n a parcel CNP(b)=CMFP(b) .*rho(b) ./(4/3*pi*rhos.*partradius~3) ;*/, # of . . . '/, particles per nT3 in a c e l l PNP(: , f ind(PCNum==b))=CNP(b) ./histo(b) ;*/. number of p a r t i c l e s in a parcel end end gg=hist(PLoc,CLoc) ; rrt=gg(l) ;'/.number of parcels in bottom c e l l per unit segment length r r f =gg(M+N) ;'/.number of parcels in top c e l l medge=Mass*(rrt+rrf)/NP; [rho(l:M+N)]=finddens(Pressure,CT(l:M+N));'/. f l u i d density in each c e l l end CSat(l:M+N)=0.01*(exp(6.24E-8.*(rho(l:M+N))."3-8.48E-5.*(rho(1:M+N)).~2+... 0.046.*rho(l:M+N)-9.74));'/, c e l l salt saturation l i m i t (mass fraction) DEGSAT(1:M+N)=CMF(1:M+N) ./CSat(1 :M+N) ;'/„ degree of saturation in each c e l l for u=l:M+N; i f DEGSAT(u)< 2; °/,JJ are the number of salt particles nucleated per unit time per cm~3 JJ(u)=0; rstar(u)=0; else JJ(u)=10E30*exp(-16*pi*Gam-3*Vmol"2/(3.*1.38E-23~3.*CT(u)."3*... (log(DEGSAT(u))).-2)); rstar(u)=2*Gam*Vmol/(1.38E-23.*CT(u) .*log(DEGSAT(u))) ;'/. c r i t i c a l radius. . '/. of nucleated salt p a r t i c l e s , m end mperpart(u)=rstar(u)*3/(moldia/2)"3;'/, # of salt molecules per salt p a r t i c l e NPN(u)=JJ(u) .*dt*(100)-3;'/, # of salt particles nucleated per m~3 mpstar (u)=4/3*pi*rstar (u) . ~3*rhos; °/,kg salt per p a r t i c l e MFN(u)=mpstar(u) .*NPN(u) ./rho(u);'/, mass. . . '/, fraction of nucleated salt (kg salt/kg soln) CMFOLD(u)=CMF(u); CMF(u) = (CMF(u)-MFN(u)) ;'/. update mass fraction of dissolved salt in each c e l l i f JJ(u)>l  CA. Main Code: Mixing, heat and mass transfer  (MixHtMassCode.m)  188  i f CMF(u)<0; line=344 end end PMF(: ,find(PCNum==u))=CMF(u) ; 7 . update dissolved salt m. f. of f l u i d parcels PMFN(:,find(PCNum==u))=MFN(u);7o mass fraction of nucleated salt in the parcel PNPN(: , f ind(PCNum==u))=NPN(u)*2/(rrt+rrf) ^/.number of nucleated p a r t i c l e s . . . 7, i n a f l u i d parcel end NPNtotal(j)=sum(NPN);7. t o t a l number of salt particles nucleated/m"3 at segment j i f NPNtotal (j)>0 XYZ=2; end NPNtot=sum(NPN); i f rstar(rstar~=0)>0; averstar=mean(rstar (rstar~=0)) ;7. mean radius of nucleated p a r t i c l e s , m else averstar=0; end diffmol=1.38e-23*(Ts(j))*l/(3*pi*viscb*moldia);7. molecular d i f f u s i v i t y . . . 7o coefficient (m"2/sec) from Stokes Einstein relation rhoave=mean(rho);7. average f l u i d density at the segment, kg/m~3 i f XYZ>1 for hf=l:M+N; i f NPN(hf) >1 i f CMF(hf)>CSat(hf) rf(hf)=((CMF(hf)-CSat(hf)).*rho(hf).*6.023E23/molmass*... Vmol/(4*pi*NPN(hf)./3))"(l/3); KD=(48*pi~2*Vmol.*NPN(hf)."2.*(CMF(hf)-CSat(hf)).*rho(hf... ).*6.023E23/molmass)"... ( - l / 3 ) * ( d i f f m o l ) - ( - l ) ;7. factor, sec syms g; TIMEtot=KD*int(l/(g"(l/3)*(l-g)),g,0,0.99);7. time to reach f i n a l particle size TIMEtot=double(TIMEtot); alph=dt/TIMEtot ;7. extent of reaction i f alph>l; alph=l; end partgrowth(hf )=rf (hf) .*alph"3;7. grown salt p a r t i c l e radius after time dt, m end end end i f rcoag>0; i f sum(NPN)>l partradius=(sum(NPN).*mean(partgrowth(partgrowth"=0))+... sum(CNP).