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Bubble columns and three-phase fluidized beds : flow regimes and bubble characteristics Zhang, Junping 1996

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BUBBLE COLUMNS AND THREE-PHASE FLUIDIZED BEDS: FLOW REGIMES AND BUBBLE CHARACTERISTICS by Junping Zhang B. Sc., Tsinghua University, 1984 M. Sc., Tsinghua University, 1987 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Chemical Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May 1996 © Junping Zhang, 1996 In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Chemical Engineering The University of British Columbia 2216 Main Mall Vancouver, Canada V6T 1Z4 Date: June 7, 1996 ii Abstract Experiments were carried out in three-phase fluidized beds containing solid particles contacted by upward cocurrent flow of air and water, to study flow patterns of gas-liquid-solid systems. The minimum fluidization velocity and the particle transport velocity in a gas-hquid-solid mixture delineate the boundaries between three types of flow systems — fixed bed, fluidized bed and transport flow. Both of these transition velocities were measured for a variety of particles. A theoretical model, the Gas-Perturbed Liquid Model, was developed to predict the minimum liquid fluidization velocity of a bed of solid particles in the presence of a fixed cocurrent superficial gas velocity. This model, together with an appropriate equation for the gas holdup on a solids-free basis, shows almost as good agreement with the present experimental data and those from the literature as the best available empirical equation for the minimum hquid fluidization velocity at low to intermediate superficial gas velocity, and has the advantage of correctly reducing to the Wen-Yu equation for minimum two-phase fluidization as the superficial gas velocity goes to zero. Two types of particle movement were observed as the superficial liquid velocity approaches the particle transport velocity. For 1.2 mm steel shot, clusters of particles were found in both liquid-solid and gas-hquid-solid systems. For 1.5 and 4.5 mm glass beads, on the other hand, no particle clusters were observed. In the latter case, a mathematical model the Particle Transport Velocity Model, was developed to predict the superficial hquid velocity for particle transport in upward gas-hquid flow. An empirical correlation was also proposed for the transition from fluidized bed to particle transport flow. Both predictions showed good agreement with experimental data obtained in the present work and in the literature for a wide range of superficial gas velocities. Within the fluidized bed, based on bubble characteristics, dispersed bubble flow, discrete bubble flow, coalesced bubble flow, slug flow, churn flow, bridging flow and annular flow regimes iii were identified and characterized, at different combinations of gas and liquid superficial velocities. These flow regimes were also observed for two-phase air-water systems. A comprehensive measurement method using a conductivity probe was developed to determine flow regime transitions based on bubble frequency, Sauter mean bubble chord length and the time taken by a bubble to pass a given point. Criteria for determining flow regime transitions were developed in an air-water two-phase system and then successfully applied to gas-liquid-solid three-phase fluidized beds. Flow regime maps were derived based on experimental data for three different three-phase systems. As in two-phase gas-liquid systems, chum flow, bridging flow and annular flow can be observed at high gas velocities in three-phase fluidized beds. Empirical correlations were developed to predict the flow regime boundaries in the three-phase fluidized systems investigated. iv Table of Contents Abstract iii List of Tables • x List of Figures  ™ Acknowledgment x*111 Chapter 1 Introduction 1 1.1 Definitions of Flow Patterns 5 1.2 Scope of Work 9 Chapter 2 Experimental Apparatus and Measurement Methods 12 2.1 Apparatus • 12 2.2 Measurement Techniques 15 2.2.1 Pressure Transducers2.2.2 Conductivity Probe 18 2.3 Data Processing 22 2.3.1 Threshold2.3.2 Signal Simplification and Bubble Frequency 24 2.3.3 Bubble Time and Local Gas Holdup 25 2.3.4 Bubble Velocity and Bubble Chord Length 26 2.3.5 Data Processing Procedure 29 Chapter 3 Experimental Methods 31 3.1 Introduction 33.2 Pressure Fluctuations 2 3.2.1 Previous Studies 33.2.1.1 Gas-liquid two-phase systems 32 3.2.1.2 Three-phase systems 34 3.2.2 PreHrninary Tests 35 v 3.2.2.1 Effect of single bubble injection on pressure fluctuations 35 3.2.2.2 Effect of continuous air supply on pressure fluctuations 37 3.3 Local Multiphase Flow Characteristics 39 3.3.1 Previous Studies 33.3.1.1 Gas-liquid two-phase systems 39 3.3.1.2 Three-phase systems 43 3.3.2 Discussion of Existing Methods 5 3.4 Summary 51 Chapter 4 Experimental Criteria for Flow Regime Transitons in Gas-Liquid Systems 52 4.1 Introduction , 54.2 Experimental Results 54.2.1 Raw Signals and their Statistical Results 52 4.2.2 Gas Holdup 6 4.3 Experimental Criteria for Flow Regime Transitions 57 4.3.1 Transition between Discrete Bubble Flow and Coalesced Bubble Flow Regimes 54.3.2 Transition between Coalesced Bubble Flow and Slug Flow Regimes 60 4.3.3 Transition between Slug Flow and Churn Flow 62 4.3.4 Transition between Churn Flow and Bridging Flow 63 4.3.5 Transition between Bridging Flow and Annular Flow 66 4.3.6 Transition between Discrete Bubble Flow or Coalesced Bubble Flow and Dispersed Bubble Flow 66 . 4.4 How Regime Transitions at Different Heights 67 4.4.1 Experimental Conductivity Probe Results4.4.2 Experimental Pressure Fluctuation Results 72 4.4.3 Comparison between Conductivity Probe and Pressure Transducer Techniques 78 vi 4.5 Flow Regime Map for Air-Water System 79 4.5.1 Experimental Results 74.5.2 Comparison 81 4.6 Summary 4 Chapter 5 Bubble Characteristics in Bubble Columns 85 5.1 Introduction 85.2 Bubble Characteristics in the Discrete and Dispersed Bubble Flow Regimes 85 5.2.1 Local Bubble Frequency 86 5.2.2 Bubble Chord Length and its Distribution 87 5.2.3 Average Bubble Velocity 89 5.3 Bubble Characteristics in the Slug and Chum Flow Regimes 91 5.3.1 Bubble Chord Length and its Distribution 92 5.3.2 Average Bubble Velocity 94 5.4 Summary 97 Chapter 6 Three-Phase Fluidization Boundaries 98 6.1 Minimum Liquid Fluidization Velocity at Low to Intermediate Gas Velocity 98 6.1.1 Introduction 96.1.2 Theoretical Models: Modifications and New Models 105 6.1.2.1 Modified Song model 1 106.1.2.2 Modified Song model H 108 6.1.2.3 Pseudo-homogeneous fluid model 106.1.2.4 Gas-perturbed liquid model 109 6.1.2.5 Gas holdup at minimum fluidization 110 6.1.3 Experimental Study 114 6.1.3.1 Experimental procedure 115 6.1.3.2 Experimental results 6 6.1.4 Comparison and Discussion 118 vii 6.1.4.1 Pressure gradient in fixed beds 118 6.1.4.2 Minimum fluidization velocity for liquid-solid fluidized beds 119 6.1.4.3 Minimum fluidization velocity for three-phase fluidized beds 120 6.2 Minimum Gas Fluidization Velocity at Zero or Low Liquid Velocity 124 6.2.1 Introduction 126.2.2 Zero Superficial Liquid Velocity 131 6.2.3 Non-Zero Superficial Liquid Velocity 136 6.3 Particle Transport Velocity in Gas-Liquid Mixtures 140 6.3.1 Introduction 146.3.2 Experimental Method 142 6.3.3 Experimental Results and Discussion 146.4 Regime Maps for Three-Phase Systems 152 6.5 Summary 154 Chapter 7 Flow Regimes in Three-Phase Fluidized Beds 157 7.1 Introduction 157.1.1 Visual Observations 157 7.1.2 Instrumental Measurements 160 7.2 Experimental Results 165 7.3 Flow Regime Transitions 9 7.3.1 Transition between Discrete (or Dispersed) and Coalesced Bubble Flow.... 170 7.3.2 Transition between Coalesced Bubble Flow and Slug Flow 174 7.3.3 Transition between Slug Flow and Chum Flow 176 7.3.4 Transition between Chum Flow and Bridging Flow 178 7.3.5 Transition between Bridging Flow and Annular Flow 180 7.3.6 Transition between Discrete (or Coalesced) and Dispersed Bubble Flow.... 180 7.4 Flow Regime Maps 183 7.4.1 Flow Regime Map for 1.5 mm Glass Beads Fluidized Bed 183 viii 7.4.2 Flow Regime Map for 4.5 mm Glass Bead Fluidized Bed 184 7.4.3 Flow Regime Map for 1.2 mm Steel Shot Fluidized Bed 185 7.4.4 Comparison and Discussion 187 7.5 Summary 196 Chapter 8 Bubble Characteristics in Three-Phase Fluidized Beds 198 8.1 Introduction 198.2 Bubble Frequency8.3 Bubble Chord Length and its Distribution 200 8.4 Average Bubble Velocity 211 8.5 Summary 219 Chapter 9 Conclusions and Recommendations 221 9.1 General Conclusions 229.2 Recommendations for Future Work 223 Nomenclature 225 References 232 Appendix A Computer Programs for Data Acquisition and Processing 244 Appendix B Experimental Data 260 Appendix C Data Validation 301 ix List of Tables Table 2.1. Properties of particles investigated 15 Table 2.2. Effect of probe time response on measured bubble velocity and bubble chord length 22 Table 3.1. Summary of some experimental methods used to delineate regime transitions in gas-Uquid two-phase systems 44 Table 3.2. Summary of experimental methods used to delineate regime transitions in gas-Uquid-solid three-phase systems 46 Table 4.1 Flow regime transition velocities determined from the conductivity probe for air-water system at = 0.0184 m/s using the criteria proposed in sections 4.3.1 to 4.3.5 72 Table 4.2. Flow regime transition velocities deterrnined from the standard deviation of absolute pressure fluctuations for U^ = 0.0184 m/s 74 Table 4.3. Flow regime transition velocities determined from the standard deviation of differential pressure fluctuations for = 0.0184 m/s 77 Table 4.4. Flow regime transition velocities determined from the skewness of differential pressure fluctuations for = 0.0184 m/s 77 Table 4.5. Flow regime boundaries for air-water system at Z = 0.65 m and D = 0.0826 m.... 79 Table 4.6. Summary of some experimental regime transition measurements from the literature 82 Table 6.1. Experimental conditions used in various investigations of minimum fluidization for three-phase systems (SI Units) 99 Table 6.2. Experimental conditions used in correlations for a 112 Table 6.3. Empirical equations for oc 113 Table 6.4. Average absolute percentage and root mean square percentage deviations between predictions from correlations for minimum fluidization velocity for three-phase fluidized beds and experimental data 122 Table 6.5. Summary of experimental operating conditions for investigations of critical gas velocity 126 Table 6.6. Experimental and predicted values of critical gas velocity (m/s) at zero superficial liquid velocity 135 Table 6.7. Mhiimum fluidization velocities at low liquid velocities 138 Table 6.8. Experimental results for the boundary between fluidized bed and transport flow regimes 143 Table 6.9. Average absolute percentage deviation between experimental results and model predictions for particle transport velocity in gas-liquid mixture 149 Table 7.1. Summary of previous investigations on flow regime transitions in three-phase fluidized beds 162 Table 7.2. Flow regime transition velocities for air-water-1.5 mm glass bead fluidized beds 17Table 7.3. Flow regime transition velocities for air-water-4.5 mm glass bead fluidized bed... 172 Table 7.4. Flow regime transition velocities for air-water-1.2 mm steel shot fluidized bed.... 173 xi List of Figures Figure 1.1. Classification of gas-liquid-solid fluidization system (from Fan, 1989) 2 Figure 1.2. Relationship between mean bubble size and bed expansion in different flow regimes (from Matsuura and Fan, 1984) 3 Figure 1.3. Effects of gas and liquid flow rates on axial dispersion coefficient in different flow regimes (from Muroyama et al., 1978): (a) Coalesced bubble flow (small particles), (b) Dispersed bubble flow (large particles) 4 Figure 1.4. Schematic diagram of flow patterns 8 Figure 2.1. Schematic diagram of experimental apparatus 13 Figure 2.2. Schematic diagram of three-phase separator 4 Figure 2.3. Typical pressure fluctuation signals in an air-water system, Z = 1.35 m; AZ = 0.1m; = 0.018 m/s; Ug = 0.041 m/s 16 Figure 2.4. Configuration of conductivity probe 9 Figure 2.5. Typical raw signals of a two-element condutfvity probe in an air-water system, Z = 1.95 m; L = 1.1 mm; = 0.018 m/s; Ug = 0.086 m/s 20 Figure 2.6. Response of conductivity probe to a gas bubble in an air-water system, Z = 1.95 m; L = 1.1 mm; \Jt = 0.018 m/s; Ug = 0.086 m/s 21 Figure 2.7. Typical conductivity probe signal for steel shot three-phase system, = 0.036 m/s; Ug = 0.037 m/s; Z = 0.65 m 24 Figure 2.8. Idealized square-wave relationship between probe, bubble and simplified signal 25 Figure 2.9. Flow chart for data processing 30 Figure 3.1. Schematic diagram of experimental apparatus used for preliminary pressure fluctuation tests 36 Figure 3.2. Pressure signals corresponding to single bubble formation and rise (air injector 0.25 m above the distributor) 37 xii Figure 3.3. Pressure signals corresponding to continuous air supply at Ug = 0.387 m/s in a stagnant column containing water 38 Figure 3.4. Ideal signal for conductivity probe 4Figure 3.5. Relationship between gas holdup and various moment parameters of an ideal signal for conductivity probe 50 Figure 4.1. Typical raw signals at different superficial gas velocities from conductivity probe for air-water system at Z = 0.65 m, = 0.0184 m/s 53 Figure 4.2. Probability density function of conductivity signal for air-water system at Z = 0.65 m, LLj = 0.0184 m/s and different gas velocities 54 Figure 4.3. Variation of moments of conductivity probe signals with superficial gas velocity for air-water system at Z = 0.65 m, = 0.0184 m/s 55 Figure 4.4. Variation of moments of conductivity probe signals with gas holdup for air-water system at Z = 0.65 m, Ue = 0.0184 m/s 56 Figure 4.5. Local gas holdup at different heights for air-water system at = 0.0184 m/s 57 Figure 4.6. Transition between discrete and coalesced bubble flow regimes in air-water system at different superficial liquid velocities 58 Figure 4.7. Method used to determine transition between coalesced bubble flow and slug flow in air-water system at various superficial liquid velocities 62 Figure 4.8. Plot of local bubble frequency at axis of column versus superficial gas velocity showing transition between slug flow and chum flow and the onset of annular flow in the air-water system for different superficial liquid velocities 63 Figure 4.9. Average bubble chord length and bubble time versus superficial gas velocity showing transition between chum flow and bridging flow for air-water system at Z = 0.65 m, = 0.064 m/s 65 xiii Figure 4.10. Average bubble time versus superficial gas velocity showing transition between chum flow and bridging flow in the air-water system at Z = 0.65 m for different superficial liquid velocities 65 Figure 4.11. Dimensionless standard deviation of bubble time plotted against superficial liquid velocity showing transition between discrete bubble flow and dispersed bubble flow for air-water system at Z = 0.65 m 67 Figure 4.12. Bubble frequency plotted against superficial gas velocity showing transition between discrete and coalesced bubble flow at different locations for air-water system at Ut = 0.0184 m/s 68 Figure 4.13. Sauter mean bubble chord length versus superficial gas velocity showing transition between coalesced bubble flow and slug flow at two different levels for air-water system at = 0.0184 m/s 69 Figure 4.14. Variation of bubble frequency with gas velocity at different heights for air-water system at \Jt = 0.0184 m/s 70 Figure 4.15. Average bubble time versus superficial gas velocity showing transition between chum flow and bridging flow at different locations for air-water system at \Ji = 0.0184 m/s 71 Figure 4.16. Probability density function of absolute pressure fluctuations for air-water system at Z = 0.65 m and Ut = 0.0184 m/s...... 73 Figure 4.17. Standard deviation of absolute pressure fluctuations for air-water system at U, = 0.0184 m/s 74 Figure 4.18. Probability density functionof of differential pressure fluctuations at Z = 0.65 m for Vt = 0.0184 m/s 76 Figure 4.19. Standard deviation of differential pressure fluctuations at different levels for = 0.0184 m/sFigure 4.20. Skewness of differential pressure fluctuations at different levels for = 0.0184 m/s 77 xiv Figure 4.21. Two-phase bubble column flow regime map for air-water system with D = 0.0826 m and Z = 0.65 m Distributor: perforated plate containing 62 2-mm circular holes 80 Figure 4.22. Comparison of flow regime maps with previous studies 83 Figure 5.1. Linear relationship between bubble frequency and superficial gas velocity for the discrete and dispersed bubble flow regimes with air-water system at Z = 650 mm and D = 82.6 mm 86 Figure 5.2. Comparison of average bubble chord length in discrete and dispersed bubble flow regimes for air-water system at Z = 0.65 m and D = 82.6 mm. 87 Figure 5.3. Probability density distribution of bubble chord length in discrete and dispersed bubble flow regimes for air-water system at Z = 0.65 m and D = 82.6 mm.... 88 Figure 5.4. Average bubble velocity at different superficial hquid velocities for air-water system at Z = 0.65 m and D = 82.6 mm 89 Figure 5.5. Relationship between bubble travel length and average bubble chord length for air-water system at Z = 0.65 m and D = 82.6 mm 91 Figure 5.6. Bubble chord length in slug and churn flow regimes at Z = 0.65 m and D = 82.6 mm 92 Figure 5.7. Probability density distribution of bubble chord length in the slug and churn flow regimes at Z = 0.65 m and D = 82.6 mm 93 Figure 5.8. Relationship between average bubble velocity and average bubble chord length in slug and churn flow regimes for air-water system at Z = 0.65 m and D = 82.6 mm 95 Figure 5.9. Relationship between bubble travel length and average bubble chord length in the slug and churn flow regimes for air-water system at Z = 0.65 m, D = 82.6 mm and LL « 0.002 - 6 m/s 9xv Figure 6.1. Prediction of gas holdup on solids-free basis at minimum fluidization, with properties corresponding to the experimental conditions of Begovich and Watson, 1978 114 Figure 6.2. Determination of U^f by pressure drop and pressure gradient methods for 2.5 mm glass beads with Ug = 0.0509 m/s 11Figure 6.3. Effect of increasing or decreasing liquid velocity on determination of for 2.5 mm glass beads with Ug = 0.0509 m/s 116 Figure 6.4. for different particle sizes and densities 117 Figure 6.5. for particles of different wettablity and sphericity 117 Figure 6.6. Three-phase fixed and fluidized bed pressure gradient measurements compared with fixed bed prediction for 3.7 mm glass beads 119 Figure 6.7. Comparison of rninimum fluidization velocity predictions and experimental results for hquid- solid fluidized beds. Predictions are for an equation of the form Re^ = -y/a2 + b Ar^ - a, with values of a and b as listed in the legend 120 Figure 6.8. Experimental minimum fluidization velocities for 2.5 mm glass beads compared with predictions of various empirical equations 121 Figure 6.9. Experimental minimum fluidization velocities for 2.5 mm glass beads compared with predictions of various models 122 Figure 6.10. Comparison of all available experimental results for with predictions of gas-perturbed liquid model, Equation (6.50) 123 Figure 6.11. Determination of critical gas velocity for full suspension of particles: dp = 1.5 mm, ps = 2530 kg/m3, = 770 mm, = 0, AP = P50 - P650 132 Figure 6.12. Determination of critical gas velocity at different bed heights: dp = 1.5 mm; ps = 2530 kg/m3, FLj = 770 mm, = 0, AP = P50 - P650, P50 - P350 and P350 -Peso 133 xvi Figure 6.13. Effect of particle loading on critical gas velocity for complete solids suspension: dp = 1.5 mm, ps - 2530 kg/m3, H,, = 440, 770 mm, = 0 134 Figure 6.14. Determination of critical gas velocity at zero superficial liquid velocity.. 135 Figure 6.15. Detennination of critical gas velocity for three-phase system with 1.5 mm glass beads at different liquid velocities 137 Figure 6.16. Determination of critical gas velocity for three-phase system with 4.5 mm glass beads at different liquid velocities 137 Figure 6.17. Detennination of critical gas velocity for three-phase system with 1.2 mm steel shot at different Uquid velocities 138 Figure 6.18. Experimental minimum fluidization gas velocities for three-phase system at zero and low liquid superficial velocities 139 Figure 6.19. Predictions and experimental results for transition from fluidized bed to transport flow regime: air-water-1.5 mm glass beads 147 Figure 6.20. Predicted and experimental particle transport velocities for 4.5 mm glass beads in air-water mixture 147 Figure 6.21. Particle transport velocity predictions compared with experimental results of Jean and Fan (1987) 148 Figure 6.22. Experimental data for low density (ps < 2876 kg/m3) particle transport velocity compared with predictions of Song et al. (1989) empirical correlation and Model H 150 Figure 6.23. Comparison between particle transport velocity empirical correlations and experimental results for 1.2 mm steel shot 152 Figure 6.24. Regime map for air-water-1.5 mm glass bead three-phase system 153 Figure 6.25. Regime map for air-water-4.5 mm glass bead three-phase system 153 Figure 6.26. Regime map for air-water-1.2 mm steel shot three-phase system 154 xvii Figure 7.1. Comparison of conductivity probe signals in two-phase and three-phase systems at Z = 0.65 m and = 0.0184 m/s: (a) air-water two-phase, Ug = 0.040 m/s; (b) air-water-1.5 mm glass beads three-phase, Ug = 0.039 m/s 166 Figure 7.2. Bubble frequency in two-phase and three-phase systems for the same liquid flow rate: Z = 0.65 m and = 0.0184 m/s 166 Figure 7.3. Average bubble chord length in two-phase and three-phase systems for the same Uquid flow rate at Z = 0.65 m and = 0.0184 m/s 167 Figure 7.4. Comparison of bubble frequency in different systems at Z = 0.65 m and LLj = 0.0455 m/s 168 Figure 7.5. Comparison of average bubble chord length in different systems at Z = 0.65 m and ILj = 0.0455 m/s 168 Figure 7.6. Summary of flow regime transition criteria 169 Figure 7.7. Transition between discrete and coalesced bubble flow regime in a three-phase fluidized bed containing 1.5 mm glass beads at different superficial hquid velocities 171 Figure 7.8. Transition between discrete and coalesced bubble flow regime in a three-phase fluidized bed containing 4.5 mm glass beads at different superficial liquid velocities 171 Figure 7.9. Transition between discrete and coalesced bubble flow regime in a three-phase fluidized bed containing 1.2 mm steel shot at low superficial liquid velocities 173 Figure 7.10. Transition between discrete and coalesced bubble flow regimes in a three-phase fluidized bed containing 1.2 mm steel shot at high superficial liquid velocities 174 Figure 7.11. Transition between coalesced bubble flow and slug flow in a three-phase fluidized bed containing 1.5 mm glass beads at various superficial liquid velocities 175 xviii Figure 7.12. Transition between coalesced bubble flow and slug flow in a three-phase fluidized bed containing 4.5 mm glass beads at various superficial hquid velocities 175 Figure 7.13. Transition between coalesced bubble flow and slug flow in a three-phase fluidized bed containing 1.2 mm steel shot at various superficial hquid velocities 176 Figure 7.14. Local bubble frequency at axis of column versus superficial gas velocity showing transition between slug flow and churn flow and the onset of annular flow for three-phase fluidized bed containing 1.5 mm glass beads at different superficial liquid velocities 177 Figure 7.15. Local bubble frequency at axis of column versus superficial gas velocity showing transition between slug flow and churn flow and onset of annular flow for three-phase fluidized bed containing 4.5 mm glass beads at different superficial hquid velocities 177 Figure 7.16. Plot of local bubble frequency at axis of column versus superficial gas velocity showing transition between slug flow and churn flow and the onset of annular flow for three-phase fluidized bed containing 1.2 mm steel shot at different superficial hquid velocities 178 Figure 7.17. Average bubble time versus superficial gas velocity showing transition between churn flow and bridging flow for a three-phase fluidized bed containing 1.5 mm glass beads at different superficial hquid velocities 179 Figure 7.18. Average bubble time versus superficial gas velocity showing transition between churn flow and bridging flow for a three-phase fluidized bed containing 4.5 mm glass beads at different superficial hquid velocities 179 Figure 7.19. Average bubble time versus superficial gas velocity showing transition between churn flow and bridging flow for a three-phase fluidized bed containing 1.2 mm steel shot at different superficial hquid velocities 180 xix Figure 7.20. Dimensionless standard deviation of bubble time plotted against superficial liquid velocity showing transition between coalesced bubble flow and dispersed bubble flow for 1.5 mm glass bead three-phase fluidized bed at different superficial gas velocities 182 Figure 7.21. Dimensionless standard deviation of bubble time plotted against superficial liquid velocity showing transition between discrete bubble flow and dispersed bubble flow for 4.5 mm glass bead three-phase fluidized bed at different superficial gas velocities 182 Figure 7.22. Dimensionless standard deviation of bubble time plotted against superficial hquid velocity showing transition between discrete bubble flow and dispersed bubble flow for 1.2 mm steel shot three-phase fluidized bed at different superficial gas velocities 183 Figure 7.23. Flow regime map for air-water-1.5 mm glass bead three-phase fluidized bed with D = 0.0826 m and Z = 0.65 m. Distributor: perforated plate containing 62 2-mm circular holes 184 Figure 7.24. Flow regime map for air-water-4.5 mm glass bead three-phase fluidized bed with D = 0.0826 m and Z = 0.65 m. Distributor: perforated plate containing 62 2-mm circular holes '. 185 Figure 7.25. Flow regime map for air-water-1.2 mm steel shot three-phase fluidized bed with D = 0.0826 m and Z = 0.65 m Distributor: perforated plate containing 62 2-mm circular holes 186 Figure 7.26. Boundaries between various bubble flow regimes 187 Figure 7.27. Comparison between predictions of Equation (7.3) and experimental results 188 Figure 7.28. Comparison between predictions of Equation (7.3) and experimental data from literature 189 Figure 7.29. Boundaries for onset of slug flow regime 190 Figure 7.30. Comparison between predictions of Equation (7.5) and experimental data 191 xx Figure 7.31. Comparison between predictions of Equation (7.6) and experimental data 192 Figure 7.32. Boundaries between slug and churn flow regimes 193 Figure 7.33. Comparison between predictions of Equation (7.7) and experimental data 193 Figure 7.34. Boundaries between churn and bridging flow regimes 194 Figure 7.35. Comparison between predictions of Equation (7.8) and experimental data 195 Figure 7.36. Boundaries between bridging and annular flow regimes 196 Figure 8.1. Average bubble chord length in coalesced and dispersed bubble flow regime for air-water-1.5 mm glass bead system 201 Figure 8.2. Average and Sauter mean bubble chord length in slug and churn flow regime for air-water-1.5 mm glass bead system 201 Figure 8.3. Bubble chord length distributions in different flow regimes for air-water-1.5 mm glass bead fluidized beds 203 Figure 8.4. Average bubble chord length in discrete and dispersed bubble flow regimes for air-water-4.5 mm glass bead fluidized bed 204 Figure 8.5. Average and Sauter mean bubble chord length in different flow regimes for air-water-4.5 mm glass bead fluidized bed 205 Figure 8.6. Bubble chord length distributions in different flow regimes for air-water-4.5 mm glass bead fluidized bed 206 Figure 8.7. Average bubble chord length in discrete and dispersed bubble flow regimes for air-water-1.2 mm steel shot fluidized bed 207 Figure 8.8. Average and Sauter mean bubble chord length in different flow regimes for air-water-1.2 mm steel shot at \Jt = 0.0455 and 0.311 m/s 208 Figure 8.9. Bubble chord length distribution in different flow regimes at low gas velocity for air-water-1.2 mm steel shot fluidized bed 209 Figure 8.10. Bubble chord length distribution in different flow regimes at high gas velocity for air-water-1.2 mm steel shot fluidized bed 210 xxi Figure 8.11. Average bubble velocity plotted against average bubble chord length in dispersed and coalesced bubble flow regimes for air-water-1.5 mm glass bead fluidized beds, Ug = 0.0018 - 0.145 m/s 211 Figure 8.12. Variation of average bubble velocity plotted against average bubble chord length in slug and chum flow regimes for air-water-1.5 mm glass bead fluidized beds '. 212 Figure 8.13. Bubble travel length plotted against average bubble chord length in coalesced and dispersed bubble flow regimes for air-water-1.5 mm glass bead fluidized beds 213 Figure 8.14. Bubble travel length plotted against average bubble chord length in different flow regimes at low liquid velocities for air-water-1.5 mm glass bead fluidized bed 214 Figure 8.15. Bubble travel length plotted against average bubble chord length in different flow regimes at high liquid velocities for air-water-1.5 mm glass bead fluidized bed 215 Figure 8.16. Average bubble velocity in discrete and dispersed bubble flow regimes for air-water-4.5 mm glass bead fluidized bed 215 Figure 8.17. Average bubble velocity in different flow regimes for air-water-4.5 mm glass bead fluidized bed 216 Figure 8.18. Bubble travel length plotted against average bubble chord length in different flow regimes for air-water-4.5 mm glass bead fluidized bed with Ug = 0.003 to 4.5 m/s 217 Figure 8.19. Average bubble velocity plotted against average bubble chord length in different flow regimes for air-water-1.2 mm steel shot fluidized bed with Ug 0.003 to 4.5 m/s 218 Figure 8.20. Bubble travel length plotted against average bubble chord length for air-water-1.2 mm steel shot fluidized bed with U„ = 0.003 to 4.5 m/s 219 xxii Acknowledgment I would like to express my sincere gratitude to Drs. N. Epstein and J. R. Grace for their guidance, support and inspiration during this work. Since the beginning, they both gave generously of their time and effort towards the creation and correction of this work. I would like to thank Dr. J.-X. Zhu for his recommendation and his co-supervision during the early stages of the project. Due to his effort I had the opportunity to he supervised by Drs. Epstein and Grace. My appreciation also goes to Dr. K.-S. Lim for his valuable comments and assistance. In addition, I would like to thank Michael Safoniuk and Dennis Pianarosa for their help and discussion, and Professors D. B. Dreisinger, S. Hatzikiriakos and P. G. Hill for acting as members of the supervisory committee. I would like to thank the Chemical Engineering workshop and stores for their cooperation and kindness during my stay in the department. The financial support of the Natural Sciences and Engineering Research Council and of fellowships provided by the C. L. Wang Memorial Scholarship and the UBC Faculty of Graduate Studies are gratefully acknowledged. Finally, I would like to make a special acknowledgement to my wife, Qi, for her understanding, sacrifice and support, and to my daughter, Maya, for brightening the days. xxiii Chapter 1 Introduction Three-phase fluidized beds have been widely used in industry for processes such as hydrotreating, Fischer-Tropsch synthesis, methanol synthesis, fermentation, and aerobic biological waste water treatment (Fan, 1989). A number of investigations have been conducted on the hydrodynamics, as well as on mass and heat transfer. Since 1968, there have been a number of review papers and books focused on this field (Ostergaard, 1968; Shah, 1979; Kolbel and Ralek, 1980; Epstein, 1981; Shah et al., 1982; Ramachandran et al., 1983; Wild et al., 1984; Darton, 1985; Muroyama and Fan, 1985; Fan, 1989). Three-phase (gas-liquid-solid) fluidized beds can be classified into three kinds of operations, in terms of the flow directions of the two fluids, namely cocurrent, countercurrent, and stationary liquid (i.e. zero-liquid flow rate) three-phase fluidization (Epstein, 1981). A more detailed classification of three-phase fluidization, including the transport operating regime, has been presented by Fan (1989) and is shown in Figure 1.1. Until now, most research has been devoted to cocurrent upward three-phase fluidization due to its wider application. Research topics have included incipient fluidization, bed expansion, initial bed contraction, phase holdups, bubble size, bubble size distribution, bubble wake characteristics, backmixing of all three phases, mass and heat transfer. Three flow regimes (dispersed bubble flow, coalesced bubble flow and slug flow) have been identified reflecting different flow patterns of the three phases involved. The flow pattern strongly affects the key properties of three-phase reactors. Matsuura and Fan (1984) reported that the mean bubble size is different in different flow regimes. In the dispersed bubble flow regime, a small mean bubble size is observed which increases only slowly with increasing bed expansion. In the coalesced bubble flow regime, on the other hand, a relatively large mean bubble size is observed. The mean 1 2 bubble size increases considerably with increasing bed expansion for the coalesced bubble flow regime, while increasing somewhat more quickly for the slug flow regime, as shown in Figure 1.2. Muroyama et aL (1978) found that in the coalesced bubble flow regime the axial dispersion coefficient of the hquid phase is significantly larger than for the dispersed bubble flow regime. Even the trends with increasing gas velocity are different, as shown in Figure 1.3. Chern et al. (1984) reported that the gas holdup in gas-hquid-solid fluidized beds varies strongly with bubble properties. Separate correlations were used to describe the variation of gas holdup in the slug flow, dispersed bubble flow and coalesced bubble flow regimes. O X N '(f) -8 « D A C o 2 0' 3.00 sjdo 19.0 19.8 u, CcmAl 5.16 12.9 5.1© 3 mm Gtass Beads A O 0 .a Binary A 0) 0 a 6 mm Glass B«ods • • • • Coalesced Bubble Flow Regime 2 3 4 Bed expansion, Hf /HQ C—1 Figure 1.2. Relationship between mean bubble size and bed expansion in different flow regimes (from Matsuura and Fan, 1984). 3 3™°t ' ' ' I I I MIIIJ I I I I I 1144 500 •g 200 I 100 g « 50 i. <i CL « .2 < 20 ! Bubt>(« column, Kito el *(. cm £f^^A j [0,«t0t«« — ><>n<0.21S<M.I ~ (a) i t nun I I i umil 0.1 0.2 0.5 1 2 5 10 20 Gas flow rate (cnysec) I I I I Kill 50 K)0 21 lit! Mill I i ! i mil ( mini 0.1 0.2 0.5 1 2 5 10 20 50 100 Gas flow rate ug0 (cnV4«c) Figure 1.3. Effects of gas and liquid flow rates on axial dispersion coefficient in different flow regimes (from Muroyama et aL, 1978): (a) Coalesced bubble flow (small particles). (b) Dispersed bubble flow (large particles). 4 With recent developments in environmental engineering, the high gas-hquid mass transfer rates of three-phase fluidized beds have been used advantageously in aerobic wastewater treatment to supply the necessary oxygen. One device used is a draft tube fluidized bed, in which a draft tube is located concentrically inside the column. Most such devices are operated at relatively high gas velocities to obtain a high oxygen concentration for microbial growth. However, the hydrodynamics of three-phase fluidized beds at such high gas velocities are still unclear. In small size columns, on increasing the gas velocity within the coalesced bubble flow regime, slug flow is encountered. There is a need for work where the gas velocity is increased further in order to fully understand the hydrodynamics of a three-phase fluidized bed. At the same time, the boundaries of any new flow regimes should be designated. 1.1 Definitions of Flow Patterns There is still a lack of consistent definitions of flow patterns. Different terminology is often used to describe the same flow pattern by different investigators. In order to avoid confusion, the flow patterns in a bubble column and/or a three-phase fluidized bed are defined, based on characteristics of bubbles, as follows: 1) Dispersed bubble flow: The dispersed bubble flow regime predominates at high hquid velocities and at low to intermediate gas velocities. In this regime, no significant bubble coalescence occurs, even though the bubble population may be very high. The bubbles are small and of relatively uniform size. It is commonly believed that the small uniform bubbles result from turbulence of the hquid phase in gas-hquid systems (Taitel et al., 1980) and from the presence of large particles in three-phase systems (Fan, 1989). 5 Discrete bubble flow: This regime predominates at low gas and low liquid velocities. Due to the low gas velocity, the initial bubble size is small when a gas distributor with small holes is used and the bubble frequency is low, giving little chance for the bubbles to coalesce. The overall bubble characteristics are similar to those in the dispersed bubble flow regime, i.e. the bubbles are small with a narrow size distribution. Coalesced bubble flow: In this regime, bubbles tend to coalesce. Both the bubble size and the bubble velocity are large and show wide distributions. Coalesced bubbles rise near the axis of the column with high velocities, causing violent agitation of the bed. Bubbles with spherical, ellipsoidal and spherical-cap shapes of various sizes are observed. This regime predominates at low liquid and intermediate gas velocities. Slug flow: In this regime most of the gas phase rises as large bullet-shaped bubbles (often called Taylor bubbles or slugs) which have volume-equivalent diameters almost equal to, or greater than, the column diameter. Some small gas bubbles exist in the multiphase plugs which separate the successive large gas bubbles or slugs. Churn flow: Chum flow has some similarities to slug flow, but the flow pattern is much more chaotic, frothy and disordered. The bullet-shaped bubbles become narrow, and then-shapes distorted. Small bubbles in the multiphase plugs coalesce, generating new Taylor bubbles. Downward motion of the liquid phase at the walls becomes more significant as the superficial gas velocity is increased. Oscillatory longitudinal motion of the liquid in alternating directions can be observed in the multiphase regions. Bridging flow: Bridging flow is a transition regime between chum flow and annular flow. Taylor bubbles are distorted and elongated in bridging flow. Multiphase plugs become very short, and finally only some multiphase layers or bridges exist between successive 6 Taylor bubbles. These multiphase layers are repeatedly destroyed by the high gas holdup in the core region of the column. At the same time, new multiphase layers can be observed at the bottom of the column due to downward flow of the hquid phase in the annular region. As this happens, hquid accumulates and forms new bridges which are again lifted or destroyed by the gas. 7) Annular flow: Annular flow is characterized by a continuous gas phase along the core of the column. The hquid phase moves upwards partly as a wavy annular hquid film and partly in the form of drops entrained by the gas in the core of the column. A schematic diagram for the different flow patterns is presented in Figure 1.4. Many factors influence flow patterns and their transitions, such as physical properties of the gas and the hquid, geometry of the column and design of the gas distributor. Flow patterns and their transitions also depend on the location at which observation and measurement are carried out, as well as the distance between this location and the exit of the fluids. For three-phase systems, the three operating regimes can be defined based on the state of particle motion. In a fixed bed, particles remain motionless, and the drag force on the particles induced by the flow of a gas-hquid mixture is smaller than the effective weight of the particles. In a fluidized bed, particles move within the system, and the drag force on the particle counterbalances the effective weight of the particles. In the transport flow regime, at high gas and/or hquid flow rates, solid particles are entrained from the column. If no makeup particles are added to the column, a particle-free two-phase flow then results. Within the transport flow regime, flow patterns can also be characterized as dispersed bubble flow, slug flow, churn flow, bridging flow and annular flow, depending on the gas and hquid flow rates. 7 8 1.2 Scope of Work Since flow patterns affect transport phenomena, such as mass and heat transfer, numerous studies have been devoted to flow regime identification and flow regime transitions in cocurrent upward gas-liquid flow (Nakazatomi et al., 1992; Monji, 1993; also see Table 3.1) and in three-phase fluidization (Fan et al., 1985; Jean and Fan, 1987; Song etal, 1989; also see Table 3.2). Most studies have been based on visual observation (Griffith and Wallis, 1961; Ermakova et al, 1970; Mukherjee et al, 1974; Muroyama et al, 1978; Taitel et al, 1980; Spedding and Nguyen, 1980; Weisman and Kang, 1981; Fernandes et al, 1983; Fan et al, 1984; Matsuura and Fan, 1984; Fan et al, 1985; Fan et al., 1986; Hasan and Kabir, 1992). However, due to the rapid and chaotic nature of multiphase flow, visualization may not be a reliable method of distinguishing flow regimes. This method is also unsuitable for non-transparent columns, such as three-phase fluidized beds in commercial units. The objectives of this work are: (1) to develop a measurement technique that can be used to determine gas-liquid and gas-liquid-solid flow regime transitions objectively, explore new flow regimes at higher superficial gas velocities and delineate the boundaries between each flow regime, and (2) to delineate the boundaries between fixed bed, fluidized bed and particle transport flow. Since the definitions of most flow patterns are based on bubble characteristics, the criteria for flow regime transitions should be based on these characteristics. An electrical conductivity probe has been used to measure bubble characteristics. The configuration of the probe, as well as data acquisition and data processing techniques, are described in Chapter 2. 