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Dimensionless hydrodynamic simulation of high pressure multiphase reactors subject to foaming Macchi, Arturo 2002

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Dimensionless Hydrodynamic Simulation of High Pressure Multiphase Reactors Subject to Foaming By Arturo Macchi B.Eng, Ecole Polytechnique de Montreal, 1995 M.A.Sc, Ecole Polytechnique de Montreal, 1997 A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF THE REQUIREMENTS FOR THE D E G R E E OF DOCTOR OF PHILOSOPHY In THE F A C U L T Y OF G R A D U A T E STUDIES (Department of Chemical and Biological Engineering) We accept this thesis as conforming to the required standard The University of British Columbia March 2002 ©Arturo Macchi, 2002 UBC Special Collections - Thesis Authorisation Form Page 1 of 1 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. The U n i v e r s i t y of B r i t i s h Columbia Vancouver, Canada Department 11 Abstract Safoniuk (1999) proposed that three-phase fluidized bed hydrodynamics can be scaled based on geometric similarity and matching of five dimensionless groups: the M-group, M = g ( p L -Pg)H-L 4/(pL 2o" 3); a modified Eotvos number, Eo* = g ( p L - pg)dp2/cr; the liquid Reynolds number, Re L = PLdpUi/p-L; a density ratio, P P / P L ; and a superficial velocity ratio, U g/UL- This approach implicitly assumes that the major physical properties of the liquid (density, viscosity and surface tension) are sufficient to characterize the bubble coalescence behaviour and that the influence of the gas density is negligible. Since many commercial reactors operate at high pressure with multicomponent liquids that may be subject to foaming, an experimental program was designed to test whether multiphase systems that match Safoniuk's criteria but differ in interfacial properties and gas density produce the same fluid dynamic parameters. The liquid density, viscosity and surface tension were found to be insufficient to characterize bubble coalescence in multicomponent solutions. Multicomponent and contaminated liquids present interfacial effects that reduce the bubble coalescence rate and hinder the bubble rise velocity resulting in greater gas holdups than in pure monocomponent liquids under similar conditions. The extent of interfacial effects depends on the bubble size and is most important for Eo < 40. Additional liquid physical properties such as dynamic surface tension and dilatational surface elasticity were also found insufficient since surface-active components were well-dispersed and in equilibrium with the gas-liquid interface. Gas density was found to be an important parameter in both gas-liquid and gas-liquid-solid systems. The dispersed bubble flow regime is sustained to higher gas velocities and gas holdups for denser gases. This phenomenon can be attributed to enhanced bubble break-up, rather than to the formation of smaller bubbles with increasing gas density. As it stands, the dimensional similitude approach will fail when the effects of surface-active contaminants are important since the physical properties and forces that effectively characterize the bubble coalescence mechanism in multicomponent/contaminated liquids are I l l still unknown. The effect of pressure via gas density can be taken into account by the dimensionless group p g / p L -As a secondary objective, a study on the role of particles in establishing radial uniformity of fluids that are initially maldistributed was undertaken in a 127 mm inner diameter column with 3.3-mm polymer particles and 3.7-mm glass beads (densities 1280 and 2510 kg/m 3, respectively), with water and air as the liquid and gas. The effects of initial gas-liquid spatial maldistribution on overall phase holdups were not very significant for the glass beads since radial non-uniformities seemed to be eliminated relatively quickly. For the lighter polymer beads, maldistribution at the distributor only caused a significant drop in overall bed voidage and gas holdup at higher gas velocities. Finally, the measurement of cross-sectional phase holdups using the attenuation and velocity change of ultrasound was attempted in a 292 mm inner diameter column with air, water and uniform glass beads of 1.3 mm diameter. The approach worked relatively well for gas-liquid and liquid-solid systems. However, signal attenuation greatly limits its use in three-phase fluidized beds, as it is difficult to operate at a frequency that ensures transmission through both dispersed phases. Slurry bubble columns with lower dispersed phase holdups and smaller particles present less attenuative media and are better suited to this technique. IV Table of Contents Abstract i i Table of Contents iv List of Tables vii List of Figures viii Acknowledgement xiii Dedication xiv 1. Introduction 1 1.1 Bitumen Upgrading in Canada 1 1.2 Investigating the Performance of Three-Phase Fluidized Beds 3 1.3 Hydrodynamic Studies under Hydrocarbon Processing Conditions 5 1.4 Hydrodynamic Dimensional Similitude 7 1.5 Thesis Objectives and Outline 10 2. Experimental Equipment and General Measurement Techniques 12 2.1 292-mm Diameter Column 12 2.2 127-mm Diameter Column 13 2.3 General Experimental Techniques 15 2.3.1 Overall Holdups 15 2.3.2 Dispersed/Coalesced Bubble Flow Regime Transition Velocity 17 2.3.3 Minimum Liquid Fluidization Velocity 18 2.3.4 Pressure Fluctuation Analysis 18 2.3.5 Gas Holdup Structure in a Bubble Column 19 3. Ultrasound as a Phase Holdup Measurement Technique 22 3.1 Introduction 22 3.2 Ultrasonic Wave Propagation in Multiphase Media 22 3.2.1 Ultrasonic Velocity Model (Warsito et al., 1995) 25 3.2.2 Ultrasonic Energy Attenuation Model (Warsito et a l , 1997) 25 3.3 Experimental Set-Up 27 3.3.1 Ultrasonic System 27 3.3.2 Experimental Procedure 28 v 3.4 Ultrasound in a Gas-Liquid System 30 3.4.1 Attenuation 30 3.4.2 Time-of-Flight 33 3.5 Ultrasound in a Liquid-Solid System 34 3.5.1 Attenuation 34 3.5.2 Time-of-Flight 38 3.6 Ultrasound in a Gas-Liquid-Solid System 39 3.7 Summary 40 4. Effects of Liquid Composition on Multiphase Reactor Hydrodynamics 42 4.1 Introduction and Literature Review 42 4.1.1 Bubble Coalescence Behaviour in Multicomponent Liquids and Saturated Solutions 43 4.1.2 Bubble Coalescence Behaviour in Contaminated Liquids 45 4.1.3 Bubble Coalescence Behaviour in Foaming Liquids 47 V 4.1.4 Experimental Attempts to Evaluate Bubble Coalescence Behaviour in a Liquid 55 4.2 Choice of Experimental Unit and Gas-Liquid-Solid Materials 59 4.2.1 Gas-Liquid Bubble Column , 59 4.2.2 Liquid-Solid and Gas-Liquid-Solid Fluidized Beds 61 4.3 Effects of Liquid Composition on Gas-Liquid Bubble Column Hydrodynamics 65 4.3.1 Dynamic Physical Properties of the Liquids 65 4.3.2 Overall Gas Holdup 68 4.3.3 Flow Regime Transition Velocity from Dispersed to Coalesced Bubble Flow 71 4.3.4 Pressure Fluctuations 73 4.3.5 Gas Holdup Structure 77 4.3.5.1 Experimental Dynamic Gas Disengagement Profiles 77 4.3.5.2 Estimated Bubble Diameters and Bubble Swarm Velocities 83 4.3.6 Statistical Analysis of Gas Holdup Data 86 4.3.7 Correlation of Data 87 4.3.8 Summary 94 4.4 Effects of Liquid Composition on Liquid-Solid Fluidized Bed Hydrodynamics 96 4.4.1 Bed Expansion and Correlation of Data 96 4.4.2 Pressure Fluctuations 99 4.4.3 Summary 101 4.5 Effects of Liquid Composition on Gas-Liquid-Solid Fluidized Bed Hydrodynamics 101 4.5.1 Bed Expansion 101 4.5.2 Gas Holdup in the Bed 103 4.5.3 Pressure Fluctuations 105 4.5.4 Flow Regime Transition Velocities 106 4.5.5 Gas Holdup in the Freeboard 108 4.5.6 Statistical Analysis of Hydrodynamic Data 109 4.5.7 Correlation of Holdup Data 111 4.5.8 Summary 115 5. Effects of Gas Density on Multiphase Reactor Hydrodynamics 117 5.1 Introduction and Literature Review 117 5.1.1 Pressure Effect on Bubble Formation Process 121 5.1.2 Pressure Effect on Bubble Coalescence Rate 122 5.1.3 Pressure Effect on Bubble Break-up Rate 123 5.1.4 Pressure Effect on Single Bubble Rise Velocity 126 5.2 Choice of Experimental Unit and Gas-Liquid-Solid Materials 127 5.2.1 Gas-Liquid Bubble Column 127 5.2.2 Gas-Liquid-Solid Fluidized Bed 129 5.3 Effects of Gas Density on Gas-Liquid Bubble Column Hydrodynamics 131 5.3.1 Overall Gas Holdup 131 5.3.2 Pressure Fluctuations 133 5.3.3 Correlation of Data 135 5.4 Effects of Gas Density on Gas-Liquid-Solid Fluidized Bed Hydrodynamics 137 5.4.1 Overall phase holdups 137 5.4.2 Pressure Fluctuations 140 5.4.3 Correlation of Holdup Data 141 VI 5.5 Summary 145 6. Fluid Maldistribution Effects on Phase Holdups in Three-Phase Fluidized Beds 146 6.1 Introduction 146 6.2 Experimental System and Procedure 147 6.3 Experimental Results and Discussion 150 6.3.1 Light Particle (Polymer Bead) System 150 6.3.2 Heavy Particle (Glass Bead) System 155 6.3.3 Relationship between Maldistribution and Bed Expansion 159 6.4 Implications for Distributor Design 162 6.5 Summary 163 7. General Conclusions and Recommendations 164 7.1 Recommendations 166 Nomenclature 168 References 176 1 V l l List of Tables Table 3.1: Summary of ultrasonic experiments in multiphase systems. 24 Table 4.1: Physical properties, operating conditions and values of the dimensionless groups for all four gas-liquid systems. 60 Table 4.2: Physical properties, operating conditions and values of the dimensionless groups for the two matched gas-liquid-solid systems and those for Syncrude's L C -Finer. 62 Table 4.3: Dynamic surface properties and foam formation ability for the four gas-liquid systems investigated. 67 Table 4.4: Dispersed/coalesced bubble flow transition velocities for all four gas-liquid systems investigated. 72 Table 4.5: Approximate bubble diameters and swarm velocities predicted from Equations (4.11) to (4.14) for the four gas-liquid systems investigated. 85 Table 4.6: A N O V A on gas holdup data of the three matched gas-liquid systems. 86 Table 4.7: Root-mean-square-deviations (RMSD) and bias factors (Fm) between gas holdups of the three matched gas-liquid systems. 87 Table 4.8: Applicable range of Luo et al. (1999) gas holdup correlation. 89 Table 4.9: Experimental and predicted values of Uj, and n, as well as the R M S D and F m between experimental and predicted liquid holdups of the two matched liquid-solid systems. 99 Table 4.10: A N O V A on the phase holdups of the two matched gas-liquid-solid fluidized beds. 110 Table 4.11: Root-mean-square-deviation (RMSD) and bias factor (Fm) between the hydrodynamic parameters of the two matched gas-liquid-solid systems. I l l Table 4.12: Root-mean-square-deviation (RMSD) and bias factor (Fm) between predicted (Han et al., 1990 correlation) and observed hydrodynamic data for the two matched gas-liquid-solid systems. 114 Table 4.13: Dimensionless groups used in Larachi et al. (2001) three-phase fluidized bed holdups correlations. 114 Table 5.1: Physical properties, operating conditions and values of the dimensionless groups for the four gas-liquid systems investigated in the gas density effect experiments. 128 Table 5.2: Physical properties, operating conditions and values of the dimensionless groups for the four gas-liquid-solid systems investigated in the gas density effect experiments. 130 Table 5.3: Root-mean-square-deviation (RMSD) and bias factor (Fm) between predicted (Equations 5.7 and 5.8) and observed phase holdups for the four gas-liquid-solid systems. 143 viii List of Figures Figure 1.1: Schematic of Syncrude's LC-Finer. 3 Figure 2.1: Schematic of 292-mm diameter column and auxiliary equipment (Safoniuk, 1999). 12 Figure 2.2: Schematic of the gas/liquid distributor in 127-mm diameter column. 14 Figure 2.3: Schematic of the gas disengagement section in 127-mm diameter column. 14 Figure 2.4: Dynamic pressure profile in an air, aqueous glycerol solution (55% wt.) and 6 mm diameter borosilicate glass beads: Re L = 75 and U G / U L = 0.86. 15 Figure 2.5: Drift-flux versus gas holdup in an air, aqueous glycerol (55% wt.), 6 mm diameter borosilicate glass beads: ReL= 101. 17 Figure 2.6: Dynamic pressure profile in an air, aqueous glycerol solution (55% wt.) and 6 mm diameter borosilicate glass beads: U G = 36 mm/s. 18 Figure 2.7: Schematic description of the disengagement of bubbles of three sizes. 20 Figure 3.1: Schematic of a synthesized transducer impulse response from a tone burst. 30 Figure 3.2: Attenuation versus gas holdup for the two modes of operation in an air-water system: U L = 0 and 7 mm/s, f n 0 m = 1 MHz, L = 292 mm. 31 Figure 3.3: Power-frequency spectrum for water and air-water systems: U L = 7 mm/s, L = 292mm, eg = 0, 1.1 and 5.2%. 32 Figure 3.4: Attenuation versus frequency in an air-water system: UL= 7 mm/s, L = 292 mm, s g = 1.1 and 5.2%. 33 Figure 3.5: Time-of-flight difference (ATGL) and full-width-half maximum (W1/2) versus gas holdup for an air-water system: U L = 7 mm/s, f n 0 m = 1 M H z and L = 292 mm. 34 Figure 3.6: Power-frequency spectrum in water and in a water-glass bead fixed bed: L = 292 mm. 35 Figure 3.7: Attenuation versus frequency in a water-glass bead fixed bed: L = 292 mm. 35 Figure 3.8: Attenuation versus frequency when water alone was circulated through the empty column: U L = 33 and 87 mm/s, L = 292 mm. 36 Figure 3.9: Attenuation versus solids holdup in a liquid-solid fluidized bed: f n o m = 0.5MHz, L = 292 mm. 37 Figure 3.10: Time-of-flight difference (ATL s ) versus solids holdup in a liquid-solid . - fluidized bed: f n 0 m = 0.5MHz, L = 292 mm. 38 Figure 3.11: Power-frequency spectrum in liquid, liquid-solid and gas-liquid-solid systems: L = 92 mm. 39 Figure 4.1: Bubble column gas holdup in a) air/aq. ethanol (Shah et al., 1985); b) air/ aq. glycerol (Bach and Pilhofer, 1978); and c) hydrogen/organic liquids (Bhaga et al., 1971). 44 Figure 4.2: Schematic of a typical foam structure (Durian and Weitz, 1994). 48 Figure 4.3: Schematic of foam lamella region (Schramm, 1994). 48 Figure 4.4: Pressure differences across surfaces in a foam lamella (Schramm, 1994). 50 Figure 4.5: Schematic description of surface tension gradient induced flow, i.e. Marangoni effect (Schramm, 1994). 51 Figure 4.6: Schematic of maximum pressure bubble method for measuring dynamic surface tension. 52 I X Figure 4.7: Variation of surface tension with bubbling frequency and bulk concentration of C14 alpha-olefin sulfonates in 1% wt. NaCl aqueous solutions (Huang etal., 1986). 53 Figure 4.8: Bikerman sparge tube apparatus (Callaghan, 1993). 58 Figure 4.9: Dynamic pressure drop versus solids holdup in a silicone oil - porous alumina fluidized bed. 63 Figure 4.10: Surface tension versus bubble formation rate for gas-liquid systems investigated. Filled-in symbols represent data obtained from the ring pull tensiometer method. 65 Figure 4.11: Foam collapse curve for water-glycerol and paraffin oil: U g * = 0.015. 66 Figure 4.12: Overall gas holdup versus U g * for the three matched gas-liquid systems. Filled-in symbols represent the transition from dispersed to coalesced bubble flow obtained from the drift-flux method. 69 Figure 4.13: Overall gas holdup versus U g for the air/aq. glycerol, air/silicone oil and air/tap water systems. 71 Figure 4.14: Drift-flux versus overall gas holdup for the air/aq. glycerol system. 72 Figure 4.15: Normalized differential pressure fluctuation standard deviations versus U g * for the three matched gas-liquid systems. Filled-in symbols represent (Ug*)trans obtained from the drift-flux method. 73 Figure 4.16: Power spectral distributions of normalized differential pressure fluctuations for the three matched gas-liquid systems at several U g * . The thick, thin and broken lines represent the water-glycerol, silicone oil and paraffin oil systems, respectively. 75 Figure 4.17: Normalized differential pressure fluctuation standard deviations versus U g for the air/aq. glycerol and air/tap water systems. 76 Figure 4.18: Power spectral distributions of normalized differential pressure fluctuations for gas-liquid systems at U g = 0.018 and 0.193 m/s. The thick and thin lines represent the water-glycerol and tap water systems, respectively. 77 Figure 4.19: Gas holdup after abruptly terminating gas flow after operating at several U g * for the three matched gas-liquid systems. The thick, thin and broken lines represent the water-glycerol, silicone oil and paraffin oil systems, respectively. Arrows indicate bubble class disengagement break points as depicted in Figure 2.7. 78 Figure 4.20: Overall and small bubble holdup versus U g * for the three matched gas-liquid systems. Open points give 8 g ; filled-in points depict egs. Arrows indicate flow transition gas holdups. 80 Figure 4.21: Large bubble holdup versus U g * for the three matched gas-liquid systems. 80 Figure 4.22: Overall minus microbubble holdup (eg - s g m) versus U g * for the three matched gas-liquid systems. 81 Figure 4.23: Gas holdup after abruptly terminating gas flow after operating at several values of U g . The thick, thin and broken lines represent the air/aq. glycerol, air/silicone oil and air/tap water systems, respectively. Arrows indicate bubble class disengagement break points as depicted in Figure 2.7. 82 Figure 4.24: Overall gas holdups versus U g * for the three matched gas-liquid systems compared with predictions from the Hikita et al. (1980), Luo et al. (1999) and Jordan and Schumpe (2001) correlations. 90 Figure 4.25: Overall gas holdups versus U g for the four gas-liquid systems investigated and the Krishna et al. (2000) correlation predictions. 94 Figure 4.26: Bed expansion versus Re L for the two matched liquid-solid systems. 97 Figure 4.27: Normalized differential pressure fluctuation standard deviations for several Re L for the two matched liquid-solid systems. 100 Figure 4.28: Power spectral distributions of normalized differential pressure fluctuations for the two matched liquid-solid systems at Re L = 52 and 101. The thick and thin lines represent the aq. glycerol/borosilicate and silicone oil/alumina systems, respectively. 100 Figure 4.29: Bed expansion versus Re g* for several Re L for the two matched gas-liquid-solid systems. Filled-in symbols represent system 1 (air/aq. glycerol/borosilicate) data, while open data points depict system 2 (air/silicone oil/alumina). 102 Figure 4.30: Bed expansion versus Re g* for Re L = 101 for the two matched gas-liquid-solid systems. 102 Figure 4.31: Gas holdup versus Re g* for several ReL for the two matched gas-liquid-solid systems. Filled-in symbols represent system 1 (air/aq. glycerol/borosilicate) data; open data points depict system 2 (air/silicone oil/alumina). 103 Figure 4.32: Photograph of freeboard, just above bed level for the air/aq. glycerol/borosilicate system: Re L = 52, Re g* = 26. 104 Figure 4.33: Photograph of freeboard, just above bed level for the air/silicone oil/alumina system: ReL = 52, Re g* = 26. 104 Figure 4.34: Power spectral distributions of differential pressure fluctuations at various Re L and Re g * for the two matched gas-liquid-solid systems. The thick and thin lines represent system 1 (air/aq. glycerol/borosilicate) and system 2 (air/silicone oiPalumina), respectively. 105 Figure 4.35: Normalized differential pressure fluctuation standard deviations at various Re L and Re g * for the two matched gas-liquid-solid systems. Filled-in symbols represent system 1 (air/aq. glycerol/borosilicate) data; open points depict system 2 (air/silicone oil/alumina). 106 Figure 4.36: Dispersed/coalesced bubble flow transition velocity versus Re L for the two matched gas-liquid-solid systems. Filled-in symbols represent system 1 (air/aq. glycerol/borosilicate) data, while open data points depict system 2 (air/silicone oiPalumina). 107 Figure 4.37: Minimum liquid fluidization velocity versus Re g* for the two matched gas-liquid-solid systems. 108 Figure 4.38: Bed and freeboard gas holdup versus Re g* at ReL= 75 for the two matched gas-liquid-solid systems. Filled-in symbols represent system 1 (air/aq. glycerol/borosilicate) data; open data points depict system 2 (air/silicone oil/alumina). 109 Figure 4.39: Parity plots between the observed and predicted (Han et al., 1990 correlation) bed expansions and gas holdups for the matched gas-liquid-solid systems. 113 Figure 5.1: Gas holdups in a 150-mm diameter bubble column with air/water at pressures of 0.2 to 1.2 MPa (Letzel et al., 1997). 118 X I Figure 5.2: Gas holdups in a three-phase fluidized bed with air/water/glass beads (d p =0.46 and 6 mm) at pressures of 0.1 and 0.7 MPa (Jiang et al., 1992). 118 Figure 5.3: Gas holdups in a three-phase fluidized bed with nitrogen/heat transfer fluid/glass beads (d p = 2.1 and 3 mm) at pressures of 0.1 to 15.6 MPa (Luo et al., 1997). 119 Figure 5.4: Gas holdup in coal liquefaction pilot plant and cold flow models (Tarmy et al., 1984). 120 Figure 5.5: Overall gas holdups versus U g * for the four gas-liquid systems. Filled-in symbols represent data obtained with 75% of the gas distributor holes closed-off. 132 Figure 5.6: Gas holdup after abruptly terminating gas flow after operating at U g * = 0.0091 for the four gas-liquid systems. The thick, thin and broken lines respectively represent the CO2, Air and He systems; open circles depict data with the SF6. Arrows indicate bubble class disengagement break points as described in Figure 2.7. 132 Figure 5.7: Normalized differential pressure fluctuation standard deviations versus U g * for the four gas-liquid systems. Filled-in symbols represent data obtained with 75% of the gas distributor holes blocked. 133 Figure 5.8: Power spectral distributions of normalized differential pressure fluctuations for the four gas-liquid systems at four values of U g * . The thick, thin and broken lines respectively represent the CO2, air and He systems; open circles depict data with the SF 6 . 134 Figure 5.9: Overall gas holdup versus U g 4 p g /ag for the four gas-liquid systems. 136 Figure 5.10: Overall phase holdups in the bed and freeboard versus Re g * = Re L U g /UL for the four gas-liquid-solid systems at Re L =101. 138 Figure 5.11: Overall phase holdups in the bed and freeboard versus Re g * = Re L U g /UL at ReL = 55 for the air/aq. glycerol/borosilicate bead and helium/aq. glycerol/ borosilicate bead systems. 139 Figure 5.12: Normalized differential pressure fluctuation standard deviations versus Re g* for the four gas-liquid-solid systems at ReL = 55 and 101. Filled-in symbols represent data for ReL = 55; open data points depict ReL = 101. 140 Figure 5.13: Overall phase holdups in the bed and freeboard versus U g 4 p g / ag for the four gas-liquid systems at ReL =55 and 101. Filled-in symbols represent data for ReL = 55; open data points depict Re L = 101. 142 Figure 5.14: Parity plots between the observed and predicted holdups (Equations 5.7 and 5.8) for the four gas-liquid-solid systems. Filled-in symbols represent data for Re L = 55; open data points depict Re L =101. 144 Figure 6.1: Patterns of active orifices in the distributors as operated. Open circles represent water inlets, while solid dots represent air inlet ports. 149 Figure 6.2: Variation of overall bed voidage with gas and liquid superficial velocities for polymer bead system with uniform distributor #1. Lines show predictions from Han et al. (1990) correlation. 150 Figure 6.3: Effects of gas and liquid superficial velocities on gas and liquid holdups for polymer bead system with uniform distributor #1. Lines show predictions from Han et al. (1990) correlation. 151 Figure 6.4: Effects of gas and liquid superficial velocities on overall bed voidage for polymer bead system with distributor #7. 152 X l l Figure 6.5: Variation of overall bed voidage with gas and liquid superficial velocities for the polymer particle system with the seven distributors shown in Figure 6.1: (a) U G = 0 (open circles only) and 1.7 mm/s; (b) U G = 16.7 mm/s. 153 Figure 6.6: Effects of gas and liquid superficial velocities on gas holdup for polymer beads system with the seven gas/liquid distributors: (a) U G = 1.7 mm/s; (b) U G = 16.7 mm/s. Symbols are as in Figure 6.5. 155 Figure 6.7: Effects of gas and liquid superficial velocities on gas holdup for glass bead system for uniform distributor # 1. 156 Figure 6.8: Effects of gas and liquid superficial velocities on liquid holdup for glass bead system for uniform distributor # 1. Symbols are as in Figure 6.7. 156 Figure 6.9: Overall bed voidage for glass bead system with distributors #1, #4 and #7 (see Figure 6.1) versus superficial gas velocity for U L (mm/s) = 35.5, 53.3, 71.0 and 106.5. 157 Figure 6.10: Gas holdup for glass bead system with distributors #1, #4 and #7 (see Figure 6.1) versus superficial gas velocity for U L (mm/s) = 35.5; 53.3; 71.0 and 106.5. 158 Figure 6.11: Schematic of solids circulation at constant gas velocity. Extension of model of Hiby (1967) and Masliyah (1989) to three-phase fluidized beds. Downward direction is taken as positive. 160 X l l l Acknowledgement I would like to first express my sincere gratitude to Drs. John R. Grace and Xiaotao B i for their guidance, support and inspiration during this work. They have done everything to make this project an enjoyable experience. Norman Epstein has also been a fantastic help, always available to give advice. I would like to thank Syncrude Canada Ltd. for believing in this project and for their generosity in sponsoring the work. I would like to especially thank Craig A. McKnight and Larry Hackman who were very helpful and supportive of my studies. Darwin Kiel of Coanda Research and Development Corporation has also been a great help. My appreciation also goes to all who work in the department. Thanks to Alex, Helsa, Horace, Graham, Lori, Peter, Qi and Robert for their fantastic help and friendship. I would like to sincerely thank my fellow classmates and friends who made my life in Vancouver entertaining. Finally, I would like to thank my family for loving and believing in me. Dedication A Papa (1919-2001) 1 Chapter 1 - Introduction Three-phase fluidized beds are employed in a wide range of applications that require intimate contact between a gas, a liquid and solid particles. Industrial applications are traditionally encountered in hydrocracking of heavy oil fractions, Fischer-Tropsch synthesis, coal liquefaction, methanation, aerobic and anaerobic wastewater treatment, production of pharmaceuticals via plant and animal cells, etc. (Fan, 1989). In this thesis, the upgrading of petroleum resids is of particular interest. 1.1 Bi tumen Upgrad ing in Canada The Canadian oil sands resource is spread across an area of 77 000 km 2 , mostly in northern Alberta. It holds an estimated 1.7 trillion barrels of bitumen, of which 300 billion barrels are recoverable with existing in-situ and surface mining technologies (Syncrude, 2000). The Athabasca oil sands deposit is located 440 km northeast of Edmonton, and by itself, is the largest petroleum resource in the world (Syncrude, 2000). Oil sand is composed of sand, bitumen, mineral rich clays and water. In its raw state, bitumen is a black, viscous tar-like liquid that requires upgrading to make it both transportable by pipeline and usable by conventional oil refineries. The Syncrude Project is a joint venture operated by Syncrude Canada Ltd. and owned by a consortium of about 10 companies. Syncrude produces crude oil through mining, extracting and upgrading bitumen from the Athabasca oil sands. The crude oil is referred to as "Syncrude Sweet Blend (SSB)" and is a light (31 to 33° API) oil with no residual bottoms and low sulphur content (0.2% wt.). It takes about 2 tons of oil sand to make one barrel (159 litres) of SSB. In 1999, the daily production of SSB averaged 223,000 barrels at a cost of C D N $12.84/barrel. By 2007, ongoing expansion projects envisage the SSB production will approximately double to 450,000 barrels/day, equivalent to 26% of Canadian crude oil consumption (Syncrude, 2000). In Syncrude's upgrading process, bitumen is first extracted from the oil sands in froth flotation tanks and then cleaned-up with centrifuges. Afterwards, the bitumen is distilled into 2 light gas oil and atmospheric topped bitumen (ATB). Part of the A T B is further distilled, under vacuum operating conditions, into light and heavy gas oils and vacuum topped bitumen (VTB). The V T B and remaining A T B are blended and broken down into naphtha and light and heavy gas oils in two LC-Finers and two fluidized bed cokers in parallel. The LC-Finers break down the bitumen through reactions with hydrogen over an ebullated catalyst bed, while the fluidized bed cokers thermally crack the large hydrocarbon molecules and produce coke. The Syncrude LC-Finer units are the sixth of its kind built in the world and can process up to 60,000 barrels/day, approximately 20% of the bitumen feedstock. The light products (naphtha, light and heavy gas oils) from the distillation units, the LC-Finer and fluidized bed cokers are sent to fixed bed hydrotreaters for the catalytic removal of nitrogen and sulphur. Finally the hydrotreaters' products are combined to give Syncrude Sweet Blend. Hydrogen for the LC-Finer and hydrotreaters is produced by catalytic steam reforming of natural gas, followed by shift conversion. For this thesis, the unit of interest is the LC-Finer. The " L C " in LC-Finer stands for "Lummus and Cities Service", which are the companies involved in licensing the technology. Figure 1.1 presents a schematic of the LC-Finer, which operates as a co-current three-phase fluidized bed. Bitumen and hydrogen are heated separately, then mixed and introduced into the reactor. The reactor contains a bed of cylindrical catalyst particles fluidized by the upward flow of hydrogen, fresh bitumen and internally recycled liquid products. The liquid is the continuous phase, while the hydrogen and catalyst constitute dispersed phases. Internal recycle provides the necessary fluid velocity to maintain a specific bed height and to ensure temperature uniformity. Gamma-ray density detectors allow the determination of the bed height, while thermocouples monitor the bed temperature. The gas-liquid region above the bed level is referred to as the "freeboard". The LC-Finer operates as a stable, well-mixed isothermal reactor. On-line catalyst addition and removal can be carried out. The unit operates at temperatures between 300 and 440°C and at pressures between 5.5 and 21 MPa (Fan, 1989). Gas bubbles pass through the reactor supplying hydrogen to the bitumen/catalyst mixture. Bubbles occupy a fraction of the reactor volume, called the gas holdup. The gas holdup is a 3 key feature in determining the liquid residence time. Liquid holdup is an important hydrodynamic characteristic, since actual liquid residence time proves to be the principal scale-up parameter for predicting product yields (Tarmy and Coulaloglou, 1992). This is usually the case for multiphase systems where the reaction rate is slower than the interphase mass transfer rate. For very fast Tactions, the available interfacial area mainly governs the space-time yield; hence high gas holdups and small bubbles are desired. Effluent Thermowell Nozzle Normal Bed Level Catalyst Catalyst Addition Line Density Detector Radiation Source Well Density Detectors Bubble Catalyst Withdrawal Line Bitumen/Hydrogen Feed Recycle _ Pump Figure 1.1: Schematic of Syncrude's LC-Finer. 1.2 Investigating the Performance of Three-Phase Fluidized Beds When investigating multiphase reactors it is important to understand and quantify the transport-kinetic interaction on a particle or single eddy scale, the interphase transport rates on particle and reactor scales, the flow and contacting patterns of each phase and their responses to changes in reactor geometry and operating conditions (Dudukovic et al., 1999). In many multiphase reactors transport rather than kinetic rates are the overall reaction rate-limiting step. Hence research on fluid dynamics and transport in multiphase systems continues to be strongly pursued. Sundaresan (2000) reported that organisations in the American Chemical Industry, including the American Institute of Chemical Engineers 4 (AIChE), had identified a better understanding of gas-solid and gas-liquid-solid flows in chemical reactors as a critical need. They called for the development of reliable simulation tools that integrate detailed models of reaction chemistry and computational fluid dynamic (CFD) modeling of macro-scale structures. Over the last few years, researchers have attempted to use CFD codes to describe various transient hydrodynamic phenomena in multiphase reactors (e.g. Krishna and van Baten, 2001; van Wachem et al., 2001). Kuipers and van Swaaij (1998) published a review on the role and limits of CFD in chemical reaction engineering. The review identified two types of approaches for CFD modeling. First, there are global system models that provide overall flow features and sometimes rely on empirical transport and kinetic relations to describe reactor performance. Secondly, there are models that describe the phenomena on various scales from first principles. However, this type of model cannot yet be implemented on multiphase reactor systems (Dudukovic et al., 1999). Thus, while available commercial CFD codes (e.g. CFDLIB, FLUENT, C F X , PHOENICS, FLOW 3D, FIDAP, etc.) have made it possible to simulate gross flow patterns in large reactors, understanding the phenomena on various length and time scales still requires experimental validation and innovative non-intrusive measuring techniques capable of monitoring the dynamics of bubbles and solids (Dudukovic et al., 1999; Tarmy and Coulaloglou, 1992). Fluid dynamics of multiphase contactors are a complex function of physical properties of the phases, operating conditions and reactor geometry. With respect to the latter, the method of gas and/or liquid injection can be of great importance. The distributor has great influence on the bubble mean size and size distribution when coalescence rates are slow. On the other hand, for systems with rapid bubble coalescence, equilibrium can be reached rapidly and distributors have minimal influence, especially for tall reactors (Tarmy and Coulaloglou, 1992). Interestingly, there has been no systematic evaluation of the effects of distributor design on the hydrodynamic behaviour of three-phase fluidized beds. Hydrodynamic correlations and models in the literature rarely consider the effect of distributor design (Wild and Poncin, 1996). This contrasts with the state of affairs in two-phase systems where the influence of distributor design has been widely studied. 5 In industrial hydrocrackers, maldistribution of the gas and liquid reactants leads to significant local temperature excursions. These temperature excursions can cause excessive coke formation and catalyst sintering, which can lead to premature shutdowns or even temperature runaway and explosion. In general, the hydrodynamic behaviour of three-phase fluidized beds can be characterized by bubble properties (size and size distribution, shape and rise velocity), gas/liquid holdups and bed expansion (and hence solids holdup). These parameters, in turn, affect mass and heat transfer rates and mixing and flow patterns of the liquid and solids. Bubble dynamics also dictate the resulting flow regime. At low gas flowrates, small bubbles of uniform size are produced with little interaction between them. The flow regime is referred to as the "dispersed bubble flow regime", and an increase of gas flowrate increases the bubble population more than the bubble size. However, this flow regime cannot be sustained indefinitely. Beyond a certain gas flowrate, the bubble population becomes sufficiently large that bubbles start to coalesce and travel faster than their smaller counterparts. There is now a wide bubble size distribution, which induces relatively strong liquid circulation patterns and mixing. This flow regime is referred to as the "coalesced bubble flow regime". 