*rcoag)/(sum(NPN)+sum(CNP)); else partradius=rcoag; end else partradius=averstar;7. i . e . , only for the f i r s t segment with nucleation end end i f NPNtotal (j)>0  CA. Main Code: Mixing, heat and mass transfer  (MixHtMassCode.m)  189  partradius; end rbalance=partradius; partradreco(j)=partradius;'/ s a l t p a r t i c l e radius at each segment, m CMFBottom=CMF(l);°/ dissolved salt mass fraction of c e l l at bottom CMFTop=CMF(M+N); dissolved salt mass fraction of c e l l at top CMFWall=(CMFBottom+CMFTop);'/, dissolved salt mass fraction of c e l l s near the wall CMFB=mean(CMF) ;'/, mean mass fraction of dissolved salt diffpart=l .38e-23*(Ts(j))*l/(3*pi*viscb*2*partradius);'/. salt p a r t i c l e d i f f u s i v i t y '/, coefficient (m~2/sec) from Stokes Einstein relation ScPart=kviscw/diffpart;'/, salt p a r t i c l e Schmidt number taup=rhos*(2*partradius)~2/(18*viscb);'/, salt p a r t i c l e relaxation time, sec tauw=rhow*V"2*F/8;% wall shear stress, N/m~2 Ustar=(tauw/rhow)"0.5;y, wall f r i c t i o n velocity, m/sec taupplus=taup*(Ustar"2)/kviscb; i f taupplus>20; Vdstar=0.18; elseif taupplus<0.2; Vdstar=0.065*ScPart"-.667; else Vdstar=3.5E-4*taupplus~2; end Vd=Vdstar*Ustar;'/, salt p a r t i c l e deposition velocity, m/sec i f taup==0; Vd=0; end radius=partradreco(j); for hf=l:M+N; CMFP(hf)=CMFP(hf)+MFN(hf); PMFP(:,f ind(PCNum==hf))=CMFP(hf); i f radius >0 CNP(hf)=CMFP(hf)*rho(hf)/(4/3*pi*rhos.*radius"3); PNP(:,f ind(PCNum==hf))=CNP(hf)./gg(hf); else CNP(hf)=0; end end PMASS(j)=sum(CMFP); for bg=l:M+N; i f CNP(bg)>l K12=8*l.38e-23*CT(bg)/(3*viscb); critcoagtime=2./(K12.*CNP(bg)); CNPco(bg)=CNP(bg)./(1+dt/critcoagtime); newpartradi=radius*(CNP(bg)./CNPco(bg))"(l/3); else 0  0  newpartradi=radius; end end i f newpartradi>0 rcoag=mean(newpartradi(newpartradi~=0)); end rbalance; partradreco(j)=rbalance; i f CMFP(1)>0 Pl=(Vd*DZ*pi*D(j)*rho(1)*(rrt+rrf)/(2*R*2*medge)); CMFPold=CMFP(l) ;  CA. Main Code: Mixing, heat and mass transfer  (MixHtMassCode.m)  CMFP(l)=(l-Pl)/(l+Pl)*CMFPold; CMFP(M+N)=CMFP(1); mpart(j)=Vd.*pi.*D(j) . *DZ. *rho(l) .*(CMFP(l)+CMFPold)*(rrt+rrf )/(2*2*R);'/, salt '/, particle deposition rate, kg/sec CMFP(1)=CMFP(1)-mpart(j)/medge; CMFP(M+N)=CMFP(1); PMFP(:,find(PCNum==l))=CMFP(l); PMFP(:,find(PCNum==M+N))=CMFP(M+N); CNP(1)=CMFP(1).*rho(l)/(4/3*pi*rhos.*radius-3); PNP(:,find(PCNum==1))=CNP(1); PNP(:,f ind(PCNum==M+N))=CNP(M+N); else mpart(j)=0; end partdep(j)=mpart(j). *dt;'/, mass of salt particles deposited in the segment kg '/. Calculation of molecular deposition rate from heat & mass transfer analogy CB=CMFB*100;°/, Balance dissolved salt cone, after the p a r t i c l e nucleation, wt'/, Sc=kviscw/diffmol;'/, Schmidt number of salt molecules h=Nu*(Kb)/D(j);'/, heat transfer coefficient from the correlation, W/m"2K Le=Sc/Prw;°/, Lewis number '/. NOTE: Choose Hm for the Nu# relation, Le~0.387 for Swenson and Le"0.2 for '/.Yamagata correlation '/.Hm=h/(rhow*Cpw*Le~0.387); Hm=h/(rhow*Cpw*Le~0.2); CW=CMFWall*100;'/. dissolved salt concentration at wall, wt'/. CWmax=exp(6.24E-8*(rhow)~3-8.48E-5*(rhow)~2+0.046*rhow-9.74);'/. maximum possible '/, dissolved salt at wall, wt'/. i f CW>CWmax; Al=Hm*pi*D(j)*rhow*DZ/medge*(rrt+rrf)/(2*R); CMFnew= ( ( l - A l / 2 ) / ( l + A l / 2 ) * C W + A l / ( l + A l / 2 ) * ( C W m a x ) ) / 1 0 0 ; ° / . u p d a t e d . . . '/. mass fraction of the edge c e