9 Aside from visual observations, other instrument methods for distinguishing flow regimes have been reported based on pressure transducers, conductivity probes and X-ray measurement systems (Vince and Lahey, Jr., 1982; Kitano and flceda, 1988; Mao and Dukler, 1989; Lee et al., 1990; Han and Kim, 1990; Franca et al., 1991; Soria and de Lasa, 1992). Chapter 3 summarizes alternative measurement techniques and criteria for flow regime transitions. Some preliminary tests carried out to investigate the different techniques and criteria are then presented. In Chapter 4 the criteria for flow regime transitions are proposed for two-phase (gas-hquid) systems based on experimental results of bubble characteristics. These gas-hquid results and criteria serve as a basis for the subsequent investigation of gas-hquid-sohd systems in later chapters. A flow regime map for the gas-hquid (air-water) system is also presented in Chapter 4. Chapter 5 presents detailed bubble characteristics, such as bubble frequency, bubble chord length and its distribution as well as bubble rising velocity in different gas-hquid flow patterns. The variation of the bubble characteristics with operating conditions in an air-water system is also presented in this chapter. On adding solid particles to a gas-hquid system, the first issue which might arise is the transition between a fixed bed and a fluidized bed, i.e., determination of the incipient fluidization velocity. Chapter 6 presents experimental results and theoretical models for minimum fluidization velocity in three-phase fluidized beds. Seven different kinds of particles were tested in this study. A successful new model is proposed based on this work. Another issue is the boundary between a fluidized bed and a sohds transport flow regime, i.e., the particle transport velocity in a cocurrent gas-hquid flow. A theoretical model and an empirical correlation are proposed, based on experiments with three different types of particles and data available from the literature. 10 An experimental study of flow regime transitions in a three-phase fluidized bed is presented in Chapter 7. The measurement technique and the criteria for flow regime transitions are identical to those already described for the two-phase gas-hquid system. Three kinds of solid particles are used to demonstrate the effect of particle size and particle density on flow regime transitions. Five empirical correlations for the boundaries between the flow regimes in three-phase fluidized beds are proposed, based on the present study. These correlations are then compared with data from the literature. Reasonable agreement is found between the predictions and the literature data. Bubble characteristics for a three-phase fluidized bed are presented in Chapter 8. Bubble frequency, chord length and its distribution, as well as rise velocity in different flow regimes are discussed in this chapter. Conclusions of this study and recommendations for future work are provided in Chapter 9. 11 Chapter 2 Experimental Apparatus and Measurement Methods A 2D Plexiglas column, of rectangular cross-section 300 mm by 13 mm and 2.0 m high, was used in this work to qualitatively observe the flow patterns at different operating conditions and the interaction between a conductivity probe and bubbles. However, all quantitative experiments in this work were carried out in a 3D Plexiglas column, of circular cross-section 82.6 mm in diameter, as described below. Both columns and their auxiliaries were designed, constructed and assembled for the present project. 2.1 Apparatus The main component of the experimental apparatus consisted of a 0.0826 m diameter by 2 m high Plexiglas column with a perforated gas-hquid distributor plate containing 62 2-mm circular holes (covered by a stainless steel screen). The region below the distributor plate was a 0.5 m long gas-hquid calming section packed with 1/2 inch (13 mm) ceramic intalox saddles as shown in Figure 2.1. A three-phase separator was designed, built and attached to the top of the column. A schematic diagram (proportionally scaled) of this separator is shown in Figure 2.2. The three-phase mixture rising from the main column entered the separator from its bottom. The gas phase was led to a draft tube with a conical lower section (1) and then ventilated by a gas vent cylinder (2). The liquid-solid mixture was forced into the liquid-solid region (DI) from the lower end of the gas vent cylinder (2) by the static head of the three-phase mixture inside the cylinder. In the liquid-solid region, a liquid-solid fixed/fluidized bed was formed which provided a clear bed surface allowing pure hquid to overflow into the outer hquid channel (IV) from where it passed to the drain. A successful design should prevent the gas phase from reaching the hquid- solid region, 12 Figure 2.1. Schematic diagram of experimental apparatus. since in a three-phase system entrainment of solid particles is mainly caused by bubble wakes (Dayan and Zalmanovich, 1982; El-Temtamy and Epstein, 1989; Page and Harrison, 1974). This was achieved with the aid of the draft tube (1). The apparent density in the draft tube is significantly lower than in region II due to the presence of gas phase in region I. Hence, a circulation is created between regions I and H This circulation prevents gas bubbles from entering region in, while, at the same time, causing the particles to return to the main column near the lower end of the draft tube (1). This separator allowed experiments to be carried out for a very wide range of operating conditions. At high gas and liquid flow rates, most particles were carried over into the separator 13 A GAS 1. Draft tube. '_ 1 1 Upward flow region. 2. Gas vent cylinder. D_ 816111111 n Downward flow region. 3. Overflow dam. m. Liquid-solid region. 4. Liquid drain channel. IV Liquid draining region. Figure 2.2. Schematic diagram of three-phase separator. where they spent considerable time in the hquid-sohd region (HI). Even under solid transport flow conditions, no particles were carried out of the separator with the hquid or gas stream A top-dense bottom-dilute solid concentration profile was observed in the main column at very high gas and hquid velocities due to the build-up of particles in the separator at the top of the column. Air and tap water were used as the gas and hquid phases respectively throughout the work described in this thesis. The water temperature was measured at the outlet to determine the hquid viscosity and density, while gas and hquid flow rates were measured by inlet rotameters. The gas velocity was corrected for the pressure difference between the rotameters and the bottom of the 14 Table 2.1. Properties of particles investigated. Type of dp, Ps, So, *, particles mm kg / m3 Glass beads 1.5 2530 0.39 1.0 2.5 2520 0.39 1.0 3.7 2510 0.38 1.0 4.5 2490 0.37 1.0 Glass beads 2.5 2520 0.39 1.0 coated with TFE Sand 2.4 2610 0.39 0.8 Steel shot 1.2 7510 0.41 1.0 column. The superficial gas velocities ranged from 0 to 6.9 m/s, while the superficial hquid velocity was varied from 0 to 0.4 m/s in this study. Seven different particle types with measured properties as given in Table 2.1 were used in the investigation of incipient fluidization at low to intermediate gas velocity (Chapter 6). The particle diameter was measured by a vernier cahper based on one hundred particles. The particle density and the static bed voidage were deterrnined by pouring a known weight of particles into a cylinder containing water, measuring both the water level increase and the bed volume. Three of these types of particles, glass beads of diameters 1.5 and 4.5 mm as well as steel shot of diameter 1.2 mm, were also chosen for the investigation of incipient fluidization at high gas velocity, transition from fluidized bed to transport flow regimes (Chapter 6) and bubble-characteristic flow regime transitions within fluidized beds (Chapter 7). Except for the sand (<(» « 0.8), sphericities were all very nearly unity. Glass beads coated with TFE (Teflon) were used to investigate the effect of wettability on minimum fluidization velocity, while the steel shot allowed study of the effect of particle density. 2.2 Measurement Techniques In order to study the flow regime transitions objectively, quantitative measurements were required. In this study, pressure transducers and a conductivity probe were utilized for this 15 1000 Time, s Figure 2.3. Typical pressure fluctuation signals in an air-water system, Z = 1.35 m; AZ = 0.1 m; = 0.018 m/s; Ug = 0.041 m/s. purpose. A personal computer (IBM 486-DX2) with a data acquisition board (Keithley DAS-1202) was used for data logging and data analysis. 2.2.1 Pressure Transducers Several pressure transducers (Omega PX603) were employed to determine pressure gradients along the column, absolute pressure fluctuations and differential pressure fluctuations. Since the dominant frequency of the pressure fluctuations was around 10 Hz (Tutu, 1982; Matsui, 1984, 1986; Fan et al., 1986; Nishiyama et al., 1989; Franca et al., 1991; Spedding and Spence, 1993; Kwon et al, 1994), the data logging sampling rate was set at 100 Hz (an order of magnitude greater than the dominant frequency). 16 Typical absolute and differential pressure fluctuation raw signals are shown in Figure 2.3. The probability density distribution, mean value, standard deviation, skewness and kurtosis of the signals were calculated based on the definitions given by Snedecor and Cochran (1989). Consider a voltage-time trace signal V(t), where the voltage scale is divided into equal increments of width AV and the time scale into At equal increments. I£ during the observation period t, the voltage is within the range (V; - AV/2, V, + AV/2) for a total of nj times, then the Probability Density Distribution Function (PDF), p(Vj), is defined as: (2.1) where P(Vj, AV) is the probability distribution function and £ P( Vj,AV) = 1, N = i=l V,-Vf o AV The Mean value of V(t) is given by V=£ViP(Vi,AV) (2.2) i=l The Variance and the Standard Deviation (av) of V(t) are given respectively by Var =l(vi-V)2P(Vi,AV) (2.3) i=l and (2.4) Similarly, the Skewness (M3) and Kurtosis (M4) of V(t) are defined respectively as M3 =z(Vi-v)3p(Vi,AV) (2.5) i=l and 17 M4 =E(vi-V)4p(Vi,AV) i=l (2.6) The physical meaning of each of these moments can be explained as follows: The mean is the average value of a distribution. The variance is a measure of the distribution about the mean. The skewness is a measure of the asymmetry of a distribution. A symmetric distribution, such as a normal distribution, has zero skewness since the mean and the median coincide. A unimodal distribution, which has a median to the left of the mean, i.e. it is skewed to the left, has negative skewness. If the distribution is skewed to the right, it has a positive skewness. The kurtosis (flatness) is a measure of the distribution's peakedness. 2.2.2 Conductivity Probe A conductivity probe was used to measure local bubble characteristics, such as bubble frequency, bubble volume fraction, bubble time (defined later), bubble velocity and bubble chord length. Numerous methods have been reported for obtaining information on bubble characteristics. Three kinds of methods have primarily been employed for observing the behavior of bubbles in fluidized beds: a) photographic methods with a "two-dimensional" column, b) non invasive methods and c) intrusive probe techniques. The most common method to obtain information on bubble characteristics in fully three-dimensional columns is the intrusive probe technique. Several kinds of probes have been utilized including: capacitance probes (e.g. Geldart and Kelsey, 1972; Werther, 1974; Wittmann et al., 1981; Gunn and Al-Doori, 1985), electro-resistivity or conductivity probes (Park et al., 1969; Rigby et al., 1970; Ueyama et al., 1980; Burgess et al., 1981; Matsuura and Fan, 1984; Choi et al., 1988) and optical fiber probes (de Lasa 18 et al., 1984; Hatano et al., 1986; Glicksman et al., 1987; Lee and de Lasa, 1987,1988; Yu and Kim, 1988; Han and Kim, 1990, 1993; Lee et al., 1990). Since conductivity probes (or electrical impedance probes) are easy to manufacture, and due to their economy and rapid response, this type of probe was chosen in this study. The simplicity, convenience and low-cost are the major advantages of electro-resistivity or conductivity probes. However, if the continuous phase were not conductive, an electro-resistivity probe might be unsuitable. Another problem can occur when bubbles strike the probe; slow drainage of a Uquid film surrounding the probe can cause a delay in the signal response (Hewitt, 1978; Burgess et al., 1981). These problems were overcome in this study by using a conductive Uquid (water in this work) and reducing the exposure area of the conductivity probe. The configuration of the two-element conductivity probe is shown in Figure 2.4. Two 0.31 mm diameter wires are used as electrodes, with only their ends electrically exposed to the Upper element Prnhp ^ ^>oxyglue -TIUUC L= 1.1 or 4.0 mm •% brum IUIIUI Signal Output Battery Battery Figure 2.4. Configuration of conductivity probe. 19 multiphase rnixture. This design minimi zed the film effect of the probe. A stainless steel tube of 5.0 mm outer diameter serves as the common ground electrode for both wires. Two Wheatstone bridges are connected with this probe to obtain electrical voltage signals. This probe was developed in a semi-circular cross-section bubble column and the interaction between the probe and bubbles was observed in the 2D column, before it was used in the 3D column. Two probes of different wire spacing (see enlarged view in Figure 2.4, L = 1.1 and 4.0 mm) were used in this study. The one with the smaller wire interval was used to measure small bubbles at low gas velocities, while the other was utilized for large bubbles at high gas velocities. Each of these probes was inserted into the column horizontally so that the ends of these two wires were aligned vertically at the axis of the column. A typical raw signal is presented in Figure 2.5. The high voltage output corresponds to the 1 2 Lower - Upper chat chan inel inel ;' 3 \ Threshold 1 i 1 / > I 2.00 2.05 2.10 2.15 2.20 2.25 Time, sec Figure 2.5. Typical raw signals of a two-element conductivity probe in an air-water system, Z = 1.95 m; L = 1.1 mm; \Jt = 0.018 m/s; U„ = 0.086 m/s. 20 liquid phase, and the low peaks to the gas phase. When bubbles strike the probe, pulses can be read from the signal output. For this particular example, four bubbles are detected by the lower element of the probe, while three by the upper element. It can be seen that there is a time shift between lower and upper element outputs. A threshold can be set between the low and high voltage output to distinguish gas bubbles and allow bubble characteristics to be computed. Detailed data processing techniques are discussed further below. Probe response time can be estimated from raw signals (Burgess and Calderbank, 1975; Burgess et al., 1981). Figure 2.6 shows detailed information on the first bubble in Figure 2.5. The probe response time, At, for the lower element is 1.2 ms. The time shift between the two elements, xl5 is 1.6 ms. The time during which the lower element is enveloped by the bubble, called the bubble time t;, is 4.0 ms. By setting a threshold, the bubble velocity, Ub, and the bubble 1.0 0.8 h 0.6 h !> 0.4 0.2 0.0 Threshold —•— Lower channel --o-- Upper channel At V 2.035 2.040 2.045 Time, sec 2.050 Figure 2.6. Response of conductivity probe to a gas bubble in an air-water system, Z= 1.95 m;L= 1.1 mm; Ut = 0.018 m/s; Ug = 0.086 m/s. 21 Table 2.2. Effect of probe time response on measured bubble velocity and bubble chord length. Bubble No. in Fig. 2.5 At, ms Ub, m/s = Uxx Ub*, m/s = L/TJ* Relative % difference between Ub* and Ub £b, mm = tiUb mm = tfub' Relative % difference between £h* and ^b 1 1.20 0.69 0.55 25.5 5.8 8.1 -28.4 2 1.20 0.69 0.69 0.0 8.1 10.0 -19.0 3 1.60 0.46 0.39 17.9 37.5 43.6 -14.0 chord length, £b, can be calculated, based on T1 and t,. An alternative method to calculate Ub and £h is based on ii* and t,*, which may avoid the effect of probe response time. However, the latter causes difficulty in searching positions A and A* (see Figure 2.6) and also takes too much time for data processing. The results for all three bubbles which pass the threshold for both channels in Figure 2.5 are summarized in Table 2.2. It is seen that the probe response time is of the order of ms and the difference between the results with and without consideration of probe response time is 0 to 26% and -14 to -29% for the bubble velocity and the bubble chord length, respectively. It also can be seen that without taking into account the probe response time, the measured bubble chord length may be underestimated. However, this is v generally acceptable from an engineering point of view, especially when discrimination logic (described below) is applied to the signal analysis to screen out obhquely rising gas bubbles for the calculation of bubble velocities and chord lengths. 2.3 Data Processing For the conductivity probe, the data processing included data logging and data analysis. In order to obtain enough signal resolution for calculating bubble velocity and bubble chord length, the data logging sampling rate had to be 2500 Hz or higher. This reduced the total test time (due to the limitation of computer memory) and generated large size data files. Hence a computer 22 program which can log the original signal, extract all useful information and then discard the original data had to be developed. 2.3.1 Threshold When a bubble strikes the probe, a pulse can be read from the signal output. As shown in Figure 2.5, the original signal is not a perfect square wave, due to high frequency noise and the time response of the probe. A threshold was set to distinguish whether a probe was surrounded by a gas bubble or by a hquid-sohd mixture. This is a critical value which affects the calculated results of bubble chord length and local gas holdup. Depending on the probe response time, the amphtude of noise and any fluctuation in the conductivity of the liquid-soM rnixture, the threshold value has been set differently by different investigators. Matsuura and Fan (1984) and Rigby et al. (1970) set the threshold at 80% of the high level of the amplified signal intensity; Werther (1974) set it at 50%. Gunn and Al-Doori (1985) found that setting the threshold voltage in the range of -12 to -25 mV could yield an accurate result when the voltage amphtude was -2V for their measurement system Since the output voltage of the conductivity probe fluctuated for the probe within the liquid phase (see Figure 2.5), the threshold in this study was set based on the Probability Density Distribution Function, PDF, rather than basing it on the mid-point between the minimum and maximum values of the raw signal. For a bimodal distribution of the PDF, it was set at the average of these two peak locations (i.e., halfway between the two peak locations). For a single peak, it was set mid-way between peak location and the nnnimum or rnaximum of the signal voltage, depending on the skewness of the signal. Several different thresholds have been set to check the effect of the threshold on the experimental results. It was found that when the threshold was in the range from 25% to 75% of the PDF peak locations, the results did not vary significantly, especially when using the results to determine flow regime transitions. 23 > ! I Time, s Figure 2.7. Typical conductivity probe signal for steel shot three-phase system, Uf = 0.036 m/s; Ug = 0.037 m/s; Z = 0.65 m When steel shot was used in a three-phase system, the electrical conductivity of the sohd particles affected the probe output. Figure 2.7 shows a typical result for a steel shot/air/water system When a particle hits the end of the probe, an upward spike appears on the trace. This is probably due to the effect of particle surface, which increases the contact area of the probe when the particle makes contact with it. The threshold was set halfway between the hquid and the gas output voltages as shown in Figure 2.7. 2.3.2 Signal Simplification and Bubble Frequency Since the sampling rate and the test time are high, it is impossible and unnecessary to store all the original data. Once the threshold is set, the original signal can be simplified into a square wave form as shown in Figure 2.8. In this study, the time when a bubble struck the probe and the 24 til Liquid Phase Lower element Upper element ti i2 Gas Phase Time Figure 2.8. Idealized square-wave relationship between probe, bubble and simplified signal. time when this bubble left the probe were recorded. Thus, the size of the data file was reduced significantly, without losing the essential information for the purpose of calculating bubble properties. The bubble frequency, f, was obtained by counting the number of pulses within the test where M is the total number of bubbles detected and t^ is the total test time. 2.3.3 Bubble Time and Local Gas Holdup The bubble time, tj, is defined as the width (i.e. duration) of the pulse as indicated in Figure 2.8. It represents the duration of the probe being immersed in the bubble. This parameter is a function of the bubble size, bubble velocity, bubble shape, position where the probe pierces the bubble, and the angle with which the bubble travels relative to the vertical direction. Here ^ was calculated from (see Figure 2.8): time, i.e. (2.7) 25 t, il ~t3~tl or ti2 = t4 -12 (2.8) The time average local gas holdup, sg; was calculated from: (2.9) The bubble time is related to both the bubble frequency and local gas holdup, i.e. I bi (2.10) t; = U, bi where Ubi and £bi are the velocity and the chord length of an individual bubble, respectively, providing the bubble rises vertically. The average value of tj is defined as: i M ti=-Ztj (2.11) M i=i Combining Eqs. (2.7), (2.9) and (2.11) leads to: ti=-^ (2.12) In other words the average bubble time is the ratio of the gas holdup to the bubble frequency. 2.3.4 Bubble Velocity and Bubble Chord Length A number of investigators have utilized two-element probes to detect bubble velocity and chord length (e.g. Rigby et al., 1970; Tutsui and Miyauchi, 1980; Ueyama et al., 1980; Wittmann et al., 1981; Lee and de Lasa, 1988; Yu and Kim, 1988; Lee et al., 1990; Han and Kim, 1993). Although some of these studies used an optical fiber probe instead of a conductivity probe or an impedance probe, the principle was the same. 26 With a two-element probe, the bubble velocity, Ub, and bubble chord length, £b, can be computed if the vertical distance, L, between the two elements is known, providing all bubbles rise vertically, i.e. Ub=— or Ub=— (2.13) b = Ubxtil or ^b=Ubxti2 (2.14In practice, after an original signal has been simplified to a square wave, a logic circuit is needed to select signals created by bubbles which are travelling upwards. This is because: (1) a bubble detected by the lower element may be deflected and never contact the upper element; (2) one bubble may be detected by the lower element while another bubble reaches the upper element at almost the same time; (3) if a bubble rises obliquely, the effect of bubble shape may cause significant error in Ub and £b when equations (2.13) and (2.14) are used. Matsuura and Fan(1984) set their logic circuit as follows (see Figure 2.8): (1) . The signal for the upstream element is used as a trigger signal. (2) . They required ti < t2 and t3 < t4. (3). They further required 0.9 < - < 1.1 0.5(1! +T2) They claimed that 50% or fewer of the signal pairs detected by their probe were ignored for typical dispersed bubble flow, whereas about 65% or fewer were neglected for the coalesced bubble flow regime and 80% or fewer for the slug flow regime. It should be noted that without the logic circuit to select the signal, there is a significant error when Ub and £b are calculated. For example, the apparent bubble chord length could have been greater than the column diameter when the column was operated in the discrete bubble flow 27 regime or the coalesced bubble flow regime. A recent study (Lim and AgarwaL 1992) revealed that the principal error results from bubbles with non-vertical rise. The logic circuit in this study required for acceptance the following criteria (see Figure 2.8): 1. tx < t2 < t3 < t4 2. 0.9 < r<l.l The first criterion screens out signals created by different bubbles. Only those bubbles which contacted the lower element first and then the upper element were considered for computing the bubble velocity and the bubble chord length. The second criterion screened out signals created by bubbles with a significant non-vertical component of rise velocity. Although this logic circuit did not guarantee that all bubbles selected were rising vertically, it helped reduce the error from the two-element probe. Almost all investigators have recognized that the measured bubble chord length distribution is not equal to the real bubble size distribution. There is a relationship between these two parameters which depends strongly on the bubble shape. If the measured bubble length distribution and the bubble size distribution at the measuring period are Z(^b) and R(db), respectively, then: oo Z('b)= Ip(db,^b)R(db)d(db) (2.15) where p(db, £\>) is the probability density function of measured chord length, ^b, when the bubble diameter is db. For spherical bubbles, p(db, ^b) can be expressed (e.g. Werther, 1974; Tutsui and Miyauchi, 1980; Matsuura and Fan, 1984; Clark and Turton, 1988; Han and Kim, 1993) by: 28 for dh>£h P(db,^b)= d2h (2.16) 0 for db<^b For bubbles of other shapes, expressions for p(db, lb) are given by Clark and Turbva (1988). 2.3.5 Data Processing Procedure A computer program was developed to perform data acquisition and data processing. The flow chart of the program is shown in Figure 2.9. The sampling rate was 2500 s"1. In principle, the higher the sampling rate the better. However, the higher sampling rate reduces the sampling time due to the finite computer memory. With the sampling rate of 2500 s1, 3 s bursts could be handled. For each 3 s sub-sample, the probability distribution function, P{V/Vmax, A(V/Vmax)} was calculated, where A^/V™*) = 0.01 in this study. The reason for using V/Vma* is to overcome the shift of the signal; also it is dimensionless. The threshold was based on the Probability Distribution Function. Then the original signal was simplified and the condensed information stored. Data logging was terminated when 500 bubbles had been detected or the total sampling time reached 120 seconds (i.e., 40 sub-samples, each of 3 s duration). The bubble frequency, local gas holdup and bubble time were computed for each element, using Equations (2.7), (2.9) and (2.8), respectively. The bubble velocity and the bubble chord length were then calculated after false signals and non-vertical rise bubble signals had been screened out by the logic circuit. The PDF and key moments of the bubble time, the bubble velocity and the bubble chord length were also obtained using Equations (2.1), (2.2) and (2.4), respectively. All computer programs are given in Appendix A. 29 Yes Data acqusition Sampling interval = 3 s Sampling rate = 2500 1/s Calculate PDF of original data Set threshold to distinguish gas or liquid phase Simplify data No Calculate 1. Bubble frequency; 2. Local gas holdup; 3. Bubble time and its distribution as well as its moments; 4. Bubble chord length and its distribution, as well as its moments; 5. Bubble velocity and its distribution, as well as its moments. Stop Figure 2.9. Flow chart for data processing. 30 Chapter 3 Experimental Methods 3.1 Introduction Flow regimes and their transitions can be detennined by visual observation and instrument measurement. Most previous studies have been based on visual observation (e.g., in gas-Uquid systems: Griffith and Wallis, 1961; Spedding and Nguyen, 1980; Taitel et al., 1980; Weisman and Kang, 1981; Fernandes et al., 1983; Hasan and Kabir, 1992; in gas-liquid-solid systems: Ermakova et al., 1970; Mukherjee et al., 1974; Muroyama et al., 1978; Fan et al, 1984; Matsuura and Fan, 1984; Fan et al., 1985; Hu et al., 1985; Fan et al., 1986; Song et al., 1989; Nacef et al., 1992, 1995). Others have determined flow regimes with the aid of instruments, e.g., pressure transducers, conductivity probes and X-ray measurements (in gas-Hquid two-phase systems: Vince and Lahey, 1982; Mao and Dukler, 1989; Franca et al., 1991; in three-phase systems: Kitano and Dteda, 1988; Han and Kim, 1990; Lee et al., 1990; Soria and de Lasa, 1992). Although visual observation provides direct information on the flow patterns, some difficulties occur due to the rapid and chaotic nature of multiphase flow. It is often difficult to identify the transition of flow patterns without quantitative means. Alternatively, various statistical measures, such as standard deviations, skewness, kurtosis, probability density functions or power spectrum functions, can be calculated from the signals obtained by the instruments. Criteria for flow transitions can then be set by analyzing these quantities. However, the results can differ significantly depending on the parameters measured and the criteria adopted. This chapter discusses existing instrumental methods for determining flow regime transitions. 31 3.2 Pressure Fluctuations Absolute and differential pressure fluctuations reflect some characteristics of multiphase systems and can be detected readily using pressure transducers. Many investigators have used pressure fluctuations to study flow regime transitions. Standard deviations (SD), probability density functions (PDF) and power spectrum functions (PSF) of the pressure fluctuations have been calculated, and criteria for chstmgmshing flow regimes have been defined accordingly. 3.2.1 Previous Studies 3.2.1.1 Gas-liquid two-phase systems Absolute pressure fluctuations were initially used by Tutu (1982) who found that the root mean square of the pressure fluctuations was much smaller in annular flow than in churn flow. Subsequently, Tutu (1984) reported that it is better to use differential pressure (AP) fluctuations to distinguish flow regimes. Two pressure transducers, vetically separated by a distance of D/2, were used to obtain the differential pressure fluctuations. It was found that the PDF of the AP fluctuations could be used as a criterion for bubble-slug transition. In bubble flow, a single peak near the value corresponding to the static head of the hquid phase was observed in the PDF plot. In annular flow, the PDF plot showed a single peak located at AP = 0, corresponding to the gas phase. In slug and churn flows, a bimodal distribution was observed in the PDF plot. Hence, the PDF curve was divided into two parts at the rninimum PDF value. The areas under the PDF curve for these two parts were calculated, one, Ag, corresponding to Taylor bubbles and the other, Ab to the hquid phase. When the fraction of the area, Ag/(Ag+A^), reached a nrinimum with respect to PFr/00375- Fr^"0 075, the transition from bubble to slug flow was assumed to occur, where P = Ug/(Ug+U|) and Fre = U//(gD). An alternative method was suggested based on the standard 32 deviation (SD) of the AP fluctuations. The bubble/slug flow transition was claimed to occur at the inflection point in a plot of the standard deviation of the AP fluctuations vs. BFr/31. Matsui (1984, 1986) analyzed the differential pressure fluctuations of two differential pressure transducers. One, with a separation of D/2, was called the short-scale AP fluctuation probe; the other, with an interval of 10D, was called the long-scale AP fluctuation probe. The PDFs of these two probes were used to determine various flow regimes. It was found that with the short-scale probe, bubble, annular and mist flow exhibited a single peak in the PDF plots, while bimodal PDFs corresponded to slug-like flow. With the long-scale probe, dispersed bubble, slug, annular and mist flow exhibited single-peaked PDFs too; however, twin-peaked PDFs appeared in chum flow. The moments (mean, standard deviation, skewness and kurtosis) of both short-scale and long-scale AP fluctuations showed different values in different flow regimes. The author proposed a flow chart to identify the respective flow regimes by using these parameters combined with 13 transition criteria, one for each of the parameters. Franca et al. (1991) calculated the PDF and the power spectral density function (PSF) of AP fluctuations in a gas-liquid horizontal flow system Although different shapes of the PDF resulted from various flow regimes, the authors claimed that these shapes were not explicit enough to be used to distinguish flow regimes. For the PSF, they claimed that a relatively continuous frequency range characterized wavy and annular flows, while a multi-peaked spectrum was associated with plug and slug flow. The authors also used fractal techniques to analyze the AP fluctuations. However, they asserted that neither the PSF nor the fractal technique could easily provide numerical criteria for flow regime identification. 33 3.2.1.2 Three-phase systems Fan et al. (1986) determined flow regimes by analyzing the statistical properties of wall pressure fluctuations in a 0.102 m ID column. It was observed that the root mean square (RMS) of the pressure fluctuations decreased nearly linearly with in the coalesced bubble flow regime, while it remained constant or decreased shghtly with in the dispersed bubble flow regime. On the other hand, the RMS of the pressure fluctuations increased linearly in the coalesced bubble flow regime and remained steady or increased shghtly in slug flow. It was also observed that the power spectral density of the pressure fluctuations exhibited different shapes with different dominant frequencies in these three flow regimes. Although pressure transducers were used to collect information on absolute pressure fluctuations, the flow regime boundaries were deterrnined by visual observation. Kitano and Ikeda (1988) used pressure transducers to study the transition between dispersed bubble flow and the coalesced bubble flow regime. The integral of the power spectra density function of the pressure fluctuations between 0 and 10 Hz was used to detect the flow regime transition. For the dispersed bubble flow regime, this integral increased linearly with decreasing hquid velocity at a given gas flow rate. The transition from dispersed bubble flow to coalesced bubble flow was assumed to take place when the values began to deviate from this linear relationship. It was also found that there was a transitional regime between the dispersed bubble flow and the coalesced bubble flow regimes. Absolute pressure fluctuations have also been used to determine the flow regimes for other three-phase reactors (Zheng et al., 1988; Chen et al., 1995). 34 3.2.2 Preliminary Tests Pressure transducers are simple devices able to determine absolute pressure and/or differential pressure fluctuations in a multiphase flow system In reviewing the definitions of the flow regimes, it can be seen that these definitions are based on multiphase flow characteristics such as bubble size, bubble shape, hquid motion and liquid film properties. There is a relationship between the flow characteristics and the pressure fluctuations. For example, when a single bubble rises in a stagnant hquid column, the pressure along the bubble centerline exhibits a significant fluctuation. But far away from the bubble centerline, this fluctuation becomes smaller, and finally vanishes. Another example: when bubbles are formed at an air injector, the injection of the bubbles causes a pressure disturbance; this disturbance can propagate throughout the whole column and can be registered by pressure transducers. In order to clarify the relationship between the multiphase flow characteristics (or flow structure) and the pressure fluctuations, some simple experiments were performed. 3.2.2.1 Effect of single bubble injection on pressure fluctuations In this test, four absolute pressure transducers (PI to P4) were mounted 50, 150, 650 and 750 mm above the distributor of the 82.6 mm ID. column. The total stagnant height of the water was 1.27 m. An air injector was located 250 mm above the distributor. The schematic diagram of the apparatus for this test is shown in Figure 3.1 (a). Quickly opening and closing the gas valve of the injector was used to create a large bubble of the same diameter as that of the column. Several experiments were carried out to check the reproducibility. A set of typical results is shown in Figure 3.2. When the bubble was introduced into the column, a pressure disturbance could be observed immediately. This pressure disturbance 35 Single Bubble Injector 150 Stagnant Liquid Column Continuous Air Supply (a) (b) Figure 3.1. Schematic diagram of experimental apparatus used for preliminary pressure fluctuation tests. could travel upwards to P3, located above the air injector, or downwards to PI, located below the injector, as shown in Figures 3.2 (a) and (h). Since PI was closer to the air injector, the amplitude of the signal from PI was greater than that from.P3. After the air bubble was injected, the mean pressure at P3 increased due to the increase of static head at this point. When this bubble passed P3, a fluctuation could be observed due to the effect of the bubble and its wake. Figures 3.2 (c) and (d) show the differential pressure fluctuations when a bubble was injected into the column. It is clear that the pressure disturbance caused by the bubble injection could be registered by both differential pressure transducers (P3 - P4) located above the injector, and (PI - P2) below the injector. When the bubble passed the transducers at P3 and P4, a pressure fluctuation could be observed too (Figure 3.2 (c)). Comparing Figure 3.2 (a) and 3.2 (c), it can be seen that the absolute pressure fluctuation caused by the air injection was stronger than that caused by the bubble itself, whereas the differential pressure fluctuation caused by the air injection 36 900 800 700 600 500 | 1500 £ 1400 1300 1200 1100 1000 900 (a) Absolute Pressure Fluctuation at 0.65 m, P3. Bubble Passes Probe (b) Absolute Pressure Fluctuation at 0.05 m, PL Bubble Formation (c) Differential Pressure Fluctuation between 0.65 and a75 m, (P4-P3). Bubble Passes Probe —i 1 1 1 1 , . (d) Differential Pressure Fluctuation between 0.05 and 0.15 m, (P2 - Pl> Formation —i • 1 1 1 > 1 ' 1— 2 4 6 8 10 0 300 250 200 -150 •100 —I ' 1 • 1 ' 1 • 1 2 4 6 8 10 300 a 250 <3 200 150 100 50 Time, s Figure 3.2. Pressure signals corresponding to single bubble formation and rise (air injector 0.25 m above the distributor). and the bubble itself were of same order. This implies that a differential pressure transducer can reduce, but not eliminate, the effect of bubble injection. 3.2.2.2 Effect of continuous air supply on pressure fluctuations The purpose of this test was to check the effect of continuous air supply on pressure fluctuations. Two absolute pressure transducers were mounted 1.65 and 1.75 m above the air distributor. The column was filled with stagnant water to a height of 1.85 m height as shown in Figure 3.1 (b). The pressure fluctuations were then recorded when the air valve was quickly opened. Typical results are shown in Figure 3.3. At around 2 s, the air valve was quickly opened. 37 First a very large bubble was created by the sudden release of pressure in the air pipe. Then small bubbles as well as some Taylor bubbles followed the large bubble, since the air valve remained open. Thus the mean pressure at 1.75 m increased before the first big bubble arrived, which happened at around 4 s. From 4 to 5 s, this bubble covered both transducers, so that AP almost reached zero in this period of time. At the same time, the mean pressure at 1.75 m dropped. Although no bubble passed the transducers before 4 s, both the absolute pressure and the differential pressure fluctuated significantly due to the air injection and other sources of pressure disturbance. Note that the amplitude of the fluctuations caused by the air injection is of the same magnitude as that after the first bubble passed the transducers. 1200' o 800-£ 400-300 250 200 H 150 100 50 H (a) Absolute Pressure Fluctuations at 0.175 m 1 1 1 1 1 1 1 1 1 1— (b) Differential Pressure Fluctuations between 0.165 and 0.175 m First Bubble Arrival t Time,s Figure 3.3. Pressure signals corresponding to continuous air supply at Ug= 0.387 m/s in a stagnant column containing water. 38 Both tests show that the absolute pressure and the differential pressure fluctuations include information not only from bubbles passing the pressure transducers, but also from other sources throughout the column, e.g. pressure disturbances caused by bubble formation. Hence, caution should be exercised when absolute and differential pressure fluctuations are used to distinguish flow regimes. This is especially true if the standard deviation of the fluctuations is adopted as the criterion for flow regime transitions, since the component of the pressure fluctuations caused by other disturbances may then contribute significantly and randomly to the total standard deviation. 3.3 Local Multiphase Flow Characteristics Local multiphase characteristics can be used to determine the flow regime transitions. Different measurement techniques (e.g., conductivity probe and X-ray measurement systems) have been used to determine the local characteristics and flow structure of multiphase systems. Most investigators have based the transition criteria on statistical information from the original signals. However, due to the intrinsic attributes of the original signals, this method has its own shortcomings. 