1.3 Hydrodynamic Studies under Hydrocarbon Processing Conditions There has been a significant amount of research on the hydrodynamics and heat and mass transfer properties of three-phase fluidized beds under ambient operating conditions using air, water and glass beads (Wild and Poncin, 1996). However, the physical properties of such systems differ considerably from those found in typical industrial hydrocracking units, these having much lower surface tensions and liquid viscosities, significantly higher gas densities and particles that are non-spherical (often cylindrical). In addition, the physicochemical properties of the phases in such systems are not always well defined and may significantly change with the progress of the reactions. Industrial hydrocrackers often operate in the dispersed bubble flow regime with high gas holdups (above 25%) and small spherical or ellipsoidal bubbles (around 1 mm in volume-equivalent diameter) with no or very small wakes, whereas other flow regimes (e.g. coalesced bubble flow), lower gas 6 holdups and spherical-cap bubbles with significant wakes are normally encountered for aqueous systems at ambient conditions (Fan, 1989). Tarmy et al. (1984) and Ishibashi et al. (2001) obtained hydrodynamic data for pilot plant coal liquefaction reactors operated at pressures up to 20 MPa and temperatures up to 450°C. Gas holdups were as high as 49%, which was attributed to the large kinetic energy of high-pressure inlet gas and surface-active components preventing bubbles from coalescing. Although these reactors operate as slurry bubble columns, they provide valuable insight to the hydrodynamics of three-phase fluidized bed hydrocrackers such as the LC-Finer. A slurry bubble column is similar to a three-phase fluidized bed, except that the particles are significantly smaller (sub-millimetre) and, as a result, the liquid-solid suspension is often treated as a pseudo-homogeneous mixture. Building a pilot plant is a costly and energy-consuming endeavour that is not a viable approach for studying the LC-Finer hydrodynamics in this Ph.D. project. In an attempt to simulate the reaction conditions for hydrocracking residual oils and coal liquefaction in a cold model reactor, Fan et al. (1987) and Song et al. (1989) used air and an aqueous t-pentanol (0.5% wt.) solution. The surfactants reduced bubble size and rise velocity and inhibited coalescence, yielding high gas holdups. The use of surfactants may simulate a specific characteristic of hydrocrackers, but does not reproduce the overall hydrodynamic behaviour of the bed. The solids holdups in aqueous surfactant systems differ from those in industrial hydrocrakers since high-pressure provides additional resistance to the growth of large bubbles (Fan, 1989). Recognizing the importance of pressure, Luo et al. (1997, 1999) studied the hydrodynamics of three-phase fluidized beds and slurry bubble columns in a lab-scale unit with an organic liquid operated up to relatively high temperatures (180°C) and high pressures (21 MPa). Their results provide valuable information on the general behaviour of high-pressure reactors involving mutlicomponent organic liquids. 7 Following a more fundamental approach, Safoniuk (1999) employed dimensional analysis to investigate the hydrodynamic behaviour of three-phase fluidized beds. Similar scaling approaches have been used with significant success in gas-solid fluidized beds (e.g. Brue and Brown, 2001; Kehlenbebeck et al., 2001; Glicksman et al., 1994; Horio et al., 1986) and in spouted beds (e.g. He et al., 1997). 1.4 Hydrodynamic Dimensional Similitude One can achieve dimensional similitude by rendering dimensionless the governing equations and boundary conditions, establishing force balances or using the Buckingham Pi Theorem. Safoniuk (1999) chose the Buckingham Pi theorem, as it is relatively quick and easy to produce a set of dimensionless groups. The basis of this approach is to first identify all variables that have a significant effect on the hydrodynamics of the studied system. Failing to include a key variable leads to misleading and confusing results, while inclusion of a variable that ultimately does not significantly influence the hydrodynamics creates additional superfluous experiments, which will eventually show the variable to be insignificant. Once the significant variables have been selected, the Buckingham Pi theorem states that for (v) dimensional variables, (v-w) independent dimensionless groups can be formed where (w) is the number of fundamental dimensions. Once the dimensionless groups have been chosen, the results obtained in experiments yield empirical data that describe the phenomena studied for all systems that are geometrically similar and have the same values of the dimensionless groups. Factors and properties that have a potential impact on the hydrodynamics of three-phase fluidized beds are: • Gas and liquid superficial velocities • Gravitational acceleration • Particle physical properties: size and size distribution, density and density distribution, shape (sphericity), wettability, coefficient of restitution. 8 • Liquid physical properties: surface tension, density, rheology (viscosity plus other properties i f non-Newtonian), dilatational elasticity, foam retention time and half-life, conductivity, volatility. • Gas physical properties: density, viscosity, solubility, diffusivity. • Column geometry: cross-sectional shape, diameter, internals, entrance and exit design, angle of inclination. • Bed height Safoniuk (1999) identified eight important variables for characterizing the hydrodynamics of three-phase fluidized beds: solid and liquid density, liquid viscosity, gas and liquid superficial velocity, surface tension, a gas-liquid buoyancy term and particle diameter as the characteristic length. By assuring geometric similarity, it is sufficient to choose a single length. There are three fundamental dimensions used in these variables: length, mass and time. The following five independent dimensionless groups were chosen. ™ § ( P L ~ P g W IT AT,-* u T, * ^ ( p L - P g ) 1 ? M-group: M = — modified Eotvos number: Eo* p 2 a 3 a Reynolds number: R e L = Density ratio: — Velocity ratio P L U (1.1) L Safoniuk (1999) employed this set of dimensionless groups to simulate the LC-Finer hydrodynamics. Air, aqueous glycerol solution (44% wt.) and aluminum cylinders with a diameter of 4 mm and a length of 10 mm were the selected materials. The shape and aspect ratio of the'particles were the same as the catalyst in the LC-Finer. The column had an inner diameter of 0.292 m and the liquid and gas superficial velocities were 0.13 m/s and 0.11 m/s respectively. Here M = lxlO" 8 , Eo* = 4.1, Re L = 148, p p /p L = 2.43, and U g / U L = 0.84. For these operating conditions, Safoniuk (1999) obtained a gas holdup of 17%, significantly lower than gas holdups reported in the LC-Finer and hydrocrackers in general (see above). The hydrodynamic scale-down was not ideal. Although the limited set of dimensionless 9 groups may be adequate for other three-phase fluidized beds, the list of selected variables may have been incomplete for the LC-Finer. The main disadvantage of using the Buckingham Pi theorem is that it does not provide a means to determine whether the list of selected variables is complete. Thus, the approach requires an excellent understanding of the variables that influence the studied phenomena. Possible reasons for the mismatch between the experimental unit of Safoniuk (1999) and the LC-Finer are the following: 1. The major physical properties of the liquid (density, viscosity, surface tension) are implicitly assumed to be sufficient to characterize the bubble coalescence behaviour. This is true for a pure monocomponent liquid (Shah et a l , 1985). However, for multicomponent and contaminated liquids, such as bitumen, these physical properties may be insufficient to characterize the bubble coalescence behaviour since properties at the gas/liquid interface tend to differ from the bulk. Multicomponent and contaminated liquids may present bubble coalescence inhibition and have the capacity to foam (Saberian-Broudjenni et al., 1987). 2. The independent effect of gas density is not accounted for. Gas density is only included in a gas-liquid buoyancy term. The LC-Finer operates at high pressure (5.5 to 21 MPa). Elevated pressures usually lead to higher gas holdups in both bubble columns and slurry bubble columns, except in systems that operate with porous plate distributors and at low gas velocities (Luo et al., 1999). The increased gas holdup is directly related to the smaller bubble size and its slower rise velocity at higher pressures (Lin et al., 1998). The bubble size reduction can be attributed to the variation in physical properties of the gas and liquid with pressure (Fan et al., 1999). However, very few researchers varied the pressure or gas density in coarse-particle (mm range) three-phase fluidized beds, and the results are somewhat contradictory. 10 3. Geometric similitude requirements were relaxed in the experimental unit and consequently boundary conditions differed. Strict equality of the ratios of column diameter to particle diameter and column diameter to particle length was deemed unnecessary since these ratios were sufficiently large (> 30) that wall effects were considered negligible. The cross-sectional shape of the column, particularly the presence of an inner column (liquid recycle line), was also assumed to be of secondary importance since the scaled system should operate in the dispersed bubble flow regime with small bubbles and high gas holdups. The gas/liquid distributor and the gas disengagement section were designed differently. The bed aspect ratio was sufficiently great (> 4) so that entrance and end effects should not have influenced overall hydrodynamics. In addition, hydrodynamic parameters of the two systems were compared in the established flow section far from any entrance or end effects. The problem lies in the efficiency of the gas disengagement section. Syncrude believes that the LC-Finer liquid recycle pan is not very efficient, i.e. a significant amount of gas is entrained with the recycled liquid, consequently increasing the once-through gas flowrate. 4. The physical properties and hydrodynamic parameters measured in the LC-Finer are not as accurate as in the experimental unit. For example, phase flowrates and physical properties vary along the column height due to hydrostatic pressure and reactions (i.e. hydrogen consumption and hydrocarbon production). 1.5 Thesis Objectives and Outline The following goals provide the scope for the present work: 1. Evaluate limitations of the dimensional similitude approach of Safoniuk (1999) for scaling LC-Finer hydrodynamics. Obtaining a hydrodynamic model of the LC-Finer is an important goal for Syncrude as they wish to optimize the product yield by increasing the liquid holdup (i.e. lowering gas holdup) and to predict the hydrodynamic response to changes in operating conditions. 11 2. Evaluate the influence of distributor geometry and initial gas-liquid flow maldistribution on the phase holdup behaviour of three-phase fluidized beds. Uniform distribution of the fluids over the column cross-section is essential for the safety and prolonged operation of the LC-Finer. This objective will allow some insight on the role of particles in establishing radial uniformity of fluids that are initially maldistributed. In addition, it is important to gain a better understanding of the operating conditions where the distributor plays an important role. 3. Explore ultrasound as a new technique for measuring the cross-sectional holdups of multiphase systems in a non-intrusive manner. The objective is to determine whether this will allow us to obtain hydrodynamic data for our unit which can help develop experimental tools for validating CFD codes. The thesis outline is as follows: The experimental equipment and general measurement techniques are presented in Chapter 2. Chapter 3 explores the use of ultrasound as a phase holdup measurement technique. The limits of the dimensional similitude scaling approach developed by Safoniuk (1999) are evaluated by investigating the effects of liquid composition (i.e. interfacial properties) and gas density on multiphase reactor hydrodynamics in Chapters 4 and 5, respectively. Chapter 6 presents the effects of distributor geometry and initial fluid maldistribution on the overall holdups of three-phase fluidized beds. Finally, the thesis presents conclusions and options for future research in Chapter 7. 12 Chapter 2 - Experimental Equipment and General Measurement Techniques Two experimental units were used during the course of this work. Most of experiments were carried out in a 127-mm diameter column, while a 292-mm diameter column was employed in the development of the ultrasonic phase holdup measurement technique. 2.1 292-mm Diameter Column This unit was designed and built by Safoniuk (1999). A schematic of the three-phase fluidized bed set-up is shown in Figure 2.1. The column is constructed of acrylic, with an inner diameter of 292 mm and a maximum expanded bed height of 1800 mm. T possible expanded bed he ight o f 1.8 m y gas flow va lve and meter assem bly air exit colum n liq u id bypass :5^ >distributor pre-m ix area safety valve orif ice m eter straighten ing vanes l iqu id recyc le glyc ero1 solut ion storage tank alum inum separating w al l l iqu id pump Figure 2.1: Schematic of 292-mm diameter column and auxiliary equipment (Safoniuk, 1999). In this unit, gas and liquid are first pre-mixed in a plenum chamber and then introduced into the column through a perforated plate containing 226 holes of diameter 6.4 mm. In the plenum chamber, a donut-shaped sparger with 30 holes of diameter 3.2 mm facing downward 13 distributes the gas into the incoming liquid. The plenum chamber is also filled with Raschig rings to homogenize the gas-liquid mixture before it enters the main section of the column. At the top of the column, an expansion section separates the gas from the liquid. The gas is vented to the atmosphere, while the liquid is directed to a storage tank and then recycled to the column. A n aluminum divider in the storage tank minimizes the entrainment of gas in the liquid feed to the column. The liquid feed line has a by-pass loop with a safety valve that allows the liquid to enter the loop i f the distributor becomes blocked or i f there is some other obstruction within the column. An orifice meter and rotameter control the liquid and gas flows, respectively. Additional details are provided by Safoniuk (1999). 2.2 127-mm Diameter C o l u m n The configuration of this three-phase fluidized bed facility is identical to that of the larger unit, except in the design of the column. The column is constructed of acrylic with an inner diameter of 127 mm and a height of 2580 mm. Along the height of the column, various 6.3-mm NPT and 12.7-mm NPT female ports are added in order to insert various probes and transducers. Gas and liquid are introduced into the bed separately, but at the same level. This allows individual distributor designs for uniform spatial distribution of the fluids. The liquid distributor was designed so that its pressure drop was always equal to or greater than 25% of that across the bed. The gas distributor was designed for a minimum orifice Weber number (We o r) of 2 in order to ensure that gas passes through all the holes (Wild and Poncin, 1996). The liquid distributor is a perforated plate with 54 holes of 4.8 mm diameter, while the gas is introduced via 60 holes of 1 mm diameter. Figure 2.2 is a schematic of the gas/liquid distributor. At the top of the column, a simple overflow system separates the gas from the liquid (see Figure 2.3). If anything, this design induces fewer end effects. The flows of gas and liquid are determined using two sets of rotameters. In this thesis, the superficial gas velocity is calculated at the column inlet conditions. Gas Gas Gas Flange hole Gas Figure 2.2: Schematic of the gas/liquid distributor in 127-mm diameter column. Gas Gas It Liquid level Screen t L Liquid Gas/Liquid Figure 2.3: Schematic of the gas disengagement section in 127-mm diameter column. r Liquid 15 2.3 General Experimental Techniques This section describes general experimental techniques employed to measure bed hydrodynamics. Other details of the measuring approaches are given as needed elsewhere in the thesis, while a separate chapter is devoted to the development of the ultrasonic phase holdup measurement technique. 2.3.1 Overall Holdups Overall holdups were obtained by measuring the dynamic pressure drop along the column at several levels. A differential pressure transducer, model PX750-30DI from Omega, was used. The reference port was 60 mm above the distributor. A t each position, the pressure difference was recorded for 120 s periods at 5 Hz . Figure 2.4 presents a typical pressure profile. The dynamic pressure drop (-AP) is defined as the total pressure gradient corrected for the hydrostatic head of liquid (i.e. - A P = - A P T - gpLAz). 2500 2000 £ 1500 < 1000 500 0 R 2 = 0.9996 / \ R 2 = 0.9990 \ f r e e b o a r d slope 9 bed slope bed height \ d * , 1 0 500 1000 1500 z, [mm] 2000 Figure 2.4: Dynamic pressure profile in an air, aqueous glycerol solution (55% wt.) and 6 mm diameter borosilicate glass beads: ReL = 75 and Ug/UL = 0.86. The bed height and hence bed expansion are determined from the intersection of the bed and freeboard pressure drop lines obtained by linear regression. The solids holdup (ss) can then be obtained from: 16 4 M d r v E s = 2 (2-1) H b P p > d r y where Mdry is the dry weight of particles contained in the bed, pPidry is the dry particle density and Hb is the bed height. The bed expansion is related to the solids holdup by: Bed expansion (%) = 100 Ssmf Y V S s J (2.2) where s s mf is the solids holdup at minimum fluidization. Neglecting the frictional drag and accelerations of the phases in the vertical direction, the gas holdup (sg) is related to the dynamic pressure drop by: (£s (Pp,wet-pL) + A P 1 § A z ) (P L -Pg) Here pp,wet is the wet particle density, which is the density of the particle with liquid fdling the pores. For non-porous particles, the dry and wet particle densities are equivalent. The slopes of the pressure drop lines are used to calculate the gas holdups. In Figure 2.4, the regressions are linear (R « 1). Assuming that s s is independent of z, axial variation of gas and liquid holdups can be considered negligible. From visual observation, for all experiments presented in this thesis, only negligible volumes of particles were entrained in the freeboard. Finally, since the sum of the phase volume fractions must be unity, the liquid holdup is: E L = l - s - 8 S (2.4) 17 2.3.2 Dispersed/Coalesced Bubble Flow Regime Transition Velocity One can estimate the dispersed/coalesced bubble flow regime transition velocity by visual observation, by plotting the gas holdup versus superficial gas velocity or drift-flux, and by the statistical, frequency and chaotic analysis of wall pressure fluctuations or any other dynamic property related to the flow pattern (Vial et al., 2001). In this work, the gas velocity corresponding to transition from dispersed to coalesced bubble flow was obtained by plotting the drift-flux ( J g L ) as a function of gas holdup. Based on the original drift-flux analysis of Wallis (1969) in gas-liquid systems, Darton and Harrison (1975) give an expression for the drift-flux in a gas-liquid-solid fluidized bed: s8 ( 1 - e g ) = U g ( 1 - £ g ) - U ^ g ( l - ^ ) A L (2.5) In dispersed bubble flow, J g L slowly increases with increasing gas holdup, while in coalesced bubble flow the increase is markedly faster. A typical example is shown in Figure 2.5. 0.1 0.05 0.07 0.09 0.11 0.13 0.15 Gas holdup, [-] Figure 2.5: Drift-flux versus gas holdup in an air, aqueous glycerol (55% wt), 6 mm diameter borosilicate glass beads: ReL= 101. 18 2.3.3 Minimum Liquid Fluidization Velocity The minimum liquid fluidization velocity was obtained from the intersection of two fitted straight lines when the bed dynamic pressure drop was monitored as the liquid velocity was reduced for a constant gas velocity (Wild and Poncin, 1996). A typical example is shown in Figure 2.6. -1000 J 1 UL , [mm/s] Figure 2.6: Dynamic pressure profile in an air, aqueous glycerol solution (55% wt.) and 6 mm diameter borosilicate glass beads: U g = 36 mm/s. 2.3.4 Pressure Fluctuation Analysis Bubble dynamics were characterized through pressure fluctuation analysis. Two absolute pressure transducers (both Omega, PX808-005GV) were employed to monitor differential pressure fluctuations. Data was sampled at 100 Hz for 90 or 180 s periods, sufficient to detect the full spectrum of hydrodynamic signals in three-phase fluidized beds (Kang et al., 1997; Vial et al., 2001). Data points were normalized by their average values. Pressure fluctuations properties were characterized by means of the standard deviation and power spectral density function (PSDF). The PSDF was obtained using commercial software Microcal Origin 6.0™. Differential pressure fluctuations are usually favoured over single point (absolute pressure) measurements since they reduce (but do not eliminate) the influence 19 of disturbances (e.g. due to bubble formation or surface fluctuations) from outside the interval across which the pressure drop is measured (Zhang, 1996). 2.3.5 Gas Holdup Structure in a Bubble Column The structure of the gas phase in a bubble column was determined by the Dynamic Gas Disengagement (DGD) technique (Sriram and Mann, 1977) using a differential pressure transducer (Omega, model PX750-30DI) connected to ports 60 mm above the gas distributor and 120 mm below the static liquid surface. The dynamic pressure drop signal was sampled at a rate of 5 Hz. The DGD technique involves following the liquid level (H) or gas holdup after the gas flow is abruptly interrupted. In the dispersed bubble flow regime, the gas holdup decreases linearly with time reflecting the disengagement of a uniform bubble size population. The bubble rise velocity can be obtained from the slope of the disengagement profile. In the coalesced bubble flow regime, there is a significant bubble size distribution and each bubble size has its escape velocity. Bubbles sizes are usually lumped into classes when the gas disengagement slopes do not significantly differ from one another. In practice, a bimodal bubble size distribution is adopted (Krishna et al., 1991). The gas holdup decreases quickly upon interruption of the gas flow due to the escape of the "large" bubbles, then at a lower rate for the "small" bubbles. For foaming liquids, the gas disengagement profile breaks at two points as. a third class of bubbles (microbubbles) is encountered. Figure 2.7 presents an idealized schematic description of the disengagement of bubbles of the three classes. 20 Height (H) Time (t) Figure 2.7: Schematic description of the disengagement of bubbles of three sizes. Periods I, II and III are respectively associated with the disengagement of large bubbles, small bubbles and microbubbles. The holdups for each bubble class are obtained from: s g i * ( H 3 - H 2 ) / H 3 ; 8 g s « ( H 2 - H i ) / H 3 ; s g m » ( H i - Ho)/H 3 (2.6) The slopes in periods II and III are used to determine the superficial gas velocity through the small and microbubble population, respectively. The bubble swarm velocity is then equal to the superficial gas velocity divided by the gas holdup: 21 U b s = U g s / s g s * (H 2 -H 1 ) / ( ( t 2 - t 1 ) s g s ) = H 3 / ( t 2 - t 1 ) ; U b m - U g m / s g m * H 3 / ( t 3 - t 2 ) ; (2.7) Ubi = (U g - U g s - U g m ) / s g i The dynamic gas disengagement technique assumes that the disengagement rate of each bubble size is independent of the disengagement rate of other sizes, that there is no axial variation of gas holdups when the gas flow is interrupted, and that there is no bubble coalescence or break-up during gas disengagement. Shumpe and Grund (1986), Desphande et al. (1990) and Lee et al. (1999) have discussed problems associated with deviations from these assumptions in coalescing systems at high gas flowrates. In reality bubble-bubble interactions play a significant role and bubble characteristics are too complex to be simplified by the disengagement profile in order to obtain a multimodal bubble size distribution. The DGD can only provide approximate measurements of bubble sizes, rise velocities, and gas holdup distributions. Hence, in this thesis, the DGD technique is primarily employed as tool to compare bubble dynamics (i.e. gas disengagement profiles) between multiphase systems. 22 Chapter 3 - Ultrasound as a Phase Holdup Measurement Technique This chapter explores the limits of ultrasound as a technique for evaluating the cross-sectional holdups of multiphase systems in a non-intrusive manner. 3.1 Introduction Several researchers have used the attenuation of transmitted energy beams to produce images of multiphase flow. In transparent media, Lee and de Lasa (1986) employed fibre optical probes to characterize bubbles in three-phase fluidized beds. Chen and Fan (1992) developed the particle image velocimetry (PIV) technique, which combines photography with image processing. In opaque media, radioactive particle tracking, nuclear magnetic resonance imaging and electrical, capacitance, gamma-ray and X-ray computer-assisted tomography have all been used to investigate hydrodynamics (Chaouki et al., 1997). In gas-liquid systems, ultrasound has been employed to measure gas holdups (Chang et al., 1984), bubble velocities (Broring et al., 1991), bubble diameters (Bugmann et al., 1991) and specific interfacial area (Stravs and von Stockar, 1985). Several researchers (Warsito et al., 1997; Stolojanu and Prakash, 1997; Soong et al., 1999) have used ultrasound to evaluate phase holdups in slurry bubble columns, but applications of this technique to three-phase fluidized beds have not yet been reported. In comparison with other measuring techniques deployed in optically opaque systems, ultrasound requires much less energy and is safer, simpler and lower in cost (Warsito et al., 1999). An additional advantage is that it provides two independent parameters (attenuation and time-of-flight) related to the system physical characteristics. Therefore ultrasound is a promising technique with which to investigate the local dynamic behaviour of multiphase reactors. 3.2 Ultrasonic Wave Propagation in Multiphase Media The ultrasound technique is based on emitting bursts of acoustic energy and measuring the velocity and attenuation of the ultrasound waves propagating through the medium. In a gas-23 liquid-solid system, the attenuation and velocity changes are functions of gas and solid holdups, bubble and particle size and size distribution, gas and solid densities, ultrasound wavelength and liquid properties (especially viscosity). The energy attenuation can be caused by scattering (reflection and diffraction) at the bubble and particle interfaces, absorption by microbubble pulsation and viscous dissipation as particles oscillate under an acoustic field (Warsito et al., 1999). The dominant mechanism depends on the range of kr, where k = 2n/X is the ultrasound wave number and r is the radius of the particles or bubbles. The scattering regime is encountered when the ultrasound wavelength is similar in size or smaller than the obstruction (i.e. kr > 1). When the wavelength is much larger than the obstruction (kr « 1), the multiphase mixture can be considered as a pseudo-homogeneous solution, and the phenomenological wave velocity model of Urick (1947) can be applied. Warsito et al. (1995) found that particle oscillation occurred when kr p « 1. In a gas-liquid system, bubble pulsation dramatically attenuates the ultrasound signal when the bubbles are excited at their resonant frequency. For air bubbles in water under ambient pressure and temperature, the resonant frequency (fr) is given (Stravs and von Stockar, 1985) by: fr-rb = f r b r = 3.3(Hzm) (3.1) where r b r is the resonant bubble radius for a specific frequency. An acoustic velocity change can be caused by sound transmission within the particles, particle oscillation, microbubble pulsation or some combination of these mechanisms (Warsito et al., 1999). The acoustic velocity change cannot be caused by transmission within the bubbles since ultrasound is almost completely reflected at gas/liquid interfaces due to the high acoustic impedance mismatch. Again, the dominant mechanism depends on the kr range. Many researchers have performed experiments in multiphase systems. Almost all these experiments were in the scattering regime (kr > 1), with the dispersed phase(s) holdup(s) and ultrasound travel distance being quite low. Table 3.1 summarizes the experimental conditions for previous studies. 24 Table 3.1: Summary of ultrasonic experiments in multiphase systems. Authors System Pulse or continu-ous signal L (mm) D T (mm) f 1 nom (MHz) kr Gas and solids hydrodynamic properties Chang et al., (1984) Bubble Column Pulse 44-64 6.35 2.25 13-20 eg < 20% 2.8<db<4.2mm Stravs and von Stockar (1985) Bubble Column Pulse 30 12.7 5 5-10 8 g < 4 % 0.5 <d b< 1 mm 100<a<400m"' Bugmann et al., (1991) Bubble Column Pulse 15 24 5 11-37 1 < db< 3.5 mm Broring et al., (1991) Aerated Tank Pulse-echo 40 5 4 ? 0<U b<0.1 m/s Soong et al., (1997) Bubble Column Pulse 89 ? 2.5 26-52 8 g < 15 % 5 <db< 10 mm Soong et al., (1999) Slurry Bubble Column Pulse 89 . 19 1 (0.02 - 0.07) particles (10-21) bubbles 8 g< 15 % 2 < Es < 17 % 10 <dp< 37 um 5 <d b< 10 mm Warsito et al., (1999) Slurry Bubble Column Pulse 140 16 10 (2-7) particles (21 - 105) bubbles (6 g + es)< 10% 1 < d b < 5 mm 100 < dp< 350 um Stolojanu and Prakash (1997) Slurry Bubble Column Pulse 25 12 4 0.3 particles (24 - 42) bubbles eg < 15 % 1< ES < 4 % 3 < d b < 5 mm dp = 35 um Atkinson & Kitomaa (1993) Liq - Sol Fluidized Bed Tone burst 100 9.5 0.1-1 0.2-2 0<s s<60% dp = 1 mm Present work Bubble Column Tone burst 292 25 1 11 EG< 15 % d b « 6 mm Liq - Sol Fluidized Bed Tone burst 292 25 0.5 1.4 25 <ss<60% dp = 1.3 mm 25 Warsito et al. (1995, 1997, 1999) attempted to model the ultrasound signal time-of-flight and attenuation in a gas-liquid-solid system. Their models are next summarized briefly. 3.2.1 Ultrasonic Velocity Model (Warsito et al., 1995) The transmission time difference, A T g L s , between a three-phase system and the liquid alone is expressed as: where L is the transmission pathlength (distance between the ultrasound transmitter and receiver), while K s and K g are coefficients that depend on the frequency and the particle or bubble diameter. This equation accounts for independent contributions of the individual phases. At sufficiently high frequency, the effect of gas holdup on the change in ultrasound velocity can be ignored (i.e. K g -> 0). The transmission time difference is then solely due to the presence of solids. 3.2.2 Ultrasonic Energy Attenuation Model (Warsito et al., 1997) The energy attenuation (Q gLs) of an ultrasonic wave transmitted through a three-phase system is expressed as: where I 0 and I are the intensities of the incident and transmitted wave respectively and a g L S is an attenuation coefficient, related to the scattering cross-sections of bubbles and particles. Assuming that individual scattering incidents are independent of each other, the attenuation coefficient is expressed (Stravs and von Stockar, 1985) as: (3.2) (3.3) <*gLs = N T JSn.appOo") " A ( r ) " F ( r ) " d r = « s + a g (3-4) o 26 where N j is the bubble or particle number density, A(r) is the bubble or particle projection area normal to the transmission vector, F(r) is the bubble or particle size distribution function and otg and ocs are attenuation coefficients for the gas bubbles and solid particles, respectively. The apparent scattering coefficient (Sn>app) is equal to the scattering coefficient (Sn) when the entering wave is essentially planar. Stravs and von Stockar (1985) proposed a simple relationship for the scattering coefficient regressed from the theoretical calculation for non-rigid spheres for kr values of 1, 2, 5 and 10: S n =2 + 1.442(kr) - 0'5 7 8 (3.5) From Equation (3.4) and by using a volume-equivalent bubble/particle mean radius, the attenuation coefficient for solid particles and gas bubbles can be expressed as: 3 S n ( k r ) - e s 3S n (kr b )-e a s = = X s - s s ; a g = — = X g - s g (3.6) where X s and X g are coefficients dependent on the ultrasonic frequency and particle or bubble diameter. The ultrasonic energy attenuation in the three-phase system can be expressed as: Q g L s = a g L s - L = ( a g + a s ) - L = ( X s £ s + X g £ g ) - L ( 3- 7) Finally, combining the ultrasound velocity model, Equation (3.2), and Equation (3.7), yields: E = X g A T g L s - K g Q g L s . e _ X s A T g L s ~ K s Q g L s ^ ^ ( K s X g - K g X s )L g ( K g X s - K s X g ) L 27 The Warsito et al. (1995, 1997) models are an extension of a two-phase model with the effect of the additional phase on the signal attenuation and velocity change assumed to be additive. This assumption is valid only under limited conditions: • f » fr (far from bubble resonant frequency) • kr >1 (scattering regime, X < d p and db) • r b or F(rb) does not change with increasing gas holdup (dispersed bubble flow only) The models were developed for slurry bubble columns. In this chapter, the models are tested in a three-phase fluidized bed subject to much higher particle size and concentration. 3.3 Experimental Set-Up 3.3.1 Ultrasonic System Experiments were performed in the 292 mm inner diameter column with air, water and uniform spherical glass beads of diameter 1.3 mm and density 2500 kg/m 3. Transducers (emitter and receiver) were placed inside pipes inserted into the bed through two ports on opposite sides of the column, 533 mm above the distributor plate. These pipes could be moved in the radial direction. Two pairs of transducers were available for the experiments: • M101-SB, Panametrics Inc., Waltham, M A , USA: Broad bandwidth frequency range, diameter of 45 mm (25 mm effective) and length of 29 mm, nominal frequency 0.5 MHz. • M102-SB, Panametrics Inc., Waltham, M A , USA: Broad bandwidth frequency range, diameter of 45 mm (25 mm effective) and length of 29 mm, nominal frequency 1 MHz. The ultrasonic signal was generated and processed by a N C A 1000 analyzer from V N Instruments Limited (Elizabethtown, Ont., Canada). Conventional ultrasonic pulse/receiver systems are operated in a pulsed mode, in which an emitting transducer is excited by a pulse of relatively high amplitude and short duration (spike). A receiving transducer detects the pulse, and the transmission time and amplitude of signals within a predetermined gate are then registered. Only a limited quantity of energy can be put into the pulses before overloading the transducers (non-linear effects). In contrast, the N C A 1000 sends a tone 28 burst. It then synthesizes an optimal transducer impulse response, thus utilising the transducer's full bandwidth and sensitivity. The information is obtained with high accuracy, and more energy can be put into the pulse. This becomes important when the ultrasonic waves must penetrate through a highly attenuative medium such as a three-phase fluidized bed. The dynamic range of attenuation is over 140 dB. Conventional ultrasonic instruments also measure the ultrasonic signal transmission time and intensity (amplitude) from the highest peak or the edge of the impulse within the selected gate. In three-phase fluidized beds, the impulse shape is very distorted (deformed) and fluctuates greatly due to the presence of gas bubbles and solid particles. It then becomes very difficult to obtain the amplitude and, even more so, the transmission time. The N C A 1000 measures the signal intensity by integrating its area, thus avoiding the problem of characterizing the signal shape. In addition, the gain is continuously and automatically adjusted so that the signal never exceeds the threshold limit of the instrument. The N C A 1000 also offers quantitative evaluation of frequency-dependent attenuation. This is an important feature since, combined with wide bandwidth transducers, one is able to investigate a medium over a broad frequency range. In order to avoid overlapped or multiple reflected pulses, which introduce errors in the evaluation of the time-of-flight and intensity, only the first transmission signal, corresponding to a straight path, is used when analyzing the signal. 