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Flow regime transitions in gas-solid fluidization and transport Bi, Xiaotao 1994

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FLOW REGIME TRANSiTIONS IN GAS-SOLID FL1JIDIZATION AN]) TRANSPORTByXiaotao BiB. Sc., Tsinghua University, 1985M.Sc., Tsinghua University, 1988A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYillTHE FACULTY OF GRADUATE STUDIES(Department of Chemical Engineering)We accept this thesis as conformingto the required standardAugust 1994© Xiaotao Bi, 1994In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)____________________________Department of______________________The University of British ColumbiaVancouver, CanadaDate 2 £‘DE-6 (2/88)AbstractExperiments were canied out in three columns to study flow patterns of gas-solidsfluidized beds. It was found that due to the existence of fluidized bed oscillations and thepropagation of pressure waves, absolute pressure fluctuation measurements pick up signals frombubble motion, bed oscillation and pressure waves. Differential pressure fluctuationmeasurements using small spacing between the ports, however, register signals mostly from thepassage of bubbles because the information from bed oscillation and pressure waves are filteredout to a great extent.The transition velocity, U, was determined by measuring absolute pressure fluctuations,differential pressure fluctuations and local voidage fluctuations in a column of 0.102 m in diameterand 2 m tall using FCC particles. It was found that U varied with the method of measurementand with the signal interpretation. A mechanism of transition from bubbling to turbulentfluidization is proposed in which the transition is considered to be triggered when bubbles grow tosuch a size that their wakes become open and turbulent. Such a mechanism is in agreement withthe experimental results from this study and with literature data.The corresponding transition in deep slugging systems has been studied using 0.22 mmdiameter sand particles. U from differential pressure fluctuation and local voidage fluctuationmeasurements was found to correspond to the condition when the slug spacing becomesapproximately the same as the slug length. It does not correspond to the transition to turbulentflow because slug flow persists beyond U. In shallow fluidized beds, U was found to be reachedwhen the amplitude of the absolute pressure fluctuations can no longer increase with increasingsuperficial gas velocity because there is no more space to allow gas bubbles/slugs to grow. U inthis case increases with increasing static bed height.Gas-solids transport operation is reached when particles are significantly entrained fromthe column with increasing superficial gas velocity. A transition velocity Use corresponding tosignificant solids entrainment is proposed to define the transition from low velocity fluidization toIIhigh velocity fluidization operations.Three types of choking are identified. Type A (accumulative) choking occurs as gasvelocity is reduced for all systems when local refluxing (downward motion) of particles begins tosuch an extent that a dense region is formed at the bottom. Type B (blower/standpipe induced)choking takes place when either the blower is incapable of providing sufficient pressure head tomaintain all the particles in suspension or when the standpipe which returns solids to the base ofthe riser is incapable of supplying the required flow of particles. Type C (classical) chokingoccurs only for systems capable of slugging, i.e. where bubbles can grow to a size comparablewith the riser internal diameter.Transition from fast/turbulent fluidization to dilute-phase transport is defined in this studyby the Type A choking velocity below which fully-suspended transport collapses to form a densebed at the bottom of the colunin. The lowest boundary of the fast fluidization, on the other hand,is defined by the Type B and C choking velocities below which steady operation becomes unstabledue to severe slugging or inappropriate pressure build-up in the whole unit.Unified flow regime maps are proposed in which the transition velocities proposed in thisstudy are incorporated to show the flow regimes ranging from packed bed to dilute-phasetransport.mTable of ContentsgcAbstract iiTable of Contents ivList of TablesList ofFigures ixAcknowledgment xviiChapter 1. Introduction 1Chapter 2. Measurements of Gas-Solids and Gas-Liquid Two-Phase Flow 82.1. Introduction 82.2. Pressure waves in gas-solids fluidized beds and gas-liquid bubble columns 102.2.1. Experiments 112.2.2. Experimental result and discussion of relevant models 152.2.2.1. Pressure waves and forced oscillations 152.2.2.2. Damping of se1fexcited bed oscillations 212.2.2.3. Attenuation and propagation ofpressure waves in fluiclizedbeds 242.2.3. Pressure waves in gas-liquid bubble columns 342.3. Origin ofpressure fluctuations 382.4. Comparison of measurement methods 402.4.1. Simplified model 412.4.2. Experimental results and discussion 462.5. Conclusion 50Chapter 3. Transition from Bubbling to Turbulent Fluidization 523.1. Introduction 523.2. Effects ofmeasurement technique on transition velocities 553.2.1. Experimental details 573.2.2. Effect ofprobe resistance 593.2.3. Effect ofport spacing of differential pressure sensors 60v3.2.4. Effect ofprobe location 603.2.5. Effect of solids return system 623.2.6. Effect of static bed height 663.2.7. Effect of data interpretation method 673.2.8. Effect ofmeasurement method 743.3. Model for transition from bubbling to turbulent fluidization 793.3.1. Transition mechanism 813.3.1.1. Transition modes 813.3.1.2. Transition velocity of Type I systems 853.3.2. Experimental results 923.3.3. Effect of gas and particle properties and column geometry on U0 933.4. Conclusion 99Chapter 4. Type II Gradual Transition to Turbulent Fluiclization 1024.1. Introduction 1024.2. Transition to turbulent fluidization in tall slugging fluidized beds oflarge particles 1034.2.1. Transition velocities 1034.2.2. Flow patterns around the transition 1104.3. Transition to turbulent flow in shallow fluidized beds of large particles 1114.4. Conclusion 117Chapter 5. Transition from Low Velocity Fluidization to High Velocity Transport 1195.1. Introduction 1195.2. Experiments 1215.3. Experimental results and discussion 1235.3.1. Termination of co-current fully suspended flow 1235.3.2. Onset of sigtiificant entrainment 1285.3.3. Critical velocity, Use 1305.3.4. Saturation concentration of fully suspended gas-solids flow 1365.4. Transport velocity 1395.5. Conclusion 143Chapter 6. Types of Choking in Vertical Pneumatic Systems 1466.1. Introduction 146v6.2. Initiation of chog 1466.2.1. Choking definitions 1466.2.2. Choking classification 1516.3. Choking predictions 1626.3.1. Accumulative choking velocity, U 1636.3.2. Blower-/standpipe-induced choking velocity, UBC 1646.3.2.1. Conveyor-blower interaction 1646.3.2.2. Conveyor-feeder interaction 1646.3.3. Classical choking velocity, U 1786.4. Slugging versus non-slugging systems 1796.5. Relationship between choking and flow regime transitions 1816.6. Conclusion 183Chapter 7. Flow Regime Diagrams of Gas-Solid Fluidization and Upward Transport... 1857.1. Introduction 1857.2. Flow regimes in gas-solid fluiclized beds 1867.3. Flow patterns in gas-solid vertical transport lines 1877.4. Conclusion 197Chapter 8. Conclusions and Recommendations 1988.1. Conclusions of this work 1988.2. Recommendations for future work 202Nomenclature 204References 212Appendix 1. Determination ofvoid phase volume fraction 237viList of TablespgcTable 1.1. Regimes of fluidization with increasing superficial gas velocity (adaptedfrom Grace, 1982) 2Table 1.2. Features of flow regime transitions 6Table 2.1. Comparison of the reported fluidized bed wave velocity data withcompressible wave theories 33Table 2.2. Summary ofpossible pressure wave sources 39Table 2.3. Spacing of differential pressure sensors used to interpret local bubblebehaviour in gas-solids fluidized beds 45Table 3.1. Summary ofUk data from pressure fluctuation measurements 53Table 3.2. Summary ofU data from pressure fluctuation measurements 67Table 3.3. Transition velocities based on different measurement techniques andinterpretation methods for the FCC particles examined in this work 75Table 3.4. Equations for U in the literature and from this work 77Table 3.5. Comparison of literature data from sources listed in Table 3.1 withcorrelations for U given in Table 3.4 78Table 3.6. Factors influencing onset of turbulent fluidization 80Table 3.7. Relationship between maximum stable bubble size and the Reynoldsnumber which determines the nature of the following wake 83Table 3.8. Comparison of the turbulent modes with prediction 84Table 3.9. Local and overall time-average voidage and void phase volume fractionat U from the literature 91Table 4.1. Summary of literature data on transition from slugging to turbulentfluidization using Group B and D particles in deep fluidized beds 110Table 4.2. Summary of literature data on transition to turbulent fluidization in shallowfluidized beds of Group B and D particles withH1/D2 112Table 4.3. Summary of literature data on the maximum amplitude ofpressurefluctuations in shallow gas-solids fluidized beds 115Table 5.1. Critical velocity and saturation voidage data in order of decreasingcolumn diameter 132Table 5.2. Summary oftransport velocity data 140Table 6.1. Summary of choking defimitions 153Table 6.2. Choking velocity correlations used in the comparison 155Table 6.3. Summary of experimental studies on choking velocity 156Table 6.4. Comparison between experimental data and choking predictions 159Table 6.5. Comparison of experimental data of Hirama et al. (1992) with modelpredictions 172Table 6.6. Bed parameters and particle properties used by Gao et al. (1991) 172Table 6.7. Criteria for distinguishing slugging and non-slugging systems 180Table 6.8. Summary of types of choking 184Table 7.1. Key characteristics ofturbulent fluidization, fast fluidization anddilute phase transport regimes 196vifiList of FigurespgcFigure 1.1. Flow patterns in gas-solids fluidized beds (adapted from Grace, 1986)Figure 2.1. Schematic diagram ofthe 50 mm fluidization column 12Figure 2.2. Pressure drop and voidage versus superficial gas velocity for FCCparticles; D: Increasing gas velocity; : Decreasing gas velocity 13Figure 2.3. Propagation of a disturbance injected 10 mm above the bottom of ade-fluidized bed as measured by three pressure probes and one opticalprobe for U=7. 5 mm/s. Time scale is arbitrary, with the pulse injectionoccurring at about 1.4 s 15Figure 2.4. Propagation of a disturbance in a fluidized bed for U=8.5 mm/s:(a) disturbance injected 10 mm above the distributor, i.e. below thesensors; (b) disturbance injected 0.46 m above the distributor, i.e. aboveall sensors except the optical probe. Time scale is arbitrary 16Figure 2.5. (a) Autocorrelation ofpressure signals in a freely bubbling bed at threeheights; (b) Cross-correlation ofpressure signals between two probes onthe bed axis as a function of distance between the probes. U80 mm/s 18Figure 2.6. Propagation of single disturbance issuing 0.01 m above the distributor.(Optical probe is located right at the bed surface before the injection ofthe disturbance). Time scale is arbitrary, with the pulse injectionoccurring at about 1.2 s 18Figure 2.7. Natural period of forced harmonic oscillation as a function of superficialgas velocity. For single disturbance tests, the natural period is determineddirectly from traces, while the natural period is determined by auto- andcross-correlation methods in the continuous bubble chain disturbancetests and freely bubbling beds. The prediction of equation (2.1) iscalculated with U=10 rn/s 20Figure 2.8. Attenuation of forced oscillations, defined as the ratio between the firstpeak amplitude and the second peak amplitude, as a function of the firstpeak amplitude for U=8.7 mm/s 23Figure 2.9. Longitudinal attenuation ofpropagating disturbance, with decay factordefined as the ratio of the first peak amplitudes of traces recorded at twodifferent locations, as a function of the first peak amplitude at the locationcloser to the source of the disturbance for U=8.7 rn/s. For injection atixz=0.01 m, the probes are at z=0. 16 m and 0.46 m; for injection atz=0.46 rn, the probes are at z=0.16 m and 0.31 iii 26Figure 2.10. Effect of superficial gas velocity on the attenuation of disturbances:(a) Single dlisturbances introduced 0.01 m above the distributor;(b) Continuous bubble chains injected 0.46 m above the distributor.Decay factor is based on the peak amplitude recorded at z=0. 16 and0.46 m for single disturbance at z=0.01 m and at z0. 16 and z=0.3 1 mfor continuous chains introduced at z=0.46 in 27Figure 2.11. Effect of continuous bubble chain injected 0.46 m above distributor on:(a) Local average voidage from the optical probe 0.26 m above thedistributor; (b) Standard deviation ofpressure fluctuations from thepressure probe 0.61 m above the distributor 28Figure 2.12. Wave velocity as a function of superficial gas velocity. For singledisturbance tests the wave velocity is determined directly by reading thetime delay between two traces, while the wave velocity is determined bycross-correlation for freely bubbling beds and for continuous gas injection. 34Figure 2.13. Longitudinal attenuation ofpropagating disturbance for gas-solids fluidizedbeds and gas-liquid bubbly/slug transport, with decay factor defined asthe ratio ofthe first peak amplitude at the position further from the sourceto that closer to the source ofthe disturbance 37Figure 2.14. Maximum amplitude of absolute pressure fluctuations as a function ofsuperficial gas velocity: D=0. 102 m, FCC particles, H.il,0.6 m, z=0.2 in... 40Figure 2.15. Spacing of differential pressure measurement ports required to give equalintensity of the pressure signals from bubble passage and from bubbleeruption at the upper surface, as a function of measuring location andsignal frequency for UB=O.5mis, Uw=lO mis, fB=fw and S0=0 45Figure 2.16. Absolute and differential pressure signals recorded in the lower sectionof the fluidized bed when the upper section is supplied with continuous gasinjection at z=0.69 mwhile the bottom section is maintained between Uand Umb: U9.3 mm/s, U=2S.S mm/s 46Figure 2.17. Maximum cross-correlation coefficients between two pressure signalsfrom different absolute pressure probes as a function of spacing betweenthe two probes 47Figure 2.18. Comparison ofpower spectra of signals measured simultaneously fromoptic fibre probe and from differential pressure measurements at the samelevel for (a) U=23 mm/s; and (b) U=113 mm/s 48xFigure 2.19. Comparison ofprobability distribution functions for signals measuredsimultaneously at the same bed level with U1 14 mm/s. (a) Optical fibreprobe; (b) Differential pressure measurement with L0.05 m;(c) Differential pressure measurement with L=O.20 m;(d) Absolute pressure probe 49Figure 3.1. Schematic diagram of the experimental apparatus 58Figure 3.2. Effect ofprobe resistance on the standard deviation ofpressurefluctuations at z=0.28 m 59Figure 3.3. Effect ofport spacing on measured differential pressure fluctuations 61Figure 3.4. Effect ofheight and superficial gas velocity on standard deviation ofabsolute pressure fluctuations 61Figure 3.5. Effect ofheight and superficial gas velocity on standard deviation ofdifferential pressure fluctuations along bed axis 62Figure 3.6. Effect of solids control valve on (a) apparent bed density from differentialpressure measurement at z=0.20 to 0.41 m, and (b) local bed density fromoptical fibre probe at z0.28 m and r/R=0.0 64Figure 3.7. Effect of solids control valve setting on standard deviation of(a) differentialpressure fluctuations at z=0.20 to 0.41 m, and (b) voidage fluctuations fromoptical probe on the bed axis at z=0.28 in, r/R=0.0 65Figure 3.8. Standard deviation of differential pressure fluctuations as a function ofapparent bed density at z=0.28 to 0.41 ni 66Figure 3.9. Reynolds number based on Uk as a function ofArchimedes number.Data sources are listed in Table 3.2 68Figure 3.10. Dimensionless standard deviation of absolute pressure fluctuationsnormalized by the time-average absolute pressure at the mid-point 69Figure 3.11. Dimensionless standard deviation of differential pressure fluctuationsnormalized by the time-average pressure drop over the same interval 69Figure 3.12. Skewness of absolute and differential pressure fluctuations and of localvoidage fluctuations as functions of superficial gas velocity 71Figure 3.13. Maximum cross-correlation coefficient between two absolute pressureprobes, one above the other, as a function of superficial gas velocity 71xFigure 3.14. Maximum cross-correlation coefficient between two differential pressuresignals across two height intervals, one above the other, as a function ofsuperficial gas velocity 72Figure 3.15. 10 to 90% amplitude of differential pressure fluctuations as a function ofsuperficial gas velocity for two height intervals 73Figure 3.16. Local void phase volume fraction determined by optical probe as a functionof superficial gas velocity, radial position and solids return valve setting.... 74Figure 3.17. Comparison ofU data from the literature and plotted in dimensionlessform from absolute and differential pressure fluctuation measurements.... 76Figure 3.18. Schematic showing idealized picture of two equal-sized bubbles invertical alignment 87Figure 3.19. Dimensionless separation between successive bubbles and at U=Uas a function ofwake angle for =0.45 88Figure 3.20. Local and spatial average void phase volume fraction at U=U as afunction ofAr. Open symbols: local void phase volume fraction fromoptical and capacitance probes; Solids symbols: spatial average voidphase volume fraction from differential pressure measurements.Data sources are listed in Table 3.1 90Figure 3.21. Standard deviation of local voidage fluctuations from the optical probe asa function of local time-average voidage 93Figure 3.22. Skewness ofvoidage fluctuations from the optical probe at z=0.28 m asa function of local time-average voidage 93Figure 3.23. Local time-average voidage at z0. 28 m as a function of radiallocation and superficial gas velocity 94Figure 3.24. Skewness of local voidage fluctuations from optical probe at z=0.28 m asa function of radial location and superficial gas velocity 94Figure 3.25. Intermittency index from optical probe at z=0. 