3.3.1 Previous Studies 3.3.1.1 Gas-liquid two-phase systems Since the electrical conductivities of the hquid and gas differ, it is possible to detect the presence of hquid or gas at a certain location using a pair of electrodes. This method has been used by many investigators (Bamea et al., 1980; Matuszkiewicz et al., 1987; Kelessidis and Dukler, 1989; Mao and Dukler, 1989; Nakazatomi et al., 1992; Soria and de Lasa, 1992; Das and 39 Pattanayak, 1993, 1994; Monji, 1993). Different probe configurations have been employed by different authors, so that the results are quite different. Barnea et al. (1980) determined flow regimes with two conductance probes, one located on the wall of the pipe, the other at the centerline. These probes shared a common ground and with only the tip of each probe was electrically exposed to the two-phase mixture. The voltage-time traces of the probes were used to identify flow regimes. In annular flow, the trace of the probe at the axis exhibited a zero output. In slug flow, periods of zero output, representing Taylor bubbles, and periods of high voltage with some downward spikes, representing small bubbles within a hquid plug, could be observed in the trace. In chum flow, near the transition to annular flow, the trace output was almost zero except for some small upward spikes; near the transition from slug flow, a group of spikes, sometimes in a form similar to a group of small bubbles, appeared in the trace. Flow transitions were adjudged based on the probe outputs. The same phenomena were observed by Mao and Dukler (1989) with a radio-frequency (RF) probe. This probe was designed to detect the local presence of either air or water. The characteristics of this probe were similar to those of a high-frequency impedance probe according to the authors. Flow patterns were discerned from visual observation of the time trace of the RF probe. Several pairs of square electrodes mounted at different heights along the column were used as conductivity probes by Matuszkiewicz et al. (1987). The Power spectrum distribution functions (PSF) of the probes presented some very sharp peaks at frequencies of £. = 1.0 and fg = 1.2 Hz in slug flow. However, only one smooth peak appeared in the PSD function for bubble flow and for the transition regime between bubble flow and slug flow. The standard deviation of each probe output went through a maximum as the gas void fraction increased. This maximum appeared at the middle of the transition between bubble flow and slug flow. Other parameters 40 were also calculated, e.g., a system phase factor, system gain factor and coherence function for each successive probe. The authors suggested that the actual bubble-slug transition might be characterized by a sudden increase in the coherence function of natural fluctuations at two successive probes for some "sensitive" frequencies (e.g., fg = 1.0 or f, = 1.2 Hz). Das and Pattanayak (1993, 1994) used two electrical impedance probes to identify flow patterns. One was called a wide-gap probe with two electrodes separated by a distance of D/2, while the other was a narrow-gap probe with a pair of electrodes separated by 1.6 mm. The outputs of the probes were converted by a complicated measuring circuit to create a digital equivalent of mixture resistance (DEMR) reading. The DEMR reading was preset to vary from 0 to 100, corresponding to 0% to 100% gas holdup. It was found that when the DEMR started to show values above 32, slug flow was observed. The criterion was adopted that if within 5 s, ten or more DEMR readings exceeded 32, the bubble-slug transition had occurred. When these two probes were separated by 8D, the number of hquid plugs longer than 8D could be counted. The criterion for the slug-chum transition was that if fewer than 10 hquid plugs (of length > 8D) were found within 5 s duration, then steady chum flow existed. Beyond the chum-annular transition, the gas core was occasionally bridged by the hquid. In a period of 5 s the number of bridgings had to be less than ten to establish annular flow. A conductance probe of the same configuration as that proposed by Bamea et al. (1980) was used by Kelessidis and Dukler (1989) in vertical concentric and eccentric annuli to detect flow patterns. The PDF of the probe output was used to set the criteria for flow regime transitions. The PDFs exhibited different shapes in various flow regimes. Bubble flow was characterized by a single peak of the PDF at V/Vmax near 1.0 such that the integral of the PDF with V/Vmax ranging from 0.75 to 1.0 should equal unity. Slug flow was characterized by two weU-defined peaks in the PDF plot. Since the peak at low voltage corresponded to Taylor bubbles, slug flow was assumed to occur when the integral of the PDF with V/Vmax ranging from 41 0 to 0.25 was greater than 0.2. The slug-churn transition took place when the integral of the PDF with V/Vmax ranging from 0.75 to 1.0 was less than 0.2. Annular flow was characterized by a single narrow peak located at low V/Vmax in the PDF plot. Vince and Lahey (1982) used an X-ray measurement system to measure void fraction fluctuations at different chord positions. PDFs and PSFs, as well as their moments, were calculated. It was found that the variance of the output could be used as a flow regime indicator. In the slug and churn flow regimes, the variance was greater than 0.04 (i.e. standard deviation > 0.2). They also found that significant differences existed in the band width and the amplitude of the PSF for various flow regimes. However, both the shape of the PSF curve and its moments could not be used as criteria for flow regime transitions. Jones and Zuber (1975) used an X-ray beam as a local probe in a 2D column. The PDF of the probe output was used to distinguish flow regimes. In bubble flow, a single-peaked PDF at low void fraction was found; in slug and churn flow, the PDF was twin-peaked; in annular flow, there was a single-peaked PDF at high void fraction. They found that the bubble-slug transition took place at sg = 0.2 and the slug-annular transition at eg = 0.8. Govier et al. (1957, 1958) studied the pressure gradient and the void fraction of two-phase systems. With increasing gas velocity, the pressure gradient decreased first and then increased to a maximum After that it decreased again and reached a second minimum, then went up again. Flow regimes were deterrnined based on the inflection points of the void fraction curves and at the minima in the pressure gradient curves. Based on a plot of pressure gradient vs. superficial gas velocity, Jayanti and Hewitt (1992) found that in bubble flow the pressure gradient decreased sharply with increasing gas velocity. It decreased more gradually in slug flow. At the slug/churn transition point, the pressure gradient 42 increased suddenly. They claimed that this transition point was quite consistent with visualization results. Table 3.1 summarizes measurement methods used for flow regime identification in gas-hquid two-phase systems. 3.3.1.2 Three-phase systems Soria and de Lasa (1992) measured the hquid volume fraction, using a set of electrical conductivity sensors in a bubble column. The sensors were composed of several pairs of square electrodes and were used to measure the conductivity of a three-phase mixture. The transition between the homogeneous bubbling regime and the churn-turbulent regime could be characterized by observing the asymptotic change in the slope of vs. Ug plots. The homogeneous bubbling regime was observed at low superficial gas velocities. The spectrum of hquid volume fraction signals showed a dominant frequency peak below 1.0 Hz in the homogeneous bubbling flow regime. A further increase in superficial gas velocity produced a vigorously turbulent regime with fingered (multi-peak) spectra showing characteristic frequencies below 10 Hz. In a three-phase fluidized bed, it was found that the transition between dispersed bubble flow and coalesced bubble flow was governed by the superficial hquid velocity. In a plot of vs. U^, a common crossover point was found for three sets of experiments carried out at different constant Ug values. This crossover point was hypothesized to be the transition between the coalesced bubble flow and the dispersed bubble flow regimes. 43 .fc f t/5 •a 'o o 0) I-l 0) •55 t3 11 Q « tS 2 •8,-a ts & 1 J3 Q 3 fl O • *H ts •g Q t-H T3 tZ5 Q fl o • 1—I ts H3 _ S Hi o I-l S3 U PH & 12 OH « 05 -55 o § CD •a o > § _ t5 r> O i ^ « • t? 5. w fl "£! u tS S -5 p , o & fl :g sl§ s 44 Han and Kim (1990) proposed a flow regime map using coordinates of gas holdup fraction s„ U„ u over bed porosity, a (= —), and gas-hquid slip velocity, Us (= — -), on the basis that Sg+S^ Sg s^ the previous flow regime maps did not account for particle size and hquid properties. The dispersed bubble flow regime was characterized by relatively low gas-hquid slip velocities (0.4 -0.5 m/s) with a in the range of 0 to 0.4. The coalesced bubble flow regime was characterized by higher shp velocities (0.4 to 0.8 m/s), with 0 < a < 0.2. The slug flow regime was characterized by high shp velocities with a from 0.2 to 0.4. Lee et al. (1990) deterrnined flow regimes based on mean bubble sizes throughout a fluidized bed fitted with a single pipe gas distributor. A progressive increase in mean bubble length with height was indicative of coalesced bubble flow. A decrease in mean bubble length with height implied dispersed bubble flow. Based on four experimental runs and literature data, a flow regime map was proposed using particle diameter and superficial hquid velocity as coordinates. The fixed bed, coalesced bubble flow, dispersed bubble flow and transport regimes were presented on this map. Table 3.2 summarizes the measurement methods used for flow regime identification in gas-hquid- solid three-phase systems. 3.3.2 Discussion of Existing Methods X-ray measurement systems, conductivity probes and electrical impedance probes are usually designed to detect the presence of either gas or hquid. These methods offer a more direct way of investigating flow regime transitions than those based on P and AP fluctuations. 45 O CO OH O CO u PH fl o • *H eg 3 I PH PH o 2 3 3 CO & es a* 1.1 .f p S o o 2 o pt, fe > s 00 o> >/-> ON ON 00 00 ON ~^ 00 « oo >o H ON UH eS u 81 o +J | 8 8 fe fe fl o •*H ts a> o 1/1 a> t_i u 2 2 M 21 is V-l 46 Except for Das and Pattanayak (1993, 1994) in a two-phase system and Lee et al. (1990) in a three-phase system, most investigators used the original signals or statistical parameters derived from the original signals, instead of the bubble characteristics, to determine flow regime transitions. Barnea et al. (1980) and Mao and Dukler (1989) used the raw signals of a conductivity probe and a RF probe respectively, to distinguish flow regimes. These are somewhat more objective than visual observation. With the X-ray technique, Vince and Lahey (1982) and Jones and Zuber (1975) calculated the PDF of the measurement system output. Both reported that the shape of the PDF was different in each flow regime. This was confirmed by Kelessidis and Dukler (1989) with a conductance probe. The variance of the probe output was used as an indicator by Vince and Lahey (1982). The shape of the PDF was used by Jones and Zuber (1975), while the integration of the PDF within a certain range was used by Kelessidis and Dukler (1989) to distinguish flow regimes. The output of an X-ray measurement system, a conductivity probe or an electrical impedance probe varies from a low voltage to a high voltage corresponding to the presence of gas and hquid respectively. The values of the low and high voltage depend on power supply, hquid properties and the probe configuration. Instead of using V directly, the outputs were normalized (as V/Vmax) such that the values would only vary from 0 to 1.0. In such a case, the PDF and its moments of the signal are related to the gas holdup. Consider an ideal voltage-time trace signal as shown in Figure 3.4. V0 and Vi correspond to gas phase and hquid phase respectively and appear alternately. According to the definitions of PDF, average, standard deviation and other moments in Equations (2.1) to (2.6), the statistical parameters of this ideal trace are as follows: 47 C/2 © > V, OS O A t2 t3 AV At Time, s Figure 3.4. Ideal signal for conductivity probe. Probability of the signal having value V0: P(V0^V)=-i-Zti=Po Hot 1=1 Probabihty of the signal having value Vx: p(v1,Av)=i--^-|;ti=p1 not 1=1 The mean, variance, skewness and kurtosis of V(t) can be expressed by: V= ZViP(Vi,AV) = V0p0+VlPl i=0 (3.1) (3.2) (3-3) Var = z(Vj-v) P(Vi,AV) = V^PQ+V^-V2 i=0 (3.4) M3 = s(Vi-V) P(Vi,AV) = V03po+V13p1-3VVar-V3 i=0 (3.5) M4 = E(vi-V)4p(Vi,AV) = V04po+V14p1-4VM3-6V2Var-V4 i=0 Assuming V0= 0 and = 1 volt, then V = Pi (3.6) (3.7) 48 Var =o-v2=p0p, (3.8) M3 =p0Pi(l-2Pl) (3.9M4 =PoPi(l-3p0Pi) (310) On the other hand, a conductivity probe can be used to measure local gas holdup. The time average gas holdup can be calculated by Equation (2.9). For the case in Figure 3.4, £g= — hi (3.H) ttot i=l Comparing this equation with Equation (3.1) we can see that 8g=p0 for V0 = 0 and V, = 1 (3.12) Hence the integral of the PDF with V(t) ranging from 0 to 0.25 volts (after Kelessidis and Dukler, 1989) is: oppCv^AV[dv = o.25p(v0,AV) o AV J and the integral of the PDF with V(t) ranging from 0.75 to 1 volt is: AV n AV 0 g V } I P(Vi,AV) Mi 1 P(^AV| i Av dV= j dV = Pl = l-sg (3.13b) 0.75 AV 0.75 AV The moments of the signal can also be expressed in terms of the gas holdup of the multiphase mixture: V = l-sg (3.14) Var = 8g(l-8g) (3.15M3 = 8g(l-8g)(28g-l) (3.16) M4 =sg(l-Sg)[l-38g(l-sg)] (3.1749 Figure 3.5 shows the variation of the moments with the gas holdup. Several loci can be found in the figure. At £g = 0.5, the variance reaches its maximum, and the skewness equals zero. At s„ = 0.21 and s„ = 0.79, the skewness reaches its rninimum and maximum, respectively. If these loci were used to determine flow regime transitions, that would not be different from using the gas holdup itself. For example, the assumption that the maximum point of the standard deviation for the variation of the signal is a flow regime transition point is the same as the assumption that the flow regime transition occurs when the measured gas holdup is equal to 0.5. It is well known that, the gas holdup increases with gas velocity at constant hquid velocity. There is, however, no dramatic change which reflects the flow regime transition in a plot of the gas holdup vs. superficial gas velocity, as shown in section 4.2.2. Figure 3.5. Relationship between gas holdup and various moment parameters of an ideal signal for conductivity probe. 50 3.4 Summary Aside from visual observation, absolute and differential pressure fluctuations and local multiphase characteristics have been used to determine the flow regime transitions. However, pressure fluctuations include information on local flow structures as well as pressure disturbances caused by other remote sources (e.g., due to air injection). When the statistical parameters of the pressure fluctuations are used as the flow regime transition criteria, these pressure disturbances may affect the results significantly and randomly. Although differential pressure measurements can reduce the amplitude of pressure disturbances, they do not totally eliminate their influence. Thus, both absolute and differential pressure fluctuation methods appear to be unsuitable for flow regime determination in multiphase systems. An objective measurement method for flow regime transitions should be based on the multiphase characteristics of the system Many investigators have attempted to achieve this goal using techniques which detect bubble characteristics. However, most such methods have used statistical parameters of the original signals from instruments, instead of the more direct manifestations of the bubble characteristics, to determine the flow regimes. Due to the intrinsic attributes of the measurement techniques, these statistical parameters are directly related to the local time-average gas holdup at the measurement location. However, information on gas holdup is not enough for determining the flow regime transitions in a multiphase system A new method is needed and is presented in the next chapter. 51 Chapter 4 Experimental Criteria for Flow Regime Transitons in Gas-Liquid Systems 4.1 Introduction This chapter presents experimental results on tests where bubble characteristics were investigated under operating conditions which span all flow regimes in order to establish criteria for the flow regime transitions. The bubble characteristics measured in this work were bubble frequency, gas holdup, bubble velocity, bubble chord length and their distributions. The flow regimes investigated are discrete bubble flow, dispersed bubble flow, coalesced bubble flow, slug flow, chum flow, bridging flow and annular flow. 4.2 Experimental Results The experimental set-up and the conductivity probe used in this work are described in Chapter 2. The probe was installed horizonally at several heights above the distributor, always at the axis of the column of inside diameter 82.6 mm 4.2.1 Raw Signals and their Statistical Results Some typical raw signals from the conductivity probe are shown in Figure 4.1. At the lowest gas velocity (Ug = 0.0099 m/s), discrete bubble flow was encountered. In the time trace of the conductivity probe, some downward spikes were observed, corresponding to small bubbles striking the probe. As the gas velocity was increased, a few large bubbles appeared in the column. At a gas velocity of 0.041 m/s, near the transition velocity to slug flow, longer periods of zero output were observed corresponding to large gas bubbles. 52 c/5 -<-> 1 ! o 10 3 0.5 -| 0.0 U =0.0099 m/s g 0.5 -| 0.0 •> r~ 0.041 QJC 0.5 -I 0.0 0.20 Discrete Bubble Flow Discrete Bubble Flow Slug Flow 0.5 -I 0.0 0.70 Slug Flow 1.0 -, 0.5 0.0 1.36 Churn Flow 1.0 -i 1 •5b 1.45 0.0 -jfLln.lih.yii ,| , 0.5 -I 0.0 1.0 r 3.55 Churn Flow Bridging 0.5 -4 6.79 Annular Flow 0.0 0.2 0.4 Time, s 0.6 0.8 Figure 4.1. Typical raw signals at different superficial gas velocities from conductivity probe for air-water system at Z = 0.65 m, IL; =0.0184 m/s. 53 A further increase in gas velocity to Ug = 0.20 m/s resulted in a transition to slug flow. In this regime periods of zero output corresponding to Taylor bubbles are interspersed with periods of high voltage with some downward spikes, corresponding to small bubbles in gas-liquid plugs. In the chum flow and bridging flow regimes, upward spikes corresponding to hquid bridging were observed in the original signals. For annular flow (Ug = 6.79 m/s), the output of the probe was always close to zero, indicating that the probe was always in the gas phase. The probability density functions (PDFs) of the signals are shown in Figure 4.2. Bimodal distributions are seen at low gas velocities corresponding to discrete bubble flow and slug flow. Single peak distribution of the PDFs are observed at high gas velocities, which correspond to chum flow, bridging flow and annular flow. However, it is probably impossible to determine the flow regime transitions based on the shape of the PDF curves. Conductivity Probe Signal, V/V, Figure 4.2. Probability density function of conductivity signal for air-water system at Z - 0.65 m, U| =0.0184 m/s and different gas velocities. 54 0.20 -0.05 0.001 -•— Variance -o— Skewnes -A—Kurtosis 0.01 0.1 1 Superficial Gas Velocity, m/s Figure 4.3. Variation of moments of conductivity probe signals with superficial gas velocity for air-water system at Z = 0.65 m, Ue =0.0184 m/s. Figure 4.3 shows the variation of the moments of the original signals with respect to the gas velocity. The variance of the signals increases with the gas velocity and reaches a maximum at Ug « 0.34 m/s. It approaches zero at high gas velocities in the annular flow regime. The skewness of the signals decreases with increasing gas velocity at low gas velocities and reaches a minimum value at Ug « 0.08 m/s. Then it increases, passing through zero at Ug = 0.34 m/s and reaching a maximum value at Ug « 1.0 m/s, before approaching zero again at high gas velocities corresponding to annular flow. The kurtosis of the signals increases first and then levels off at Ug « 0.08 m/s. It begins to decrease at Ug « 1.0 m/s and approaches zero at high gas velocities. Several characteristic features are seen in Figure 4.3. These features, however, are directly related to gas holdup as shown in Figure 4.4. The maximum variance of the signals appears at e„ « "55 0.15 m 0.10 4 CD I 0.05 0.00 -0.06 Gas Holdup, eg, Figure 4.4. Variation of moments of conductivity probe signals with gas holdup for air-water system at Z = 0.65 m, =0.0184 m/s. 0.5, while the minimum value, the zero point and the maximum value of the skewness appear at sg « 0.25, 0.5 and 0.75, respectively. Using these moments to determine the flow regime transitions is equivalent to basing the transitions on the gas holdup. 4.2.2 Gas Holdup The variation of time-average gas holdup at the centre of the column with respect to the gas velocity is shown in Figure 4.5 at four different heights. It can be seen that gas holdup, Sg, increases with gas velocity monotonically for all four levels. There are no obvious turning points indicating flow regime transitions. 56 1.0 0.001 0.01 0.1 1 10 Superficial Gas Velocity, m/s Figure 4.5. Local gas holdup at different heights for air-water system at =0.0184 m/s. 4.3 Experimental Criteria for Flow Regime Transitions In addition to the statistical properties of the original signals and gas holdup, bubble characteristics can be obtained from the conductivity probe signals. For this section, the measurement location was always on the axis of the column 0.65 m above the distributor. 4.3.1 Transition between Discrete Bubble Flow and Coalesced Bubble Flow Regimes At low hquid flow rates, when small amounts of gas are introduced into the column, small bubbles appear. The bubble size distribution is narrow and strongly dependent on the gas distributor. The number of bubbles and the gas holdup are also small. Bubbles do not have sufficient time to coalesce since the distance between mdividual bubbles is large compared to the 57 sizes of the bubbles. Hence, the overall behavior of the gas bubbles may be characterized as homogeneous. With increasing gas velocity, larger bubbles of wider size distribution are encountered. The population of bubbles increases, while the distance between individual bubbles decreases. Some bubbles coalesce as they ascend. The overall behavior of the multi-phase mixture is categorized as coalesced bubble flow or as heterogeneous. In this study, it was found that the relationship between bubble frequency and superficial gas velocity is different in the discrete and coalesced bubble flow regimes. In the discrete bubble flow regime, bubble frequency increases linearly with gas velocity, with a proportionality constant of 545 m"\ On further increasing the gas velocity, the bubble frequency deviates from this linear relationship when the transition to coalesced bubble flow takes place. Hence, the Superficial Gas Velocity, m/s Figure 4.6. Transition between discrete and coalesced bubble flow regimes in air-water system at / different superficial hquid velocities. 58 discrete/coalesced bubble flow transition can be obtained from a plot of bubble frequency versus superficial gas velocity, corresponding to the point where the bubble frequency deviates significantly from a linear relationship. Figure 4.6 displays some typical results showing this transition. In discrete bubble flow, assuming all small bubbles are spherical and of uniform size, distributed uniformly across the column, then bubble detection area No. of bubbles passing detection area column cross - sectional area No. of bubbles passing cross - sectional area The detection area is dependent on the bubble size. A bubble of diameter d^ can be detected only when the distance between the probe and the center of the bubble is less than cL^. Therefore, The equation above can be written as: 4VS_ ft Ac Ac Ugt T "vs 6 where f is the measured local bubble frequency and Ag is the cross-sectional area of the column. Rearranging this equation, the local or point bubble frequency can be expressed by: f = ^-Ug (4.1) where cL^ is the bubble diameter, which is a function of the diameter of the holes in the distributor, and of the gas and hquid flowrates and physical properties. For stagnant hquid columns, Kumar et al. (1976) correlated the bubble diameter by: 59 ( Y4 1.56 Re 0.058 N (Pt "Pg)g for 1 < Re>j < 100 V J (4.2) Y4 1/ 74 0.32 Re 0.425 (Pt -Pg)g for 100<ReN<2100 In the present study, when Ug was varied from 0.004 to 0.1 m/s, R^ in Equation (4.2) changed from 15.5 to 388. The bubble size, cL^, predicted by Equation (4.2), varied from 4.2 to 9.3 mm Taking an average bubble diameter, d^ = 6.8 mm, and since the bubble frequency is proportional to the gas velocity, by Equation (4.1) the linear constant relating them is 1.5/0.0068 or 221 m"1. This value is of the same order as 545 m"1 (see Figure 4.6). Since Equation (4.2) was obtained for a stagnant hquid column, the predicted bubble diameter may be overestimated and the corresponding linear constant underestimated. The discrete/coalesced flow transition criterion can also be applied to flow regime transitions at high U^, i.e. the transition between dispersed bubble flow and coalesced bubble flow or, if the coalesced bubble flow regime is absent, between dispersed bubble flow and slug flow. However, this transition criterion may be difficult to apply when discrete bubble flow exists only within a small gas velocity range. 4.3.2 Transition between Coalesced Bubble Flow and Slug Flow Regimes As the gas velocity is increased further, bubbles become larger and more elongated, and some bubble cross-sectional dimensions approach the diameter of the column. The appearance of 60 Taylor bubbles indicates that the flow pattern has changed to slug flow. In the slug flow regime, many small bubbles with diameter approximately equal to 4 mm are observed in the hquid plugs which follow the Taylor bubbles. Both the Taylor bubbles and the small bubbles are detected by the conductivity probe. These small bubbles result in a small value of the arithmetic mean bubble chord length, when few Taylor bubbles are present in the column. In order to detect the point at which Taylor bubbles begin to appear in the column, the Sauter mean bubble chord length, M 1 = 1 - (4.3) b,sv M . i =1 is used as the parameter to set the criterion in this study, This parameter gives more weight to large bubbles than small ones. A sample calculation may be useful to exhibit this. Consider 10 bubbles, one of which has a chord length of 10 mm while the rest ah have a chord length of 1 mm. The Sauter mean chord length is then 9.26 mm, while the arithmetic average chord length is only 1.9 mm The appearance of bullet-shaped or Taylor bubbles marks the transition between coalesced bubble flow and slug flow. In the air-water system, the bubble chord length at the center of a Taylor bubble is usually equal to or greater than the diameter of the bubble. Hence, the criterion for the transition between coalesced bubble flow and slug flow is set as the point at which the Sauter mean bubble chord length, £h measured at the center of the column, reaches the column diameter, D, 0.0826 m in this study. Figure 4.7 shows the experimental results identifying this transition. 61 Figure 4.7. Method used to determine transition between coalesced bubble flow and slug flow in air-water system at various superficial hquid velocities. 4.3.3 Transition between Slug Flow and Churn Flow The transition between slug and chum flow can be taken to occur when the gas holdup within the hquid plugs corresponds to a rmximum volumetric packing of bubbles (Brauner and Bamea, 1986; Mao and Dukler, 1989). Beyond this point, the bubble frequency decreases with increasing gas velocity due to coalescence of the small bubbles within the hquid plugs. Hence, the maximum bubble frequency in a plot of bubble frequency vs. superficial gas velocity can be used to distinguish between slug flow and chum flow. Figure 4.8 shows experimental results for this transition. 62 Superficial Gas Velocity, m/s Figure 4.8. Plot of local bubble frequency at axis of column versus superficial gas velocity showing transition between slug flow and churn flow and the onset of annular flow in the air-water system for different superficial hquid velocities. Note that Figure 4.8 is plotted on semi-log coordinates, while Figure 4.6 is on a linear scale. This causes the shapes of the bubble frequency curves in Figure 4.8 to differ from those in Figure 4.6. 4.3.4 Transition between Churn Flow and Bridging Flow Bridging flow occurs when there are hquid bridges spanning the core region of the column linking the hquid film occupying the annular region of the column in any cross-section. In churn flow, some distorted Taylor bubbles were observed. As the gas velocity was increased, the distorted Taylor bubbles became elongated. Some successive Taylor bubbles coalesced fonning larger bubbles, while the hquid plugs between successive Taylor bubbles became thinner. The 63 measured bubble frequency continued to decrease (as shown in Figure 4.8), and the average bubble chord length showed a sharp increase with respect to the gas velocity, as illustrated in Figure 4.9. The abrupt change in slope in Figure 4.9 can be taken to denote the onset of bridging flow. Figure 4.9 also shows the variation of the average bubble time (defined in section 2.3.3, Chapter 2) with the gas velocity under the same conditions. The average bubble chord length shows the same tendency as the average bubble time. This is because the average bubble chord length is related to the average bubble time. The definition of the average bubble chord length is: 1 M / \ *b=— Z(tiUw) (4.4) M i=i If Ubi is a constant, then from Equation (2.11), one can write Equation (4.4) as: €b=Ubti (4.5) Equation (4.5) indicates that the average bubble chord length is proportional to the average bubble time, providing that the bubble velocities are the same. Because the measurement of £b requires a two-element probe, while t, requires only a single element, the average bubble time was used to determine the transition between churn flow and bridging flow throughout this work. This avoids several problems which might be associated with a two-element probe, such as the measurement error resulting from bubbles with a significant non-vertical component of rise velocity. As illustrated in Figure 4.9, this method does not cause a significant error in deterrnining the flow regime transition, and it also simplifies the measurement system Figure 4.10 shows the variation of the average bubble time with respect to Ug for other operating conditions. 64 1000-o o tN H i cf I 100-1 10 o Average bubble chord length • Average bubble time o °o °<>o Chum Flow Bridging Flow —i—i—i—i—11111— 0.001 0.01 TT1 ' I 0.1 1 0.1 0.01 8 I 1 PQ CD cf I 0.001 10 Superficial Gas Velocity, l|, m/s Figure 4.9. Average bubble chord length and bubble time versus superficial gas velocity showing transition between chum flow and bridging flow for air-water system at Z = 0.65 m, = 0.064 m/s. 1000-o o «/-) CN X H i PQ I 1004 104 U^, m/s —•—0.00205 —O— 0.00615 —A—0.0184 —V— 0.0455 —•—0.0638 —•— 0.0729 —•—0.100 —A—0.155 —•—0.219 Chum / Bridging Transition 0.001 TTT!— 0.01 1 I I I I I l| 0.1 I I I I I I 11 1 Superficial Gas Velocity, m/s 10 Figure 4.10. Average bubble time versus superficial gas velocity showing transition between chum flow and bridging flow in the air-water system at Z = 0.65 m for different superficial hquid velocities. 65 4.3.5 Transition between Bridging Flow and Annular Flow Annular flow is characterized by a continuous gas region at the core and a continuous hquid region at the wall. In some cases, small bubbles were found in the hquid annular region. At the center of the column, in the annular flow regime, bubble frequency or hquid bridge frequency should be zero, and measured bubble chord length, infinite. This is used to determine the onset of annular flow. In this work, since the probe was always on the axis of the column, by extrapolating the measured bubble frequency to zero in a plot of f vs. Ug, the transition velocity between bridging flow and annular flow can be obtained experimentally as shown in Figure 4.8. 4.3.6 Transition between Discrete Bubble Flow or Coalesced Bubble Flow and Dispersed Bubble Flow At a constant low gas flow rate, as hquid flow is increased, bubbles become smaller and their size distributions become narrower. This regime is the dispersed bubble flow regime. The bubble behavior in this regime is relatively independent of the gas distributor. In this study, it was found that both the average and standard deviation of £b (or t; ) decreased in the discrete and dispersed bubble flow regimes. (Bubble characteristics for different flow regimes in the air-water system are presented in the next chapter.) However, the ratio of standard deviation of tj to average ti5 o~t / ti; increased for either discrete or coalesced bubble flow, but decreased for dispersed bubble flow. The transition from the discrete (or coalesced bubble flow regime when the discrete regime does not exist) to the dispersed bubble flow regime was assumed to correspond to the maximum value of at /1,. This parameter is equal to o^ / £b, providing that the velocities of all bubbles are the same. Figure 4.11 shows the variation of ot / tj with respect to the superficial hquid velocity. 66 Discrete / Dispersed Transitions 0.0 -| 1 r—-i—i—i i i 11 1 1—i—i—i i i 11 1 1—i—i—I-T 0.001 0.01 0.1 1 Superficial liquid Velocity, m/s Figure 4.11. Dimensionless standard deviation of bubble time plotted against superficial liquid velocity showing transition between discrete bubble flow and dispersed bubble flow for air-water system at Z = 0.65 m. 4.4 Flow Regime Transitions at Different Heights 4.4.1 Experimental Conductivity Probe Results In order to compare the results with those from pressure signals, the conductivity probe was installed at the same positions as the pressure transducers. The same criteria as described previously in section 4.3 were used to determine the flow regime transitions experimentally. The raw signals and the corresponding PDFs of the signals for the conductivity probe at different locations were similar to those shown in Figures 4.1 and 4.2. 67 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Superficial Gas Velocity, Ug m/s Figure 4.12. Bubble frequency plotted against superficial gas velocity showing transition between discrete and coalesced bubble flow at different locations for air-water system atUf = 0.0184 m/s. Figure 4.12 presents the bubble frequency at several different levels in the column. The bubble frequency increases linearly with gas velocity in the discrete bubble flow regime. At a certain gas velocity, depending on the measurement location, the bubble frequency deviates abruptly from this line; at this point coalesced bubble flow is encountered. It would appear that coalescence begins at the top of the column and develops downward from the top to the bottom of the column. The transition gas velocity is smallest at Z = 1.95 m and highest at 0.15 m As proposed in section 4.3.2 above, the transition from coalesced bubble flow to slug flow occurs when the Sauter mean bubble chord length equals the diameter of the column. Figure 4.13 shows the variation of the Sauter mean bubble chord length with respect to the superficial gas velocity. It can be seen that the Sauter mean bubble chord length reaches the column diameter at a 68 Figure 4.13. Sauter mean bubble chord length versus superficial gas velocity showing transition between coalesced bubble flow and slug flow at two different levels for air-water system at = 0.0184 m/s. lower Ug for Z = 1.95 m than for Z = 0.65 m. This indicates that bubbles continue to coalesce as they rise from Z = 0.65mto 1.95m Thus, slug flow is encountered at the top of the column first, leading to a lower gas velocity for this transition. The results are in good agreement with visual observations. When the gas velocity is increased further, the bubble frequency as shown in Figure 4.14 reaches a maximum corresponding to the transition from slug flow to churn flow. It is seen that the transition gas velocities, deterrnined as proposed in section 4.3.3, do not vary significantly with respect to the measurement level. Once Ug is great enough, the transition from slug flow to churn flow occurs thoughout the column. This implies that churn flow may not be the result of an entrainment effect as claimed by Taitel et al. (1980). 69 0.001 0.01 0.1 1 10 Superficial Gas Velocity, U m/s Figure 4.14. Variation of bubble frequency with gas velocity at different heights for air-water system at = 0.0184 m/s. The onset gas velocities for annular flow at different locations can also be determined from Figure 4.14 by extrapolating the bubble frequency curves to f = 0. It can be seen that the onset gas velocities for Z = 0.15, 0.65 and 1.35 m are essentially the same. However, the onset velocity for Z = 1.95 m is significantly lower than those at the other three levels. This could be an exit effect since Z = 1.95 m is very close to the top of the column. (The column height is 2.1 m, including a section in the separator.) Consistent with section 4.3.4 above, the transition from chum flow to bridging flow can be determined from the plot of average bubble time vs. gas velocity, and this is shown in Figure 4.15. It is seen that the transition gas velocity at 1.95 m is lower than for the other heights. As the gas velocity is increased, bridging flow can be observed at 1.35 m, 0.65 m, and even near the bottom of the column, at Z = 0.15 m. 70 10 | i—i—i i i 111| 1—i—i i 11111 1—i—i i i 1111 1—i—i • • ••• I 0.001 0.01 0.1 1 10 Superficial Gas Velocity, Ug m/s Figure 4.15. Average bubble time versus superficial gas velocity showing transition between chum flow and bridging flow at different locations for air-water system at Uf = 0.0184 m/s. The experimental flow regime transitions determined with the conductivity probe at different locations are summarized in Table 4.1. It can be seen that the transition gas velocities for the discrete/coalesced bubble flow and the coalesced bubble/slug flow regimes are almost the same. This implies that the coalesced bubble flow regime exists only over a narrow range of gas velocity for the experimental system used. Since the column diameter is small (82.6 mm), once the bubbles coalesce, Taylor bubbles can be observed almost immediately and slug flow is encountered. 71 Table 4.1 Flow regime transition velocities determined from the conductivity probe for air-water system at IL_ = 0.0184 m/s using the criteria proposed in sections 4.3.1 to 4.3.5. Probe locations, Z, m Superficial gas velocity corresponding to : low regime transition, m/s Discrete/ Coalesced Coalesced/ Slug Slug/ Churn Churn/ Bridging Bridging/ Annular 0.15 0.10 not measured 1.3 2.4 7 0.65 0.066 0.068 1.2 2.0 7 1.35 0.047 not measured 1.1 2.0 7 1.95 0.038 0.038 1.0 1.4 5.3 4.4.2 Experimental Pressure Fluctuation Results As discussed in section 3.2.2, a pressure transducer registers not only pressure fluctuations caused by bubbles passing the probe, but also pressure waves caused by other disturbance sources. Nevertheless, some experiments were carried out since this is the simplest among all instrument methods. Four pressure transducers were mounted on the column wall, 0.15, 0.65, 1.35 and 1.95 m above the distributor. For periods of 20 s these pressure fluctuation signals were acquired by a computer at a sampling rate of 100 s"1. While the superficial hquid velocity was maintained constant at = 0.0184 m/s, the gas velocity was varied from 0.0035 to 6.2 m/s, spanning discrete bubble, slug and churn flow regimes and coming very close to annular flow. The probability density distribution functions of the absolute pressure fluctuations at 0.65 m are shown in Figure 4.16. The results show that with an increase in superficial gas velocity, the mean pressure at this height decreases. The fluctuations in pressure first increase to a maximum, then decrease. It can also be noted that the peak of the PDF shifts to the left with increasing Ug. These characteristics are reflected in the standard deviation and the skewness of the signal. Figure 4.17 presents the variation of the standard deviation of the absolute pressure fluctuations at different levels. It can be seen that there is not much difference among the results at these 72 p I I 1 I I I 1 I 200 400 eOO 800 1000 Pressure Signal, mm H20 Figure 4.16. Probability density function of the absolute pressure fluctuations for air-water system at Z = 0.65 m and = 0.0184 m/s. locations except for Z = 1.95 m As this location is close to the exit, this could be due to an exit effect. The first toning point is at Ug= 0.026 m/s. This could correspond to the first bubble/slug transition. From visual observations and Figure 4.13, Taylor bubbles develop first at the top of the column. With increasing gas velocity, Taylor bubbles can be observed near the distributor. This phenomenon, however, is not manifested by the pressure fluctuations since the pressure transducer registers pressure waves from within the entire column. 73 200 Superficial Gas Velocity, U m/s Figure 4.17. Standard deviation of absolute pressure fluctuations for air-water system at Ut = 0.0184 m/s. The slug/chum flow transition could take place at the maximum of the standard deviation in Figure 4.17. The transition velocities which can be determined from pressure fluctuation signals are summarized in Table 4.2. Pressure fluctuation signals are not helpful in delineating higher gas velocity transitions. Table 4.2. Flow regime transition velocities determined from the standard deviation of absolute pressure fluctuations for = 0.0184 m/s. Probe location, m Superficial gas velocity corresponding to flow regime transition, m/s Bubble/Slug Slug/Chum 0.15 0.026 0.90 0.65 0.026 0.80 1.35 0.026 0.90 1.95 0.026 0.43 74 Some experiments were also performed to determine differential pressure fluctuations. The vertical distance between the two pressure transducer ports was 100 mm. The differential pressure was zero when a Taylor bubble passed the transducers. The PDFs of the differential pressure fluctuations are presented in Figure 4.18. It can be seen that, with increasing superficial gas velocity, the mean value of AP decreases. The corresponding fluctuations of AP increase first, then decrease. This phenomenon is related to the standard deviation of the signal as shown in Figure 4.19. It can also be seen in Figure 4.18 that at a certain gas velocity, a peak becomes evident near AP = 0, causing asymmetry of the PDF curves. However, at high gas velocities, the PDF curves become symmetric again. This phenomenon is reflected in the skewness as shown in Figure 4.20. In Figure 4.19, two characteristic features can be seen. One is the sharp increase in the standard deviation at Ug « 0.026 m/s. The other is the maximum value of the standard deviation. If we assume that the bubble/slug flow transition occurs where the standard deviation of the AP fluctuations increases sharply, while the slug/chum flow transition takes place where the standard deviation reaches its niaximum, then the flow regime transition velocities can be summarized in Table 4.3. With the same assumptions, but using the skewness as the indicator instead of the standard deviation, the transition velocities can also be obtained from Figure 4.20. In addition, if we assume that annular flow takes place where the skewness returns to zero, by extrapolating the skewness curves in Figure 4.20, the transition velocity for annular flow can also be estimated. The results are summarized in Table 4.4. 