l l www=2; mmol (j) =Hm*DZ*pi*D ( j) *rhow* ((CMFnew*100+CW) /2-CWmax) /100* (rrt+rrf)/(2*R) ; '/, mol '/.ecule deposition rate, kg/sec CMF(1)=CMF(1)-mmol(j)/medge; dsd=mmol(j); CMF(M+N)=CMF(1); PMF(:,find(PCNum==l))=CMF(l); PMF(:,find(PCNum==M+N))=CMF(M+N); else mmol(j)=0; end moldep(j)=mmol(j)*dt;'/, mass of salt molecules deposited in the segment, kg massdep(j)=moldep(j)+partdep(j);'/, t o t a l salt mass deposited in the segment, kg setOnassfrac,'XData',CMF,'YData',CLoc) set(temp,'XData',CT-273.15,'YData',CLoc) set(Nucl,'XData',MFN,'YData',CLoc) '/.set(pplot, 'XData' .segment, 'YData' .partdep) '/.set(mplot, 'XData' .segment, 'YData' .moldep) set(histogram,'XData'.histo,'YData',CLoc) title([' ',num2str(j)... ],'Color','b','Fontsize',12) '/, Updating conditions for the next segment length  C.4. Main Code: Mixing, heat and mass transfer  (MixHtMassCode.m)  191  A=cp(2:nT,2:nP); Cpe=interp2(P,T A,Pressure,CT(l));7. specific heat at wall conditions CTold=CT(l) ; CT(l)=CT(l)+qprime*DZ/(medge*Cpe); PT(:,find(PCNum==l))=CT(l); CT(M+N)=CT(1); PT(:,f ind(PCNum==M+N))=CT(1); PW=h*pi*D(j)*(rrt+rrf)/(2*R); Tif (j)=qprime*DZ/PW+(CT(l)+CTold)/2;7. fluid-salt/tube interface temp, after heating Ts(j + l)=Tif (j) ;7. calculate interface properties for the next segment TMC=mean(CT) ;7. updating mixed cup temperature after heating devo(j)=(moldep(j)+partdep(j)),/rhos; 7. volume of deposited salt layer, m~3 deth(j) = (Rin-(((Rin*2)~2-4*devo(j)./(pi*DZ))."(0.5))/2) ;7. salt layer thickness, m i f D(j)>deth(j) ; D(j)=D(j)-deth(j); else disp(['plugging']); end Rl(j)=D(j)/2; i f Rin==Rl(j); Tw(j)=Tif(j); else Tw(j)=Tif (j)+Q*log(Rin./Rl(j))/(2*pi*Ksalt*L) ;7. tube inner surface temp, end To(j)=Tw(j)+q*Rin/(2*Ktube)*((Rin/Rout)~2-log((Rin/Rout)~2)-l)/(l-(Rin/Rout)"2); savedl(j)=segment; saved2(j)=TMC-273.15; saved3(j)=dt; BalSaltkg=Saltkg-massdep; Saltkg=BalSaltkg; kg(j)=Saltkg(j); Saltkg=Saltkg(j); RecoSaltkg(j)=kg(j) ;'/, salt mass present for the next segment, kg end Ts(j)=Tif (j) ;7. this is done to update interface temp for the next z i f z==l; T c l e a n d : NZ)=Ts (1: NZ)-273.15 ;*/, clean tube inner surface temp end mas sdepnew(1:NZ)=mas sdep(1:NZ)+mas sdeptot al(1:NZ); massdeptotal=massdepnew;'/, t o t a l mass of salt deposited (kg) after z # of cycles 7, this is used to find deposit thickness yy = [savedl; saved2; moldep;partdep;massdep;partradreco;NPNtotal;saved3;PMASS]; f i d = fopen('depositoutl.dat','w'); fprintf ( f i d , '7.4.Of 7.5.2f 7.12.8e 7.12.8e 7.12.8e 7.12.8e 7.12.8e 7.5.4E 7.8.7E\n',yy); fclose(fid); y = [savedl; RecoSaltkg; Tif-273.15;Tw-273.15;To-273.15;Tclean;mmol+mpart]; f i d = fopen('depositout2.dat','a'); fprintf ( f i d , '7.4. Of 7.1.3E 7.5.2f 7.5.2f 7.5.2f 7.5.2f 7.4.5E\n',y) ; 7.Variables are: segment number, undeposited mass (kg) of salt after every segment, 7.fluid-tube/salt layer interface temperature,inside wall temp, 7»outside wall temp, salt mass deposition rate fclose(fid); end [j]=depositfigs(j) ; )  CA. Main Code: Mixing, heat and mass transfer  C.4.1  (MixHtMassCode.m)  192  Figures Code: Mixing, heat and mass transfer (Depositfigs.m)  '/.clear '/.This code runs with deposit.m and is used to draw figure # 2 to 6 function [j]=depositfigs(j) load depositoutl.dat load depositout2.dat load depositinput.dat [NZ,vn]=size(depositoutl); length=depositoutl(l:NZ,1); 7.1ength=0:0. 