3.3.2 Experimental Procedure The ultrasonic time-of-flight and intensity were first measured in a bubble column and in a liquid-solid fluidized bed for different gas and solids holdups, with the cross-sectional holdups determined from local pressure drops around the transducers. Experiments were then attempted in a three-phase fluidized bed containing the same particles. The original distributor employed by Safoniuk (1999) was replaced by a perforated plate with 52 holes of 2-rnm diameter on a 40 mm square pitch when the unit was operated as a bubble column and by a perforated plate with 308 holes of 2-mm diameter on a 15 mm square pitch when it was operated as a liquid-solid or gas-liquid-solid fluidized bed. These 29 different plates uniformly distributed the dispersed phase(s) for all' systems. The ultrasound wave velocity increases as the temperature of water increases. Therefore, all experiments were performed at a constant liquid temperature of 20 ± 1°C. The ultrasound signal averaging can be adjusted between 1 and 256 tone bursts. The transit time of the bubbles (Tb = D-r/Ub) and the characteristic time scale of particle acceleration (T p = rpPp/18|j,f ) are usually much longer than the period of oscillation of the acoustic wave ( T w = l/27if). Thus, for each tone burst, the bubbles and particles act as i f they are frozen in space. However, between successive tone bursts there are fluctuations in the position and concentration of bubbles and particles so very different signals can be received. In the present work, the data were logged at a frequency of 2 Hz for 150 seconds with signal averaging over 125 tone bursts, giving 300 data points (i.e. 300 data points x 125 tone bursts/data point = 37500 tone bursts). The data file logged from the N C A 1000 provides the signal intensity (IR), the time-of-flight and the full-width-half-maximum (W1/2). The latter is a measure of the width of the signal and is used to characterize signal deformation due to scattering. Figure 3.1 presents a schematic of a synthesized transducer impulse response from a tone burst. From repeated experiments, the coefficient of variation and standard deviation of the signal intensity and time-of-flight were estimated to be 5% and 0.05 ps in the gas-liquid system and 2.2% and 0.25 ps in the liquid-solid system, respectively. 30 60000 5 1 50000 | 40000 | 30000 i £ 20000 'a & 10000 0 Area under curve =  signal intensity (IR) ' i w 1 / 2 y Time-of-flight \ ^ r • 190 191 192 193 194 195 196 197 198 199 Time, [us] Figure 3.1: Schematic of a synthesized transducer impulse response from a tone burst. 3.4 Ultrasound in a Gas-Liquid System Experiments were performed both in a co-current mode (both gas and liquid forced to flow upwards) and a semi-batch mode (no net liquid flow). In the co-current mode, the liquid superficial velocity was fixed at 7 mm/s. The results presented in this section were obtained with the 1 M H z nominal frequency transducers flush with the inside column wall, the separation distance being 292 mm. 3.4.1 Attenuation The attenuation as a function of the gas holdup is presented in Figure 3.2 for the two modes of operation. The linear relationship is in agreement with the experimental results of earlier investigators (Warsito et al., 1999; Soong et al., 1997; Stolojanu and Prakash, 1997; Stravs and von Stockar, 1985). For the same gas holdup, signal attenuation is less pronounced for no liquid flow ( U L = 0) because larger bubbles are formed. This was confirmed by the fact that for the same superficial gas velocity, gas holdups were always lower when the liquid flow was interrupted. Thus for the same volume of gas, the scattering projection area is smaller by (rb,circ/rb,stiii) when U L = 0. 31 Gas holdup, [%] 0 2 4 6 8 10 12 14 -120 J : 1 Figure 3.2: Attenuation versus gas holdup for the two modes of operation in an air-water system: U L = 0 and 7 mm/s, f n 0 m = 1 MHz, L = 292 mm. From the slopes of the graph, X g = 679 m"1 and 564 m"1 for U L = 7 mm/s and no liquid flow, respectively. Solution of Equations (3.5) and (3.6) gives predicted bubble diameters of 5.2 mm and 6.2 mm, while corresponding values of S n are 2.4 and 2.3 for U L = 7 mm/s and no liquid flow, respectively. From visual inspection, the average bubble diameter was approximately 4 to 8 mm, indicating that the scattering model seems to be appropriate. The ultrasonic system is sufficiently sensitive to distinguish the attenuation due to different bubble characteristics. Figure 3.3 presents the power-frequency spectrum for signals passing through water alone and through the co-current gas-liquid bubble column. The signal intensity is lower for the higher gas concentrations at all frequencies. The shape of the envelope does not change significantly, confirming that only the initial signal not encountering bubbles is perceived by the receiving transducer. 32 200 400 600 800 1000 1200 1400 1600 1800 Frequency, [kHz] Figure 3.3: Power-frequency spectrum for water and air-water systems: U L = 7 mm/s, L = 292 mm, s g = 0, 1.1 and 5.2%. In Figure 3.4, the signal attenuation is obtained as a function of frequency by subtracting the frequency spectra in Figure 3.3. In the scattering regime, the signal attenuation is expected to increase as the ultrasound frequency is increased (Kitomaa, 1995). The present results show the reverse trend. Below 800 kHz, the signal intensity (IR) significantly decreases with decreasing frequency, with the biggest drop occurring around 250 kHz. These results suggest that microbubbles were present in the system, greatly attenuating the lower frequency components of the signal. From Equation (3.1) a resonant frequency of 250 kHz corresponds to a bubble diameter of 0.026 mm. Many microbubbles (diameter of order 100 um or less) could be observed visually through the transparent wall of the column, these being formed at the distributor, which operated in the jetting regime. In addition, some surface-active components must inevitably have been present, helping to stabilize microbubbles. 33 Frequency, [kHz] 200 400 600 800 1000 1200 1400 1600 1800 Figure 3.4: Attenuation versus frequency in an air-water system: UL= 7 mm/s, L = 292 mm, 6 g = 1.1 and 5.2%. 3.4.2 Time-of-Flight Figure 3.5 presents the time-of-flight difference (ATgL) and full-width-half-maximum (W1/2) as functions of the gas holdup in the co-current bubble column. As with earlier investigators (Warsito et al., 1999; Soong et al., 1997; Stolojanu and Prakash, 1997), the time of flight difference should be independent of gas holdup (K g -> 0), since only signals not encountering bubbles are measured. In the present case, this was only true up to a gas holdup of about 4%. At higher gas holdup, the signal became greatly distorted due to multiple scattering and diffraction around bubbles, making accurate measurement of AT g L very difficult. This is a common problem for ultrasound analysis instruments that measure the time-of-flight from the major peak of a signal that continuously changes shape. The signal distortion is confirmed by the full-width-half-maximum, which also starts to increase significantly for gas holdups above about 5%. Using light instead of ultrasound, Sridhar and Potter (1980) noted that multiple scattering prevented accurate measurement of the interfacial area per unit volume of column (a) when a-L > 20. For the present experimental conditions, a-L « 20 34 when s g « 6%. Finally, the transmission time differences as a function of gas holdup were similar for the two modes of operation. Gas holdup, [%] Figure 3.5: Time-of-flight difference (ATGL) and full-width-half maximum (W1/2) versus gas holdup for an air-water system: U L = 7 mm/s, f n 0 m = 1 M H z and L = 292 mm. 3.5 Ultrasound in a Liquid-Solid System The results in this section were obtained with the 0.5 M H z nominal frequency transducers flush with the inside column wall, with a separation distance of 292 mm. The superficial liquid velocity was varied between 2.4 and 6.2 times the minimum fluidization velocity, corresponding to bed expansions of 22 to 125%. 3.5.1 Attenuation Figure 3.6 presents the power-frequency spectrum in water and in a water-glass bead fixed bed. The power spectrum shape differs from that for the gas-liquid system. The signal of the liquid-solid mixture begins to deviate from the water curve at a frequency of approximately 200 kHz (krp = 0.7), corresponding to the onset of the scattering regime. Atkinson and Kitomaa (1993) obtained kr p = 0.75 at the onset of the scattering regime. Only components with frequencies below 400 kHz (krp = 1.1) are able to penetrate through the bed of particles. 35 0 200 400 600 800 1000 Frequency, [kHz] Figure 3.6: Power-frequency spectrum in water and in a water-glass bead fixed bed: L = 292 mm. Attenuation in the fixed bed is presented as a function of frequency in Figure 3.7. The signal attenuates as the frequency is increased, with the attenuation coefficient (a s) approximately proportional to the frequency to the power of 5.8 between 200 and 375 kHz. Theoretically, in the scattering regime, the attenuation coefficient varies with frequency to the power of 4 (Atkinson and Kitomaa, 1993). Frequency, [kHz] Figure 3.7: Attenuation versus frequency in a water-glass bead fixed bed: L = 292 mm. 36 In order to obtain different solids holdups, the bed was fluidized at superficial liquid velocities from 33 mm/s and 87 mm/s. Figure 3.8 presents the attenuation as a function of frequency when water alone was circulated through the empty column. Frequency, [kHz] 100 200 300 400 500 600 700 Figure 3.8: Attenuation versus frequency when water alone was circulated through the empty column: U L = 33 and 87 mm/s, L = 292 mm. A small quantity of gas was probably entrained in the liquid recycle line through the pump forming microbubbles, which, as indicated above, were likely stabilized by natural surfactants in the system. The effect of microbubbles is more important at higher liquid flowrates where more gas is entrained in the liquid recycle line. Although the volume of gas was very small (eg < 0.5%), the effect of the microbubble pulsation on the signal intensity is dramatic, especially at frequencies below 400 kHz. It seems that the resonant frequency is still between 150 and 250 kHz. This poses a serious problem. It is necessary to operate at frequencies above 500 kHz to avoid the influence of microbubbles, but all frequencies above 400 kHz are attenuated by the particles. Figure 3.9 shows the attenuation as a function of solids holdup. Due to the microbubbles, the reference intensity (IR<,) was adjusted for each liquid velocity. 37 20 25 Solids holdup, [%] 30 35 40 45 50 55 60 Figure 3.9: Attenuation versus solids holdup in a liquid-solid fluidized bed: f n o m = 0.5MHz, L = 292 mm. The signal attenuation decreased as the solids holdup increased, and the relationship is not linear. This is contrary to Equation (3.6), which predicts a linear increase in attenuation with increasing solids holdup. However, Warsito et al. (1999) only. investigated low solids holdups over a limited range (0 < s s < 5 %). Our results are in agreement with those obtained by Atkinson and Kitomaa (1993) under similar experimental conditions. They found that at ss < 20%, the signal attenuation increased as the solids holdup increased. When the solids holdup exceeded 20%, the attenuation responded in a dramatic fashion, first levelling off and then decreasing at higher concentrations, resulting in better penetration at higher solids fractions. The maximum peak was more pronounced in the scattering regime (krp > 0.75). At lower frequencies (0.4 < kr p < 0.75), the signal attenuation remained relatively constant between solids holdups of 20 to 50%) before decreasing. Wang and Chang (1991) also reported a maximum attenuation for s s = 24 to 44%. Attenuation only increases monotonically with concentration i f one assumes linear superposition of losses due to individual scattering events (obstructions), an 38 assumption which is valid only for low concentrations (e.g. for bubble column with s g < 12%). At high dispersed phase holdups, interactions between the occurrences of scattering need to be taken into account. Finally, from Figure 3.9, signal attenuation is not very sensitive to solids holdup for the range investigated. Perhaps at higher kr p values, the attenuation would be more sensitive to solids holdup within the range of interest (20 < s s < 40%). 3.5.2 Time-of-Flight Figure 3.10 presents the time-of-flight difference ( A T L s ) as a function of solids holdup. A linear relationship is obtained as predicted by Equation (3.2). However, for s s < 40%, the ultrasound time-of-flight is longer than for water alone. Warsito et al (1995), Stolojanu and Prakash (1997), Atkinson and Kitomaa (1993) and Soong et al. (1999) all measured a monotonic increase in ultrasound velocity as the solids holdup increased from zero to the maximum value investigated. The non-monotonic behaviour of our results may well be due to multiple scattering and diffraction, since kr > 1 and 323 < a-L < 782. Solids holdup, [%] Figure 3.10: Time-of-flight difference ( A T L s ) versus solids holdup in a liquid-solid fluidized bed: f n o m = 0.5MHz, L = 292 mm. 39 3.6 Ultrasound in a Gas-Liquid-Solid System Instead of using the attenuation and time-of-flight as two of the three independent holdup equations (the third being that the sum of the three holdups must give unity), one could substitute an alternate measure. Under the present experimental conditions ultrasound attenuation is not very sensitive to solids holdup. The time-of-flight at high frequency (f > 1 MHz) should therefore be used to determine the solids holdup. The local pressure drop can then be used to determine the liquid and gas holdups. Experiments were performed in a three-phase fluidized bed with the 1.3-mm glass beads with a small static bed height (H b =152 mm) in order to minimize bubble coalescence. The transducers were positioned 89 mm above the distributor. No signal could be detected for an operating frequency of 1 MHz and a travel distance of 292 mm, no matter how low the gas flowrate. The transducers had to be inserted into the bed until the path length was reduced to about 100 mm before a measurable signal was received. Figure 3.11 presents measured power frequency spectra for L = 92 mm. No further tests were performed due to the intrusive nature of the experiments. 100 300 500 700 900 1100 1300 1500 1700 1900 Frequency, [kHz] Figure 3.11: Power-frequency spectrum in liquid, liquid-solid and gas-liquid-solid systems: L = 92 mm. 40 Warsito et al. (1999) suggested that total holdups (gas and solids) up to 20% may be the upper limit for the ultrasonic measurement technique. This value seems to correspond to the practical limit of operation before the signal is completely attenuated in a gas-liquid or gas-liquid-solid system for the scattering regime. Transmission distance also appears to be important given that Sridhar and Potter (1980) suggested that the light transmission technique allowed accurate measurement of the interfacial area only when a L < 20. This creates problems for three-phase fluidized beds where the dispersed phases usually occupy at least 50% of the total volume. In addition, the distance that the signal must travel (292 mm in the present case) is significantly longer than separation distances employed by other research teams. Most importantly, the experiments were performed in the scattering regime (kr > 0.75). In this regime, the ultrasound attenuation coefficient is proportional to the frequency to the power of 4 and bubble/particle diameter to the power of 3 (Kitomaa, 1995). Therefore, the operating frequency becomes crucial. One needs to use a very high frequency (above ~ 1 MHz) to avoid the effect of microbubbles (d b ~ 30 pm), but still have a value of kr p that wil l give reasonable attenuation. In slurry bubble columns, by using smaller particles and lower solids holdups, researchers can minimize attenuation due to the solids while operating at high frequency. Finally, in the selection of the operating frequency there exists an inherent compromise between the need to minimize the wavelength for better spatial resolution (e.g. attenuation sensitivity to solids holdup), while maximizing the wavelength for better penetration. 3.7 Summary The objective of this study was to explore an ultrasonic technique for evaluating the cross-sectional holdups of multiphase systems in a non-intrusive manner. Experiments were first performed successfully in a relatively large (292-mm-inside-diameter) bubble column and liquid-solid fluidized bed for different gas and solids holdups, respectively. Experiments were then attempted in a three-phase fluidized bed. Experiments were performed in the ultrasound scattering regime, far from the bubble resonant frequency, while keeping the attenuation as low as possible. 41 The experimental method worked relatively well in two-phase systems. In the bubble column, the time-of-flight did not vary for low gas holdups (less than 4%). However, at higher gas holdups (up to 12%), the time-of-flight increased due to multiple scattering and diffraction. The signal attenuation followed the scattering model, which is based on linear superposition of losses due to individual scattering occurrences. The predicted bubble diameter was within the range of bubble diameters observed visually. In the liquid-solid fluidized bed, the signal attenuation did not follow the scattering model. For the range of solids holdup studied (25 to 60%), the attenuation decreased as the solids fraction increased. The time-of-flight increased linearly as the solids concentration decreased. However, the values were not bounded by those of a packed bed and water alone, due to multiple scattering and diffraction. Signal attenuation greatly limits the use of ultrasonic vibrations for determining holdups in three-phase fluidized beds. When large particles are used (mm range), it is difficult to operate at a frequency that ensures transmission through both dispersed phases. To eliminate the strong attenuating effect of microbubbles, the operating frequency must be set well above the resonant frequency (i.e. > 0.5 MHz). However for 1.3-mrn glass beads, only signals of frequency below 0.4 M H z could be detected. In addition, the total concentration of the two dispersed phases is very high and strongly contributes to the attenuation. To compensate for such strong attenuation, the ultrasound travel distance must be reduced. In the present case, this would require that this method become highly intrusive. Slurry bubble columns with lower dispersed phases holdups and smaller particles present a less attenuative media and are better suited to this technique. As a result of these findings, the attempt to use ultrasonics in this work was abandoned. Simpler more direct experimental techniques were employed as detailed in subsequent chapters. 42 Chapter 4 - Effects of Liquid Composition on Multiphase Reactor Hydrodynamics This chapter tests the limits of the dimensional similitude scaling approach of Safoniuk (1999) by investigating the bubble coalescence behaviour in multicomponent and/or contaminated liquids. 4.1 Introduction and Literature Review To understand how gas bubbles coalesce in a liquid, it is important to understand the forces present at the interface. The van der Waals forces between liquid molecules are felt equally by all molecules except those in the gas-liquid interfacial region. This imbalance pulls the molecules of the interfacial region towards the bulk of the liquid. The contraction force at the surface is known as surface tension. Surface tension and surface free energy are also defined as the work required to increase the area of a surface isofhermally and reversibly by unit amount. Because the surface has a tendency to contract spontaneously in order to minimize the surface area, gas bubbles tend to adopt a spherical shape. There is a pressure difference across the interface, the pressure being greater on the concave side (i.e. inside the gas bubble). The Young-Laplace equation relates this pressure difference to the surface tension and the principal radii of curvature. For a spherical bubble of radius (rb), the Young-Laplace equation reduces to: Coalescence of two gas bubbles in a liquid occurs in three steps. First, bubbles approach each other trapping a small amount of liquid between them. Next, this liquid drains until the film separating the bubbles reaches a critical thickness. Finally, at this critical point, the film ruptures resulting in bubble coalescence. Bubble collisions can be induced by a variety of mechanisms such as fluctuations of the liquid turbulent velocity and bubble wake capturing (Lin et al., 1998). The duration of film thinning is usually considered the limiting step. Twin injected bubbles form a flat disk of liquid film vertically separating them. For a pure (4.1) 43 monocomponent liquid, Sagert and Quinn (1977) found that the rate of thinning of this liquid disk (vd) can be expressed by: where h is the film thickness, R d the radius of the disk and a measure of the surface drag or velocity gradient at the surface due to the adsorbed layer of gas. The term 4o/d b represents the capillary pressure due to curvature of the bubble surface (i.e. Young - Laplace equation) and is usually orders of magnitude larger than the term A h /(67ih 3 ), which represents the pressure due to Hamaker-London dispersion forces (mutual attraction force between two induced dipoles on the opposite sides of the liquid film). 4.1.1 Bubble Coalescence Behaviour in Multicomponent Liquids and Saturated Solutions In bubble columns and slurry bubble columns, many studies (Shah et al. 1982; Reilly et al. 1986; Pino et al. 1990; Wilkinson et al. 1992) have demonstrated that the physical properties of liquid mixtures are insufficient to characterize the bubble coalescence behaviour since properties at the gas/liquid interface differ from the bulk. Dynamic interactions at the gas/liquid interface have to be taken into account. Most often, there are surface tension gradients at the bubble surface that hinder its rise velocity and increase its surface elasticity. A more detailed presentation of the importance of interfacial phenomena on bubble coalescence is presented in section 4.1.3 below. V d = - - 7 T = dh _ 8h 3 ( 4a A h (4.2) dt 3(()H L R^d b 67m 3 J Figure 4.1 presents examples of gas holdups obtained in bubble columns with a) air/aqueous ethanol (Shah et al., 1985); b) air/aqueous glycerol (Bach and Pilhofer, 1978); and c) hydrogen/organic liquids (Bhaga et al., 1971). 44 io 0.8t o. 0.6 0.4 0.2 i i i > n 111 1—i—i i i 1111 Superficial Gas Velocity, m/s O 0.00779 A 0.01330 a 0.01869 0 0.02457 0.04871 A 0.1058 0.1574 0.2083 1 i l i i i l l -1 1 l i l 11 MOLE FRACTION OF ETHANOL IN WATER 3 O X a Liquid viscosity X 10 [kg/ms] 2 0 18 o —I o I CO < CD O N-OCTANE-TOLUENE • TOLUENE-AMS O TOLUENE-CUMENE A TOLUENE-ETHYL8ENZENE Q ACETONE-BENZENE 25°C U r c = 2.13 cm /sec c) 0 5 0 100 W T % MORE V O L A T I L E C O M P O N E N T Figure 4.1: Bubble column gas holdup in a) air/aq. ethanol (Shah et al., 1985); b) air/ aq. glycerol (Bach and Pilhofer, 1978); and c) hydrogen/organic liquids (Bhaga et al., 1971). 45 Under certain operating conditions, the aqueous ethanol and glycerol solutions exhibited foaming. Shah et al. (1985) concluded that the onset of foaming caused a significant increase in gas holdup and that even in the absence of foaming, systems with foaming capacity experience larger gas holdups than non-foaming systems for similar operating conditions. For pure monocomponent liquids, gas holdup decreases with increasing liquid viscosity (Wilkinson et a l , 1992). From Figure 4.1b, Bach and Pilhofer (1978) demonstrate that the gas holdup does not decrease i f the viscosity of water is increased by adding glycerol, but passes through a maximum. Wilkinson et al. (1992) suggested that the initial increase of gas holdup occurs because the bubble coalescence rate in liquid mixtures is lower than in monocomponent liquids. There is no available theory that permits quantification of the effect of using a liquid mixture on the fluid dynamics of a bubble column (Pino et al., 1990). Therefore, correlations based on data from pure monocomponent liquids cannot predict the gas holdups of liquid mixtures with similar physical properties (Wilkinson et al., 1992). In three-phase fluidized beds, researchers have almost exclusively used mixtures to evaluate the effects of liquid properties on bed hydrodynamics, ignoring any interfacial effects. Very few have used pure monocomponent liquids due to the difficulties, cost and dangers involved. Saberian-Broudjenni et al. (1987) performed a systematic study on the effect of liquid properties in three-phase fluidized beds using cyclohexane, kerosene, gas oil, CC1 4 and water. They compared kerosene to cyclohexane (both liquids having very similar physical properties) and observed completely different fluidizing behaviour due to the foaming nature of kerosene. Cyclohexane being a monocomponent liquid does not foam. Bed expansions and gas holdups in the kerosene system were consistently greater than those for cyclohexane at similar operating conditions. 4.1.2 Bubble Coalescence Behaviour in Contaminated Liquids Many industrial grade liquids contain trace impurities. The addition of solutes (e.g. alcohols, proteins, organic acids, electrolytes, surfactants) and/or finely divided particulates (e.g. catalyst, clays, emulsions) to a liquid can enhance or severely hinder the bubble coalescence behaviour. Surfactants are molecules that form oriented monolayers at interfaces and show 46 surface activity (Bickerman, 1973). As there is a balance between adsorption and desorption due to thermal motions, the interfacial condition requires some time to establish. Thus, surface activity should be considered a dynamic phenomenon. Most surfactants lower interfacial tension by accumulating at the surface and providing an expansion force acting against the normal interfacial tension (Schramm, 1994). Gibbs described the lowering of surface free energy due to surfactant adsorption in terms of thermodynamics. The general Gibbs adsorption equation for a binary, isothermal system that contains excess electrolyte is: T, = — = — — « — ^ i - (for dilute solutions a, « c,) (4-3) 1 R T d l n a , RT da, RT dc, where Tl is surface excess concentration of solute, R is the gas constant, T is the absolute temperature, and ax and cx are the activity and molar concentration of the solute, respectively. Liquids containing impurities have been extensively studied in bubble columns, slurry bubble columns and three-phase fluidized beds. Researchers have varied the type of contaminant, its concentration and the height of the reactor since adsorption of surfactants at the bubble surface is a dynamic process (e.g., surfactants can accumulate as the bubble rises) (Shah et al., 1982). Most studies have ignored the mechanism of bubble coalescence inhibition or enhancement. In many practical cases, it is impossible to determine the exact composition of the solutes present. As with many researchers, Del Poso et al. (1994) simulated bubble coalescence inhibition and enhancement by adding surfactants and measured the bed response (overall holdups, mass/heat transfer rates, mixing, flow regime transition). Some researchers correlated their hydrodynamic data to the number of carbon molecules of the alcohol (Kelkar et al., 1983), to the ionic strength of the salts (Keitel and Onken, 1982) or to the type of surfactant (Gorowara and Fan, 1990). In the dispersed bubble flow regime, the gas holdup can be modeled by the drift-flux, which incorporates the rise velocity of an isolated bubble (Darton and Harrison, 1975). For small spherical or ellipsoidal bubbles (Eo < 40), surface impurities eliminate internal gas circulation, thereby significantly increasing the drag and reducing the rise velocity (Clift et 47 al., 1978). For very small spherical bubbles (Eo < 40 and Re b < 1), the Stokes and Hadamard-Rybczynski models provide the limits for bubble rise velocities in contaminated and pure systems respectively. For large spherical-cap bubbles (Eo > 40), liquid inertial forces dominate over surface tension and viscous forces, and the presence of contaminants is less important (Fan, 1989). Indeed, the high shear force generated by the high relative velocity between the bubble and liquid could readily sweep away the contaminants on the surface. As a result contaminants induce negligible effects on the internal circulation of the gas for spherical-cap bubbles (Clift et al., 1978). 4.1.3 Bubble Coalescence Behaviour in Foaming Liquids The study of liquid foaming behaviour is important since foam results from coalescence inhibition. When a foaming agent (surfactant, macromolecule or fine solids) is present, the merging of two bubbles rising in a liquid is much less probable because the film between them is not different from that found in the foam itself (Bickerman, 1973). Many multicomponent and contaminated liquids have the capacity to foam under the proper operating conditions. Examples of foaming liquids include aqueous solutions of glycerol, acetic acid, various alcohols, salts and proteins, as well as organic liquids like industrial multicomponent oils (Shah et al., 1985). Foaming occurs when relatively small gas bubbles are injected at a rate such that the rate of liquid drainage is slow enough that the bubbles form clusters. Once foam is formed, the foam height reaches a state of equilibrium where the rates of formation and decay balance each other. Figure 4.2 shows a schematic of a typical foam structure. In the lower part of the foam, bubbles are relatively small in size and spherical. This type of foam is called "wet" or "kugelschaum" (Durian and Weitz, 1994). As the liquid drains from the foam at higher levels, bubbles coalesce and distort to form polyhedra. The gas volume fraction here is greater than at the bottom and the foam is called "dry" or "polyderschaum" (Durian and Weitz, 1994). As shown in Figure 4.3, a lamella is defined as the region that encompasses the thin liquid film, the two interfaces on either side of the thin film and part of the junction to other lamellae. The connection of three lamellae, at an angle of 120°, is referred to as a Plateau border. Figure 4.2: Schematic of a typical foam structure (Durian and Weitz, 1994). Figure 4.3: Schematic of foam lamella region (Schramm, 1994). 