28 m as a function of localvoidage, radial position and solids return valve setting 95Figure 3.26. Effect ofparticle properties on transition velocity U based on literaturedata listed in Table 3.1 and model predictions 96Figure 3.27. Effect of axial location on the transition velocity U from differentialpressure fluctuation measurement 98xliFigure 4.1. Schematic diagram of gas slugs in deep slugging fluidized beds 104Figure 4.2. Pressure fluctuations due to slug passage at a location of fully developedslugging fluidized beds. Adapted from Kehoe and Davidson (1972a) 104Figure 4.3. Dimensionless standard deviation of absolute pressure fluctuations onthe axis of a fully slugging fluiclized bed due to slug passage as afunction of dimensionless superficial gas velocity 105Figure 4.4. Predicted standard deviation of differential pressure fluctuations acrossa region ofheight L as a function of dimensionless superficial gasvelocity in a fully slugging fluidized bed 107Figure 4.5. Predicted standard deviation of local voidage fluctuations at a point onthe axis of a fully slugging fluidized bed as a function of dimensionlesssuperficial gas velocity 107Figure 4.6. Standard deviation of local voidage fluctuations from optical probe atz=0.28 m as a function of dimensionless superficial gas velocity 108Figure 4.7. Standard deviation of differential pressure fluctuations as a function ofdimensionless superficial gas velocity between: (a) z=0.20 to 0.28 m,and (b) z=0.03 to 0.20 m above the distributor 109Figure 4.8. Experimental standard deviation of absolute pressure fluctuations atz=0.0l m as a function of superficial gas velocity for D=0. 102 m,H,0.050 m, d,,=2.0 mm, p,=l400 kg/m3 113Figure 4.9. Effect of static bed height on the maximum amplitude of absolute pressurefluctuations for FCC particles of d60 tm, p1,=1580 kg/rn3 in the51 mm diameter column. D: U=0.08 mis; : U=0.04 rn/s 114Figure 4.10. Dimensionless maximum amplitude of absolute pressure fluctuations asa function of static bed height. Data sources are given in Table 4.3 115Figure 4.11. (Re-Re) withH11,JD2 as a function ofAr based on data ofSatija and Fan (1985) and Duiiham et al. (1993) 116Figure 4.12. (ReRe.)/Ar°45as a function ofHD based on data listed inTable 4.2 117Figure 5.1. Flow modes of gas-solids two-phase vertical transport systems 120Figure 5.2. Schematic diagram of the circulating fluidized bed apparatus 122XIIIFigure 5.3. Apparent bed density as a function of solids circulation rate for foursupefficial gas velocities: (a) from differential pressure transducer overinterval from 0.71 to 0.86 m; (b) from differential pressure transducerover interval from 0.10 to 0.25 m; (c) from optical fibre probe at height0.775m. U:U=4.lm!s; +:U=4.8mJs; L]:U=5.7mJs; x:U=6.6mIs.... 124Figure 5.4. Standard deviation of differential pressure and voidage fluctuations asfunctions of solids circulation rate. (a) and (b) from differential pressuretransducers; (c) from optical fibre probe. Probe locations, gas velocitiesand operating conditions are as in Figure 5.3 125Figure 5.5. Standard deviation of differential pressure and voidage fluctuations as afunction of apparent or local density. (a) and (b) from differential pressuretransducers; (c) from optical fibre probe. Probe locations, gas velocitiesand operating conditions are as in Figure 5.3 127Figure 5.6. (a) Skewness and (b) intermittency index from optical fibre probe as afunction of local density at wall. Conditions and gas velocities areas in Figure 5.3(c) 128Figure 5.7. Type A choking velocity as a function of solids circulation rate 129Figure 5.8. Reciprocal ofbed emptying time as a function of superficial gas velocitybased on data ofPerales et aL (1991) 131Figure 5.9. Effect of pd and column diameter on Use based on data sourcesinTable5.l(a) 134Figure 5.10. Effect of and column height on Use based on data sourcesinTable5.1(a) 135Figure 5.11. Res=pgU5dp/ g as a function ofAr based on data from sources inTable 5.1(a), and compared with terminal Reynolds number 137Figure 5.12. Saturation volumetric solids fraction corresponding to Use plotted as afunction ofAr. Data sources are listed in Table 5.1(a) 138Figure 5.13. Definition of transport velocity based on Yerushalmi and Cankurt (1979).. 139Figure 5.14. (a) Schematic ofvoidage variation in CFB riser and (b) Simplifiedestimation ofMax[8(dP/dz)/8G] 141Figure 5.15. Predicted maximum pressure gradient, [8(dP / dz) / 0G3], as a functionof superficial gas velocity. (a) Effect of axial location; (b) Effect of riserxvheight; (c) Effect of separation distance between two pressure taps usedfor differential pressure measurement; (d) Effect of decay constant, a.FCC particles with d,,=60 tim, p,l5OO kg/rn3,fluidized by air at 20 °Cand 100 kPa in a column of D=0.15 in. 144Figure 6.1. Operational instability due to insufficient pressure head supplied bygas blower 148Figure 6.2. Typical circulating fluidized bed system. L0 is the height of the densebed in the downcomer when all the particles are stored there 165Figure 6.3. Operational instability due to imbalance ofpressures at the base ofriser and downcomer 166Figure 6.4. Comparison of model predictions (shown by the lines) with theexperimental data of Gao et al. (1990) for FCC particles 173Figure 6.5. Comparison ofmodel predictions (shown by the lines) with theexperimental data of Gao et aL (1990) for catalyst particles 173Figure 6.6. Comparison ofmodel predictions (shown by the lines) with theexperimental data of Gao et al. (1990) for silica gel particles 174Figure 6.7. Predicted effect of solids inventory on the maximum solids circulation ratefor=l5OO kg/rn3,d=60 tm, H0=10 m, L0=5 in, D=Dd=D=DV=0.15 m.Dotted line is the Type A choking velocity predicted by Bi and Fan (1991);dashed curve is Type C choking velocity curve ofYousfi and Gau (1974)... 175Figure 6.8. Predicted effect of standpipe size on solids circulation rate.Conditions and broken curves as in Figure 6.7 176Figure 6.9. Predicted effect of solids control valve on solids circulation rate.Conditions and broken curves as in Figure 6.7 176Figure 6.10. Predicted effect ofpressure on solids circulation rate.Conditions as in Figure 6.7 177Figure 6.11. Reynolds number based on slip velocity at classical choking point as afunction ofArchimedes number compared with Reynolds numberbased on U, Use and particle terminal velocity 179Figure 6.12. Flow chart showing the transitions between dense-phase transport, fastfluidization and pneumatic transport with decreasing gas flow andconstant solids flux 182xvFigure 7.1. Flow chart showing regime transitions in gas-solid fluidized beds 187Figure 7.2. Flow regime map for gas-solids fluidization. Heavy lines indicate transitionvelocities, and the regions indicated by light lines are the typical operatingranges ofbubbling fluidized beds and turbulent fluidized beds 188Figure 7.3. Flow chart showing regime transitions in gas-solids upward transport lines.. 189Figure 7.4. Idealized flow regime map for gas-solids upward transport. Heavy linesindicate transition velocities, and the region indicated by light lines isthe typical operating range ofbubbling fluidized beds 192Figure 7.5. Flow chart showing flow regime transitions in gas-solids upward transportrisers with decreasing gas flow 193Figure 7.6. Practical flow regime maps for gas-solid upward transport in the presenceof restrictions for (a) FCC particles, d,,=6O urn, p,=lSOO kg/rn3,U=O. 15 mIs, D=O. 1 m; (b) sand particles, cL13=200 tm, p,26OO kg/rn3,U=4.4 mIs, D=O.1 m. 195xviAcknowledgmentMy sincere gratitude goes to Dr. JR. Grace for his excellent guidance, support andencouragement over the course of this work. Appreciation is expressed to Dr. J.-X. Zhu for hisencouragement and helpful discussions. Useful discussions with Dr. K. S. Lim are acknowledged.Also, I would like to thank Dr. L.-S. Fan for the opportunities and discussions which he provided.Other faculty members in the Chemical Engineering Department and my fellow graduate studentsin the fluidization research group also deserve special credit for continuous interest and assistance.The equipment and instrumentation owe a great deal to the Chemical Engineering Workshop, Dr.G.L. Sun, Mr. J. Thou and Prof S.Z. Qin. The financial support of Natural Sciences andEngineering Research Council and fellowships provided by the Aluminum Company of Canadaand the Faculty of Graduate Studies of the University of British Columbia are also gratefullyacknowledged.Finally I want to express my special thanks to my wife for her understanding andcontinuous support over the past five years which made my working evenings and weekendsdelightful.xvChapter 1IntroductionThe introduction of gas from the bottom of a column containing solid particles via a gasdistributor can cause the particles to be fluidized. As shown in Figure 1.1 and Table 1.1, severalflow patterns/regimes have been identified with increasing gas velocity (i.e., fixed bed, delayedbubbling or particulate fluidization, bubbling fluidlization, slugging fluidization, turbulentflujidization, fast fluiclization and dilute pneumatic conveying). Some of the transitions betweenthe hydrodynamic regimes are well understood, while those delineating the higher velocityregimes of fluidization and solids transport are generally poorly characterized in the literature.The purpose of this thesis is to provide an improved understanding of high-velocity fluidization, inparticular of the regime transitions.INCREASING U, £Figure 1.1 Flow patterns in gas-solids fluidized beds (adapted from Grace, 1986)..‘-tFASTFLU IDIZAT IONFJXED BEDORLAYEDBUBBLING—.PNEUMATICCONVEYING4BUBBLING SLUG FLOW TURBULENTREGIME REGIMEAGGREGATIVE FLUIDIZATION41Table 1.1. Regimes of fluidization with increasing superficial gas velocity (adapted from Grace,1982).Velocity range [ Regime Appearance and principal featuresO<U<Umf Fixed bed Particles are quiescent; gas flows through interstices.U<U<Umb Particulate Bed expands smoothly in a homogeneous manner; topfluiclization surface is well-defined; some small-scale particle motion;little tendency for particles to aggregate; very little pressurefluctuation.Umb<U<Ums Bubbling Void regions form near the distributor, grow mostly byfluidization coalescence, and rise to the surface; top surface is well-defined with bubbles breaking through periodically; irregularpressure fluctuations of appreciable amplitude. Bubble sizeincreases as U increases.Ums<U<Uk or Slugging Voids fill most ofthe column cross-section; top surface risesUms<U<Uc fluidization and collapses with a reasonably regular frequency; large andregular pressure fluctuations.Uk<U<Utr or Turbulent Small voids and particle clusters dart to and fro; top surfaceUc<U<Utr fluidization difficult to distinguish; small amplitude pressure fluctuationsonly.Utr<U Fast No upper surface to bed; particles are transported out thefluidization top and must be replaced by adding solids at or near thebottom. Clusters or strands of particles move downward,mostly near the wall, while gas, containing widely dispersedparticles, moves upwards in the interior. Increasingly diluteas U is increased at a fixed solid feed rate.The transition from a fixed bed to fluidization is delineated by the minimum fluidizationvelocity, U The minimum fluidization velocity has been extensively studied, and a number ofequations are available to predict this transition velocity (e.g. Grace, 1986). The effect oftemperature and pressure on this transition has also been investigated (Knowlton, 1992). Theonset of bubbling is indicated by the minimum bubbling velocity, Umb, which corresponds to thegas velocity at which the first bubble forms in the bed (Abrahamsen and Geldart, 1980). The2minimum bubbling velocity has been found to be a strong function of particle properties. It ishigher than the minimum fluidization velocity for line Group A particles and equal to theminimum fluidization velocity for Group B and Group D particles (Geldart, 1973). The delayed-bubbling regime between U and Umb only exists in fluidized beds of relatively fine particleswhen interparticle forces are significant. With fhrther increase in superficial gas velocity, gasbubbles become larger, eventually leading to slugging when the bubble size grows to becomparable with the column diameter (Kehoe and Davidson, 1970; Baeyens and Geldart, 1974;Clift et aL, 1978). However, slugging is rarely if ever encountered for shallow beds, in columnsof very large diameter or for fine particles (e.g. d,,<60 tm) because the bubble is unable to growto be of comparable size to the column diameter.In recent decades, high velocity fluidization has become more and more attractive owingto its potential superiority over conventional bubbling/slugging fluidized beds for many processes.In the mean time, many studies have been carried out to investigate the fluid dynamics (Grace,1990; Horio, 1991), heat transfer and mass transfer characteristics (see Leckner,1991) as well asreactor characteristics (Contractor and Chaouki, 1991) of high velocity systems. However theoperating regimes and corresponding transitions remain controversial, especially with respect tothe transitions from low velocity (bubbling and slugging fluidization) to high velocity (turbulentand fast fluidization) regimes.High velocity fluidization is generally taken to include both the turbulent fluidizationregime and the fast fluidization regime. Two different definitions are commonly used todistinguish between the bubbling regime and the turbulent regime. The first defines U, thesuperficial gas velocity at which the pressure fluctuation curve (usually rms values plotted againstU) reaches a maximum, as the onset of the turbulent regime. U is believed to reflect thecondition at which bubble coalescence and break-up reach a dynamic balance, with bubblebreak-up becoming predominant if the gas velocity is further increased. The experimental results3obtained by different investigators, however, seem to be inconsistent with each other, withdifferences attributed to the effects of column diameter, bed stmcture, measurement methods andthe locations of probes, as well as different particle size distributions (Brereton and Grace, 1992;Grace and Sun, 1991; Yang et aL, 1990; Cai et al. 1989). Systematic studies are required toresolve these inconsistencies and to model this transition properly.The second definition used to indicate the transition from bubbling fluidization to turbulentfluidization is based on Uk, the superficial gas velocity at which the pressure fluctuation curvestarts to level off This implies that bubble coalescence and break-up have become stabilized, withonly small dispersed voids identifiable. The meaning of Uk, however, is still poorly understood;whether or not it is even an experimentally identifiable parameter is open to question (Rowe andMacGiliivray, 1980; Rhodes and Geldart, 1986b; Brereton and Grace, 1992; Johnsson et aL,1992). In addition, Rhodes and Geldart (1986b) found that Uk is a function of solid elutriationrate or solid flow rate and can be predicted by the choking correlation of Punwani et al. (1976).This suggests that such a transition may also be affected by the solids circulation rate as well asthe superficial gas velocity. The choking phenomena therefore also need to be considered inanalyzing regime transitions.The transition from turbulent to fast fluidization is said to occur at the transport velocity,Utr, where significant numbers ofparticles are carried out from the top of the column (Yerushalmiand Cankurt, 1979). According to Yerushalnñ and Cankurt (1979), a sudden change of pressuredrop with increasing solid flow rate disappears when the superficial gas velocity exceeds Utr. ThiSvelocity is found to be higher than the terminal velocity of single particles due to the formation ofparticle clusters (Yerushalmi and Cankurt, 1979). However, the choice of Utr appears to bedependent on the location of the two taps across which the pressure drop is measured. Rhodesand Geldart (1986a) and Schnitzlein and Weinstein (1988), using the same method as Yerushalniiand Cankurt (1979), reported that the transport velocity could not be identified. A recent analysis4by Bi and Fan (1991) further showed that Utr appears to be equal to Uk if Uk is obtained usingpressure transducers. The behaviour around this transition point needs to be explored.Using a completely different approach, Takeuchi et al. (1986) found that a critical velocityis reached in a circulating fluidized bed with decreasing gas velocity at which the pressure in theriser fluctuates to such an extent that stable operation becomes impossible. This critical gasvelocity was defined as the minimum velocity required for operation of a circulating fluidized bedsystem at a given solid flow rate. This velocity is quite similar both qualitatively andquantitatively to the choking velocity adopted in the gas-solid vertical transport literature. ReddyKarri and Knowlton (1991) named it the “premature choking velocity” after comparing the criticalvelocity data obtained by Bader et al. (1988) in a 305 mm diameter column with predictions of thecorrelation of Yousfi and Gau (1974); the latter, however, successfully predicts the data ofTakeuchi et al. (1986) measured in a comparatively small column (D=100 mm). What triggerssuch a critical condition needs to be explored.Choking is generally considered to take place in a vertical gas-solid transport line when astepwise change in bed voidage or pressure drop occurs. Understanding choking, whichrepresents a transition between hydrodynamically different flow regimes and is closely interrelatedwith the flow regime transitions from low velocity fluidization to high velocity fluidization, isimportant in the design of pneumatic conveyors, riser reactors and circulating fluidized beds.While a number of empirical equations have been developed to predict the choking velocity, thereremain substantial interpretative differences regarding the nature and mechanism of choking.These may result from differences in the manner in which choking is defined. Thus, analysis isneeded to examine available definitions and to elucidate the mechanism of choking.A summary of the regime transitions and their current level ofunderstanding is provided inTable 1.2. It is clear that improved mechanistic understanding and better predictive methods for5distinguishing the regime are needed.Table 1.2. Features of flow regime transitions.Transition Transition Nature Status of Transition superficial velocityvelocity understanding dependent onMinimum U usually good d, p, g(pp-pg), 1gfluidization sharpMinimum Umb sharp fair cL1,, gas properties, interp articlebubbling forcesMinimum slugging Urns diffuse good Umf, g, D, 11mfOnset of turbulent U, Uk rather fair pr,, D, H z, particle sizefluidization diffuse distribution,?Onset of fast Utr diffuse poor d11, pr,?fluidizationChoking Uh sharp fair U, g, d, D,?Minimum dilute Ud diffuse poorconveyingIn this thesis, the propagation of pressure waves in fluidized beds is first examined(Chapter 2) and then used to evaluate the difference between diagnostic measurement techniques,in particular absolute pressure fluctuation signals, differential pressure fluctuation signals andoptical fibre probes. These techniques are widely utilized in distinguishing flow regimes. InChapters 3 and 4 the transition from bubbling/slugging to turbulent fluidization regimes is studiedexperimentally in a 102 mm diameter column based on measurements of absolute pressurefluctuations, differential pressure