2 : NZ*3/0 .2 moldep=depositoutl(1:NZ,3); partdep=depositoutl(l:NZ,4); massdeptotal=depositoutl(1 :NZ,5) ;°/,kg of salt deposited partradreco=depositoutl(1:NZ,6); NPNtotal=depositout1(1:NZ,7); dt=depositoutl(l:NZ,8)'; PMass=depositoutl(l:NZ,9); Pressure=depositinput(l,1); MassA=depositinput(1,2); MassB=depositinput(l,3); MFA=depositinput(1,4); TB=depositinput(1,6); TA=depositinput(l,7); Ksalt=depositinput(1,8); Ktube=depositinput(1,9); Gam=depositinput(l,10); RunTime=depositinput(1,11); Rin=depositinput(l,12); Rout=depositinput(1,13); qprime=depositinput(1,14); q=depositinput(1,15); numtime=depositinput(1,16); nloca=depositinput(1,17); DZ=depositinput(1,18); rhos=depositinput(1,19); M=depositinput(l,20); N=depositinput(l,21); L=depositinput(l,22); loca(l:nloca)=depositinput(1,23:nloca+22); DZloca(l:nloca)=round(round(loca(l:nloca)/DZ)/1000); Tclean=depositout2(l :NZ,6) ';'/. clean surface temperature, oC GG=depositout2(l:NZ,7) ;'/,kg/sec of salt deposition WW=depositout2(l :NZ,3);'/, f l u i d / s a l t i r tube interface temperature, oC s t r l ( l ) = {['q = ' ,num2str(q/1000, "/.3.2f'),' kW/nT2'] };'/.heat flux, kW/m*2 strl(3) = {['T_{B} = ' ,num2str(TB-273.15),' "oC']};'/. temp, of hot water stream, oC strl(4) = {['T_{A} = ' ,num2str(TA-273.15),' "oC']};'/ temp, of salt solution, oC strl(5) = {['m_{B} = ',num2str(MassB*60),' kg/min']};'/. flow of hot water, kg/min strl(6) = {['m_{A> = ' , num2str (MassA*60),' kg/min']};'/, m.f. of salt solution, kg/min 0  CA. Main Code: Mixing, heat and mass transfer  (MixHtMassCode.m)  193  strl(7) = {['\gamma = num2str (Gam, ' 7 . 5 . 3 f ) , ' N/m']}; /, surface tension, N/m strl(8) = {['salt m.f. i n A = ' , num2str(MFA)] };*/, salt m. f. of salt solution stream strl(9) = {['dx = ' , num2str(DZ, "/.1.6f'),' m']};7. segment length strl(2) = {['P = ' , num2str(Pressure),' MPa']}; /, system pressure strl(10) = {['\Deltad = ' , num2str (6.2/1000/(M+N),'7.1. 5 f ' ) , ' m']};7. 7, CHECK i f the tube i s plugged before RunTime dtnew=dt'; DThickFinal (1: NZ) =GG(1: NZ) . *dtnew; 7,this i s kg of salt deposit depvolume=DThickFinal./rhos; depthickness=(Rin-(Rin."2-depvolume./(pi*DZ))."(0.5));7, deposit thickness i n m DThickFinal(1:NZ) = 1000*depthickness;7. mm of deposit thickness i n one residence time slopfinal(l:NZ)=DThickFinal(l:NZ)./dt(l:NZ);7. slope mm/sec slopsort=slopfinal(1:NZ) ; [maxslop,maxd]=max(slopfinal); plugtime=(2/maxslop)/60;7,time to plug, minutes 1  0  7,###############################################################  figure (2) 7,###############################################################  7,this figure plots the molecule and p a r t i c l e deposition at various TS . . . 7, ..locations after one residence time at each segment text(500,moldep(500)/DZ, 'molecule m a s s ' , ' C o l o r ' , ' r ' , ' V e r t i c a l A l i g n m e n t ' , . . . 