49 The lifetime of a thin liquid film (i.e., foam stability) is a function of many factors involving both bulk solution and interfacial properties, as well as external forces (Schramm, 1994): • gravity drainage • capillary suction a dispersion force attraction • electrical double-layer repulsion , steric repulsion • surface elasticity s viscosity (bulk and surface) In addition, the nature of the filler gas and liquid composition influence foam stability. Throughout the foam there are differences in the sizes of adjacent bubbles. Smaller bubbles have larger capillary pressure than larger ones, so that gas diffuses from small to large bubbles (Garret, 1993). Heavy metal salts, short-chain carboxylic acids and alkyl phenols of molecular weight < 400 are major foam stabilizers in crude oils (Callaghan, 1993). Detailed discussions of all these foam-stabilizing factors can be found, among others, in Schramm (1994), Garret (1993), Schmidt (1995), Narsimhan and Ruckenstein (1995), Durian and Weitz (1994) and Bickerman (1973). The main forces of interaction that govern the drainage of thin liquid films are gravity, capillary suction and disjoining pressure (Garret, 1993). Immediately after foam generation, liquid drains through the interior of the lamellae due to gravity. Capillary forces become competitive with gravity once gas bubbles are no longer spherical (kugelschaum), but polyhedral and separated by thin planar lamellae (polyderschaum) (Schramm, 1994). Figure 4.4 shows that at the Plateau borders, the gas-liquid interface is curved thus generating a low-pressure region (PB) in the Plateau area (as given by the Young-Laplace equation (Eq. 4.1)). Because the interface is flat along the thin-film region, a higher pressure region (PA) is present there. This pressure difference forces liquid to flow toward the Plateau borders and causes thinning of the film and motion within the foam. 50 Figure 4.4: Pressure differences across surfaces in a foam lamella (Schramm, 1994). Liquid flow carries with it surfactant molecules producing uneven distribution of surfactant along the surface. The resulting non-uniform surfactant concentration on the surface leads to local variation of surface tension. If a surfactant-stabilized film undergoes sudden expansion due to liquid drainage, then the expanded portion of the film has a lower concentration of surfactant because of the greater surface area (see Figure 4.5). This causes an increased local surface tension that provides increased resistance to further expansion. A local rise in surface tension produces immediate contraction of the surface and coupled with viscous forces, induces liquid flow in the thin film from the low to the high surface tension region. The transport of bulk liquid due to surface tension gradients is termed the Marangoni effect and provides resistance to film thinning by gravity and capillary pressure (Schramm, 1994; Garrett 1993). As discussed below, this kind of resisting force exists only until the surfactant adsorption equilibrium is re-established in the film. 51 Expansion Expansion Surface Tension Gradients Figure 4.5: Schematic description of surface tension gradient induced flow, i.e. Marangoni effect (Schramm, 1994). The disjoining pressure becomes important in very thin lamellae (film thickness of the order of a few hundred nanometres), just prior to rupture. When two interfaces that bind a foam lamella are electrically charged (e.g. by an ionic surfactant), the interacting diffuse double layers exert a hydrostatic pressure that acts to keep the interfaces apart and stabilize the foam. The disjoining pressure represents the net pressure difference between the gas bubbles and the bulk liquid from which the lamellae extend, and is the total of the electrical, dispersion and steric forces that operate across the lamellae, perpendicular to the interface (Schramm, 1994). As discussed above, the factors that influence foam stability are primarily governed by the dynamic surface properties of the system. A popular experimental technique for measuring dynamic surface tension is the maximum pressure bubble method (MBMP) (Schramm and Green, 1992), based on measuring the maximum pressure necessary to blow a bubble in a liquid from the tip of a capillary. In practice, the pressure increases within the capillary at constant gas flowrate until a bubble appears at the tip of the orifice. The Young-Laplace equation (Eq. 4.1) relates the pressures inside and outside the bubble to the capillary orifice radius and liquid surface tension. A schematic of a typical apparatus is shown in Figure 4.6. The larger capillary is a reference, eliminating hydrostatic pressure. This technique yields the dynamic surface tension for a specific bubbling rate. 52 thermocouple Liquid Figure 4.6: Schematic of maximum pressure bubble method for measuring dynamic surface tension. Huang et al. (1986) determined the dynamic surface tension for a series of alpha-olefin sulfonates (AOS) by the M P B M . Figure 4.7 presents the variation of surface tension with bulk concentration and bubbling frequency for C14 AOS with 1% wt. aqueous NaCl solution. Their results show that as the surfactant concentration increases, the equilibrium surface tension decreases and levels out at the C M C (critical micelle concentration). For low and medium surfactant concentrations, the dynamic surface tension departs from its equilibrium value, and this difference increases with increasing bubbling rate. 53 Figure 4.7: Variation of surface tension with bubbling frequency and bulk concentration of C 1 4 alpha-olefin sulfonates in 1% wt. NaCl aqueous solutions (Huang et al., 1986). As gas is injected into the liquid, the surface of the bubble expands with time until it detaches from the capillary tip. This results in a surface concentration different from the equilibrium value and thus the local surface tension increases. To restore the equilibrium surface concentration, the surfactant molecules in the bulk diffuse to the expanding surface. This diffusion controlled adsorption process depends upon the time scale of the bubble creation. Thus, at fixed concentration and high frequencies, less time is available for surfactant molecules to diffuse to the surface; consequently the local surface tension is higher. To reach the same surface tension at higher frequencies, the rate of diffusion must be faster. This can only be achieved by the bulk concentration so that the concentration gradient and diffusivity are larger. As the surfactant concentration increases, the dynamic surface tension gradually falls to an equilibrium value since the diffusion rate is high. Hence, with concentrated surfactant solutions, diffusion rates are rapid and surface tension gradients tend to be eliminated. This is why saturated solutions are considered to be poorly foaming liquids (Bickerman, 1973; Shah et al., 1985). The dissipation of surface tension gradients to achieve equilibrium effectively provides the interface with a finite elasticity. Surface elasticity can be measured directly or obtained by 54 measurements of dynamic surface tension coupled with some information about surfactant diffusion rates (Schramm, 1994). Therefore, the maximum pressure bubble method can also be used to determine the surface elasticity. The dilatational surface elasticity (E M ) is defined as the surface tension variation with respect to the bubble surface unit fraction area (A b) change, i.e. E M = d a / d l n A b = A b d a / d A b (4-4) Here A b can be characterized by the tip diameter of the small capillary, thus d A b / A b is proportional to the rate of bubble formation since approximately equal bubble areas are produced at the maximum bubble pressure condition for all bubbling rates (Huang et al., 1986). The dilatational surface elasticity is then directly proportional to the slope of the dynamic surface tension as a function of the bubbling rate. Huang et al. (1986) also evaluated the dilatational surface elasticity for the series of alpha-olefm sulfonates. Their results suggested a correlation between surface elasticity and thin film drainage time, static foam half-life and dynamic foam height. These correlations all reflect the fact that high surface elasticity promotes high film stability. In summary, the first requirements for foaming are surface tension lowering and surface elasticity. Gradients may occur i f surface tensions depart from equilibrium values. This will happen when foam film gas-liquid surfaces are expanded at rates so fast that the equilibrium with the bulk surfactant concentration cannot be maintained. A greater surface elasticity tends to produce more stable bubbles. However, i f the restoring force contributed by surface elasticity is not sufficient in magnitude, then persistent foam may not be formed because of the overwhelming effects of gravitational and capillary forces. As for the action of antifoams, the addition to a foaming system of any soluble substance that can become incorporated into the interface may decrease dynamic foam stability i f the substance increases surface tension, decreases surface elasticity, decreases surface viscosity, or decreases surface electrical potential (Schramm, 1994). Such effects may be caused by 55 cosolubilization effects in the interface, or by partial or even complete replacement of the original surfactants at the interface. Alternatively, adding a chemical that actually reacts with the foam-promoting agent(s) can destroy foam. Finally, foams may also be destroyed or inhibited by the addition of certain insoluble substances, such as a second liquid phase or a solid phase into the foam. For hydrocarbons, silicone oil has been demonstrated as an effective antifoaming agent (Callaghan, 1993). It would appear that there has not been a systematic study on liquid foaming in three-phase fluidized beds. In fact, most researchers that have used foaming liquids (e.g. kerosene, surfactants) do not mention whether they encountered foaming. Saberian-Broudjenni et al. (1987) using kerosene, Blum and Toman (1978) using light mineral oil, and Fan et al. (1987) and Nacef et al. (1992) both using a 0.5% wt. t-pentanol aqueous solution have reported operating the bed under foaming conditions. There have been many more studies on simpler systems such as bubble and slurry bubble columns (Pino et al., 1990,1992; Guitian and Joseph, 1998). The onset of foaming was found to be dependent on the gas and liquid superficial velocities, column diameter, liquid bulk and interfacial properties and particle properties (diameter, shape, density, wettabiltiy and holdup). Unfortunately, there is no general model to predict the onset of liquid foaming. 4.1.4 Experimental Attempts to Evaluate Bubble Coalescence Behaviour in a Liquid a) One can observe the contact between two identical bubbles injected into the liquid by nozzles and measure the coalescence time or probability (Zahradnik et al., 1999). Based on the work of Marrucci (1969) and Andrew (1960), Sagert and Quinn (1978) concluded that the bubble coalescence time in solutions of surfactants and electrolytes was well characterized by the dimensionless concentration group (£,0 2r b/a). For a binary solution: 5 = -2r, da dc, 2a, l + ( x , V , / x 2 V 2 ) RT da da. da dc. l + ( x , V , / x 2 V 2 ) and Q = 12Tca A h r b (4.5) 56 where Tj is surface excess concentration of solute, ax and cx are the activity and molar concentration of the solute, respectively, R is the gas constant, T is the absolute temperature, X ! and x 2 and V ! and V 2 are the molar fractions and molar volumes of the solute and solvant, respectively, and A h is the Hamaker-London constant. For £,92rb/c> < 2, bubble coalescence is very rapid as in the case of pure monocomponent liquids. For £,62rb/o~ > 28, local surface tension gradients immobilize the gas-liquid interface, suppressing bubble coalescense (Chaudaheri and Hofmann, 1994). The bubble coalescence time models require a priori knowledge of the bubble diameter and other physical characteristics that are not easily estimated, especially for multicomponent industrial liquids where the composition is unknown and may vary with time. Furthermore, in order to derive a mechanistic model for predicting the gas holdup and interfacial area from bubble coalescence times, information on the bubble contact time, contact frequency and break-up mechanism is also required (Chaudaheri and Hofmann, 1994). b) One can define a standard bubble column and compare the bubble size distributions obtained with different stagnant liquids at given gas flowrates (Wild and Poncin, 1996). c) Snape et al. (1992) mentioned that although equilibrium surface tension was an important parameter in determining the bubble behaviour, the dilatational surface elasticity was also required. d) Gorowara and Fan (1990) presented an interesting way of characterizing aqueous solutions of surface-active agents based on three criteria: • Surface tension drop caused by the surfactant. • Difference between the dynamic and equilibrium surface tension. This indicates i f the surfactant is well dispersed throughout the solution. • Variation of dynamic surface tension with the bubbling rate. By definition, this is the dilatational surface elasticity and indicates whether or not the surfactant adsorption is mass transfer limited. 57 They concluded that dynamic surface tension is a much more important parameter than equilibrium surface tension in three-phase fluidized beds with surfactants. They proposed determining the presence of a surfactant by bubble rise velocity experiments. The rise velocity of an ellipsoidal bubble in the liquid solution is compared to a similar bubble in a pure liquid with the same dynamic surface tension. The rise velocity of an isolated ellipsoidal bubble is hindered by a surfactant since Eo < 40. However, they cautioned that the bubble rise velocity is not an accurate overall index of the gas holdup behaviour, but will indicate that a surfactant is present affecting the gas holdup. e) Bhaga et al. (1971) using mixtures of organic liquids proposed a dimensionless coalescence parameter (C), defined as the increase of gas holdup measured at 50% by weight divided by the holdup calculated at this composition by linear interpolation between the measured pure individual components (i.e. on Figure 4.1c; C = ab/bc). f) For foaming liquids, a typical experiment (Bickerman, 1973) is to sparge saturated gas into a graduated cylinder containing a certain volume of liquid, see Figure 4.8. Two parameters related to the foam-forming tendency can be derived from this exercise: # Foam retention time (R f), which is the ratio of the foam volume generated at a given gas flowrate to that flowrate. _ foam volume 4^ ^ f gas flowrate * Foam half-life (tf>(1/2)) is determined from the collapse curve once the gas flow has been stopped. Assuming that first-order kinetics describe the foam volume decay: _ 0-693 where k f is the foam decay rate constant. (4.7) Lf,(l/2) - ^ 1 J 58 graduated glass cylinder g l a s s \^ J s i n t e r s F L O w| c o N T R O L L E R - g a s supply Oil O r e s c h e l bottle Figure 4.8: Bikerman sparge tube apparatus (Callaghan, 1993). From all these previous methods, it is suggested that in addition to the liquid surface tension, viscosity and density, the following dynamic physical properties should be measured in an attempt to evaluate the bubble coalescence behaviour in a liquid. 1) Foam retention time and half-life These parameters indicate which liquids are more likely to foam. 2) Dynamic surface tension and surface elasticity For components at the gas-liquid interface to be well dispersed and in equilibrium with the bulk concentration, the dynamic surface tension must equal the equilibrium surface 59 tension. For non-mass transfer limited solutions, the surface elasticity tends towards zero since the dynamic surface tension does not change with the bubble formation rate. Surface elasticity characterizes the rate of adsorption of surfactants. If possible, the surface excess concentration of solute (T,), which characterizes the extent of adsorption at the gas-liquid interface and the dimensionless group (^02rb/cr), which includes (T,) and characterizes the bubble coalescence time, should be estimated. 4.2 Choice of Experimental Unit and Gas-Liquid-Solid Materials This section describes the experimental unit and gas-liquid-solid materials chosen to achieve dimensional similitude based on the groups proposed by Safoniuk (1999). 4.2.1 Gas-Liquid Bubble Column Experiments were performed at ambient temperature and pressure in the 127 mm inner diameter column. In bubble columns with no net liquid flow (i.e. U L = 0) and no particles present, the number of parameters from the original list (see Chapter 1.4) is reduced from 8 to 5, so that (with still three dimensions) the number of independent dimensionless groups to be matched is reduced from 5 to 2: the liquid physical property group (M-group) and a gas velocity group (U g*) = UgU - L / o \ Experiments were carried out in three systems in which these two dimensionless groups were closely matched: a 55% wt. aqueous glycerol solution, silicone oil and paraffin oil, as well as in a mismatch system: tap water. Air was the gas in all four cases. Results obtained in the air-tap water system were utilized to compare the gas-liquid systems under similar operating conditions (i.e. disregard need of the dimensional similitude) and to provide additional data when evaluating gas holdup correlations found in the literature. The silicone oil is Dow Corning® 244 fluid, which is essentially (> 99%) octamethylcyclotetrasiloxane, with traces of the pentamer and hexamer. The paraffin oil is Penreco® Drakesol 220, a blend of saturated hydrocarbons (C 1 2 -C 1 7 ) . Table 4.1 presents the physical properties, operating conditions and values of the dimensionless groups for all four systems. A l l physical properties were determined experimentally. The liquid density was obtained with a 60 pycnometer, the viscosity by the falling ball method (Gilmont, model GB-104234) and the equilibrium surface tension by the duNouy ring pull method (Cenco, Model 70545). Table 4.1: Physical properties, operating conditions and values of the dimensionless groups for all four gas-liquid systems. Physical property or dimensionless group System 1 (air/aq. glycerol) System 2 (air/silicone oil) System 3 (air/paraffin oil) System 4 (air/tap water) M L (Pa-s) 0.0069 ± 0.0002 0.0024 ± 0.0001 0.0033 ± 0.0001 0.0010 ±.0001 o(N/m) 0.067 ± 0.001 0.0178 ±0.0002 0.027 ± 0.0005 0.072 ± 0.001 P L (kg/m3) 1125 + 3 953 ± 2 795 ± 2 1000 ± 2 U g(m/s) 0 to 0.27 0 to 0.2 0 to 0.2 0 to 0.2 ±0.001 ±0.001 ± 0.001 ± 0.001 M ( 6 ± l)xl0" 8 (6± l)xl0" 8 (7 ± l)xl0" 8 (3± l ) x l 0 - n UgP-L/O- 0 to 0.028 0 to 0.027 0 to 0.024 . 0 to 0.0028 ± ~7% ± -7% ± ~7% ± -7% Pi/Pg 938 ± 3 794 ± 2 663 ± 2 833 + 2 Errors in the physical properties were estimated from repeated experiments, while errors on the dimensionless groups were estimated from the Taylor series analysis: • A X i (4-8) where Y and x are, respectively, the dependent and independent variables. The static liquid height was 1520 mm, corresponding to an aspect ratio (H/D) of 12. Wilkinson et al. (1992) suggested that the overall gas holdup is virtually independent of i=l 8Y 61 column dimensions provided that D > 100 - 150 mm and H/D > 5. At this stage, it was assumed that the difference in (PL/P g) between the systems did not significantly affect the hydrodynamics. A separate study on the effect of gas density is presented in Chapter 5. 4.2.2 Liquid-Solid and Gas-Liquid-Solid Fluidized Beds Experiments were also carried out at ambient temperature and pressure in the 127 mm internal diameter column with two dimensionally similar three-phase systems: the 55% wt. aqueous glycerol solution with spherical borosilicate particles and the Dow Corning® 244 fluid with spherical porous alumina particles, with air as the gas in both cases. A new solution of aqueous glycerol was prepared for this set of experiments. Table 4.2 presents the physical properties, operating conditions and values of the dimensionless groups for these two systems and those of Syncrude's LC-Finer. The three-phase fluidized beds were chosen so that values of the five dimensionless groups were relatively close to those of the LC-Finer. Note that the Archimedes (Ar p) number is not an additional independent group since: gP L (p p -P L )dp g ( p L - p g ) ( p p - p L ) d ; (Eo*)3 (4.9) M 62 Table 4.2: Physical properties, operating conditions and values of the dimensionless groups for the two matched gas-liquid-solid systems and those for Syncrude's LC-Finer. Physical property or dimensionless group System 1 (air/aq. glycerol/glass) System 2 (air/silicone oil/alumina) LC-Finer p L (Pas) 0.0068 ± 0.0002 0.0024 ± 0.0001 o-(N/m) 0.067 + 0.002 0.0178 ±0.0002 P L (kg/m3) 1128 ± 3 953 ± 2 PP,wet (kg/m3) 2230 ± 2 1881 ± 5 dp(m) 0.0060 ± 0.0001 0.0032 ± 0.0003 U L(m/s) 0.052 to 0.119 (±0.001) 0.041 to 0.093 (± 0.001) U g (m/s) Oto 0.129 (± 0.001) 0 to 0.954 (± 0.001) A r p 57000 ± 12000 49000 ± 20000 P L / P G 940 ± 3 794 ± 2 18.7 D/dp 21.2 ±0 .4 40 ± 4 «2500 M (6± l )xl0" 8 ( 6 ± l )xl0" 8 lxlO" 8 Eo* 5.9 ±0 .4 5.4 ±0.9 4.1 P P / P L 1.98 ±0.01 1.97 ±0.01 2.43 Re L 52 to 119 (± -6%) 52 to 119 (±-15%) 148 U g / U L Oto 1.5 (±~4%) Oto 1.5 (±~4%) 0.84 £ s m f ( a t U g = 0) 0.58 0.58 The porous alumina wet particle density (P P ; W e t) was calculated from the slope of the bed dynamic pressure drop versus solids holdup in a liquid-solid fluidized bed as shown in Figure 63 4.9. The solids holdup (es) is determined from Equation (2.1) with the dry particle density (pP,dry) obtained by weighing and measuring the diameter of 150 particles. 450 400 350 300 . 250 ^ 200 % 150 i 100 50 0 -j» y = 927.54x / r 2 = = 0.9996 / 3 p , v ^ t = P L + slope = 953 + 928 = 1881 kg/m3 0.1 0.2 0.3 Solids holdup, [-] 0.4 0.5 Figure 4 . 9 : Dynamic pressure drop versus solids holdup in a silicone oil - porous alumina fluidized bed. The borosilicate beads were considered to be wetted by the water-glycerol solution. The porous alumina spheres seemed to be wetted by the silicone oil (i.e. all the pores seemed imbibed with liquid when sample particles were sliced open after the particles had been fluidized by air and silicone oil). However, the measured wet particle density differs slightly from the theoretical estimate: 'p,wet : Pp,dry Pp,dry Palu P L (4.10) mm a J with the dry particle, pure alumina and silicone oil densities, respectively being, 1394 kg/m , 3990 kg/m and 953 kg/m , then the wet particle density from this equation should have been 2014 kg/m . This value is 7% higher than the 1881 kg/m determined from the slope in Figure 4.9, indicating that the particles did not fully imbibe the silicone oil. It is possible that 64 the porous alumina spheres contained dead-end pores and/or that they were not as wettable as the glass beads (i.e. a larger contact angle is formed by the liquid phase as it touches the gas and solid phases). Greater bed expansions and lower gas holdups are obtained in gas-liquid-solid systems with non-wettable particles. The particle size distribution was very narrow for the borosilicate spheres (dp = 6.0 ± 0 . 1 mm), while it was less so for the porous alumina spheres (dp = 3.2 ± 0.3 mm). The difference in particle size distribution was considered acceptable since the two systems presented virtually the same solids holdups at minimum fluidization (s s m f = 0.58 at U g = 0 and £ s m f ~ 0.63 for U g > 0). The particle density distribution was uniform for both types of particles. The ratio of column to particle diameter (D/dp) was not matched. However, since this ratio in both cases was greater than 20, wall effects were assumed to be small for both systems. For the two systems, the static bed height was 560 mm. The bed aspect ratio (H b/D) exceeds 4, thus reducing the impact of entrance and exit effects on overall hydrodynamics. In addition, as presented in Chapter 2.2, the column design provided a uniform initial spatial distribution of the fluids and minimized end effects for all systems. 65 4.3 Effects of Liquid Composition on Gas-Liquid Bubble Column Hydrodynamics Experiments were performed at several gas velocities in order to operate in both the dispersed and coalesced bubble flow regimes. The hydrodynamic data relate to the foaming behaviour, overall gas holdups, dispersed/coalesced bubble flow regime transition velocity, pressure fluctuations, and gas holdup structure. 4.3.1 Dynamic Physical Properties of the Liquids The dynamic surface tension (odyn) and dilatational surface elasticity (E M ) were obtained by the maximum pressure bubble method (Sensadyne 5000) with 4 mm and 0.5 mm inner diameter glass capillaries. Figure 4.10 presents the surface tension as a function of the bubble formation rate (ft,) for all four gas-liquid systems. The filled-in symbols represent data obtained from the static ring pull method. d g 'a & <u o CO 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 • o • o 4A 0.5 O water-glycerol • silicone oil A paraffin oil o tap water 1.5 ft, [Hz] 2.5 Figure 4.10: Surface tension versus bubble formation rate for gas-liquid systems investigated. Filled-in symbols represent data obtained from the ring pull tensiometer method. For all four gas-liquid systems, the surface tensions did not significantly vary with the bubbling rate and are similar to the static or equilibrium value obtained from the ring pull 66 method. These results suggest that surface-active contaminants, i f present, are well dispersed in the liquid and that their transport from the bulk to the gas bubble surface is rapid. Huang et al. (1986) obtained a similar conclusion for high concentrations of Q 4 AOS in a 1% wt. aqueous NaCl solution (see far right portion of Figure 4.7). Over the range of operating conditions, the water-glycerol mixture and paraffin oil experienced foaming, while silicone oil and tap water did not. The foam retention time (Rf) and half-life (tf,(i/2)) were obtained in the bubble column set-up employed in this work. The foam retention time was determined from the slope of foam height generated versus superficial gas velocity for 0 < U g * < 0.0025. The foam half-life was calculated from the foam height collapse curve after the gas flow (U g * = 0.015) was suddenly interrupted (see Figure 4.11). Table 4.3 summarizes the dynamic surface properties and the foam formation characteristics of the four gas-liquid systems investigated. Time, [s] Figure 4.11: Foam collapse curve for water-glycerol and paraffin oil: U g * = 0.015. 67 Table 4.3: Dynamic surface properties and foam formation ability for the four gas-liquid systems investigated. Gas/ Air/ Air/ Air/ Air/ Liquid Aq. glycerol Silicone oil Paraffin oil Tap water LX l (Pas) 0.0069 0.0024 0.0033 0.0010 p L(kg/m 3) 1125 . 953 795 1000 CT(N/m) 0.0670 0.0178 0.0270 0.0720 o d y n (N/m) 0.0682 0.0186 0.0275 0.0721 4 = 1 Hz E M (N-s/m) « 0 «o * 0 ~0 0.1 <f b <3 Hz Rf(s) 0 0 2.8 0 0 < U g * < 0.0025 lf,(l/2) ( S ) 23 0 15 0 U g * = 0.015 Relative foaming tendency + ++ Aqueous glycerol is considered a poorly foaming liquid (Bikerman, 1973). The water-glycerol mixture foam retention time was zero. At low gas flowrates, corresponding to the dispersed bubble flow regime, no foam was generated. Instead, bubbles reaching the liquid surface quickly coalesced with the interface. As the water-glycerol mixture entered the coalesced bubble flow regime, the liquid was no longer clear, but became milky, like a froth. Microbubbles generated at the distributor are likely to have been responsible for the opacity of the liquid. The transition to the coalesced bubble flow regime greatly increased mixing and turbulence, creating more microbubbles. A proper foam layer above the liquid level was 68 only visible upon interruption of the gas flow as microbubbles rising from the froth did not have time to coalesce. Hence the foam layer was composed of uniform small spherical bubbles (visually with d b < 1 mm). The paraffin oil foam retention time was greater than for the water-glycerol mixture. Throughout the dispersed bubble flow regime, bubbles reaching the liquid surface were sufficiently inhibited by surface-active components to produce a layer of foam. The foam structure was different from that of the water-glycerol mixture as there was an axial gradient of bubble size (e.g. as in Figure 4.2). At the top of the foam layer, bubbles were polyhedral in shape. Near the bottom of the foam layer, just above the bubbly liquid, bubbles were smaller and nearly spherical. As the paraffin oil underwent a transition to the coalesced bubble flow regime, the interface between the foam layer and clear liquid became fuzzy and eventually disappeared causing the entire liquid to resemble a froth. The liquid opacity is then also due to microbubbles emanating from the gas distributor and from the foam layer, which is now intimately mixed with the frothy liquid. The paraffin oil, being less viscous, had a shorter foam half-life than the water-glycerol mixture, despite a greater initial foam height. 4.3.2 Overall Gas Holdup Overall gas holdups were determined from dynamic pressure drops along the column at several levels. The axial variation of gas holdups was considered negligible since the dynamic pressure drop slopes (-AP/Az) were almost perfectly linear (R 2 > 0.98). From repeated experiments, the coefficients of variation (standard deviation divided by the average)of gas holdups were less than 2%. The coefficients of variation between gas holdups obtained from the rise of the liquid level and the dynamic pressure drop were also less than 2%. Overall gas holdups are plotted versus U g * for the three matched systems in Figure 4.12. The triangular symbols represent the paraffin oil gas holdups, including the foam layer above the liquid level, while the circular symbols represent gas holdups for the same system in the bubbly liquid below the foam layer. Paraffin oil gas holdups including the foam layer were 69 determined from the rise of the (liquid + foam) level, which neglects the liquid fraction in the foam layer (i.e. eg in foam layer = 1). The filled-in symbols represent the transition velocity points from dispersed to coalesced bubble flow obtained by the drift-flux method. This transition is discussed in section 4.3.3 below. U g * = U g U L / a , [ - ] Figure 4.12: Overall gas holdup versus U g * for the three matched gas-liquid systems. Filled-in symbols represent the transition from dispersed to coalesced bubble flow obtained from the drift-flux method. Gas holdups were lower and the change of slope from dispersed to coalesced bubble flow smoother for silicone oil than for the water-glycerol mixture and paraffin oil. Hence silicone oil exhibited a higher bubble coalescence rate. Krishna and Ellenberger (1996) also reported lower gas holdups with a monocomponent liquid (tetradecane: p.L = 0.0022 Pas, a = 0.027 N/m, p L = 763 kg/m3) than for a multicomponent liquid (paraffin oil: U L = 0.0023 Pa-s, a = 0.028 N/m, p L = 795 kg/m ), despite very similar physical properties. They did not report whether or not their paraffin oil foamed. When the foam fraction above the bubbly liquid is excluded, gas holdups between the paraffin oil and water-glycerol mixture are very similar. Although, the quantity and nature of 70 surface-active components present in the two liquids must have been different, these differences did not seem to affect the bubbling behaviour in the clear liquid. For low gas flowrates (i.e. s g < -6%), gas holdups were similar among the gas-liquid systems. Bubbles were well dispersed and surface-active components affected the rise velocities to a similar extent. However, at higher gas holdups, bubbles in the silicone oil gradually start to coalesce, while coalescence is inhibited in the liquid mixtures. The differences in gas holdups increase with increasing gas flowrate, until the multicomponent liquids abruptly reach the coalesced bubble flow regime. The slopes of the curves in the coalesced bubble flow regime are almost parallel, suggesting that the effect of gas velocity on gas holdup is virtually independent of liquid physical properties. In the coalesced bubble flow regime, Krishna et al. (1991) and Wilkinson et al. (1992) proposed a gas holdup model with a bimodal bubble size distribution. Gas in excess of that required to achieve the dispersed/coalesced bubble flow transition velocity is assumed to flow through the column as "large" bubbles, while the gas holdup due to "small" bubbles reaches a maximum at the transition and remains relatively constant throughout the coalesced bubble flow regime. Krishna and Ellenberger (1996) reported that the small bubble holdup was influenced by the gas distributor and by the gas and liquid physical properties, but not by the column diameter. Grund et al. (1992) and Krishna and Ellenberger (1996) found that the large bubble holdup was influenced by the column diameter, but virtually independent of the gas distributor and liquid physical properties. The rise velocity of large bubbles was insensitive to liquid properties, as predicted by the well-known Davies-Taylor relationship for spherical-cap bubbles in low-viscosity liquids. Our results are consistent with these findings. Figure 4.13 presents overall gas holdups versus U g for the tap water, water-glycerol and silicone oil systems. Here and elsewhere in Chapter 4.3, hydrodynamic data from the air-tap water system is presented in a dimensional manner in order to show similarities with the other gas-liquid systems under similar range of operating conditions. 71 Natural contaminants in the tap water inhibited bubble coalescence and reduced bubble rise velocities prolonging the dispersed bubble flow regime and leading to relatively high gas holdups. For spherical and ellipsoidal bubbles (Eo < 40) typically found in the dispersed bubble flow regime, surface impurities eliminate internal circulation of the gas, thereby significantly increasing drag and reducing the rise velocity (Clift et al., 1978). In the coalesced bubble flow regime, at high bubbling/coalescence rates, tap water seemed to overcome the effect of surface-active components and gas holdups converged with those of silicone oil. In this flow regime, large spherical-cap bubbles (Eo > 40) form and the effects of surface tension forces and surface-active components are less significant (Clift et al., 1978). Krishna and Ellenberger (1996) reported similar gas holdups for demineralized water and tetradecane for superficial gas velocities ranging from 0.1 to 0.9 m/s. - 0 - - silicone oil —B-- water-glycerol —SK-- tap water 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Ug,[m/s] Figure 4.13: Overall gas holdup versus U g for the air/aq. glycerol, air/silicone oil and air/tap water systems. 4.3.3 Flow Regime Transition Velocity from Dispersed to Coalesced Bubble Flow The transition from dispersed to coalesced bubble flow was marked by an increase in bubble size, a broader bubble size distribution, local liquid circulation patterns and small amplitude fluctuations in liquid level. While the flow regime transition occurred over a gas velocity 72 range, a specific transition point was estimated by plotting the drift-flux versus gas holdup. A typical example appears in Figure 4.14. 0.14 -, , Gas holdup, [-] Figure 4.14: Drift-flux versus overall gas holdup for the air/aq. glycerol system. Table 4.4 presents (U g ) t r ans , (U g*)trans and (sg) t rans determined in this manner for all four gas-liquid systems investigated. The gas holdup and dimensionless gas velocity at the transition are similar for the aqueous glycerol and paraffin oil, but lower for the silicone oil. Tap water and aqueous glycerol gave similar holdups and dimensional gas velocities at the transition. Table 4.4: Dispersed/coalesced bubble flow transition velocities for all four gas-liquid systems investigated. Gas/ Air/ Air/ Air/ Air/ Liquid Aq. glycerol Silicone oil Paraffin oil Tap water (Ug)trans [m/s] 0.048 0.0277 0.036 0.046 (Ug*)trans ["] 0.0047 0.0037 0.0044 0.0007 (£g)trans ["] 0.21 0.10 0.18 0.18 73 4.3.4 Pressure Fluctuations Pressure fluctuations in multiphase systems originate from dynamic phenomena taking place on different length and time scales. Vial et al. (2001) reported that the influence of macroscopic fluid circulation and bed level oscillation is restricted to frequencies below 1 Hz, while the influence of bubbles dynamics (formation, coalescence/break-up, passage and eruption) is in the range of 1 - 20 Hz. Turbulence in the continuous phase leads to pressure fluctuations of much higher frequencies. Absolute pressure transducers 380 and 1300 mm above the gas/liquid distributor determined absolute and differential pressure fluctuations for 180 s periods at 100 Hz. Figure 4.15 presents differential pressure fluctuation standard deviations, normalized by their average values, versus U g * for the three matched systems. 0 -I 1 1 , 1 1 1 1 0 0.004 0.008 0.012 0.016 0.02 0.024 0.028 U g * = U g p L / C T , [-] Figure 4.15: Normalized differential pressure fluctuation standard deviations versus U g * for the three matched gas-liquid systems. Filled-in symbols represent (U g *) t r ans obtained from the drift-flux method. In the dispersed bubble flow regime, the standard deviations first decrease, then remain relatively constant for the water-glycerol mixture and paraffin oil, while they steadily 74 increase for the silicone oil. This indicates stronger bubble coalescence in the silicone oil. The initial decrease of standard deviation is due to improved distributor performance (i.e. more uniform bubble spatial distribution and reduced average bubble size) as the superficial gas velocity increases. As the coalesced bubble flow regime is encountered, the bubble size and breadth of the bubble size distribution significantly increase, resulting in a strong increase in the standard deviations. The change of slope is more pronounced and abrupt for the water-glycerol mixture and paraffin oil. This again suggests a smoother transition to coalesced bubble flow for the silicone oil. The changes of slope occur at similar U g * values as the (U g *) t r a n s obtained from the drift-flux method (filled-in symbols). Pressure standard deviations are smaller for the water-glycerol mixture than for silicone oil in dispersed bubble flow, but are larger when the flow regime changes to coalesced bubble flow. That is because the equilibrium bubble size, after coalescence and break-up, is smaller in low surface tension liquids than in high surface tension liquids (Fan, 1989). Figure 4.16 presents power spectra of normalized differential pressure fluctuations for the three matched systems at several values of U g * , with dimensionless frequency (f* = fUg/g) as the abscissa. A Strouhal number (frequency x length scale/velocity) was not employed since a characteristic length scale was not available. Bubble diameters were unknown and the column diameter is not an appropriate length scale (i.e. bubbles dynamics do not vary monotonically with column size). The pressure power spectrum peak increases in intensity and decreases in frequency with increasing gas velocity, due to the formation of larger bubbles as the flow regime changes from dispersed to coalesced bubble flow. The relative peak intensity between the gas-liquid systems matches the trend presented by the pressure standard deviations in Figure 4.15. The major peak intensity of the water-glycerol mixture is lower than for silicone oil in the dispersed bubble flow regime, but larger in the coalesced bubble flow regime. For the water-glycerol mixture and paraffin oil, there is a definite shift in major peak frequency as U g * increases, while for silicone oil the shift is less pronounced. 