fluctuations and local voidage fluctuations. Simplifiedmechanistic models are proposed to describe abrupt and gradual transitions. The transition to fastfluidization is studied in a circulating fluidized bed (Chapter 5) by measuring both differentialpressure fluctuations and local voidage fluctuations in the lower section of the riser and byproposing a critical velocity where significant entrainment occurs. By distinguishing different6definitions, choking phenomena are clarified and verified using literature data in Chapter 6.Finally in Chapter 7, a unified flow regime map is proposed in which the flow regimes of packedbed, bubbling, turbulent and fast fluidization, and dilute-phase pneumatic transport are delineated.Conclusions and recommendations for further work are presented in Chapter 8.7Chapter 2Measurement of Gas-Solids and Gas-Liquid Two-Phase Flow2.1. IntroductionA number of experimental parameters have been utilized to determine regime transitionsincluding pressure fluctuations, voidage fluctuations and bed expansion. Instruments haveincluded pressure transducers, capacitance probes, optical fibre probes, x-ray detectors as well asmanometers. Recorded signal traces have been interpreted in terms of average peak-to-peakvalues, maximum peak-to-peak values, peak-to-average values, standard deviations, normalizedstandard deviations etc. Roy et al. (1990) suggested that the information registered by absolutepressure measurements may differ from that from differential pressure measurements in fluidizedbeds. Information provided by optical fibre probes and capacitance probes may also differ fromthat which can be derived from pressure fluctuation measurements. Systematic analysis isrequired to evaluate different measurement methods (Grace, 1992). To properly interpret flowpatterns based on the measured pressure and voidage signals and to resolve the differencebetween different measurement methods, the relationship between measured signals and flowpatterns needs to be evaluated. The purpose of this chapter is to examine and compare theexperimental techniques (pressure fluctuation methods and optical fibre probe measurements)which are most commonly employed to distinguish between flow regimes of fluidization.Fluidized bed fluctuations include bed density fluctuations, bed surface fluctuations andpressure fluctuations. In bubbling beds these fluctuations result primarily from bubble formation,bubble motion and bubble eruption at the bed surface. Pressure fluctuation information has beenutilized for diagnosis of fluidization performance, verification of fluidized bed scale-up, deductionof bubble behaviour and determination of flow regime transitions. A number of methods havebeen used to measure fluctuations, including pressure transducers, capacitance probes, optical8fibre probes and X-ray facilities. The recorded signal traces have been analyzed in terms ofstandard deviations, power spectral distributions (PSD) and probability density functions (PDF).Littman and Homolka (1970, 1973) explored the feasibility of determining bubble sizes and risingvelocities using pressure transducers. The effects of the “dead volume” between the pressureprobe and the transducer were reported by Clark and Atkinson (1988). Sitnai (1983) and Clark etaL (1991) proposed the use of pressure drop fluctuations to study bubble behavior, intending tomake the measurement localized and hence more accurate. The signals obtained in such a way,however, rely strongly on the distance between the two pressure taps across which the differentialpressure is measured (Roy, 1989) due to the propagation of pressure waves in fluidized beds.Capacitance probes and optical fibre probes have been widely used to determine particleconcentration fluctuations, which are again closely related to local bubble motion in the bubblingregime. The accuracy of these measurements has been recently analyzed by Lischer and Louge(1992) and Louge and Opie (1990). However, no systematic analysis has been performed tocompare different measurement methods, although some doubts have been recently raised (Grace,1991) because of contradictory results on regime transition velocities obtained with differentmeasurement techniques.When absolute pressure fluctuations are measured in freely bubbling fluidized beds, boththe amplitude and the dominant frequency are almost independent of location in the bed (Taylor etal., 1973; Baeyens and Geldart, 1974; Fan et aL, 1981; Baskakov et aL, 1986; Seo and Park,1988; Roy et al., 1990). On the other hand, the amplitude and the dominant frequency fromdifferential pressure measurements, optical fibre probes and capacitance probes vary with height(Lanneau, 1960; Baeyens and Geldart, 1974; Fan et al., 1984; Seo and Park, 1988; Grace andSun, 1991). Dominant frequencies from an absolute pressure probe, a differential pressure probeand an optical fibre probe also differ markedly from each other (Hiby, 1967; Broadliurst andBecker; 1976; Davidson, 1991; Kaneo et al., 1988). These findings strongly suggest that theinformation obtained from absolute pressure measurements, differential pressure measurements9and optical fibre/capacitance probes differ from one another. In this chapter, the propagation ofpressure waves and forced-oscillations in gas-solids fluidized beds are studied and used toexamine the difference between absolute pressure fluctuation measurements, differential pressurefluctuation measurements and optical fibre probe measurements.2.2. Pressure waves in gas-solids fluidized beds and gas-liquid bubble columnsIn recent years, the propagation of soundJpressure waves in fluidized beds has beenstudied to explain pressure fluctuations measured in fluiclized beds (Cai et al., 1986; Roy et aL,1990; Filla et al., 1991). Cai et aL (1986) generated a small disturbance by using a small firecracker below the gas distributor and registered the disturbance at two locations of a pre-bubblingfluidized bed using pressure sensors. The wave velocity was then deduced from the time-delayand the distance between the two positions. Roy et aL (1990) used a two-section fluidized bed inwhich the lower section was maintained in particulate fluidization while slugs were formed byinjection of gas into the upper section, causing periodic pressure waves. Pressure fluctuations inboth the lower and upper sections showed that almost the same fluctuation information wasobtained in both sections, indicating that pressure waves generated at the upper section werecapable of propagating downward through the emulsion phase. Musmarra et al. (1992) studiedthe propagation ofboth single disturbances and periodic disturbances generated by single bubblesor jets and bubble chains issuing from a vertical tube above an undisturbed section of a fluidizedbed. These measurements all show that waves can propagate in fluidized beds. The wavepropagation velocity ranged from 5 to 30 m/s, in agreement with a simple analysis of Roy et al.(1990) in which a fluidized bed was treated as a single phase, with allowance for the effect ofparticles on the compressibility. Such a theory, predicting that pressure waves are always dampedas they propagate, is consistent with most experiments, but fails to explain why the amplitude of apulse in interstitial gas pressure may increase with distance from the source of the disturbance(Musmarra et al., 1992; Clift, 1993). Chit (1993) suggested that the disturbance sets up an elastic10wave which is propagated by the particles, with momentum progressively transferred to the gas toincrease the amplitude ofthe gas pressure pulse.There are two common kinds of waves in nature. Transverse waves propagate with themedium being displaced at right angles to the propagation direction, while longitudinal wavestravel in the same direction as that of medium displacement. A longitudinal wave generally travelsfaster than a transverse wave in the same medium because the forces involved in stretching themedium are greater than those needed to bend the medium sideways by the same amount. Soundwaves in any fluid medium are longitudinal waves, for the medium is displaced by a pressure pulsein the direction that the pulse is moving. Solid materials can sustain transverse as well aslongitudinal waves because they can be stretched, bent and sheared. A gas-fluidized bed iscomposed of both gas and particles. While interstitial gas supports longitudinal waves only, theparticle phase can also support transverse waves. To elucidate the mechanism of wavepropagation and attenuation in gas-solids fluidized beds, the gas-solids flow structure needs to beconsidered. In the present study, the propagation and attenuation of pressure waves in fluidizedbeds of Group A particles have been examined while an optical fibre probe has been used tomeasure local voidage variations as pressure waves pass.2.2.1. ExperimentsA Plexiglas column was used to examine the measurement methods. As shown in Figure2.1, the column is 50 mm in diameter and 2 m high. A perforated steel plate covered with finescreen was employed as the gas distributor. There are 58 holes of 1.5 mm in diameter uniformlydistributed in the plate, giving an open area ratio of 5.2%. Pressure probes and an optical fibreprobe were installed along the column with their tips located on the axis of the column. The tipsof the pressure probes were covered with fine screens to prevent entry of or blockage by, fineparticles. Two bubble injectors, each with a tip diameter of 4 mm, were inserted to the axis, 0.0111and 0.69 m above the gas distributor, respectively. In single disturbance test, a gas pulse ofvolume ranging from 1 to 3x10-5 m3 was injected from the injector by a rubber ball connected tothe injector. In continuous disturbance tests, bubbles were injected into the upper section of thecolumn independently from the upper injector using high pressure air, while the fluidizing air wassupplied by a blower to the windbox which is 50 mm in diameter and 80 mm in length below thegas distributor.50mm-ø2m0.61 m =Hmf =0.60 mpperlnjedor== 0.46 mO.31mOptical Probe= 0.26 m0.16 mLoerlnjector 0.01 m—DistributorFigure 2.1. Schematic diagram of the 50 mm fluidization column.Fresh fluid catalytic cracking (FCC) particles of Sauter mean size 60 p.m and particledensity 1580 kg/rn3 were used as bed material. These particles had a wide size distribution, thesame as the n-FCC particles used by Grace and Sun (1991). The static bed height was maintainedat 0.6 m for all tests. Figure 2.2 shows the pressure drop and local voidage versus superficial gasvelocity curves for the FCC particles in the 50 mm column. Hysteresis is evident in all three parts12of the figure. When the gas velocity is increased, there is a higher pressure drop, implying thatparticles are tightly packed. However, after the particles are fluidized, they re-anange themselvesand settle down relatively slowly with decreasing gas velocity, causing a lower pressure drop anda higher voidage. The minimum fluidization velocity for the FCC particles used in the presentstudy ranges from 7.5 to 8.5 mm/s, depending on whether the gas velocity is raised or reduced,while the minimum bubbling velocity, Umb, is aroUnd 15 mm/s.(a)I::__________________2.5 (b)a01.51.0Pressure drop betweenO.26and046ma_ __ _ __ _ _ __ _ __ _ _ __ _(c)a)0.48•E 0.46>C 0.440_J 042 Opti0I probe atz0.26 m0.462 4 6 6 10 12 14 16Superficial Gas Velocity mm/sFigure 2.2. Pressure drop and voidage versus superficial gas velocity for FCC particles;D: Increasing gas velocity; •: Decreasing gas velocity.Pressure fluctuations are registered by low pressure (0 to 10 kPa), differential pressuretransducers (Omega PX162) which have a nearly linear relationship between pressure drop andoutput voltage. The volume of the tube which connects the transducer to the probe tip is aboutAbsolute pressure atzO.26 m134200 mm3. A preliminary test showed that damping of signals having a frequency ranging from 0to 10 I{z becomes negligible when the volume of the tube is smaller than 8000 mm3, in agreementwith the findings of Clark and Atkinson (1988). The output pressure signals are recorded by adigital data logging system (DAS 8 board) at a frequency of 100 to 300 Hz for periods of 40 s.The reflection type optical fibre probe has a tip thameter of 1.5 mm and has been usedpreviously in our laboratory (He et aL, 1994; Zhou et al., 1994). The principle of operation wasdescribed by Qin and Liu (1982). It is composed of two bundles of 0.0 15 mm diameter fibresarranged layer by layer, with alternate layers for light projection and light reception. Visible lightprojected from the light source to the fluidlized bed is reflected by particles and received by thereceiving optical fibres. The light signals are then converted to electric signals by aphotomultiplier. The solids concentration is nearly proportional to the light intensity received(Zhou et al., 1994; He et al., 1994). Signals from the optical fibre probe are recordedsimultaneously using Labtech Notebook software, the same digital data-logging system as used torecord the pressure transducer signals, enabling the power spectrum distribution of the signals tobe calculated. To obtain detailed information on pressure fluctuations over the whole frequencyrange, a narrow bandwidth is chosen for the power spectrum analysis, while the reliability isensured by verifying that the results from two different sets of data for each run are in closeagreement. Cross-correlation analysis is used to check the propagation velocity and direction ofpressure waves, while auto-correlation is used to check the periodicity of pressure fluctuations.Both cross-correlation and auto-correlation analyses are based on the original raw signals withoutwindowing and filtration, and both the first and the last 100 data points (total 4000 data points)are left to allow for a maximum 1 s time shift. The standard deviation is used to evaluate theattenuation ofpressure waves. In the single pulse test, however, both the amplitude and the time-delay are determined directly by reading traces. The wave propagation velocity is thendetermined from the time-shift between the first peaks of the traces.142.2.2.1. Pressure waves and forced oscifiationsThe gas-solids mixture is lirst considered solely as a wave propagation medium. When anexternal pressure/sound wave is supplied, the wave propagates through the medium. Figure 2.3shows typical pressure traces generated by the injection of a gas pulse. It is seen that theamplitude of a pressure pulse, after injection into the de-fluidized bed, decreased monotonicallywith time at a fixed location and with distance from the injection point. This indicates that thepressure wave was attenuated gradually during propagation in the gas-solids medium. Note fromthe voidage signal that the void passes the 0.26 m level more than a second after the pressuredisturbance.0I I I2 3 42.2.2. Experimental Results and Discussion of Relevant Models54Cu0Cl)a)-Q2aL..0Cl)ci)0E0cuc0)C,)3 26a).02a-Cu00.6 .0.0E0.4ci)0)CuO.20Time, sFigure 2.3. Propagation of a disturbance injected 10 mm above the bottom of a de-fluidized bedas measured by three pressure probes and one optical probe for U7. 5 mm/s. Timescale is arbitrary, with the pulse injection occurring at about 1.4 s.15a,.000.8(6U0.4 -8,.000.8COC.)0.0600)0.46Figure 2.4 shows typical pressure traces generated by a gas pulse into a well-fluidizedmedium. Oscillation of the bed appears, as reported by Kobayashi et al. (1970), Rietema andMusters (1973) and Roy et al. (1990). This suggests that self.oscillation has been set up by theexternal pressure wave. Resonance has been observed in a fluiclized bed with pulsed gas flow(Wong and Baird, 1971) and in vibro-fluidized beds (Ryzhkov and Tolniachev, 1983) when thepulsing gas flow frequency was the same as, or higher than, the se1foscillation frequency. Aconstant supply of energy compensates for the dissipation of energy and thus maintains theoscillation of the bed. Kobayashi et al. (1970) further revealed that when bed oscillations wereinitiated by a disturbance in gas flow, the bed height was first raised and then dropped gradually7(60U,6).000)U,4U,41)0E30I.(60,(0CO0(1)0).0041)C63COII)0E0(60,Co0.21.5Time, s022Figure 2.4. Propagation of a disturbance in a fluidized bed for U=8.5 mm/s: (a) disturbanceinjected 10 mm above the distributor, i.e. below the sensors; (b) disturbance injected0.46 m above the distributor, i.e. above all sensors except the optical probe. Timescale is arbitrary.16after the disturbance was cut off Meanwhile, the pressure showed oscillations before the nextdisturbance was supplied. The implication is that the oscillations do not result from bed heightvariations. Instead, such oscillations may correspond to relaxation of layers of particles after theyare compressed. Figures 2.3 and 2.4 show the variation of local voidage when a disturbancepasses the probe. It is seen that the local structure of the gas-solids mixture is disrupted slightlywhen pressure waves pass by, with the disruption being more pronounced when bed oscillationsare present (see Figure 2.4).To test the behaviour of the fluidized bed when subjected to periodic driving forces,pressure waves were introduced into the top section of the bed by injecting bubble chains from anorifice 0.46 m above the distributor. With the bed operated in the pre-bubbling regime (i.e.U<U<Umb), the dominant frequency of pressure signals from the power spectrum analysis wasalmost the same as the natural frequency of the bed oscillation. When the bed was operated in thefree bubbling regime, a dominant frequency about 4 Hz appears in the auto-correlation diagram ofpressure fluctuations [Figure 2.5(a)] and in the cross-correlation diagrams ofpressure fluctuations[Figure 2.5(b)]. This provides further evidence that bed oscillations are set up, and suggests thatresonance can exist in the fluidized bed.The occurrence of such bed oscillations is also supported by experimental findings on thedirection of wave propagation in fluidized beds. With a single disturbance injected from thebottom, the amplitudes of signals from two pressure transducers, one above the other, were foundto decrease with height, suggesting that pressure waves generated from bubble injection arepropagating upward (see Figure 2.6). The time delay between the first peaks of the two pressuresignals, on the other hand, suggests that some waves propagate downward. Similar results can befound from pressure traces reported by Littman and Homolka (1973) and Cai (1989). In freelybubbling fluidized beds, Figure 2.5 shows that major waves propagate downward. These results17suggests that pressure waves from forced bed oscillation are set up immediately after the bedsurface is raised and that they propagate downward.0C-)0CaI-0.2-0.4lime Shift, sFigure 2.5. (a) Autocorrelation of pressure signals in a freely bubbling bed at three heights; (b)Cross-correlation of pressure signals between two probes on the bed axis as afunction of distance between the probes. U=80 mm/s.0a)00D00a)0E0c1D)0)Figure 2.6. Propagation of singleprobe is located rightTime scale is arbitrary,a).00.8 200.60E00.4a)(0t30.2>disturbance issuing 0.01 m above the distributor. (Opticalat the bed surface before the injection of the disturbance).with the pulse injection occurring at about 1.2 s.