75 Figure 4.18. Probability density function of differential pressure fluctuations at Z = 0.65 m for =0.0184 m/s. Figure 4.19. Standard deviation of differential pressure fluctuations at different levels for XJl 0.0184 m/s. 76 2.5 -0.5 -\ 1—i—i i i 111| 1—i—i—i 11111 1—i—i—i i 1111 1—i—i i i 1111 0.001 0.01 0.1 1 10 Superficial Gas Velocity, U m/s Figure 4.20. Skewness of differential pressure fluctuations at different levels for IL; = 0.0184 m/s. Table 4.3. Flow regime transition velocities deterrnined from the standard deviation of differential pressure fluctuations for = 0.0184 m/s. Probe location, m Superficial gas velocity corresponding to flow regime transition, m/s Bubble/Slug Slug/Churn 0.15 0.059 0.65 0.65 0.026 0.41 1.35 0.026 0.46 1.95 0.026 0.28 Table 4.4. Flow regime transition velocities determined from the skewness of differential pressure fluctuations for Ue = 0.0184 m/s. Probe location, m Superficial gas velocity corresponding to flow regime transition, m/s Bubble/Slug Slug/Churn Bridging/Annular 0.15 0.075 1.4 20 0.65 0.043 1.4 6.9 1.35 0.052 1.8 8.5 1.95 0.052 1.8 5.0 77 4.4.3 Comparison between Conductivity Probe and Pressure Transducer Techniques Tables 4.1 to 4.4 summarize the experimental results at different heights from the conductivity probe and pressure transducer techniques using different criteria. For the conductivity probe, the results are in good agreement with the visual observations. They also reflect the development of each flow pattern along the column. All flow regime transitions can be determined by the two-element probe using the criteria proposed in section 4.3. For the pressure transducers, however, only some transitions can be detected. It can be seen that for the bubble/slug transition, the results from the standard deviation of absolute pressure fluctuations (in Table 4.2) are close to those from the standard deviation of differential pressure fluctuations (in Table 4.3). Since the standard deviation is a measure of the distribution about the mean, the pressure disturbance caused by air injection and/or other pressure disturbances could enhance the value of the standard deviation in the same ways for both P and AP. The results also indicate that even with a differential pressure transducer, the effect of air injection and other pressure disturbances cannot be totally eliminated. Comparing with the results from the conductivity probe, we see that the techniques based on standard deviations of absolute and differential pressure fluctuations underestimate the gas velocities corresponding to the bubble/slug transition. However, the results from the skewness of the different pressure fluctuations are comparable to those from the conductivity probe; since the skewness is a measure of the asymmetry of a distribution, the effect of the air injection and other pressure disturbances may be small. For the slug/chum transitions, the technique using the standard deviation of differential pressure fluctuations underestimates the transition gas velocities significantly, compared with the results from the conductivity probe. However, the results from the standard deviation of absolute 78 pressure and from the skewness of differential pressure fluctuations are comparable to those from the conductivity probe. Tables 4.3 and 4.4 demonstrate that, with the same measurement technique, different parameters used as transition criteria provide different results. 4.5 Flow Regime Map for Air-Water System 4.5.1 Experimental Results The flow regime boundaries based on conductivity measurements as derived from Figures 4.6, 4.7, 4.8, 4.10 and 4.11 are summarized in Table 4.5. They are also plotted in Figure 4.21. It can be seen that the discrete bubble flow regime predominates at low gas and hquid velocities, while the dispersed bubble flow regime is encountered at higher hquid velocities. Both discrete and dispersed bubble flow regimes are characterized by small bubbles with relatively uniform size distributions. The bubbles in the dispersed bubble flow regime, however, are smaller and more Table 4.5. Flow regime boundaries for air-water system for Z = 0.65 m and D = 0.0826 m Discrete / Dispersed Discrete / Coalesced Coalesced / Slug Slug/ Chum Chum/ Bridging Bridging / annular \Jb m/s Ug, m/s U^, m/s Ug, m/s 0.064 0.0050 0.00205 0.047 0.047 1.3 1.77 6.3 0.064 0.0080 0.00615 0.052 0.061 1.3 1.77 6.7 0.064 0.012 0.0184 0.061 0.068 1.2 1.72 6.7 0.073 0.023 0.0455 0.048 0.056 1.1 1.72 6.7 0.073 0.032 0.0638 0.036 0.048 1.3 1.77 6.7 0.073 0.050 0.0729 0.040 0.048 1.4 1.77 5.7 0.10 0.070 0.100 0.062 0.069 1.1 1.85 5.1 0.10 0.10 0.155 0.13 0.13 0.99 1.72 5.2 0.219 0.26 0.23 0.36 1.85 5.2 79 Figure 4.21. Two-phase bubble column flow regime map for air-water system with D = 0.0826 m and Z = 0.65 m. Distributor: perforated plate containing 62 2-mm circular holes. uniform resulting from the turbulence of the hquid, while the bubble size and distribution in the discrete bubble flow regime could be a function of the gas distributor. The coalesced bubble flow regime in Figure 4.21 appears in a very narrow gas velocity range between the discrete bubble flow regime and slug flow regime due to the small column used in this study. The slug flow regime spans a wide range of gas velocities. At low hquid velocities, the onset of slug flow is almost independent of the superficial hquid velocity while at high hquid velocities the transition from dispersed bubble flow to slug flow is a function of the hquid velocity. With increasing superficial hquid velocity, the transition gas velocity from dispersed bubble flow to slug flow increases. 80 The transitions among the slug, churn, bridging and annular flow regimes are nearly independent of the superficial hquid velocity. For the conditions studied in this work, the churn flow regime only exists within a small range of gas velocity. 4.5.2 Comparison Many investigators have studied flow regime transitions experimentally. Some earlier studies have been based on visualization. Others deterrnined the flow regime with the aid of instruments, e.g., pressure transducer, conductivity probe and X-ray measurement systems. Table 4.6 summarizes some previous studies in vertical gas-hquid two-phase flow. In comparison with this study, it should be mentioned that none of them used a gas distributor. In addition, the column diameter used in most previous studies was much smaller, usually 25 or 51 mm, and the measurement locations were several meters above the gas injector. This makes comparison difficult. Nevertheless, a comparison between this study and some previous studies is shown in Figure 4.22. It can be seen that there is a wide discrepancy among results in the literature, and that the results obtained in this work are similarly discrepant. 81 53 3 D O o" o' cn vo o © CN T3 * s cn NO I T3 g CN •a 00 cn NO" cN NO" i-l NO 5 T3 S '3 g m H i i^i !3 iS ,2 £ 1 O I 1(2 I a CO 3 CO IS SO co p (S T3 q g •5 8 ^ J Q 43 •3 3! ,a> CA 1 0 1 s g §j j3 0) 1) It 8* • g (2 2 X •a CO CO I PH u s I T3 O C oo M CN 1 t/1 01 so § Ui 9 1-1 nl oo SON —H u oo "2 ON 53 ~—• H cs ^ oo ON NO 3 ON N ? 00 2 ON 5i ON S ON ON S 2 3 r-. ON JH l-H as <Nl ON I ON 82 10 This work Superficial Gas Velocity, U m/s Figure 4.22. Comparison of flow regime maps with previous studies. IA: Bubble/Slug Flow Transition, Annunziato and Girardi (1985) 2A: Slug/Chum Flow Transition, Annunziato and Girardi (1985) 3A: Churn/Annular Flow Transition, Annunziato and Girardi (1985) 1G: Bubble/Slug Flow Transition, Govier et al. (1957) 2G: Slug/Froth Flow Transition, Govier et al. (1957) 3G: Froth/Ripple Flow Transition, Govier et al. (1957) 4G: Ripple/Film Flow Transition, Govier et al. (1957) IT: Bubble/Slug Flow Transition, Taitel et al. (1980) 2T: Slug/Chum Flow Transition, Taitel et al. (1980) 3T: Churn/Annular Flow Transition, Taitel et al. (1980) 4.6 Summary A conductivity probe directly reflects the behavior of a two-phase mixture. By measuring bubble frequency, Sauter mean bubble chord length and either average bubble length or average bubble time, flow pattern transitions can be determined. Methods for delineating these transitions are given in this chapter, and experimental results are presented for air-water in a column of diameter 82.6 mm. 83 A pressure transducer registers all pressure fluctuation information including the pressure fluctuations caused by bubbles passing the probe and the pressure disturbances caused by other sources (e.g., air injection). Although a differential pressure transducer may give more weight to the signals which relate to local bubble characteristics by reducing the amphtude of disturbances from outside the interval of interest, it does not totally ehrninate the effect of other pressure disturbance sources. Both methods do not appear to be suitable for flow regime determination in gas-liquid systems. Measurement location plays an important role on flow regime transitions, especially at low gas velocities, since bubbles grow as they ascend in coalesced bubble flow. A flow regime map for the air-water system, determined at 0.65 m above the distributor, is obtained. This is in reasonable agreement with previous studies considering the differences in the experimental conditions. This map and the techniques developed for distmguishing flow regime transitions serve as the basis for further investigation on flow regime transitions in three-phase systems, as discussed in later chapters. 84 Chapter 5 Bubble Characteristics in Bubble Columns 5.1 Introduction As described in the previous chapter, several flow regimes were observed in a bubble column: discrete bubble flow, dispersed bubble flow, slug flow, chum flow, bridging flow and annular flow. This chapter presents experimental results to demonstrate bubble characteristics in these flow regimes. The bubble properties measured in the present work are bubble frequency, gas holdup, bubble velocity, bubble chord length and the chord length distribution. Some results have already been presented in Chapter 4 for the purpose of estabhshing criteria for flow regime transitions. The experimental apparatus and conductivity probe used in this work to measure the bubble characteristics are presented in Chapter 2. The probe was inserted horizontally 650 mm above the gas-liquid distributor with the end of the probe on the axis of the column of inside diameter 82.6 mm. A perforated plate with 62 orifices of diameter 2.0 mm served as the air distributor. 5.2 Bubble Characteristics in the Discrete and Dispersed Bubble Flow Regimes The discrete and dispersed bubble flow regimes are both characterized by small bubbles and narrow size distributions as noted in Chapter 1. The difference between these two flow patterns is that the uniform small size bubbles in the dispersed bubble flow regime result from turbulence of the hquid phase, while in the discrete bubble flow regime, small bubbles are generated mainly by the gas distributor at low gas and hquid velocities. These two regimes can be distinguished from each other by the ratio of the standard deviation of bubble time to the average bubble time, as described in Chapter 4. The discrete bubble flow regime was observed for hquid 85 velocities between 0 and approximately 0.07 m/s and gas velocities from 0.00205 to approximately 0.05 m/s. The dispersed bubble flow regime was found at higher hquid velocities in the air-water system, as shown in Figure 4.21. 5.2.1 Local Bubble Frequency The local bubble frequency in these two regimes is plotted against the superficial gas velocity in Figure 5.1. A linear relationship between the bubble frequency and the superficial gas velocity is found in both the discrete and dispersed bubble flow regimes. The superficial hquid velocity does not significantly affect this linear relationship. As discussed in Chapter 4, the local bubble frequency can be expressed by Equation (4.1), assuming that all small bubbles are spherical and of uniform size, distributed uniformly across the column. The linear constant for the bubble frequency and the superficial gas velocity is 545 ± 80 m"1. 140 5? 0 0.00 0.05 0.10 0.15 0.20 0.25 Superficial Gas Velocity, U m/s Figure 5.1. Linear relationship between bubble frequency and superficial gas velocity for the discrete and dispersed bubble flow regimes: air-water system at Z = 650 mm and D = 82.6 mm 86 5.2.2 Bubble Chord Length and its Distribution Figure 5.2 presents experimental results for the average bubble chord length as a fimction of the superficial gas and hquid velocities. The average bubble chord length increases with increasing gas velocity. It can be seen that the average bubble chord length decreases with increasing hquid velocity. As the hquid velocity is increased, a gradual transition takes place between discrete and dispersed bubble flow. Some typical distributions of bubble chord length in the discrete and the dispersed bubble flow regimes are presented in Figure 5.3. The four left-hand plots are for the discrete bubble flow regime at IL; = 0.0184 m/s, while the four right-hand plots correspond to the dispersed bubble flow regime at IL_ = 0.155 m/s. The standard deviation of the bubble chord length for each 0.1 } I PQ 8P I 0.01 0.001 U(,m/s Ug."* -•— 0.00205 0.00475-0.0426 -•—0.00615 0.00472 - 0.0400 -A— 0.0184 0.00389 - 0.0402 -•—0.0455 0.00213-0.0226 -•— 0.0638 0.00426 - 0.0262 -•—0.0729 0.00211-0.0220 -O— 0.100 0.00206 - 0.0209 -A—0.155 0.00181-0.120 -V—0.219 0.00359-0.249 0.001 I I I I I I • • • • • • I I I 0.01 0.1 Superficial Gas Velocity, m/s Figure 5.2. Comparison of average bubble chord length in discrete and dispersed bubble flow regimes for air-water system at Z = 0.65 m 87 Discrete Bubble Flow XJ( = 0.0184 m/s Dispersed Bubble Flow U,= 0.155 m/s 1 i Ug=0.0039 m/s \ ae= 0.0074 m • \ ^" • | Us== 0.00503 m/s IL a,= 0.00082 m 1 i L J | Ug= 0.0107 m/s T T a,= 0.0086 m • • \ m 1 T"^"'1 1 I 1 Ug= 0.0190 m/s ? a^=0.00109 m • BBB^i » r ^ ™ "i 1 Ug= 0.0278 m/s o^= 0.0101m • J \/\ Ug= 0.0484 m/s a^=0.00121 m B B^ • | i | • | >p • • Ug=0.0402 m/s a/= 0.0107 m • : / V / ^« I 1 1 ^B^ . 1 • Ug= 0.0931 m/s c(= 0.00534 m /v. : 400 300 200 100 0 400 300 200 100 0 400 300 200 100 0 400 300 200 h800 600 400 h200 600 400 200 0 800 600 400 200 0 800 600 400 200 0 0.020 0.000 0.005 0.010 0.015 0.000 0.005 Bubble Chord Length, m 0.010 0.015 Figure 5.3. Probability density distribution of bubble chord length in discrete and dispersed bubble flow regimes for air-water system at Z = 0.65 m 88 operating condition is also given in the figure. It can be seen that the peak values of the PDF curves appear at an average bubble chord length of approximately 5 mm for the discrete bubble flow and 2.5 mm for the dispersed bubble flow, indicating that smaller bubbles were detected in the dispersed bubble regime. The standard deviation of the bubble chord length distribution increases with the gas velocity in both flow regimes. However, the standard deviation of the bubble chord length distribution in the dispersed bubble flow regime is smaller than in the discrete bubble flow regime, indicating a narrower distribution in the dispersed bubble flow regime. 5.2.3 Average Bubble Velocity The experimental results for the average bubble velocities in the discrete and dispersed bubble flow regimes are plotted against average bubble chord length in Figure 5.4. It is seen that the average bubble velocity increases with increasing chord length. The bubble velocities at high 1 I PQ 60 3 2.5 4 2.0-1.5-1.0-0.5 4 -•—0.00205 0.0O475-O.O426 -•—0.00615 000472-0.0400 -A— 0.0184 0.00389 - 0.0402 -yf— 0.0455 0.00213 - 0.0226 -•—0.0638 000426 - 0.0262 -•—0.0729 0.00211 - 0.0220 -O—0.100 0.00206 - 0.0209 -A— 0.155 0.00181 - 0.120 -y—0.219 000359-0.249 0.000 0.005 0.010 0.015 Average Bubble Chord Length, m 0.020 Figure 5.4. Average bubble velocity at different superficial hquid velocities for air-water system at Z = 0.65 m 89 liquid superficial velocities are greater than at low hquid velocities. The bubble velocity and the bubble chord length can be correlated in an alternative way. Consider a system with uniform spherical bubbles of diameter db, during a period of time t; the local gas holdup measured by a conductivity probe can then be expressed by: The left-hand side of the above equation, defined here as bubble travel length, -y-Ub, is plotted against the average bubble chord length in Figure 5.5 for the discrete and the dispersed bubble flow regimes. A non-linear relationship between the bubble travel length and the average bubble chord length is observed. This could he due to the difference between the bubble chord length and the bubble diameter and the difference between the model assumptions and the real situation. The following empirical correlation can be used to describe the relationship between the bubble travel length and the average bubble chord length for the discrete and the dispersed bubble flow regimes: J (5.1) Rearrangement of Equation (5.1) yields: (5.2) Ub = 0.00730 log £h +0.0211 (SI units) (5.3) 90 0.012 4 9 0.010' 2r CO 8 1 CD 1 pa 0.008 0.006 H o.ooo H -0.002 sgUb/f=(2/3)^b ^ ' m *v / / / / Equation (5.3) y / • u U^, m/s Ug,m/s • 0.00205 0.00475 - 0.0426 o 0.00615 0.00472 - 0.0400 • 0.0184 0.00389-0.0402 V 0.0455 0.00213-0.0226 • 0.0638 0.00426-0.0262 • 0.0729 0.00211 - 0.0220 • 0.100 0.00206 - 0.0209 A 0.155 0.00181 -0.120 • 0.219 0.00359-0.249 0.000 0.005 "T 0.010 r 0.015 T~ 0.020 0.025 Average Bubble Chord Length, m Figure 5.5. Relationship between bubble travel length and average bubble chord length for air-water system at Z = 0.65 m and D = 82.6 mm 5.3 Bubble Characteristics in the Slug and Churn Flow Regimes The slug and the chum flow regimes are defined in Chapter 1. In the slug flow regime, one can observe bullet-shaped bubbles and small bubbles in the hquid plugs separating them In the chum flow regime, the bullet-shaped bubbles become narrow and their shapes are distorted. Small bubbles in the hquid plugs coalesce and generate new bullet-shaped bubbles. The overall bubble frequency then increases with the gas velocity in the slug flow regime and decreases with the gas velocity in chum flow. This difference in trends can be used to determine the transition from slug to chum flow as shown in Figure 4.9. In Chapter 4, the slug flow regime was observed when the gas velocity varied from approximately 0.05 to 1 m/s, while the chum flow regime was found at higher gas velocities, 1 to 2 m/s, in the air-water system with D = 0.0826 m, as shown in Figure 4.23. 91 5.3.1 Bubble Chord Length and its Distribution As discussed in Chapter 4, the onset of the slug flow regime was detennined by the Sauter mean bubble chord length since this parameter gives added weight to large bubbles. Figure 5.6 plots the Sauter mean bubble chord length and the average bubble chord length against the superficial gas velocity. It is seen that the Sauter mean bubble chord length is always greater than the average bubble chord length at the same gas velocity. The average bubble chord length is always less than the column diameter in the slug and the churn flow regimes due to the large number of small bubbles in the system Both the Sauter mean bubble chord length and the average bubble chord length increase shghtly with Ug in the slug flow regime. The bubble chord length distributions in the slug and churn flow regimes are presented in Figure 5.7. 10-H4 I 0 1 1 -i 0.1 4 0.01 4 0.001 -•— Average Bubble Chord Length at Ve = 0.0184 m/s -O— Average Bubble Chord Length at = 0.155 m/s -A— Sauter Mean Bubble Chord Length at = 0.0184 m/s -V— Sauter Mean Bubble Chord Length at U( = 0.155 m/s A A / IE, Superficial Gas Velocity, m/s Figure 5.6. Bubble chord length in slug and churn flow regimes at Z = 0.65 m and D = 82.6 mm 92 Slug Flow Churn Flow 80 60 40 20 0 80 60 40 20 0 80 60A 40 20 0 80 60 40 20 £b = 0.021m, ^ = 0.035111 • • • • • • • •\A%'\7V. er,= 0.047 m -+o -80 U^O.O^m/s, U =0.71 m/s U^O.Omm/s, Ug = 1.81 m/s 4,=0.036m, 0^ = 0.055 m V, v. U,, = 0.155 m/s, Ug = 0.297 m/s th = 0.027m, n^ = 0.042 m U, = 0155 m/s, U = 1.33 m/s 1'L U,, = 0.155 m/s, Ug = 0.678 m/s <r, = 0.052 m U, = 0.155 m/s, U = 1.66 m/s 7b = 0.035m, at = 0.064 m v. V, 0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20 Bubble Chord Length, m Figure 5.7. Probabihty density distribution of bubble chord length in the slug and churn flow regimes at Z = 0.65 m and D = 82.6 mm 93 It is seen that the average bubble chord length and the standard deviation for slug flow (left-hand side of Figure 5.7) under different operating conditions vary from 21 to 31 mm and from 35 to 52 mm, respectively, while the peaks of the PDF of the bubble chord length appear at a bubble chord length of 6 to 7 mm This indicates that there are many small bubbles in the slug flow regime. In the churn flow regime (right-hand side of Figure 5.7), both the average and the standard deviation of the bubble chord length are higher than in the slug flow regime. However, the peak values of the PDF curves at low bubble chord length decrease and the PDF curves become wider, indicating that the population of small bubbles in the churn flow regime decreases while the population of large bubbles increases, due to coalescence of small bubbles. 5.3.2 Average Bubble Velocity The difference between the slug and the churn flow regimes can also be seen from a plot of the average bubble velocity versus the average bubble chord length, as shown in Figure 5.8. The dashed line in the figure corresponds to the flow regime boundary in Figure 4.21 of Chapter 4. It is seen that the average bubble velocity increases sharply as the average bubble chord length varies from approximately 0.02 to 0.03 m in the slug flow regime. The reason could be the following: in the slug flow regime, the average bubble velocity is not only dependent on the average bubble chord length, but also on the superficial gas velocity. As discussed in the previous section, the average bubble chord length does not change significantly as the superficial gas velocity varies from approximately 0.05 to 1 m/s, due to the large number of small bubbles in the slug flow regime. Hence, a small increase in the average bubble chord length requires a large increase in superficial gas velocity, which increases the average bubble velocity significantly. In the churn flow regime, the average bubble chord length increases with gas velocity, by reducing the population of small bubbles and increasing the number of large bubbles. The average bubble velocity, however, increases only shghtly in the churn flow regime, probably due to the relatively 94 4.0-3.5 H 3.0 2.5 H J% 2.0 4 1.5H 1.0H 0.5 H 0.0-1 4 0 1 PQ i Churn How Slug How ^Jty VA • 0.00205 0104- 1.90 O 0.00615 0119-213 A 00184 0107-215 V 0.0455 0.113-213 • 00638 0135-212 • 00729 0109-210 • 0100 0164-206 A 0155 0296-L97 W 0219 0473-239 0.00 —I— 0.01 0.02 0.03 0.04 Average Bubble Chord Length, m 0.05 Figure 5.8. Relationship between average bubble velocity and average bubble chord length in slug and churn flow regimes for air-water system at Z = 0.65 m and D = 82.6 mm. small change in the gas velocity, as the average bubble chord length increases from approximately 0.03 to 0.045 m The relationship between the bubble characteristics can be correlated by the bubble travel length and the average bubble length. Figure 5.9 presents the experimental results for the bubble travel length with respect to the average bubble chord length. Three distinctive regions corresponding to different flow regimes deterrnined by the methods described in Chapter 4 can be found in this figure. At lower average bubble chord length, corresponding to the discrete and dispersed bubble flow regimes, the relationship between the bubble travel length and the average bubble chord length can be correlated by Equation (5.3). At intermediate average bubble chord length, corresponding to the slug and churn flow regimes, the relationship between the bubble travel length and the average bubble chord length can be expressed by another empirical correlation, 95 Figure 5.9. Relationship between bubble travel length and average bubble chord length in the slug and churn flow regimes for air-water system at Z = 0.65 m, D = 82.6 mm and U„ « 0.002 - 6 m/s. yUb = 0.1312 log £h +0.2276 (5.4) as shown in Figure 5.9. It is also seen in Figure 5.9 that at high average bubble chord length, corresponding to the bridging and the annular flow regimes, the experimental data for the bubble travel length are significantly greater than predicted by Equation (5.4). The relationship between the bubble travel length and the average bubble chord length can also be used as an alternative method to determine the flow regimes in gas-liquid cocurrent upward systems. By measuring the bubble/void characteristics with a two-element conductivity probe, if the measured bubble velocity, gas 96 holdup, bubble frequency and average bubble chord length satisfy Equation (5.3), then the flow pattern corresponds to the discrete or dispersed bubble flow. If the measured bubble characteristics satisfy Equation (5.4), then we have slug or churn flow. If the bubble travel length is significantly greater than predicted by either Equation (5.3) or Equation (5.4), then the flow pattern is either bridging or annular flow. 5.4 Summary Bubble characteristics in the different flow regimes exhibit different variation with respect to the gas and the hquid flowrates. Bubble frequency increases linearly with superficial gas velocity in the discrete and dispersed bubble flow regimes. Bubble frequency also increases with gas velocity in the slug flow regime but decreases in the churn flow, bridging flow and annular flow regimes. Bubble chord length and its distribution in the dispersed bubble flow regime are smaller and narrower than in the discrete bubble flow regime. Both the average and the standard deviation of the bubble chord length increase with increasing superficial gas velocity in the discrete, dispersed and churn flow regimes. However, the average bubble chord length does not change significantly in the slug flow regime due to the high population of small bubbles in the hquid plugs which separate successive Taylor bubbles. The bubble travel length, defined as (egUb)/f, can be used to correlate the bubble characteristics. The relationship between the bubble travel length and the average bubble chord length can be expressed by Equation (5.3) for the discrete and dispersed bubble flow regimes and by Equation (5.4) for the slug and the churn flow regimes. These two equations provide an alternative method to determine the flow regimes. Further study is needed to extend this new method. 97 Chapter 6 Three-Phase Fluidization Boundaries 6.1 Minimum Liquid Fluidization Velocity at Low to Intermediate Gas Velocity 6.1.1 Introduction Three-phase fluidized beds, containing solid particles fluidized by upward cocurrent flow of hquid and gas, have important applications in hydrocarbon and coal processing and in some biological reactors. Accurate design of such reactors is complicated by many factors, such as lack of knowledge of the minimum gas and hquid velocities required to achieve fluidization, although considerable research, mostly experimental, has been devoted to this subject. Begovich and Watson (1978) studied the minimum fluidization velocity in columns of 76.2 and 152 mm diameter with ah and water as the gas and the hquid, respectively. Various types of particles were used as the solid phase. The experimental conditions are listed in Table 6.1. Since fluidization is achieved when the upward drag force exerted on the particles by the fluid matches the buoyant weight of the bed, neither the column diameter nor the mass (as opposed to density) of solids in the column have any significant effect upon the minimum fluidization velocities. As the gas velocity is increased, the minimum hquid velocity required to achieve fluidization in each system studied decreases. The magnitude of this decrease differs considerably for different particles. At the same gas velocity, the hquid velocity required to achieve fluidization for large/heavy particles is greater than for small/hght particles. An empirical correlation was obtained by Begovich and Watson (1978) for the rninimum hquid fluidization velocity at a fixed cocurrent gas velocity: Re^ = 5.121 x IO"3 Ar/'662 Frg"°118 (6.1) 98 0.0 to 0.060 0.05 0.03 0.08 0.08 0.07 0.06 0.06 <=> *' © 0.15 0.06 0.02 fN O 0.0519 0.06 0.152 o X 0.22 to 0.453 l 1 i i i j i l 0.60 to 0.69 P 0.0762 and 0.152 0.0762 0.10 0.0712 0.0762 0.0762 0.0762 0.0826 0.001 0.001 to 0.0112 0.001 0.001 0.001 0.001 0.00089 0.00135 to 0.00143 CL os Os 995 to 1160 oo OS Os oo Os Os oo OS Os 00 Os Os t-» Os Os 1000 o w • • 1 1 i • j 1 1 1 i i 0.39 0.39 0.38 0.37 0.39 0.39 0.41 -©- T—1 - - 0.75 0.68 oo o I -CL 1720 2240 2240 2200 1990 1170 2240 2450 2450 2560 2590 2520 2530 2200 3690 2500 2472 2876 2525 2470 2200 1890 2000 2472 2470 2530 2520 2510 2490 2520 2610 7510 TT 0.0019 0.0032 0.0046 0 0062 0.0062 0.0063 0.0046 0.0012 0.002 0.00403 0.00608 0.00304 0.00399 0.00611 0.0055 0.00046 0.00078 0.001 0.00304 0.00399 0.00611 0.00151 0.0019 0.00078 0.004 0.0015 0.0025 0.0037 0.0045 0.0025 0.0024 0.0012 Type of articles Glass beads Alumina Plexiglas Glass beads Glass beads Glass beads Glass beads Alumina beads Glass beads Cylindrical catalyst Glass beads Glass beads Glass beads coated with TFE Sand Steel shot Authors Begovich (1978) Bloxom et al. (1975) Ermakova et al. (1970) Lee and Al-Dabbagh(1978) Fan etal. (1985) Fan etal. (1987) Song etal. (1989) This work 99 Clearly Equation (6.1) is not valid for zero gas flow rate. To produce a three-phase correlation that reduces to an acceptable two-phase correlation as the gas flow rate goes to zero, they proposed another correlation (SI units): %^ = 1 - 1622 Tjr6 uT7 d°598 ( PS - Pe ( 6- 2) Costa et al. (1986) proposed that the well-known drift flux model could be used for three-phase systems. Liquid and gas were considered to form a homogeneous combined fluid. A constant ratio ztlz was assumed for the whole bed. The superficial velocity and properties of the pseudo-homogeneous fluid were described by: UH=U,+Ug (6.3) PH = 7P, + 7-P8*7P, (6.4u.H = n, (6.5) The homogeneous fluid and the solids were treated as if they constituted a two-phase flow using the drift flux model proposed by Wallis (1969). According to this model the frictional pressure gradient is given by a Fanning-type equation: dP dz •) =(l-e)CDAp(ipHU&) (6.6) where CD is the drag coefficient for a given bed porosity and Ap is the projected surface area of the particles per unit volume in the flow direction. For non-spherical particles of volume-equivalent-sphere diameter dp, 100 A. = 2dpd> (6.7) According to Wen and Yu (1966), for a system consisting of a single fluid and solid particles, C (6.8) where CDOO is the drag coefficient for individual particles as the solids concentration approaches zero. By substituting Equations (6.4), (6.7) and (6.8) into Equation (6.6), we can express the frictional pressure drop along a three-phase bed by: v2 _ AP^ _3(l-s)CDoo(l-a)Pi(U,+Ug Y . AZJf 4<|)dDsn (6.9) where a = sg/s. When particles are fluidized, the buoyed weight of the solid particles is supported by drag from the upward homogeneous fluid so that ^- 77 I =g(l-e)(ps-pH) AZ (6.10) Combining Equations (6.4), (6.9) and (6.10) leads to with n = 5.7-8U„ [sn4(bd g[ps-(l-amf )pt ] 3CDoo (l-amf )pf CDco = ^-(l + 0.15Reoo0-687) Reoo (Re ^lO3) (6.11) (6.12) (6.13) 101 CDoc = 0.44 (103< Re^lO5) where R&JC = Uocdp(l-amf)p^ -1 (6.14) (6.15) (6.16) amf = 3.464 x 10" uM-°-66((t>dPrps2-1 + L74 . 3.74 U&nf Utof + ug J Ho { Pe ~ P„ j DT 08 (6.17) Equation (6.17) is the particular case at rninimurn fluidization (for which U^ = U^ and a = CW) of three-phase fluidized beds. Values of U^ calculated by this method were usually higher than experimental values. Costa et al. (1986) claimed that this was due to underestimation of a as minimum fluidization is approached. They therefore proposed an alternate empirical correlation for Uftnfl a n£n 1 n^t TT-0328/x , \l-086 f \0-865 0.O42 -0.355 Uflrf = 6.969x10 Ug (<t>dP) iP.-p,) DT (6.18) which is again invahd for Ug = 0. Song et al. (1989) considered the gas and hquid to be separated and assumed that sohd particles are completely wetted by the hquid so that there is no direct contact between the gas and solids. Under such conditions, the system is viewed as three distinct phases. The equivalent diameter, De, of the hquid channels was expressed by: 102 D.-^J[i-vq»d. (6.19) The pressure gradient along the three-phase fixed packed bed was written as f dP, , , -— =(l-a )pe g + ap g + (l-a ) dz ( dP "dzA (6.20) The final term includes the frictional pressure gradient between the hquid and the solid phase which was expressed by Farming's equation as ( dPTs 1 (6.21) Here f^. can be correlated empiricaUy as a function of the modified Reynolds number and gas particle Froude number: f,_s(l- 0.572 Frg138) (Re',-U0) f,_s(l+2.29Frg00755) (Re'/>10) (6.22) where f).s is calculated from the Ergun equation (1952) and can be expressed by 33.3 f,_8 = 0.583 + -Re'* (6.23) with Re'^ = — 103 At minimum fluidization conditions, the pressure gradient is given for small pg by f dP^ V dz = (e, Pe +es Ps )g (6.24) Combining Equations (6.20), (6.21), and (6.24), one can obtain an equation which allows the minimum hquid fluidization velocity to be calculated, i.e. (1-ttmf )i 4fc 1 1—1 1 ( z V Ufmf ( 1-amf )smf = [(l-amf )£mf Pt +(1-£mf )P8]g ^(l-CCnrf )p,g (6.25) where empirically, Song el al. wrote: \ - 0.531 U,-J350 Ii,0'977 (dp > 3 mm) (1-Otmf ) = i 1" L 69 U^0902 Ug0555 ( dp < 3 mm) (6'26) and Smf for particles of known § was estimated (Wen and Yu, 1966) from Equation (6.39) below. U^mf can then be obtained iteratively from Equations (6.22), (6.23), (6.25) and (6.26). Song et al. (1989) also suggested an alternate empirical correlation for U^: VemC =l-376ur>r7dp0213(Ps-p,)"°-423 (SI Units) (6.27) U" ftnf Ermakova et al. (1970) proposed a simple empirical equation, VeM = 1 - 8 - 0.5 U 0 075 (SI Units) (6.28) U n 8 8 (tti 104 Lee and Al-Dabbagh (1978) measured the pressure drop and the phase holdup in both packed and fluidized beds of 4.03 mm and 6.08 mm glass beads. Initially, at constant gas velocity, pressure drop and hquid phase holdup both increased with increasing hquid velocity. Prior to fluidization, however, a particle jumping movement was observed which led to a measurable decrease of both bed porosity and pressure drop. Fluidization occurred at a lower hquid flow rate than in the absence of gas. 6.1.2 Theoretical Models: Modifications and New Models 6.1.2.1 Modified Song model I Starting from the Song et al. (1989) model and rearranging Equation (6.25), one can obtain the following equation at incipient fluidization: 4f„ f 1 A 1 U&nf ( 1 - amf )£mf = (l-Smf) (l-OCmf ) Pi g (6.29) From Equations (6.22) and (6.23), fc = K 0.583 + 33.3 De Pt Ufmf (6.30) where , 1-0.572 Fr K = J 8 l + 2.29Fr. 0.0755 8 (Re', < 10) (Re', > 10) (6.31) Combining Equations (6.29) and (6.30), we find that: 105 2K 0.583 + 33.3 De ^ dpp,Uftrf dp £e V-e ) g (6.32) Multiplying by p/ (L/Vpf2 and rearranging, one can obtain: 1166K 2 66.6dpK _ , Jl-aJ P' — Ke^mf + ,^2 Ke^mf - U £mf/~7 v De ££ De dp ( ps - pe ) (6.33) Solution of this quadratic equation gives „ dp P( Uem[ I 2 Re&if =— = Va2+bAr, -a p, with a = 33.3 dpe^ 1.166 De (6.34) (6.35a) b = 1.166 (l-«mf ) Ps"P/ •P/ De£? (l-£mf) dpK (6.35b) 3 / 2 and Ar, = p, ( ps - pe ) g dp /p., . Note that Equation (6.34) has the same form as that often used for two-phase fluidized beds. In the Song et al. model, the equivalent diameter of hquid channel, De, was defined by Equation (6.19), obtained from the separated flow model of Chern et al. (1983) by erroneously 106 adding the gas-hquid interfacial perimeter to the hquid-sohd interfacial perimeter in their expression for solid-wetted perimeter. A general definition of the equivalent diameter of hquid channels in a bed of particles is more reasonable, i.e. = 4 x hquid volume =lilzlA(l.aHd (6.36) wetted particle surface 3 ss a result also obtainable from the separated flow model of Chern et al. (1983) if one excludes the gas-hquid interface in the calculation of wetted perimeter. Replacing De in Equation (6.35) by De' from (6.36) and rearranging, with 8, = e,^ - sg = ( 1- ), we obtain a = 42.84 (1~e°^) (6.37a) b = 0.5718£mf + (1"amf )2 ( 1 + ) (6.37b) K Ps" Pt In order to avoid the bifurcation caused by Equation (6.31) which leads to numerical difficulties, we take K = 1. Equations (6.34) and (6.37), together with Song's a,^ [Eq. (6.26)], is called the Modified Song Model I. When the gas velocity is zero, only hquid supports the particles and oc^ = 0. According to Wen and Yu (1966), l-£. mf _ 3 0.2 £mf <!> and 1 11 (6.38) (j) £ 3 =14 (6.39) mf On substituting Equations (6.38) and (6.39) into Equation (6.34), with Ug = 0, Equation (6.34), in conjunction with either Equation (6.35) or Equation (6.37), degenerates to the well-known Wen and Yu (1966) equation: 107 Re",^ = ^33.7 2 + 0.0408 Ar^ - 33.7 (6.40) 6.1.2.2 Modified Song model II The gas holdup at minimum fluidization plays an important role in modelling minimum fluidization velocities (as discussed below). Instead of Equation (6.26), a recently developed correlation (Yang et al, 1993) for a, Equation (6.53) with C0 = 0.16, is used in Equation (6.37) (with K = 1 again). Together with Equations (6.34) and (6.37), these equations constitute the Modified Song Model H 6.1.2.3 Pseudo-homogeneous fluid model Here we develop two models for rninimum fluidization in a cocurrent upward flow system One is a pseudo-homogeneous fluid model while the other is a gas-perturbed hquid model. In the pseudo-homogeneous model, the gas-hquid mixture is treated as a single phase with physical properties expressed by: s g IV ~(1 + )\ie =(l + a)pf (6.41) an approximation applicable up to a « 0.05 (Wallis, 1969). Pgs8 +P'fie 8g +8, (l-a)p (6.42) while dP Pgi (Ps-Pgi )g ^ (1-a) [pg-(l-a)p<] pg/ (1 + oc)2 Ps-P^ Ar, •i (6.43) Re gfmf ~ dp( Uimf + Ug ) Pgt ^ dp( U(mf + Ug ) p, (1 - a) Vet M1 + a) (6.44) 108 At rmnimum fluidization, from Equation (6.40), = >/ 33.72 +0.0408^ -33.7 (6.45) so that U^rnf = -^-^-^(J 33.72 + 0.0408 Ar„, -33.7)-U„ (6.46) dp Pi 1 - a v Note that as Ug approaches zero, Equation (6.46) reduces to the Wen and Yu equation (6.40) for hquid-sohd fluidization. 6.1.2.4 Gas-perturbed liquid model In the gas-perturbed model, it is assumed that the only effect of the gas phase is to occupy space and hence to change the absolute hquid velocity. The pressure gradient of the pre-fluidization packed bed is assumed to result from the friction between hquid and solid. The hydraulic radius of the hquid channel is expressed by: d) d„ s, 6(1-8 ) which is equivalent to Equation (6.36), since the equivalent diameter is defined as four times the hydraulic radius. The Ergun equation is correspondingly modified (Zhang et al., 1995) to: v-dp dzjf = 150 ' 8. ^ 1-8 V— + 1.75-<t>2 dD2 1-8 ( n, ) 2 f '• ) (6.48) 109 When minimum fluidization is reached, r dp V = (l-s)(p,-Pt )g (6.49) Combining Equations (6.48) and (6.49) at the minimum fluidization condition, one can obtain: which again reduces to the Wen and Yu (1966) equation as Ug goes to zero when Equations (6.38) and (6.39) are used. 6.1.2.5 Gas holdup at minimum fluidization Two different kinds of models are derived above. When the gas and hquid are assumed to form a pseudo-fluid, the niinimum fluidization velocity is obtained when the pressure drop caused by friction is equal to the buoyed weight of the solids per unit cross-section. The physical properties of the pseudo-fluid are expressed in terms of the physical properties of the gas and hquid, as well as the holdups of gas and hquid at minimum fluidization. The Costa et al. (1986) model and the above pseudo-homogeneous fluid model belong to this category. Another way to approach the niinimum fluidization velocity is to neglect the friction caused by the gas. The gas phase occupies some space in the packed bed; as the gas velocity is increased, gas holdup increases, reducing the hquid holdup. Hence the absolute velocity of the hquid is increased, causing an increase in frictional pressure drop between the hquid and sohd. Beyond a certain gas velocity for a given hquid velocity (or vice versa), this drag causes the particles to be fluidized. The Song et al. (1989) model, as well as its modifications, and the above Re + 0.5715<|>8^f'(l-alrf )3 Ar, -42.86 (1-eJ (6.50) 110 gas-perturbed liquid model belong to this category. Both approaches require information on the gas holdup at minimum fluidization. Since gas holdup is a function of the superficial gas and hquid velocities, an iterative process is required to predict the nrinimum fluidization velocity. Several correlations for a are available from the literature. The experimental conditions used to obtain these correlations are listed in Table 6.2. Begovich and Watson (1978) correlated the gas holdup in a three-phase fluidized bed at minimum fluidization by: JJO.720 ^0.168 jy-0.125 amf = 1.61—i ? (6.51) £mf Costa et al. (1986) reported that in a three-phase fluidized bed, a can be expressed by Equation (6.17) generalized beyond minimum fluidization as shown in Table 6.3. However, this equation led to higher than average deviations close to nummum fluidization. Song et al. (1989) used Equation (6.26), generalized to < U^f, to correlate a, based on the data of Chern et al. (1984) for packed beds. Based on a study of pressure drop for gas-hquid cocurrent flow in packed beds, Turpin and Huntington (1967) proposed a = 1.035-0.182 f \0.24 vugPg for 10 < ( A024 U* Pe <6.0 (6.52) for upward flow with tabular alumina of diameters 7.62 and 8.23 mm In a systematic study of hquid retention in fixed bed reactors, Yang et al (1993) found a major difference between non-foaming and foaming hquids. However, the effect of hquid 111 viscosity, surface tension and column diameter could be neglected. The low retention of hquid phase observed for foaming hquids may, as they claim, be explained by the stability of very small bubbles attached to the sohd surface, causing a significant decrease in total hquid retention after introduction of gas. Table 6.2. Experimental conditions used in correlations for a. Author Gas Phase Liquid Phase Sohd Phase Column Begovich and Watson (1978) Air: Ug= 0-0.173 m/s Water: Ue = 0-0.120m/s Glass, plexiglas, alumina, and alumino-silicate: dp = 1.9 - 6.3 mm ps= 1170-2240 kg/m3 D = 76.2 and 152 mm Combines the gas holdup data from: Kim et al, 1975. Bhatia and Epstein, 1974. Michelsen and Ostergaard, 1970. Efremov and Vakhrushev, 1970. Ostergaard and Michelsen, 1968. Costa et al. (1986) Air, carbon dioxide, helium, methane: pg=0.15- 1.6 kg/m3 Hg= 10"5-2xl0"3 kg/(ms) Ug =0.020-0.16 m/s Water and aqueous solutions of cellulose: Pi=994 - 998 kg/m3 VU = 9.7x10^-8.12x10-3 kg/(ms) He =0.020-0.16 m/s Glass, aluminum, and benzoic acid (paint film) dp = 3.0-5.9 mm. ps = 1200 - 2700 kg/m3-D = 46.0 - 151mm Ho = 110- 410 mm Song et al. (1989) [from Chern et al. (1984)] Air: Ug = 0-0.257 m/s Water: =0.022-0.17 m/s Glass and poly-vinyl chloride: <j>sdp = 3.0 - 6.0 mm. ps = 1470 - 2520 kg/m3-D = 76.2 mm Ho = 600- 690 mm Turpin and Huntington (1967) Air: Water: ( V'24 1.0 < U'P< <6.0 lug PgJ Alumina tabular: d=7.62, 8.23 mm. ps« 4000 kg/m3. D = 50,100, and 150 mm Ho = 2133 mm Yang et al. (1993) Air and nitrogen: Ug= 0-0.14 m/s Water, aqueous solution of NaCl, heptane, cyclohexane, kerosene, propanol, L.C.O., and diesel fuel: P^=684-1050 kg/m3 tie = 1.7x10-5 _ 4.2x10-3 pa.g Y = 2.0x10-2-7.4x10-2 N/m Ut = 0 - 0.40 m/s Alurnina: dp = 2.2, 2.8 mm. ps = 2920 , 3420 kg/m3. D = 50, 100, and 150 mm Ho = 1150-2133 mm 112 In three-phase systems, the wettability of particles affects the hydrodynamics of the fluidized beds. Gas attaches to the non-wetting particles in the form of small bubbles, even when a non-foaming hquid is employed. This situation may be similar to the case of a foaming hquid with wettable particles as described by Yang et al. (1993), who proposed U„ a = s U„ (6.53) with C0 = 0.16 for non-foaming liquids and C0 = 0.28 for foaming liquids. This correlation was shown to be in good agreement with experimental data reported by others. The various correlations are summarized in Table 6.3. In this study, each of these a correlations has been used to predict the minimum fluidization velocity with different theoretical models. Figure 6.1 shows typical predictions of a at minimum fluidization. The predictions are seen to be widely scattered. Table 6.3. Empirical equations for a Authors Correlations (SI units) System Begovich and Watson (1978) TT0.720 , 0.168 T^-0.125 a =1.61^ d* ^ 8 fluidized beds Costa et al. (1986) 3 161-10- U^UdJV fluidized beds a -iwxiu 1 + 174 TT ^TT H„ (p, pg J DT u, V U/+ Ug ) Song etal. (1989) a = 0.531u^350 U^!'77 dp > 3 mm a = 1.69U7°0902 Ug 955 dp < 3 mm fixed beds Turpin and Huntington (1967) f \0.24 / \0.24 a = 1.035 0.182 U'P' ; for 1.0< U'P' <6.0 fixed beds Yang etal. (1993) 0.16 Ug a- TT TT ; for non-foaming liquid 8 Ug + fixed beds 113 1.0-r 0.9-0.8-a 0.7-o 0.6-• 0.5-lum 0.4-0.3-0.2-8 0.1-0.0--0.1-Predictions of a for 4.6 mm glass beads, air and water Begovich and Watson (1978) Costa etal. (1986) Song et al. (1989) Turpin and Huntington (1967) — Yang etal (1993) 0.20 Ug, m/s Figure 6.1. Prediction of gas holdup on solids-free basis at minimum fluidization, with properties corresponding to the experimental conditions of Begovich and Watson, 1978. 