75 0.00014 0.00012 U g * = 0.0010 0.00016 0 0.01 0.02 0.03 0.04 0.05 f* = fug/g,[-] c 3 CJ o CL. s 1 C3 0.0005 0.0004 0.0003 0.0002 0.0001 0 U g * = 0.0025 ^ 0.025 0 0.03 0.06 0.09 0.12 f*=fUg/g, H U a * = 0.01 0.1 0.2 0.3 0.4 f* = fUg/g, [-] 0.5 0.02 0.04 0.06 0.08 0.1 f* = fug/g, H 0. 0.05 0.1 0.15 0.2 0.25 S 1 0.1 0.2 0.4 0.6 0.8 f = f U B / & [ - ] Figure 4.16: Power spectral distributions of normalized differential pressure fluctuations for the three matched gas-liquid systems at several U g * . The thick, thin and broken lines represent the water-glycerol, silicone oil and paraffin oil systems, respectively. 76 The significant frequency shift and strong increase in major peak intensity again indicate that the transition from dispersed to coalesced bubble flow was more distinct and abrupt for the water-glycerol mixture and paraffin oil than for the silicone oil. In the dispersed bubble flow regime, the peak frequencies are mismatched. The dominant frequencies in the coalesced bubble flow regime are matched at f* « 0.05, corresponding to approximately 2.5 Hz for the water-glycerol mixture and 3.5 Hz for the paraffin and silicone oils. This indicates that the large bubble holdup, which dominates the dynamics in this regime, is not very sensitive to the liquid physical properties. Figure 4.17 presents normalized differential pressure fluctuation standard deviations versus U g , while Figure 4.18 plots power spectra of normalized differential pressure fluctuations for tap water and water-glycerol. 0 -I 1 1 1 1 1 1 1 0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 U g , [m/s] Figure 4.17: Normalized differential pressure fluctuation standard deviations versus U g for the air/aq. glycerol and air/tap water systems. 77 0.00006 0.00002 5 10 15 20 25 30 35 40 45 50 Frequency, [Fiz] 5 10 15 20 25 30 35 40 45 50 Frequency, [Hz] Figure 4.18: Power spectral distributions of normalized differential pressure fluctuations for gas-liquid systems at U g = 0.018 and 0.193 m/s. The thick and thin lines represent the water-glycerol and tap water systems, respectively. The tap water standard deviations and power spectra resemble results obtained in the water-glycerol mixture. In dispersed bubble flow, both liquids presented similar bubbling behaviour and gas holdups. In coalesced bubble flow, gas holdups differed, at least in part because the water-glycerol mixture foamed, while the tap water did not. However, in this flow regime, pressure fluctuations are not significantly affected by microbubbles from the froth, but by large bubbles, which are virtually independent of liquid physical properties for the limited range of liquid viscosity and density covered in this study. 4.3.5 Gas Holdup Structure The structure of the gas phase was determined by the Dynamic Gas Disengagement (DGD) technique (see Chapter 2.3.5) using a differential pressure transducer connected to ports 60 mm above the gas distributor and 120 mm below the static liquid surface. The dynamic pressure drop signal was sampled at a rate of 5 Hz . 4.3.5.1 Experimental Dynamic Gas Disengagement Profiles Figure 4.19 presents the gas disengagement profiles for the three matched systems for several pre-interruption values of U g * , with dimensionless time (t* = tg/U g ) as the abscissa. 78 a, i o CO O 0.1 0.08 0.06 0.04 0.02 0 \ U * = 0.0019 s. 27000 28000 29000 30000 31000 32000 33000 34000 35000 36000 t* = tg/Ug,[-] ' 0.24 0.2 1 0.16 si 1 0.12 o CO CM 0.08 o 0.04 0 u g * = 0.005 10000 10500 11000 11500 12000 12500 13000 13500 14000 14500 15000 t*=tg/U g ) [-] CO ca O 3000 3400 3800 4200 4600 5000 5400 5800 6200 6600 t*=tg/Ug, [-] Figure 4.19: Gas holdup after abruptly terminating gas flow after operating at several U g * for the three matched gas-liquid systems. The thick, thin and broken lines represent the water-glycerol, silicone oil and paraffin oil systems, respectively. Arrows indicate bubble class disengagement break points as depicted in Figure 2.7. 79 In the dispersed bubble flow regime (U g * = 0.0019), the collapse lines for the gas-liquid systems are relatively linear indicating a narrow bubble size distribution. For U g * = 0.005, the water-glycerol mixture and paraffin oil are still operating in the dispersed bubble flow regime as indicated by nearly linear collapse profiles. However, the silicone oil has already undergone transition to the coalesced bubble flow regime, as indicated by the small break in the collapse profile. In the coalesced bubble flow regime (U g * = 0.015), the gas disengagement profiles of the water-glycerol mixture and paraffin oil break at two points (see arrows on figure) due to microbubbles slowly rising from the froth. The profiles are quite similar as they break at nearby points suggesting similar gas holdup fractions. The slopes for the large and small bubble fractions are similar, but microbubbles escape at a faster rate for the paraffin oil. The silicone oil did not foam, leading to different gas holdups and disengagement times. The holdups of large bubbles (s gi), small bubbles (sg s) and microbubbles (s g m) were determined from break points in the gas disengagement profiles as described in Chapter 2.3.5. Figure 4.20 presents overall and small bubble holdups versus U g * for the three matched systems. For silicone oil, small bubble holdups remain relatively constant in the coalesced bubble flow regime and are approximately equal to the transition gas holdup (Sg)trans- For the water-glycerol mixture and paraffin oil, holdups of small bubbles decrease during the flow regime transition zone, then remain relatively constant once the coalesced bubble flow regime is well established. Small bubble holdups are slightly greater for the water-glycerol mixture and paraffin oil (s g s -12%) than for the silicone oil (s g s -10%). In Figure 4.21, large bubble holdups are plotted versus U g * for the three matched systems. The holdups of large bubbles are very similar and the slopes are parallel, in agreement with the parallel slopes obtained in the coalesced bubble flow regime in Figure 4.12. In the coalesced bubble flow regime, i f the small and large bubble fractions of the gas-liquid systems are relatively similar, then the differences between overall gas holdups must be mostly due to microbubbles. 80 g ja M 1 e ha > O 0.004 0.008 0.012 0.016 U g * = U g M i / a , [-] 0.02 Figure 4.20: Overall and small bubble holdup versus U g * for the three matched gas-liquid systems. Open points give eg; filled-in points depict sg s. Arrows indicate flow transition gas holdups. 0.14 0.12 0.1 S1 % 0.08 1 0.06 0.04 0.02 • water-glycerol O silicone oil O paraffin oil 0.004 0.008 0.012 0.016 U g*=UgUL/o,[-] 0.02 0.024 Figure 4.21: Large bubble holdup versus U g * for the three matched gas-liquid systems. 81 Figure 4.22 plots overall gas holdups minus the microbubble contribution (s g - e g m) versus U g * for the three matched systems. It is seen that removal of the microbubble fraction greatly improves the match. 0.28 0.24 0.2 ^ 0.16 ! w ' 0.12 0.08 0.04 0 & • • • O o o o o o - E b • water-glycerol O silicone oil O paraffin oil 0 0.004 0.008 0.012 0.016 0.02 0.024 U g * = U g u L /o [.] Figure 4.22: Overall minus microbubble holdup (sg - s g m) versus U g * for the three matched gas-liquid systems. Figure 4.23 presents the gas disengagement profiles for the tap water, water-glycerol mixture and silicone oil at three gas velocities. In dispersed bubble flow ( U g = 0.0184 m/s), the tap water and water-glycerol mixture profiles are very similar, differing slightly from that for silicone oil. At U g = 0.073 m/s, tap water and the water-glycerol mixture have just entered the coalesced bubble flow regime and their profiles start to diverge as the water-glycerol mixture is foaming, while tap water is not. The silicone oil is, however, well into the coalesced bubble flow regime. Although some microbubbles were probably formed at the distributor for the tap water and silicone oil systems, both liquids remained transparent. The gas disengagement profiles show a bimodal bubble size population, suggesting that the majority of microbubbles must have coalesced very quickly. 82 0.1 0.08 cZ 0.06 O JS 0.04 0.02 0 ug = 0.018 m/s ~ •* >. 52 53 54 55 56 57 58 59 60 61 62 63 64 Time, [s] 0.28 0.24 % 0.16 T3 6 0.08 0.04 0 An u g = 0.073 n i/s A , 52 54 56 58 60 62 Time, [s] 64 66 68 70 0.32 0.28 v 0.24 2 0.16 0.12 O 0.08 0.04 0 = 0.147 m/s — W ' 1 *i 48 50 52 54 56 58 60 62 64 66 68 Time, [s] Figure 4.23: Gas holdup after abruptly terminating gas flow after operating at several values of U g . The thick, thin and broken lines represent the air/aq. glycerol, air/silicone oil and air/tap water systems, respectively. Arrows indicate bubble class disengagement break points as depicted in Figure 2.7. 83 In the coalesced bubble flow regime ( U g = 0.147 m/s), the tap water and silicone oil gas disengagement profiles are now similar and differ from the water-glycerol mixture. In agreement with Figure 4.13, these gas disengagement tests suggest that once the coalesced bubble flow regime is well established, the effects of surface-active contaminants on tap water gas holdups are no longer as significant and the holdup characteristics are relatively well defined by the physical properties. 4.3.5.2 Estimated Bubble Diameters and Bubble Swarm Velocities It is useful to estimate the average bubble diameter of each bubble class since the extent of interfacial effects depends on the bubble size and is most important for spherical and ellipsoidal bubbles with Eo < 40. As detailed in Chapter 2.3.5, the gas disengagement slopes are used in this section to estimate the superficial gas velocity through each bubble class. The bubble swarm velocity is then equal to the superficial gas velocity divided by the bubble holdup. Afterwards, the bubble swarm velocity is related to the rise velocity of a single isolated bubble, from which the average bubble diameter is finally extracted. This approach is not very accurate, but does give and order of grander of the bubble size. The bubble swarm velocity (Ub) can be related to the terminal rise velocity of a single bubble (Ubco) as follows: For small dispersed bubbles (Eo < 40) U b = U boo(l- £ g ) m _ 1 (1< m < 2.4) (Darton and Harrison, 1975) (4.11) where m is an exponent that takes into account the hindering effect of neighbouring bubbles. As suggested by Darton and Harrison (1975), m is taken as 2. For large spherical-cap bubbles (Eo > 40) U b = U b o o (SF)(AF)(DF) (Krishna et al., 2000) (4.12) 84 where a scale correction factor (SF) accounts for the influence of column diameter, an acceleration correction factor (AF) accounts for the increase in the large bubble swarm velocity over that of a single, isolated bubble due to wake interaction, and a density correction factor (DF) accounts for the influence of pressure. Details of these correction factors are presented in section 4.3.6 below. The terminal rise velocity, Ubco, can be related to the average bubble diameter using the correlation of Fan and Tsuchiya (1990): ub M=u PL M -0.25 \1.25 ( d b ) 2 - q + -,-1/ 2c - + PL-Pg PL (4.13) where db* is a dimensionless bubble diameter given by: d b = d b ( p L g / a ) X (4.14) Empirical parameters, q, c and K b in Equation (4.13) are said by the authors to reflect the contamination level of the liquid phase, variation due to dynamic surface tension changes with mono- and multicomponent liquids, and the viscous nature of the surrounding medium, respectively. Suggested values are: q = 0.8 and 1.6 for contaminated and purified liquids, respectively, c =1.2 and 1.4 for mono- and multicomponent liquids, respectively. K b = ( K b o M " 0 0 3 8 or 12), whichever is greater, with K b o = 14.7 and 10.2 for aqueous solutions and organic solvents/mixtures, respectively. Although contamination levels differ, all four gas-liquid systems are considered contaminated with respect to Equation (4.13). 85 Table 4.5 gives bubble swarm velocities and average bubble diameters predicted in this manner for all four gas-liquid systems in both the dispersed and coalesced bubble flow regimes. Bubbles in the dispersed bubble flow regime and small bubbles in the coalesced bubble flow regime were ellipsoidal in shape with Eo < 40, hence subject to the effects of contaminants, in accord with the dissimilar holdups between the matched gas-liquid systems in Figure 4.20. Large bubbles in the coalesced bubble flow regime give Eo » 40, for which surfactants are assumed to have a negligible impact on holdups, in agreement with the similar holdups between the matched gas-liquid systems in Figure 4.21. Table 4.5: Approximate bubble diameters and swarm velocities predicted from Equations (4.11) to (4.14) for the four gas-liquid systems investigated. Gas-Liquid System Dispersed bubble U g * = 0.0019 U g = 0.019 m/s (tap water) Coalesced bubble flow U g * = 0.015 U g = 0.15 m/s (tap water) u b s (mm/s) d b s (mm) u b , (mm/s) dbi (mm) u b s (mm/s) d b s (mm) Ubm (mm/s) dbm (mm) Eo Eo Eo Eo air/aq. glycerol 230 12.5 1080 29 240 13.9 13 0.5 26 135 32 0.04 air/silicone oil 210 10.4 980 22 190 9.5 0 0 57 259 47 0 air/paraffin oil 180 6.1 960 21 200 10.6 25 0.5 11 125 33 0.07 air/tap water 250 12.9 1020 21 270 17.5 0 0 22 60 41 0 86 4.3.6 Statistical Analysis of Gas Holdup Data In order to determine i f the gas-liquid systems were similar on a statistical basis, an A N O V A (analysis of variance) was performed on the gas holdup data. This test also provides the percentage of variability attributed to each factor on the response variable. A n F-value greater than F a= 0.o5 indicates that the factor is statistically significant at a confidence level of 95%. Table 4.6 summarizes the A N O V A results. Table 4.6: A N O V A on gas holdup data of the three matched gas-liquid systems. Response variable Factor Sum of squares Degrees of freedom F F a=0.05 % of total variability G-L Aq. glycerol vs. Paraffin oil 0.00001 1 3.6 4.1 0.01 Gas System Silicone oil vs. (Aq. glycerol & paraffin oil) 0.0433 1 13022 4.1 7.5 Holdup Gas velocity (U g*) 0.5103 11 13937 2.08 88.6 Interactions 0.0224 22 305 1.88 3.9 Intra-variability (error) 0.0001 36 - 0.02 Total 0.5761 71 - 100 As expected, the variance due to the gas-liquid system significantly affects the gas holdup. The system effect can be broken down into individual factors. The water-glycerol mixture and paraffin oil systems are statistically similar, while the silicone oil system differs significantly from the other two. The principal source of variability is U g * . The interaction between the effects of gas velocity and gas-liquid system is significant indicating that gas holdups respond differently to an increase of U g * for the different liquids (e.g. smoother and longer transition to the coalesced bubble flow regime for the silicone oil). 87 The differences between the gas-liquid systems can be characterized quantitatively by the root-mean-square-deviation (RMSD) and the bias factor (Fm), where 1 J R M S D = T £[(System(a)-System(b))/System(b)] i=l (4.15) F m = exp 1 j — £ ln(System(a)/System(b)) J i=i (4.16) Table 4.7 presents the root-mean-square-deviations and the bias factors between the gas holdups of the three matched gas-liquid systems. The gas holdup data between silicone oil and the water-glycerol mixture or paraffin oil are heavily skewed (F m « 1.36) and the RMSD is of the order of 28%. Table 4.7: Root-mean-square-deviations (RMSD) and bias factors (Fm) between gas holdups of the three matched gas-liquid systems. G-L systems compared RMSD F m Aq. glycerol vs. Silicone oil 0.282 1.33 (Aq. glycerol presents higher values) Aq. glycerol vs. Paraffin oil 0.126 0.96 (Aq. glycerol presents slightly lower values) Paraffin oil vs. Silicone oil 0.286 1.39 (Paraffin oil presents higher values) 4.3.7 Correlation of Data Ozturk et al. (1987) studied gas holdups in 50 different gas-liquid systems comprising monocomponent and mixed organic liquids and various gases at atmospheric pressure. They compared correlations reported in the literature with the data; the best fit (average absolute error of 11%>) was obtained with the correlation of Hikita et al. (1980). 88 s = 0.672\|/ ' U B H L N0.578 -0.131 VPiJ 0.062 ,0.107 (4.17) where \\i = 1 for monocomponent liquids and non-electrolyte solutions while for salt solutions y is a function of ionic strength, see Hikita et al (1980). The ranges of dimensionless groups used to develop the correlation were: l . l x l O " 3 < (UgU - L / a ) < 8 .9x l0 " 2 2.5xl0- n < ( U - L V ^ P L ) < 1.9x10"' 8.4xl0" 5<(p g/p L)< 1.9xl0"3 1.0xl0" 3 <(Li g /Lx L )< 1.8xl0"2 Luo et al. (1999) developed an empirical correlation to determine gas holdups in high-pressure slurry bubble columns operated in the coalesced bubble flow regime. For bubble columns, the correlation reduces to: 2.9 U gPg °"g 1 - 8 , cosh(M 0 0 5 4 ) ] 4 J where 5 = 0 . 2 1 M 0 0 0 7 9 and P = 0.096M" •0.011 (4.18) Here U gPg , <*g , UgPgPL ° g ( P L - p g ) PL) M (4.19) This correlation was developed based on data for a wide variety of gas-liquid systems comprising monocomponent and a few multicomponent aqueous and organic liquids, with various gases at several operating pressures. The average absolute error of the predictions is 13% and the maximum error is 53%. The applicable ranges of this gas holdup correlation are summarized in Table 4.8. 89 Table 4.8: Applicable range of Luo et al. (1999) gas holdup correlation. Parameter (units) Range p L (kg/m3) 668 - 2965 p L (Pas) 0.0003 - 0.03 a(N/m) 0.019-0.073 Pg (kg/m3) 0.2 - 90 U g(m/s) 0.05 - 0.69 U L (m/s) 0 (batch liquid) D(m) 0.1-0.61 H/D >5 Distributor types Perforated plate and bubble caps Jordan and Shumpe (2001) also developed a correlation to determine the gas holdup in high-pressure bubble columns. ^ - = 0.112Eo 0 1 6 Ar 1 ? 0 4 Fr 0 - 7 0 l - s „ 0 . 5 8 ^ l + 27Fr e 0 5 2 Pg V IPLJ J (4.20) This correlation uses a constant bubble diameter of 3 mm as the characteristic length in the dimensionless groups. For their operating conditions, they found that £ g / (k L a) was virtually independent of the superficial gas velocity and gas density. Hence they concluded that there was little variation of the bubble size or similar contributions by the large and small bubble holdups. The correlation was developed with their own data and those of Ozturk et al. (1987) giving a total of 687 data points in 23 different liquids (mainly organic). The average absolute error of the predictions is 11.2%. 90 The intended range of the Jordan and Schumpe (2001) gas holdup correlation is: 1.21<Eo<5.39 825 <Ar b <l .55x10 6 93xl0"6 < ( p g / p L ) < 0.059 0.06 <Fr B < 1.22 Figure 4.24 compares gas holdups of the three matched systems with those predicted by the Hikita et al. (1980), Luo et al. (1999) and Jordan and Schumpe (2001) correlations. Figure 4.24: Overall gas holdups versus U g * for the three matched gas-liquid systems compared with predictions from the Hikita et al. (1980), Luo et al. (1999) and Jordan and Schumpe (2001) correlations. 91 The best fits are obtained with the correlations of Hikita et al. (1980) and Luo et al. (1999), which closely follow the silicone oil gas holdups but underestimate those obtained with the water-glycerol and paraffin oil systems. Although the three correlations were obtained with a wide variety of liquids, the data were mainly for monocomponent liquids. Our results suggest that these correlations should only be used for relatively pure monocomponent liquids showing negligible surface-activity. It interesting to note that gas holdups measured in the water-glycerol mixture are very similar (RMSD = 0.08) to those obtained by Bach and Pilhofer (1978) with an air-aqueous glycerol (58% wt.) system. As previously mentioned, Krishna et al. (1991) developed a gas holdup model based on a bimodal bubble population where the small bubble gas holdup reaches a maximum at the transition to coalesced bubble flow and then remains relatively constant. According to the model, all gas flow beyond that required to reach the transition to coalesced bubble flow passes through the column in the form of large bubbles. This leads to: 8 g = U g / U b s for U g < (UgVans (4.21) Sg = (UgVans/Ubs + ( U g - ( U g ) t r a n s ) / U b l for U g > (Ug)trans (4.22) The model of Krishna et al. (2000) proposes that the small bubble swarm velocity be obtained from: U b s = U b o o ( l - e g s ) (4.23) Krishna et al. (2000) employed the dimensional correlations of Reilly et al. (1994) to estimate Ubco and (sg)trans: U b o o = a 0 1 2 / 2 . 8 4 p ° 0 4 (4.24) 92 ( U a ) g / trans : (S ) t r ans = ^j'pf^Jp^ (4.25) Reilly et al. (1994) developed these correlations with varsol, trichloroethylene, isoparaffinic oils and water as the liquids, and helium, nitrogen, air, argon and carbon dioxide as the gases. Their systems operated at various pressures. The large bubble swarm velocity is correlated in the form: U b l = 0.7lVgdb7(SF)(AF)(DF) (4.26) where three correction factors are introduced into the classical Davies and Taylor (1950) relationship for the rise velocity of a single spherical-cap bubble in an infinite volume of liquid. The scale correction factor (SF) accounts for wall effects, i.e. for the influence of column diameter. Collins (1967) suggested: SF = 1 for d b l /D< 0.125 SF = 1.13exp(-dbi/D) for 0.125 < db,/D < 0.6 (4.27) SF = 0.496(D/d b,)° 5 for db,/D > 0.6 where, d b, = 0.069(U - ( U g V a n s f 3 7 6 (Krishna et al., 2000) (4.28) The acceleration correction factor (AF) accounts for the increase in velocity due to wake interaction in swarms of large bubbles over the velocity of a single, isolated bubble of equal size. A F = 2.73 + 4.505(U g - (UgVans) (Krishna et a l , 2000) (4.29) The constants in Equations (4.28) and (4.29) were obtained by multiple regression of measured rise velocities of large bubbles in low viscosity liquids < 0.0039 Pa-s) in columns of diameter 51 to 630 mm. The liquids employed were demineralized water, tetradecane and paraffin oils. 93 The density correction factor (DF) accounts for the influence of elevated pressures. Using the Kelvin-Hemholtz stability theory as a basis, Letzel et al. (1998) concluded that this factor is inversely proportional to the square root of the gas density. The model parameters were obtained with air at ambient conditions, giving: DF = (1.29/p g)° 5 with p g in unit of kg/m 3 (4.30) Figure 4.25 presents the gas holdups of the four gas-liquid systems investigated with those predicted by the Krishna et al. (2000) correlation. Again, gas holdups of multicomponent and/or contaminated solutions are underestimated. The gas holdup approach of Krishna et al. (2000) incorporates fundamental bubble dynamics and properly predicts trends in the dispersed and coalesced bubble flow regimes with a limited number of parameters related to the gas and liquid physical properties. Its major limitation lies in predicting the gas velocity and holdup at the transition to the coalesced bubble flow regime, with both being extremely sensitive to the gas and liquid physical properties and to the distributor geometry. The onset of the transition zone is delayed for liquids with surface-active contaminants and for distributors with very small holes (d o r < 1 mm). However, the correlation is not overly concerned with inaccurately predicting gas holdups in the transition zone since most industrial bubble column reactors operate well into the coalesced bubble flow regime at gas velocities typically above 0.1 m/s (Krishna and Ellenberger, 1996). Once the coalesced bubble flow regime is established, the correlation works quite well for non-foaming liquids since the effects of contaminants and distributor geometry are no longer as significant (e.g for tap water and silicone oil). However, the correlation cannot predict gas holdups of both foaming and non-foaming systems with the same correlation parameters unless an additional term is included to account for microbubbles. 94 U g , [m/s] U g> ^ Figure 4.25: Overall gas holdups versus U g for the four gas-liquid systems investigated and the Krishna et al. (2000) correlation predictions. 4 . 3 . 8 Summary The objective of this study was to compare gas holdups, bubble properties and related phenomena of multicomponent and monocomponent liquids in a bubble column where two key dimensionless groups (M and U g *) were matched. Experiments were carried out to compare three closely matched systems: 5 5 % wt. aqueous glycerol solution, silicone oil and paraffin oil, and also with one mismatch system: tap water. Air was the gas in all four cases. The water-glycerol mixture and paraffin oil experienced foaming, while silicone oil and tap water did not. The water-glycerol mixture did not foam in dispersed bubble flow, but 95 became milky/frothy in the coalesced bubble flow regime. The paraffin oil formed a foam layer above the clear liquid level throughout the dispersed bubble flow regime. As the flow reached transition to the coalesced bubble flow regime, the interface between the foam layer and clear liquid below became fuzzy and eventually disappeared. Despite different foaming behaviour, bubble dynamics were quite similar between the water-glycerol mixture and paraffin oil. The overall gas holdups, dimensionless dispersed/coalesced bubble flow transition velocity, trends presented by the pressure fluctuations standard deviations and power spectra, and the gas holdup structure were all very similar. As an essentially monocomponent liquid, silicone oil exhibited enhanced bubble coalescence compared with the water-glycerol and paraffin oil. The silicone oil overall gas holdups were therefore significantly and consistently lower, while the transition from dispersed to coalesced bubble flow started earlier and was more gradual. This suggested a different gas holdup structure, and this was confirmed by the gas disengagement experiments. From the dynamic gas disengagement experiments, in the coalesced bubble flow regime at high bubbling/coalescence rates, i f a multicomponent/contaminated liquid does not foam, the effects of surface-active components are no longer as significant. Furthermore, i f the liquid does foam, the increase in gas holdup is mainly due to microbubbles since the large and small bubble holdups are similar to those obtained in an otherwise matched non-foaming liquid. The Hikita et al. (1980), Luo et al. (1999), Jordan and Schumpe (2001) and Krishna et al. (2000) correlations provide conservative estimates of gas holdups in liquid mixtures and contaminated solutions. The Krishna et al. (2000) bimodal bubble population model is a good approach as it incorporates fundamental bubble dynamics. The major difficulty lies in predicting the gas velocity and holdup at the dispersed/coalesced bubble flow transition, both being extremely sensitive to the gas and liquid physical properties. When comparing bubble column gas holdups of a monocomponent liquid to a multicomponent and/or contaminated liquid, geometric similitude, coupled with matching of 96 the chosen set of dimensionless groups, is clearly insufficient to assure dynamic similarity. Differences in dimensionless pressure fluctuations and gas disengagement profiles also demonstrate that the local and dynamic bubble structures of the gas-liquid systems differ significantly despite the matching of key dimensionless groups based on the major liquid physical properties (surface tension, viscosity, density). Multicomponent and contaminated liquids are capable of foaming, and even when these liquids do not foam, their bubble coalescence rates and rise velocities can be inhibited. Much more work is required to identify the physical properties that effectively characterize the bubble coalescence mechanism in multicomponent/contaminated liquids. In this work, the bubble coalescence behaviour could not be predicted by additional liquid physical properties such as dynamic surface tension and dilatational surface elasticity since surface-active components, i f present, were well-dispersed and in equilibrium with the gas-liquid interface. One had to resort to indirect physical characteristics from foamability tests (foam retention time and half-life) to differentiate the bubble coalescence behaviour. Finally, from this study, it is clear that evaluating the effect of liquid physical properties by adding solutes (e.g. another liquid or solids) can lead to misleading conclusions as a result of complex interfacial phenomena. 4.4 Effects of Liquid Composition on Liquid-Solid Fluidized Bed Hydrodynamics Liquid-solid fluidized beds were employed to test the dimensional similitude approach of Safoniuk (1999) for the limiting case of zero gas velocity (i.e. four groups). The previous section demonstrated that interfacial phenomena can significantly affect bubble dynamics. The following section evaluates the impact of interfacial activity on the hydrodynamics of liquid-solid systems. 4.4.1 Bed Expansion and Correlation of Data Solids holdups were obtained by measuring the dynamic pressure drop and bed height. The coefficient of variation between the two methods was less than 1%. Figure 4.26 plots the bed expansion versus ReL for the two matched systems. The filled-in points represent the aq. 97 glycerol/borosilicate system, while the open points depict the silicone oil/alumina system. The match is reasonable; the slightly higher expansions for the silicone oil/alumina system may be due to its slightly smaller Archimedes number (49 000 vs 57 000). rf o CD CQ 170 150 130 110 90 70 50 30 -| 10 I aq. glycerol/borosilicate • silicone oil/alumina • • • 40 60 80 100 Re L , [-] 120 140 Figure 4.26: Bed expansion versus Re L for the two matched liquid-solid systems. Both systems agree well with the well-known equation of Richardson and Zaki (1954): 1-e. (4.31) where Uj is the intercept liquid velocity at S L = 1 on a log (sL) vs. log(UL) plot. Least-squares fits gave n = 2.44, Re ; = 253 and n = 2.63, Rej = 261 for the aq. glycerol/borosilicate and silicone oil/alumina systems, respectively. 98 The parameters U; and n from the Richardson and Zaki (1954) equation can be predicted by the following equations. The intercept liquid velocity (Uj) is estimated by correlations that predict the particle terminal velocity (vt). log 1 0 v^, =-1.64758 + 2.94786-s-1.09703-s2+0.17129-s3 (Clift et al. 1978) (4.32) where v ^ = v t o o [ p 2 / p L g ( p p - p L ) p and s = log I 0 (Ar p ) 1 / 3 (4.33) Khan and Richardson (1989) proposed a correction factor that takes into account the effect of boundary walls on the isolated particle terminal velocity (v t00) and is valid for 0.001 < d p/D < 0.2 and 0.01 <Re t<7000. v t / v t 0 0 = [ l - 1 . 1 5 ( d p / D ) ° - 6 _ (4.34) The exponent (n) was estimated by a correlation developed by Khan and Richardson (1989) that takes into account the effect of boundary walls and is valid for 0.001 < d p/D < 0.2 and 10"2< A r p < 10 1 0. l -1 .24(d p /D)°- 2 7 ] (4.35) 1 1 — z-.t Table 4.9 presents the experimental and predicted values of Uj, and n, as well as the root-mean-square-deviation (RMSD) and bias factor (Fm) between the experimental and predicted liquid holdups from Equation (4.30). The RMSD and F m are calculated from Equations (4.15) and (4.16), with "Systems (a) and (b)" substituted by the predicted and experimental values, respectively. The correlations provide good estimates of Uj and n. The Richardson and Zaki (1954) equation slightly underestimates liquid holdups (RMSD » 2%, F m » 0.98). ^ ^ = 0.043Arf 7 „ 1 A P 99 Table 4.9: Experimental and predicted values of Uj, and n, as well as the R M S D and F, between experimental and predicted liquid holdups of the two matched liquid-solid systems. Liquid-Solid Uj (m/s) n v t (m/s) n RMSD F m System (exp.) (exp.) (pred.) (pred.) Aq. glycerol/borosilicate 0.253 2.44 0.282 2.62 0.02 0.99 Silicone oil/alumina 0.205 2.61 0.217 2.60 0.03 0.97 4.4.2 Pressure Fluctuations Although the two liquid-solid systems had similar bed expansions, visually they appeared to differ. The aqueous glycerol/borosilicate system displayed particulate fluidization behaviour, while the silicone oil/alumina system seemed to behave somewhere between particulate and aggregative fluidization. The tendency of the porous alumina particles to form "clusters" may be due to being electrically charged by electrostatic discharges from the circulating silicone oil. Absolute pressure transducers 170 and 600 mm above the gas/liquid distributor determined absolute and differential pressure fluctuations for 180 s periods at 100 Hz. Figure 4.27 presents differential pressure fluctuation standard deviations, normalized by their average values, for several Re L for the two matched systems. The standard deviations of the aq. glycerol/borosilicate system are always smaller than for the other system. The former remained relatively constant with increasing flowrate, while it is unclear whether the latter increase or decreased. Figure 4.28 presents power spectra of normalized differential pressure fluctuations for Re L = 52 and 101 for the two matched systems. The power spectra of the two systems differ in intensity for a given dimensionless frequency (Strouhal number). The major peak for the aq. glycerol/borosilicate system has a smaller intensity and is at a higher frequency than the silicone oil/alumina system. These results support the visual assessment that the bed behaviour of the aq. glycerol/borosilicate system was closer to particulate fluidization with smaller, more rapid fluctuations 100 Q ii -a o 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 • - B -• aq. glycerol/borosilicate • silicone oiValurnina • • 50 60 70 80 90 100 110 120 130 140 Re L , [-] Figure 4.27: Normalized differential pressure fluctuation standard deviations for several ReL for the two matched liquid-solid systems. 0.00016 I 0.00012 CD I a . | 0.00008 c CD 0.00004 0.00016 1 2 3 4 Sa = fdpAJL, [-] 0.00012 CD a . .| 0.00008 C O C CD 0.00004 0.5 1 1.5 2 2.5 SrL = fdp/UL, [-] Figure 4.28: Power spectral distributions of normalized differential pressure fluctuations for the two matched liquid-solid systems at ReL = 52 and 101. The thick and thin lines represent the aq. glycerol/borosilicate and silicone oil/alumina systems, respectively. 101 4.4.3 Summary Surface-active contaminants present in the liquids did not significantly affect bed expansions. The match was quite good with both systems following the Richardson-Zaki (1954) equation. However, the dimensional similitude approach is not perfect as the local and dynamic behaviour of the two liquid-solid fluidized beds differed slightly. The discrepancy may be due to electrostatic discharges from the circulating silicone oil, which may have contributed to the tendency of the porous alumina particles to form "clusters". 4.5 Effects of Liquid Composition on Gas-Liquid-Solid Fluidized Bed Hydrodynamics The previous sections demonstrated that interfacial phenomena can significantly affect bubble dynamics but are not as influential in a liquid-solid system. This section evaluates the impact of surface activity on the hydrodynamics of gas-liquid-solid systems. 