-0.4 -0.2 0 0.2 0.44320 012 1.4 1.6 1.8 2Time, s18Several theories have been proposed to explain natural fluidized bed oscillation. Hiby(1967) considered oscillation of bed particles up and down around their equilibrium positions.This theory was further examined by Verloop and Heertjes (1974), Rietema and Musters (1973),and Jones and Pyle (1971), and has been extended to explain the elastic behaviour of fluidizedbeds (Musters and Rietema, 1977). Such self-excited oscillations in shallow fluidized beds(FL’d<1O) cannot, however, explain the oscillation of deep beds. Another theory considers thebed to act as a piston, with the air in the windbox compressed and expanded periodically to set uppressure fluctuations (Davidson, 1968; Wong and Baird, 1971). Such fluctuations are onlysignificant for low-resistance distributors, and cannot explain the oscillations observed in othersystems. Baskakov et al. (1986) considered the fluidized bed to act like liquid in a U-tubemanometer, arguing that when a single bubble rises in the centre of the bed, the dense phase in thecentre region is raised while the dense phase near the wall moves downward to compensate forthe upward movement in the central region. This mechanism cannot, however, explain why bedoscillations are also generated by raising and dropping the whole fluidized bed, or by introducinga disturbance below the distributor. Roy et al. (1990) treated the fluidized bed as an organ pipewith a fixed boundary at the bottom and a free boundary at the top surface. In this analysis thewaves are reflected from the fixed boundary provided by the distributor at the bottom and may bepartially reflected from the free boundary (top bed surface). The fundamental wavelength for anorgan pipe with a perfect free boundary and a perfect fixed boundary is 4 times the bed depth, i.e.,2=4H. The resonant wave frequency can then be writtenf 1U. U(1—) (2.1)W ç 4H 4Hmf(lEmf)This equation successfully predicts the natural frequency data of Roy et al. (1990) and theresonant frequency data of Ryzhkov and Tolinachev (1983). Our data are also in agreement withthis equation as shown by Figure 2.7 ifthe wave velocity is taken as a constant, 10 mi’s.190.8 i I I IEl From disturbance tests0.6 • From free bubbling testsa)0_u •HE —El4H/U0 I I5 10 20 50 100 200Superficial Gas Velocity mm/sFigure 2.7. Natural period of forced harmonic oscillation as a function of superficial gas velocity.For single disturbance tests, the natural period is determined directly from traces,while the natural period is determined by auto- and cross-correlation methods in thecontinuous bubble chain disturbance tests and freely bubbling beds. The predictionof equation (2.1)is calculated with U=1O mis.It is seen from equation (2.1) that the natural frequency is mainly determined by the totalbed height if the wave velocity is assumed to be constant in a specific system. The data ofRyzkov and Tolmachev (1983) and Cai et al. (1986), however, showed that the resonantfrequency increases with increasing particle size for a fixed bed height, presumably because wavevelocity increases with particle size (Cai et al., 1986) due to gas-particle and particle-particleinteractions (Ryzkov and Tolmachev, 1983). However, the variation of natural frequency withdistributor design and volume of the gas chamber below the distributor (Baird and Klein, 1973;Little, 1987; Kage et al., 1991) cannot be explained in terms of the variation of wave velocity.The likely explanation is that the fluidized bed is not bound by a perfectly free boundary and aperfectly fixed boundary; instead, there is only partial reflection of waves from both boundaries.The 2=4H assumption requires that the node and the antinode be located at the boundaries, whichcan only be achieved if there is complete reflection of waves from the fixed boundary (i.e. thebottom distributor). When the reflection is only partial, the node may be shifted. The wavelengththen tends to be larger than 4H, which corresponds to a lower frequency. This appears to be inagreement with experimental findings that the frequency is independent of the gas chamber20volume in beds with high-resistance gas distributors (Tamarin, 1964; Little, 1987) because thewaves are then almost completely reflected from the distributor plates, as indicated by negligiblepressure oscillations in the windbox (Little, 1987), while the oscillation frequency in lowresistance distributor systems increases with decreasing gas chamber volume (Baird and Klein,1973) because the effective wave length, ?, becomes smaller. The latter is indicated by theincrease of the amplitude of pressure fluctuations in the windbox with increasing gas chambervolume (Little, 1987). Installation of internal tubes in the fluidized bed may increase theoscillation frequency (Little, 1987) because partial reflection of waves between the boundariesand the internals decreases the wavelength.These experimental findings indicate that there exists a natural frequency for a givenfluidized bed. When pressure waves supplied to the bed have a low amplitude and much lowerfrequency than this natural frequency, the fluidized bed, acting as a wave propagation medium,propagates pressure waves only. On the other hand, when the imposed frequency is close to orhigher than the natural frequency, forced oscifiation is established in the bed. For a singledisturbance, the amplitude of the oscillation is damped by energy losses from the oscillator due toparticle-particle coffisions, particle-gas friction or wall ffiction. However, when the energy iscontinuously supplied through continuous pressure waves or bubble injection, oscillations can besustained at an amplitude where the energy dissipation is balanced by the energy supplied. In abubbling bed, such oscillation can be sustained so that the dominant frequency determined frompressure fluctuations is almost unchanged with variation of gas velocity, although the bubblefrequency may change with gas velocity (Lirag and Littman, 1971; Jones and Pyle, 1971).2.2.2.2. Damping of self-excited bed oscifiationsThe attenuation of harmonic oscillations with light damping can be considered to followan exponential decay of energy21(2.2)diThe energy of the pressure wave averaged over a cycle is related to the square of the amplitudeof the pressure wave. The following relationship for the amplitude of the harmonic motion canthen be derived (Matthews, 1978; Main, 1993):A=4ev (2.3)where T=2’tE. Based on the measured harmonic motion proffles, the decay factor whichreflects the attenuation of signals, can be evaluated using the first peak (A0) and second peak (A1)amplitudes and the period of oscillation (t.j, i.e.=-ln(4IA1) (2.4)Figure 2.8 shows the decay factor data based on our single disturbance tests. While there isconsiderable scatter, as indicated by the hand-fitted line forced through the origin [since dampingis negligible for disturbance of small amplitude (Kok, 1991)], the results suggest that disturbancesof higher amplitude are damped more quickly. This implies that the oscillation of gas-solidsfluidized beds does not correspond to harmonic motion because the damping of bed oscillationsdoes not follow an exponential decay function (Main, 1993).If a fluidized bed is assumed to behave like a Newtonian liquid, the attenuation of theoscillation due to viscous dissipation can be estimated (Needham, 1984) by=2 (2.5)(1—where 1d is the dynamic viscosity of the dense phase, typically 0.4 to 1 Ns/m2 (Grace, 1970).Kok (1991) found that this equation gave good prediction of their experimental data obtained in agas-solids fluidized bed with low frequency low amplitude waves propagating at a velocity lowerthan 3 mIs, but failed to predict the data for waves of frequency higher than 1.5 Hz and22ria,4J00cdcd0a,propagation velocity around 6 mIs. This equation also severely underestimates the attenuation ofour present data. The equation appears to be applicable only for attenuation of low amplitudesurface waves by viscous ffiction and cannot predict the attenuation of pressure waves whenoscillation occurs within the bed.12• z=0.16m10 - X z=0.26m caCdubiceat0.01rnE z=O46m /8 * z=0.26 rn, dCdub&,ce at 0.46 m6-x2 25 3A5 kPaFigure 2.8. Attenuation of forced oscillations, defined as the ratio between the first peakamplitude and the second peak amplitude, as a function of the first peak amplitudefor U=8. 7 mm/s. Scatter reflects wide variation of bed structure with U close toUmfWhen the attenuation of bed oscillations is attributed to energy dissipation due tofluctuating relative motion between the gas and particles, the decay factor can be estimated (Royet al., 1990) by4 =(OJ)2Umj)/2g (2.6)This attenuation factor is an order of magnitude smaller than our experimental data and the dataofRoy et al. (1990).The attenuation factor calculated from the equation of Verloop and Heertjes (1974),which attributes damping to the loss of kinetic energy by the flowing fluid, arguing that “kineticenergy of vibration” stored in the fluid cannot be recovered as “potential energy of vibration”23when the fluid leaves the system, is about two orders smaller than our experimental results. Thissuggests that the kinetic energy loss due to the flowing fluid has only a secondary effect on theattenuation of oscillations in fluidized beds.The contribution from thermal dissipation also needs to be considered. In gas-particlesystems, the thermal relaxation time VT = dpC /l2kg is about 0.02 s for FCC particles used inthis study. The period ofthe pressure waves, 1If, on the other hand, is about 0.2 s, one order ofmagnitude larger than the thermal relaxation time. Therefore, thermal relaxation is not expectedto be an important factor for attenuation of low frequency pressure waves in gas-solids densefluidized beds (Ryzbkov and Tohnachev, 1983; Roy et aL, 1989).Harmonic oscillation would require that the resistive force supplied by the gas-solidsmixture to the oscillations be a linear function of the instantaneous velocity of the two-phasemotion, leading to an exponential decay of energy (Matthews, 1978; Main, 1993). The non-harmonic oscillations of fluidized beds are likely caused by non-Newtonian behaviour of the gas-solids mixture and by particle-particle contact and/or particle relaxation due to disruption of themixture. Experimental lindings that the extent of energy dissipation, indicated by the amplitudedamping, is much higher than predicted by viscous dissipation and gas-solids friction, while beingdependent on the intensity of the supplied pressure waves, suggest that the relaxation of particlesand particle-particle contact, which are directly related to the extent of disruption of the mixture,may be the main contributors to energy dissipation ofnon-harmonic motion.2.2.2.3. Attenuation and propagation of pressure waves in fluidized bedsAs already noted, pressure waves tend to propagate in fluidized beds from one location toanother. The mechanisms of the wave propagation and attenuation need to be understood inorder to predict wave propagation velocities.24(a) Attenuation of pressure wavesThe longitudinal damping of single pressure pulses as they propagate away from theirsources may be expressed as a longitudinal decay factor, defined asAln(-)(2.7)z1 — z0It is seen in Figure 2.9 that the longitudinal decay factor increases with the amplitude of thedisturbance when the disturbance is introduced at the bottom of the bed, consistent with the resultin Figure 2.8. Since both bed oscillations and pressure waves are subject to the same resistanceforces, the amplitude of pressure waves does not fall off exponentially as they propagate awayfrom their sources, again suggesting that the resistance force is a non-linear function of theinstantaneous velocity of the mixture motion. As discussed above, this cannot be explained by thedissipation of energy due to the viscous resistance, drag resistance and friction. Thermalrelaxation also is not an important factor for the attenuation of low frequency pressure waves indense gas-solids fluidized beds (Ryzhkov and Tolnmchev, 1983; Roy et aL, 1989), although itmay be important for sound waves of frequency around 100 Hz (Epstein and Carhart, 1953;Gregor and Rumpf 1976). If these thermal dissipation models are extended to dense fluidizedbeds with voidage around 0.5, the attenuation is predicted to be around 1000 rn1, in reasonableagreement with the attenuation of sound waves of low amplitude and frequency about 120 Hzmeasured in line particle fluidized beds (Chirone et al., 1993).Figures 2.10(a) and (b) show the effects of superficial gas velocity on the longitudinalattenuation for a single disturbance and for recurrent waves generated by continuous gasinjection, respectively. It is seen that the attenuation is very high before the bed is fluidized andthen decreases with increasing gas velocity because fluidized particles can move more freely. For2565N0C,( 2ido 10As, kPaFigure 2.9. Longitudinal attenuation ofpropagating disturbance, with decay factor defined as theratio of the first peak amplitudes of traces recorded at two different locations, as afunction of the first peak amplitude at the location closer to the source of thedisturbance for U=8.7 mm/s. For injection at z=0.0l m, the probes are at z=0.16 mand 0.46 m; for injection at z=0.46 m, the probes are at z=0. 16 m and 0.31 niU>U the decay factor tends to approach a constant value independent of the superficial gasvelocity. Figures 2.10(b) shows that the decay factor is smaller for continuous injection withU0. 16 rn/s than for U=0.092 rn/s. Waves are seen to penetrate downward to the lower sectionfor U well below U This can be explained when the effect of pressure waves on the localstructure of the lower section is considered. Comparison of the local voidage in Figure 2.11(a)where a disturbance was introduced at a higher level with Figure 2.2(c) shows that the bedvoidage in the lower section was higher when a continuous disturbance was supplied to the uppersection, implying that fluidization was reached at a lower superficial gas velocity. As a result, thewave attenuation tends to be lower and to level off for U much lower than U1f [see Figure2.10(b)]. This is consistent with the results of Chirone et aL (1993) which show that fluidizationquality can be improved when sound waves are provided. Figure 2.11(b) further shows that thepressure fluctuations in the upper bubbling section undergo a sudden jump when the fluidizingvelocity reaches U while the flow rate from the bubble injector is maintained constant atU=0. 16 mIs. Such a jump can be explained by resonance, modulation or superposition of forced0.5 1 1.5 2 2.5 326oscillations of the bed when it is fluidized. More random motion of particles in the lower sectionpromotes propagation of pressure waves, and the self-oscillation of particles increases thedisplacement of gas and then the amplitude of waves when they propagate. Pressure waves canthus be modulatedJamplifled when they propagate away from the source as reported by Musmarraet al. (1992) and Nowak et al. (1993), and the modulation is expected to be more significant whenthe bed is well fluidized. The wave intensity in the fluidized bed, therefore, can be either dampedor amplified because it can either be attenuated when waves propagate away from the source dueto energy dissipation or modulatedlamplifled by local particle oscillations due to forcedoscillations set up by disturbances. In the absence of particles, the amplitude of pressure wavesalways decreases during their propagation, as in gas-liquid bubbly flow (Nakoryakov et al., 1990).H4.0CC3.5‘.1.8C,Cd2.5>,CdC,6Ha 5HCJ 4$4o 3C)Cd 2>Cd 1C,0)04 6 8 10 12Superficial Gas Velocity, mm!sFigure 2.10. Effect of superficial gas velocity on the attenuation of disturbances: (a) Singledisturbances introduced 0.01 m above the distributor; (b) Continuous bubble chainsinjected 0.46 m above the distributor. Decay factor is based on the peak amplituderecorded at z=0.16 and 0.46 mfor single disturbance at z=0.01 m and at z=0J6 andz=0.3 1 m for continuous chains introduced at z=0.46 m.1.52 10 12Superficial Gas Velocity, mm!sD•4=l6OmmlsL t.=92mmIs(b)I270.60)a-v0.52>(08 0.48-J0.440.4(00.30.25(0> 0.2ci)0.15(00.1ci)Ci) 0.522 4 6 8Superficial Gas Velocitç mm/sFigure 2.11. Effect of continuous bubble chain injected 0.46 m above distributor on: (a) Localaverage voidage from the optical probe 0.26 m above the distributor; (b) Standarddeviation of pressure fluctuations from the pressure probe 0.61 m above thedistributor.(b) Propagation velocity of pressure wavesSeveral kinds of waves may exist in gas-solids fluidized beds. Continuity waves orconcentration (density) waves are longitudinal waves resembling porosity fronts which move in asingle direction. The wave velocity can be calculated (Walls, 1969) byU =(1—e) (2.8)wThe velocity of continuity waves or shock waves predicted by equation (2.8), in conjunction withother equations relating U and 6, like the Richardson and Zaki equation, generally ranges from 10to 100 mm/s. These values are more than an order of magnitude smaller than velocities ofpressure waves in gas-solids fluiclized beds (5-30 mIs). Furthermore, the fact that pressure wavespropagate in both directions is at variance with the behaviour of continuity waves.