'bottom', 'HorizontalAlignment','left','FontSize',8) text(2100,moldep(2)/DZ,strl,'HorizontalAlignment','left','VerticalAlignment'... , 'top','Fontsize',10) h l l = line(lengthd:80:NZ) ,moldep(l:80:NZ)/DZ,'Color','r') ; axl = gca; ylabel(['Mass of deposited salt molecules per segment length (kg/m)'],'FontSize',12) set(axl,'XColor','r','YColor','r','FontSize',9) ax2 = a x e s ( ' P o s i t i o n ' , g e t ( a x l , ' P o s i t i o n ' ) , ' Y A x i s L o c a t i o n ' , ' r i g h t ' , ' C o l o r ' , ' n o n e ' , . . . 'XColor' , ' k ' , ' Y C o l o r ' , ' b ' , ' F o n t S i z e ' , 9 ) ; hl2 = line(lengthd:80:NZ),partdep(l:80:NZ)/DZ,'Color','b'); xlabel (['Test section location (mm)'],'FontSize',12) ylabel(['Mass of deposited salt particles per segment length (kg/m)'],'FontSize',12) text(500,partdep(500)/DZ, [' p a r t i c l e m a s s ' , ] , ' C o l o r ' , ' b ' , 'VerticalAlignment'... ,'bottom','HorizontalAlignment','left','FontSize',8) 7,axis([0 NZ 0 1.4001E-8]); 7,###############################################################  figure (3) 7.###############################################################  7,plots the p a r t i c l e radius and # of salt particles at various TS l o c a t i o n s . . . 7,after one residence time at each segment text(600,partradreco(600), ['particle d i a m e t e r ' ] , ' C o l o r ' , ' k ' , . . . 'VerticalAlignment','bottom','HorizontalAlignment','right','FontSize',9) text(600,partradreco(500), ['particulate salt mass f r a c t i o n ' ] , ' C o l o r ' . . . , ' k ' , 'VerticalAlignment','bottom','HorizontalAlignment','right','FontSize',9) text(600,partradreco(1000),['number of p a r t i c l e s / m " 3 ' , ] , ' C o l o r ' , ' k ' , . . . 'VerticalAlignment','bottom','HorizontalAlignment','left','FontSize',9) text(600,partradreco(500),strl,'HorizontalAlignment','left'.... 'VerticalAlignment','top','Fontsize',10) h l l = line(length,partradreco*2E7,'Color','k'); hl4 = line(length,PMass*1000,'Color','k');  CA. Main Code: Mixing, heat and mass transfer  (MixHtMassCode.m)  194  axl = gca; ylabeK['Average salt p a r t i c l e diameter (m x 10"7) Particulate salt m. f. ( g / k g ) ' . . . . ] , 'FontSize',12) set(axl,'XColor','r','YColor','k') ax2 = a x e s ( ' P o s i t i o n ' , g e t ( a x l , ' P o s i t i o n ' ) , ' Y A x i s L o c a t i o n ' , ' r i g h t ' , ' C o l o r ' , ' n o n e ' . . . ,'XColor', ' k ' , ' Y C o l o r ' , ' k > ) ; hl3 = line(length,NPNtotal,'Color','k','Parent',ax2); xlabel (['Test section location (mm)'],'FontSize',12) ylabeK['Number of nucleated salt particles/m"3'],'FontSize',12) '/.############################################################### figure (4) '/.############################################################### '/.this figure plots the deposit thickness after "RunTime" minutes of running depthick=depthickness*RunTime*60./dt;'/, salt thickness m plot (length, depthick* 1000, 'k-');'/, plots the mass fraction of salt at c e l l locations xlabel (['Test section location (mm)'],'Fontsize',12) ylabeK['Salt deposit thickness (mm) after ' num2str(RunTime),' min'],'Fontsize',12) text(1500,depthick(5),strl,'HorizontalAlignment','left','VerticalAlignment'... , 'top','Fontsize',10) •/.############################################################### '/.figure (5) '/.