4.5.1 Bed Expansion Overall phase holdups were determined from dynamic pressure drops along the column at several levels. Assuming that s s is independent of z, axial variation of gas and liquid holdups was considered negligible since the dynamic pressure drop slopes (-Ap/Az) were almost perfectly linear (R 2 > 0.98). From repeated experiments, the coefficients of variation of the holdups were less than 2%. The bed expansion is plotted versus Re g* = R e L U g / U L for several Re L in Figure 4.29 for the two matched systems. Here and elsewhere in Chapter 4.5, the filled-in symbols represent system 1 (air/aq. glycerol/borosilicate) data, while the open data points depict system 2 (air/silicone oil/alumina). In both systems the bed expands as Re L and Re g* increase, the effect of Re L being larger. At first glance the two systems match reasonably well, especially at low Re g*, i.e. dispersed bubble flow regime. On closer inspection trends differ. Figure 4.30 presents the results for Re L = 101 using an expanded ordinate scale. For system 1, when gas is introduced into the column, the bed expands quickly, then at a lower rate. However, for system 2, the bed height increases slowly at first, then more rapidly. The different expansion trends and diverging bed expansions as Re g* increases indicate a higher bubble coalescence rate for system 2. 102 o Re L = 52 A Re L = 75 • , • Re L = 101 ® o Re L = 119 0 20 40 60 80 100 120 Reg* = Re L U g /U L , [-] Figure 4.29: Bed expansion versus Re g* for several ReL for the two matched gas-liquid-solid systems. Filled-in symbols represent system 1 (air/aq. glycerol/borosilicate) data, while open data points depict system 2 (air/silicone oil/alumina). 145 135 125 rf .2 115 • air/aq. glycerol/borosilicate • air/silicone oiValumina 15 30 45 60 75 90 Reg* = Re L U g /U L , [-] 105 120 Figure 4.30: Bed expansion versus Re g* for Re L = 101 for the two matched gas-liquid-solid systems. Error bars correspond to one standard deviation. 103 4.5.2 Gas Holdup in the Bed Figure 4.31 shows the gas holdup versus Re g* for several ReL for the two matched systems. In both systems, as Re g* increases the gas holdup increases, then flattens out as the coalesced bubble flow regime is encountered. For the same Re g*, slightly higher gas holdups are obtained at higher ReL since higher liquid flowrates cause bubbles to break-up. For all ReL, gas holdups for system 2 are slightly lower than for system 1, again suggesting more coalescence in system 2. 0.16 0.15 0.14 0.13 0.12 0.11 a 0.1 6 0.09 -0.08 0.07 0.06 -0.05 o • • A A A • «0 A • O • ffi O O i o Re L = 52 A , A Re L = 75 • , • Re L = 101 O Re L = 119 10 20 30 40 50 60 70 80 90 100 110 120 Reg* = Re L U g /U L , [-] Figure 4.31: Gas holdup versus Re g* for several ReL for the two matched gas-liquid-solid systems. Filled-in symbols represent system 1 (air/aq. glycerol/borosilicate) data; open data points depict system 2 (air/silicone oil/alumina). Figures 4.32 and 4.33 present photographs of the bubble behaviour in the freeboard, just above the bed level for the systems 1 and 2, respectively. There were many more large bubbles in system 2. Although the ratio of average bubble size to particle size may be similar for the two systems, system 2 appeared to have a broader bubble size distribution. 104 Figure 4.32: Photograph of freeboard, just above bed level for the air/aq. glycerol/borosilicate system: ReL = 52, Re g* = 26. Figure 4.33: Photograph of freeboard, just above bed level for the air/silicone oil/alumina system: ReL = 52, Re g* = 26. 105 4.5.3 Pressure Fluctuations Absolute pressure transducers 170 and 600 mm above the gas/liquid distributor determined absolute and differential pressure fluctuations for 180 s periods at 100 Hz. Figure 4.34 presents power spectra of normalized differential pressure fluctuations for the two matched systems at various ReL and U g * . For each Re L , the low and high Re g* correspond to the dispersed and coalesced bubble flow regimes, respectively. 0.007 0.006 0.005 CU I b 0.004 | 0.003 S3 ^ 0.002 0.001 0 ReL = 52, Reg* = 52 2 4 6 8 10 12 Srg = fdp/Ug, [-] —i 1 1 — 2 3 4 Srg = fdp/Ug, [-] 1 2 3 4 5 6 7 Srg = fdp/Ug, [-] 8 9 0.5 1 1.5 2 2.5 Srg = fdp/Ug, [-] Figure 4.34: Power spectral distributions of differential pressure fluctuations at various ReL and Re g* for the two matched gas-liquid-solid systems. The thick and thin lines represent system 1 (air/aq. glycerol/borosilicate) and system 2 (air/silicone oil/alumina), respectively. The spectra of the two systems differ. For system 1, there is a definite shift in peak frequency as Re g* increases, while for system 2 the shift is less pronounced. The major peak 106 is lower for system 1 than for system 2 in the dispersed bubble flow regime, but larger in the coalesced bubble flow regime. The frequency shift and strong increase in major peak intensity indicate a more distinct and abrupt regime transition for system 1. This is consistent with the wider bubble size distribution for system 2 giving a smoother change in the s g versus Re g* slope. Figure 4.35 presents normalized differential pressure fluctuation standard deviations for the two matched systems at various ReL and Re g*. Consistent with the power spectra and visual observations, the standard deviation is smaller for system 1 than for system 2 at low or zero gas velocity, but larger as the flow regime shifts to coalesced bubble flow. •a •3 o 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 H 0.01 0 i o • • • • o $ o • • • o • • , o Re L = 52 • , • Re L = 101 20 40 60 80 Reg* = Re L U g /U L , [-] 100 120 Figure and Re; (air/aq. 4.35: Normalized differential pressure fluctuation standard deviations at various ReL .* for the two matched gas-liquid-solid systems. Filled-in symbols represent system 1 glycerol/borosilicate) data; open points depict system 2 (air/silicone oil/alumina). 4.5.4 Flow Regime Transition Velocities The gas velocity for transition from dispersed to coalesced flow was obtained by plotting the drift-flux as a function of gas holdup. The gas transition velocity is plotted versus ReL for the two matched systems in Figure 4.36. As ReL increases, both systems can sustain a higher 107 gas velocity (Reg*) trans in dispersed bubble flow. The (UgVans/UL ratio decreases as Re L increases. Luo et al. (1997) found a similar trend in an air-Paratherm NF heat transfer fluid-glass bead (d p = 3 mm) system. For the same ReL, system 1 appears to reach coalesced bubble flow at a slightly lower Re g*, but the transition from dispersed to coalesced flow is gradual, not abrupt. With this in mind, the match between the two systems seems reasonable, though well short of being perfect. 60 50 40 30 20 -\ 0.8 0.7 0.6 0.5 0.4 40 60 80 100 120 140 Re L, [-] 5. Figure 4.36: Dispersed/coalesced bubble flow transition velocity versus ReL for the two matched gas-liquid-solid systems. Filled-in symbols represent system 1 (air/aq. glycerol/borosilicate) data, while open data points depict system 2 (air/silicone oil/alumina). The minimum liquid fluidization velocity was determined by the classical method of plotting the bed pressure drop versus decreasing liquid velocity for a constant gas velocity (see Chapter 2.3.3). Figure 4.37 shows ReLmf versus Re g* for the two matched systems. In both systems, as gas is first introduced, ReLmf decreases greatly; then as U g is increased further its influence is smaller. Since A r p is slightly higher for system 1, ReLmf at Re g* = 0 is also higher. As gas is introduced, the curves cross, and for the same Re g*, ReLmf is slightly lower for system 1. A possible explanation is that for the same ReL and Re g*, system 1 has higher 108 gas holdups. A higher gas holdup increases the linear liquid velocity, and the bed fluidizes at a lower Re L for the same Re g*. 35 j 30 <> 25 -e 20 -0 20 40 60 80 100 120 140 R e g * = R e L U g / U L , [-] Figure 4.37: Minimum liquid fluidization velocity versus Re g* for the two matched gas-liquid-solid systems. 4.5.5 Gas Holdup in the Freeboard The freeboard gas holdup should also be equal for the two systems given the equality of M , U g * , and U g /UL in the two systems. With no particles present, d p and p p no longer play important roles so the number of independent dimensionless groups to be matched drops from 5 to 3. Just as in the (gas-liquid-solid) bed, freeboard gas holdups for system 1 were always somewhat greater than for system 2. A typical example is shown in Figure 4.38. For both systems, gas holdups in the freeboard were always slightly higher than in the bed. Gorowara (1988) and Fan (1989) also reported that gas holdup in the freeboard was greater than in the bed, but smaller than in a bubble column. However, they did not mention if the liquid superficial velocity in the bubble column was matched. They also noted that the freeboard gas holdup is closer to the bed gas holdup than the solids-free bed gas holdup (%soiids-free= sg/(l-e s)), in agreement with our results. • air/aq. glycerol/borosilicate O air/silicone oi^alumina 109 0.17 0.15 0.13 a o.n oo s o 0.09 H 0.05 • • Re L = 75 0.07 -• o • O freeboard • • bed 10 30 50 70 90 Reg* = Re L U g /U L , [-] 110 Figure 4.38: Bed and freeboard gas holdup versus Re g* at ReL= 75 for the two matched gas-liquid-solid systems. Filled-in symbols represent system 1 (air/aq. glycerol/borosilicate) data; open data points depict system 2 (air/silicone oil/alumina). 4.5.6 Statistical Analysis of Hydrodynamic Data In order to determine i f the two systems were similar on a statistical basis, an A N O V A was performed on the bed expansion and gas holdup data. Table 4.10 summarizes the A N O V A results. Although the variance due to the system is small, this factor significantly affects bed expansion and gas holdup. As expected, the principal sources of variability in the bed expansion and gas holdup data are ReL and Re g*, respectively. 110 Table 4.10: A N O V A on the phase holdups of the two matched gas-liquid-solid fluidized beds. Response variable Factor Sum of Squares Degrees of Freedom F Fa=0.05 % of total variability Bed G-L-S system 118 1 27 3.98 0.1 expansion Re L 181981 3 13850 2.72 97.7 Re g* 2516 3 192 2.72 1.4 Interactions 1037 24 10 1.65 0.6 Intra variability 280 64 - 0.2 Total 185932 95 - 100 Gas holdup G-L-S system 0.003265 1 99 3.99 7.4 Re L 0.003279 3 33 2.74 7.5 Re g* 0.033554 3 340 2.74 76.5 Interactions 0.001665 24 2.1 1.69 3.8 Intra variability 0.002109 64 - 4.8 Total 0.043872 95 - 100 Table 4.11 presents the root-mean-square-deviation (RMSD) and the bias factor (FjJ between the hydrodynamic parameters of the two matched systems. The data are slightly skewed (0.90 < F m < 1.12) and RMSD is of the order of 12%. Although there are statistically significant differences between the two systems, these differences are small. The aqueous glycerol solution did not appear to foam during the three-phase fluidization experiments. As previously mentioned, a new solution of aqueous glycerol was prepared. The measured physical properties of both solutions were very similar, but the new aqueous glycerol solution used for the three-phase experiments probably contained less surface-active Ill components. In addition, circulating the liquid and having particles present may delay or even eliminate foaming (Pino et al., 1990). Had the aqueous glycerol solution begun to foam, the mismatch would likely have been greater as in the bubble column experiments (RMSD * 28%). Table 4.11: Root-mean-square-deviation (RMSD) and bias factor (Fm) between the hydrodynamic parameters of the two matched gas-liquid-solid systems. Hydrodynamic parameter RMSD F m m Bed expansion 0.125 0.927 (system 1 presents slightly lower values) Gas holdup in the bed 0.118 1.122 (system 1 presents slightly higher values) (Re g*) t r a n s 0.107 0.931 (system 1 presents slightly lower values) R- e Lmf 0.144 0.904 (system 1 presents slightly lower values) Although differences between the matched multiphase systems were much greater in the bubble column experiments, trends and conclusions remain the same for the three-phase fluidization study. The silicone oil system exhibited a higher bubble coalescence rate than the aqueous glycerol system. Gas holdups are lower and the transition from dispersed to coalesced bubble flow was smoother for the silicone oil system. Pressure standard deviations and power spectra intensities of the aqueous glycerol system are lower in the dispersed bubble flow regime, but larger in the coalesced bubble flow regime. 4.5.7 Correlation of Holdup Data Han et al. (1990) measured overall holdups under very similar experimental conditions. They used aqueous glycerol solutions with the viscosity varied from 0.001 to 0.060 Pas. 112 The particles were glass beads ranging from 1 to 8 mm in diameter and 2500 kg/m3 in density, and the experiments were performed in columns of inner diameter 100 to 380 mm. Their measured liquid and solids holdups together with literature data were correlated by: n ( l -0 .374Fr g ° - 3 5 2 We c - 0 1 7 3 ) (4.36) for 0.054 < ^  < 0.899 \ 0.0063 < F r < 1.598 ; 0.000918 < We < 5.013 v, g v v t j n ( l + 0.123Fr g°- 6 9 4We° 0 3 7) (4.37) for 0.029 < H L < O . 481 ; 0.0042 < F r < 1.946 \ 0.00895 < We < 5.479 Here F r = _ J = « R e , 8 ^ I U L . v ( E o 7 , 1 /4 ; We c = U 2 L P L d r v d p y (4.38) The solids holdup correlation was developed for systems where the bed expands when gas is introduced. The liquid holdup correlation was based on 2875 points, while the solids holdup correlation used 1946 data points. The average relative errors were 8.7% and 6.4% for the liquid and solids holdups, respectively. Note that more than half of the literature points were obtained in air-water-glass bead systems (Wild and Poncin, 1996). Han et al. (1990) may have committed errors on the variation ranges of the dimensionless groups. For example, in one of their experiments water circulated at a superficial velocity of 100 mm/s in a column of 380 mm in diameter giving We c = 53, an order of magnitude greater than 5.5. We c is different for systems 1 and 2 since the ratio of column to particle diameter was not scaled. As noted above, it was assumed in our work, as long as D/dp was above 20, that the column diameter does not significantly affect the global hydrodynamic parameters, 113 especially in dispersed bubble flow. If the column diameter in system 1 was doubled to match the D/d p ratio of system 2, the correlations of Han et al. (1990) predict an insignificant change in solids holdup and a 7% decrease in gas holdup. If these trends are correct, a properly scaled column diameter for system 1 would have slightly improved the agreement between the two systems. Figure 4.39 presents parity plots between the observed and predicted bed expansion and gas holdup values for the two matched systems. Predicted parameters n and v t were taken from Table 4.9. The bed expansion data are slightly underestimated, while the gas holdups are somewhat overestimated by the Han et al. (1990) correlations. Table 4.12 summarizes the results. Predicted bed expansion, [%] Predicted gas holdup, [-] Figure 4.39: Parity plots between the observed and predicted (Han et al., 1990 correlation) bed expansions and gas holdups for the matched gas-liquid-solid systems. 114 Table 4.12: Root-mean-square-deviation (RMSD) and bias factor (Fm) between predicted (Han et al., 1990 correlation) and observed hydrodynamic data for the two matched gas-liquid-solid systems. Gas-liquid-solid system Bed expansion Gas holdup RMSD F m R M S D F m (air/aq. glycerol/borosilicate) 0.094 0.92 0.156 1.09 (air/silicone oil/alumina) 0.117 0.89 0.197 1.16 Larachi et al. (2001) combined neural network computing and dimensional analysis to derive complex correlations for the gas, liquid and solids holdups. The data bank used to develop these correlations is impressive as it includes 23,000 measurements taken from about 80 references over the last four decades. Table 4.13 provides the resulting dimensionless groups for each correlation. Table 4.13: Dimensionless groups used in Larachi et al. (2001) three-phase fluidized bed holdups correlations. Gas holdup (sg) Liquid holdup (sL) Voidage (£ = 1 - £s) U g / g D P U L / v t c o U L / g d p U g ^ g / G ( u g + U L ) a g / a ( u g + U L K d p / j i L P g U g / p L U 2 L E^L/PL^ 3 ( u g + U L V L / g p L d J ^ L / ^ 2 d p P L ( p p - P L ) (PP-PL)/P P U L / v t c o 9d p/D H / D g(p P -P i>pA Coalescence Index (1 = "coalescing liquid") (2 = "non-coalescing liquid") cpdp/D 115 Larachi et al. (2001) provide a user-friendly Microsoft Excel™ spreadsheet that allows the computation of the phase holdups (see http://www.gch.ulaval.ca/~flarachi). Unfortunately, for the present operating conditions, the correlation estimates gave serious deviations from our data (RMSD « 0.5). It is possible that the spreadsheet contained parameter input errors. Notwithstanding possible input errors, there are fundamental problems in the manner with which the set of correlations was developed: • There are three independent holdup correlations, which do not sum to unity. Only two can be truly independent since the sum of phase holdups must give unity. • The gas density and coalescence index are included solely in the gas holdup correlation, which is wrong as the liquid and/or solids holdups must also be affected. • A characteristic particle size (9dp) is only used in the column scale factor. It should presumably also be used in all dimensionless groups that require a characteristic length. • o • The gas and liquid holdup correlations are underspecified. They respectively contain 12 and 10 dimensional variables. With three fundamental dimensions, the gas and liquid holdup correlations must have 9 (8) and 7 (6) independent dimensionless groups, respectively. (Numbers in parenthesis apply i f the characteristic particle size (9dp) is considered a single lumped variable). • The authors propose a binary coalescence index (non-coalescing or coalescing liquid), which in itself does not represent reality, but fail to mention which types of liquids are non-coalescing and more importantly under which operating conditions do these liquids foam. 4.5.8 Summary The scaling approach for three-phase fluidized bed hydrodynamics proposed by Safoniuk (1999), based on matching five dimensionless groups, was tested using two matched systems: an aqueous glycerol solution with glass beads (system 1) and silicone oil with porous alumina particles (system 2), with air as the gas in both cases. 116 Although bed expansions were qualitatively similar for the two systems, quantitative trends differed. Gas holdups in the bed, as well as in the freeboard, were always slightly higher for system 1. The dimensionless transition velocities from dispersed to coalesced flow were similar. The minimum liquid fluidization velocity Reynolds number was slightly higher for system 1 without gas, but somewhat lower with gas present. The correlation of Han et al. (1990) gave relatively good (RMSD « 14%) estimates of the phase holdups. On statistical grounds, there are significant differences between the two systems. However the differences are generally of the order of 12%, so that the dimensional similitude approach based on five groups, under the present operating conditions, gives a reasonable basis for most scale modelling of global hydrodynamic parameters where errors of the order of 15% are often acceptable. However, differences between the systems, in particular in the pressure power spectra and probability distributions, suggest that more than five dimensionless groups are required to fully characterize the local dynamic bed behaviour. As in the bubble column experiments, the mismatch likely arises primarily from lower bubble coalescence rates in a liquid mixture (water-glycerol) compared to a relatively pure monocomponent liquid (silicone oil). Had the aqueous glycerol solution foamed, the mismatch would likely have been considerably greater as in the bubble column experiments (RMSD ~ 28%). Electrostatic discharges from the circulating silicone oil, which may have promoted the formation of clusters of alumina particles, may have also contributed to the mismatch of the local dynamic behaviour of the three-phase systems. A l l in all, multicomponent/contaminated liquids present interfacial effects that reduce the bubble coalescence rate and hinder the bubble rise velocity, resulting in higher gas holdups than in pure monocomponent liquids under similar conditions. The extent of interfacial effects depends on the bubble size and is most important for Eo < 40. It is not known if Syncrude's LC-Finer foams, and no known method is available to predict with accuracy the onset of foaming. The expected equilibrium bubble diameter is approximately 1 mm, corresponding to Eo = 1.4. Hence the LC-Finer is still potentially subject to the effects of surface-active components, including clays and fine dust originating from the catalyst. 117 Chapter 5 - Effects of Gas Density on Multiphase Reactor Hydrodynamics This chapter tests the limits of the dimensional similitude scaling approach of Safoniuk (1999) by investigating the effects of gas density on the hydrodynamic behaviour of multiphase systems. 5.1 Introduction and Literature Review The LC-Finer operates at high pressure (5.5 to 21 MPa). It is commonly stated that elevated pressures lead to higher gas holdups in both bubble columns and three-phase fluidized beds, except in systems that operate with porous plate distributors and at low gas velocities (Luo et al., 1999). The increased gas holdup is directly related to the smaller bubble size and its slower rise velocity at higher pressures (Lin et al., 1998). The bubble size reduction can be attributed to the variation in physical properties of the gas and liquid with pressure (Fan et a l , 1999). The transition velocity from the dispersed to coalesced bubble flow regime increases with pressure as a result of the reduced bubble size and size distribution. From Letzel et al. (1997), Figure 5.1 provides an example of the effect of pressure on the gas holdup and dispersed/coalesced bubble flow regime transition velocity in a bubble column. A pressure increase only reduces the bubble size and size distribution so far. In an air-water bubble column, Fan (1995) noticed no change in the mean bubble size for pressures above 1.5 MPa. Very few researchers varied the pressure or gas density in a coarse-particle (mm range) three-phase fluidized bed and the results are somewhat contradictory. Figure 5.2 presents experimental results of Jiang et al. (1992) who used an air-water-glass bead (d p = 0.46 and 6 mm) system at ambient temperature and pressures of 0.1 and 0.7 MPa. The column was two-dimensional, 0.25 m x 0.05 m cross-section and 1.0 m high, with various types of distributors. For the small particles (d p = 0.46 mm), the effect of pressure on gas holdup only became important above a superficial gas velocity of 10 mm/s. At lower superficial gas velocities, the system probably operated in the dispersed bubble flow regime where the bubble size and 118 size distribution would have already been small. As the system entered the coalesced bubble flow regime, pressure effects became important; For large particles (d p = 6 mm), there was no significant effect of pressure on the gas holdup for gas velocities up to 140 mm/s. This result is somewhat surprising since the system entered the coalesced bubble flow regime as indicated by the break in the gas holdup slope. DL o JC to Oi 76 o 0.7 r-0.6 0.5 0.4 0.3 0.2 0.1 0 1 O p = 0.2 MPa O p = 0.3 MPa • p = 0.4 MPa A p = 0.5 MPa V p = 0.7 MPa X P= 1.2 MPa 0 0.1 0.2 0.3 0.4 0.5 Superficial gas velocity, U/[m s-1] Figure 5.1: Gas holdups in a 150-mm diameter bubble column with air/water at pressures of 0.2 to 1.2 MPa (Letzel et al., 1997). Figure 5.2: Gas holdups in a three-phase fluidized bed with air/water/glass beads (dp =0.46 and 6 mm) at pressures of 0.1 and 0.7 MPa (Jiang et al., 1992). 119 As for the effect of the original bubble size, they noticed no variation in the gas holdup when the distributor was changed from a porous plate (cU « 0.075 mm) to a perforated plate (d o r = 3 mm), and then to bubble caps (9 mm x 4 mm rectangular slots). Saberian-Broudjenni et al. (1987) performed experiments with different gases (He, N2 and CO2) in a three-phase fluidized bed. The column inner diameter was 50 mm and the liquid and particles were perchloroethylene and 2.55-mm diameter alumina beads, respectively. Although there was considerable scatter in the data, they showed that for identical volumetric flowrates the nature of the gas had no effect on the bed porosity. Figure 5.3 presents the results of Luo et al. (1997) obtained in 127-mm diameter column at ambient temperature and pressures up to 15.6 MPa. They used a nitrogen-Paratherm NF heat transfer fluid (a = 0.029 N/m, u.L = 0.018 Pa-s, pL= 863 kg/m3)-glass bead (d p = 2.1 and 3 mm) system. For both particle sizes, an initial increase of pressure increased the gas holdup. They also reported increased bed expansions with increasing pressure. Pressure effects disappeared above approximately 6 MPa. Figure 5.3: Gas holdups in a three-phase fluidized bed with nitrogen/heat transfer fluid/glass beads (d p = 2.1 and 3 mm) at pressures of 0.1 to 15.6 MPa (Luo et al., 1997). 120 Tarmy et al. (1984) performed experiments in coal liquefaction pilot plants operated at a temperature of 450°C and a pressure of 17 MPa. The resulting physical properties were very similar to those in Syncrude's LC-Finer. The liquid density, viscosity and surface tension were 810 kg/m 3, 0.0003 Pas and 0.005 N/m, respectively. The gas density was 75 kg/m 3 and the particle density and Sauter-mean diameter were 2200 kg/m 3 and 0.70 mm, respectively. The largest pilot plant had a column diameter of 0.61 m and height of 18 m. For this case, the liquid superficial velocity was set at 16 mm/s, while the gas superficial velocity varied between 46 and 65 mm/s. In addition, nitrogen, heptane and coal at ambient temperature and elevated pressure (up to 0.52 MPa) were used in cold flow units. Figure 5.4 presents the solids-free gas holdups (e g/(l - £ s)) as a function of gas superficial velocity for the different cold flow and pilot plant units. Air/Water, Ambient 5 10 15 20 Gas Superficial Velocity, crr\/s 25 Figure 5.4: Gas holdup in coal liquefaction pilot plant and cold flow models (Tarmy et al 1984). It is seen that a pressure increase had a significant effect on the gas holdup. The pilot plant operation remained in the dispersed bubble flow regime for the range of operating conditions with a maximum gas holdup of 49%. Tarmy et al. (1984) attributed the effect of pressure on 121 gas holdup to the formation of smaller bubbles at the gas distributor due to increased gas momentum. A pressure increase will increase the liquid viscosity, lower the surface tension and increase the gas density (Lin et al., 1998). In the proposed dimensional similitude approach, the gas density has only been included in a gas-liquid buoyancy term. If one were to consider the influence of gas density independently, the ratio of particle or liquid density to gas density between the LC-Finer and the scaled unit of Safoniuk (1999) would be greatly mismatched. In order to determine i f gas density is potentially an important parameter, an analysis of bubble dynamics was undertaken in the current project. The bubble behaviour is characterized by: • Formation process • Coalescence rate • Break-up rate (maximum stable bubble size, bubble-particle interaction) • Rise velocity 5.1.1 Pressure Effect on Bubble Formation Process The phenomenon of bubble formation from a submerged orifice connected to a gas chamber varies with gas injection conditions, which are characterized by the dimensionless capacitance number, N c = 4gV cp L/7rd 2 ) rP c (Kumar and Kuloor, 1970). For N c < 1, the gas flowrate through the orifice is essentially constant. In most industrial gas distributors, the gas chamber volume (V c) is large and the bubble formation process is under constant pressure or intermediate conditions (i.e. N c > 1) (Fan et al., 1999). In these cases, the orifice gas flowrate is not constant and depends on the fluctuating pressure difference between the gas chamber and bubble. In the case of the LC-Finer, the bubble formation operating conditions are difficult to characterize since gas and liquid enter simultaneously through the same orifice. Under constant pressure and intermediate bubble formation conditions, the effect of pressure and gas density play an important role on the initial bubble size (Yang et al., 1999). An 122 increase of gas density increases the gas momentum through the orifice causing bubbles to detach earlier, resulting in smaller bubbles (Wilkinson and van Dierendonck, 1994). However, under constant flow conditions, the effect of pressure on the initial bubble size is insignificant. Luo et al. (1998) concluded that the decrease in the buoyancy (upward force) and the increase in the Basset and liquid drag forces (downward forces) counterbalance the increase of gas momentum (upward force). Wilkinson and van Dierendonk (1994) also observed a negligible effect of pressure and gas density on the initial bubble size under constant flow conditions. At low gas velocity, discrete bubbles are formed. However, at a high gas velocity, jetting occurs and bubbles form at the top of the jet. Bubbles formed from a jet are of wide bubble size distribution (Fan et al., 1999). The transition gas velocity from bubbling to jetting decreases with an increase of pressure or gas density (Lin et al., 1999). In an air-water system, Idogawa et al. (1987a) found that the bubbling-jetting transition velocity is inversely proportional to the gas density raised to the power of 0.8. In the coalesced bubble flow regime, the competing effects of coalescence and break-up determine the equilibrium bubble size. The original bubble size only influences the height required to obtain the equilibrium bubble size. However, in the dispersed bubble flow regime, the original bubble size can have a considerable influence on the equilibrium bubble size, especially in short columns. 5.1.2 Pressure Effect on Bubble Coalescence Rate A pressure increase decreases the bubble coalescence rate (Lin et al., 1998). From Equation (4.2), a pressure increase decreases the liquid film drainage rate by increasing the liquid viscosity, decreasing the surface tension and increasing the surface drag ((()) (Fan et al., 1999). In addition, the frequency of bubbles contacting each other decreases with increasing pressure since a tight bubble size distribution reduces the extent of wake capturing. The liquid film drainage rate, which determines the bubble coalescence rate, is independent of the gas density. 123 5.1.3 Pressure Effect on Bubble Break-up Rate Wilkinson et al. (1992) concluded that enhanced bubble break-up with increasing pressure or gas density is the main reason for the increase in gas holdup. The upper limit of the bubble size is set by the maximum stable bubble size, db,maX, above which the bubble is unstable. Several theories have been postulated to predict the maximum stable bubble size in gas-liquid and gas-liquid-solid systems. However, the exact mechanism for bubble break-up at high pressure remains unknown (Fan et al., 1999). Hinze (1955) proposed that bubble break-up is caused by velocity fluctuations induced by turbulent eddies. Bubbles disintegrate when the maximum hydrodynamic force in the liquid is larger than the surface tension force (i.e., above a critical Weber number = p L u d b m a x / o ) . Walter and Blanch (1986) used this concept and proposed a semi-empirical correlation to evaluate the maximum stable bubble size: .0.6 db,max =1-12 f \ 0 A M L P L P (5.1) where p = gpiUg is the specific power input. This approach does not consider the effect of gas density. Luo et al. (1999) and Wilkinson et al. (1990) showed that this theory underestimates the maximum stable bubble size and cannot predict the observed effect of pressure on bubble size. A maximum stable bubble size exists for bubbles rising freely in a stagnant liquid without external stresses (Grace et al., 1978). Rayleigh-Taylor instability has been regarded as the mechanism for bubble break-up under such conditions. A horizontal interface between two stationary fluids, where the upper fluid has greater density than the lower one, is unstable to disturbances with wavelengths exceeding a critical value (Xc) (Bellman and Pennington, 1954): 124 Xr = 2n S(PL-Pg) (5.2) For a bubble with a diameter greater than (A,c), gravitational forces acting on the bubble roof dominate over surface tension forces. If an indentation forms at the roof, the bubble may eventually break up. For gas-liquid-solid systems, it has been suggested that a particle with a diameter greater than half the critical wavelength generates enough disturbance to split the bubble (Henricksen and Ostergaard, 1974). Luo et al. (1997, 1999) showed that models based on the Rayleigh-Taylor instability theory predict an almost negligible effect of pressure on the maximum stable bubble size and thus are unable to evaluate the effect of pressure on bubble break-up in gas-liquid and gas-liquid-solid systems. In order to improve the Rayleigh-Taylor theoretical prediction, Wilkinson and van Dierendonck (1990) incorporated the Kelvin-Helmholtz theory, which accounts for the relative motion between the two phases. The critical wavelength is then: 2TZ V APL-PS) P L u2 / 2 ( p L p g u 2 / 2 ) 2 P L +Pg V ^ H P L - P g j \ ( p L + p g ) 2 a g ( p L - p g ) (5.3) Here u r is the relative velocity between the gas and liquid phases at the gas-liquid interface. This relative velocity can be as high as 1.5 times the terminal bubble rise velocity (Bhaga and Weber, 1981). From the Kelvin-Helmholtz theory, Letzel et al. (1998) concluded that the bubble rise velocity is inversely proportional to the square root of the gas density (Ub a 1/pg0'5). Although the analysis based on this theory gives better results than the original Rayleigh-Taylor instability theory, Fan et al. (1999) argued that the critical wavelength is not equivalent to the maximum stable bubble size and Equation (5.3) alone cannot quantify the effect of pressure on bubble size. 125 For continuity of the tangential velocity in the gas and liquid phases, the bubble internal gas circulation velocity is of the same order of magnitude as its rise velocity (Luo et al., 1999). A centrifugal force is induced by this circulation, outwards to the bubble surface, which can disintegrate the bubble as it increases with increasing bubble size. The bubble breaks up when the centrifugal force exceeds the surface tension force. Based on the work of Levich (1962), Luo et al. (1999) proposed a mechanistic model for the break-up, due to circulation-induced centrifugal forces, of an isolated spherical-cap bubble rising in a stagnant liquid without any disturbances at the gas-liquid interface. Their analysis leads to the following simplified equation for estimating the maximum stable bubble size: b, max 2.53 (for a bubble aspect ratio of 0.21) (5.4) The rise velocity of an isolated spherical-cap bubble is proportional to the square root of the bubble diameter (Davies and Taylor, 1950). Thus, the maximum bubble rise velocity is inversely proportional to the gas density raised to the power of 0.25 (Ub,max oc 1/pg025). With this approach, the importance of gas density on the maximum stable bubble size is less than obtained by Letzel et al. (1998) using Kelvin-Helmholtz instability theory. The presence of contaminants in the liquid does not alter the model, since for large spherical-cap bubbles (Eo > 40), impurities induce negligible effects on the internal circulation of the gas. Fan et al. (1999) compared experimental data with predictions from various bubble break-up models and concluded that bubble break-up is governed by the internal gas circulation mechanism at pressures above 1 MPa, whereas the Kelvin-Helmholtz instability is the dominant mechanism at lower pressures. In addition, the two models predict that the bubble or bubble swarm velocity quickly decreases, then at a lower rate, with an increase of gas density from ambient conditions. 