• LJ=16OmmIso U=92 mm/s(a)• L16O mm/sLI U=92 mm/s0(b)28Dynamic waves, associated with the propagation of pressure, can be propagated either bythe compression or interstitial gas (Roy et al., 1990) or by the elastic deformation of the fluidizeddense phase (Rietema and Musters, 1973). To describe dynamic waves, several theories havebeen proposed. Needham (1984) showed that the equations describing small amplitude waves onthe surface of a homogeneously fluidized bed are identical to those for surface transverse waveson a liquid. The wave velocity can be calculated byU=o/k (2.9)where n is the angular wave frequency and k is the wave number. Recently, Kok (1991) showedthat such a theory is in good agreement with data obtained at low frequencies (<1.5 Hz), but failsto predict the dramatic increase ofwave velocity for frequencies greater than 1.5 Hz. Kok (1991)suggested that waves of frequency lower than 1.6 Hz are surface or transverse waves while wavesofhigher frequency are of other types.Another approach assumes elastic behaviour of fluidized beds. The velocity of one-dimensional longitudinal waves in a non-porous material without lateral extension is given byU=jE/p (2.10)where E is the Young’s modulus/elasticity modulus of the material. The velocity of waves in aporous material or a packed bed can be approached by substituting the modified elasticitymodulus and apparent/mixture density into equation (2.10) (Gregor and Rumpf 1975). Thesound velocity in a non-porous solid material is of order 1000 mIs. The elasticity of a packed bedcan be approximated (Shorokhod, 1963) byEb =E(l—2s) (2.11)The wave velocity calculated by combining equations (2.10) and (2.11) is then of order 100 m/s,one order higher than the wave velocity in fluidized beds (5-30 m/s). On the other hand, when theelasticity modulus of homogeneously fluidized beds is chosen to be around 10 to 100 N/rn2(Musters and Rietema, 1977), the wave velocity predicted from equation 20 is less than 1 m/s,one order smaller than the true wave velocity in fluidized beds. The elastic theory thus appears to29be unable to predict wave phenomena in fluidized beds based on the limited information on thefluidized dense phase elastic behaviour.When a gas-solids mixture is considered as a pseudo-homogeneous phase without relativemotion and interaction, the velocity ofwave propagation is given by the Laplace equation=(2.12)Assuming that compression is an adiabatic process, the wave velocity in fluidized beds can then beevaluated by substituting the mixture density into equation (2.12), givingu=c/ Pg (2.13)[p,(i— ) +pgE]Ewhere C is the velocity of sound in the pure gas phase (330 m/s for air at atmospheric pressureand room temperature).Such a pseudo-homogeneous model was found to be capable of predicting thepropagation of pressure waves in gas-liquid upward flow systems (Henry et al., 1969). Tn gas-solids fluidized beds, however, allowance may be needed for the relative motion between gas andparticle phases, particle-particle coffision and particle relaxation. To allow for the relative slipbetween gas phase and solids phase and for particle-particle and gas-particle interactions, the gasand particle phases need to be treated separately. The separated phase flow model proposed byGregor and Rumpf(1975) for gas-solids dilute-phase transport lines assumes that the gas phase iscompressible while the solids phase is incompressible, with relative motion between gas and solidsand different phase acceleration for the two phases. The wave propagation velocity can bederived based on these assumptions as301+ (‘- +6 6U =C p (2.14)W6with G = g if Stokes’ law is assumed to apply (Gregor and Rumpf 1975). Note thatPg (OUrequation (2.14) can be simplified to equation (2.13) when there is no relative motion between thetwo phases, when the phase accelerations for both phases are the same or when the parameter Gapproaches infinity (i.e. the frequency goes to zero).With the assumptions that the particles are incompressible while the gas is compressibleand drag is subject to Stokes law, the propagation velocity of small perturbations in arelaxing/disperse gas-solids fluidized mixture was derived by Ryzhkov and Tolmachev (1983) asI p l+o2TBTT—PI g ff22 21+owhere tf is the relaxation time ofparticles given byr,. =Ppd/18/Jg (2.16)while Bf is a density ratioPBB= g (2.17)Pp (1— ) +Pg8An increase in frequency and/or an increase in size or density ofparticles makes the particle inertiaimportant because the particles no longer follow the gas fluctuations. Given that Bf is always <1,equation (2.15) then predicts that the wave velocity increases with the wave frequency andparticle size and density. When the wave frequency goes to zero and p<<p(l-6), equation(2.15) reduces to equation (2.13).31The most important difference between the pseudo-homogeneous and separated flowmodels is that the gas-solids fluidized mixture is considered as a dispersive medium in theseparated flow model because the wave velocity varies with wave frequency due to the relaxationof the perturbation in the medium. In gas-solid fluidized beds, however, the particle-to-gasdensity ratio is around 1000 and the angular frequency is small since the frequency is generally oforder several Hz. The terminal velocity is of order 1 m/s for commonly used Group A and smallGroup B particles. The parameter G then tends to be generally larger than 1000. It is thenstraightforward to show that the separated phase flow model, equation (2.14), can be simplified tothe pseudo-homogeneous model, equation (2.13).To examine the feasibility of the two compressible wave theories, all wave propagationvelocity data available in the open literature are listed in Table 2.1 in comparison with the twowave theories. It is seen that both the pseudo-homogeneous and separated flow compressiblewave theories predict pressure wave propagation velocities of the right order. However, thepseudo-homogeneous model predicts that the wave velocity is independent of wave frequency andparticle size, while the separated flow models correctly predict an increase of wave velocity withincreasing wave frequency and particle size. The experimental data of Kok (1991) show a slightincrease of wave velocity with increasing wave frequency when the latter is higher than 1.6 Hz.Ryzhkov and Tolmachev (1983), based on their own data and other literature data, also detectedan increase of wave velocity with increasing wave frequency, although the effect was insignificantfor wave frequencies below 10 Hz. The experimental data of Cai et al. (1986) show that the wavevelocity increases with particle size for Group A and B particles. These findings suggest that theseparated flow model may be more realistic than the pseudo-homogeneous model in view of themodulation of wave propagation by the oscillation of particles. Both models predict a very weakvariation of wave velocity with bed voidage for 6<0.60. Despite the large scatter, this appears toagree with our data obtained with the bed operated above the minimum fluidization velocity inwhich the wave velocity is not sensitive to increasing gas velocity (see Figure 2.12). However,32the dramatic change of propagation velocity around Uin Figure 2.12 cannot be explained basedon these theories. This suggests that compressible wave theories can only be applied when thebed is well fluidized. When a gas-solids mixture is not well fluidized, particles cannot follow theoscillation of the gas due to interparticle contact. As a result, pressure waves may propagate inthe form of elastic waves, like elastic waves in porous/packed materials. The propagation velocityof elastic waves in a packed bed is then higher, as indicated by equations (2.10) and (2.11) and asconlirmed by Figure 2.12.Table 2.1. Comparison of the reported fluidized bed wave velocity data with compressible wavetheoriesSource of Data D H11 dp Pp UW,exp UW,call UW,cal2 UW,cal3mm cm urn kg/rn3 m/s rn/s m/s m/sLiragandLittman 63.5 32 500 2500 6.9 14.8 18.2 18.4(1973)Filla et al. (1986) 350 30 —300 2600 6-10 14.5 16.8 15.1RoyetaL(1990) 45 160 70 1250 11.3 21.0 21.3 21.0120 160 240 2600 9 14.4 15.4 14.845 160 220 384 19 37.8 40.8 37.9Musmarra et al. 350 30 -150 2600 6-16 14.5 15.4 14.6(1992) 100 105 -150 2600 15-30 14.5 15.7 14.6Thiswork 51 60 60 1600 10 8-13 18.9 18.5* UW,call -- calculated based on pseudo-homogeneous model, equation (2.13)UW,cal2 -- calculated based on separated flow model, equation (2.14)UW,cal3 -- calculated based on separated flow model, equation (2.15)To summarize, there appear to exist two distinct modes of pressure propagation andattenuation in fluidized beds. When the superficial gas velocity is around Uor lower, pressurewaves propagate at relatively high velocities and show relatively rapid attenuation. When thesuperficial gas velocity is well above U11 so that the bed is well expanded, both the propagationvelocity and the attenuation rate tend to remain nearly constant and to be lower than at lower gasvelocities. For the well fluidized beds, pressure waves likely propagate as compression waves,while for U<U pressure waves likely propagate in the form of elastic waves. Elastic waves and33Figure 2.12. Wave velocity as a function of superficial gas velocity. For single disturbance teststhe wave velocity is determined directly by reading the time delay between twotraces, while the wave velocity is determined by cross-correlation for freely bubblingbeds and for continuous gas injection.continuity waves may still exist in well fluidized beds, although they may interact with thecompressible pressure waves during their propagation and not be detected by pressure transducersdue to their low amplitudes compared to those of compression waves. Continuity waves can beidentified from concentration measurements by making a step change in gas flow rate (Didwaniaand Homsy, 1980), while elastic waves may become important when the bed is de-fluidized.30U)E20C.)01002 5 10 20 50Superficial Gas Velocity, mm/s100 2002.2.3. Pressure waves in gas-liquid bubble columnsPressure waves propagate in gas-liquid systems at a speed generally lower than in either ofthe components on their own. A gas-liquid bubble column behaves, to some extent, like the gas-solids fluidized bed, because pressure waves can propagate through both the liquid phase and thegas phase. When the liquid is the continuous phase (e.g. bubbly, slug and churn flow) the34presence of gas voids reduces the speed of sound to very low values (Nishihara and Michiyoshi,1981). When, however, the gas is the continuous phase (e.g. annular and mist flow), the presenceof droplets and a liquid film does not appreciably reduce the speed of sound below that of the gasalone (Henry et aL, 1969; Grolmes and Fanske, 1969; Nishihara and Michiyoshi, 1981).Assuming that (i) gas bubbles and liquid form a pseudo-homogeneous mixture, (ii) there isnegligible slip between them, (iii) there is no heat and mass transfer between them, (iv) the liquidis incompressible, and (v) the compression of gas follows an isothermal process, an equationsimilar to equation (2.13) based on pseudo-homogeneous wave theory of gas-solids fluidized bedcan be derived (Henry et al., 1969; Miyazaki and Fujii, 1981; Martin and Padmanabhan, 1979),u=c/ (2.18)[Pi(E)+PgEJSuch a pseudo-homogeneous model was found to be in good agreement with most ofexperimental data obtained by analyzing the time delay between signals from two pressuretransducers in both air-water vertical flow systems (Henry et aL, 1969; Nishihara and Michiyoshi,198 1) and steam-water vertical flow systems (Miyazaki and Fujii, 1981) if C in equation (2.18) isthe sound propagation velocity in steam alone. However, the velocity predicted by equation(2.18) systematically underpredicts the experimental data for cases ofhigh void fraction.To explain the higher propagation velocity of sound for high void fractions, in most casescorresponding to the slug flow condition, Henry et aL (1969) treated the penetration ofwaves in atube in which there is slug flow in terms of waves propagating through alternate layers of gas andliquid. Pressure waves may thus propagate in the gas-liquid slug flow with a speed higher than ina single gas flow (Henry et al., 1969). However, Martin and Padmanabhan (1979) and Nishiharaand Michiyoshi (1981) found that such a simple model overpredicted their experimental data. Thepropagation velocity of sound in slug flow is almost the same as the acoustic velocity inhomogeneous bubbly flow for void fractions smaller than 0.5. For e>O.50, the wave propagation35velocity is slightly higher than the acoustic velocity in homogeneous bubbly flow (Matsui, 1981;Nishikawa and Michiyoshi, 1981; Miyazaki and Fujii, 1981). To explain the discrepancy,Miyazaki and Fujii (1981) argued that the wave propagation in slug flow can neither beconsidered homogeneous non-slip flow nor as uncoupled gas-slug and liquid-slug flow, becauseof the heterogeneity of the mixture. Therefore, both the gas-liquid slip caused by theheterogeneity and the coupled flow of gas and liquid slugs need to be considered. Thepropagation velocity can be better predicted by including the contribution of the dynamic gas-liquid slip which causes both the increase in propagation velocity and the dissipation ofmechanical energy.The effect of wave frequency on the propagation velocity of sound waves is uncertain.Karplus (1958) found that wave speed increased with increasing wave frequency, probably due tothe dispersion of the propagating wave with the test frequency which ranged from 0.25 to 1.5kHz. Mecredy and Hamilton (1969) attributed such an effect to the non-equilibrium momentumand heat transfer between the gas and the liquid phases. However, Nishihara and Michiyoshi(1981) did not detect any effect of wave frequency on wave propagation velocity for frequenciesfrom0.5to 1.0kHz.The attenuation of pressure waves in gas-liquid bubble columns has also been studied.Nakoryakov et al. (1990) generated a bell-like pressure pulse from the bottom of a gas-liquidbubble column and recorded pressure signals at several higher locations using a series of pressuretransducers. The amplitude of pressure waves was found to decrease as the waves propagatedupward. Their duration, however, increased due to interaction between waves and bubbles. Thisinteraction was demonstrated by tracing the motion of a single freon bubble in water in thepresence of a pressure wave, where both the size and the shape of the freon bubble changed withvarying wave intensity. Moreover, the attenuation increased with the intensity of the appliedpressure pulse (see Figure 2.13), suggesting that the resistance supplied by the bubble-liquid36mixture is not a linear function of the instantaneous velocity of the mixture motion. This is likelyassociated with the non-linear or chaotic behaviour of bubble-bubble interactions (Daw andHalow, 1992). The experimental attenuation coefficient is, in general, much larger than predictedby available simple pseudo-homogeneous theories in which the damping is caused only by heatconduction and viscosity (Carstensen and Foldy, 1947; Nishihara and Michiyoshi, 1981).Compared to gas-solids fluidized beds, the attenuation is much smaller as shown in Figure 2.13where the decay factors for gas-solids and gas-liquid systems are plotted against the amplitude ofthe pressure pulse.102Gas-sdki systemsI] Thisstudy0 Musirarraet. (1992)101Cs-hqiid systems10• NaxIv et . (1990)• AkagaetaL(1981)V Matsi.i(1981)102 I I I1& 101 ia3A, kPaFigure 2.13. Longitudinal attenuation of propagating disturbance for gas-solids fluidized beds andgas-liquid bubbly/slug transport, with decay factor defined as the ratio of the firstpeak amplitude at the position fhrther from the source to that closer to the source ofthe disturbance.As for wave propagation in gas-solids fluidized beds, the attenuation of pressure waves ingas-liquid flow systems increases with increasing wave frequency (Karplus, 1958); this effect isinsignificant for low frequencies (<100 Hz).I372.3. Origin of Pressure fluctuationsIn freely bubbling fluidized beds, where many bubbles are present at any time and wherebubble coalescence and splitting take place naturally and continuously, pressure waves can comefrom bubble formation and eruption (Littman and Homolka, 1973; Baeyens and Geldart, 1974;Kage et a!., 1991), selfexcited oscillations of fluidized particles (Hiby, 1967; Verloop andHeertjes, 1974), pressure oscillations in the plenum chamber due to piston-like motion of the bed(Davidson, 1968; Wong and Baird, 1971), and bubble coalescence and disintegration (Fan et aL,1981). Table 2.2 summarizes six possible sources of pressure waves. Waves from each of thesesources are capable of propagating through the emulsion phase, although the amplitude of thesignals may be attenuated during their propagation. Waves from all six sources may contribute topressure fluctuations at any location ofthe fluidized bed.Selfexcited particle oscillations have been reported to be significant only near thedistributor [z<(lO-lOO)dj (Hiby, 1967; Verloop and Heertjes, 1974), while selfexcited plenumchamber oscillations prevail only for distributors of low resistance. Both kinds of oscillations areinitiated by external driving forces. Pressure waves generated by bubble formation at thedistributor have a higher frequency and contribute little to the total pressure fluctuations measuredwell above the distributor (Cai, 1989; Kage et al., 1991), although they can be important near thedistributor (Hong et aL, 1988; Leu et al., 1989). The dominant frequency from absolute pressuremeasurements generally corresponds to the bubble eruption frequency detected at the bed surfacethrough video cameras and visual observations (Baeyens and Geldart, 1974; Broacthurst andBecker, 1976; Noordergraaf et al., 1987; Kage et al., 1991). The pressure drops almostsimultaneously in the upper and lower sections of the bed as bubbles break through the bedsurface (Baskakov et al., 1986). All these experimental findings suggest that bubble eruption atthe bed surface is a key element in generating pressure waves in fluidized beds.38Table 2.2. Summary ofpossible pressure wave sources in gas fluidized beds.Pressure sources Investigators RemarksSelf-excited oscillation of Tamarin (1964), Hiby (1967), Prediction can be based onfluidized particles Verloop and Heertjes (1974) force balance on particles.Self-excited oscillation of gas Davidson (1969), Wong and Gas in chamber is compressedin plenum chamber Baird (1971) and expanded periodically bythe piston-like motion ofthebed.Oscillation due to bubble/jet Littman and Homolka (1973), Pressure fluctuations due toformation Cai (1989) periodic bubble formation anddetachment.Oscillation due to bubble Littman and Homolka (1973), Bed surface fluctuates due toeruption at bed surface Baskakov et al. (1986), Sun bubble bursting, causinget aL (1988) variation in hydrostaticpressure.Oscillation due to bubble/slug Davidson (1961), Kehoe and Change in hydrostaticpassage Davidson (1972a), Baeyens pressure head with theand Geldart (1974) passage ofbubbles/slugsOscillation due to bubble Fan et al. (1981, 1983) Local pressure changes due tocoalescence and splitting bubble coalescence andsplittingIn fluidized beds operated with U<U<Umb, forced oscillations of fluidized beds havebeen identified when a single pulse is injected at the bottom as shown in section 2.2. To sustainsuch forced oscillations, driving forces need to be supplied, e.g. due to bubble formation anderuption. The amplitude of the oscillation is mostly determined by the bubble eruption (Main,1993). According to Roy and Davidson (1989), the maximum amplitude of pressure fluctuationsfrom bubble eruption can be estimated byAP = 0. 54p(U— Urnj )°4(H + 4J)8g08 (2.19)where the maximum pressure amplitude is assumed to be proportional to the bubble size near theupper bed surface (Davidson, 1961; Littman and Homolka, 1973) and the bubble size is estimatedfrom the equation of Darton et al. (1977). The maximum amplitude of pressure fluctuationscaused by the oscillation of fluidized particles can be predicted by an equation developed byAizabrani and Wall (1993) based on the concept proposed by Hiby (1967) and Verloop and39Heertjes (1970) in which the fluidized bed is treated as a mechanical system oscillating around itsequilibrium position, leading tor3(l_s)(l_s)EfJg 1/22Bmi 1 (2.20)where a. = Y(&,, +6d) (see Grace, 1982). A comparison with our data is shown in Figure 2.14.It is seen that equation (2.20) severely underestimates the maximum amplitude of absolutepressure fluctuations. Equation (2.19), on the other hand, somewhat underestimates the data.This again suggests that the major contribution comes from eruption of bubbles at the upper bedsurface, although pressure fluctuations from bubble passage and pressure waves due to bubbleformation, coalescence and splitting also need to be considered.50- 4a)DEDExl00.5Figure 2.14. Maximum amplitude of absolute pressure fluctuations as a function of superficial gasvelocity: D=0. 