6.1.3 Experimental Study The experimental apparatus employed in this work is described in Chapter 2. Six pressure transducers, located at 0.10 m intervals starting 0.15 m above the distributor, were used to obtain the pressure gradient along the test section. A personal computer (IBM 486 DX2-66 MHz) was used for data acquisition. Liquid temperature was measured at the outlet to determine the hquid viscosity and density, while gas and hquid flow rates were measured by inlet rotameters. Seven different types of particles were used, with key properties listed in Table 6.1. 114 6.1.3.1. Experimental procedure Begovich and Watson (1978) and Lee and Al-Dabbagh (1978) obtained XJimf by plotting pressure drop vs. superficial hquid velocity, while Fan et al. (1985) plotted overall pressure gradient vs superficial hquid velocity. Figure 6.2 plots the pressure gradient and the pressure drop vs. superficial hquid velocity at constant gas flow rate for one of the present runs. It is seen that there is no significant difference between these two methods. In this study, all values of were deterrnined from the intersection of the fixed bed and fluidized bed pressure gradient curves in plots of pressure gradient versus superficial hquid velocity at a constant gas flow rate, as shown in Figure 6.3. It can be seen from Figure 6.3 that there was negligible difference in U^f obtained by increasing or decreasing the hquid velocity. The standard deviations, defined by Equation (2.4), of the pressure fluctuations are shown as the error bars in the same graph. 0.00 0.01 0.02 0.03 0.04 0.05 Superficial Liquid Velocity, IL, m/s 0.06 Figure 6.2. Determination of by pressure drop and pressure gradient methods for 2.5 mm glass beads with Ug = 0.0509 m/s. 115 2.5 2.0 H 1-5H 1.0H 0.5 H u, • decreasing liquid velocity A increasing liquid velocity 0.0 o.oo 0.01 0.02 0.08 0.04 0.05 0.06 U^, m/s Figure 6.3. Effect of increasing or decreasing liquid velocity on determination of for 2.5 mm glass beads with Ug =0.0509 m/s. 6.1.3.2 Experimental results The experimental nunimum fluidization results are shown in Figures 6.4 and 6.5. As expected, U^f decreased with increasing gas velocity and increased with increasing particle diameter and particle density. Figure 6.5 shows the effect of particle wettability and sphericity on U^jjjf. The minimum hquid fluidization velocity required for 2.5 mm glass beads coated with TFE was shghtly less than for the same beads without coating. The decreased sphericity of the sand (4> « 0.8) compared to the glass beads = 1) does not influence U^f very much in a three-phase fluidized bed, although there is obviously a significant difference in a hquid-solid fluidized bed (i.e. at Ug = 0), part of which may be due to the increased roughness of the sand. 116 0.04 0.00 0.02 0.04 1 ' r 0.O3 0.03 Ug, m/s i 1 r 0.10 0.12 0.14 0.16 Fgure 6.4. U^f for different particle sizes and densities. 1 i 0.025 0.020-0.0154 0.0104 0.0054 • 2.5 mm glass beads • 2.5 mm glass beads coated with TFE A 2.4 mm sand 0.000-1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1-0.00 0.02 0.04 0.06 0.03 0.10 0.12 0.14 0.16 Ug, m/s Figure 6.5. for particles of different wettablity and sphericity. 117 6.1.4 Comparison and Discussion 6.1.4.1 Pressure gradient in fixed beds The overall pressure gradient in a three-phase fixed bed in which the sohds are enveloped by the continuous hquid phase can be expressed as the sum of hydrostatic and frictional terms: l-^r(1-8°)p<8+£°ps8T^Jf (6.54) If Equation (6.48) is substituted into Equation (6.54), and the term containing gas density is neglected, the following equation can be obtained: dZy = (l-sj +150 (1-B0 )2 Pi U 4>2 s3(l-a)3 dp p,U, dpg + 1.75- (1-SQ) U2 <t.83(l-a)3 dpg (6.55) If a is obtained from Yang's Equation (6.53) with C0 = 0.16, the overall pressure gradient can be predicted by Equation (6.55). Figure 6.6 compares predictions and experimental results. At high gas velocities, predicted values are in good agreement with experimental values, especially at the nnnimum fluidizing condition; however, at low gas velocity, predictions are about 17% less than the corresponding experimental values, possibly due to some inaccuracy of Equation (6.53) at low values of U„. 118 3.5 3.0-— 2.5 H ¥ 2.0-1 1.0H • Experimentaldata at Ug = 0.0127 m/s Prediction by Equation (6.55) with Yang's a at Ug =0.0127 m/s • Experimentaldata at Ug = 0.153 m/s Prediction by Equation (6.55) with Yang's a at U =0.153 m/s 0.000 0.005 0.010 0.015 0.020 IL,, m/s 0.025 0.030 Figure 6.6. Three-phase fixed and fluidized bed pressure gradient measurements compared with fixed bed predictions for 3.7 mm glass beads. 6.1.4.2 Minimum fluidization velocity for liquid-solid fluidized beds A number of investigators have studied rninimum fluidization velocities in both gas-solid and hquid-sohd fluidized beds. Figure 6.7 shows some predictions and corresponding experimental results for hquid-sohd fluidized beds, generated by investigators of three-phase fluidization. The predictions by Wen and Yu (1966), Richardson (1971) as well as Grace (1982) are all in good agreement with the experimental data. The root mean square percentage deviations defined by 1 N N i = i ^predicted value - experimental value ^ experimental value were 10.3%, 11.7% and 13.4%, respectively, for these three correlations. (6.56) 119 1000-100-j CD (4 • o A o Begovich (1978) Ermakova etal (1970) Lee and Al-Dabbagh (1978) Fan etal. (1985) Fan etal (1987) Song etal (1989) This work 10? 104 Ccardation a b Wen and Yu (1965) 33.7 0.0408 Richardson (1971) 23.7 0.0365 Saxenaand Vogel (1977) 25.3 0.0571 Bebuetal (1978) 25.3 0.0651 Grace (1982) 27.2 0.0408 Chitesteretal (1984) 2a7 0.0494 1 ' 1 10s iii) 10s Figure 6.7. Comparison of rninimum fluidization velocity predictions and experimental results for liquid-solid fluidized beds. Predictions are for an equation of the form Refmf = -\/a2 + b Afy - a, with values of a and b as listed in the legend. 6.1.4.3 Minimum fluidization velocity for three-phase fluidized beds Five empirical correlations, Equations (6.1), (6.2), (6.18), (6.27) and (6.28), were used to predict U^f. The results for 2.5 mm glass beads are plotted in Figure 6.8. It can be seen that Equation (6.1) gives the best predictions. The average absolute percentage deviation, 8a, defined by l N N i = i predicted value - experimental value experimental value (6.57) 120 0.022-4, Q024-1 \'.\ > ErmakDvaet al. (1970), Eq. (6.28) Begovich and Watson(1978),Eq. (6.1) Begovich and Watson (1978), Eq. (6.2) Costa et al. (1986), Eq. (6.18) Song et al. (1989), Eq. (6.27) 0.0204 • E^porimaital data for 2.5 nm glass beads three-phase system Q0184 QO064 QOO Q05 Q10 Q15 Ug,m/s Figure 6.8. Experimental minimum fluidization velocities for 2.5 mm glass beads compared with predictions of various empirical equations. and the root mean square percentage deviation, 8S, defined by Equation (6.56), are listed in Table 6.4 for the various empirical correlations. The smallest deviations again correspond to Equation Figure 6.9 presents experimental data from this work (2.5 mm glass beads) compared with predictions of all the models. It is evident that both the pseudo-homogeneous fluid model and the Costa et al. model can be used only for very small gas velocities. For high gas velocities, they predict negative values of U^f. The other models all predict the correct trends, with the gas-perturbed hquid model giving the best results. It can also be seen that at low gas velocities, the gas perturbed model overestimates U^f somewhat. This probably results from underestimation of the overall pressure gradient at low U~ as discussed previously. (6.1). 121 Table 6.4 Average absolute percentage and root mean square percentage deviations between predictions from correlations for niinimum fluidization velocity for three-phase fluidized beds and experimental data. Mean percentage deviation Data from this work All data, excluding 6.3 mm plexiglas in shallow bed Authors 5a 5s 5a 5S Ermakova et al., Eq. (6.28) * 37 42 28 38 Begovich and Watson, Eq. (6.1) * 12 15 18 28 Begovich and Watson, Eq. (6.2) * 90 98 54 73 Costa et al., Eq. (6.18)* 73 78 66 81 Song etal.,Eq. (6.27)* 65 71 42 57 Costa et al. model 643 958 494 789 Song et al. model 57 73 43 57 Modified Song model 1 115 119 94 115 Modified Song model 2 80 85 68 93 Gas perturbed liquid model 19 24 26 34 Pseudo-homogeneous fluid model 803 1190 536 1030 * Empirical equations. 0.030 -0.015 0.00 0.06 Costa etal. model (1986) Song etal.model (1989) Modified Song model I Modified Song model II Gas-perturbed liquid model Pseudo-homogeneous fluid model Bqxrimaital data for 2.5 mm glass beads 0.10 0.15 Ug, m/s Figure 6.9. Experimental minimum fluidization velocities for 2.5 mm glass beads compared with predictions of various models. 122 Figure 6.10 presents the predictions of Re^ by the gas-perturbed hquid model, Equation (6.50), versus all the available experimental data (275 data points). Most experimental data are in good agreement, including those for the non-wettable particles. For our own data the average absolute and the root mean square percentage deviations are 19.0% and 24.2%, respectively. The points represented by stars, taken from Begovich (1978), are for 6.3 mm plexiglas beads in a column of diameter 152 mm and static bed height 220 mm. The large deviations for these points could be due to the effect of relative bed shallowness (low FL/D), since the author also had some data for 6.3 mm plexiglas beads in a column of diameter 76 mm and static bed height 273 and 408 mm which are in good agreement with the predictions. Table 6.4 lists the average absolute and the root mean square percentage deviations for all the models tested. For the present experiments, was taken as equal to the static bed voidage, Figure 6.10. Comparison of all available experimental results for with predictions of gas-perturbed hquid model, Equation (6.50). 123 s0, while for other spherical particle studies, was assigned a value of 0.39, after Lee and Al-Dabbagh (1978). For non-spherical particles, the Wen and Yu (1966) Equation (6.39) was employed to determine or <j) when one of these quantities was not available. The eleven shallow bed data points of Begovich (1978) are excluded from the comparisons in Table 6.4, as are data for Ug = 0. It is seen from this table that, amongst the models, the gas-perturbed hquid model decisively gives the best predictions. It is also seen that the relative performance of the various predictive methods with respect to the experimental data generated in the present work (72 data points) differs very little from that with respect to the combined data from this work and the literature (264 data points). 6.2 Minimum Gas Fluidization Velocity at Zero or Low Liquid Velocity At low gas velocities, particles are suspended mainly by the hquid phase in a three-phase fluidized bed. At high gas velocities and zero or very low hquid velocities, however, particles are suspended mainly by the gas phase, which provides energy for generating intense turbulent flow in the hquid phase. The resulting hquid motion imparts energy to the sohd particles by which they can remain in a suspended condition. Many studies have been devoted to this field. The gas velocity at which all particles are fully suspended at zero (or very low) hquid velocity is defined as the critical gas velocity (Ugc) for complete suspension of particles. The critical gas velocity is a function of particle loading, height of the stagnant hquid phase, physical properties of the particle and the hquid and column diameter. 6.2.1 Introduction Knowledge of Ugc is crucial for the design of three-phase bubble columns. Investigations of this parameter have been carried out by Roy et al. (1964), Imafuku et al. (1968), Narayanan et al. (1969), Koide et al. (1983,1984,1986), Pandit and Joshi (1984, 1987), Smith et al. (1986), 124 Heck and Onken (1987) and Abraham et al. (1992). Experimental conditions and the range of variables covered in these studies are summarized in Table 6.5. Roy et al. (1964) measured the critical gas velocity by means of a pressure transducer mounted below the gas distributor in a 50 mm i.d. column. A break point, observed in a plot of total pressure versus superficial gas velocity, was taken to correspond to the complete suspension of sohd particles. Solids holdup at this condition was defined as the critical sohds holdup. This critical sohds holdup increased with Ugc. Two regions of critical sohds holdup were observed. In the first, at lower gas velocity, the critical sohds holdup depended on the nature of the sparger. In the second region, at higher gas velocity, the critical sohds holdup was found to be independent of the nature of the sparger. The effects of sparger design, particle size, hquid surface tension, hquid viscosity and solid-liquid wettability on critical sohds holdup were studied. An empirical correlation was proposed: -0.18 -0.23 (6.58) 1.072 x 10" ^ReJ^N- (Yf) Cu forReg>500 with (6.60) and = 0.1558 + 0.0264 log( u.,) + 0.1026 log2 (\ie) (6.61) 125 Measurement Technique visual observation, pressure drop and sampling pressure drop visual observation visual observation and pressure drop visual observation and pressure drop visual observation visual observation and pressure drop visual observation and sampling pressure drop visual observation visual observation visual observation Q S 0.05 0.05, 0.10 and 0.20 0.114 and 0.141 0.10, 0.14 and 0.30 0.10, 0.14, 0.218 and 0.30 0.10, 0.20 and 0.385 0.14 Di = 0.066, 0.082, 0.094 and 0.104 0.0762 0.20 0.20 0.200 and 0.385 0.0826 Particle Loading VI H ri ll U I m SO g rt ^ II CO ci rj" oo oo rt 1 w-l rs II rt o o o "* m II M m o ! II M m O w-i rs to o ^ o to" || CO O o o -9 o rt 1 o II o" -Sbg to o . rs ,_, i to" II to o • —-' rt ' o to" II t oo O • oo w-i II o *3 O , o rs 0.0135 -0.11 in water 0.0103 0.0125 -0.11 0.0048 -0.0749 0.0109-0.0779 0.0085 -0.164 0.0020 -0.021 0.0125 -0.164 0.008 -0.290 0.195 -0.395 °-% M 1440-3466 2550 2630 2500-8770 2500-8770 2260-2500 2500-4680 2420-3870 2440 2260-2500 2500-4000 2490-7510 0.13-0.675 0.111 0.125-0.675 0.0077-0.0846 0.079 -0.498 0.070 -2.0 0.079-0.20 0.0485 -0.084 0.308 0.110-2.0 0.067 -2.10 Wl 1 rs Solid quartz, coal, Ni-Al alloy and F-T catalyst glass beads quartz glass beads and bronze spheres glass beads and bronze spheres glass beads and quartz glass beads glass beads and carborundum glass beads glass beads and quartz glass beads and alurnina particles glass beads and steel shot Liquid and Ug, m/s water, aq. alcohol soln. and oil. zero-velocity water zero-velocity water zero-velocity water, glycerol and aq. ethylene glycol soln. zero-velocity water, glycerol and aq. glycol soln. zero-velocity water 0.0 - 0.030 water zero-velocity water zero-velocity water zero-velocity aq. solns. of alcohols, electrolytes, glycerol, CMC, guar gum, polyethylene oxide and polyacrylamide zero-velocity water zero-velocity water 0.0 - 0.04 Gas and U„, m/s .tt ra air 0.03 - 0.20 air 0.05-0.23 air 0.015 - 0.20 air 0.0-0.10 air 0.0 - 0.80 air 0.0-0.022 air 0.013 - 0.20 air 0.0 - 0.20 air 0.0-0.06 air 0.0 - 0.60 air 0.0-1.4 Author Roy et al. (1964) Imafuku et al. (1968) Narayanan et al. (1969) Koide et al. (1983) Koide et al. (1984) Pandit and Joshi(1984) Koide et al. (1986) "B Z oo •3 os •tn rt 6 ^ Heck and Qnken (1987) Pandit and Joshi (1987) Abraham et al. (1992) Present work 126 Irrmfuku et al. (1968) studied the effect of sohd concentration, sparger design and the shape of column bottom on Ugc in 50, 100 and 200 mm i.d. columns. A pressure transducer was mounted at the bottom of the column. The pressure difference between the total pressure at a non-zero gas velocity and at zero gas velocity was used to determine Ugc in a plot of the pressure difference versus the gas velocity. Contrary to the findings of Roy et al. (1964), Ugc was found to decrease with increasing sohds concentration. Ugc increased with increasing column diameter. For the 50 mm column, the sparger design had no effect on Ugc. However, for larger columns, the shape of the column bottom and the position of the sparger strongly influenced Ugc. Narayanan et al. (1969) studied sohds suspension in 114 and 141 mm i.d. columns with FL/D = 1. A theoretical model for Ugc, determined based on bubble movement, was proposed: Ugc=n 2g(ps-Pf) 2d P , CS2 Hc 3 Pi Ps + CS2 Pi 1 2gHcs c 'Pi -pg^ v. Pi ) (6.62) with eg=<: 0.062U g 0.38 for Ug< 0.067 m/s (6.63) for 0.067 <Ug< 0.213 m/s [0.133Ug Experimental values of Ugc were as much as four times greater than the predicted values at low sohds concentrations, but they were in good agreement for CS2 > 0.10. A correction factor was employed to obtain the final prediction: ugc = 4.3(19.69 D)m Ug exp(-10 CS2) for CS2<0.10 1.25 (19.69 D)m U„ exp(-3 CS2) for CS2>0.10 (6.64) 127 0.5 where m = < 0.2 for dp > 0.2 mm for dp < 0.1mm Koide et al. (1983) worked with 100, 140 and 300 mm i.d. columns with conical bottom sections such that the ratio Dd/D could be varied, where Dd is the area of the distributor plate. It was found that Ugc increases with increasing particle size, sohd loading and column diameter. However, no effect of hquid height on Ugc was found when Hg varied from 0.55 to 1.5 m (i.e., fL/D ratio of 3.33 - 10). A reduction in Ugc can be achieved by using a conical bottom with a small value of Dd/D for the smallest diameter column. They proposed U ( ^-=0.801 Ps ~Pt Pt 0.600 , x 0.146 / /—— f 1-1.20 V D 0.0301 ,0.24 ( u 1 + 807 8H/ 4A 0.578 \Pt r ' D g Pt (6.65) Pandit and Joshi (1984) carried out a systematic study of Ugc with an air-water-particle system for a wide range of particle sizes (110-2000 urn). The effects of es, IT/D ratio, superficial hquid velocity and column diameter on Ugc were investigated. Ugc was found to increase with particle terminal setting velocity (Ut) and sohd holdup (es), but was independent of IL/D. However, Ugc decreased with increasing column diameter, contrary to the findings of Narayanan et al. (1969), Koide et al. (1983) and Imafuku et al. (1968). It was also found that, in the presence of hquid flow, Ugc was reduced significantly and the dependence of Ugc on CS4 (actual volume of sohds per unit cross sectional area of the column) was considerably weakened. Pandit and Joshi suggested that complete suspension of the particles occurs when the axial component of hquid 128 fluctuating velocity, given by Uz = 0.3275-UD (ug+U,)(l-sg)- eg U^-s.U. f \ Ps-Pc Pt Pc-Pg (6.66) equals the settling velocity of the particles. Here Pc =P* &£ +Ps£s and USN = 1.44 Ut078 Ug023 ( A15 v1 8»y (6.67) (6.68) For air-water systems, they suggested: U0 g 2Ug+Ub00 with Ubco =0.3 m/s. (6.69) Koide et al. (1984) reported values of Ugc in bubble columns with draught tubes. They observed that draft tubes reduced the value of Ugc. Ugc increased with increasing terminal settling velocity, sohds concentration, hquid surface tension, diameter of gas distributor and density difference between sohd and hquid phases, but decreased with increasing column diameter (contrary to their early report) and hquid viscosity: Hsi = 4.6r/ U, Pt y>.750 , v '-'S3 0273 Y \ -0.634 / <> \ -0.340 fo ^0J46 / -^0.454 1 + 897 pty3 xO.290 + L47xl(T4|^I D 1-1.32 1 (6.70) D 0.997 Koide et al. (1986) studied the effects of column size, properties of the sohd particles and mixed particle sizes on Ugc in bubble columns with and without draft tubes. It was observed that the effect of column dimension on Ugc of mixed sohd particles is similar to that on Ugc for 129 monosize particles. For a small weight fraction of particle having the largest value of Ut, the properties of the other particles had almost no effect on Ugc. When the weight fraction of particles having the largest value of Ut was greater than 0.33, the correlation of Koide et al. (1983) for monosize particles, Equation (6.70), was used to predict the Ugc of a mixed particle system by appropriately modifying CS3 and Ut in Equation (6.70). Smith et al. (1986) proposed a sedimentation dispersion model for the axial concentration distribution of sohds in slurry bubble columns. Using this model, Ugc was predicted when the sohds concentration at the bottom of the column was less than the concentration of settled sohds. However, this model gives very conservative estimates of Ugc: 0.1551n(dp) +1.78] [exp(A) - l] (l-sJ(l-A)A where (6.71) A = >gjEs and 2 + (l-Sg)E Here USN can be calculated from Equation (6.68) 0.35/ u '72 -l (SI units) (6.72) Heck and Onken (1987) found a hysteresis effect when pressure drop was used to determine Ugc in bubble columns with and without draft tubes. Ugc, measured as the superficial gas velocity was increased, was higher than when the gas velocity was reduced. Pandit and Joshi (1987) reported the effects of surface tension, hquid viscosity, pseudo-plasticity, drag reducing agents and the presence of electrolytes on Ugc in 200 mm i.d. column. Their model (Pandit and Joshi, 1984), Equation (6.66), was used to analyze the effect of these variables on Ugc (in terms of the effect of bubble size, bubble rise velocity, sohds holdup and particle settling velocity) for zero superficial hquid velocity. 130 Abraham et al. (1992) studied the effect of sparger on Ugc. An empirical correlation for Ugc was proposed, in which particle terminal setting velocity, gas holdup, sohds loading and column diameter served as the variables: TT n^TT 0-46 „ 0.66 N 0.39 T^O.27 IS 71\ Ugc=0.54Ut eg CS4 D (6.73) where 8g=L44| U, 0.71 p/18 y021 D004 1 + 600 exp 0.62 ec c TT 0.47 JT 0.69 V 8^Ut Ug J (6.74) Good agreement between the prediction and experimental results, including previously published data, was found for a wide range of operating conditions. Careful analysis of the foregoing published literature reveals the following points: (1) Most investigators performed experiments in a semibatch manner. Predetermined batches of sohd particles and hquid were added to a column while the gas flow was continuous. The effect of hquid velocity on Ugc is needed to complete the investigation of the transition from a three-phase fixed bed to a fluidized bed. (2) Experiments with large/heavy particles in three-phase systems are required to determine the effect of particle size and density on Ugc. 6.2.2 Zero Superficial Liquid Velocity Experiments were carried out in an 82.6 mm i.d. Plexiglas column. The pressure drop between 50 mm and 650 mm above the distributor was measured to determine the critical gas velocity for the complete suspension of particles. Figure 6.11 shows a typical result for the 1.5 mm glass bead three-phase system at zero superficial hquid velocity. 131 o I 1200-1100-1000-900-800-TOO-600-500-400-300' 200' —A— increasing gas velocity / ^ —v— decreasing gas velocity / V Fixed bed 0.0 0.5 1.0 r 1.5 T 2.0 Superficial Gas Velocity, U, m/s 2.5 Figure 6.11. Determination of critical gas velocity for full suspension of particles: dp = 1.5 mm, ps = 2530 kg/m3, HQ = 770 mm, U, = 0, AP = P50 - P650 It is seen that as the gas velocity is increased, the total pressure drop increases before particles are suspended. This is due to the frictional pressure drop between the particles and the fluids. As the gas velocity is increased further, the pressure drop decreases after the particles are observed to be completely suspended, due to the relatively large gas holdup which now exists in the test section. A maximum pressure drop is observed corresponding to Ugc. As the gas velocity is subsequently decreased, the pressure drop also passes through a maximum at almost the same gas velocity, as shown in Figure 6.11. The pressure drop in the fixed bed regime, however, exhibits different values when the gas velocity decreases compared to when it increases. The transition velocity from fixed to fluidized bed is apparently unaffected by this hysteresis. This result was confirmed by Abraham et al. (1992) and Pandit and Joshi (1984). 132 The effect of measurement location on Ugc was examined before other experiments were carried out. Figure 6.12 compares the pressure drop across the lower part, the upper part and the combined interval. It can be seen that complete particle suspension condition is reached at the same gas velocity in each case. The particles in the upper part of the column were not suspended earlier than in the lower part. This implies that once the gas velocity is high enough, the entire sohds phase is suspended, i.e. no gradual process of particle suspension is observed. In order to confirm this conclusion, different static bed heights were used to carry out the experiment. . Figure 6.13 shows how critical gas velocities were deterrnined for different sohd loadings. It is seen that Ugc for different static bed heights, H,, = 440 and 770 mm3 are the same at zero hquid velocity. This result, together with the results shown in Figure 6.12, suggests that the suspension of large particles could be caused by drag from the gas phase. 1200 Superficial Gas Velocity, U m/s Figure 6.12. Determination of critical gas velocity at different bed heights: dp = 1.5 mm, ps = 2530 kg/m3, FLj = 770 mm, = 0, AP = P50 - P650, P50 - P350 and P350 - P650. 133 1100 0.0 0.5 1.0 1.5 2.0 2.5 Superficial Gas Velocity, Ug, m/s Figure 6.13. Effect of particle loading on critical gas velocity for complete solids suspension: dp = 1.5 mm, ps = 2530 kg/m3, H,, = 440, 770 mm, = 0. Three different types of particle with properties given in Table 2.1 were used to study Ugc. Figure 6.14 shows the variations of pressure drop with respect to superficial gas velocity for deterrnining Ugc. The results are listed in Table 6.6. The predicted values of Ugc according to the Wen and Yu (1966) equation for gas-sohd fluidization, Regmf = V33-7 2 + °-0408 Arg - 33.7 (6.75) are also listed in Table 6.6. The viscosity and density of air used here are 1.8 x 10"5 Pa.s and 1.25 kg/m3, respectively. 134 I I I I I I I I I I 0.1 1 Superficial Gas Velocity, TJ m/s Figure 6.14. Determination of critical gas velocity at zero superficial liquid velocity. Table 6.6. Experimental and predicted values of critical gas velocity (m/s) at zero superficial liquid velocity. 1.5 mm glass beads 4.5 mm glass beads 1.2 mm steel shot Experimental results 0.55 1.07 1.32 Prediction by Equation (6,75) 0.78 1.51 1.39 Prediction by Equations (6.66) and (6.69) 1.00 7.69 9.36 Prediction by Equations (6.66) and (6.51) 0.422 4.01 4.74 Prediction by Equations (6.66) and (6.53) 0.552 4.47 5.32 It is seen that the predicted values of Ugc for the 1.5 mm and 4.5 mm glass beads by Equation (6.75) are approximately 50% greater than the experimental data, while for the 1.2 mm 135 steel shot there is only a 5% difference between the predicted and the experimental results. This result implies that the suspension of large/heavy particles at = 0 could be caused by two forces. One is the drag force resulting from the internal chculating motion of the hquid phase, generated by the gas phase. The other is the drag force directly resulting from contact between the particles and the gas phase. For particles of lower density, such as glass beads, both forces are significant in the suspension of the particles. For particles of higher density, such as steel shot, the latter force plays the main role in the suspension of the particles. In such a case, Equation (6.75) can be used to predict Ugc. 6.2.3 Non-Zero Superficial Liquid Velocity As mentioned previously, most studies of critical gas velocity have focused on zero superficial hquid velocity. In this study, the superficial gas velocity required for complete suspension of particles at non-zero superficial hquid velocity, U^f, decreases with increasing superficial hquid velocity. This confirms the investigation by Pandit and Joshi (1984), in which 0.85 and 2.0 mm glass beads were used to study the effect of superficial hquid velocity on U^f. Figure 6.15 plots pressure drop versus gas velocity for determining Ugmf at three different low hquid velocities for the three-phase system using 1.5 mm glass beads. Determination of Ug^ for the 4.5 mm glass beads and the 1.2 mm steel shot systems are shown in Figures 6.16 and 6.17, respectively. All experimental results for U^f, including those for (Ugc) with zero superficial hquid velocity, are summarized in Table 6.7. 136 1100-10004 900 H 800 H 7004 600-500 / \ A , m/s —o— 0.00152 J m —±— 0.00205 —v— 0.00307 / A V 0.1 Superficial Gas Velocity, U, m/s Figure 6.15. Deteraiination of critical gas velocity for three-phase system with 1.5 mm glass beads at different hquid velocities. Figure 6.16. Determination of critical gas velocity for three-phase system with 4.5 mm glass beads at different hquid velocities. 137 3500 500 | -.ii,, , , i i i i i" |" • •' i i ^ 0.1 1 Superficial Gas Velocity, Ug, m/s Figure 6.17. Determination of critical gas velocity for three-phase system with 1.2 mm steel shot at different hquid velocities. Table 6.7. IVJinimum fluidization gas velocities at low hquid velocities. U^f, m/s U|, m/s 1.5 mm Glass Beads 4.5 mm Glass Beads 1.2 mm Steel Shot 0 0.55 1.07 1.32 0.00102 - 1.00 0.99 0.00150 0.54 -0.00205 0.48 0.91 0.69 0.00307 0.25 - -0.00410 - 0.54 0.50 0.00717 - 0.48 0.36 138 Figure 6.18 plots the miirimum gas velocity versus superficial hquid velocity for 1.5 mm glass beads, 4.5 mm glass beads and 1.2 mm steel shot three-phase systems at zero and low hquid velocities. The predictions of Equation (6.66) with Equation (6.69) for these three systems are also plotted in the same figure. It is seen that these equations overestimate Ugmf significantly at zero hquid velocity. In addition, the predicted values for U^f do not change with increasing hquid velocity vvithin the operating range. Other correlations for gas holdup, i.e. Equations (6.51) and (6.53) with sg = a s, have been used with Equation (6.66) to predict Ugmf. The predicted values of Ugjjyc level off again with increasing U^, no matter which correlation for gas holdup is used. However, the predicted Ugc (U^ at = 0) with Equation (6.53) agrees well with the experimental data for the 1.5 mm glass beads (see Table 6.6). o • Experimental data for 1.5 mm glass beads Experimental data for 4.5 mm glass beads Experimental data for 1.2 mm steel shot Prediction by Equations (6.66) and (6.69) for 1.5 mm glass beads Prediction by Equations (6.66) and (6.69) for 4.5 mm glass beads Prediction by Equations (6.66) and (6.69) for 1.2 mm steel shot 0.1 1 1 1 1 1 1 r-0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 Superficial Liquid Velocity, m/s Figure 6.18. Experimental minimum fluidization gas velocities for three-phase system at zero and low hquid superficial velocities 139 6.3 Particle Transport Velocity in Gas-Liquid Mixture 6.3.1 Introduction At high gas and/or hquid flow rates, sohd particles can be entrained from the column. The particle transport velocity in a gas-hquid mixture demarcates the boundary between a fluidized bed and a transport three-phase system and sets the upper limit at which a three-phase fluidized bed can be operated. It is a function of gas and hquid superficial velocities, as well as the physical properties of the hquid and the sohd particles. However, little information can be found regarding this aspect in the literature. Jean and Fan (1987) determined the boundary between the expanded bed regime and the transport regime by extrapolating the overall voidage, (sg + s^), to unity at a given gas velocity. They found that the transition hquid velocity decreased as the superficial gas velocity increased for glass beads of diameter greater than 0.46 mm. Fan et al. (1987) confirmed this finding. For 0.33 mm and 0.46 mm glass beads, Jean and Fan (1987) found that the transition velocity was nearly independent of Ug. A mechanistic model was developed to predict this transition velocity, based on a momentum balance on a single particle, taking into account the drag and buoyancy forces due to the hquid phase, bubble wake and particle interaction. This led to 3 r Pt 4 dp Uf Ug k l-(l + k)e. ks pf +2c 2 DW d (pP -pJg = o (6.76) where 24 ReT ( 1 +0.173 ReLa657) 0.413 1 +16300 ReL -109 (6.77) ReT = Vidppf Vt (6.78) 140 VT = IL, - Ug k l-(l + k)s„ (6.79) k = 0.398U?-246 U^°646 s= 0.00164Uaa988(-0.221xl0"5U»2 -0.564U, + 28.821) for^j 8 8 8 V t i > |0.0327<lL<0.3218m/s 0<U„<0.0519m/s (6.80) (6.81) 0.2933 U 0.34 TJ, 0.0863 < U„ < 0.1208 m/s Q0\ 8 exp(-0.248R) + exp(0.243R) TJ 0.648 [0.0327<UL <0.3218m/s 8 Ret = l + 1.147Ret UtdpPi Vt -2.876 rdp^ -4.0 (6.83) (6.84) Note that CDW was estimated by parameter regression in the study of Jean and Fan (1987). Using the same experimental method, Song et al. (1989) proposed an empirical correlation for particle transport velocity in a gas-hquid medium: \ —0.509 -^ = l-0.518Fra0310 Ut 8 Ps -Pi V Pt J (6.85) where Fr„ = —— and d„ = g gdp P 1/ ^3 2 V3 — d £ \ for cylindrical particles. v2 J Liang et al. (1995) studied the flow regimes in a three-phase circulating fluidized bed. An external loop for particle circulation allowed the apparatus to be operated with continuous particle feeding at the bottom and entrainment from the top of the column. Glass beads of 0.4 mm diameter were used as the sohds phase, while air and water served as the gas and hquid phases. 141 The transition to a circulating bed was determined by the pressure drop between lower and upper sections of the particle riser. The sohds circulation rate reached a constant value at Ug = 2.0 mm/s for > 61 mm/s (slightly greater than the terminal velocity of a single particle in the hquid phase, 53 mm/s. With increasing gas velocity, the onset hquid velocity for the circulating bed decreased. A flow regime map at one gas velocity was plotted based on the sohds circulation rate versus the superficial hquid velocity. Coalesced bubble flow, dispersed bubble flow, circulating bed and pneumatic transport flow regimes were observed. 6.3.2 Experimental Method In this study, a high efficiency low pressure drop three-phase separator was used to prevent sohd particles from being entrained from the column. At high gas and hquid flow rates, most particles were carried over to, and stored within, the separator, while some were allowed to return to the column. Due to entrainment and back-mixing of the particles, there was a sohds concentration gradient in the column, with a dense region at the top and a dilute region at the bottom The system typically took 30 s to reach a new steady state when either the gas or the hquid flow rate was changed. The transition from a fluidized bed to a transport flow regime was considered to occur when the bottom section (one diameter of the column above the distributor) of the column was emptied of particles as the hquid flow rate was increased at a given gas velocity (or vice versa). 6.3.3 Experimental Results and Discussion Three different types of particles (1.5 mm glass beads, 4.5 mm glass beads and 1.2 mm steel shot) were used to investigate the effects of particle size and density on the transition from a fluidized bed and a transport flow regime. The experimental results are summarized in Table 6.8. 142 Table 6.8. Experimental results for the boundary between fluidized bed and transport flow regimes. 1.5 mm Glass Beads 4.5 mm Glass Beads 1.2 mm Steel Shot Ug,m/s U^, m/s Ug,m/s IL, m/s Ug,m/s IL, m/s 0.0 0.227 0.0 0.472 0.0 0.500 0.0021 0.223 0.0030 0.467 0.021 0.498 0.0058 0.187 0.0054 0.467 0.037 0.482 0.015 0.178 0.010 0.467 0.053 0.482 0.022 0.169 0.016 0.451 0.074 0.482 0.039 0.160 0.021 0.404 0.11 0.482 0.055 0.160 0.037 0.388 0.14 0.482 0.077 0.160 0.053 0.357 0.17 0.482 0.11 0.154 0.075 0.326 0.22 0.482 0.89 0.100 0.11 0.311 0.32 0.482 1.6 0.0729 0.14 0.295 0.34 0.482 3.0 0.0364 0.17 0.280 0.49 0.404 3.7 0.0184 0.23 0.233 1.6 0.311 4.1 0.0103 0.21 0.218 3.4 0.200 4.9 0.00512 0.64 0.155 4.6 0.155 0.89 0.128 5.9 0.100 1.3 0.100 1.9 0.0729 2.1 0.0638 2.3 0.0546 2.7 0.0455 2.8 0.0364 It is evident that the superficial hquid velocity required for transport flow decreases with increasing gas velocity. The presence of gas bubbles in the column may affect the particles in two ways: (a) they increase the interstitial hquid velocity by occupying some of the volume in the column; and (b) bubble wakes entrain particles due to the fact that the average bubble velocity always exceeds the interstitial hquid velocity. Assuming that the only effect of the gas bubbles is to increase the interstitial hquid velocity, the particle transport velocity in a gas-hquid mixture can be obtained from a force balance on a single spherical particle: 143 771 dp" (ps-pJg = c 6 Pt DL (6.86) Hence 4 dp (ps-p/)g 3 CDL Pt where the drag coefficient can be estimated from (6.87) 24/Ret 24(l +0.14 Ret0J)/Ret 0.445 d„ Pe for Ret<0.1 for l<Ret<1000 for 1000 < Ret < 3.5x 105 (6.88a) (6.88b) (6.88c) where Ret = For a cylindrical particle, according to Chfl et al. (1978), the terminal velocity of a single cylinder with its axis normal to the flow can be expressed as: rc d(ps -pjg 2 CDL p| (6.89) where for long cylinders, 9.689Ret~ -0.78 (1 + 0.147 Re?82) (1 +0.227 Ret055) (1 + 0.083 847 Re?82) for0.1<Ret<5 for 5<Ret<40 for40<Ret <400 (6.90a) (6.90b) (6.90c) The hquid holdup, zb in above equations must be determined before the particle transport velocity can be calculated. Many correlations exist for hquid holdup in bubble columns and three-phase fluidized beds (Hughmark, 1967; Kato and Nishiwaki, 1972; Kim et al., 1972; Akita and 144 Yoshida, 1973; Hikita and Kikukawa, 1974; Darton and Harrison, 1975; Gestrich and Rahse, 1975; Kim et al., 1975; Kumar et al., 1976; Kito et al., 1976; Begovich and Watson, 1978; Bach and Pilhofer, 1978; Mersmann, 1978; Hikita et al., 1980; Friedel et al., 1980; Iordache and Nuntean, 1981; Jean and Fan, 1987). Most of these, however, are based on experiments in the batch operation mode, i.e., IL. = 0, or are only applicable over small ranges of gas and hquid flow rates. Based on the Wallis (1969) drift flux theory, Darton and Harrison (1975) found that the correlation Ug(l-6g)-U, sg(l-sg) / =0.186 'g V- "g/ "*"g \x "g//s^ "~"g (6-91) fitted the experimental data of Michelson and Ostergaard (1970) for the dispersed bubble flow regime of three-phase fluidized beds. At the transition from fluidized bed to transport flow, the sohds holdup approaches 0. With sg + s£ = 1 and IL. = lL.t at this point, s£ can then be derived as: 0.18 + Ujt 0.18 + UA +Ug (6.92) Jean and Fan (1987) conducted experiments in an air-water bubble column of 72.6 mm diameter. Based on 72 experimental results, two complementary empirical correlations, Equations (6.81) and (6.82), were obtained for gas holdup in bubble columns. The accuracy of these correlations was within ±22% of their experimental results. These correlations cover wide ranges of Ug and U^, with a gap for 0.0519 < Ug < 0.0863 m/s. In the present work, the gas holdup within the gap was calculated by linear interpolation between the two correlations: 88 = - s U„ =0.0863 8 U„ =0.0519 0.0863-0.0519 (u -0.0519) +s 8 lu„ =0.0519 (6.93) 145 In this study, gas holdup correlations proposed by Darton and Harrison (1975) and Jean and Fan (1989) were used with Equations (6.87) and (6.88) to predict the transition between fluidized bed and transport flow regimes. Equations (6.87) and (6.88) together with Equation (6.92) are referred to as Transport Velocity Model I. Equations (6.87) and (6.88), together with Equations (6.81), (6.82), (6.93) and 8^ = 1 - Sg, will be referred to as the Transport Velocity Model JJ. For cylindrical particles, Equations (6.87) and (6.88) are replaced by Equations (6.89) and (6.90) in both models. Figure 6.19 compares the predictions of the Jean and Fan (1987) model, the Song et al. (1989) empirical correlation, and Models I and JJ with the experimental data for the air-water-1.5 mm glass beads three-phase system The experimental results also appear in the figure. It is seen that all four models work well for Ug less than approximately 0.2 m/s. For higher superficial gas velocities, only the Transport Velocity Model JJ follows the trend of the experimental results. The theoretical model proposed by Jean and Fan (1987) fits the experimental results only for Ug < 1 m/s for the air-water-1.5 mm glass bead system Figure 6.20 compares predicted values with the experimental results for the air-water-4.5 mm glass bead system Again, Model U agrees with the experimental results very well for Ug < 3.0 m/s. A strange peak is seen for the Jean and Fan model at low gas velocity for the 4.5 mm glass bead system A similar result can be observed for their experiments with 6.1 mm glass beads, as shown in Figure 6.21, although the authors did not comment on this. In addition, this model fails in Figure 6.20 for Ug > 0.2 m/s, as does the empirical correlation of Song et al., Equation (6.85). It is seen that the Jean and Fan model gives accurate predictions only for small particles and low Ug. Model I gives better predictions for the 4.5 mm glass bead than for the 1.5 mm glass beads. This is because Equation (6.92) was developed for the dispersed bubble flow regime, and the bubble characteristics in the 4.5 mm glass bead system are much closer to that regime than in the 1.5 mm glass bead system 146 1 1 0.1 -i H 73 I PH 0.01 -d 0.001 Experimental results for 1.5 mm glass beads - Model I: Equations (6.87), (6.88) and (6.92) • • Model JJ: Equations (6.87), (6.88), (6.81), (6.82) and (6.93) Jean and Fan (1987) model Song et al. (1989) empirical correlation: Equation (6.85) 0.001 -i—i—i—i 11 n]— 0.01 ~rr\ 0.1 1 10 Superficial Gas Velocity, m/s Figure 6.19. Predictions and experimental results for transition from fluidized bed to transport flow regime: air-water-1.5 mm glass beads. 