126 A l l previous models were developed for bubble columns or slurry bubble columns where particles are not likely to contribute to the bubble break-up mechanism. For coarse-particle three-phase fluidized beds, the penetration of a bubble by a particle can be the main mechanism for bubble break-up (Chen and Fan, 1989). Chen and Fan (1989) considered the collision between an ascending spherical-cap bubble and a descending particle and established three criteria for particle penetration: N -+ • , P L - P P 6 4 + d p / d b ) Criterion 1: a 0 = g + —-——~ < 0 Criterion 2: (ub+Up0)ro >1 P Pd p p where oo - 2 £ k _P_ V 2 P P d p J .1/2 (5.5) 11/2 r .. • , a Q - [ag - (u b -U p Q ) 2 co 2 ] ' Cntenon 3 : — > L v Physically, criterion 1 states that a particle always penetrates a bubble when the inertial particle acceleration upon collision is downwards. Criterion 2 implies that when the particle inertia is sufficient, the particle penetrates a certain depth into the bubble; beyond that depth the liquid head above the particle is so large that the particle continues to penetrate the bubble. Criterion 3 indicates that the particle velocity should be smaller than the ascending velocity of the bubble during the collision process in order for the particle to penetrate the bubble. When any of these three criteria is satisfied, the particle will penetrate the bubble. Luo et al. (1997) confirmed the validity of these criteria for high-pressure systems. A pressure increase causes a decrease in (ao) and an increase in (U b + Up)co/ao. Hence particles can penetrate smaller bubbles at higher pressures. None of the criteria explicitly depend on the gas density, but the equilibrium bubble size (db) and resulting rise velocity (Ub) are likely functions of the gas density. 5.1.4 Pressure Effect on Single Bubble Rise Velocity The characteristics of a single rising bubble can be described in terms of the rise velocity, shape and motion of the bubble. These rise characteristics are closely associated with the 127 flow and physical properties of the surrounding medium as well as the interfacial properties of the bubble surface. The rise velocity of an isolated bubble can be estimated by the correlation of Fan and Tsuchiya (1990) (Equation 4.13). Increasing pressure decreases the bubble rise velocity by increasing the liquid viscosity, decreasing the surface tension and increasing the gas density. However, the bubble rise velocity is a function of the gas-liquid buoyancy, not the gas density explicitly. In summary, an increase in pressure increases the gas holdup and delays the dispersed/coalesced bubble flow regime transition by decreasing the original bubble size, decreasing the bubble coalescence rate, increasing the bubble break-up rate and reducing the bubble rise velocity. The variation of bubble dynamics is due to a change in the physical properties of the gas and liquid with pressure. Gas density, through an increase of gas momentum, may reduce the original bubble size and increase the bubble break-up rate. However, i f the flow regime is already in dispersed bubble flow at atmospheric pressure, increasing the pressure or gas density will not have as great as an effect on the gas holdup. The effect of particles on bubble dynamics at high pressure is not established, and experimental results give contradictory trends. 5.2 Choice of Experimental Unit and Gas-Liquid-Solid Materials This section describes the experimental unit, gas-liquid-solid materials and operating conditions chosen to evaluate the effect of gas density on the hydrodynamic behaviour of bubble columns and three-phase fluidized beds. 5.2.1 Gas-Liquid Bubble Column Experiments were carried out at ambient temperature and pressure in the 127 mm inner diameter column with a new solution of 55% wt. aqueous glycerol and several gases: helium, air, carbon dioxide and sulphur hexafluoride. The static liquid height was 1520 mm, corresponding to an aspect ratio of 12. Table 5.1 presents the physical properties, operating conditions and values of the dimensionless groups for the four gas-liquid systems investigated. The liquid physical 128 properties were determined experimentally, while the gas physical properties were obtained from the CRC Handbook of Chemistry and Physics (68 th edition). Note that all gas viscosities are similar. Table 5.1: Physical properties, operating conditions and values of the dimensionless groups for the four gas-liquid systems investigated in the gas density effect experiments. Physical property or dimensionless group System 1 (He/aq. glycerol) System 2 (air/ aq. glycerol) System 3 (C0 2/ aq. glycerol) System 4 (SF6/ aq. glycerol) U-L (Pa-s) 0.0063 ± 0.0002 0.0063 ± 0.0002 0.0063 ± 0.0002 0.0063 + 0.0002 a d y n (N/m) fb = 1Hz 0.0684 ± 0.0005 0.0684 ± 0.0005 0.0684 + 0.0005 0.0684 ± 0.0005 p L (kg/m3) 1131 ± 3 1131+3 1131 ± 3 1131 ± 3 Pg (kg/m3) 0.166 1.206 1.830 6.073 p-g (Pas) 1.480xl0"5 1.834xl0"5 1.941xl0"5 1.506xl0"5 Ug(m/s) 0 to 0.263 ± 0 . 0 0 1 0 to 0.263 + 0.001 0 to 0.193 + 0.001 0 to 0.096 + 0.001 M (4.3 ± 0.7)xl0"8 (4.3 + 0.7)xl0"8 (4.3 + 0.7)xl0"8 (4.3 ± 0.7)xl0"8 UgP-L/G 0 to 0.025 ( ± ~ 5 % ) 0 to 0.025 ( ± ~ 5 % ) 0 to 0.018 ( ± ~ 5 % ) 0 to 0.009 ( ± ~ 5 % ) PL/pg 6813 + 36 938 ± 3 618 ± 2 186.2 + 0.5 The liquid surface tension was measured in contact with air and helium by the maximum pressure bubble method at a bubble formation frequency of 1 Hz. Since no significant difference between surface tensions was observed (i.e. < 0.0005 N/m), it was assumed that surface tensions of all four gas-liquid systems were the same. Errors in the physical 129 properties were estimated from repeated experiments, while errors on the dimensionless groups were estimated from Taylor series analysis (Equation 4.8). 5.2.2 Gas-Liquid-Solid Fluidized Bed The same gases and aqueous glycerol solution were employed in both gas-liquid and gas-liquid-solid experiments. The 6-mm borosilicate beads were added when the unit operated as a three-phase fluidized bed. The static bed height was 560 mm, corresponding to an aspect ratio of 4. Table 5.2 presents the physical properties, operating conditions and values of the dimensionless groups for the four gas-liquid-solid systems investigated. In order to obtain the effect of gas density at different particle concentrations, experiments were conducted at two liquid velocities when helium and air were used. 130 Table 5.2: Physical properties, operating conditions and values of the dimensionless groups for the four gas-liquid-solid systems investigated in the gas density effect experiments. Physical property or dimensionless group System 1 (He/ aq.glycerol/glass) System 2 (air/ aq.glycerol/glass) System 3 (ccy aq.glycerol/glass) System 4 (SF6/ aq.glycerol/glass) PL (Pa-s) 0.0063 ± 0.0002 0.0063 ± 0.0002 0.0063 ± 0.0002 0.0063 ± 0.0002 fj(N/m) 0.0684 ± 0.0005 0.0684 ± 0.0005 0.0684 ± 0.0005 0.0684 ± 0 . 0 0 0 5 p L (kg/m3) 1131 ± 3 1131 ± 3 1131+3 1131 ± 3 Pg (kg/m3) 0.166 1.206 1.830 6.073 p g (Pa-s) 1.480xl0"5 1.834xl0-5 1.941xl0'5 1.506xl0"5 dp (mm) 6.0 + 0.1 6.0 ± 0 . 1 6.0 ± 0 . 1 6.0 + 0.1 Pp.wet (kg/m3) 2230 ± 2 2230 ± 2 2230 ± 2 2230 ± 2 U L (m/s) 0.052 and 0.102 + 0.001 0.052 and 0.102 ± 0 . 0 0 1 0.102 ± 0 . 0 0 1 0.102 ± 0 . 0 0 1 U g(m/s) 0.01 to 0.154 + 0.001 0.01 to 0.154 ±0.001 0.01 to 0.154 ± 0 . 0 0 1 0.01 to 0.083 ± 0 . 0 0 1 M (4.3 ± 0.7)xl0"8 (4.3 ± 0.7)xl0"8 (4.3 ± 0.7)xl0"8 (4.3 ±0.7)xl0"8 Eo* 5.8 + 0.3 5.8 + 0.3 5.8 ± 0 . 3 5.8 ± 0 . 3 Pp/pL 1.97 ± 0 . 0 1 1.97 ± 0 . 0 1 1.97 ± 0 . 0 1 1.97 ± 0 . 0 1 Re L 55 and 101 (± ~6 %) 55 and 101 (± ~6 %) 101 ± 6 101 ± 6 u g /u L 0.1 to 2.9 (+ -7%) 0.1 to 2.9 (± -7%) 0.1 to 1.5 (± -6%) 0.1 to 1.5 (+ -6%) P ^ P g 6813 ± 3 6 938 ± 3 6 1 8 ± 2 186.2 + 0.5 131 5.3 Effects of Gas Density on Gas-Liquid Bubble Column Hydrodynamics Experiments were performed at several gas velocities in order to operate in both the dispersed and coalesced bubble flow regimes. The hydrodynamic data relate to overall gas holdups and pressure fluctuations. 5.3.1 Overall Gas Holdup Based on the bubble column experiments in Chapter 4.3, the axial variation of gas holdups was considered negligible and overall gas holdups were determined from the dynamic pressure drop across a single interval (Az = 1343 mm). There were no repeated experiments. However, the coefficients of variation between gas holdups obtained from the rise of the liquid level and the dynamic pressure drop were less than 2%. Figure 5.5 presents overall gas holdups versus U g * = XJg\xJo for the four gas-liquid systems. The filled-in symbols represent data obtained for helium with the gas distributor open area reduced by 75%, corresponding to We o r equal to that of air with all orifices open. As with Lin et al. (1998), Reilly et al. (1994), Wilkinson et al. (1992) and Idogawa et al. (1987b), greater gas holdups were obtained with the denser gases. Experiments with SF 6 remained essentially in the dispersed bubble flow regime, except at U g * = 0.0091 where the flow was in the transition zone. The coalesced bubble flow regime was encountered with the other three gases. This was confirmed by the gas disengagement curves presented in Figure 5.6. The collapse lines of He, air and CO2 break at two points (see arrows on figure) indicating a bubble size distribution. This batch of aqueous glycerol exhibited foaming. Under similar dimensionless conditions, air holdups were very similar to those presented in Figure 4.12. Helium holdups did not significantly vary when 75% of the gas distributor orifices were closed-off This suggests that the increase in gas holdup with increasing gas density can be attributed to enhanced bubble break-up and a reduction of the maximum stable bubble size (Wilkinson et al., 1992) rather than to the formation of smaller bubbles due to increased gas momentum through the distributor (Tarmy et al., 1984). 132 0.4 0.36 0.32 -0.28 0.24 -i 0 2 O 3 0.16 O 0.12 0.08 0.04 8 i o, • He o Air A c o 2 0 SF6 0 0.005 0.01 0.015 U g * - U g U L / a , [-] 0.02 0.025 Figure 5.5: Overall gas holdups versus U g * for the four gas-liquid systems. Filled-in symbols represent data obtained with 75% of the gas distributor holes closed-off. 0.4 U * = 0.0091 47000 50000 53000 t* = gt/Ug, [-] 56000 59000 Figure 5.6: Gas holdup after abruptly terminating gas flow after operating at U g * = 0.0091 for the four gas-liquid systems. The thick, thin and broken lines respectively represent the CO2, Air and He systems; open circles depict data with the SF6. Arrows indicate bubble class disengagement break points as described in Figure 2.7. 133 5.3.2 Pressure Fluctuations Absolute pressure transducers 380 and 1300 mm above the gas/liquid distributor determined absolute and differential pressure fluctuations for 90 s periods with a sampling frequency of 100 Hz. Figure 5.7 presents differential pressure fluctuation standard deviations, normalized by their average values, versus U g * for the four gas-liquid systems. Filled-in symbols represent data obtained with 75% of the gas distributor holes blocked. 0.18 0.16 0.14 . 2 0.12 T3 O 0.1 3 0.08 0.06 0.04 0.02 0 • , • He o Air A C 0 2 O SF6 o A 8 A B o 0.005 0.01 0.015 U g *=U g p L /a ,[-] 0.02 0.025 Figure 5.7: Normalized differential pressure fluctuation standard deviations versus U g * for the four gas-liquid systems. Filled-in symbols represent data obtained with 75% of the gas distributor holes blocked. In general, the pressure fluctuation standard deviations are smaller for the higher density gases. The magnitude of pressure fluctuations increases with increasing bubble size and an increase in gas density decreases the maximum stable bubble size. For SF6, the pressure 134 standard deviations are considerably lower than for the other three gases indicating smaller average bubble sizes and size distributions. Standard deviations for helium were similar for both gas distributors, again suggesting that the overall bubbling behaviour is independent of the bubble formation stage. Figure 5.8 presents power spectra of normalized differential pressure fluctuations for the four gas-liquid systems at several values of U g * , with dimensionless frequency (f* = fUg/g) as the abscissa. f*=fU g/g,[-] f*=fU g/g,[-] Figure 5.8: Power spectral distributions of normalized differential pressure fluctuations for the four gas-liquid systems at four values of U g * . The thick, thin and broken lines respectively represent the CO2, air and He systems; open circles depict data with the SF6. 135 The relative peak intensity between the gas-liquid systems matches the trend presented by the pressure standard deviations in Figure 5.7. Major peak intensities for SF 6 are always lowest. At U g * = 0.0091, a small low frequency peak (f* = 0.07) appears for the SF 6 indicating that the gas-liquid system had entered the transition zone between dispersed and coalesced bubble flow. The others gases are well into the coalesced bubble flow regime with the dominant peak frequency lower and intensity stronger. 5.3.3 Correlation of Data None of the available literature correlations and models can accurately predict the experimental data since the aqueous glycerol solution foamed with each of the four gases. However, the predicted and experimental trends of the effect of gas density on gas holdup can be compared. Luo et al. (1999) proposed a hydrodynamic similarity rule for high-pressure bubble columns based on three dimensionless groups: M , p g / p L and Ug/Ub,max- From their bubble break-up mechanism (see Chapter 5.1.3), they found that db,m a x is proportional to (o7gp g) 0 5. From Davies and Taylor (1950), Ub.max, assuming spherical-cap bubbles at break-up, is proportional to (gd b ,max)° 5 - As a result Ub.max is proportional to (ag/p g) 0 ' 2 5 and (U g /U b ,ma X ) 4 is proportional to U g 4 p g /ag , which is a dimensionless group in their gas holdup correlation (Equation 4.18). As shown in Equation (4.19), U g 4p g/crg is a function of M , p g / p L and Ugpi/a. Hence the dimensional similitude approach proposed by Luo et al. (1999) for high-pressure bubble columns is identical to that employed in this study when the effect of gas density (i.e. p g / p O is included. Figure 5.9 presents gas holdups versus U g 4 p g / o g for the four gas-liquid systems. The data seem to collapse onto a single line. From a power law regression, the gas holdup is proportional to p g ° 1 7 9 with R2 = 0.94. The Hikita et al. (1980) correlation (Equation 4.17) gives 8 g proportional to p g 0 0 6 2 . If the data are correlated with s g/(l - sg) as the dependant variable, gas density is raised to the power of 0.209 with R2 = 0.96. The correlation of Luo et al. (1999) gives s g /(l - sg) proportional to p g 0 ' 2 9 9 . Idogawa et al. (1987b) performed 136 experiments in a 50 mm inner diameter bubble column with water, acetone, methanol, ethanol and various aqueous ethanol solutions as the liquids and hydrogen, helium and air as proportional to pg"". In view of the above, the effect of gas density on overall gas holdup is within the range reported in the literature. Jordan and Schumpe (2000) and Wilkinson et al. (1990) found that the effect of gas density on gas holdup increased with increasing gas density and gas velocity. Furthermore, Fan et al. (1999) showed that the effect of pressure on bubble dynamics is not continuous, as it levels off for pressures above approximately 6 MPa. For the present operating conditions, no significant interaction effects were detected as the data was fairly well correlated by a single parameter Ug p g/ag. Note that the gas holdup correlations of Hikita et al. (1980), Luo et al. (1999) and Idogawa et al. (1987b) do not include interaction effects between the gas density and gas velocity. However, Luo et al. (1999) correlated the effect of gas density as a function of the liquid physical properties (i.e. M-group). the gases, with the systems operated at various pressures. They found that e g/(l - sg) is <>AD 0 • 0 1.0E-10 1.0E-08 1.0E-06 1.0E-04 1.0E-02 U g pg/gCT, [-] Figure 5.9: Overall gas holdup versus U g 4 p g / ag for the four gas-liquid systems. 137 5.4 Effects of Gas Density on Gas-Liquid-Solid Fluidized Bed Hydrodynamics The previous section demonstrated that gas density significantly affects bubble dynamics in a gas-liquid system. This section evaluates the effects of gas density on bubble dynamics in a gas-liquid-solid system where particles may contribute to the bubble break-up mechanism. 5.4.1 Overall phase holdups Except for experiments with SF6, overall phase holdups were determined from dynamic pressure drops along the column at several levels. Assuming that es is independent of z, axial variation of gas and liquid holdups was considered negligible since the dynamic pressure drop slopes (-AP/Az) were almost perfectly linear (R 2 > 0.99). From repeated experiments, the coefficients of variation of the holdups were less than 2%. For the SF6 experiments, the bed height was determined visually and the gas and liquid holdups were obtained from a single dynamic pressure drop measurement across the bed height. Figure 5.10 presents overall phase holdups in the bed and freeboard versus Re g * = ReiIJg/UL for the four gas-liquid-solid systems at Re L =101. Gas holdups and bed expansions increase with increasing gas density. The increase in bed expansion is insufficient to maintain a constant liquid holdup. Experiments with SF6 essentially remained in the dispersed bubble flow regime as phase holdups varied linearly with Re g*. The coalesced bubble flow regime was encountered with the other gases. As in Figure 4.38, gas holdups in the freeboard are somewhat greater than in the bed. Under similar dimensionless conditions, air holdups are greater than in Figure 4.31 since this batch of aqueous glycerol foamed. Saberian-Broudjenni et al. (1987) and Jiang et al. (1992) found no significant effect of gas density or pressure on overall gas holdups in coarse-particle three-phase fluidized beds, contrary to the findings reported by Luo et al. (1997). Our results suggest that despite the presence of large particles, an increase of gas density enhances the bubble break-up rate, producing a smaller equilibrium bubble size resulting in greater gas holdups. Fan (1989) reported that "At high pressure, when the particle size is greater than the bubble size, the particle size effects on the prevailing bubble size becomes minimal, yielding bubble size 138 characteristics in the bed similar to those in a gas-liquid bubble column". This statement is in agreement with our observations. 0.24 0.2 0.16 ? 0.12 0.08 0.04 o A o o A A O °? • A • • O Re L = 101 A o • • He O Air • A co2 • i O SF 6 160 140 c 120 .2 c " 100 <U CO 80 ffi 60 30 60 90 120 150 180 Re g* = R e L U g / U L , [-] 0.71 0.68 |TJ 0.65 3 I 0.62 12 3 ST 0.59 0.56 0.53 Re L =101 • • • O O • He O Air • A CC-2 O SF 6 A • • • o 0.28 0.24 r—i - 0.2 §" J§ 0.16 « "H 0.12 O £ 008 tin 0.04 0 O O O O A 0 A O • A O • Re L = 101 • He 0 Air A C 0 2 o SF 6 30 60 90 120 150 180 Re g* = R e L U g / U L , [-] 6 o A • • A • O • Re L = 101 A • He • O Air • A C 0 2 I 1 — i 30 60 90 120 150 180 Re g * = R e L U g / U L , [-] 30 60 90 120 150 180 Re g* = R e L U g / U L , [-] Figure 5.10: Overall phase holdups in the bed and freeboard versus Re g * = ReLUg/UL for the four gas-liquid-solid systems at ReL = 101. 139 Experiments were also conducted at ReL = 55 (see Figure 5.11) in order to operate at bed expansions closer to that of the LC-Finer. The effects of gas density on overall holdups remained the same despite the greater solids concentration and greater bubble-particle interactions. 0.18 0 30 60 90 120 150 180 Re g* = Re L Ug/U L , [-] 36 33 -SI 30 a o o. X C D -a m 27 24 21 18 on • • • • o • • • Re L = 55 O Air • He 30 60 90 120 150 180 Re g* = R e L U g / U L , [-] 0.53 30 60 90 120 150 180 Re g* = R e L U g / U L , [-] 0.28 0.24 0.2 -§ 0.16 cn "H 0.12 £ S> 0.08 v+ 0.04 o m o o • o • <>• • • • Re L = 55 O A i r • He 0 30 60 90 120 150 180 Re g* = R e L U g / U L , [-] Figure 5.11: Overall phase holdups in the bed and freeboard versus Reg* = ReLUg/UL at ReL = 55 for the air/aq. glycerol/borosilicate bead and helium/aq. glycerol/ borosilicate bead systems. 140 5.4.2 Pressure Fluctuations Absolute pressure transducers 170 and 600 mm above the gas/liquid distributor determined absolute and differential pressure fluctuations for 90 s periods for a sampling frequency of 100 Hz. Figure 5.12 presents differential pressure standard deviations, normalized by their average values, versus Re g* for the four gas-liquid-solid systems at ReL = 55 and 101. Filled-in symbols represent data for ReL = 55, while open data points depict ReL = 101. Consistent with the gas-liquid bubble column experiments, the differential pressure standard deviations are smaller for the higher density gases. For SF6, the pressure standard deviations varied slightly with Re g*, indicating that the gas-liquid-solid system remained in the dispersed bubble flow regime. rf .9 -a 1 "3 in -o O 30 60 90 120 150 180 Reg* = Re L U g /U L , [-] Figure 5.12: Normalized differential pressure fluctuation standard deviations versus Re g* for the four gas-liquid-solid systems at ReL = 55 and 101. Filled-in symbols represent data for ReL = 55; open data points depict ReL =101. 141 Pressure standard deviations are greater for Re L = 55 suggesting that at lower liquid velocities and higher particle concentrations bubble coalescence rates are greater, producing larger bubbles. Similar results are presented in Figure 4.35. Possibly the larger gas-liquid slip velocity and increased bubble-particle interaction increase the bubble contact momentum and frequency and hence the coalescence rate. Furthermore, the superficial gas velocity corresponding to the dispersed/coalesced bubble flow transition increases with increasing Re L . 5.4.3 Correlation of Holdup Data In a bubble column, the gas holdup was relatively well correlated by the dimensionless group Ug 4p g/ag, which is related to the internal gas circulation bubble break-up mechanism proposed by Luo et al. (1999). For a three-phase fluidized bed, this group is a function of the five original dimensionless groups (see Chapter 1.4) as well as (p g/pL): g(p L " u L PL M (Bo7 Re 4 L (5.6) Figure 5.13 presents overall phase holdups in the bed and freeboard versus U g 4p g/org for the four gas-liquid-solid systems. Filled-in symbols represent data for Re L = 55, while open data points depict Re L = 101. Holdups are moderately well correlated (0.76 < R 2 < 0.94). Gas holdups in the bed and freeboard are both proportional to the gas density raised to the power of 0.16, slightly smaller than the 0.18 obtained in the bubble column experiments. The effect of gas density is smaller on the bed voidage and liquid holdup, with s proportional to p g° 0 0 6 and s L proportional to p g ~ 0 0 1 8 . The effect of gas density on holdups seems to be independent of ReL and hence solids concentration. No comparison with the literature can be made since no correlation or model is yet available to quantify the effect of pressure or gas density on three-phase fluidized bed holdups. Although the correlation of Larachi et al. (2000) includes the effect of gas density, it was impossible to obtain reasonable predictions from it. 142 0.25 0.2 H " 0.15 G . 3 O 0.1 0.05 0.163 y = 0.697x R = 0.936 0 1.0E-10 1.0E-08 1.0E-06 1.0E-04 1.0E-02 0.8 0.75 „ 0.7 u sn 7 0 '5 > -a it CQ 0.65 0.6 0.55 y = 0.782x 0.006 y = 0.598x R = 0.795 • • He o' • Air A C 0 2 o SF6 0.5 1.0E-10 1.0E-08 1.0E-06 1.0E-04 1.0E-02 U g pg/ga, [-] Ug pg/ga, [-] 0.7 0.65 a . s -a T3 '5 or 0.5 0.45 0.6 ] • • He o] • Air 0.55 A C 0 2 O SF6 y = 0.368x R2 = 0.886 •0.016 0.35 0.3 E 0.25 cZ 3 g 0.2 js ca •B 0.15 C3 O X) u 2 0.1 0.05 0.4 1.0E-10 1.0E-08 1.0E-06 1.0E-04 1.0E-02 • • He o' • Air A c o 2 y = 0.977x R = 0.923 0 1.0&10 1.0E-08 1.0E-06 1.0E-04 1.0E-02 U g pg/ga, [-] Ug pg/ga, [-] Figure 5.13: Overall phase holdups in the bed and freeboard versus U g 4 p g / ag for the four gas-liquid systems at ReL =55 and 101. Filled-in symbols represent data for ReL = 55; open data points depict ReL = 101. 143 The holdup correlations of Han et al. (1990) (Equations 4.36 and 4.37) were developed with data from experiments carried out at ambient temperature and pressure and with essentially air as the gas. These equations have been modified to include the effect of gas density: v v . J l - 0 . 3 7 4 F r a 3 5 2 W e - ° - 1 7 3 1.209 (5.7) , v t J l + 0.123Fr g°- 6 9 4We° 0 3 7 1.209 (5.8) The gas density factor (pg/1.209), with p g in units of kg/m3, is introduced in such a manner that the correlations still reduce to the Richardson-Zaki equation for U g = 0. Exponents 5 and (5 are obtained by isolating (pg/1.209) and performing power law regressions. Here, as a first approximation, the exponents are assumed to be independent of the superficial gas and liquid velocities (i.e. no interaction effects). For the experimental data presented in Figure 5.13, 8 = 0.145 and p = 0.212. Figure 5.14 presents parity plots between the observed and predicted phase holdups. Filled-in symbols represent data for ReL = 55, while open points depict ReL = 101. Gas holdups were estimated by subtracting the predicted liquid holdup from the predicted bed voidage. Bed voidage and liquid holdups are slightly, but consistently underestimated. Gas holdups show the greatest scatter. The root-mean-square-deviation and bias factor between predicted and observed phase holdups are given in Table 5.3. Table 5.3: Root-mean-square-deviation (RMSD) and bias factor (Fm) between predicted (Equations 5.7 and 5.8) and observed phase holdups for the four gas-liquid-solid systems. Hydrodynamic parameter RMSD F m Bed voidage 0.022 0.98 Liquid holdup 0.037 0.98 Gas holdup 0.327 1.07 144 0.75 CD ccj o > T 3 CD X I -a CD CD CO X> o 0.65 0.55 0.5 0.55 0.6 0.65 0.7 0.75 0.8 Predicted bed voidage, [-] 0.4 0.45 0.5 0.55 0.6 0.65 0.7 Predicted liquid holdup, [-] 0 0.24 0.04 0.08 0.12 0.16 0.2 Predicted gas holdup, [-] Figure 5.14: Parity plots between the observed and predicted holdups (Equations 5.7 and 5.8) for the four gas-liquid-solid systems. Filled-in symbols represent data for ReL = 55; open data points depict ReL =101. Equations (5.7) and (5.8) are probably inappropriate for estimating holdups in the LC-Finer. By including the column diameter, We c is out of the experimental range. However, Han et al. (1990) found that the effect of scale on overall holdups levels off above D « 250 mm. 145 There are also problems regarding the shape of the particles (i.e. correlations were developed with spherical beads), the experimental range of the gas density effect and quantification of the bubble coalescence ability of the liquid (i.e. foaming versus non-foaming). 5.5 Summary The independent effect of gas density on the hydrodynamics of gas-liquid and gas-liquid-solid systems was investigated. Experiments were performed at ambient temperature and pressure in the 127 mm inner diameter column with a 55% wt. aqueous glycerol solution, 6-mm spherical borosilicate beads and four gases: helium, air, carbon dioxide and sulphur hexafluoride. The independent effect of gas density needs to be added to dimensional similitude approach proposed by Safoniuk (1999). The additional group can be chosen as p g/p L. The dispersed bubble flow regime was sustained up to higher gas velocities and gas holdups for the denser gases. It seems that this phenomenon can be attributed to the reduction of the maximum stable bubble size (i.e. enhanced bubble break-up) rather than to the formation of smaller bubbles with increasing gas density. The effect of gas density remains significant with large particles (6 mm in diameter) present as gas holdups increase, bed expansions increase and liquid holdups decrease with increasing gas density. Based on the holdup correlations of Han et al. (1990), equations taking into account the effect of gas density were developed. However, these equations are probably not appropriate for predicting LC-Finer holdups. 146 Chapter 6 - Fluid Maldistribution Effects on Phase Holdups in Three-Phase Fluidized Beds The primary objective of this chapter is to show the influence of distributor geometry and initial gas-liquid flow maldistribution on the phase holdup behaviour of three-phase fluidized beds. A second objective is to explain the bed contraction which occurs when gas, liquid and solids are distributed non-uniformly, in comparison with cases where they are distributed uniformly across the column cross-section. Experiments, analysis and write-up of this part of the work were done in collaboration with Dr. DongHyun Lee during his stay at the University of British Columbia as a visiting scholar. 6.1 Introduction Gas-liquid-solid fluidized bed reactors are very difficult to commercialize due to their complex flow patterns (Tarmy and Coulaloglou, 1992). The gas-liquid distributor is one of their most important design features. A good distributor should introduce fine bubbles and distribute them, as well as the liquid, uniformly over the entire cross-section, while preventing solids from plugging the distributor and minimising the pressure drop (Wild and Poncin, 1996). The gas-liquid distributor can influence heat and mass transfer rates, as well as mixing and flow patterns of the gas, liquid and solids. Despite its importance, there are no generally accepted procedures for the proper design of a gas-liquid distributor for three-phase systems. The gas and liquid phases can be injected together, or separately via nozzles, bubble caps, tuyeres, and perforated or sintered plates. In addition to the lack of design criteria, there is little appreciation of the consequences of maldistribution, e.g. caused by faulty design, fouling or hole blockage Hydrodynamic correlations and models in the literature rarely consider the effect of distributor design (Wild and Poncin, 1996). As in bubble columns, the dispersed bubble flow regime is reduced in size with an inefficient gas distributor. Nacef et al. (1992) used the 147 drift-flux model to characterize the efficiency of the gas distributor. The lower the drift-flux, the more evenly and finely dispersed are the gas bubbles. In two-phase systems, the effect of distributor design has received considerably more attention. In a liquid-solid fluidized bed, Asif et al. (1992) compared the liquid axial dispersion coefficient from experiments where a tracer was injected immediately above the distributor with those where the tracer was injected far above the distributor. The difference between the two axial dispersion coefficients indicated the importance of distributor design on liquid backmixing. Furthermore, the difference between the tracer mean residence times gave a quantitative measure of the presence of dead zones in the distributor region. Although there have been numerous studies of liquid mixing in three-phase fluidized beds (e.g. Tang and Fan, 1990; K i m et al., 1992), none have used the approach of Asif et al. (1992) to evaluate distributor effects. In bubble columns, Reese and Fan (1994, 1997) investigated the entrance length using particle image velocimetry. Tsuchiya and Nakanashi (1992) correlated their hydrodynamic data with a distributor parameter that includes a factor relating to the interaction between neighbouring bubbles at injection and a factor controlling the gas flow through each hole. Zahradnik and Kastanek (1979) calculated the minimum gas velocity required for gas to pass through all holes of a perforated plate. They related this velocity and grid design to the Weber number (We o r = U 2 r p g d o r / a ) and concluded that for a given distributor, We o r must be greater than 2 to ensure a uniform spatial distribution of the gas. 6.2 Experimental System and Procedure Experiments were performed in "light" and "heavy" particle systems. The light particles were polymer blend spheres of 3.3-mm diameter and density 1280 kg/m 3, while the heavy particles were spherical glass beads of 3.7-mm diameter and density 2510 kg/m 3. In both cases, compressed air and tap water were employed as the gas and liquid, respectively. Experiments were carried out at ambient temperature and pressure in the 127-mm diameter column. The static bed height was 700 mm in all cases, corresponding to an aspect ratio 148 ( H b / D ) of 5.5. For experiments with the glass beads, the uniform distributor, labelled #1 in Figure 6.1, was a perforated plate where liquid flows through 54 holes of 4.8-mm diameter and gas is separately introduced via 60 holes of 1-mm diameter. For the polymer beads, a new gas/liquid distributor was employed with water entering through a perforated plate with 34 holes of 4-mm diameter, while air was separately introduced via 25 holes of 0.8-mm diameter. For the light particle (polymer bead) experiments, six other distributors (#2 to #7 shown schematically in Figure 6.1) were also tested where selected holes in the original distributor were blocked. In the case of distributor #2, the gas and liquid were pre-mixed in the plenum chamber of the fluidization column (packed with 16-mm plastic intalox saddles) and then passed together through the perforated plate. For the heavy particle (glass bead) system, only distributors #4 and #7 were tested in addition to the uniform distributor, #1. Overall holdups were obtained by measuring dynamic pressure drops along the column at several intervals. For experiments with the glass beads, assuming that s s is independent of z, axial variation of the holdups was considered negligible since the slopes of the dynamic pressure drop (-AP/Az) were almost perfectly linear (R2 > 0.99). However, slight axial variation of the holdups occurred at the highest gas and liquid velocities for the polymer beads. 149 Distributor tt 6 Distributor tt 7 Figure 6.1: Patterns of active orifices in the distributors as operated. Open circles represent water inlets, while solid dots represent air inlet ports. 150 6.3 Experimental Results and Discussion 6.3.1 Light Particle (Polymer Bead) System Figure 6.2 shows the variation of overall bed voidage (e = 1 - ss) with superficial gas and liquid velocities for distributor #1. The overall voidage increases monotonically with increasing liquid velocity. As shown, predictions of the Han et al. (1990) correlation (Equation 4.37) are in good agreement with the experimental results for a liquid-solid fluidized bed ( U g = 0), where the correlation reduces to the equation of Richardson and Zaki (1954) (Equation 4.30). However, with air introduced, the predictions fall below the experimental results. 