102 in, FCC particles, Hmf’=O.6in, z=0.2 im2.4. Comparison of Measurement MethodsWhen absolute pressure fluctuations are measured in freely bubbling fluidized beds, thestandard deviation of signals increases with the elevation of the probe and may decrease afterU, rn/s40reaching a maximum value ( Hong et al., 1988; Leu et aL, 1990a). The dominant frequency isalmost independent of location in the bed (Taylor et aL, 1971; Baeyens and Geldart, 1974; Fan etaL, 1981; Baskakov et al., 1986; Seo and Park, 1988; Roy et aL, 1990). Kaneo et al. (1988)found that power spectrum diagrams of absolute pressure fluctuations and voidage fluctuationsdiffer significantly from each other, with the dominant frequency from an absolute pressure sensorlower than that deduced by counting major peaks of optical fibre probe signals. These resultssuggest that information from absolute pressure measurements differs from that derived fromoptical fibre probes, capacitance probes and x-rays.To avoid the disadvantages of absolute pressure fluctuation measurements, differentialpressure/pressure drop fluctuation measurements have been utilized (Sitnai et al., 1981; Sitnai,1982; Clark et al., 1991; Grace and Sun, 1991; Brereton and Grace, 1992). The signalsare thenbelieved to reflect behaviour between the two taps only. However, the spacing between the twotaps between which the differential pressure is measured may have significant influence, and thedifference between the differential pressure measurement and the optical fibre probe measurementneeds to be evaluated.2.4.1. Simplified modelThe difference between a pressure sensor and an optical fibre probe arises firstly from thedifference in the measurement volume. A well-designed miniature optical probe can have a verysmall field of view, less than 10 mm in depth and 100 mm2 in cross-sectional area (Lischer andLouge, 1992). Therefore, the measurement can be considered as localized. On the other hand,bubbles passing many radii from the tip of a pressure sensor can still cause appreciable pressurevariation at the probe tip. For a single bubble (Davidson, 1961):PB(t) = pg(1— )-cosO for r>RB (2.21a)41PB(t) = pg(l— e )r cosO for r<RB (2.21b)Pressure signals therefore include contributions from bubbles passing in the vicinity, as well asfrom bubbles passing directly over the probe tip. The information from pressure signals thereforediffers significantly from that conveyed by localized optical fibre probes.Another obvious difference between a pressure sensor and an optical fibre probe relates tothe variation of the amplitude of signals. In a bubbling bed, an optical fibre probe essentiallyregisters either zero voidage when the probe is covered by a bubble or the dense-phase voidagewhen it is exposed to the dense phase. Therefore, one cannot distinguish a small bubble from alarge bubble based on the signal amplitude. In multi-bubble systems, the standard deviation willnot change if the ratio of bubble size to the spacing between bubbles remains the same. For apressure sensor, the amplitude of pressure signals caused by bubble motion is related to bubblesize, as shown by equations (2.21), with both the amplitude and standard deviation of pressurefluctuations increasing with bubble size.The main difference between absolute and differential pressure signals arises from theeffect of pressure waves, with signals recorded by a differential pressure transducer primarilycaused by fluctuations within the measuring interval while those coming from outside are mostlyifitered out. However, three aspects need to be verified before differential pressure signals can beclaimed to permit useflul local measurements. First, one must ensure that the signals from twoprobe tips are similar so that similar information is registered at the two points. Secondly, thedisturbance from extraneous pressure waves must be small relative to bubble-induced signals.Finally, signal intensity from passing bubbles needs to be much stronger than local interferencefrom noise and turbulence.The fluctuating component of the signals from the absolute pressure measurement can beexpressed as:42P(t)=P8(t)+P,(t) (2.22)where PB(t) represents the contribution from passing bubbles, and P(t) from pressure wavesoriginating from other sources. For the differential pressure measurement, the fluctuationcomponent is the same as the difference registered at two locations separated by distance L, if it isassumed that there is no damping ofthe signals, i.e.AP(t) (2.23)Both periodic pressure signals and pressure waves can be expressed byPB(t) = p + F sin(2rfBt)} (2.24)P(t) = F0+ F sin(2itf1t)so that,A1’B(t) = {F sin(2ltfBIt)—P8 sin[2içf1(t1:1L LBi (2.25)={2P1 sin(tfB j—)cos[7cfBI(t—2U8similarlyAP(t) = {2P1sin(itf1—--)coitf1(t— 2U)j} (2.26)For a component of frequency the amplitude registered by the differential sensor isproportional to sin(nLfilUj). For O<f<n/2, sin(7tLf/U) increases with (7tLfIUi), so that acomponent of lower frequency and/or higher velocity is ifitered out more severely by thedifferential pressure sensor. As a result, a component having higher frequency and lower velocitycontributes more to the pressure drop fluctuations.43To simplify the analysis, the intensity of the fluctuations is considered to be mainlydetermined by the component corresponding to the dominant frequency. Furthermore, theamplitude of pressure fluctuations caused by the passage of bubbles at a height z is estimated byequation (2.19), while pressure waves come mainly from bubble eruption at the bed surface andcan also be estimated by equation (2.19) with z=H. The ratio of the amplitude of the pressuresignals from the local bubble passage and pressure waves can thus be approximated by/z +4O.8sin(fBL / UB) (228)B W H+4J) sin(tfL/U)when a porous plate type distributor is used, So can be taken as zero.For a differential pressure measurement to provide clear information on local bubblemotion, the intensity from the bubbles needs to be at least as large as the intensity from pressurewaves. Figure 2.15 shows the spacing , L, corresponding to APB/APw=1, as a function of z/H,for a bubble rise velocity of 0.5 rn/s and a wave velocity of 10 mIs, while both the bubblefrequency and the wave frequency are considered to be the same, varying from 1 to 10 Hz. It isseen that L generally needs to be smaller than 0.5 m for this frequency range. Due to bubblegrowth with height, the spacing needs to be smaller lower in the column than at higher positions.In general, L should be smaller than 0.2 m for the typical frequency range of 2 to 10 Hz, and lessthan 0.1 m in the bottom region.Table 2.3 summarizes pressure tap spacings used successfully by some investigators tointerpret local bubble/slug behaviour in gas-solids bubbling/slugging fluidized beds. The spacingis seen to be 0.1 m or smaller, consistent with the present analysis.440.6E-J0.50.40.30.20.10 0Figure 2.15. Spacing of differential pressure measurement ports required to give equal intensity ofthe pressure signals from bubble passage and from bubble eruption at the uppersurface, as a function of measuring location and signal frequency for UB=O.5 mis,U=l0 mis, fw=fB and So=0.Table 2.3. Spacing of differential pressure measurements used to interpret local bubble behaviourin gas-solids fluidized bedsAuthors Column dimensions Probe spacingm mHiby (1967) 0.09x0.04 0.01Sitnai(l982)&SitnaietaL (1981) l.2x1.2 0.1Roy and Davidson (1989) 0.1, 0.27 0.04Clark et al. (1991) 0.14 0.013-0.025Ramayya et al. (1991) 0.4x0.02 0.01GeldartandXie(l992) 0.152 0.060.2 0.4 0.6 0.8z/H452.4.2 Experimental results and discussionFigure 2. 16 shows differential pressure signals deduced from the differences betweensignals from three absolute pressure probes located below the point of the gas injection into thebubbling section of the bed for U<U<Umb. The differences between pairs of signals should beidentical to the signals obtained by a differential pressure transducer having a spacing equal to thedistance between the two pressure ports. It is seen that the amplitude of differential pressuresignals decreases as the spacing between ports is reduced.4.5P1, z0.16 m, s37 Pa4.03.5 P2, z0.26 m, s40 Pa3.0 P3, z0.31 m, s40 Pa2.01.5 P1-P3, L0.15 m, s=38 PaP1-P2, L0.1O m, s34 Pal.OVWAfVP2-P3, L0.05 m, s13 Pa0.50.0.00 1 2 3 4 5Time, sFigure 2.16. Absolute and differential pressure signals recorded in the lower section of thefluidirzed bed when the upper section is supplied with continuous gas injection atz=O.69 m while the bottom section is maintained between U and Umb: U=9.3mm/s, U25.5 mm/s.Figure 2.17 shows the maximum dimensionless cross-correlation coefficient as a functionof spacing between two absolute pressure sensors for two different operating conditions. Themaximum correlation coefficient is seen to decrease with increasing spacing between the ports. It46increases with gas velocity because of the existence of larger bubbles. The information obtainedby differential pressure measurement with a large separation between the two ports cannot fillyreflect the bubble motion. A probe spacing smaller than about 150 mm is required to maintain across-correlation coefficient larger than 0.5.1.0________________________0.80.6 -12, max0.40.20.0 I I I0 5C0Figure 2.17. Maximum cross-correlation coefficients between two pressure signals from differentabsolute pressure probes as a fi.mction of spacing between the two probes.Let us finally examine the difference between differential pressure measurements andoptical fibre probes. As noted above, optical fibre probes measure local voidage fluctuationsincluding information from both large and small bubbles. The frequency range of the signals istherefore expected to be wide. Closely spaced differential pressure measurements ifiter mostwave signals and some low frequency andlor high velocity information, with the remaininginformation mainly due to bubbles within the measuring interval. As a result, the bandwidth of thespectral diagram tends to be narrower than for absolute pressure probes and optical fibre probes.In addition, as indicated by equations (2.21), larger bubbles contribute more to the intensity oftotal pressure fluctuations. Therefore, higher power appears in the low frequency range of thepower spectrum diagram. These trends are evident in the experimental results shown in Figure2.18 where the power spectrum of differential pressure fluctuations with closely spaced ports isz’O.26-O.31 mU27 mm/s U=80 mm/s• LIz=O16-O.46 mB z=O.16-O.61 niico 20D 3c0L, mm47compared with the corresponding spectrum of local voidage fluctuations from the optical fibreprobe at the same height as the bottom port. Note that the differential pressure signals differsubstantially from the optical fibre probe signals.10,000___________________________8 CXX)6,(XXJ4,0002,0000 2 4 6 8Frequency, Hz(a) U23 mm/s (b) U113 mm/sFigure 2.18. Comparison of power spectra of signals measured simultaneously from optic fibreprobe and from differential pressure measurements at the same level for (a) U=23mm/s; and (b) U=l 13 mm/s.40,0CC30,000jOptical probez =0.26 mA‘II20,00010,0001,0CC900800700G) 600500Q_ 400300200100Differential pressureL0.05mz10.26mz2=0.31 mFrequency, Hz10The difference between the two methods can also be observed from probabilitydistribution function (PDF) diagrams. As shown in Figure 2.19, a bimodal distribution is presentfrom the optical fibre probe, with the right peak corresponding to bubble phase and the left peakto the dense phase. The proffle from differential pressure measurements is again a function of thespacing between the two ports. For a large spacing (L0.20 m), the PDF prolile has one peakonly, similar to that from an absolute pressure sensor [Figure 2.19(d)] due to the largemeasurement volume and the inclusion of some wave information. However, a bimodal PDFproffle is achieved when the spacing between the two pressure ports is reduced to 0.05 m. This48suggests that a differential pressure sensor of sufficiently small spacing can be used to deducesimilar averaged local bubble information as an optical fibre probe, although the information willnever be identicaL0C-)0C-)0C-.)003.6 4Pressure, kPaFigure 2.19. Comparison of probability distribution functions for signals measured simultaneouslyat the same bed level with U=1 14 mm/s. (a) Optical fibre probe; (b) Differentialpressure measurement with L=O.05 m; (c) Differential pressure measurement withL=O.20 m; (d) Absolute pressure probe.Since pressure waves are also capable of propagating in gas-liquid bubble columns, theinformation registered by different methods is also expected to be different. Nishikawa et aL(1969) found that absolute pressure fluctuation signals in a gas-liquid bubble column arise fromlocal behaviour near the measurement point and from system behaviour. Matsui (1984) further49showed that differential pressure signals also vary with the spacing between the ports. Theprobability distribution function of signals with L1 1 mm was bimodal, while only a single peakappeared for a large spacing, L200 mm, consistent with our results from gas-solids bubblingbeds.In summary, optical fibre probes having small measurement volumes can measure localbehaviour. Absolute pressure sensors have a much larger measurement volume and are affectedby superposition ofpressure waves from every direction, making signals very difficult to interpret.Differential pressure measurements with closely-spaced ports can increase bubble resolution, andreduce the disturbance of pressure waves, so that the visibility of local bubbles is enhanced.However, differential pressure signals still suffer from distortion from near-by bubbles due to thelarge measurement volume, while the amplitude discrimination causes more information to beregistered from large bubbles than from smaller ones.2.5. ConclusionPressure waves propagate in fluidized beds at speeds of order 10 rn/s. The velocity tendsto be higher when the bed is de-fluidized. There exists a natural frequency for a given fluidizedbed. When a disturbance of similar frequency is supplied to the bed, forced oscillations can beestablished. Such oscillations interfere with the propagation of pressure waves in fluidized beds.As a result, the amplitude of pressure waves can be attenuated or amplified during theirpropagation. Our results suggest that the natural frequency of fluidized beds can be wellpredicted by the equation of Roy et al. (1990). However, the attenuation cannot be predictedbased only on viscous dissipation or gas-solids relative fluctuations. This behaviour can beexplained by the interaction between particles and the fact that forced oscillations of fluidizedbeds are coupled with propagating pressure waves.50The propagation velocity of pressure waves in gas-solids fluidized beds can be wellpredicted by both the pseudo-homogeneous compressible wave theory and by the separated flowcompressible wave theory. Although the separated flow theory appears to be more appropriate,showing the effects ofwave frequency and particle size, the difference between the two theories isinsignificant for Group A and B particles, so that either theory can be used to predict thepropagation velocity of pressure waves in well fluidized beds. For U<U both theories fail topredict the dramatic increase of wave velocity with decreasing gas velocity, probably due to thechange in the form of waves as particle-particle contacts cause gas-solids mixtures to lose theircompressibility. Pressure waves may then propagate as elastic waves, which travel at highervelocity in a porous medium, rather than as compressible waves.The existence of pressure waves affects measurements in fluidized beds. Optical fibreprobes register local voidage fluctuations mainly caused by passage of voids. Absolute pressure(single-point) measurements include both pressure fluctuations due to bubble passage andpressure waves propagated there from other locations. Therefore absolute pressuremeasurements do not provide localized measurements. Pressure waves can be ifitered to areasonable extent by using differential pressure measurements. However, appropriate spacing isrequired to be able to determine local bubble behaviour successfiully. If the spacing between thetwo ports is too large, poor signal correlation and strong interference from extraneous sourcesprevents accurate measurement of local bubble properties. Even with appropriate spacing,differential pressure measurements do not provide the same information as optical fibre probesbecause of much larger measurement volumes and due to different dependencies of proberesponse on bubble size.51Chapter 3Transition from Bubbling to Turbulent Fluidization3.1. IntroductionTurbulent fluiclization is generally characterized by low-amplitude fluctuations of voidageand pressure which are, in turn, believed to correspond to the absence of large bubbles or voids.The lower limit of the turbulent fluidization regime is usually considered to be set by U, thesuperficial velocity at which fluctuations reach a maximum and begin to decrease with increasinggas velocity, or by Uk, the superficial velocity at which fluctuations level off Compared tobubbling fluidized beds, turbulent beds have upper surfaces which are more diffuse, while the gas-solid contact efficiency and chemical conversion are significantly higher (Massimilla, 1973; Graceand Sun, 1991). Hence it is advantageous to operate in the turbulent regime. However, thetransition to this regime and flow patterns in turbulent fluidized beds are not well understood.The purpose of this chapter is to provide a better understanding of the transition from bubbling toturbulent fluidization.To determine the transition from bubbling or slugging to turbulent fluidization, severalmeasurement methods have been utilized, including visual observation, local capacitancemeasurement, pressure fluctuations, local and overall bed expansion (see Table 3.1). Theinstruments have involved pressure transducers, capacitance probes, optical fibre probes, x-rayfacilities as well as manometers. The recorded signal traces have been interpreted in terms ofaverage peak-to-peak amplitude, maximum peak-to-peak amplitude, peak-to-average amplitude,standard deviation, normalized standard deviation, skewness, etc. (Brereton and Grace, 1992).Some researchers (Avidan and Yerushalmi, 1982; Lee and Kim, 1990) have claimed that the sametransition point can be obtained from different measurement methods. Others (Lee and Kim,1988; Cai, 1989; Brereton and Grace, 1992) found that U, the onset velocity for turbulent52fluidization regime, evaluated from different interpretations of raw signals can differ. However,no systematic analysis has been performed to examine similarity or dissimilarity among differentmeasurement methods, although there are wide variations in the values reported by differentresearchers (Grace, 1992).Table 3.1. Summary ofU data from pressure fluctuation measurementsDxH Method Height above Signal analysisAuthor (mm x m) distributor(m)Satija and Fan (1985b) 102x6 APF 0. 