1 § 0.01- • 4.5 mm glass beads u • Model I: Equations (6.87), (6.88) and (6.92) £ '. Model II: Equations (6.87), (6.88), (6.81), (6.82) and (6.93) PH Jean and Fan (1987) model Song et al. (1989) empirical correlation: Equation (6.85) 0.001 1—i—i—i i 1111 1—i—i—i i 1111 1—i—i—i i 1111 1—i—i—i i 111 0.001 0.01 0.1 0 Superficial Gas Velocity, Ug, m/s Figure 6.20. Predicted and experimental particle transport velocities for 4.5 mm glass beads in air-water mixture 147 1 a 0 1 H 0.8-0.7' 0.6-0.5-0.4-0.3-0.2-0.1 -0.0 • • • • dp,m -0.00033 - 0.00046 - 0.00078 - 0.0010 - 0.0030 - 0.0040 -0.0061 • • *V V-oo o- -Q- . _0_ . -v-- A-0.00 T" 0.02 0.04 0.06 0.08 0.10 Superficial Gas Velocity, U m/s 0.12 0.14 Figure 6.21. Particle transport velocity predictions compared with experimental results of Jean and Fan (1987). A comparison of the various model predictions with all available experimental data, including those of Song et al. (1989), Jean and Fan (1987) and this study, is shown in Table 6.9 as average absolute percentage deviation between predicted value and experimental results, given by Equation (6.57). The empirical correlation of Song et al. (1989) is seem to work well for three-phase systems with glass bead particles of diameter greater than 0.5 mm or cylindrical particles when Ug < 0.23 m/s. Model n, given by Equations (6.87), (6.88), (6.81), (6.82) and (6.93), is the best theoretical model which covers all operating conditions and fluid flow rates for the low particle density systems. Although Equations (6.81), (6.82) and (6.93) are based on experimental data which are limited to small gas and hquid velocity ranges, they can evidently be extended to 3.0 m/s and 0.5 m/s for the gas and the hquid velocities, respectively, to predict the particle transport velocity with Equations (6.87) and (6.88) or Equations (6.89) and (6.90). 148 IKS IS "3 u o 1 -<F CM 00 sd II •a •a 8 B 3 4 Q J 3 o SO o •3 1 VI •a ,1 Q s? a o IT? vi §1 1 o VI I*1 VI 149 The two best prediction methods are compared with available low density experimental data in Figure 6.22. It can be seen that most data points he on both sides of the diagonal line on the plot of the predicted versus experimental UA. Exceptions are those points underestimated by the Song et al. empirical correlation, Equation (6.85), for high gas velocities. ' The experimental measured transport velocities in water for the three types of particles studied here are 0.227, 0.472 and 0.50 m/s for the 1.5 mm glass beads, 4.5 mm glass beads and 1.2 mm steel shot, respectively. The theoretical predicted terminal velocity for these particles in water are 0.195, 0.444 and 0.395 m/s, respectively. The measured particle transport velocity for the 1.2 mm steel shot is significantly greater than its single particle terminal velocity. This is probably due to the occurrence of particle clusters. 0.6-0.44 ^ -0.2-1 -0.4 4 -0.6-prediction ^ it, experiment A • Prediction by Model II: A A A A Equations (6.87), (6.88) [or Equations (6.89) and (6.90)] with (6.81), (6.82) and (6.93) A Prediction by Song et al. (1989) correlation: Equation (6.85) 0.0 —I— 0.2 —I— 0.4 0.6 U it, experiment Figure 6.22. Experimental data for low density (ps < 2876 kg/m3) particle transport velocity compared with predictions of Song et al. (1989) empirical correlation and Model U. 150 In gas-solid fluidization, fine solids can combine loosely into assemblies, denned as clusters (Yerushalmi et al., 1976; Grace and Tuot, 1979; Li and Kwauk, 1980; Horio and Clift, 1992; Brereton, and Grace, 1993). The mean effective size and density of the clusters are usually such that their terminal velocities exceed the gas velocity, causing the transport velocity of the particles to be an order of magnitude greater than the terminal velocity of mdividual particles (Yerushalmi, 1986). For the 1.2 mm steel shot, clusters were observed at high IL. both in the water and the air-water mixtures, leading to higher transport velocities compare to single particle terminal velocity. Equations (6.87) and (6.88), or Equations (6.89) and (6.90), can be apphed to predict single particle terminal velocities, which are close to the transport velocity when particle clusters are not formed. For the particles which form clusters, the transport velocity in hquid can be obtained through experiments. The transport velocity of the hquid in gas-hquid mixtures can be estimated by the empirical correlation: = i- 0.2172 Fr/2072 Ar/1013 Ut v. Pi J -0.5 (6.94) based on 125 sets of experimental data, 79 from the literature and 46 from this study, including three-phase systems with glass beads, cylindrical particles and steel shot. As indicated in Table 6.9, the mean deviation is 11.7% for Ug < 0.23 m/s and 13.8% for Ug < 3.0 m/s. For steel shot, the mean deviation between the experimental data and Equation (6.94) is 14.0%, while the mean deviation for the Song et al. (1989) correlation, i.e. Equation (6.85), is 115.0%. Figure 6.23 compares the transport velocity predictions for the 1.2 mm steel shot with the experimental results. It can be seen that Equation (6.94) works well over a wide range of Ug. A comparison of Equation (6.94) with other experimental results is also given in Table 6.9. 151 0.8 0.6-a 0.4-5 % o.2i il is 00-1 [!H IB © « -02-1 .9 -0.6-1 -0.8-0.01 Experimental data for 1.2 mm steel shot Prediction by Equation (6.85) • Prediction by Equation (6.94) • • i 1111 1—i—i—i i 1111 0.1 1 Superficial Gas Velocity, Ug, m/s 10 Figure 6.23. Comparison between particle transport velocity empirical correlations and experimental results for 1.2 mm steel shot. 6.4 Regime Maps of Three-Phase Systems Three-phase systems can be generally classified into three operating regimes: fixed beds, fluidized beds and transport flow. Minimum fluidization velocities demarcate the boundary between a fixed bed and a fluidized bed, while particle transport velocities delineate the boundary between a fluidized bed and the transport regime. Regime maps which illustrate these three regimes for the 1.5 mm glass beads, 4.5 mm glass beads and 1.2 mm steel shot with air and water are presented in Figure 6.24, 6.25 and 6.26, respectively. 152 101 10° Transport Flow Regime • Experimental transport velocity data . Prediction by empirical correlation, Equation (6.94) Prediction by Transport Velocity Model II, Equation; (6.87), (6.88), (6.81), (6.82) and (6L93) O Experimental minimum fluidization velocity data - - - Prediction by Gas-Perturbed Liquid Model, Equations (630) and (6.53) Prediction by empirical correlation, Equation (6.1) o 10 Superficial Gas Velocity, U , m/s Figure 6.24. Regime map for air-water-1.5 mm glass bead three-phase system j • Experimental transport velocity data ; Prediction by empirical correlation, Equation (6.94) • PredieticnbyTranspDrt VelocityM O Experimentalrriirrimum fluidization velocitydata Superficial Gas Velocity, U m/s Figure 6.25. Regime map for air-water-4.5 mm glass bead three-phase system 153 1 d o id H-l 0 r/3 10°-J 10"1 10"Z-J io-35b • Experimental transport velocity data Prediction by empirical correlation, Equation (6.94) O Experimental minimum fluidization velocity data Prediction by Gas-Perturbed Liquid Model, Equations (6.50) and (6.53) Prediction by empirical correlation, Equation (6.1) - •—•» » » »r» * ^ Transport Flow V/f-0 10": iRegime Fluidized Bed ~--CL. O D-O- rj Fixed Bed 10"' • 11111 i II .-1 10' 10u 101 Superficial Gas Velocity, U , m/s Figure 6.26. Regime map for air-water-1.2 mm steel shot three-phase system It is clear that both the particle size and particle density affect the transitions. The greater the particle density and size, the higher the rninimum gas and/or hquid fluidization velocities. For the onset of transport flow, the particle transport velocities increase with particle density over the entire operating range. For the glass beads, the particle transport velocities increase with particle size at low gas velocities but appear to be independent of particle size at high gas velocities. 6.5. Summary Several correlations are available to predict the rninimum fluidization velocity in three-phase fluidized beds. Pseudo-homogeneous fluid models do not predict the minimum fluidization velocity well. The best agreement with experimental data was obtained from the first empirical equation of Begovich and Watson (1978), Equation (6.1). Nearly as good agreement was obtained from a "gas-perturbed hquid model", in which the gas is assumed to decrease the area available for hquid flow. This model has the advantage of having no new fitted constants and goes 154 to the proper limit, the Wen and Yu (1966) equation for a liquid-solid fluidized bed, as the superficial gas velocity approaches zero. The resulting generalized rninimum fluidization model Equation (6.50), can thus be used to predict incipient fluidization velocity in both two-phase and three-phase fluidization. However, the model is expected to break down when the momentum transfer to the particles is provided rnainly by the gas. The ratio, a, of gas holdup to bed voidage plays a very important role in the model. Among several correlations for a, the correlation proposed by Yang et al. (1993), Equation (6.53), is recommended. At zero or very low hquid velocities and high gas velocities, particles are mainly supported by the gas phase. The gas provides energy for generating turbulence in the hquid phase, which imparts energy to the sohd phase so that particles can remain suspended. This mechanism has been established by many investigators for small or light particles. For large or heavy particles, the particles could be supported by the drag force caused by gas flow, similar to the incipient fluidization mechanism in a gas-sohd system In such a case, e.g. for the 1.2 mm steel shot, Equation (6.75) can be used to predict the critical gas velocity for complete suspension of the particles at zero superficial hquid velocity. The minimum gas fluidization velocity is reduced significantly by increasing the hquid velocity. Further study is needed to understand the effect of on the rninimum fluidization velocity at high gas velocities. The particle transport velocity delineates the transition between a fluidized bed and the transport flow regime. For particles which do not form clusters, i.e., 1.5 and 4.5 mm glass beads, the particle transport velocity of the hquid is similar to the single particle terminal velocity in the hquid phase, which can be calculated using Equations (6.87) and (6.88) for spherical particles. In gas-hquid mixtures, the particle transport velocity of the hquid decreases with increasing gas velocity, since the gas phase occupies some of the column cross-section, leading to an increase of the interstitial hquid velocity, which plays the main role in supporting the particles. The effect of the bubble wakes on the particle transport velocity can be ignored for large particles at low 155 superficial gas velocities. The Transport Velocity Model IL Equations (6.87) and (6.88) for spherical particles or Equations (6.89) and (6.90) for cylindrical particles, together with Equations (6.81), (6.82) and (6.93), is based on the above mechanism. It agrees with 112 sets of experimental data, including 79 data sets from the literature, but excluding the 1.2 mm steel shot results obtained in the present work, with an average absolute deviation of 14.2% for gas velocities up to 3.0 m/s. For the 1.2 mm steel shot, particles aggregate to form particle clusters, causing the particle transport velocity of the hquid to be significantly greater than the single particle terminal velocity in the hquid phase. Knowing the particle transport velocity in the hquid phase, an empirical correlation proposed in the present work, Equation (6.94), can be used to predict the transport velocity in air-water mixtures. This correlation also gives good agreement with 125 sets of experimental data, including 79 data sets from the literature, with an average absolute deviation of 13.8% for gas velocities up to 3.0 m/s, a much higher value than explored previously, previous upper hmits being of order 0.1 m/s. 156 Chapter 7 Flow Regimes in Three-Phase Fluidized Beds 7.1 Introduction Many flow pattern characteristics are shared by three-phase fluidized beds and gas-hquid two-phase flow. For example, at low gas and hquid velocities, three-phase fluidized beds can operate in the coalesced bubble flow regime. As hquid velocity is increased, the dispersed bubble flow regime is commonly encountered. Correspondingly, two similar regimes, often labelled heterogeneous flow and homogeneous flow, respectively, exist in (gas-hquid) bubble columns. As the gas velocity is increased, three-phase fluidized beds can operate in the slug flow, chum flow, bridging flow or annular flow regime. These hydrodynamic regimes are analogous to similar regimes in gas-hquid two-phase flow systems. The definitions of the flow patterns in Chapter 1 are also apphcable to three-phase fluidized beds. 7.1.1 Visual Observations A number of studies have been devoted to the investigation of flow patterns and flow regime transitions in three-phase fluidized beds. Most of these studies have rehed solely on visual observation. Mukherjee et al. (1974) reported that three distinct flow patterns could be observed in a three-phase fluidized bed. At very low gas flow rates, bubble flow was encountered . As the gas flow rate was increased, slug flow occurred. At an even higher gas flow rate, gas continuous flow was observed. The range of gas flow rates for the bubble flow and slug flow regimes was wider at higher hquid flow rates. 157 Muroyama et al. (1978) found that, with low to intermediate gas and hquid flow rates, coalesced bubble flow, dispersed bubble flow and slug flow could be observed in an air-water-large particle system They also reported a transition regime between the dispersed bubble flow regime and the slug flow regime. The boundary between the dispersed bubble flow regime and this transition regime was a positively inclined line on a plot of vs. Ug. Similar flow regime maps have been presented by Fan et al. (1984), Matsuura and Fan (1984) and Fan et al. (1985). For a given fluidized bed, Fan et al. (1985) found that there was a strong correlation between the free-settling particle terminal velocity in the hquid phase, Ut, and the superficial hquid velocity , (U^)dc, separating the coalesced bubble flow regime from the dispersed bubble flow regime. As Ut increased, (Uf)dc increased and reached a maximum at Ut = 0.343 m/s (corresponding to the terminal velocity of 2.55 mm glass beads with a density of 2520 kg/m3 in water). The variation of (U^)dc with Ut could be expressed by: / T v [o.696Ut150 for Ut < 0.343 m/s (UJ, =1 t ... t (7.1) dc [0.0228 Ut"L70 for Ut>0.343 m/s These four different flow regimes (coalesced bubble flow, dispersed bubble flow, transition flow and slug flow) were also observed in three-phase fluidized beds of binary niixtures of particles with different sizes and/or densities. The gas velocity exhibited negligible influence on (Uf)dc for both monocomponent and binary sohds systems. Qn the other hand, the boundary between coalesced bubble flow and slug flow was strongly affected by gas velocity and only shghtly by hquid velocity. Slug flow occurred at a relatively high gas velocity for a binary mixture. Fan et al. (1986) analyzed the statistical properties of wall pressure fluctuations in a 0.102 m ID column. Pressure transducers were used to determine absolute pressure fluctuations, while the flow regime boundaries were deterrnined by visual observation. It was found that the 158 transition velocity between the coalesced bubble and the dispersed bubble regimes increased with particle terminal velocity for small particles and decreased for large particles. This trend is the same as that given by Equation (7.1) above. The transition velocity, (U|)dc, shifted upward in the large column for systems with low particle terminal velocities. However, the transition velocity, (U^)dc, remained the same in both columns for systems with higher particle terminal velocities. The boundaries between coalesced bubble flow and slug flow, as well as between dispersed bubble flow and slug flow, were independent of particle terminal velocity. Ermakova et al. (1970) reported three regimes: (a) fixed bed at low gas and hquid velocities; (b) heterogeneous fluidization; (c) homogeneous fluidization at high hquid velocities. The boundary on a vs. Ug plot between the fixed bed regime and heterogeneous fluidization began at Ug = 0, = U^f"; as the gas velocity was increased, U^f decreased. The boundary between homogeneous and heterogeneous fluidization at high hquid velocity also began at Ug = 0, Vi = U^f", but as the gas velocity was increased, (U^ )dc also increased. An empirical equation (U^)dc ~ Uftnf 1 + 13.4 0.5 (7.2) was proposed to predict the transition between homogeneous and heterogeneous fluidization. Song et al. (1989) studied the effect of surface tension on bubble hydrodynamics in three-phase fluidized beds. The flow regimes in surfactant systems were found to differ from those in air-water systems. Dispersed large bubbles (db = 5 to 7 mm) appeared at low hquid velocities and low to intermediate gas velocities (Ug = 0 to 0.15 m/s). Dispersed small bubbles (db = 1 mm) were found at high hquid velocities. Between these two regimes there was a transition regime in which bubble size exhibited a bimodal distribution. At high gas velocities a foaming regime was observed instead of slug flow. 159 The effect of hquid properties on flow patterns was also investigated by Nacef et al. (1992, 1995). The dispersed bubble regime was more extended when water + 1% ethanol was employed as hquid phase compared with water alone. A sohd piston flow (or square-nose slug) regime was observed, characterized by the appearance of several moving packed beds separated by a hquid-gas mixture. Sohds rained down through this hquid-gas mixture. The average diameter of the gas bubbles in the hquid-gas slabs was of order 1 mm. 7.1.2 Instrumental Measurements Soria and de Lasa (1992) measured the hquid volume fraction using electrical conductivity sensors in bubble columns and three-phase fluidized beds. These sensors were composed of several pairs of square electrodes which measured the conductivity of a multiphase mixture. In a three-phase fluidized bed, it was found that the transition between dispersed bubble flow and coalesced bubble flow was governed by the superficial hquid velocity. In a plot of vs. IL,, a common crossover point was found for three sets of experiments, each at a different but constant value of Ug. This crossover point was hypothesized to be the transition between the coalesced bubble flow and dispersed bubble flow regimes. Han and Kim (1990) proposed a flow regime map using coordinates of the ratio of gas holdup to bed porosity, a (= £g/(sg +s^)), and gas-hquid shp velocity, Us (= Ug /eg - U^/s^), noting that previous flow regime maps did not take particle size and hquid properties into account. The dispersed bubble flow regime was characterized by relatively low gas-hquid shp velocities (0.4 - 0.5 m/s), with a in the range 0 to 0.4. The coalesced bubble flow regime required higher shp velocities (0.4 to 0.8 m/s), with a varying from 0 to 0.2. The slug flow regime was found to be associated with by high shp velocities with a from 0.2 to 0.4. 160 Lee et al. (1990) determined flow regimes based on mean bubble sizes throughout a fluidized bed fitted with a single pipe gas distributor. A progressive increase in mean bubble length as bubbles rose indicated coalesced bubble flow. A decrease in mean bubble length with height implied dispersed bubble flow. Based on four experimental runs and some literature data, a flow regime map was proposed using particle diameter and superficial hquid velocity as coordinates. The fixed bed, coalesced bubble flow, dispersed bubble flow, and transport regimes appeared on this map. Kitano and Ikeda (1988) used pressure transducers to study the transition between the dispersed bubble flow and coalesced bubble flow regimes. The integral of the power spectra density function of the pressure fluctuations between 0 and 10 Hz was used to detect the transition. For the dispersed bubble flow regime, this integral increased linearly with decreasing hquid velocity at a given gas flow rate. The transition from dispersed flow to coalesced flow was assumed to take place when the values began to deviate from this linear relationship. It was also found that there was a transition regime between dispersed bubble flow and the coalesced bubble flow regime. Absolute and differential pressure fluctuations have also been used to determine the flow regimes for other three-phase systems (Zheng et al., 1988; Chen et al., 1995; Vunjak-Novakovic et al., 1992). Table 7.1 summarizes previous investigations of flow regime transitions in three-phase fluidized beds. 161 Map and correlation Map f Map Map Flow regimes identified Fixed bed Homogeneous Heterogeneous Bubble Slug Gas continuous Coalesced bubble Dispersed bubble Slug Transition (D-S) Coalesced bubble Dispersed bubble Slug Transition (D-S) Coalesced bubble Dispersed bubble Slug Transition (D-S) Column diameter, m 0.10 0.20 0.052 0.060 0.10 0.076 0.076 Measurement tedmique Visualization Visualization Visualization Visualization Visualization Liquid and its velocity, m/s Water; Aqueous solution of glycerin; Aqueous solution of n-heptane. HfO.42-6.05 x lO"3  Pa.s 0-0.10 Water: 0.0927-0.2136 0.0921 -0.1386 0.0131 -0.1203 0.0098 - 0.0675 Water: 0.0845-0.168 Water: 0-0.169 Water: 0.0516-0.129 Gas and its velocity, m/s Air: 0-0.20 M o oo \o — r~ O O ci d <5 ci <j o o o o Air: 0-0.30 Air: 0-0.124 Air: 0.050-0.198 Coordinates i tf > tD i tf tf > tf Particle diameter, m 0.0006 0.0012 0.0020 0.00412 0.0028 0.0014 0.000287 0.0026 0.0048 0.0069 0.003 0.004 0.006 0.003 0.006 Particles & tkeir density, kg/m3 Glass beads Glass beads 2780 2920 2860 2960 Glass beads 2475 Glass beads 2520 Glass beads 2590 2520 Author and year Ermakova etal. 1970 3 n 2 S Muroyama etal. 1978 Fan etal. 1984 Matsuura and Fan 1984 162 .1 o U Map or correlation Map and correlation 1 Map Map and correlation Map Flow regimes identified Coalesced bubble Dispersed bubble Coalesced bubble Transition (C-D) Dispersed bubble Coalesced bubble Dispersed bubble Slug Dispersed small bubble Dispersed large bubble Transition regime Transport regime Dispersed Transition (D-C) Coalesced Column diameter, m 0.0762 0.284 0.102 0.076 0.152 0.090 and 0.200 Measurement technique Visualization Visualization Visualization (& Pressure fluctuations) Visualization (Pressure drop) Liquid and its velocity, m/s Water: 0-0.16 Water: 0.018-0.040 Water: 0-0.16 1-Z ° <? $ 2 1 a ^1 * 2 II § 2 o !; « 8 oo <r> II § S d 8 d Water: 0.0176-0.0917 0.0262 - 0.144 0.0172-0.106 0.0319-0.116 Gas and its velocity, m/s Air: 0 - 0.22 Air: 0.022 - 0.068 Air: 0 - 0.22 Air:. 0 - 0.08 O d • i i i oo NO 00 00 NO NO NO CS ON CS ON TJ- CS ..i—I«»>I—'VOI—••^•I—I .booooooo <i<=>d<5dc><5c> Coordinates i Particle diameter, m 0.00250 0.00174 0.00100 0.00304 0.00399 0.00611 0.00227 0.00550 0.001 O O >r\ cs l~ H n ^ « w o o o o o o o o o o o o o <5 d <5 d d <5 ON • O o» O ON o 00 O O o — °8 oS II d II 9 i *v o 0.00129 0.00308 Particles & then-density, kg/m3 Nylon beads 1150 Activated carbon 1280 Glass beads 2870 2520 2530 2200 Alumina beads 3690 3690 Glass beads 2407 Glass beads Nylon beads Alumina Activated carbon Cylindrical Hydrotreating Catalysts (alumina support) ij)=0-68-0.75 p =1890-2000 Glass beads 2490 2480 Author and year Fan et al. 1985 Huetal. 1985 Fan et al. 1986 Song et al. 1989 Kitano and Dceda 1988 163 Map or correlation Map i f Flow regimes identified Bubble coalescing Bubble disintegrating Slug Fixed bed Transport bed Dispersed bubble regime Coalesced bubble regime Dispersed bubble flow Coalesced bubble flow Solid piston flow Coalesced bubble Dispersed bubble Column diameter, m 0.152 0.200 0.152 0.200 Measurement technique Visualization (Bubble velocity) Visualization (Bubble size) Visualization Liquid volume fraction Liquid and its velocity, m/s Water, Glycerol aqueous solution IV=1 -60 x lO"3  Pa.s 0.01 -0.14 Water 0.0039 - 0.0156 1 •sails Ii iH"3 H a 0 x • + + + + pj — ^ B ta" ta "8 B >p n . Water 0-0.025 Gas and its velocity, m/s Air: 0.0-0.12 Air: 0.06 Nitrogen 0 - 0.12 Air: 0-0.05 Coordinates 1 !=" $ ui II % E5 tf> Particle diameter, m 0.0010-0.0080 0.00025 C-« O O O — — I-I <H to c< ci o o o o o o o o o o o o ci o a d ci <5 0.000250 Particles & their density, kg/m3 Glass beads 2500 Glass beads Glass beads 2525 Polypropylene particles <H).82, 0.87 Ps=1350,1700 Glass beads (2500). Author and year Han and Kim 1990 Lee etal. 1990 Nacef et al. 1992,1995 Soria and deLasa 1992 164 7.2 Experimental Results All experiments were carried out in an 82.6 mm I.D. Plexiglas column as described in Chapter 2 with air and water as the gas and hquid phases. Three types of sohd particles were used to study flow regime transitions: 1.5 mm glass beads, 4.5 mm glass beads and 1.2 mm steel shot, with static bed heights of 0.72 m, 0.82 m and 0.74 m, respectively. Superficial gas velocities ranged from 0.0026 to 5.9 m/s, while superficial hquid velocities varied from 0 to 0.6 m/s. Since the hquid temperature was 7 to 8 °C, the hquid density and viscosity were 1000 kg/m3 and 0.0014 Pa.s, respectively. At high gas and/or hquid flow rates, large quantities of particles can be entrained by the gas/liquid flow. Some of the particles are returned to the test section by internal circulation of the hquid within the separator designed in this study, while the rest are stored within the separator. The conductivity probe was mounted at the center of the column, 0.65 m above the distributor. Details of the experimental apparatus, the probe configuration and data processing are provided in Chapter 2. In a three-phase fluidized bed, bubble characteristics differ from those in a gas-hquid system at the same gas and hquid flow rates due to the particles. The changes are reflected by the raw signals of the conductivity probe. Figure 7.1 compares the raw signals of the two-phase and three-phase systems. It is clear that the bubble frequency in the two-phase system is greater than in the three-phase system, while the bubble chord length is smaller for the same gas and hquid flow rates. The variations of these two parameters with Ug in the two-phase and the three-phase systems at = 0.0184 m/s are presented in Figures 7.2 and 7.3. The bubble frequency in the three-phase system is significantly lower than in the two-phase system until after the maximum value representing the transition between slug flow and chum flow is reached. The average bubble chord length in the three-phase system is significantly greater than in the two-phase system for superficial gas velocities less than approximately 1 m/s. 165 > 0.5 3 0.4 f 0.3 O 02 £ 0.1 2 o.o •£ 0.3 •§ 02 a °° llfl fit 1 1 - (b) fir . —1 i 0.0 0.8 1.6 Time, s 2.4 32 Figure 7.1. Comparison of conductivity probe signals in two-phase and three-phase systems at Z = 0.65 m and ILj = 0.0184 m/s: (a) air-water two-phase, Ug = 0.040 m/s; (b) air-water-1.5 mm glass beads three-phase, Ug = 0.039 m/s. 80-70-60-50-40-o 30-| PQ 204 104 -•— air-water two-phase -o— 1.5 mm glass beads three-phase -o-o o-o _o-cr 0.001 T T T | T I I I I I I I | ! I I 1 I I I I 0.01 0.1 Superficial Gas Velocity, m/s 10 Figure 7.2. Bubble frequency in two-phase and three-phase systems for the same hquid flow rate at Z = 0.65 m and = 0.0184 m/s. 166 a 0.35-0.304 0.25 • 8' 2 0.204 £ 0.15-1 I PQ <u 0.104 <j 0.05-I 0.00 —•— air-water two-phase system —o— 1.5 mm glass beads three-phase system 0.001 ^ 0000\ P O I 0 V** ' '1 '"I 0.01 0.1 1 Superficial Gas Velocity, m/s 10 Figure 7.3. Average bubble chord length in two-phase and three-phase systems for the same hquid flow rate at Z = 0.65 m and U, = 0.0184 m/s. At = 0.0184 m/s, three-phase systems with 4.5 mm glass beads and 1.2 mm steel shot operated in the fixed bed regime. Hence Figures 7.2 and 7.3 do not contain data for these systems. Comparisons at a higher hquid velocity for all four systems investigated appear in Figures 7.4 and 7.5 for the bubble frequency and average bubble chord length, respectively. At = 0.0455 m/s, the bubble frequency in a 1.5 mm glass bead three-phase fluidized bed is always smaller than for the other systems at low to intermediate gas velocities, as shown in Figure 7.4. The average bubble chord length in the 1.5 mm glass bead fluidized bed is greater than for the other systems, as shown in Figure 7.5. This is because small particles lead to coalescence of gas bubbles. The average bubble chord length in the 4.5 mm glass beads and the 1.2 mm steel shot three-phase fluidized beds are almost the same as in the air-water two-phase system at low gas velocities. 167 80-60 -•— air-water two-phase -o— 1.5 mm glass beads three-phase -A— 4.5 mm glass beads three-phase -v— 1.2 mm steel shot three-phase /A 10 Superficial Gas Velocity, m/s Figure 7.4. Comparison of bubble frequency in different systems at Z = 0.65 m and IL = 0.0455 m/s. 0.15-8 3 I I 0.10-0.054 0.00' —•— air-water two-phase —o— 1.5 mm glass beads three-phase —A— 4.5 mm glass beads three-phase —v— 1.2 mm steel shot three-phase -w vv 0.001 0.01 ""1 0.1 'TT! IT]-1 10 Superficial Gas Velocity, m/s Figure 7.5. Comparison of average bubble chord length in different systems at Z = 0.65 m and IL = 0.0455 m/s. 168 7.3 Flow Regime Transitions In this study, the experimental criteria for flow regime transitions in three-phase fluidized beds are assumed to be qualitatively the same as those described in Chapter 4 for air-water two-phase flow. A brief svrmmary is given in Figure 7.6. Flow Regime Transition Criterion Schematic Diagram i Bu )iscre bbleF e D ow Bu spers jbleFl ed ow Dimensionless standard deviation of bubble time reaches its maximum with respect to liquid velocity. ' . i°g(uj E Bu t *>° )iscret t>bleF e C ow Bu °ci -A?. oalesc bbleF ed ow Bubble frequency deviates from a straight line in a plot of bubble frequency versus gas velocity. f ^ • ug C Bu oaleso bbleF ed ow Slug Flow Sauter mean bubble chord length equals column diameter. D / ) / & Slug Flow ^ Churr Flow Bubble frequency reaches its maximum f A L log{Ug) Chum Flow E s ridgir Flow lg Average bubble time increases sharply with respect to gas velocity. log(t.) " / 1 L_ log(ug) E a Iridgir Flow lg > ^ Vjuuil Flow ar Bubble frequency approaches zero. f ^Al. log(Uc) Figure 7.6. Summary of flow regime transition criteria. 169 7.3.1 Transition between Discrete (or Dispersed) and Coalesced Bubble Flow The transition between discrete and coalesced bubble flow regimes was determined from plots of bubble frequency versus superficial gas velocity as shown in Figures 7.7 to 7.10. According to the criterion established in Chapter 4, the transition occurs when the bubble frequency deviates from a straight line through the origin. Figure 7.7 presents experimental results for 1.5 mm glass bead three-phase fluidized beds at different superficial hquid velocities. At superficial hquid velocities of 0.064 to 0.16 m/s, the bubble frequency increases first linearly with gas velocity, with a slope of 545 m"1. When the gas velocity was increased further, coalesced bubble flow or slug flow was encountered and the bubble frequency deviated from the linear line. The transition velocities were determined by the points at which the bubble frequency deviated significantly from the linear line. At low hquid velocities (XJ( = 0.0154 to 0.0455 m/s), instead of discrete bubble flow, coalesced bubble flow was encountered at very low gas velocities in the 1.5 mm glass bead three-phase fluidized bed due to coalescence. This is in good agreement with visual observations both in this study and in previous investigations (Ermakova et al., 1970; Fan et al., 1986, 1987; Kitano and Dceda, 1988; Song et al., 1989; Han and Kim, 1990). Therefore, the bubble frequency deviates immediately from f = 545Ug for low hquid velocities, as shown in Figure 7.7. Figure 7.8 plots bubble frequency against superficial gas velocity for a three-phase fluidized bed containing 4.5 mm glass beads at different superficial hquid velocities. At low gas velocities, discrete bubble flow was encountered and the bubble frequency varies linearly with gas velocity. As the gas velocity was increased, coalesced bubble flow and slug flow were encountered. The flow regime transition velocities were again determined by the points at which the bubble frequency deviates significantly from the initial linear relationship. 170 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 Superficial Gas Velocity, m/s Figure 7.7. Transition between discrete and coalesced bubble flow regime in a three-phase fluidized bed containing 1.5 mm glass beads at different superficial hquid velocities. U^, m/s ] —•—0.0364 —•—0.0455 —A—0.0546 —•—0.0638 —•—0.0729 —•—0.100 —o— 0.128 —A—0.155 —V—0.218 T ' 1 '— 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Superficial Gas Velocity, m/s Figure 7.8. Transition between discrete and coalesced bubble flow regime in a three-phase fluidized bed containing 4.5 mm glass bead at different superficial hquid velocities. 171 The behaviour for the three-phase fluidized bed containing 1.2 mm steel shot was similar, with discrete bubble flow encountered at low Ug. Increasing Ug led to coalesced bubble flow and slug flow. Figures 7.9 and 7.10 show the variation of bubble frequency with Ug for the 1.2 mm steel shot three-phase fluidized bed at different U^. The relationship between f and Ug is linear at low Ug with a proportionality constant of 545 and 860 m"1, respectively, for low in Figure 7.9 and higher in Figure 7.10. For the steel shot, f in the case of the discrete-coalesced transition spanned a much larger range than for the other systems because of the larger hquid velocities required to expand the bed. The flow regime transition data are given in Tables 7.2, 7.3 and 7.4. Table 7.2. Flow regime transition velocities for air-water-1.5 mm glass bead fluidized beds. Dispersed / Coalesced / Slug/ Churn / Bridging/ Coalesced / Dispersed Coalesced Slug Churn Bridging Annular Up, m/s Ug, m/s U^, m/s Ug, m/s 0.0051 1.9 3.2 7.6 0.046 0.0025 0.0082 1.6 3.6 7.6 0.046 0.0031 0.0154 1.6 3.0 7.6 0.064 0.005 0.0184 0.016 1.5 3.0 7.4 0.064 0.008 0.0273 0.017 1.4 2.6 6.7 0.064 0.012 0.0455 0.018 1.1 2.1 6.2 0.100 0.02 0.0638 0.010 0.016 0.97 1.7 6.0 0.100 0.03 0.0728 0.016 0.019 1.1 1.75 5.7 0.100 0.05 0.0729 0.016 0.019 1.1 1.75 5.7 0.100 0.036 0.027 1.0 1.73 5.3 0.155 0.16 0.14 1.0 1.73 5.1 Table 7.3. Flow regime transition velocities for air-water-4.5 mm glass bead fluidized bed. Discrete / Coalesced / Slug/ Churn / Bridging / Discrete / Dispersed Coalesced Slug Churn Bridging annular U^, m/s Ug, m/s U^, m/s Ug, m/s 0.0364 0.020 0.028 1.2 2.1 6.3 0.0729 0.0035 0.0455 • 0.020 0.031 1.2 2.1 6.1 0.0729 0.0050 0.0546 0.028 0.031 1.1 1.5 6.0 0.0729 0.0080 0.0638 0.028 0.031 1.2 1.6 6.0 0.0729 0.012 0.0729 0.035 0.051 1.0 1.6 6.2 0.100 0.020 0.100 0.050 0.056 1.0 1.5 5.7 0.100 0.030 0.128 0.069 0.078 1.0 1.4 5.5 0.100 0.040 0.155 0.11 0.10 1.0 1.4 6.0 0.218 0.16 0.23 0.98 1.4 5.0 172 Table 7.4. Flow regime transition velocities for air-water-1.2 mm steel shot fluidized bed. Discrete / Coalesced Coalesced / Slug Slug/ Churn Churn / Bridging Bridging / annular Discrete / Dispersed U^, m/s Ug,m/s U^, m/s Ug, m/s 0.0364 0.021 0.043 1.4 2.8 5.0 0.0820 0.0035 0.0455 0.027 0.050 1.4 2.8 4.8 0.0860 0.0050 0.0546 0.027 0.059 1.6 2.5 4.8 0.100 0.0080 0.0638 0.027 0.061 1.6 2.2 4.7 0.100 0.012 0.0729 0.025 0.059 1.7 1.8 4.8 0.155 0.020 0.100 0.027 0.052 1.6 1.6 4.6 0.155 0.030 0.155 0.22 0.10 0.77 1.3 4.7 0.155 0.040 0.200 0.51 0.19 0.92 1.2 . 4.8 0.311 0.13 0.44 0.62 1.8 4.9 0.404 0.18 0.32 0.32 1.8 3.9 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Superficial Gas Velocity, m/s Figure 7.9. Transition between discrete and coalesced bubble flow regimes in a three-phase fluidized bed containing 1.2 mm steel shot at low superficial hquid velocities. 173 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Superficial Gas Velocity, m/s Figure 7.10. Transition between discrete and coalesced bubble flow regimes in a three-phase fluidized bed containing 1.2 mm steel shot at high superficial hquid velocities. 7.3.2 Transition between Coalesced Bubble Flow and Slug Flow Transitions between the coalesced bubble flow and slug flow regimes were determined from plots of the logarithm of the Sauter mean bubble chord length versus log(Ug) as shown in Figure 7.6. As described in Chapter 4, the transition occurs when the Sauter mean bubble chord length equals the column diameter, 0.0826 m in this study. Figures 7.11, 7.12 and 7.13 plot the Sauter mean bubble chord length against superficial gas velocity on log-log coordinates at different hquid velocities for three-phase fluidized beds of 1.5 mm glass beads, 4.5 mm glass beads and 1.2 mm steel shot, respectively. The experimental data are summarized in Tables 7.2, 7.3 and 7.4. The gas velocity for the transition from coalesced bubble flow to slug flow does not vary significantly with respect to the hquid flow rate at low superficial hquid velocities. At higher hquid velocities, however, the transition velocities increase with U^. 174 Figure 7.11. Transition between coalesced bubble flow and slug flow in a three-phase fluidized bed containing 1.5 mm glass beads at various superficial hquid velocities. Figure 7.12. Transition between coalesced bubble flow and slug flow in a three-phase fluidized bed containing 4.5 mm glass beads at various superficial hquid velocities. 175 Figure 7.13. Transition between coalesced bubble flow and slug flow in a three-phase fluidized bed containing 1.2 mm steel shot at various superficial hquid velocities. 7.3.3 Transition between Slug Row and Churn Flow Transitions between slug flow and churn flow were taken to occur at the points at which the bubble frequency reaches a maximum with increasing Ug, as shown in Figures 7.14 to 7.16 for three-phase fluidized beds of 1.5 mm glass beads, 4.5 mm glass beads and 1.2 mm steel shot, respectively. It should be noted that under certain circumstances, two maximum bubble frequency values appear in the same curve, e.g. for U^ = 0.155 m/s in Figure 7.14 and for U^ = 0.128 m/s in Figure 7.15. The first maximum in both curves corresponds to the transition between dispersed and coalesced bubble flow or slug flow, while the second maximum was used to delineate the transition between the slug and churn flow regimes. 176 120 100 0.001 0.01 0.1 1 Superficial Gas Velocity, m/s Figure 7.14. Local bubble frequency at axis of column versus superficial gas velocity showing transition between slug flow and chum flow and the onset of annular flow for three-phase fluidized bed containing 1.5 mm glass beads at different superficial hquid velocities. 1 PQ 0.001 0.01 0.1 1 Superficial Gas Velocity, m/s 10 Figure 7.15. Local bubble frequency at axis of column versus superficial gas velocity showing transition between slug flow and chum flow and onset of annular flow for three-phase fluidized bed containing 4.5 mm glass beads at different superficial hquid velocities. 177 i CO 0.1 1 Superficial Gas Velocity, m/s Figure 7.16. Plot of local bubble frequency at axis of column versus superficial gas velocity showing transition between slug flow and churn flow and the onset of annular flow for three-phase fluidized bed containing the 1.2 mm steel shot at different superficial hquid velocities. 7.3.4 Transition between Churn Flow and Bridging Flow Transitions between churn flow and bridging flow were determined from the points where the average bubble time increases sharply with gas velocity on log-log plots, as shown in Figures 7.17 to 7.19. Figure 7.17 presents the average bubble time vs. superficial gas velocity for a three-phase fluidized bed of 1.5 mm glass beads, while Figures 7.18 and 7.19 are for 4.5 mm glass beads and 1.2 mm steel shot, respectively. 178 1000 o o in H (L> 1 I 100-1 10-} Churn / Bridging ^y^# Transitions 3 i i i i i i 0.01 0.1 1 Superficial Gas Velocity, m/s 10 Figure 7.17. Average bubble time versus superficial gas velocity showing transition between churn flow and bridging flow for a three-phase fluidized bed containing 1.5 mm glass beads at different superficial hquid velocities. lOCO-CS o cN H 1 ca I 100-10-1 Chum / Bridging Transitions 1 0.001 0.01 0.1 1 Superficial Gas Velocity, m/s ••—0.0364 •—0.0455 A—0.0546 T— 0.0638 -•—0.0729 -•— 0.100 O— 0.128 A— 0.155 V— 0.218 10 Figure 7.18. Average bubble time versus superficial gas velocity showing transition between churn flow and bridging flow for a three-phase fluidized bed containing 4.5 mm glass beads at different superficial hquid velocities. 179 —A—0.200 —V—0311 1 1 1—i i i 1111 1 1—i i i 111| 1 1—i i i 1111 1 1—i—i i 111 0.001 0.01 0.1 0 Superficial Gas Velocity, m/s Figure 7.19. Average bubble time versus superficial gas velocity showing transition between churn flow and bridging flow for a three-phase fluidized bed containing 1.2 mm steel shot at different superficial hquid velocities. 7.3.5 Transition between Bridging Flow and Annular Flow The onset of annular flow was determined from the point when the bubble frequency approaches zero in a plot of bubble frequency vs. superficial gas velocity, as described in Chapter 4. Figures 7.14, 7.15 and 7.16 present the experimental results for three-phase fluidized beds of 1.5 mm glass beads, 4.5 mm glass beads and 1.2 mm steel shot, respectively. The transition velocities are also summarized in Tables 7.2, 7.3 and 7.4. 7.3.6 Transition between Discrete (or Coalesced) and Dispersed Bubble Flow At low gas and hquid velocities, coalesced bubble flow was encountered for the 1.5 mm glass bead three-phase fluidized beds, while there was discrete bubble flow for both the 4.5 mm 180 glass bead and 1.2 mm steel shot three-phase fluidized beds. With increasing hquid velocity, dispersed bubble flow was encountered for all these systems. The transition between the discrete (or coalesced) and dispersed bubble flow regimes was obtained by plotting the dimensionless standard deviation of bubble time vs. superficial hquid velocity at constant gas velocities. The transition occurs when the dimensionless standard deviation of bubble time, at/t, reaches a maximum with increasing hquid velocity. Figure 7.20 shows the transition between coalesced and dispersed bubble flow for 1.5 mm glass bead three-phase fluidized beds. An obvious maximum value of at/t appears for each gas velocity, indicating the flow regime transitions. Figure 7.21 presents the same type of plot for the 4.5 mm glass beads. It is seen that at low gas and hquid velocities, o"t/t does not vary significantly with U^. On further increasing the hquid velocity, ajt decreases without showing a peak as observed in the air-water two-phase and 1.5 mm glass bead three-phase systems. The reason could be the breakup effect of large particles on the gas bubbles as reported by previous studies (Ostergaard, 1971; Lee et al., 1974; Fan, 1989). Hence, the bubble characteristics in the discrete bubble flow do not significantly differ from those in the dispersed bubble flow, rmking it difficult to distinguish between these flow regimes for the 4.5 mm glass bead three-phase fluidized bed. For these curves, the transition velocities were determined by the points at which ajt starts to decrease in the plot of ot /1 vs. hquid velocity. The transition between the discrete and dispersed bubble flow for the 1.2 mm steel shot three-phase fluidized bed is presented in Figure 7.22. A maximum value of ajt can be found for each curve. The flow regime transition velocities for 1.5 mm glass beads, 4.5 mm glass beads and 1.2 mm steel shot three-phase fluidized beds are summarized in Tables 7.2, 7.3 and 7.4, respectively. 