############################################################### '/.plots the increase i n temperature with time at "loca" locations of test section for locax=l: nloca;'/, this loop i s for each location where temp i s to be plotted for runtime=l: 1 :RunTime'/, this loop i s for variation of time at each location DThick(locax)=DThickFinal(DZloca(locax)); slop(locax)=DThick(locax)./dt(DZloca(locax)); TotalThick(runtime,locax)=(slop(locax).*runtime*60); Rfoul(runtime,locax)=Rin-TotalThick(runtime,locax)./1000; Tintface(locax)=WW(DZloca(locax)); Twallin(runtime,locax)=Tintface(locax)+qprime*log(Rin./Rfoul... (runtime,locax))/(2*pi*Ksalt); Twallout(runtime,locax)=Twallin(runtime,locax)+q*Rin/(2*Ktube... )*((Rin/Rout)~2-log((Rin/Rout)*2)-l)/(l-(Rin/Rout)*2); end end t ime = 1:1:RunTime; '/.############################################################### figure(6) '/,############################################################### '/.plots outer surface temp of clean tube and after "RunTime" minutes of exposure depthick=depthickness*RunTime*60./dt;'/, salt thickness m RfoulFinal(1:NZ)=Rin-depthick(1:NZ); TintfaceFinal(l:NZ)=WW(l:NZ); TwallinFinal(l:NZ)=TintfaceFinal(l:NZ)+qprime*... log(Rin./RfoulFinal(1:NZ))/(2*(pi)*Ksalt); TwalloutFinal(l:NZ)=TwallinFinal(l:NZ)+q*Rin/(2*Ktube)*... ((Rin/Rout)"2-log((Rin/Rout)*2)-l)/(l-(Rin/Rout)*2); TCwallout(l:NZ)=Tclean(l:NZ)+q*Rin/(2*Ktube)*((Rin/Rout)"2-... log((Rin/Rout)"2)-l)/(l-(Rin/Rout)~2) ;'/.clean surface outer temp.  C.4. Main Code: Mixing, heat and mass transfer  (MixHtMassCode.m)  plot(length,TwalloutFinal,'k-',length,TCwallout,'k-.') xlabeK['Test section location (mm) '],'FontSize',12) ylabeK['Outer surface temperature ( ~oC) '],'FontSize',12) text(1500,TwalloutFinal(5),strl,'HorizontalAlignment','left' 'VerticalAlignment','top','Fontsize',10) text(500,TCwallout(500), 'clean s u r f a c e ' , ' C o l o r ' , ' k ' , 'VerticalAlignment 'bottom','HorizontalAlignment','left','FontSize',8) text(500,TwalloutFinal(500),['after ',num2str(RunTime),' minutes'],'Color 'VerticalAlignment','bottom','HorizontalAlignment','left','FontSize',8) %############################################################### '/, the following figure i s plotted to confirm the linear growth . . . '/, of deposit with repeatetive exposure of test section to the scaling f l u i d i f numtime>l figure (7) •/,############################################################### [nl,nK]=size(depositout2); GG=depositout2(1:nl,7); sect=10;'/.enter section location (mm) where deposit . . . '/, . . .profile i s to be drawn for numtime>l inc=dt(sect); depprof(1:numtime,1)=GG(sect:NZ:NZ*(numtime-1)+sect); times(1:numtime)=inc:inc:inc*numtime; plot(times(1:numtime),depprof(1:numtime),'-r"'); xlabeK[num2str(sect),' mm location exposure time (sec)'])  ylabeK['deposit thickness (mm) ']) end  Bibliography [1] R . E . Sonntag, Borgnakke C , and G . J . V a n W y l e n . Fundamentals of Thermodynamics. J o h n W i l e y and Sons, New York, 6 edition, 2003. th  [2] P. K r i t z e r and E . Dinjus. A n assessment of supercritical water oxidation ( S C W O ) existing problems, possible solutions and new reactor concepts. Chemical Engineering Journal, 83:207-214, 2001. [3] R . W . Shaw and N . Dahmen. 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