15-0.3 r.m.s.3m et aL (1986) 300XNS APF middle r.nis.Lee and Kim (1988) 100x3 APF 0.3-0.5 SD, SkewnessMori et a!. (1988) 50x2.8 APF NS SDSonetal. (1988) 380x9.l APF NS averageIshii et aL (1988) 200x1.6 APF 0.2 rims.Horioetal.(1988) 200x1.6 4pi 0.2 r.nis.Sun and Chen (1989) 800x7 APF 0.5 peak-to-meanaverageCai (1989) 0.050.5 APF middle coherencefunctionThao and Yang (1990) 300x4.5 AFF NS peak-to-meanaverageLeuetaL(1990b) 108x5.3 APF NS SDPerales et al. (1990) 92x3 APF NS SDYang et aL (1990) 114x2.44 APF 0.05-0.25 SDTsukada et al. (1993) 50x0.5 APF various SDThis work 102X2.5 APF various SDCanada et al. (1978) 300XNS DPF NS peak-to-peakaverageYerushainri and 152x9 DPF NS peak-to-peakCankurt (1979)average53Table 3.1 (Continue)Rhodes and Geldart 152x3 DPF NS average(1986a)Schnitzlein and 152x8.4 DPF 0.41 SDWeinstein (1988)Grace and SUn (1991) 102X2.5 DPF various SD, normalizedBrereton and Grace 152x10 DPF 0.23-0.69 SD(1992)Chaouki (1992) 82xNS DPF various SDSvensson et aL (1993) 1470x1420x13.5 DPF various SDMei et al. (1993) 300x6 DPF various SDDunham et al. (1993) 200x6 DPF various SD, normalizedThis work 102X2.5 DPF various SDAvidan and Yerushalmi 152x9 BE NS bed voidage(1982)Abed (1984) 152XNS OP NS localvoidageLee and Kim (1990) 100xNS BE NS bed voidageAsai et al. (1990) 200x6 OP NS bed voidageChaouki (1992) 82xNS OP NS local voidageKehoe and Davidson 100xNS V NA visualization(1970) 5OxNSMassimilla (1973) 156XNS V NA visualizationThiel and Potter (1977) 51x3.6 V NA visualization102x4.7218x6.9Cresciteffi et al. (1978) 152x6 V NA visualizationYang and Chitester 2-D bed V NA visualization(1988) 203x1.3x1.8* APF: absolute pressure fluctuations; DPF: differential pressure fluctuations; SD: standard deviation of signals;OP: optical fibre probes; BE: bed expansion; V: visual observations; NA: not applicable; NS: not specified;In Chapter 2, it was shown that absolute pressure sensors, differential pressure dropsensors and optical fibre probes do not provide the same information on bed fluctuations. In thischapter, the effects of measurement method and signal analysis method on the transition velocitiesU and Uk, are first investigated. The mechanism of transition to turbulent fluidization and theflow behaviour in turbulent fluidized beds are then examined.543.2. Effects of Measurement Technique on Transition VelocitiesThe first photograph of a three-dimensional turbulent fluidized bed appears to have beenpublished by Matheson et al. (1949). A turbulent fluidization regime was also included in the flowregime diagram of Zenz (1949) as a region between bubbling fluidization and choking. Turbulentflow patterns have also been observed by Kehoe and Davidson (1970) and Yang and Chitester(1988) in two-dimensional beds. The first quantitative study seems to have been performed byLanneau (1960).Kehoe and Davidson (1970), based on visualization of a two-dimensional bed, definedturbulent fluidization as a state of “continuous coalescence -- virtually a channeling state withtongues of fluid darting in zigzag fashion through the bed”. Beyond the point where this regimewas initiated, it was impossible to detect any slugs on traces from capacitance probes. Thisdefinition was subsequently adopted by Massimilla (1973), Thiel and Potter (1977), Cresciteffi etal. (1978), Yang and Chitester (1988) and Jiang and Fan (1992). The determination of thetransition point, however, appears to be arbitrary because the break-up of large bubbles or slugsmay take place over a considerable range of gas velocity instead of abruptly (Rowe andMacGillivray, 1980; Brereton and Grace, 1992).Avidan and Yerushalmi (1982), Abed (1984), Lee and Kim (1990), Asai et aL (1990) andNakajima et al. (1988) defined the transition to the turbulent fluidization regime as the velocity atwhich a step change in the gradient of the voidage occurs with increasing gas velocity. However,in fluidized beds where entrained particles are efficiently returned to the bed at high gas velocities,such a step change may not be clear (Geldart and Rhodes, 1986; Grace and Sun, 1991). Thismethod hence tends to be system-dependent.55Yerushalnii and Cankurt (1979) defined U as the beginning of the transition to turbulentfluidization. Uk then marks the end of the transition to the turbulent fluidization regime. BeyondUk, the flow pattern was said to have completely transformed into the turbulent regime. Laterauthors have commonly assumed that U0 and Uk demarcate the boundaiy between the bubbling orslugging and turbulent fluidization regimes. Extensive studies have also been carried out toquanti1j these transition points [see Table 3.1 and Bi and Fan (1991)].Two “apparent transitions” must be avoided when measuring pressure fluctuations. One isencountered when a probe tip becomes exposed to the dilute suspension, i.e. the bed surface fallsbelow the probe tip (Rhodes and Geldart, 1986a). Another results from the attenuation of highfrequency signals caused by the use of manometers instead ofpressure transducers (Yerushalmi etaL, 1978).Local voidage fluctuations measured by capacitance and optical fibre probes have alsobeen used to deduce the transition to turbulent fluidization. However, it was not possible toobtain both U and Uk based on the standard deviation of the recorded signals (Lanneau, 1960;Abed, 1984; Chaouki, 1992). Therefore, some alternative approaches like “trace reading” or“heterogeneity function”, were developed to deduce U and Uk (Lanneau, 1960; Crescitelli et al.,1978; Lancia et al., 1988). The physical meaning of these points, however, is unclear.All the transition criteria proposed for the onset of the turbulent regime relate thistransition to a change ofbubble behaviour. However, proper measurement ofbubble behaviour influidized beds relies greatly on the instrumentation employed. Different information is registeredby different probes. Measurement methods therefore need to be evaluated before the transitionmechanism around U0 and Uk can be understood. In the present study, absolute and differentialpressure fluctuations and voidage fluctuations have been measured using pressure transducers andan optical fibre probe.563.2.1. Experimental detailsTests were carried out in a 102 mm diameter aluminum column of height 2.5 m (seeFigure 3.1). Two cyclones are installed in series to capture entrained particles and return them tothe column. Further details of the unit were reported by Sun and Grace (1992). Pressures weremeasured at four locations, 0.03, 0.20, 0.28 and 0.41 m above the distributor. The tips of allpressure probes were flush with the wall and covered with fine screen to prevent blockage by fineparticles. The probes were connected to lOw pressure, differential pressure transducers (OmegaPX162). To ensure that pressure fluctuations in the gas-solids fluidized beds could be reliablyextracted, a tube of 0.3 m length having a dead volume 4.2 cm3 connected the pressure probe tothe transducer. The output signals were recorded by a digital data logging system (DAS 8 board)at a frequency of 100 Hz for intervals of 40 seconds.A reflection-type optical fibre probe described in Chapter 2 was installed 0.28 m above thedistributor with its tip 40 mm from the wall. The tip diameter was 1.5 mm. At minimumfluidization, the measurement volume is about 3x3x5.5 mm, estimated as proposed by Lischer andLouge (1992). Signals from the optical probe were recorded by the same digital data loggingsystem as that used to record the pressure signals, simultaneously and with the same frequencyand time interval.Raw data were logged using Labtech Notebook software. Standard deviations werecalculated to determine the transition velocities. Most of the experimental results were repeatedand showed very good reproductivity. Cross-correlation analysis was used to check the similarityof pressure signals measured at different locations. Other characteristic parameters (probabilityfunction and skewness) used by previous researchers were also calculated to determine whetheror not they lead to the same transition point. The same FCC particles were used as the bedmaterial as in Chapter 2. The static bed height was always 0.60 m.57Figure 3.1. Schematic diagram of the experimental apparatus.81: Gas distributor2: Main column3: Expanded section4: First cyclone5: Second cyclone6: Pariicle collector7: Ball valve8: Filter583.2.2. Effect of probe resistanceIn measurements of pressure fluctuations, tubes of various lengths are connected to apressure transducer. To prevent particles from blocking the probe, the probe needs to be eitherpurged by air or fitted with a ifiter. When the probe is continuously purged by air, the air issuingfrom the probe may disturb the flow field around the probe tip. The pressure signals can bedamped by a high resistance filter. In the present study, the probe tip was covered by a thin layerof fine screen to prevent particles from entering the probe. To ensure that pressure fluctuations inthe fluidized bed were properly registered, the resistance ofthe filter was varied to check its effecton the recorded pressure fluctuations.Figure 3.2 shows typical standard deviations of absolute pressure fluctuations obtainedwith probes of different filter thickness, where the resistance coefficient is defined as= IXPp/O.5jOgU (3.1)1.00.800.60.0 —0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8Sqerfic G sVelocity, rn/sFigure 3.2. Effect ofprobe resistance on the standard deviation ofpressure fluctuations at z=O.2.59is the pressure drop across the probe for a gas velocity of U, inside the probe. The intensityof pressure fluctuations is seen to decrease with increasing probe resistance. However, the peakpoint does not shift, indicating that U, defined as the gas velocity at which the standard deviationof pressure fluctuations reaches a maximum, is not significantly affected by the probe resistance,so long as the probe has the same resistance in all experiments.3.2.3. Effect of port spacing of differential pressure sensorsAlthough pressure fluctuations from other locations can be ifitered out by usingdifferential pressure sensors as discussed in Chapter 2, the extent of signal ifitering depends on thespacing between the ports, with extraneous pressure waves filtered better with reduced spacing.Figure 3.3 shows two sets of data measured using two different spacings. The magnitude of thestandard deviation is seen to be lower for the smaller spacing, but the two curves reach peaks atalmost the same superficial gas velocity, indicating that U is not greatly affected by the portspacing within the test range (L0.08 to 0.38 m).3.2.4. Effect of probe locationThe flow pattern in fluidized beds varies with axial location. Hence there may be differentpeak points at different locations (Grace and Sun, 1991). Figure 3.4 shows the variation ofstandard deviation of absolute pressure fluctuations with height. The intensity of absolutepressure fluctuations at three different levels is similar, and the three resulting curves give nearlythe same U. On the other hand, the standard deviation of differential pressure fluctuations,plotted in Figure 3.5, tends to increase with height, with the curve for the upper section reaching amaximum at a lower gas velocity. This is because pressure waves generated from other locationsare mostly ifitered out so that the differential signals mainly come from disturbances within theinterval between the pressure taps; greater fluctuations are therefore generated higher in the bed60where the bubbles are larger.0.30.0 02 0.4 0.6 0.8 1.0 1.2 1.4&çerficial Gas Velocity, rntsFigure 3.3. Effect ofport spacing on measured differential pressure fluctuations.0Figure 3.4. Effect of height andpressure fluctuations.superficial gas velocity on standard deviation of absoluteC z.03to0.41mDC C C) z).20to0.28m0.90.80.70.60.50.4I . I . I I I . I I I I1.6 1.8 2.0I z0.20mzJ.28mA z=O.41m1.21.0 -0.80.60.40.20.0 —0.0I . I . I • I I . I0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8SuperfldGasWodty,m/s610.70.60• 0.4Cl)0.30.20.0 1.6 1.8 2.0Figure 3.5. Effect of height and superficial gas velocity on standard deviation of differentialpressure fluctuations along bed axis.3.2.5. Effect of solids return systemSome researchers reported the existence of a leveling-offpoint, Uk, while others found noleveling-off of the standard deviation vs. superficial gas velocity curve. Rhodes and Geldart(1986a) argued that the leveling-off point is caused by emptying the interval of particles. Ananalysis of literature data (Bi and Fan, 1991) also suggests that Uk does not exist for Group B andGroup D particles. Using Group B sand particles, Brereton and Grace (1992) and Johnsson et al.(1992) found that the standard deviation of pressure fluctuations did not level off until U wasmuch higher than the terminal velocity of single particles when the bed was maintained atrelatively dense conditions (overall voidage less than 0.80). Recent experimental results (Mei etaL, 1993) confirm that Uk corresponds to the condition where the bed particles are carried overfor Group D particles. In our present study using Group A particles, the standard deviation did-I0.2 0.4 0.6 0.8 1.0 1.2 1.4Superfid Gas Velodty, rn/s62not level off until U> 1.5 rn/s when the bed was maintained under relatively dense condition (<0.8) with an effective solids return system. On the other hand, there was considerable carry-overof solids for U>0.6 rn/s. Since the studies of U0 and Uk have been carried out in bothconventional and circulating fluidized beds, the role of the solids return system needs to beevaluated in order to compare the leveling-off phenomenon registered in some circulatingfluidized bed systems (Yernshalmi and Cankurt, 1979; Schnitzlein and Weinstein, 1988; Horio eta!., 1992). In the present study, the solids recycle rate was adjusted by varying the setting of thebail valve which controls solids recirculation (see Figure 3.1).Figure 3.6 shows the effect of the valve position on the local density and apparent beddensity. During operation, the bed was always maintained in steady state operation, although theinventory of particles in the standpipe increases and the inventory in the column undergoes acorresponding decrease as the bail valve is closed, due to the pressure balance. It is seen that thebed density drops drastically with increasing gas velocity when solids recycle is limited by thecontrol valve. As a result, both voidage and pressure fluctuations decrease with increasing gasvelocity (see Figure 3.7), with the bed transforming more quickly to dilute operation when thevalve provides a greater restriction to solids flow.The implication of this finding is that pressure fluctuations tend to be a strong function ofbed density which, in turn, is related to the superficial gas velocity and solids recycle system. Therelation between standard deviation of differential fluctuations and apparent bed density is shownin Figure 3.8. It is seen that differential pressure fluctuations at a single location can be wellcorrelated by a single curve, even though the data were obtained with different solids recyclerates. In circulating fluidized beds, a relatively dense suspension (voidage about 0.8) can bemaintained in the lower part of a column at high gas velocities if there is sufficient recycle ofentrained solids to bottom of the riser (Schnitzlein and Weinstein, 1988; Brereton and Grace,1992). With increasing gas velocity, the bed voidage first increases and then levels off63900Figure 3.6.800oo1200ci)E1=600400300100Effect of solids control valve on (a) apparent bed density from differential pressuremeasurement at z=0.20 to 0.41 iii, and (b) local bed density from optical fibre probeat z=0.28 m and r/R=0.0.0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Superfidel Gas Velocity, rn/s00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Superfidel Gas Velocity, m/s64ICl)2.0Figure 3.7. Effect of solids control valve setting on standard deviation of(a) differential pressurefluctuations at z0.20 to 0.41 m, and (b) voidage fluctuations from optical probe onthe bed axis at z=0.28 m, r/R=0.0.0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Superfidel Gas Velocity, rn/sSuperfici Gas Veiodty, rn/s650.8(Uo 0.6C0(U0.4-ø(U0C(U0.2Figure 3.8. Standard deviation of differential pressure fluctuations as a function of apparent beddensity at z=0.28 to 0.41 in.Correspondingly, the standard deviation of pressure fluctuations levels off (Yerushalmi andCankurt, 1979; Schnitzlein and Weinstein, 1988; Horio et aL, 1992).Figure 3.9 shows Rek as a function of the Ar for the literature Uk data listed in Table 3.2.For comparison, equation (5.3), based on data discussed in Chapter 5 for the onset of significantentrainment ofparticles from the top of tall risers is in excellent agreement with the Uk data. Thisagain suggests that Uk is reached when particles are significantly entrained from fluidized beds.3.2.6. Effect of static bed heightGrace and Sun (1991) studied the effect of static bed height on differential pressurefluctuations using the same FCC particles and equipment as in the present investigation. Thetransition velocity U determined from differential signals over the same bed section was almostindependent of the static bed height which varied from 0.4 to 1.0 in. Similar results were reportedby Jin et al. (1986) and Satija and Fan (1985b).0.6 0.7 0.8Local Time-Average Voidage66Table 3.2. Summary ofUk data from pressure fluctuation measurementsAuthor D, mm d, im pr,, kg/rn3 Uk, rn/sYerushalmi and 152 33 1670 1.07Cankurt (1979) 49 1070 0.6149 1450 1.37103 2460 2.74268 2650 5.50Rhodes and Geldart 152 223 327 1.98(1986a) 42 1015 1.3838 1308 1.4440 1618 1.4566 2335 2.5269 2665 2.80Morietal. (1988) 50 56 729 1.2678 2400 2.10134 2400 2.30Schnitzlein and 152 59 1450 1.30Weinstein (1988)LeuetaL(1990) 108 90 2600 1.67PeralesetaL (1990) 92 80 1715 2.10160 2650 1.90Horio et al. (1992) 50 60 1000 0.60106 2600 3.50Meietal.