181 H CD 1 PQ *8 2.0 1.8-1.6-1.4-8 ;-s 1.2-1.0 -I 0.8. 8 & 0.6-1 °-4" 8 0.2-0.0 Coalesced / Dispersed| Transitions 0.01 0.1 Superficial Liquid Velocity, U^, m/s Figure 7.20. Dimensionless standard deviation of bubble time plotted against superficial liquid velocity showing transition between coalesced bubble flow and dispersed bubble flow for the 1.5 mm glass bead three-phase fluidized bed at different superficial gas velocities. 1 1 PQ t3 1 CO 1 & 2.0-1.8 1.6-1.4-1.2-1.0-1 0.8 0.6-0.4-0.2-0.0 U ,m/s g -•—0.0035 -•— 0.0050 -A—0.0080 -•—0.012 -•—0.020 -•—0.030 -O— 0.040 Discrete / Dispersed Transitions o-/ -0'° / 0.01 -1 1 1 1—I—I—I— 0.1 Superficial Liquid Velocity, U^, m/s Figure 7.21. Dimensionless standard deviation of bubble time plotted against superficial hquid velocity showing transition between discrete bubble flow and dispersed bubble flow for the 4.5 mm glass bead three-phase fluidized bed at different superficial gas velocities. 182 0.4 -| 1 1 1 1 r-^i—i—i—| 1 1 1 1 0.01 0.1 Superficial Liquid Velocity, \J(, m/s Figure 7.22. Dimensionless standard deviation of bubble time plotted against superficial liquid velocity showing transition between discrete bubble flow and dispersed bubble flow for the 1.2 mm steel shot three-phase fluidized bed at different superficial gas velocities. 7.4 Flow Regime Maps 7.4.1 Flow Regime Map for 1.5 mm Glass Bead Fluidized Bed A flow regime map for 1.5 mm glass bead three-phase fluidized bed is presented in Figure 7.23. Note that the discrete bubble flow regime does not exist due to the effect of the relatively small particles on bubbles. It has been found (Darton, 1985; Henriksen and Ostergaard, 1974) that bubble coalescence is more intensive in air-water systems containing glass beads of diameter less than 2.5 mm, compared to a corresponding gas-hquid system, since small particles increase both the apparent continuous phase viscosity and density. Figure 7.23 indicates that a dispersed bubble flow regime exists at high hquid velocities. This is because the sohds holdup of the three-phase fluidized bed decreases towards zero as the hquid velocity is increased, and the system approaches the corresponding gas-hquid two-phase limit. 183 I Based on pressure gradient Based on visual observation 1st criterion in Fig. 7.6 2nd criterion in Fig. 7.6 3rd criterion in Fig 7.6 4th criterion in Fig 7.6 5th criterion in Fig 7.6 6th criterion in Fig 7.6 Legend o -icr3 10" ,-2 10" 10 Superficial Gas Velocity, U , m/s Figure 7.23. Flow regime map for air-water-1.5 mm glass bead three-phase fluidized bed with D = 0.0826 m and Z = 0.65 m Distributor: perforated plate containing 62 2-mm circular holes. 7.4.2 Flow Regime Map for 4.5 mm Glass Bead Fluidized Bed Figure 7.24 presents a flow regime map for the 4.5 mm glass bead three-phase fluidized bed. A discrete bubble flow regime is observed, and the domain of the coalesced bubble flow regime is decreased. This feature is due to the large particles that break up bubbles. It has been found (Ostergaard, 1971; Lee et al., 1974) that dispersed bubbles of uniform small size occur for glass beads of diameters greater than 2.5 mm in air-water systems. Findings of the present study are in good agreement with previous investigations. The coalesced bubble flow regime exists at Ug = 0.02 to 0.04 m/s and = 0.02 to 0.05 m/s. In this regime, the gas passes through the liquid-solid nrixture as bubbles of irregular shape and large size at low hquid velocities. This differs from what is observed in the 1.5 mm glass bead system, where bubble shapes are either spherical or spherical-cap in the coalesced bubble flow regime. 184 Figure 7.24. Flow regime map for air-water-4.5 mm glass bead three-phase fluidized bed with D = 0.0826 m and Z = 0.65 m Distributor: perforated plate containing 62 2-mm circular holes. 7.4.3 Flow Regime Map for 1.2 mm Steel Shot Fluidized Bed Figure 7.25 shows the flow regime map for the 1.2 mm steel shot three-phase fluidized bed system Both the discrete bubble flow and coalesced bubble flow regimes are present. Since the density of the steel shot, 7800 kg/m3, is much greater than that of glass beads, the particles are able to penetrate and break bubbles at lower gas and hquid superficial velocities, causing the fluidized bed to operate in the discrete bubble flow regime. As the gas velocity is further increased at low hquid velocities, coalesced bubble flow is encountered. At high hquid velocities, coalesced bubble flow is also found between dispersed bubble flow and slug flow, which appears at relatively high gas velocities. This may be related to the sohds holdup. Since the particle density is larger than that of the glass beads, the sohds holdup in the dispersed bubble flow regime is expected to be higher for the same operating conditions. The higher apparent continuous phase 185 0 10"3 10"2 10"1 10° 101 Superficial Gas Velocity, U , m/s Figure 7.25. Flow regime map for air-water-1.2 mm steel shot three-phase fluidized bed with D = 0.0826 m and Z = 0.65 m Distributor: perforated plate containing 62 2-mm circular holes. density and viscosity cause gas bubbles to coalesce and form Taylor bubbles at relatively high gas velocities. Churn flow, bridging flow and annular flow are also observed in three-phase fluidized beds at high gas velocities. Since the glass beads are already entrained from the column before the transition from bridging to annular flow occurs, the boundaries between the bridging and the annular flow regimes in Figures 7.23 and 7.24 are similar to those for the corresponding gas-hquid two-phase system On the other hand, for the 1.2 mm steel shot three-phase system, three-phase annular flow is observed. In this regime, particles are observed in the annular region, which contains hquid film and some small gas bubbles (db - 2 to 4 mm). 186 7.4.4 Comparison and Discussion Figure 7.26 presents the onset velocities for dispersed bubble flow for the two-phase and three-phase systems. For the 4.5 mm glass beads and the 1.2 mm steel shot at low gas velocities, the transition hquid velocities from discrete to dispersed bubble flow are greater than for the corresponding two-phase system A similar situation exists at higher gas velocities for the transition from slug flow (or coalesced bubble flow) to dispersed bubble flow. For the 1.5 mm glass beads, coalesced bubble flow is encountered at low gas velocities instead of the discrete bubble flow observed for other systems. For these particles, the transition hquid velocity increases with gas velocity and approaches the value for two-phase systems at high gas flow rate due to the low concentration of sohds. By comparing the 1.5 mm glass bead system with the 4.5 mm glass bead system, it can be seen that the onset hquid velocity for dispersed bubble flow increases with particle size at low gas velocities. No clear influence of particle size is observed at the higher gas velocities. However, there is a clear effect of particle density when one compares the 1.5 mm 1 o 0 C/3 0.1 4 0.01 0.001 Dispersed Bubble Flow mm*~m Slug How S .A- - -A- 'ii V) n \? V7 ' 9^ ~Q "O—— V Two-phase Discrete or Coalesced 0 1.5 mm glass beads Bubble How A 4.5 mm glass beads • 1.2 mm steel shot 0.01 0.1 Superficial Gas Velocity, U , m/s Figure 7.26. Boundaries between various bubble flow regimes. 187 glass beads with the 1.2 mm steel shot in Figure 7.26. An empirical correlation, Equation (7.3), is proposed to predict the transition hquid velocity for the onset of the dispersed bubble flow regime: Values of from Equation (7.3) are plotted against the experimental data in Figure 7.27. The average absolute percentage deviation, calculated by Equation (6.57), is 8.0% for 44 sets of experimental results. Many investigators have studied the transition between the coalesced bubble flow and dispersed bubble flow regimes. Different particle sizes and densities were used in their investigation, making directly comparison between each other difficult. Hence, Equation (7.3) is used to predict the transition hquid velocity for the onset of the dispersed bubble flow regime. Experimental Transition Liquid Velocity for Onset of Dispersed Bubble Flow, m/s Figure 7.27. Comparison between predictions of Equation (7.3) and experimental results. (7.3) 188 Figure 7.28 plots the predicted results versus their experimental data. The prediction goes through the middle for 102 sets of data from literature, but there is considerable scatter, with an average absolute percentage deviation of 70.3% between the predicted and experimental values. The worst prediction (open square and circles) come from the data of Fan et al. (1985, 1986), in which the authors argued that the transition hquid velocity for the onset of dispersed bubble flow is only a function of particle settling velocity and independent of the superficial gas velocity. Figure 7.29 shows the onset of the slug flow regime for all four systems. At low hquid velocities, the onset gas velocity increases with both particle size and density in the three-phase systems. At high hquid velocities, the onset of the slug flow regime does not differ significantly for the systems tested. For low superficial hquid velocity, when (7.4) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Experimental Liquid Transition Velocity for Onset of Dispersed Bubble Row, m/s Figure 7.28. Comparison between predictions of Equation (7.3) and experimental data from literature. 189 the transition gas velocity for the onset of slug flow can be predicted by: ^i-=6.97xl0-5Re,-0918V-8°5 U, vdpy 101 (7.5) For high superficial hquid velocity, when is greater than the right-hand term of Equation (7.4), the transition gas velocity for the onset of slug flow can be predicted by: U, ^- = 20.3xFr. gD 0.302 -0.0861 vdpy -0.318 (7.6) Figure 7.29. Boundaries for onset of slug flow regime. 190 Comparisons between the experimental data and the predictions of Equations (7.5) and (7.6) are presented in Figures 7.30 and 7.31, respectively. The average absolute percentage deviation between Equation (7.5) and the experimental data of the present study is 6.7%, based on 20 sets of data. For the 8 sets of available literature data obtained by visualization, the predicted transition gas velocity is overestimated with a mean deviation of 52.3%. The deviation between Equation (7.6) and the experimental data of the present study is 12.4%, based on 19 sets of data. For 14 sets of data from the hterature, the mean deviation is 22.3%. 0.1 • 1.5 mm glass beads • 4.5 mm glass beads A 1.2 mm steel shot v Matsuura and Fan (1984) 0.01 0.1 Experimental Transition Gas Velocity for Onset of Slug How at Low Liquid Velocities, m/s Figure 7.30. Comparison between predictions of Equation (7.5) and experimental data. 191 I 1 0.01 0.1 Experimental Transition Gas Velocity for Onset of Slug Flow at High Liquid Velocity, m/s Figure 7.31. Comparison between predictions of Equation (7.6) and experimental data. Figure 7.32 presents the boundaries between the slug flow and chum flow regimes for all four systems. It is seen that the particles affect this transition only slightly. The presence of the smaller glass beads results in an increase of the transition gas velocity at low hquid velocities, but does not significantly affect this transition at higher hquid velocities where there is a low sohds concentration. The dense particles in most cases lead to higher transition gas velocities at given hquid velocities. Equation (7.7) below can be used to predict the boundary between the slug and chum flow regimes. This correlation is based on 30 sets of data for three-phase systems of the present study with an average absolute percentage deviation of 14.3%. No reports are available for the slug/chum flow transition in three-phase systems, so that only the data of the present study are plotted in Figure 7.33. U, 0.468 Ps s x - 0.454 g = 53.4 x Re -1.30 Ar, (7.7) U •e VPtJ 192 1 1 o ^3 p-1 •0 0.1 4 0.01 d 0.001 0.1 Slug Flow • Two-phase O 1.5 mm Glass Beads] A 4.5 mm Glass Beads| V 1.2 mm Steel Shot Churn Flow -i—i—i—i—i—p-1 I III 10 Superficial Gas Velocity, U , m/s Figure 7.32. Boundaries between slug and churn flow regimes. Experimental Transition Liquid Velocity for Onset of Chum Flow, m/s Figure 7.33. Comparison between predictions of Equation (7.7) and experimental data. 193 Figure 7.34 shows boundaries between churn flow and bridging flow. For the gas-hquid system, this transition is independent of superficial hquid velocity. For the three-phase systems, the transition gas velocities increase with decreasing U^. By comparing the transitions for the three types of particles, it is seen that particle size does not affect this transition, but the increase of particle density leads to increases in transition hquid velocities, at least at higher Ug. Equation (7.8) below is proposed to present the boundary between the churn/bridging flow regimes. Figure 7.35 compares the predicted and experimental values. The average absolute percentage deviation for the 30 sets of data of the present study is 11.1%. No other data have been found in the hterature. U, u, £ = 219xRerL24 Ar, 0.367 - 0.444 (7.8) 1 d o r-i 8* VI 0.1 4 0.01 4 0.001 0.1 • Air-water two-phase O 1.5 Glass Beads A 4.5 mm Glass Beads V 1.2 mm Steel Shot Chum Flow 1» V i v fcvtyi Bridging Flow 8' Superficial Gas Velocity, U , m/s 10 Figure 7.34. Boundaries between churn and bridging flow regimes. 194 0.001 0.01 0.1 1 Experimental Transition Liquid Velocity for Onset of Bridging Flow, m/s Figure 7.35. Comparison between predictions of Equation (7.8) and experimental data. Figure 7.36 presents the transition between bridging flow and annular flow. For the two-phase system, the transition gas velocities decrease with increasing hquid velocities at high hquid flow rates, but remain almost constant at lower U^. For the glass beads, before this transition occurs, the particles have all been entrained from the column, so the transitions from bridging flow to annular flow are virtually identical to those for the gas-hquid system For the 1.2 mm steel shot, however, the presence of sohd particles causes a decrease of transition gas velocities. Most experimental data for this transition obtained in the present study correspond to absence of particles. There are insufficient data to construct an empirical correlation for three-phase systems. 195 Superficial Gas Velocity, U , m/s Figure 7.36. Boundaries between bridging and annular flow regimes. 7.5. Summary Experimental criteria for determining flow regime transitions in an air-water two-phase system have been successfully extended to gas-hquid-sohd three-phase fluidized beds. Flow regime maps have been presented based on experimental data for three different three-phase systems. Relatively small/light particles, i.e. 1.5 mm glass beads, cause gas bubbles to coalesce. Hence coalesced bubble flow can be observed at low gas and hquid velocities in three-phase fluidized beds of such particles. However, dispersed bubble flow still can be observed at high hquid velocity for three-phase fluidized beds of 1.5 mm glass beads, since the increase of hquid velocity leads to a decrease in sohds concentration. Large or dense particles (4.5 mm glass beads or 1.2 mm steel shot) lead to bubble coalescence only at relatively high gas velocities. At low gas velocities, discrete and dispersed bubble flow can be observed at low and high hquid velocities, respectively. As in two-phase systems, slug flow, churn flow, bridging flow and annular flow can 196 be observed at high gas velocities in three-phase fluidized beds. Particle properties clearly influence flow regime transition for the onset of slug flow, bridging flow and annular flow. Five empirical correlations are proposed for the flow regime boundaries. The average absolute percentage deviation between the experimental data and the predictions is 8.0% for the onset of dispersed bubble flow, 6.7% and 12.4% for the onset of slug flow at low and high hquid velocity respectively, 14.3% for the boundary between the slug and chum flow regimes and 11.1% for the churn/bridging flow transition.. These correlations give favourable agreement with experimental data from the literature, especially considering the variation in measurement techniques employed in the literature. 197 Chapter 8 Bubble Characteristics in Three-Phase Fluidized Beds 8.1 Introduction In Chapter 7, it was shown that discrete bubble flow, dispersed bubble flow, coalesced bubble flow, slug flow, churn flow, bridging flow and annular flow exist in three-phase systems. The presence of particles changes the characteristics of bubbles significantly, compared to solids-free gas-hquid systems. Many studies have been devoted to bubble behavior in three-phase fluidized beds under different operating conditions (Rigby et al., 1970; Page and Harrison, 1972; Henriksen and Ostergaard, 1974; Darton and Harrison, 1975, 1985; Kim et al., 1977; de Lasa et al., 1983; Sisak and Ormos, 1985a, b; Lee and de Lasa, 1986; Peterson et al., 1987; Kim et al., 1988; Lee and de Lasa, 1988; Meernik and Yuen, 1988a, b; Muroyama et al., 1988; Sun and Furusaki, 1988; Yu and Kim, 1988; Lee and de Lasa, 1989; Bly and Worden, 1992; Deshpande et al., 1992; Han and Kim, 1993; Chen et aL 1995). This chapter demonstrates some bubble characteristics for the different flow regimes in three-phase fluidized beds. Three types of particles were used in the fluidized beds with air and water as gas and hquid phases, respectively. The variations of bubble frequency, bubble chord length and its distribution as well as average bubble velocity are presented in this chapter. 8.2 Bubble Frequency The variation of the bubble frequency with respect to the gas velocity in various flow regimes for the three-phase fluidized bed containing 1.5 mm glass beads is presented in Figures 7.7 and 7.14 of Chapter 7. A linear relationship with a proportionality constant of 545 m"1 between the bubble frequency and the superficial gas velocity can be seen for the dispersed bubble 198 I flow regime in Figure 7.7. As with the air-water two-phase system, this constant does not change with superficial hquid velocity in the dispersed bubble flow regime. The bubble frequency in the coalesced bubble flow and slug flow regimes increases with the superficial gas and hquid velocities, but decreases as Ug is increased in the churn and bridging flow regimes, as shown in Figure 7.14. For the 4.5 mm glass beads, depending on the hquid velocity, dispersed and discrete bubble flow were observed at low gas velocities. In these two flow regimes the bubble frequency is proportional to the superficial gas velocity as shown in Figure 7.8. Qn further increasing the gas velocity, the bubble frequency increases at a slowly increasing rate in the slug flow regime and reaches a maximum value at the transition between the slug and churn flow regimes. The bubble frequency continues to decrease in the bridging flow regime and approaches zero in the annular flow regime, as shown in Figure 7.15. For the three-phase fluidized bed of 1.2 mm steel shot, the bubble frequency in the discrete and the dispersed bubble flow regimes is proportional to the superficial gas velocity and also a function of the hquid velocity as shown in Figures 7.9 and 7.10. For low hquid velocities, the proportionality constant relating the bubble frequency to the superficial gas velocity is approximately 545 m"1, while for high U£, the constant is 860 m"1. The bubble frequency continue to increase slowly with the gas velocity in the coalesced bubble flow and slug flow regimes, but decreases in the churn and bridging flow regimes as shown in Figure 7.16. It is also seen that the bubble frequency increases with the hquid velocity at higher hquid velocities, but does not change significantly with IL_ in the coalesced and slug flow regimes at low hquid velocities. 199 8.3 Bubble Chord Length and its Distribution Bubble characteristics strongly depend on particle size and density in three-phase fluidized beds. Relatively small/light particles (e.g. 1.5 mm glass beads) generally cause bubbles to coalesce to form larger bubbles, while large/heavy particles (such as 4.5 mm glass beads and 1.2 mm steel shot) promote bubble breakup and formation of smaller bubbles. In a three-phase fluidized bed, the sohds holdup decreases with increasing superficial hquid velocity, so that the system approaches a gas-hquid two-phase system For the three-phase fluidized bed with 1.5 mm glass beads, the coalesced bubble flow regime was observed at low superficial gas and hquid velocities. Figure 8.1 shows the average bubble chord length in the dispersed and coalesced bubble flow regimes. The average bubble chord length increases with increasing superficial gas velocity, but decreases as the superficial hquid velocity increases. The average bubble chord length in the coalesced bubble flow regime is significantly greater than in the dispersed bubble flow regime. The transition between the coalesced and dispersed bubble flow regimes, however, is a gradual process from the average bubble chord length point of view. The average and the Sauter mean bubble chord lengths are plotted against Ug at two different values of in Figure 8.2. It is seen that the average value of bubble chord length is always less than the corresponding Sauter mean value. In the slug flow regime, at = 0.0184 m/s, both the average and Sauter mean bubble chord length increase with Ug at low gas velocities. On further increasing Ug, the average bubble chord length decreases due to the increased number of small bubbles. The variation of the average bubble chord length in the air-water-1.5 mm glass bead fluidized bed differs from that in the air-water two-phase system (Chapter 5) in which the average and Sauter mean bubble chord lengths increased slightly or levelled off in the slug flow regime. 200 0.1 8 TJ s 6 °-°H CD 1 PQ CO I 0.001 Coalesced Bubble Flow | Dispersed Bubble How 1 1 1 1 I— 0.01 -i—i—i i i i 0.1 Superficial Gas Velocity, m/s Figure 8.1 Average bubble chord length in coalesced and dispersed bubble flow regime for air-water-1.5 mm glass bead system. 10-B i i PQ 0.1 4 0.014 0.001 —D— Average bubble chordlengm,U,= 0.0184 m/s —O—Average bubble chord length, U^ = 0.100 m/s —•— Sauter mean bubble chord length, U t = 0.0184 m/s —#— Sauter mean bubble chord length, = 0.100 m/s l,U, = 0.1UOm/B TJ M : / 7^ J2-U Coalesced Bubble Flow j oN /f "uo0 o0 Slug Flow T 0.001 I I I I I I | 0.01 0.1 1 Superficial Gas Velocity, m/s ChiinjBridging Flow ;Flow D 10 Figure 8.2 Average and Sauter mean bubble chord length in slug and churn flow regime for air-water-1.5 mm glass bead system 201 Figure 8.3 shows some typical probability density distributions of the bubble chord length in the different flow regimes. Narrow distributions with peaks which occur between 2.1 and 2.6 mm are observed in the dispersed bubble flow regime. As the superficial hquid velocity is decreased to the coalesced bubble flow regime, the bubble chord length distributions become wider and the average bubble chord length increases by almost an order of magnitude. As Ug is increased, the average bubble chord length and the standard deviation increase significantly in the slug flow regime. However, the peaks of the PDF curves occur at small bubble chord lengths, due to the large number of small bubbles in the slug flow regime. Even in the churn flow and bridging flow regimes, there are still many small bubbles present due to the turbulence of the gas and hquid flows. In bridging flow, the standard deviation of the bubble chord length increases sharply, although the average bubble chord length does not change as much as in the churn flow regime. This indicates that large bubbles exist in the system since the bridging flow regime is transitional between the churn flow and the annular flow regimes. A number of investigators have reported that large particles cause bubbles to break up in air-water fluidized beds. In the present study, small bubbles with a narrow size distribution were found in the discrete and dispersed bubble flow regimes. Figure 8.4 shows the measured average bubble chord length in these two flow regimes for the air-water-4.5 mm glass bead fluidized bed. It is seen that the average bubble chord length increases with increasing gas velocity but decreases with increasing hquid velocity. The average bubble chord length in the discrete bubble flow regime is always greater than in the dispersed bubble flow regime at the same gas velocity. The transition between the discrete and dispersed bubble flow regimes occurs gradually from the point of view of bubble size. 202 500 400 300 200 100 0 100 H 80 60 40 H 20 0 100-1 80 60 A 40 A ill Dispersed Bubble Flow , m/s 0.100 U^, m/s 0.100 Ug, m/s 0.0020 - Ug, m/s 0.0148 Average £b, m 0.0030 £ Averse £b,m 0.0044 Standard Deviation of £b, m 0.0016 " | Standard D eviati on of £b, m 0.0056 £b for PDF Peak Value, m 0.0026 "• £b for PDF Peak Value, m 0.0021 Coalesced Bubble Flow Ue, m/s Ug, m/s Average £b, m Standard Deviation of £b, n £b for PDF Peak Value, m 0.0184 0.0021 0.019 0.010 0.0089 J 0 "WA 7 Dispersed Bubble Flow Coalesced Bubble Flow , m/s Ug,m/s Average m Standard Deviation of L, m L for PDF Peak Value, m 0.0184 0.015 0.034 0.023 0.024 500 400 300 200 100 0 100 80 60 40 20 0 100 80 60 40 20 0 100 80 60 40 20 Slug Flow 20 A Vt, m/s Ug, m/s Average £b, m Standard Deviation of £b, n £b for PDF Peak Value, m 0 100 80 60 40 20 A;. •• • \ B. 0.0273 0.077 0.045 0.051 0.0072 Slug Flow Ut,ta/a 0.0273 Ug, m/s 0.359 Average £b, m 0.042 Standard Deviation of £b, m 0.085 £b for FDF Peak Value, m 0.0052 Churn Flow Bridging Flow U^, m/s 0.0273 l)t, m/s 0.0273 Ug, m/s 1.43 Ug,m/s 2.83 Average £b, m 0.032 Average £b, m 0.049 Standard Deviation of £b, m 0.053 Standard Deviation of £b, m 0.13 £b for PDF Peak Value, m 0.0043 ^* £b for PDF Peak Value, m 0.015 00 0.05 0.10 0.15 0.20.00 0.05 0.10 0.15 0.20 Bubble Chord Length, m Figure 8.3 Bubble chord length distributions in different flow regimes for air-water-1.5 mm glass bead fluidized beds. 203 0.1 Tt I ID i cf I 0.01 4 0.001 Discrete Bubble Flow U^, m/s —•— 0.0364 —•— 0.0455 —A—0.0546 —0.0638 —•— 0.0729 —O— 0.100 —A—0.128 —V— 0.155 -—O— 0.218 Dispersed Bubble How 0.001 0.01 T 0.1 Superficial Gas Velocity, m/s Figure 8.4 Average bubble chord length in discrete and dispersed bubble flow regimes for air-water-4.5 mm glass bead fluidized bed. The variation of the bubble chord length with gas velocity in other flow regimes is presented in Figure 8.5 for two typical sets of results at IL_ = 0.0455 and 0.155 m/s. The flow regimes labeled in the figure are for the lower hquid velocity (i.e. 0.0455 m/s). Both the average and the Sauter mean bubble chord length increase with increasing superficial gas velocity in the discrete and coalesced bubble flow regimes. The Sauter mean bubble chord length continues to increase at a lower rate in the slug and the churn flow regimes, then increases sharply in the bridging flow regime. However, the average bubble chord length first increases sharply at low gas velocities and then decreases shghtly at intermediate gas velocities in the slug flow regime for = 0.0455 m/s. At high hquid velocity, viz. = 0.155 m/s, the average bubble chord length always increases with the superficial gas velocity. 204 10^ 8 1 CD 1 ffl —•— Avenge Bubble Chord Length, U, = 0.0455 m/s —•—Averts Bubble Chord Lengfli, U t = 0. 155 mM —n— Sauter Mean Bubble Chord Lengfli, U, = 0\O455 mh —O— Sauter Mean Bubble Chord Length, U, = 0.155 m/a 0.01 -4 0.001 Superficial Gas Velocity, m/s Figure 8.5 Average and Sauter mean bubble chord length in different flow regimes for air-water-4.5 mm glass bead fluidized bed. The bubble chord length distribution in different flow regimes for this system is shown in Figure 8.6. For the dispersed bubble flow regime, the distributions of bubble chord length are generally narrow with average bubble chord length ranging from 2.2 to 2.4 mm and the standard deviation from 0.8 to 1.1 mm for gas velocities from 0.00311 to 0.011 m/s. The peaks of the PDF of bubble chord length occur at a bubble chord length of 1.7 mm In the discrete bubble flow regime, the average bubble chord length, the standard deviation of bubble chord length and the bubble chord length at which the peak of the PDF occurs are greater than for the dispersed bubble flow regime, but bubble chord length distributions remain narrow, as shown in Figure 8.6. 205 1000 800 600 400 200 0 1000-800-600-400-200-0 100 80-| 60 40-20-0 100 80 60 40-1 20-Dispersed Bubble Flow , m/s Ug,m/s 0.155 0.00311 0.0022 Average £b, m Standard Deviation of £b, m 0.0008 £b for PDF Peak Value, m 0.0017 Discrete Bubble Flow , m/s Ug ,m/s Average £b, m 0.0455 0.00312 0.0046 Standard Deviation of £b, m 0.0043 £b for PDF Peak Value, m 0.0027 Dispersed Bubble Flow , m/s Ug,m/s Average £b, m Standard Deviation of tb, m 00011 tb for PDF Peak Value, m 0.0017 0.155 0.0110 0.0024 Discrete Bubble Flow , m/s Ug,m/s Average £b, m 0.0455 0.0108 0.0054 Slug Flow U, , m/s 0.0455 Ug,m/s 0.109 Average £b, m 0.036 Standard Deviation of £v m 0.048 £b for PDF Peak Value, m 0.0060 •/" W,^..*'""%.*.*^\'.."T.... Churn Flow , m/s Ug,m/s Average £b, m 0.0455 1.78 0.033 A.. Standard Deviation of £b, m 0.064 0-0.00 £b for PDF Peak Value, m 0.0077 Standard Deviation of £b, m 0.0062 £b for PDF Peak Value, m 0.0027 Slug Flow , m/s Ug,m/s Average £b, m 0.0455 0.637 0.022 Standard Deviation of £b, m 0 051 £b for PDF Peak Value, m 00045 A, Bridging Flow V,, m/s 0.0455 Ug,m/s 2.12 Average 4, m 0.036 Standard Deviation of £b, m 0.059 £b for PDF Peak Value, m 0.0068 V - 80 - 60 - 40 - 20 0.02 0.04 0.06 0.08 0.10 0.12 0.140.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Bubble Chord Length, m Figure 8.6 Bubble chord length distributions in different flow regimes for air-water-4.5 mm glass bead fluidized bed. 206 The bubble chord length distributions in the slug flow regime are wider than in the dispersed and discrete bubble flow regimes, with average values and standard deviations of bubble chord length approximately one order of magnitude greater than in the discrete bubble flow regime. Despite the increase in £b and its standard deviation in the slug flow, chum flow and bridging flow regimes, the peaks of the distributions remain at a small bubble chord length, indicating that many small bubbles are present in these flow regimes. For the 1.2 mm steel shot fluidized bed, discrete, dispersed and coalesced bubble flow regimes were observed at low superficial gas velocities. Figure 8.7 shows the average bubble chord length in the discrete and dispersed bubble flow regimes. It is seen that the average bubble chord length increases with increasing superficial gas velocity and decreases with increasing superficial hquid velocity. The average bubble chord length in the discrete bubble flow regime is greater than in the dispersed bubble flow regime. 0.01 a CD I CQ 3 0.001 Discrete Bubble How Dispersed Bubble How O —A— —V-— —•-—•-—A-U^, m/s - 0.0364 -0.0455 0.0546 0.0638 0.0729 0.100 0.155 0.200 0.311 0.404 0.001 1 I—I—I—I I I I— 0.01 I 0.1 1 Superficial Gas Velocity, m/s Figure 8.7 Average bubble chord length in discrete and dispersed bubble flow regimes for air-water- 1.2 mm steel shot fluidized bed. 207 The experimental average and Sauter mean bubble chord lengths at two different superficial hquid velocities are presented in Figure 8.8. The demarcations for the flow regimes shown are for IL_ = 0.0455 m/s. The Sauter mean bubble chord length mainly increases with the superficial gas velocity. Figures 8.9 and 8.10 show typical bubble chord length distributions for different flow regimes. Small bubbles with narrow size distribution were seen in the dispersed bubble flow regime at high hquid velocity. On decreasing the superficial hquid velocity, discrete bubble flow is encountered, leading to higher values of both the average and the standard deviation of bubble chord length. a i CO 1 PQ 5i 3 1 -i 0.1 4 0.01 4 0.001 —•— Average bubble chord length at TJ g= 0.0455 m/s —•— Average bubble chord length at U^= 0.311 m/s —•— Sauter mean bubble chord length at U f = 0.0455 m/s j —O— Sauter mean bubble chord length at U^= 0.311 m/s ^Q'0 O • 7 Si "" •—•—• J?-° / 2-.-.. Discrete and Coalesced Flow Slug and Chum Flow Bridging How 0.001 TTTT 0.01 T-0.1 I 1111 1 D 10 Superficial Gas Velocity, m/s Figure 8.8 Average and Sauter mean bubble chord length in different flow regimes for air-water-1.2 mm steel shot at IL = 0.0455 and 0.311 m/s. 208 500 400 300 § 2ooliL: VI « 100 0 600 500 400 300-| 200 100 -I 0.00 0.01 Dispersed Bubble Flow , m/s 0.200 Ug, m/s 0.0030 Average ^ m 0.0025 Standard Deviation of £b, m 0.0013 £b for PDF Peak Value; m 0.0020 —I 1 1 1 r Discrete Bubble Flow Ug,m/s 0.0455 0.0030 i 0.0055 Average iv m Standard Devk ^b for PDF Peak Valuer m 0.0019  Deviation of £b, m 0.0070 Coalesced Bubble How U, , m/s 0.0455 Ug, m/s 0.37 Average £b, m 0.0082 Standard Deviation of £b, m 0.015 £b for PDF Peak Value, m 0.0021 0.02 0.03 0.04 0.00 0.01 Dispersed Bubble Flow , m/s 0.200 Ug , m/s 0.014 Average tb, m 0.0028 Standard Deviation of £b, m 0.0017 £b for PDF Peak Value, m 0.0021 Discrete Bubble Flow , m/s Ug,m/s Average £b, m 0.0455 0.014 0.0079 L for PDF Peak Value, m 0.0017 Coalesced Bubble Flow U, , m/s 0.200 Ug,m/s 0.10 Average £b, m 0.0043 Standard Deviation of £b, m 0.0064 £b for PDF Peak Value, m 0.0020 0.02 0.03 0.04 Bubble Chord Length, m 500 400 300 200 H 100 Figure 8.9 Bubble chord length distribution in different flow regimes at low gas velocity for air-water-1.2 mm steel shot fluidized bed. 209 h-5 o 100 80-60 40 20 0 100 ShigFlow TJ^ , m/s Ug,m/s Average 0.0455 0.47 0.017 eb for PDF Pak Value, m 0.0034 A-ShigFlow , m/s 0.200 Ug, m/s 0.46 Average ^b,m 0.022 Staida-d Deviation of ib, m 0.048 £h for PDF Peak Value, m 0.0060 v.. U 60- / PQ o PH 80 60-I 40-20 Chum Flow JJ(, m/s Ug,m/s Average £b, m 0.0455 2.0 0.023 "1 ' 1 " ShigFlow , m/s 0 100 80 60 40 20 Standard Deviation of tb, m0.058 lb for PDF Peak Value, m 0.0053 0.200 0.92 0.019 Ug,m/s Average <?b, m Standard Deviation of £b,m 0.030 eb for PDF Pek Value, m 0.0060 ShigFlow , m/s Ug,m/s Average ^b, m Standard Devia ^b for PDF Peak Value,m 0.0062 0.0455 3.3 0.023 Slug How U,, m/s 0.200 Ug,m/s 1.9 Average t^m 0.039 Standard Deviation of 0.097 tb for PDF Peak Value, m 0.0083 0.00 0.02 0.04 0.06 0.08 0.10 0.120.00 0.02 0.04 0.06 0.08 0.10 0.12 Bubble Chord Length, m Figure 8.10 Bubble chord length distribution in different flow regimes at high gas velocity for air-water-1.2 mm steel shot fluidized bed. As the superficial gas velocity is increased, the average value and the standard deviation of bubble chord length increase. The peaks of the PDF curves occur at low values of the bubble chord length, indicating that there are still many small bubbles in the slug, chum and bridging flow regimes. 210 8.4 Average Bubble Velocity The average bubble velocity is plotted against the average bubble chord length in the dispersed and coalesced bubble flow regimes for the air-water-1.5 mm glass bead fluidized bed in Figure 8.11. It is seen that the average bubble velocity increases with the average bubble chord length and the superficial hquid velocity. The rate of increase of the average bubble velocity with respect to the average bubble chord length in the dispersed bubble flow regime is greater than in the coalesced bubble flow regime. 1.4 A 1.2 A 1.0 H 0.8 0.6-^ 0.4 0 Dispersed Bubble Flow Coalesced Bubble Row Regime U^, m/s U m/s -•—0.0184 -•—0.0273 -A—0.0455 -V—0.0638 -O—0.0729 -•—0.100 -O—0.155 g-0.00211-0.00209-0.00208-0.00207-0.00205-0.00200-0.00179-0.0152 0.0151 0.0149 0.0150 0.0148 0.0206 0.145 1 0.005 —I— 0.010 —I— 0.015 —I— 0.020 —I— 0.025 —I— 0.030 0.000 Average Bubble Chord Length, m 0.035 Figure 8.11 Average bubble velocity plotted against average bubble chord length in dispersed and coalesced bubble flow regimes for air-water-1.5 mm glass bead fluidized beds, Ug = 0.0018- 0.145 m/s. 211 The average bubble velocity is plotted against the average bubble chord length at three different superficial hquid velocities in the slug and churn flow regimes in Figure 8.12. It is seen that the average bubble velocity increases consistently with the superficial gas velocity, while the average bubble chord length at first increases as the gas velocity increases and then describes an S-shape with respect to the average bubble velocity. The relationship between average bubble velocity and average bubble chord length can be correlated by Equation (5.3) for the dispersed and discrete bubble flow regimes in the air-water two-phase system as described in Chapter 5. Figure 8.13 shows the bubble travel length versus the average bubble chord length in the dispersed and coalesced bubble flow regimes for the air-water-1.5 mm glass bead fluidized beds. It is seen that Equation (5.3) also agrees well with the experimental data in the dispersed bubble flow regime well. A linear relationship between the 1 •f 0 1 CO 0 1 3.5 4 3.0 A 2.5 H 2.0 H 1.5 H 1.0' 0.5 • TJ,, m/s U , m/s • 0.0184 0.0222-3.02 A. / / */ • 0.0455 0.0220- 1.77 A 0.100 0.0352-2.03 Churn Flow Slug How 7 A / A A/ A • J n ^> ^ • 0.00 0.02 0.04 0.06 0.08 Average Bubble Chord Length, m 0.10 Figure 8.12 Variation of average bubble velocity plotted against average bubble chord length in slug and churn flow regimes for air-water-1.5 mm glass bead fluidized beds. 212 0.1 a s i—i 1 CD 1 pa o.oi H 0.001 U^, m/s Ug, m/s • 0.0184 0.00211 - 0.0152 • 00273 0.00209-00151 A 00455 0.00208 - 00149 (^Ub)/f= 0.7667 £b • 00638 OOQ207 - O0150 O 00729 000205-O0148 A 0100 O00200-00206 V 0155 000179- 0.145 Dispersed Coalesced Bubble Flow o5{ \ Bubble Flow r A Equation (5.3) 0.001 0.01 Average Bubble Chord Length, m 0.1 Figure 8.13 Bubble travel length plotted against average bubble chord length in coalesced and dispersed bubble flow regimes for air-water-1.5 mm glass bead fluidized beds. bubble travel length and the average bubble chord length is obtained for the coalesced bubble flow regime in the air-water-1.5 mm glass bead fluidized bed, expressed by: e„^- = 0.7667 S>h 8 £• D (8.1) The variation of the bubble travel length with the average bubble chord length in other flow regimes at low hquid velocities is shown in Figure 8.14. It can be seen that the linear relationship between the bubble travel length and the average bubble chord length for the coalesced bubble flow regime can be extended to the slug flow regime at low gas velocities. At high gas velocities in the slug flow regime, the average bubble chord length decreases with the gas velocity (see Figure 8.2), but the bubble travel length is independent of both Ug and U^. 213 mM mM • 0.0051 0113 -5.22 O O0082 00223 -5.22 • O0154 00152 - 5.20 V 0.0184 O002U-5.86 + 00273 O00209 - 5.10 (%TJ„)/f=l.5 tb 0.01 i •—i—i i | 0.1 0.01 Average Bubble Chord Length, m Figure 8.14 Bubble travel length plotted against average bubble chord length in different flow regimes at low hquid velocities for air-water-1.5 mm glass bead fluidized bed. At high hquid velocities, the sohds holdup decreases significantly for the air-water-1.5 mm glass bead fluidized bed; the relationship between the bubble travel length and the average bubble chord length then approaches that in the corresponding air-water two-phase system It can be seen in Figure 8.15 that the experimental results for the dispersed bubble flow and the slug/chum flow regimes agree well with Equations (5.3) and (5.4), respectively, both developed for the air-water two-phase system The average bubble velocity is plotted against the average bubble chord length in the discrete and dispersed bubble flow regimes for the air-water-4.5 mm glass bead fluidized bed in Figure 8.16. The average bubble velocity is seen to increase with both the average bubble chord length and the hquid velocity in both these flow regimes. 214 Figure 8.15 Bubble travel length plotted against average bubble chord length in different flow regimes at high hquid velocities for air-water-1.5 mm glass bead fluidized bed. 1.4-1 1.2-• 0 1.0-o IP > CD 0.8-•8 m • CD 0.6-< • 0.4-Dispersed Bubble Flow —•— 0.0364 000313-0.0150 —•—acn55 O0O312-0.0150 —A— 0.0546 000311 -tt0218 —•—00638 000305-00216 —•—00729 000304 -00214 —•—O100 000288-00508 —O—0128 000277-00672 —A—0155 000311-00772 —V-0218 000306-0142 Discrete Bubble Flow 0.000 0.002 0.004 0.006 0.008 0.010 Average Bubble Chord Length, m 0.012 Figure 8.16 Average bubble velocity in discrete and dispersed bubble flow regimes for air-water-4.5 mm glass bead fluidized bed. 215 The average bubble velocity in the coalesced, slug and churn flow regimes at three typical hquid velocities is shown in Figure 8.17. S-shape curves can be seen for the relationship between the average bubble velocity and the average bubble chord length at low hquid velocities. This indicates that the average bubble velocity is not only a function of the average bubble chord length but also of the superficial gas velocity. At high superficial hquid velocity, viz. = 0.155 m/s, the sohds holdup decreases so that the three-phase fluidized bed approaches an air-water two-phase column, and the average bubble velocity increases with the average bubble chord length. The relationship between the bubble travel length and the average bubble chord length for the three-phase fluidized bed is shown in Figure 8.18. The variation of the bubble travel length with the average bubble chord length is different in different flow regimes. In the discrete and dispersed bubble flow regimes, Equation (5.3) adequately describes the relationship between the Figure 8.17 Average bubble velocity in different flow regimes for air-water-4.5 mm glass bead fluidized bed. 216 Figure 8.18 Bubble travel length plotted against average bubble chord length in different flow regimes for air-water-4.5 mm glass bead fluidized bed. Ug = 0.003 - 4.5 m/s bubble travel length and the average bubble chord length. In the slug and the churn flow regimes, at high hquid velocities, Equation (5.4) represents the experimental data well. In the bridging flow regime, the relationship between the bubble travel length and the average bubble chord length can be described by: eg^ = l.5lh (8.2) as shown in the figure. The variation of the average bubble velocity with the average bubble chord length for the air-water-1.2 mm steel shot fluidized bed is presented in Figure 8.19. It can be seen that the average bubble velocity increases with the average bubble chord length in the dispersed bubble flow regime. For other flow regimes, the relationships between the average bubble velocity and 217 the average bubble chord length are not very clear. Nevertheless, it still can be seen that for discrete bubble flow, the average bubble chord length ranges from 5 to 10 mm, while the average bubble velocity ranges from 0.5 to 1 m/s. For slug and churn flow, the average bubble chord length ranges from 10 to 40 mm, while the average bubble velocity varies from 1 to 5 m/s. The relationship between the bubble travel length and the average bubble chord length for the air-water-1.2 mm steel shot fluidized bed is shown in Figure 8.20. It is seen that the two parameters can be correlated by Equation (5.3) for the discrete and dispersed bubble flow regimes and, at higher superficial hquid velocities, by Equation (5.4) for the slug and chum flow regimes. 