0.70 U g = 0 mm/s 0.65 • = 1.7 mm/s A U 9 = 4.0 mm/s o = 6.5 mm/s 0.60 • - y = 9.1 mm/s o . . . . U g = 16.7 mm/s 0.55 0.50 0.45 0.40 12 16 20 24 Ui.., [mm/s] 28 32 Figure 6.2: Variation of overall bed voidage with gas and liquid superficial velocities for polymer bead system with uniform distributor #1. Lines show predictions from Han et al. (1990) correlation. As previously mentioned, Han et al. (1990) employed a very large data set, but more than 50% of the data points were obtained with air-water-glass bead systems; the polymer particles had a much lower density. Moreover, in the correlation, the uniformity of the gas and liquid flow is implicitly assumed to play no part. It is unlikely that all gas/liquid 151 distributors employed by previous authors were perfectly uniform, and this may well have led to lower overall voidages, as demonstrated below. Figure 6.3 shows the effects of gas and liquid superficial velocities on gas and liquid holdups for distributor #1. As expected, gas holdup increases with increasing gas velocity. Liquid holdup tends to decrease with increasing gas velocity for pp/pL significantly greater than 1, as shown by the lines based on the correlation of Han et al. (1990) (Equation 4.36). However, for the polymer particles, where pp/pL is close to 1, the liquid holdup increased slightly or remained nearly constant with increasing gas velocity. Saberian-Broudjenni et al. (1987) similarly observed that liquid holdup increased with increasing gas velocity for a system where the solids density was only 24% greater than the liquid density (p p = 2015 kg/m 3, pL = 1620 kg/m3). 0.3 ! 10 U g , [mm/s] 15 20 Figure 6.3: Effects of gas and liquid superficial velocities on gas and liquid holdups for polymer bead system with uniform distributor #1. Lines show predictions from Han et al. (1990) correlation. 152 Figure 6.4 shows the effects of gas and liquid superficial velocities on overall bed voidage for distributor #7 where all of both the gas and liquid entered through the same half of the distributor. Observations showed that both the half where gas and liquid entered and the blocked half were fluidized, with substantial upflow of solids occurring on the active side and downflow on the blocked side. The overall bed voidage rises slowly with increasing U G , reaching a maximum when U L is relatively large. The different behaviour at higher U L may be partially attributed to solids circulation caused by the non-uniform introduction of gas and liquid at the distributor. However, a similar trend can be observed for distributor #1. The same trend was also observed for distributor #1 with glass beads, as outlined below. The maximum voidage at high U L seemed to coincide with the transition from dispersed to coalesced bubble flow. At high bed voidages, large bubbles entrained a significant amount of liquid in their wakes, reducing the flow of liquid available for support of the solids. 0.65 0.60 0.551-0,50 r 0.45 0.40 + A + A • + A • • # U L = 15.5 mm/s • U L = 18.6 mm/s A U L = 24.8 mm/s + U L = 27.9 mm/s 10 U g , [mm/s] • 15 20 Figure 6.4: Effects of gas and liquid superficial velocities on overall bed voidage for polymer bead system with distributor #7. 153 Figure 6.5 shows the variation of overall bed voidage with gas and liquid superficial velocities for all seven gas/liquid distributors shown in Figure 6.1. 0.60 0.56 0.52 (a) 0 , • Distributor # 1 • Distributor # 2 A Distributor # 3 V Distributor # 4 • Distributor # 5 0 Distributor* 6 + Distributor # 7 • 0.48 0.44 O L-O-15 o 20 25 U L , [mm/s] 30 0.64 0.60 0.56 1 0.52 1 (b) 0.48 15 • Distributor # 1 • Distributor # 2 • Distributor # 3 V Distr ibutor* 4 • Distributor # 5 O Distributor # 6 + Distributor # 7 f o • + • V • 20 25 U L , [mm/s] 30 Figure 6.5: Variation of overall bed voidage with gas and liquid superficial velocities for the polymer particle system with the seven distributors shown in Figure 6.1: (a) U g = 0 (open circles only) and 1.7 mm/s; (b) U g = 16.7 mm/s. 154 At the low gas velocity of 1.7 mm/s in (a), maldistribution made very little difference. However, at the higher gas velocity of 16.7 mm/s in (b), a non-uniform distribution always led to reduced bed expansion and lower overall voidage. Note that distributor #2, though its hole pattern is uniform, still gave a significantly lower overall voidage than distributor #1, presumably because the packing in the plenum chamber was unable to eliminate gas maldistribution. In addition, the bubbles at the exit of the packing, just below the perforated plate, are likely to have been significantly larger than those produced from the 0.8-mm holes of gas distributor #1. Figure 6.6 shows the effects of gas and liquid superficial velocities on gas holdup for the seven gas/liquid distributors. Increasing the superficial liquid velocity increases the absolute bubble rise velocity, but decreases the average bubble size. Hence the gas holdup may decrease or increase. K im et al. (1972) found that the presence of particles caused the gas holdup in a two-dimensional bed of 6-mm glass beads fluidized by air and water to be less than in the corresponding bubble column without solids; gas holdups increased with increasing gas velocities, but decreased slightly with increasing liquid velocities. On the other hand, the widely employed correlation of Han et al. (1990) predicts a slight increase in gas holdup with increasing UL -For the polymer particles, the gas holdup decreases with increasing liquid velocity for all distributors employed. There is a greater absolute variation in gas holdup for U G =16.7 mm/s than for U G = 1.7 mm/s. The distributors with the worst maldistribution (#6 and #7) generally give the greatest reduction in gas holdup due to gas channeling. 155 0.02 0.01 0.00 (a) 0 g $ ffi 0 0 + 15 20 25 U L , [mm/s] 30 Figure 6.6: Effects of gas and liquid superficial velocities on gas holdup for polymer beads system with the seven gas/liquid distributors: (a) U g = 1.7 mm/s; (b) U g = 16.7 mm/s. Symbols are as in Figure 6.5. 6.3.2 Heavy Particle (Glass Bead) System Figures 6.7 and 6.8 present the effects of gas and liquid superficial velocities on gas and liquid holdups, respectively, for uniform distributor #1. As for the polymer particles, gas holdups for the glass beads three-phase system increase with increasing gas velocity and decrease with increasing liquid velocity. However, unlike the polymer particles, liquid holdups decrease with increasing gas velocity for pp/pL significantly greater than 1. 156 0.16 0.12 •—1 0.08 J00 0.04 0.00 _ o o B -O A A * o • A i o 1 o U L = 35.5 mrrVs o • • U L = 53.3 mnYs • A • * A • U L = 71 mrri/s UL=l()6.5rnnYs UL=142rrinVs • 1 - j 1 5 0 1 0 0 1 5 0 U , [mm/s] Figure 6.7: Effects of gas and liquid superficial velocities on gas holdup for glass bead system for uniform distributor # 1. 0.75 U , [mm/s] Figure 6.8: Effects of gas and liquid superficial velocities on liquid holdup for glass bead system for uniform distributor # 1. Symbols are as in Figure 6.7. 157 Figure 6.9 shows the variation of overall bed voidage with gas and liquid superficial velocities for distributors #1, #4 and #7. For U G = 0, bed voidages for distributors #1 and #4 were, as expected, almost equal, while those for distributor #7 were consistently lower due to maldistribution and more vigorous solid circulation patterns. The differences in bed expansion and voidage increased as the liquid velocity increased. When gas was introduced, overall voidages remained the lowest for distributor #7. Overall bed voidages obtained with distributor #4 were slightly lower than for distributor #1, due to gas maldistribution. 0.47 0.46 0.45 T 0.44 « 0.43 0.42 0.41 0.4 0.53 -0.52 -Odist.l • dist.7 U L = 53.3 mm/s 0.51 -• dist.4 O T 0.5 - o w 0.49 -O o 1 n 0.48^ > ° 0.47 1 1 ®® • 0.46 -0 50 100 U G , [mm/s] 150 0 50 100 U G , [mm/s] 150 50 100 U G , [mm/s] 150 0.67 0.66 0.65 V 0.64 » 0.63 0.62 0.61 0.6 Odist.l • dist.7 • dist.4 O U L = 106.5 mm/s o 50 100 U G , [mm/s] 150 Figure 6.9: Overall bed voidage for glass bead system with distributors #1, #4 and #7 (see Figure 6.1) versus superficial gas velocity for U L (mm/s) = 35.5, 53.3, 71.0 and 106.5. 158 The effect of gas and/or liquid maldistribution on bed voidage followed the same trends as for the polymer particles, discussed above. However, differences in overall bed voidages due to maldistribution were less significant for the denser glass beads than for the polymer beads. Similar gas holdups were obtained with distributors #1, #4 and #7 as shown in Figure 6.10. However, at lower gas velocities (i.e. dispersed bubble flow), gas holdups were slightly greater for distributors #4 and #7. w 0.18 0.14 0.1 0.06 0.02 U L = 35.5 mm/s • o 0.14 50 100 U G , [mm/s] 150 0.14 0.1 0.06 0.02 U L = 71 mm/s • o • • o S O d i s t . l • dist.7 0 • dist.4 50 100 U G , [mm/s] 150 0.06 0.02 U L = 53.3 mm/s I o O d i s t . l • dist.7 • dist.4 50 100 150 oij CO 0.14 0.1 0.06 0.02 U G , [mm/s] • U L = 106.5 mm/s - • o • o • • o • o • o O d i s t . l • dist.7 1 • dist.4 50 100 150 U G , [mm/s] Figure 6.10: Gas holdup for glass bead system with distributors #1, #4 and #7 (see Figure 6.1) versus superficial gas velocity for U L (mm/s) = 35.5; 53.3; 71.0 and 106.5. 159 This result is counter to what was expected based on the polymer beads experiments. Also, one might expect that an increase in gas flow through a reduced number of orifices would increase the initial bubble size, or at least cause gas channelling, leading to a reduction in gas holdup. From visual inspection, maldistributed radial gas holdup profiles appear to correct themselves quite quickly (within the first 20% of the expanded bed height). Safoniuk (1999) reported similar results with air, water-glycerol and 4-mm diameter x 10-mm long aluminum cylinders in a column of 292-mm diameter. The gas/liquid distributor appeared to push the gas towards the column walls. However, with the aid of a conductivity probe, he showed that the radial gas holdup profile always evened itself out within the bed. It is interesting to note that helium holdups also remained relatively constant when the distributor open area was reduced (see Figure 5.5). In our case, the gas distributor operated in the gas jetting regime (We o r >2) for distributor #1. In this regime, a wide initial bubble size distribution is produced (Fan et al., 1999). Thus, it is possible that reducing the available area for gas flow caused a larger number of finer bubbles to be generated. Although the number of gas introduction orifices for distributors #4 and #7 was similar, distributor #7 produced slightly higher gas holdups, possibly due to stronger liquid recirculation patterns, re-entraining and recycling smaller bubbles. The effect of gas and/or liquid maldistribution on gas holdup with the glass beads system is opposite to that observed for the polymer beads system. With the polymer particles, maldistribution caused gas channeling and a significant lowering of the gas holdup, especially at the higher gas flowrates. It appears that the light polymer particles could not correct the non-uniformities in the radial gas holdup profiles as quickly. 6.3.3 Relationship between Maldistribution and Bed Expansion Hiby (1967) showed that the overall expansion of a liquid-fluidized bed decreases as a result of a solids circulation which features upward flow in one region and downward flow in another. Masliyah (1989) refined Hiby's analysis and reported that stirring decreased the height of a water-fluidized bed. Epstein et al. (1981) observed a similar effect in one of their experimental runs with liquid-fluidized binary mixtures of solids where unintended swirling 160 was present. The results of the present study are qualitatively consistent with the predictions of both Hiby and Masliyah. Maldistribution of gas and/or liquid caused observable overall solids circulation and led to a smaller bed expansion for a given gas and liquid flowrate than for a uniform distribution of both fluids. For the particular case where solids circulation in the vertical direction occurs with uniform gas distribution, the derivation of Masliyah (1989) can be modified by assuming, after Zhang et al. (1998), that full support for the solids is provided by the liquid, while the gas simply occupies space within the bed ("gas perturbed liquid model"). Figure 6.11 shows a schematic diagram of the solid circulation at constant gas velocity in a three-phase fluidized bed. Left region R ight region s Ll _ 8 L 0 + A £ L 8 L2 _ 8 L0 " ^ 8 L v L i VL2 Vsl i i L • VS2 Figure 6.11: Schematic of solids circulation at constant gas velocity. Extension of model of Hiby (1967) and Masliyah (1989) to three-phase fluidized beds. Downward direction is taken as positive. The fluidized bed has an average liquid holdup (SLO) and an average linear liquid velocity (VLO), where the average liquid flowrate Qo = -AV L O£LO - If one assumes that on the left side, the liquid holdup is greater than the average liquid holdup by a quantity A S L while on the right side it is A s L lower than the average liquid holdup, then particles in the right region will 161 move downwards and the linear liquid velocity will be decreased to vL2- In the left region, particles will move upwards and the linear liquid velocity will be increased to v L i . A-volumetric flow balance for the particles gives: AtiVsifr-ego - £ L O - A £ L ) = - A t 2 v s 2 ( l - s g 0 - s L 0 + A s L ) (6.1) where A t i and At2 are the empty-tube areas for the left and right regions, respectively. The relative velocity between the solids and liquid, for constant physical properties, is given (Richardson and Zaki, 1954) by: v s - V L = v t e L - 1 =F(e L) (6.2) For a perfectly uniform bed, the solids velocity (vs) is zero and Equation (6.2) gives: - V L 0 = v t S L 0 =F (SLO) (6.3) For the left and right regions, one can write using Equation (6.2) vsi - V LI = F ( s L 0 + A e L ) and v s 2 - v L 2 = F ( s L 0 - A s L ) (6.4) where (sLo + AeL) and ( E l 0 - As L) are the liquid holdups in the left and right regions, respectively. Expanding Equation (6.4) using the first term in Taylor's series expansion and making use of Equation (6.3) lead to 'si ~ V L 1 = - V L 0 + dF ds. (As L ) and v s 2 - v L2 : - V L 0 -dF dSr (As L ) (6.5) The downward direction in Figure 6.11 is taken as positive. The required flowrate to maintain the same bed height for a non-uniform liquid holdup is given by: 162 Q = - ( A t i V L 1 s L 1 + A t 2 v L2 (6.6) Assuming that the flow areas of the left and right regions are the same, and making use of Equations (6.1) to (6.5) and the fact that Qo = -AIVLOSLO, Equation (6.6) becomes Qo and Q are the flowrates required to maintain the same bed height for uniform and non-uniform holdup, respectively. Since vS2 is positive and the Richardson and Zaki (1954) index n > 1, Equation (6.7) gives Q > Qo. Hence for a given liquid flowrate Qo, a bed with a laterally non-uniform porosity expands less than a uniform porosity bed. Note that in the absence of gas, i.e. for s g 0 = 0, Equation (6.7) reduces to an equation derived by Masliyah (1989). 6.4 Implications for Distributor Design The results show that the uniformity of the gas/liquid distributor plays a significant role in establishing the phase holdups for three-phase fluidized beds. The effect of maldistribution is clearly larger for lighter particles and for increased gas flowrates. Maldistribution can result not only from hole blockage, but also from premixing of gas and liquid below the distributor plate. The gas holdup and overall bed expansion generally decrease as a result of maldistribution. However, hole blockage can also change the bubble size at the bottom of the column, and this can also affect the holdups. For gas-solid fluidized beds, it is common to specify that the pressure drop across the distributor be at least 20-30% of that across the bed to ensure proper gas distribution. In this study the pressure drop across the liquid distributor was always equal to or greater than 25% of that across the bed. While this criterion may be helpful, as in gas-solid systems it is insufficient to ensure adequate distribution. Hole blockage leads to an increase in distributor pressure drop, but a deterioration in performance. Maintaining a uniform spatial distribution (6.7) 163 of gas and liquid entry is clearly essential to ensure uniform motion and maximum fluid holdups in three-phase fluidized beds. 6.5 Summary The effects of fluid maldistribution on overall phase holdups have been determined using air and water, together with light and heavy particles (3.3-mm diameter polymer beads and 3.7-mm diameter glass beads, respectively) in a 127-mm diameter column. A uniform distributor and various degrees of maldistribution of the gas and/or the liquid were investigated for each type of particle. For the polymer beads ( p p / p L = 1 -28) at low gas flow, the bed expansion and phase holdups were insensitive to maldistribution caused by blockage of some holes in the distributor plate. At higher gas velocities maldistribution at the distributor caused a significant drop in overall bed voidage and gas holdup. The decrease in voidage is explained by extending the liquid-solid bed circulation analysis of Hiby (1967) and Masliyah (1989) to three-phase fluidization. For the glass beads ( p p / p L = 2.51), the effect of gas/liquid maldistribution on overall bed voidage generally followed trends observed with the polymer particles, but differences among the distributors were less significant since the radial non-uniformities seemed to be eliminated relatively quickly within the bed. In addition, under some conditions a smaller area available for gas entry led to higher orifice velocities and smaller bubbles which could, under some circumstances, eliminate or even reverse the effect of spatial maldistribution. 164 Chapter 7 - General Conclusions and Recommendations Safoniuk (1999) proposed that three-phase fluidized bed hydrodynamics can be scaled based on geometric similarity and matching of five dimensionless groups: the M-group, M = g(pL -Pg)|^L4/(PL2o"3); a modified Eotvos number, Eo* = g(pL - p g )d p 2 /a; the liquid Reynolds number, ReL = PLdpUVp-L; a density ratio, P P /PL ; and a superficial velocity ratio, U g / U L . This approach implicitly assumes that the major physical properties of the liquid (density, viscosity and surface tension) are sufficient to characterize the bubble coalescence behaviour and that the influence of the gas density is negligible. LC-Finers, as well as other chemical and biological multiphase reactors, operate at high pressure with multicomponent liquids that may be subject to foaming. Thus, the primary objective of this thesis was to test whether multiphase systems that match Safoniuk's criteria but differ in interfacial properties and gas density produce the same fluid dynamic parameters. The liquid density, viscosity and surface tension were found to be insufficient to characterize bubble coalescence in multicomponent solutions. Multicomponent and contaminated liquids present interfacial effects that reduce the bubble coalescence rate and hinder the bubble rise velocity resulting in greater gas holdups than in pure monocomponent liquids under similar conditions. The extent of interfacial effects depends on the bubble size and is most important for Eo < 40. In this work, additional liquid physical properties such as dynamic surface tension and dilatational surface elasticity were also insufficient since surface-active components were well-dispersed and in equilibrium with the gas-liquid interface. One had to resort to indirect physical characteristics from foamability tests (foam retention time and half-life) to differentiate the bubble coalescence behaviour. Gas density was found to be an important independent parameter in both gas-liquid and gas-liquid-solid systems. The dispersed bubble flow regime was sustained to higher gas velocities and gas holdups for denser gases. It seems that this phenomenon can be attributed to the reduction of the maximum stable bubble size (i.e. enhanced bubble break-up), rather than to the formation of smaller bubbles with increasing gas density. Based on the three-phase fluidized bed holdup correlations of Han et al. (1990), equations taking into account the effect of gas density were developed. 165 As it stands, the dimensional similitude approach will fail when the effects of surface-active contaminants are important since the physical properties and forces that effectively characterize the bubble coalescence mechanism in multicomponent/contaminated liquids are still unknown. Although very difficult to estimate, perhaps the dimensionless group ^9 r b/a, which takes into account the surface excess concentration of solute, the surface tension gradient and the London dispersion forces, should be added to the original five groups proposed by Safoniuk (1999). The effect of pressure via gas density can be taken into account by the dimensionless group pg/pL-Another objective of this project was to study the role of particles in establishing radial uniformity of fluids that are initially maldistributed. Experiments were carried out in a 127 mm inner diameter column with 3.3-mm polymer particles and 3.7-mm glass beads (densities 1280 and 2510 kg/m 3, respectively), with water and air as the liquid and gas. For the "light" polymer beads maldistribution at the distributor caused a significant drop in overall bed voidage and gas holdup. The reduction in bed voidage is explained by extending the liquid-solid circulation analysis of Hiby (1967) and Masliyah (1989) to three-phase fluidization. For the "heavy" glass beads, the effect of gas-liquid maldistribution on overall bed voidage generally followed trends observed with the polymer particles, but differences among the distributors were less significant since the radial non-uniformities seemed to be eliminated near the bottom of the bed. Finally, the measurement of cross-sectional phase holdups based on the attenuation and velocity change of ultrasound was attempted in a column of 292 mm inner diameter with air, water and uniform glass beads of 1.3 mm diameter. The technique worked relatively well for two-phase systems. However, signal attenuation greatly limits the use of ultrasonic vibrations for determining holdups in three-phase fluidized beds. When large particles are used (mm-range), it is difficult to operate at a frequency that ensures transmission through both dispersed phases. For example, to eliminate the strong attenuating effect of microbubbles, the operating frequency must be well above the resonant frequency (i.e. > 0.5 MHz). However for 1.3-mm glass beads, only signals of frequency below 0.4 M H z could be detected. In addition, the total concentration of the two dispersed phases is very high and 166 strongly contributes to the attenuation. Slurry bubble columns with lower dispersed phases holdups and smaller particles present a less attenuative media and are better suited to ultrasonic sensing of hydrodynamic properties. 7.1 Recommendations Much more work is required to identify the physical properties that effectively characterize the bubble coalescence mechanism in multicomponent/contaminated liquids and to delineate the influence of gas density on the bubble break-up mechanism with and without particles present. Then, an even bigger challenge resides in combining the bubble coalescence and break-up models as a function of operating conditions in order to obtain phase holdups. In order to increase the LC-Finer liquid holdup, work related to the liquid foaming tendency and the hydrodynamic effects of recycling gas should be undertaken. Further, actions should be taken to ensure the best possible gas/liquid separation at the reactor exit, to avoid jetting of gas entering the bed (i.e. formation of microbubbles) and to keep the hydrogen flowrate as low as possible. This study led to some insight on the role of particles in establishing radial uniformity of fluids that are initially maldistributed. The effects of initial gas-liquid spatial maldistribution on overall phase holdups were not very significant in a bubble-coalescing liquid (water) with relatively dense particles. Catalyst particles in the LC-Finer may modify radial holdup profiles so that overall holdups are virtually independent of distributor effects. However, assuring uniform distribution of the fluids over the column cross-section remains crucial for the safety and prolonged operation of the reactor. Complementary work on the effects of distributor geometry in a more representative system (i.e. non-coalescing bubbles) should be undertaken. Unfortunately, ultrasound could not be employed to measure phase holdups under the operating conditions of this project. However, results and conclusions of this study should ultimately help scientists develop ultrasound as a non-invasive experimental tool. Future 167 research should attempt to map the range of operating conditions under which the use of ultrasound is appropriate for measuring phase holdups. 168 Nomenclature a = specific interfacial area per unit volume of column, m"1 ai — activity of solute in a two component system, mol/m A = area, m 2 ao = initial particle acceleration upon collision between bubble and particle, m/s2 A b = bubble surface area, m A h = Hamaker-London constant, J A t i = left empty-tube cross-sectional area in Figure 6.11, m At2 = right empty-tube cross-sectional area in Figure 6.11, m A F = acceleration factor defined in Equation (4.29), -A r b = bubble Archimedes number = g p L ( p L - p g ) d b / / p 2 , -Ar p = particle Archimedes number =gp L (p p - P L ^ P / V L >" A(r) = projected area of bubble or particle of radius r, m c = parameter in Equation (4.13), -ci = concentration of solute in a two component system, mol/m 3 C = coalescence index defined in Figure 4.1c, -D = column diameter, m d b = spherical or volume-equivalent bubble diameter, m d b* = dimensionless bubble diameter = d b (p L g/a)^ , -dbi = large bubble diameter, m dbm = microbubble diameter, m dbs = small bubble diameter, m db.max = maximum stable bubble diameter, m d o r = distributor orifice diameter, m dp = spherical or volume-equivalent particle diameter, m D T = ultrasound transducer diameter, m DF = gas density factor defined in Equation (4.30), -E M = dilatational surface elasticity, N-s/m 169 Eo = bubble Eotvos number = g(pL - p g jdj; / a , -Eo* = modified Eotvos number = g(pL - p g )d 2 Ja, -f = frequency, Hz P = dimensionless frequency = f U g / g , -F = (inter-group variance)/(intra-group variance), -Fa=o.o5 = Fisher-Snedecor distribution parameter (95% probability), -fb = bubble formation frequency, Hz F m = bias factor defined in Equation (4.16), -f i o m = nominal frequency, Hz fr = bubble resonance frequency, Hz Fr g = gas Froude number = U g / / ^ g d p , -F(r) = bubble or particle size distribution function, m"1 g = acceleration due to gravity, m/s h = thickness of the liquid film between two coalescing bubbles, m H = liquid level, m Ho = static liquid level, m Hi = liquid level after small bubble disengagement in Figure 2.7, m H 2 = liquid level after large bubble disengagement in Figure 2.7, m H 3 = liquid level at start of gas disengagement in Figure 2.7, m Hb - bed height, m Hf = foam height, m H«) = initial foam height, m I = transmitted ultrasound intensity, W/m 2 I 0 = incident ultrasound intensity, W/m 2 IR = transmitted wave intensity through multiphase system = 10 log(I), dB IRo = transmitted wave intensity through liquid alone =10 log(I0), dB j = number of determinations in Equations (4.8), (4.15) and (4.16), -J g L = drift-flux defined in Equation (2.5), m/s k = ultrasound wave number = 2n/X, m"1 K b = parameter in Equation (4.13),-170 K b o = parameter in Equation (4.13),-kf = foam decay rate constant, s"1 Kg, K s = coefficients in Equation (3.2), ps/m k L = liquid mass transfer coefficient, m/s L = ultrasound path length, m Lb = bubble chord length, m m = parameter in Equation (4.11) M = physical property group (M-group) = g ( p L - p g ) p . L / p 2 a 3 , -Mdry = bed weight of dry particles, kg n = Richardson and Zaki exponent in Equation (4.31), -N C = gas chamber capacitance number = 4 g V c p L / ™ i 2 r P c , -N T = bubble or particle number density, m" p = specific power input, W/m 3 PA = high-pressure region in foam lamella, Pa PB = low-pressure region in foam lamella, Pa P c = gas chamber pressure, Pa P g = pressure in gas phase, Pa PL = pressure in liquid phase, Pa q = parameter in Equation (4.13) Q = volumetric flowrate of liquid required to maintain liquid holdup s L for a laterally non-uniform bed in Figure 6.11, m3/s Qo = volumetric flowrate of liquid required to maintain liquid holdup SL for a uniform fluidized bed in Figure 6.11, m3/s r = bubble or particle radius, m R - gas constant, J/(°K-mol) RIA = polyhedral bubble radius defined in Figure 4.4, m RIB = polyhedral bubble radius defined in Figure 4.4, m R 2 = proportion of explained variation, -^ = bubble radius, m rb.circ = bubble radius in co-current bubble column, m r^stiii = bubble radius in semi-batch bubble column, m rbr = resonant bubble radius, m Rd = radius of contacting circle between two coalescing bubbles, m Rf = foam retention time, s r p = particle radius, m Reb = bubble Reynolds number = p L d b U L / i i L , -Re g* = modified gas Reynolds number = p L d p U g / p , L , -(Reg*)trans = modified transition Reynolds number = pLdp(ug) j\xh , -Rei = Reynolds number based on UL(SL =1) in liquid-solid system = p Ld pU i/p. L . ReL = liquid Reynolds number = p L d p U L / u . L , -ReLmf = minimum liquid fluidization velocity Reynolds number = p L dpU L m f /p. L , Re t = particle terminal velocity Reynolds number = p L d p v t /u . L , -RMSD = root-mean-square-deviation defined in Equation (4.15), -s = variable defined in Equation (4.32), -S n = scattering coefficient, -Sn,app = apparent scattering coefficient, -SF = column scale factor defined in Equation (4.27), -Sr g = gas Strouhal number = fd p / U , -Sr L = liquid Strouhal number = f d p / U L , -t = time, s t* = dimensionless time = t g / U g , -T = temperature, °K to = time at start of gas disengagement in Figure 2.7, s ti = time after large bubble disengagement in Figure 2.7, s t2 = time after small bubble disengagement in Figure 2.7, s t3 = time after microbubble disengagement in Figure 2.7, s Tb = transit time of bubbles passing in front of ultrasound transducer, s tf,(i/2) = foam half-life, s T p = characteristic time scale of particle acceleration, s T w = period of oscillation of acoustic wave, s = root mean square of liquid velocity fluctuations, m 2/s 2 u b = bubble swarm velocity, m/s Uboo = isolated terminal bubble rise velocity, m/s U b o o * = dimensionless isolated terminal bubble rise velocity, U b o o p L / o g , -U b , = large bubble swarm velocity, m/s U b m = microbubble swarm velocity, m/s Ubs = small bubble swarm velocity, m/s Ub,max = maximum stable bubble rise velocity, m/s u g = superficial gas velocity, m/s U g * = dimensionless superficial gas velocity = U g p L / a , -(U g ) t r ans = superficial gas velocity for dispersed/coalesced bubble flow transition, m/s (U g *) t r ans = dimensionless transition superficial gas velocity = ( U G ) triLns p L / a , -U g i = superficial gas velocity through large bubble population, m/s U g m = superficial gas velocity through microbubble population, m/s U g s = superficial gas velocity through small bubble population, m/s U i = intercept liquid velocity from Richardson and Zaki equation at s L = 1 from log plot, m/s U L = superficial liquid velocity, m/s U L m f = superficial liquid velocity at minimum fluidization, m/s U o r = gas velocity based on the orifice diameter of distributor plate, m/s U p o = initial descending velocity of particle, m/s u r = relative velocity between liquid and gas inside a bubble, m/s v = number of dimensional variables employed in Buckingham Pi theorem, -V] = molar volume of solute in a two component system, m 3/mol V 2 = molar volume of solvant in a two component system, m 3/mol V c = gas chamber volume, m 3 V d = liquid film thinning rate, m/s v L = absolute linear liquid velocity = UL/EL , m/s VLO = absolute linear liquid velocity for uniform fluidized bed in Figure 6.11, m/s v L i = absolute linear liquid velocity in left region in Figure 6.11, m/s v L2 = absolute linear liquid velocity in right region in Figure 6.11, m/s v s = absolute solids velocity, m/s v s i = absolute solids velocity in left region in Figure 6.11, m/s v s 2 = absolute solids velocity in right region in Figure 6.11, m/s v t = particle terminal velocity, m/s v t c o = isolated particle terminal velocity, m/s v t 0 0* = dimensionless isolated particle terminal velocity = v t 0 0 (p L /p L g(p p - p L ))^, w = number of fundamental dimensions employed in Buckingham Pi theorem, -W1/2 = full-width-half-maximum of ultrasonic wave (see Figure 3.1), ps We = liquid Weber number = U L p L d p / a , -We c = column Weber number = U L p L D / o " , -We o r = gas orifice Weber number = UlTp d0T/a, -x = independent variable in Equation (4.8) xi = molar fraction of solute in a two component system, -x 2 = molar fraction of solvant in a two component system, -X g , X s = coefficients in Equation (3.6), m"1 Y = dependent variable in Equation (4.8) z = axial position along column, m Greek letters a g = ultrasound attenuation coefficient due to bubbles, m"1 ctgLs = ultrasound attenuation coefficient in gas-liquid-solid system, m"1 a s = ultrasound attenuation coefficient due to particles, m"1 (3 = parameter in Equations (4.18) and (5.8) 8 = parameter in Equations (4.18) and (5.7) A S L = incremental change in liquid holdup between average value and corresponding value in left or right region in Figure 6.11, -174 - A P = dynamic pressure drop = - A P T - gpiAz, Pa -APT = Total pressure drop = gAz (s gp g + SLPL + £spp), Pa A T g L = ultrasound travel time difference between gas-liquid and liquid systems, u.s A T g L s = ultrasound travel time difference between gas-liquid-solid and liquid systems, p.s A T L s = ultrasound travel time difference between liquid-solid and liquid systems, u.s Az = vertical distance between taps for differential pressure measurement, m s = bed voidage = 1 - es, -sg = gas holdup, -sgo = gas holdup for uniformly fluidized bed in Figure 6.11,-E g i = large bubble holdup, -e g m = microbubble holdup, -sgs = small bubble holdup, -(sg)trans = dispersed/coalesced bubble flow transition gas holdup, -sg,soiids-free = solids-free gas holdup = s g/(l- ss), -CL = liquid holdup, -sLo = liquid holdup for uniformly fluidized bed in Figure 6.11,-6LI = liquid holdup in left region in Figure 6.11,-E L 2 = liquid holdup in right region in Figure 6.11,-E S = solids holdup, -£ s m f = solids holdup at minimum fluidization velocity, -T i = surface excess concentration of solute in a two component system, mol/m (j) = parameter in Equation (4.2) reflecting surface drag, -cp = sphericity (i.e. surface area of a sphere having the same volume as the particle divided by the surface area of the particle), -X = ultrasound wavelength, m Xc = critical instability wavelength, m Uf = fluid viscosity, Pas p,g = gas viscosity, Pas P»L = liquid viscosity, Pa-s 175 e = parameter defined in Equation (4.5), m"1 Palumina = density of pure alumina, kg/m Pg = gas density, kg/m3 PL = liquid density, kg/m Pp = particle density, kg/m3 Pp.dry = dry particle density (pores filled by gas), kg/m 3 Pp,wet = wet particle density (pores filled by liquid), kg/m3 a = surface tension, N/m 0"dyn = dynamic surface tension, N/m ^gLs = ultrasound attenuation in gas-liquid-solid system = -ln(I/I0), -= Force defined in Equation (4.5), N = parameter in Equation (4.17), -176 References Andrew, S.P.S., "Frothing in Two-Component Liquid Mixtures", in "International Symposium on Distillation", Rottenburg, P.A., Ed., Institution of Chemical Engineering, London (1960), pp 73-78. 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