10-1 m I Coalesced Bubble Flow \ Bridging Flow O v o Dispersed Bubble Flow Slug and Chum Flow Discrete U^, m/s • 0.0364 • 0.0455 A 0.0546 • 0.0638 • 0.0729 • 0.100 o 0.155 A 0.200 V 0.311 O 0.404 -I 1—i—r" 0.001 0.01 0.1 Average Bubble Chord Length, m Figure 8.19 Average bubble velocity plotted against average bubble chord length in different flow regimes for air-water-1.2 mm steel shot fluidized bed. Ug = 0.003 - 4.5 m/s 218 ! 0.14 H 0.001 0.001 I I I I I I 0.01 -I 1 1—I—I—I I I I— 0.1 Average Bubble Chord Length, m -i—i—111 Figure 8.20 Bubble travel length plotted against average bubble chord length for air-water-1.2 mm steel shot fluidized bed. Ug = 0.003 - 4.5 m/s 8.5 Summary Although particle properties affect bubble characteristics and consequently govern the flow regimes, the variation of bubble characteristics in turn depends on flow regime. In the discrete and dispersed bubble flow regimes, bubble frequency changes proportionally with the superficial gas velocity for the different particles tested in this study. It increases at a slower rate with the superficial gas velocity in the coalesced bubble flow and slug flow regimes, but decreases in the churn and bridging flow regimes for the different systems studied in this work. Average bubble chord length increases with the superficial gas velocity but decreases with the superficial 219 liquid velocity in the discrete, dispersed and coalesced bubble flow regimes. The average bubble chord length in the coalesced bubble flow regime is greater than in the discrete bubble flow regime, and the latter is greater than in the dispersed bubble flow regime. In the bridging flow regime, the average bubble chord length increases sharply with the superficial gas velocity. The distributions of bubble chord length reveal that, despite the increase of average bubble chord length, there still exist many small bubbles in the slug, chum and bridging flow regimes in the three-phase fluidized beds. The standard deviation of the bubble chord length increases with increasing superficial gas velocity but decreases with the superficial hquid velocity. For the 1.5 mm and 4.5 mm glass beads, the average bubble velocity increases with both the average bubble chord length and the superficial hquid velocity in the discrete, dispersed and coalesced bubble flow regimes. For other fluidized beds flow regimes with the 1.5 mm and 4.5 mm glass beads as well as the fluidized bed with 1.2 mm steel shot, the relationship between the average bubble velocity and the average bubble chord length is complex due to the interaction of the effects of the gas and hquid velocities. The bubble travel length, defined as (egUb)/f in Chapter 5, can also be used to correlate the bubble characteristics in three-phase fluidized beds. Equation (5.3), developed in Chapter 5, describes the relationship between the bubble travel length and the average bubble chord length in the discrete and dispersed bubble flow regimes for the three-phase fluidized beds. Equation (5.4) is apphcable to the slug and chum flow regimes at high hquid velocity in the three-phase fluidized beds. The relationship between bubble travel length and average bubble chord length appears to provide an alternative method to determine flow regimes in multi-phase systems. Further study is needed to extend this finding. 220 Chapter 9 Conclusions and Recommendations 9.1 General Conclusions 1. A new set of flow regime transition criteria based on conductivity probe measurements of bubble characteristics, summarized in Figure 7.6, was developed to determine flow regime transitions in an air-water bubble column and then successfully applied to air-water-sohd three-phase fluidized beds. Other measurement techniques, such as absolute and differential pressure fluctuation methods and the conductivity probe based on the original signal, were carefully studied and shown to be unsuitable for flow regime determination. 2. The best agreement with new and previously published experimental data was obtained from the first empirical equation of Begovich and Watson (1978), Equation (6.1). However, this correlation breaks down when superficial gas velocity approaches zero. Agreement was nearly as good with the Gas-Perturbed Liquid Model, which has the advantage of having no new fitted constants and goes to the appropriate limit as the superficial gas velocity approaches zero. The resulting generalized rninimum fluidization model, Equation (6.50), can thus be used to predict the incipient fluidization hquid velocity in both two-phase and three-phase fluidization. 3. The Transport Velocity Model n, Equations (6.87) and (6.88) for spheres, or Equations (6.89) and (6.90) for cylindrical particles, together with Equations (6.81), (6.82) and (6.93), was proposed to predict the boundary between fluidized beds and particle transport flow. It gives good agreement (average deviation of 14.2%) with 112 sets of experimental data for superficial gas velocity up to 3.0 m/s, including 79 data sets from the literature, but excluding the results from the 1.2 mm steel shot in the present work. An empirical correlation, Equation 221 (6.94), was also proposed to predict the transport velocity in air-water mixtures for all systems. It gives good agreement with 125 sets of experimental data with an average absolute deviation of 13.8%, again for gas velocities as high as 3.0 m/s, a much higher value than explored previously. 4. New complete flow regime maps were presented based on experimental data for cocurrent upward three-phase systems. According to particle movement, three different operating regimes can be observed: fixed bed, fluidized bed and particle transport flow. Based on bubble characteristics, the flow patterns in a three-phase fluidized bed can be classified into dispersed bubble flow, discrete bubble flow, coalesced bubble flow, slug flow, churn flow, bridging flow and annular flow. The same flow patterns were observed for air-water systems, also in a column of inside diameter 82.6 mm. 5. Several empirical correlations were developed to predict the flow regime boundaries in the three-phase fluidized beds investigated. Equation (7.3) can be used to predict the onset of dispersed bubble flow, Equations (7.5) and (7.6) for the onset of slug flow, Equation (7.7) for the onset of churn flow and Equation (7.8) for the onset of bridging flow, respectively. In addition, the following new findings were also observed in this work: 1. At high superficial hquid velocity, two types of particle movement were observed. For 1.2 mm steel shot, i.e. small heavy particles, clustering occurs. In such a case, the particle transport velocity of the hquid (with superficial gas velocity equal to zero) is significantly greater than the settling velocity of single particles in the hquid phase. For 1.5 and 4.5 mm glass beads, on the other hand, no clusters were observed. In the latter case, the particle transport velocity of 222 the hquid (for superficial gas velocity equal to zero) is similar to the single particle terrninal velocity in the hquid phase. 2. Bubble characteristics in three-phase systems exhibit different trends with respect to variation of gas and hquid flowrates in the different flow regimes. As in bubble columns, many small bubbles exist in slug, churn and bridging flow. This differs from what is observed in slug and turbulent flow for gas-solid fluidized beds at high gas velocities. 3. The relationship between bubble travel length and average bubble chord length in the discrete and dispersed bubble flow regimes of a three-phase fluidized bed is the same as that in the corresponding flow regimes of a bubble column. This relationship is given by Equation (5.3), regardless of the different combinations of superficial gas and hquid velocities and of differences in particle properties. 9.2 Recommendations for Future Work Bubble characteristics exhibit different dependencies on gas and hquid superficial velocities in different flow regimes. It is important to keep the flow regime in mind when undertaking further study of hydrodynamics and scale-up of multiphase systems. Flow patterns and their transitions are governed by bubble characteristics, which depend not only on the gas and hquid superficial velocities, but also on the physical properties of the hquid phase. More work is needed to investigate the influence of the hquid properties, such as viscosity and surface tension, on flow regime transitions. 223 At different levels in a column, the flow patterns can be different for the same operating conditions. For example, at low gas velocities, bubbles grow as they ascend in coalesced bubble flow and this can lead to flow regime transition within the column. More work is needed to investigate flow regime transitions at different levels of the column, especially for the coalesced/slug transition in small columns. In addition, further study is needed to investigate the effect of column diameter on the flow regime transitions. The relationship between bubble travel length and average bubble chord length provides a potential alternative method to detennine flow patterns in multi-phase systems. This new method needs further exploration and development. 224 Nomenclature A parameter defined by Equation (6.72) a parameter defined by Equations (6.35a) and (6.37a) Ag cross-sectional area of column, m Ag area that corresponds to Taylor bubbles in a plot of probability density distribution function for differential pressure fluctuations area that corresponds to hquid phase in a plot of probability density distribution function for differential pressure fluctuations Ap projected surface of the particles per unit volume of the particles in the direction of the flow, 1/m Arg gas Archimedes number, dp3Pg(ps-pg)g/iJ,g2 Aig hquid Archimedes number, dp3p/ps-p^)g/ir/ Arg^ gas-hquid Archimedes number denned by Equation (6.43) b parameter defined by Equations (6.35b) and (6.37b) C0 parameter defined by Equation (6.53) CD drag coefficient, defined by Equation (6.6) CDL drag coefficient due to hquid flow CDW bubble-wake and particle interaction coefficient CDoo drag coefficient for mdividual particle. CS1 critical sohds concentration, sohd weight/slurry weight CS2 sohds concentration, sohd weight/liquid weight CS3 average sohds concentration in gas-free solid-liquid system, kg- solids/m3- slurry CS4 actual volume of sohds per unit cross sectional area of the column, m3/m2 C^ viscosity correction factor defined by Equation (6.62) D column diameter, m Dd distributor plate diameter, m 225 hydraulic diameter of hquid channel defined by Equation (6.19), m De' hydraulic diameter of hquid channel defined by Equation (6.36), m d cylindrical particle diameter, m db bubble diameter, m dN diameter of distributor orifice, m do diameter of distributor orifice, m dp equivolume sphere diameter, m dvs Sauter mean diameter or volume-surface diameter of bubble, m Es longimdinal dispersion coefficient for sohds, m2/s Frg gas Froude number, Ug2/(gdp) Fr, hquid phase Froude number, U/ / (g D) Frm gas-hquid Froude number, (Ug + U,)2/ (g D) FrgD gas Froude number based on colulmn diameter, Ug2/(gD) f local bubble or hquid bridging frequency, s_1 modified friction factor in gas-hquid-sohd fixed bed modified friction factor in hquid-sohd fixed bed fs signal frequency, Hz g gravitational acceleration, m/s2 Ho static bed height, m He static height of slurry above the bottom plate, m He height of draft tube, m K parameter defined by Equation (6.31) k ratio of the wake volume fraction to the gas holdup L distance between two elements of conductivity probe, m Ld dispersion height of slurry, m £ length of cylindrical particle, m h local individual bubble chord length, m 226 lh vs Sauter mean bubble chord length, m 1b local number average bubble chord length, m M number of bubbles observed during observation period M3 skewness of a distribution M4 kurtosis of a distribution m exponent in Equation (6.64) N number of signal increments NB modified bubble flow number, y/(Ubu^) n bed expansion index in Equation (6.8) nA number of signals having value of Vi ± (AV/2) P pressure, mm H20 P(Vi, AV) probability distribution function of Vi with signal increment of AV Po = P(Vo, AV) Pi = P(Vi, AV) p(db, £b) probabihty density distribution function of measured chord length, £b, when bubble diameter is db p(Vi) probabihty density distribution function of Vi Qg gas phase volumetric flow rate, m3/s hquid phase volumetric flow rate, m3/s R parameter defined by Equation (6.82) R(db) bubble size distribution function Reg superficial gas Reynolds number, UgPgD/iig Re'gmf Reynolds number at rmnimum hquid-sohd fluidization, Ugmf"dppg/^g ReL Reynolds number defined by Equation (6.78) Re/ modified Reynolds number with equivalent diameter, Dep^JYdx^) Re^ Reynolds number at rninimum gas-hquid-solid fluidization, U&nfdpp/u^ Re"^ Reynolds number at mmimum hquid-sohd fluidization, U^/dep^/u^ 227 RCmfg^ gas-liquid Reynolds number defined by Equation (6.44) Rejvf Reynolds number for gas at distributor orifice, UNdNPg/pg. Ret Reynolds number for particle terminal velocity in liquid phase, Utdpp/p,. ReA Reynolds number for linear hquid velocity, (U/s,)dpP/u^. Re^ Reynolds number for particle terminal velocity in homogeneous fluid, UoodpPjj/pH rH hydrauhc radius of hquid channel, m Sa cross-sectional area of annulus when a draft tube is installed, m2 Sc cross-sectional area of column, m2 Sd cross-sectional area of draft tube, m2 observation period, s ti_4 time sequence duration of conductivity probe in gas bubble or bubble time, s average bubble time, s bubble time measured from the upper element of probe, s ti2 bubble time measured from the lower element of probe, s t^ total test time, s Ub local number average bubble velocity, m/s _ . , , . gas volumetric flow rate LL superficial gas velocity, : , m/s 5 cross- sectional area of column Ugc critical gas velocity for complete suspension of particles at zero hquid velocity, m/s Ugjjjf minimum gas velocity for three-phase incipient fluidization, m/s Ugmf" minimum gas velocity for gas-sohd incipient fluidization, m/s UH homogeneous fluid velocity, defined by Equation (6.3), m/s „.,,..,,. hquid volumetric flow rate IL, superficial liquid velocity, 2 , m/s cross- sectional area of column (U^)dc transition hquid velocity between dispersed and coalesced bubble flow, m/s. Uftnf lrhnimum hquid velocity for three-phase fluidization, m/s il 228 minimum liquid velocity for liquid-solid fluidization, m/s uA particle transport liquid velocity in gas-liquid medium, m/s. UN superficial gas velocity based on orifice area, m/s. Us gas-liquid slip velocity, = Ug/sg - U/s^, m/s USN settling velocity of solid particles in aerated column, m/s ut particle teirninal velocity in liquid phase, m/s uz' axial component of hquid turbulence intensity, m/s terminal velocity of individual particle in homogeneous fluid, m/s V signal voltage, V V, discrete signal value, V VL relative linear velocity between hquid and particles defined by Equation (6.78), m/s Vmax maximum of the signal voltage, V vs particle pickup velocity, m/s V(t) voltage-time trace signal, V V mean value of V(t) Vo signal voltage of gas phase for conductivity probe, V Vi signal voltage of hquid phase for conductivity probe, V Var variance of a distribution Z height above distributor, m z(4) measured bubble length distribution function Greek letters: a fraction of gas phase holdup over total fluid volume fraction, = sg/(sg+s^) amf fraction of gas phase holdup over total fluid volume fraction at nritnmum fluidization. 3 = Ug/(Ug + U,) 229 AP pressure drop, mm H20 At time increment, s AT time shift between two signals from same probe, s AV signal increment, V 5A average absolute deviation defined by Equation (6.56) 5S root mean square deviation defined by Equation (6.57) s total fluid volume fraction = sg+e^, mVm3 static bed voidage, m3/m3 sg gas holdup, m3/m3 hquid holdup, m3/m3 £mf total fluid volume fraction under incipient fluidization condition, m3/m3 sohds holdup, m3/m3 particle sphericity y hquid surface tension, N/m Yf sohds relative wettability; for all systems tested in this study, yf = 1 gas viscosity, Ns/m2 viscosity of gas-hquid mixture defined by Equation (6.41), Ns/m2 *»H pseudo-homogeneous fluid viscosity defined by Equation (6.5), Ns/m2 Vi hquid viscosity, Ns/m2 Pc apparent continuous phase density defined by Equation (6.67), kg/m3 Pg gas phase density, kg/m3 Pgi density of gas-hquid mixture defined by Equation (6.42), kg/m3 PH pseudo-homogeneous fluid density defined by Equation (6.4), kg/m3 Pt liquid phase density, kg/m3 Ps particle density, kg/m3 °t standard deviation of bubble chord length, m standard deviation of bubble time, s 230 ov standard deviation of V(t), V xh T2 time shift between two elements of conductivity probe defined in Figure 2.8, s 231 References Abraham, M., A. 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ScL, 43, 2195-2200 (1988). 243 Appendix A Computer Programs for Data Acquisition and Processing A.1 Program for Data Acquisition and Calculation of PDF 'CONDl.BAS DAS-1600/1400/1200 ' - To run from the QuickBASIC Enviroment (up to Ver 4.5) you must load ' the appropriate quick library using the command line switch IL, 1 as follows QB IL D1600Q40 QBEXAMP1 (using version 4.0) QB IL D1600Q45 QBEXAMP1 (using version 4.5) ' - To run from the QuickBASIC Enviroment (Ver 7.0 and up) you must load ' the supplied quick library: D1600QBX.QLB using the command line . ' switch IL, as follows QBX IL D1600QBX QBEXAMP1 [IMPORTANT] When using QBX, make sure to replace the $INCLUDE file Q4IFACE.BI below with Q7IFACE.BI (both supplied to you ' with this software) 1 This file includes all function DECLARation supported by the driver. SINCLUDE: 'Q4IFACE.Br ' Dimension integer array to recieve A/D data. Note that, for reliable ' operation, this array should dimensioned twice a big as needed. 'Statement of subroutine COMMON SHARED maxl, max2, mini, min2 AS SINGLE COMMON SHARED pl(), p2() COMMON SHARED Xl(), Yl(), X2(), Y2() COMMON SHARED contrl, KI, K2, MA, MI AS INTEGER 'bubble number, control the loop DECLARE SUB SignalMM (F1N$, TP AS INTEGER) DECLARE SUB Compress (F1N$, TP AS INTEGER) DECLARE SUB Probability (F1N$, TP AS INTEGER) REM $DYNAMIC DIM BUFFA(30000) AS INTEGER REM $STATIC ' Variable used by driver functions. DIM NumOfBoards AS INTEGER DIM DERR AS INTEGER ' Error flag DIM STARTINDEX AS INTEGER ' Actual Index where data starts DIM DEVHANDLE AS LONG ' Device Handle DIM ADHANDLE AS LONG ' A/D Frame Handle 244 DIM STATUS AS INTEGER DIM count AS LONG DIM ADDR AS LONG DIMTFP AS LONG 1 Holds Status durin DMA ' Holds DMA transfer count ' Holds address needed by KSetDMABuf ' TOTAL SAMPLE POINT DIM FF AS STRING DIM CR AS LONG DIMDl AS SINGLE DIM D2 AS SINGLE ' SAVED DATA FILE NAME ' CLOCK RATE= 1 OMHz/F ' REAL DATA CHANNEL 1 ' REAL DATA CHANNEL 2 DIM FIN AS STRING DIM KEY1 AS STRING DIM FF1 AS STRING DIM DELAY AS STRING DIM TP AS INTEGER 'EXPERIMENT RUN NUMBER 'TEMPERATELY FILE NAME 'FOR CHECKING THE PROGRAM TOTAL POINT IN TEMPERATELY FILE DIM pl(l 10), p2(l 10), XP1(110), XP2(110) 'PROBABILITY FUNCTION DIM Xl(3000), Yl(3000), X2(3000), Y2(3000) 'COMPRESSED DATA DIM I AS INTEGER DIM X, Y AS SINGLE 'USED FOR SCREEN DISPLAY DIM FBI, FB2, EPG1, EPG2 AS SINGLE 'BUBBLE FREQUENCY AND HOLDUP DIM PTR1, PTR2 AS SINGLE 'USED FOR SEARCH PDF PEAK DIM TRA1, TRA2, TRB1, TRB2 AS INTEGER 'USED FOR PDF PEAKS POSITION DAS-1600/1400/1200" CLS COLOR 10, 8 LOCATE 1, 3: PRINT "COND1.BAS PRINT PRINT " This program can be used to" PRINT " (1) acqusite data," PRINT " (2) calculate the probability density function (PDF) of the data" PRINT " (3) calculate the probability function of Ti" PRINT PRINT " Make sure follow things before start this program" PRINT PRINT " 1. Two channels, 0# and 1# will be scaned" PRINT " 2. Sampling frequency is 2500 Hz" PRINT " 3. Sampling time is 3 sec. for every loop." PRINT " Note, the total sampling time will equal to (3 sec.X contrl)" PRINT " The max. contrl is 40. " PRINT " 4. If the number of the bubble is greater than 300, this program" PRINT " will stop even at (contrl < 10)." PRINT " 5. Several results are available." PRINT " (a) PDF (in the form of 4 column, 1 st and third are X-axes)" PRINT " will be saved in E:\JP\XXXX-p.dat" PRINT " (b) Compressed data (in the form 4 column,Xl(),Yl()....)" PRINT " will be saved in E:\JP\XXXX-c.dat" PRINT " (c) The probability function of bubble time (4 columns)" PRINT " will be saved in E:\JP\XXXX-s.dat" PRINT 245 COLOR 7, 8 DELAYS = INPUT$(1) 'Name the results file. INPUT "Input 4 characters to name the results file (automatic with '.DAT'):"; FF1$ 5 IF LEN(FF1$) <> 4 THEN BEEP: INPUT "File name should has 4 charaters. Type it again. ", FF1$ PRINT GOTO 5 END IF ON ERROR GOTO ErrorHandler ' OPEN "E:\JP\" + FF1$ + ".DAT" FOR INPUT AS #2 OPEN "E:\JP\" + FF1$ + "-p.DAT" FOR INPUT AS #2 CLOSE #2 COLOR 13, 8 BEEP: PRINT FF1$;: COLOR 14, 8: PRINT " has been used. Enter another file name. " COLOR 12, 8: INPUT "If you want to overwrite it TYPE y, if not TYPE file name again"; a$ PRINT COLOR 7, 8 IF a$ = "Y" OR a$ = "y" THEN GOTO ok ELSE FFl$ = a$ END IF GOTO 5 ok: CLOSE #2 ' PRINT "Sampling time (T) times Sampling frequency (f) should <=7500" '1010 INPUT "What is the sampling time"; T ' INPUT "What is the sampling frequency"; F ' COLOR 11, 12 ' PRINT "Time="; T;" sec", "Frequency="; F; "Hz." ' COLOR 7, 8 ' INPUT "Are you sure for T and F ? Y/N"; KEY1$ ' LF KEY1$ = "Y" OR KEY1$ = "y" THEN GOTO 1020 ELSE GOTO 1010 T = 3 F = 2500 1020 CLS ' STEP 1: This step is mandatory; it initializes the internal data tables ' according to the information contained in the configuration file ' DAS1600.CFG. Specify another filename if you are using a different ' configuration file. (ie. DAS1400.CFG, DAS1200.CFG) a$ = "U3-P1200.CFG" + CHR$(0) DERR = DAS1600DEVOPEN%(SSEGADD(a$), NumOfBoards) IF DERR <> 0 THEN BEEP: PRINT "ERROR "; HEX$(DERR);" OCCURRED DURING '..DEVOPEN'": STOP ' STEP 2: This step is mandatory; it establishes communication with the driver ' through the Device Handle. DERR = DAS 1600GETDE VHANDLE%(0, DEVHANDLE) 246 IF (DERR <> 0) THEN BEEP: PRINT "ERROR "; HEX$(DERR);" OCCURRED DURING ..GETDEVHANDLE"': STOP ' STEP 3: To perform any A/D operations, you must first get a Handle to an ' A/D Frame (Data tables inside the driver pertaining to A/D operations). DERR = KGetADFrame%(DEVHANDLE, ADHANDLE) IF (DERR <> 0) THEN BEEP: PRINT "ERROR "; HEX$(DERR);" OCCURRED DURING 'KGET ADFRAME'": STOP ' STEP 4: Before specifying the destination buffer for the acquired data, you ' must first call KMAKEDMABuf% to determine a suitable buffer address for the ' DMA controller to use. TFP = INT(T * F * 2) LOCATE 15, 1 ' D? TFP > 15000 OR TFP = 0 THEN COLOR 11,12: BEEP: PRINT "WARNING!!! Buffa is too large OR =0. Reduce T or F. T*F<=7500 BUT <> 0": COLOR 7, 8: GOTO 1010 DERR = KMAKEDMABuf%(TFP, BUFFA(), ADDR, STARTINDEX) IF DERR <> 0 THEN PRINT "Make Dma Buffer Error": STOP l ' STEP 5: Assign the data buffer address to the A/D Frame and specify the ' number of A/D samples. DAS1600ERR = KSetDMABuf%(ADHANDLE, ADDR, TFP) JJ? DAS1600ERR <> 0 THEN BEEP: PRINT "ERROR "; HEX$(DAS1600ERR);" OCCURRED DURING 'KSetDMABuf": STOP ' STEP 6: Choose the Start and Stop channels and overall gain code to use ' during acquisition. DERR = KSetStartStopChn%(ADHANDLE, 0, 1) IF DERR <> 0 THEN BEEP: PRINT "ERROR "; HEX$(DERR);" OCCURRED DURING 'KSetStrtStpChn'": STOP ' STEP 7: This example program uses the internal (by default) conversion clock ' source; the following call specifies the divisor to the Clock Source ' (1MHz or 10MHz) CR= 10000000 / INT(F) DERR = KSetClkRate%(ADHANDLE, CR) IF DERR <> 0 THEN BEEP: PRINT "ERROR "; HEX$(DERR);" OCCURRED DURING 'KSetClkRate'": STOP ' STEP 8 : Specify Free Run mode. DERR = KSetADFreeRun%( ADHANDLE) IF DERR <> 0 THEN BEEP: PRINT "ERROR "; HEX$(DERR);" OCCURRED DURING 'KSetADFreeRun'": STOP COLOR 17, 11 LOCATE 15, 1: PRINT "Press a key to START A/D Acquisition..." COLOR 7, 8 DO LOOP WHILE INKEY$ = "" ' STEP 9: Start data acquisition according to the setup performed above. CLS LOCATE 10, 3 COLOR 16, 11 PRINT "THE COMPUTER IS ACUQISITING THE DATA " 247 PRINT "" PRINT "DONT TOUCH THE KEYBOARD" PRINT "" PRINT "Time="; T;" sec", "Frequency="; F; "Hz." COLOR 7, 8 FOR contrl = 1 TO 10 DERR = KDMAStart%(ADHANDLE) IF DERR <> 0 THEN BEEP: PRINT "ERROR "; HEX$(DERR);" OCCURRED DURING 'KDMA'": STOP ' COLOR 16, 11 ' LOCATE 15, 1: PRINT "Press a key to STOP Acquisition... " ' COLOR 7, 8 ' STEP 10: Monitor the status and sample transfer count untill done 100 DERR = KDMAStatus%(ADHANDLE, STATUS, count) LF DERR <> 0 THEN BEEP: PRINT "ERROR "; HEX$(DERR);" OCCURRED DURING 'KDMAStatus'": GOTO 300 ' LOCATE 13, 1: PRINT "COUNT : "; count IF LNKEY$ <> "" GOTO 300 LF (STATUS = 1) THEN GOTO 100 ' LOCATE 15, 1: PRINT "Data acquisition completed. . . ' STEP 11: Stop DMA operation in case user interrupted or an error occurred. ' This step is not required upon normal termination of DMA; but it can't hurt! 300 DERR = KDMAStop%(ADHANDLE, STATUS, count) LF DERR <> 0 THEN BEEP: PRINT "ERROR "; HEX$(DERR);" OCCURRED DURING 'KDMAStop'": STOP STEP 12: Save the data just acqusited. . .Use Startlndex as obtained earlier through call to KMAKEDMABuf as shown. COLOR 3, 9 LOCATE 15, 1 FF$ = "e:\jp\" + FF1$ + ".DAT" FF$ = "e:\jp\pzte.DAT" OPEN FF$ FOR OUTPUT AS #1 FORI% = 0TOTFP/2- 1 DI = BUFFA(2 * 1% + 1 + STARTLNDEX) /16 DI = SGN(D1) * (ABS(D1) - 2048) / 4096 * 10 D2 = BUFFA(2 * 1% + 2+ STARTLNDEX)/16 D2 = SGN(D2) * (ABS(D2) - 2048) / 4096 * 10 PRINT #1, DI, D2 PRINT ; DI, D2 NEXT 1% CLOSE #1 ' STEP 13: Free a frame and return it to the pool of available frames ' DERR = KFreeFrame%(ADHANDLE) ' LF DERR <> 0 THEN BEEP: PRINT "ERROR "; HEX$(DERR);" OCCURRED DURING 'KDMAFreeRun'": STOP STEP 14: Display the data on the screen in the form of graph TP% = TFP COLOR 11, 12 LOCATE 20, 5 INPUT "Do you want to display the ORIGINAL DATA? Y/N "; KEY1$ LF (KEY1$ = "n" ORKEYl$ = "N") THEN GOTO 1030 ELSE 1025 248 COLOR 7, 8 1025 SignalMM FF$, TP%, max 1, min 1, max2, min2 DisplaySignal FF$, TP%, maxl, mini, max2, min2 ' Step 15 calculate the probability of the signal '1030 COLOR 11, 13 ' LOCATE 20, 5 ' INPUT "Do you want to calcualte the PROBABILITY DISTRIBUTION? Y/N "; KEY1$ ' IF (KEY1$ = "n" OR KEY1$ = "N") THEN GOTO 1040 ELSE 1035 ' COLOR 7, 8 1035 SignalMM FF$, TP% Probability FF$, TP% FORI%= 1 TO 101 XP1(I%) = XP1(I%) * (FIX(contrl) - 1) / FlX(contrl) + pl(I%) / FlX(contrl) XP2(I%) = XP2(I%) * (FIX(contrl) - 1) / FIX(contrl) + p2(I%) / FIX(contrl) NEXT 1% 'Step 16: display PDF SCREEN 1 COLOR 11,0 LOCATE,, 0 CLS LINE (30, 15)-(300, 90), 1, BF LINE (30, 110)-(300, 185), 1, BF LOCATE 1, 1 PRINT "Distribution of the DATA" LOCATE 3, 5 PRINT "UPPER—2" LOCATE 15, 5 PRINT "LOWER— 1" FOR 1% = 1 TO 101 X = INT(FIX(I% - 1) * 2 + 30.5) Y = INT(90 - XP2(I%) * 600 + .5) LINE (X, 90)-(X, Y), 2 Y = INT(185 - XP1(I%) * 600 + .5) LINE (X, 185)-(X, Y), 2 NEXT 1% 'Step 17: compress the data Compress FF$, TP% KILL "e:\jp\TEMP.DAT" IF (KI >= 500 AND K2 >= 500 AND contrl >= 6) THEN GOTO 1050 NEXT contrl contrl = contrl - 1 1050 LOCATE 13, 1: PRINT "Data acquisition completed. . . BEEP: BEEP: BEEP DELAYS = JJNPUT$(1) LOCATE,, 1 SCREEN 0 WIDTH 80 'Step 18: save PDF LOCATE 15, 5 249 PRINT "Save the PROBABILITY data." PRINT "PDFs data will be saved in" PRINT " e:\jp\"; FF1$; "-p.dat" OPEN "E:\JP\" + FF1$ + "-P.DAT" FOR OUTPUT AS #2 FORI% = lTO 101 PRINT #2, FLX(I% - 1) * .01, XP1(I%), FLX(I% - 1) * .01, XP2(I%) NEXT 1% CLOSE #2 'Step 19: save compressed data PRINT "Compressed data will be saved in" PRINT " e:\jp\"; FF1$; "-c.dat" EPG1 = 0 FORI%=lTOKl EPG1=EPG1 +Y1(I%) NEXT 1% EPG1 = EPG1 / F / FLX(contrl) / T EPG2 = 0 FOR 1% = 1 TO K2 EPG2 = EPG2 + Y2(I%) NEXT 1% EPG2 = EPG2 / F / FIX(contrl) / T FBI = FIX(K1) / FIX(contrl) / T FB2 = FIX(K2) / FIX(contrl) / T OPEN "E:\JP\" + FF1$ + "-c.DAT" FOR OUTPUT AS #2 OPEN "E:\JP\TEM1.DAT" FOR OUTPUT AS #3 PRINT #2, "Sampling Time=", FIX(contrl) * T, "Sampling frequency-", F PRINT #2, "Measuring loop", contrl PRINT #2," Channel 0 Channel 1" PRINT #2, "No. of bubbles", Kl, K2 PRINT #2, "Bubble freq. ", FBI, FB2 PRINT #2, "Gas holdup ", EPG1, EPG2 LF Kl >= K2 THEN MA% = Kl ELSE MA% = K2 FORI%= lTOMA% PRINT #2, X1(I%), Y1(I%), X2(I%), Y2(I%) PRINT #3, Y1(I%), Y2(I%) NEXT 1% CLOSE #3 CLOSE #2 'Step 20: calculate the distribution of bubble length LF Kl<= K2 THEN MI% = Kl ELSE MI% = K2 TP% = 2* MI% F1N$ = "E:\JP\TEM1.DAT" SignalMMFlN$, TP% Probability F1N$,TP% 'Step 21: save the distribution of bubble size PRINT "PDF data of the (Ti) will be saved in" PRINT " e:\jp\"; FF1$; "-s.dat" OPEN "E:\JP\" + FF1$ + "-s.DAT" FOR OUTPUT AS #2 FOR 1% = 1 TO 101 PRINT #2, FIX(I% - 1) * .01 * (maxl - mini) + mini, pl(I%), FIX(I% - 1) * .01 * (max2 - min2) + min2, p2(I%) 250 NEXT 1% CLOSE #2 BEEP DELAYS = INPUT$(1) 'Step 22: display the distritution of the bubble size SCREEN 1 COLOR 5, 3 LOCATE,, 0 CLS LINE (30, 15)-(300, 90), 1, BF LINE (30, 110)-(300, 185), 1, BF LOCATE 1, 1 PRINT "Distribution of (Ti)"; "CONTRl="; contrl LOCATE 3, 5 PRINT "UPPER—2", "K2="; K2 LOCATE 15, 5 PRINT "LOWER—1", "Kl="; KI FOR 1% = 1 TO 101 X = INT(FIX(I% - 1) * 2 + 30.5) Y = INT(90 - p2(I%) * 300 + .5) LINE (X, 90)-(X, Y), 2 Y = INT(185 - pl(I%) * 300 + .5) LINE(X, 185)-(X, Y),2 NEXT 1% DELAYS = INPUT$(1) LOCATE,, 1 SCREEN 0 WIDTH 80 1100 END ErrorHandler: RESUME ok SUB Compress (FINS, TP%) PTR1 = pl(l): TRA1 = 1 PTR2 = p2(l): TRA2 = 1 FOR I = 2 TO 101 IF PTR1 < pl(I) THEN PTR1 = pl(I): TRA1 = I IF PTR2 < p2(I) THEN PTR2 = p2(I): TRA2 = I NEXT I IF TRA1 >= 20 AND TRA1 <= 70 THEN PRINT "#1—The peak is within 20%-70%" thresl = mini + .5 * (maxl - mini) ELSEIF TRA1 < 19 THEN PTR1 =pl(101): TRB1 = 101 FOR I = 71 TO 100 JJ? PTR1 < pl(I) THEN PTR1 = pl(I): TRB1 = I NEXT I thresl = mini + ((FIX(TRA1) + FIX(TRB1)) / 2 - 1) * (maxl - mini) * .01 ELSE TRB1 =TRA1 PTR1 = pl(l): TRA1 = 1 251 FOR I = 2 TO 19 LF PTR1 < pl(I) THEN PTR1 = pl(I): TRA1 = I NEXT I thresl = mini + ((FIX(TRA1) + FIX(TRB1)) / 2 - 1) * (maxl - mini) * .01 END LF LF TRA2 >= 20 AND TRA2 <= 70 THEN PRINT "#2—The peak is within 20%-70%" thres2 = min2 + .5 * (max2 - min2) ELSELF TRA2 < 19 THEN PTR2 = p2(101): TRB2 = 101 FOR I = 71 TO 100 LF PTR2 < p2(I) THEN PTR2 = p2(I): TRB2 = I NEXT I thres2 = min2 + ((FIX(TRA2) + FIX(TRB2)) / 2 - 1) * (max2 - min2) * .01 ELSE TRB2 = TRA2 PTR2 = p2(l): TRA2 =1 FORI = 2T019 LF PTR2 < p2(I) THEN PTR2 = p2(I): TRA2 = I NEXT I thres2 = min2 + ((FLX(TRA2) + FIX(TRB2)) / 2 - 1) * (max2 - min2) * .01 END IF ST1 = maxl ST2 = max2 OPEN F1N$ FOR INPUT AS #1 FOR I = 1 TO TP% / 2 INPUT #1, si, s2 LF (ST1 > thresl AND si <= thresl) THEN X1(K1) = I + (contrl - 1) * TP% / 2 LF (ST1 <= thresl AND si > thresl) THEN Y1(K1) = I + (contrl - 1) * TP% / 2 - X1(K1): Kl = K1+ 1 ST1 = si LF (ST2 > thres2 AND s2 <= thres2) THEN X2(K2) = I + (contrl - 1) * TP% / 2 LF (ST2 <= thres2 AND s2 > thres2) THEN Y2(K2) = I + (contrl - 1) * TP% / 2 - X2(K2): K2 = K2 + 1 ST2 = s2 NEXT I CLOSE #1 END SUB SUB Probability (F1N$, TP%) ' This programm is used for calculation of the probability density ' distribution function of the signal or bubble chold length, etc.. ' DLMP1(500),P2(500) '3125 LET iii = INT((maxl - mini) * 100 + .5) + 2 '3127 LET ii2 = INT((max2 - min2) * 100 + .5) + 2 ' LFiil >ii2 THEN ii = iii ELSE ii = ii2 II = 101 FOR 1 = 1 TO II pl(l) = 0 p2(l) = 0 NEXT 1 OPEN F1N$ FOR INPUT AS #1 FORI= 1 TOTP%/2 INPUT #1, si, s2 11 = INT(100 * (si - mini) / (maxl - mini) + 1.5) pl(ll) = pl(ll) + 2/TP% 252 12 = rNT(100 * (s2 - min2) / (max2 - min2) + 1.5) p2(12) = p2(12) + 2 / TP% NEXT I CLOSE #1 END SUB SUB SignalMM (F1N$, TP%) OPEN F1N$ FOR INPUT AS #1 LET maxl = -5: LET mini = 5 LET max2 = -5: LET min2 = 5 FORj= 1 TOTP%/2 INPUT #1, si, s2 IF si >= maxl THEN LET maxl IF sl<= mini THEN LET mini IF s2 >= max2 THEN LET max 2 IF s2 <= min2 THEN LET min2 NEXT j CLOSE #1 END SUB A.2 Calculation for Moments of a Distribution PROGRAM pc C driver for 2-channel data processing routine moment C cu uses gammq, gser, gcf, gammln, beta INTEGER ND,I,L1,L2,L,Y(3) REAL S1(3000),P1(3000),S2(3000),P2(3000) REAL MEAN1,MEAN2,SD1,SD2,SK1,SK2 REAL DFCH,CHSQ,PROBCH REAL F,DFF,PROBF,BETAI REAL T,VAR,DFT,PROBT CHARACTER FNAME*6, FLD* 1, LLD* 1,X(3) CHARACTER*40 FN CHARACTER*40 FN1 C open data file for MOMENT calculation and then close it WRTTE(*,*) "Eiiiiitiiiiiiiiiiiiiiiiiiiiiiii WRITE(*,*) "° This program takes the data from E:\JP\xxxx-y.dat' WRlTE(*,*) ""calculate the mean, standard deviation and skewness. WRtTE(*,*) "° !!! Make sure there are 4 columns of data !!! 0 " WjcJTEC*,*)"° The data is the probability function 0 " WRITE(*,*)"° Data file name should has 6 characters0" WRTTE(V) "° The results will be saved in E:\JP\xxxx-yR.DAT °" WRTTE(*,*) "miiiiiiiiiiiiiiiiiniiiiiiiin " WRITE(*,*) •' c c Step 1: open file and obtain the probability function WRTTE(*,*) 'First LETTER of the data file e.g. L or M, etc' READ(*,'(A)') FLD = sl = sl = s2 = s2 253 WRITE(*,*) 'Last LETTER of the data file e.g. p or s, etc' READ(*,'(A)') LLD WRITE(*,*) 'jjata file name series, e.g. 123,132, etc' READ(*,*)L1,L2 DO3000L=Ll,L2 Y(1)=(MOD(L,10)) Y(2)=(MOD(L/10,10)) Y(3)=(MOD(L/100,10)) X(l)=CHAR(Y(l)+48) X(2)=CHAR(Y(2)+48) X(3)=CHAR(Y(3)+48) FNAME=FLD // X(3) // X(2) //X(l)// '-'//LLD WRITE(*,*) FNAME FN='e:\jpV // FNAME // '.daf OPEN(UNlT=l,FILE=FN,STATUS='OLD,) ND=0 DO WHILE (EOF(l) .NEQV. .TRUE.) ND=ND+1 READ(1,*) S1(>ID),P1(ND),S2(ND),P2(ND) ENDDO CLOSE(l) c Step 2: calculate mean, SD and skewness MEAN1=0. MEAN2=0. DOI=l,ND MEAN1=MEAN1+S 1(I)*P1(I) MEAN2=MEAN2+S2(I)*P2(I) ENDDO SD1=0. SD2=0. DO 1=1, ND SD1=SD1+P1(I)*(S1(I)-MEAN1)**2 SD2=SD2+P2(I)*(S2(I)-MEAN2)**2 ENDDO SD1=SQRT(SD1) SD2=SQRT(SD2) SK1=0. SK2=0. DOI=l,ND SK1=SK1+P1(I)*((S1(I)-MEAN1)/SD1)**3 SK2=SK2+P2(I)*((S2(I)-MEAN2)/SD2)**3 ENDDO write(*,*) meanl,sdl,skl write(*,*) mean2,sd2,sk2 C C Step 3: calculate Chi-squred, F-test and T-test DOI=l,ND P1(I)=P1(I)*ND P2(I)=P2(I)*ND ENDDO CALL CHSTWO(Pl ,P2,ND, 1 ,DFCH,CHSQ,PROBCH) 254 WRITE (*,*) DFCH,CHSQ,PROBCH C C Step 3.1: F-test IF(SD1 .GT. SD2) THEN F=(SD1/SD2)**2 ELSE F=(SD2/SD1)**2 ENDIF ND=2*ND DFF=ND-1 PROBF=2. *BET AI(0.5 *DFF,0.5 *DFF, 1/(1+F)) IF (PROBF .GT. l.)PROBF=2.-PROBF write(*,*) dff,F,PROBF C C Step 3.2: T-test c DFT=2*ND-2 c VAR=(ND-1)/DFT*(SD1**2+SD2**2) c T=(MEAN1-MEAN2)/SQRT(VAR*(2./ND)) c PROBT=BETAI(0.5*DFT,0.5,DFT/(DFT+T**2)) c write(*,*) dft, t, probt c Step 4: save the result FN1='E:\JPY//FNAME//'R.DAT OPEN(UWr=2,FILE=FNl,STATUS='UNKNOWN') . write(2,'(lx,a/)') 'Moments of the original signal distribution' write(2,'(lx,t29,a,t42,a/)') 'Channel l','Channel2' write(2,'(lx,a,t25,2fl2.4)') 'Mean :',MEAN 1 ,MEAN2 vvrite(2,'(lx,a,t25,2fl2.4)') 'Standard Deviation :',sdl,sd2 write(2,'(lx,a,t25,2fl2.4)') 'Skewness :',skl,sk2 write(2,'(lx,a,t25,2el2.4)') 'Chi-squred :',chsq,probch write(2,'(lx,a,t25,2el2.4)') 'F-test :',f,probf CLOSE(2) 3000 CONTINUE STOP END A.3 Calculation of Bubble Velocity and Bubble Chord Length DECLARE SUB Compress (FLN$, TP%) 'BVC.BAS ' This is used to calculate bubble velocity and bubble chord length. ' Source file shall be in E:\JPY File name would be xxxx-c.dat. ' When file name is been asked by the computer, only xxxx is needed to key in. ' The probability density function of bubble velocity and cord length will ' be saved in E:\JP\ under the name of xxxx-cr.dat. ' Total number of the bubble (KI and K2), number of the bubbles which ' meet the critera, as well as the distribution of the bubble velocity and ' bubble cord length will be record in this file. 255 'Statement of subroutine COMMON SHARED maxv, maxl, minv, mini AS SINGLE COMMON SHARED pv(), pl() AS SINGLE COMMON SHARED Vb(), Lb() AS SINGLE COMMON SHARED CONTR1, Kl, K2, MA, MI AS INTEGER 'bubble number 'contrail the loop DECLARE SUB SignalMM (TP AS INTEGER) DECLARE SUB Probability (TP AS INTEGER) REM $STATIC ' Variable used by this program. DIM FF AS STRING ' SAVED DATA FILE NAME DIM D1 AS SINGLE ' REAL DATA CHANNEL 1 DIM D2 AS SINGLE ' REAL DATA CHANNEL 2 DIM FLN AS STRING 'EXPERIMENT RUN NUMBER DLMKEY1 AS STRING DLM S, T, FFF AS STRING 'TEMPERATELY FILE NAME DIM DELAY AS STRING 'FOR CHECKING THE PROGRAM DLM TP AS INTEGER 'TOTAL POINT IN TEMPERATELY FLLE DLM pv(l 10), pl(110) AS SINGLE 'PROBABILITY FUNCTION DLM Xl(4000), Yl(4000), X2(4000), Y2(4000) 'COMPRESSED DATA DLM Vb(4000), Lb(4000) AS SINGLE 'BUBBLE VELOCITY AND CORD LENGTH DLM I, J, N, Ifn, II, 12 AS INTEGER DLM X, Y AS SINGLE 'USED FOR SCREEN DISPLAY DLM FBI, FB2, EPG1, EPG2 AS SINGLE 'BUBBLE FREQUENCY AND HOLDUP DLM F AS SINGLE 'SAMPLING FREQUENCY DLM AVEV, AVEL, SDV, SDL, SKV, SKL AS SINGLE 'AVERAGE, SD, AND SKEWNESS DLM SUMAV, SUMAL AS SINGLE 'FOR MOMENTS CALN COLOR 10, 8 LOCATE 1, 3: PRINT " Bubble Velocity and Bubble Cord Length BVC.BAS " PRINT "" PRINT " This program calculates bubble velocity and bubble cord length." PRINT " Source file shall be in E:\JPY File name would be xxxx-c.dat." PRINT " When file name is been asked, only xxxx is needed to key in." PRINT "" PRINT " The results will be saved be saved in E:\JP\ under the name" PRINT " ofxxxx-cr.dat." PRINT "" PRINT " Total number of the bubble (Kl and K2), number of the bubbles" PRINT " which meet the critera, as well as the distribution of the" PRINT " bubble velocity and bubble; cord length will be recorded" PRINT " in this file." COLOR 3, 9 'Step 1: input the file name INPUT "Type the FRIST letter of the experamental run No. e.g. R or C"; FFF$ INPUT "What is the serial number? (Begin with and end with. e.g. from II to 12)", II, 12 FOR Ifn = 11 TO 12 S$ = FFF$ + LTRIM$(STR$(Ifn)) T$ = STRING$(4 - LEN(S$), "0") S$ = FFF$ + T$ + LTRLM$(STR$(Ifn)) . FF$ = "E:\JP\" + S$ + "-C.DAT" ' INPUT "Source file? 4 characters (automatic with '-c.DAT'):"; FF1$ 256 COLOR 7, 8 FF$ = "e:\jp\" + FF1$ + "-c.DAT" OPEN FF$ FOR INPUT AS #1 INPUT #1, XX, XX, T, XX, XX, F INPUT #1, XX, XX, CONTR1 INPUT #1, A$ INPUT #1, XX, XX, XX, KI, K2 INPUT #1, A$, B$ IFK1 >= K2 THEN MA = K1 ELSE MA = K2 ENDIF FORI%=lTOMA INPUT #1, X1(I%), Y1(I%), X2(I%), Y2(I%) NEXT 1% CLOSE #1 ' Calculate bubble velocity and cord length J% = 0 N = 0 FORI=lTOKl-l 100 IF I - N >=K2 - 2 THEN GOTO 300 IF (X1(I) < X2(I - N) AND X2(I - N) < X1(I) + Y1(I) AND X1(I) + Y1(I) < X2(I - N) + Y2(I - N)) THEN J% = J% + 1 Vb(J%) = .001 * F * 2 / (2 * X2(I - N) + Y2(I - N) - 2 * X1(I) - Y1(I)) Lb(J%) = Vb(J%) * Y1(I) / F GOTO 200 ELSEIF X1(I) > X2(I - N) THEN N = N-1 GOTO 100 ELSE N = N+ 1 END IF 200 NEXT I 300 PRINT "OOOK" 'Calculate mean, SD, and skewness SUMAV = 0 SUMAL = 0 FOR I = 1 TO J% SUMAV = SUMAV + Vb(I) SUMAL = SUMAL + Lb(I) NEXT I AVEV = SUMAV / FIX(J%) AVEL = SUMAL / FIX(J%) SUMAV=0 SUMAL = 0 FOR I = 1 TO J% SUMAV = SUMAV + (AVEV - Vb(I)) A 2 SUMAL = SUMAL + (AVEL - Lb(I)) A 2 NEXT I SDV = SQR(SUMAV / FIX(J% - 1)) SDL = SQR(SUMAL / FIX(J% - 1)) SUMAV = 0 257 SUMAL = 0 FORI = 1 TOJ% SUMAV = SUMAV + ((AVEV - Vb(I)) / SDV) A 3 SUMAL = SUMAL + ((AVEL - Lb(I)) / SDL) A 3 NEXT I SKV = SUMAV / FIX(J%) SKL = SUMAL / FLX(J%) ' Calculate the probability of the signal SignalMM J% Probability J% 'Display PDF SCREEN 1 COLOR 11,0 LOCATE,, 0 CLS LINE (30, 15)-(300, 90), 1, BF LINE (30, 110)-(300, 185), 1, BF LOCATE 1, 1 PRINT "Kl="; Kl; "K2="; K2; "J%="; J% LOCATE 2, 13 PRINT "Distribution of Velocity" LOCATE 4, 18 PRINT "AVE-V="; AVEV LOCATE 5, 19 PRINT "SD-V="; SDV LOCATE 6, 19 PRINT "SK-V="; SKV LOCATE 14, 10 PRINT "Distribution of Cord Length" LOCATE 16, 18 PRINT "AVE-L="; AVEL LOCATE 17, 19 PRINT "SD-L="; SDL LOCATE 18, 19 PRINT "SK-L="; SKL FORI%=lTO 101 X = INT(FIX(I% - 1) * 2 + 30.5) Y = INT(90 - pv(I%) * 500 + .5) LINE (X, 90)-(X, Y), 2-Y = LNT(185 - pl(I%) * 500 + .5) LINE (X, 185)-(X, Y), 2 NEXT 1% DELAYS = LNPUT$(1) LOCATE,,1 SCREEN 0 WIDTH 80 'Save the distribution of bubble velocity and cord length PRINT "PDF data of Vb and Lb will be saved in" PRINT " e:\jp\"; S$; "-vr.dat" OPEN "E:\JP\" + S$ + "-vr.DAT" FOR OUTPUT AS #2 ' PRINT #2, "Kl=", Kl, "K2="; K2, "J%=", J% 258 ' PRINT #2, "Average", AVEV, AVEL ' PRINT #2, "SD", SDV, SDL ' PRINT #2, "Skewness", SKV, SKL ' PRINT #2, "Vb", "PDFVb", "lb", "PDFlb" FOR 1% = 1 TO 101 PRINT #2, FIX(I% - 1) * .01 * (maxv - minv) + minv, pv(I%), FIX(I% - 1) * .01 * (maxl - mini) + mini, pl(I%) NEXT 1% CLOSE #2 NEXT Ifn END SUB Probability (TP%) ' This programm is used for calculation of the probability density ' distribution function of the signal or bubble chold length, etc.. 11= 101 FOR 1 = 1 TO II pv(l) = 0 pl(l) = 0 NEXT 1 FOR I = 1 TO TP% 11 = INT(100 * (Vb(I) - minv) / (maxv - minv) + 1.5) pv(ll) = pv(U) + 1 / FIX(TP%) 12 = INT(100 * (Lb(I) - mini) / (maxl - mini) + 1.5) pl(12) = pl(12) + 1 / FIX(TP%) NEXT I END SUB SUB SignalMM (TP%) LET maxv = -5: LET minv = 100 LET maxl = -5: LET mini = 100 FORI=lTOTP% IF Vb(I) >= maxv THEN LET maxv = Vb(I) IF Vb(I) <= minv THEN LET minv = Vb(I) IF Lb(I) >= maxl THEN LET maxl = Lb(I) IF Lb(I) <= mini THEN LET mini = Lb(I) NEXT I END SUB 259 Appendix B Experimental Data 260 CO w <tH NO Tf OO iff ^—' CO o o CN oaT CO w cn oo Tf ON oo Tf ON CN ON T-H NO NO Tf l> CN ON Tf cn r- ON CN CN cn CN Tf T-H t~ Wl © Tf IV 00 © Wl CN cn oo T-H ON © 00 Os T-H NO 00 1-H NO Tf r- Os Tf wi Wl NO 00 cn Wl cn 00 CN r- Wl 00 cn Wl CN wi T—< W) Tf ON -H Os NO NO wi © CN NO 00 Tf r-~ Tf Tf Os ON CN 00 © O o T—1 CN cn Tf NO NO I-- Os 0\ cn Wl r-» 00 cn cn cn cn T-H Wl CN Tf cn o o o © © © o ©' ©' © © T-H CN CN CN CN CN CN CN CN CN NO wi OS so NO 00 T-H Os in 00 ON OS Tf Wl 00 NO Tf Tf c~ Tf ON 00 Tf Tf © Tf (~ cn as t~ © r-~ 00 Tf ON NO cn © r- cn r~-r~- Tf Wl T-H cn cn 00 Tf r- © Wl CN ON 00 T-H 00 NO CN CN C~ cn cn NO w> wi Tf 00 Tf 1-H 00 ON NO cn ON cn 00 ON Wl cn Tf Wl Tf OO T-H o O i—i cn Wl NO © 00 ON T-H T-H C NO Wl NO NO Wl © Wl cn cn cn © © © ©' ©' o © © © • cn Tf Tf Tf c~ 00 r-- 00 CN CN Wl NO ON T-H Os NO Wl Tf cn CN l> Tf Tf Tf 00 wi wi wi T-H cn 00 T-H Tf T-H r- Tf T-H r- Wl Os wi NO r- CN OO Os Os ON CN cn Tf Tf oo CN © CN cn ON ON © NO o O o T-H i-H T-H T-H f-H CN T-H CN CN CN CN cn Tf Wl NO NO 00 © CN o o o o o © © © © © © © © © © © © © © © T-H Tf © © ©' © © o ©' © © © © .© © o' ©' ©' ©' ©' © ©' ©' © ©' • 00 CN NO NO T-H Tf 00 NO Wl Tf Tf r- ON Tf 00 2925 ON r- NO CN cn T-H f- 00 ON NO T-H 00 © oo T—1 r-. 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