(1993) 300 3180 1100 7.713.2.7. Effect of data interpretation method.As noted by Brereton and Grace (1992), the transition point may depend on theparameters derived from pressure or voidage fluctuation data.67Figure 3.9. Reynolds number based on Uk as a function of Archimedes number. Data sourcesare listed in Table 3.2. Equation shown is discussed in Chapter 5.Figure 3.10 shows the standard deviation of absolute pressure fluctuations at threeheights, with the standard deviation made dimensionless by dividing by the average absolutepressure. From the same set of data, the dimensional curves shown in Figure 3.4 give a maximumat about 0.7 mIs, independent of height. After normalizing (see Figure 3.10), the dimensionlesscurves reach maxima at lower gas velocities, and the resulting U0 value decreases somewhat withheight. This is not surprising since the standird deviation is divided by the average pressurewhich increases with increasing superficial gas velocity. Figure 3.11 shows corresponding resultsfor differential pressure fluctuations. The dimensionless standard deviation in Figure 3.11 reachesa peak at higher gas velocities than the dimensional standard deviation in Figure 3.5 because thestandard deviation is divided by the average pressure drop which decreases with increasingsuperficial gas velocity. Furthermore, the curve becomes flatter after normalizing, especially forz=0.03 to 0.20 in. As discussed in Chapter 2, differential pressure fluctuations in gas-solidsfluidized beds or gas-liquid bubble columns are directly related to bubble size and the location ofthe bubble. The dimensionless standard deviation normalized by dividing by the average pressuredrop, however, is influenced by the bed density variation with increasing superficial gas velocity.The dimensional standard deviation may therefore provide a more clear-cut indication of bubbleAr68behaviour.I0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8Superfict Gas Velodty, rn/sFigure 3.10. Dimensionless standard deviation of absolute pressure fluctuations normalized by thetime-average absolute pressure at the mid-point.1.00.90.80.70.50.30.20.10.0Figure 3.11. Dimensionless standard deviation of differential pressure fluctuations normalized bythe time-average pressure drop over the same interval.0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Superficial Gas Velocity, rn/s69The bed density has been used by several research groups to determine the transitionvelocity. It is argued that a sudden change in bed density or slope of density occurs as U isincreased around the transition point (Avidan and Yerushalmi, 1982). Such a sudden change hasbeen further attributed to carry-over of bed particles (Rhodes and Geldart, 1986a) or dense phaseexpansion (Asai et al., 1990). However, such a sudden change did not show up in units whereentrained solids were effectively returned to the column (Matheson et al., 1949; Rhodes andGeldart, 1986a; Sun, 1991; Brereton and Grace, 1992). In the present tests, a sudden change didnot appear when entrained solids were effectively returned to the bottom ofthe column, but somechange of slope did appear when solids recycle was restricted [see Figures 3.6(a) and (b)J.Lee and Kim (1990) found that the skewness of absolute pressure fluctuations shifts fromnegative to positive with increasing gas velocity. The zero skewness point was considered as thetransition point to turbulent fluidization. It is seen in Figure 3.12 that the skewness of absolutepressure fluctuations indeed shifts from negative to positive, but the gas velocity for zeroskewness is about 0.47 mIs, significantly lower than U=0.7 mis determined from the standarddeviation method. In addition, the skewness tends to decrease again after reaching a maximumand again passes through zero at a gas velocity of about 1.2 mIs. Figure 3.12 further shows thatthe skewness of differential pressure fluctuations is always positive. The skewness of voidagefluctuations, on the other hand, increases with gas velocity and reaches zero at a gas velocity ofabout 0.66 mIs. One can conclude that the transition velocity from the skewness analysis of bothabsolute and differential pressure signals is generally not the same as that determined from othermethods.The similarity between signal traces measured by two absolute pressure transducers, oneabove the other, has been used to explain the transition to turbulent fluidization (Cai et al., 1990).It was argued that the cross-correlation of the signals reaches a maximum at the same702.00.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Superfid Gas Velocity, rn/sFigure 3.12. Skewness of absolute and differential pressure fluctuations and of local voidagefluctuations as functions of superficial gas velocity.Figure 3.13. Maximum cross-correlation coefficient between two absolute pressure probes, oneabove the other, as a function of superficial gas velocity.1.51.00.5Cl)-0.5(I)-1.0-1.5-2.0-2.50.0 0.2 0.40.90.80.70.60.50.40.30.20.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8Superficiel Gas Velocity, rn/s71velocity as the standard deviation. Our results in Figure 3.13 indicate that the maximum cross-correlation coefficient plotted versus superficial gas velocity also gives a peak at about 0.7 mIs,close to the value from standard deviation method. A maximum exists at U0.5 rn/s when themaximum cross-correlation coefficient between two differential pressure signals, determined oneabove the other is plotted against U, as shown in Figure 3.14.0.5______________________________0.4 - -0.3IE 0.20.10.00.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Superfidel Gas Velocity, rn/sFigure 3.14. Maximum cross-correlation coefficient between two differential pressure signalsacross two height intervals, one above the other, as a function of superficial gasvelocity.The maximum amplitude and the 10 to 90% amplitude of differential pressure fluctuationshave also been used to determine the transition velocity (Cresciteffi et al., 1978; Yerushalmi et al.,1978; Lee and Kim, 1990). The standard deviation of pressure fluctuations is proportional to themaximum amplitude if the probability distribution of pressure fluctuations follows the samenormal distribution function (Roy and Davidson, 1989). Figure 3.15 shows the 10 to 90%interval of differential pressure fluctuations as a function of superficial gas velocity. The transitionI I • Iz10.03-0.20 m,z20.28-0.41 mDi::iDI I • I I • I I I72velocities corresponding to the maximum are seen to be nearly the same as from a plot of standarddeviation versus superficial gas velocity (Figure 3.5).21.8ai 1.61.4E 1.20’0)a0.60 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8U, rn/sFigure 3.15. 10 to 90% amplitude of differential pressure fluctuations as a function of superficialgas velocity for two height intervals.When capacitance probes are used, a factor delined as the “0-5% probability interval”(Lancia et a!., 1988) from the minimum value of signals has been proposed to determine thetransition. In the present study, the 0-5% probability interval of signals from the minimum valueof optical fibre probe signals was found to increase monotonically with gas velocity with noapparent transition. The bubble volume fraction has also been used to determine the transition tothe turbulent regime by Asai et aL (1990) who reported a sudden change in void volume fractionwith increasing gas velocity. In the present study, the void volume fraction was estimated byassuming that the boundary between the dilute phase and the dense phase is at the point where theprobability density distribution (PDF) has a minimum (Tutu, 1984) (also see Appendix 1). Figure3.16 plots the void phase volume fraction against superficial gas velocity. It is seen that there isno sudden change for the probe at the axis.• z=O.20-O.28 mz z=O.28-O.41 mI I I I I I I730.8___________Ea, 0.40.20.0 -0.0 0.8 1.2 1.6 2.0U,mlsFigure 3.16. Local void phase volume fraction determined by optical probe as a function ofsuperficial gas velocity, radial position and solids return valve opening. Error barsare shown for representative points.3.2.8. Effect of measurement methodTransition velocities determined for the FCC particles in this work using different methodsare summarized in Table 3.3. Where transition values were found, they range from 0.43 to 1.15rn/s for the same FCC particles in the same column. Clearly not all of these methods areappropriate. The difference between absolute and differential pressure fluctuation methods canalso be seen from a comparison of literature data in Figure 3.17, with sources of data listed inTable 3.1 for various column sizes. It is seen that U values from absolute pressure probes areclearly lower than those from differential pressure measurements. This is also reflected in the twobest-fit equations from regression of the experimental data:Re (0.56 ±0.05)Ar°’°°°7 (3.2)from absolute pressure fluctuation data with 95% confident limits and• r/R0.0o r/R0.80.474Table3.3.TransitionvelocitiesbasedondifferentmeasurementtechmiquesandinterpretationmethodsfortheFCCparticlesexaminedinthiswork.InstrumentationLocationDimensionalNornmlizedY12,maxSkewnessVoidvolumemstand.devn.stand.devn.methodmethodfractionmethodmisrn/smismismisAbsolutepressurez=0.200.70±0.020.57±0.020.47±0.02*transducerz0.280.70±0.020.52±0.020.70±0.02z0.410.70±0.020.43±0.02O.70±0.06**Differential pressurez=0.03-0.200.82±0.02NEtransducerz=0.20-O.280.70±0.021.10±0.040.50±0.02#NFz0.20-0.410.70±0.02zz0.280.4l0.52±0.021.05±0.02Opticalfibreprobez0.28r/R=0.00.70±0.04NP0.66±0.02NErLR=0.8NPNE1.40±0.020.70±0.02*z1r=0.20in,z2=0.28m;**z1=O.20m,z2=0.41m;#z10.03-0.20m,z20.28-0.41m;NP-Notfound.Errorrangesarebasedonasubjectivejudgementhowcloselythemaximumorzero-crossingpointcanbeidentified.cJRe = (L24 ± 0.09)Ar 0.447±0.006 (3.3)from differential pressure fluctuation data with 95% confidence limits. The correlationcoefficients for equations (3.2) and (3.3) are 0.974 and 0.981, respectively. The standarddeviations are 22% and 29%, respectively.Figure 3.17. Comparison of literature U data plotted in dimensionless form from absolute anddifferential pressure fluctuation measurements.Since the influences of the measurement technique and interpretation method are sosignificant, it is essential either that some standardization be adopted (Brereton and Grace, 1992)or that all experimental details be fully reported in such a way that experimental data fromdifferent sources can be compared. A number of equations have previously been proposed topredict the transition velocity U, as listed in Table 3.4. All available literature data listed in Table3.1 have been used to examine the feasibility of these equations. As indicated in Table 3.5,equation (3.2) and the equation from Cai et al. (1989) based on absolute pressure fluctuation datagive the best prediction for absolute pressure fluctuation measurements, while equation (3.3) bestpredicts the differential pressure fluctuation data. For differential pressure fluctuation data, it isseen that the root mean square deviation is generally larger than 30%, indicating considerablescatter in the data. This is at least in part because U vanes with axial location, a factor neglectedCAr76in all the correlations. It is further shown that equation (3.2) also gives good prediction for thedata from bed expansion measurements, suggesting that the transition velocity based on bedexpansion measurements are close to those from absolute pressure fluctuation measurements. Allequations show poor agreement with the data from visual observation methods, these tending togive much smaller transition velocities than the other methods.Table 3.4. Equations for U in the literature and from this work.No Source Equation1 Nakajima et al. (1988) Re0 =0.663Ar°4472 Lee and Kim(1988) Re0 =0.700Ar°4853 Horio (1991) Re0 =0.936Ar°4 Leu et aL (1990) Re0 =0.568Ar°5785 This work, DPF data Re0 = L24Ar 0.4476 This work, APF data Re0 = 0.56Ar °‘7 Cai et al. (1989) U0 — (Pg20 )O.2 0. 211 0.00242 11027 (Pg20 )(PP Pg )(D)]O.27— Pg D°27 + D’27 Pg Pg d0.58 SunandChen(1989)Pg ‘emf z5 mfwhere Z = 2.25 1 0.6D0\IDBmax+0.6Dand D8 (PP )(PP P Pg) 8mf )2Pg ‘Em!77Table3.5.ComparisonofliteraturedatafromsourceslistedinTable3.1withcorrelationsfor UgiveninTable3.4.Method#TeofNo.ofRootmeansquarede4ation:—Ue)!Ud,]2/Nparticlesdatapoints1*2345678GroupA290.270.350.670.281.040.240.250.53APFGroupB200.380.690.990.151.110.190.134.58GroupD30.551.101.430.051.380.180.061.77Total520.330.560.850.711.070.220.242.93GroupA170.500.450.310.460.240.580.480.63DPFGroupB130.420.360.380.520.430.510.575.90GroupD80.320.090.140.620.120.480.7229.8Total380.430.360.301.270.290.520.5613.3BEGroup80.340.490.791.031.100.280.273.21A,BVGroupA144.324.766.324.648.123.604.743.08—.1*1,2,3,4,5,6,7,8correspondtoequationsNo.ito8listedinTable3.4#APF:absolutepressurefluctuation;DPF:differentialpressurefluctuation;BE:bedexpansion;V:visualobservations.3.3. Model for transition from bubbling to turbulent fluidizationAlthough extensive studies have been carried out to quantify the transition to turbulentfluidization (see Table 3.1), the flow patterns in turbulent fluidized beds are still not wellunderstood.Previous experimental work obtained using a variety of techniques and indices hasindicated that there are at least two different types oftransitions to turbulent fluidization:Type I: A relatively sharp transition to a hydrodynamic regime which is physically distinct fromother regimes. This kind of transition has been reported by Kehoe and Davidson (1970),Yerushalini et aL (1978), Cresciteffi et aL (1978), Yang and Chitester (1988) andTsukada et a!. (1993).Type II: A gradual transition involving intermittent slug-like structures interspersed with periodsof fast-fluidization-like behaviour, the latter becoming predominant with increasingsuperficial gas velocity. This type of transition has been viewed, for example, byCresciteffi et aL (1978), Rowe and MacGillivray (1980) and Brereton and Grace(1992a).Both these modes of transition need to be accounted for in any model which seeks toexplain the behaviour of fluidized beds operating in the turbulent regime or to predict the onset ofturbulent fluidization. In addition, any model should be consistent with the observed parametriceffects of various operating variables on the superficial velocity, U, which is usually assumed tocorrespond to the beginning of the transition. These variables and their respective influences onU are summarized in Table 3.6, together with relevant references. It has also been noted (e.g.Yang and Chitester, 1988) that there are differences between two-dimensional and three-dimensional beds, and these differences should again be explainable in terms of any model.79Table 3.6. Factors influencing onset of turbulent fluidization.Variable Increased Effect on U ReferencesBed diameter Increase The! and Potter (1977), Cal (1989)Distance above distributor Decrease Grace and Sun (1991), This workMean particle diameter Increase Yerushalnii et al. (1978), Jin et aL (1986)Breadth ofparticle size Decrease Grace and Sun (1991)distributionSphericity ofparticles Decrease Judd and Goosen (1989)Absolute pressure Decrease Yang and Chitester (1988), Cai et al. (1989),Tsukada et aL (1993)Temperature Increase Cal et aL (1989)Empirical equations have been suggested by a number of workers for predicting U (seeTable 3.4). While they may correlate data over restricted ranges, none of these equationsaccounts for the effects of particle size distribution and height above the distributor, whileimportant variables like bed diameter, pressure and temperature are also omitted in some of theseequations.Previous mechanistic attempts to explain the onset of turbulent fluidization have not led tofully satisfactory models or predictive equations. Yang (1984) explained the transition in terms ofclusters of particles obeying laws similar to those governing the behaviour of individual particlesfluidized in a homogeneous manner and in terms of propagation of continuity waves in fluidizedbeds. The transition from bubbling to turbulent fluidization was defined as the point where thecontinuity wave speed reached a maximum. Geldart and Rhodes (1986) accounted for U interms of transport of material from the interval between two pressure taps. Sun and Chen (1988)defined the transition as the point where bubbles reached a maximum size at a certain distance80above the distributor. Cal et al. (1990) postulated that bubble splitting dominated overcoalescence beyond the onset of turbulent fluidization. While these ideas are generally helpful,they fail to explain the full range of observations reported in the literature.All these criteria closely relate the transition process to a change of bubble behaviour.Bubble behaviour at high gas velocities, however, is not well understood due to severe distortioncaused by bubble-bubble interactions (Grace and Harrison, 1969). A key point in seeking thetransition mechanism is to understand void behaviour at high gas velocities.In this section, a transition mechanism is proposed based on a simple and idealized modelof bubble-wake interaction. The model is compared with experimental results obtained in thesame system as described above, i.e. a 102 mm diameter column with FCC particles of meandiameter 60 pm and density 1548 kg/rn3. Semi-empirical predictive equations are also derivedand compared with U data from the literature.3.3.1. Transition mechanism3.3.1.1. Transition modesThe transition from well-defined bubble flow to turbulent flow has often been attributed tocoalescence and splitting of bubbles. Bubble instability may occur naturally or be induced bynear-by bubbles. Bubbles in gas-solids fluidized beds are generally of spherical-cap shape andaccompanied by laminar closed wakes (Clifi et al., 1978). However, turbulent open wakes arepresent for large bubbles in low viscosity media. For liquids it has been found (e.g. Crabtree andBridgwater, 1971; Komasawa et al., 1980) that open turbulent wakes give much more disturbanceto following bubbles than closed laminar wakes, and often cause the trailing bubbles to break up.Therefore, one may postulate that bubbles in fluidized beds become unstable when they grow to81such a size that their wakes undergo a transition from closed to open. This is consistent with xray observations (Rowe and MacGillivray, 1980) showing that wakes become more and moreturbulent with increasing bubble size and rising velocity. Turbulent open wakes may also beresponsible for reported “maximum stable bubble sizes” in fluidized beds of line particles. In gas-liquid systems, bubbles with open turbulent wakes were found to rupture on collision (Komasawaet aL, 1980; DeKee et al., 1986). Table 3.7 shows the maximum stable bubble size obtained inlarge columns by Matsen (1973), Sun and Chen (1989) and Asai et aL (1990). Reynolds numberscorresponding to the maximum bubble size have been calculated byReBm =071jfjD5 I V (3.4)where the bubble rise velocity is estimated by UB=O. 71(B,max)°5 There is no satisfactorycorrelation for the prediction ofthe kinematic viscosity of the dense phase. The data for sphericalparticles evaluated from bubble size and shape (Grace, 1970) and from a rotating cylinderviscometer (Schugerl et al., 1961) can be correlated (in SI units) by,Vd =0.000374Ar°°7 (3.5)Falling-sphere data have not been included because the kinematic viscosity measured by thefalling-sphere method is a strong function of the diameter of the falling sphere due to thecompaction of the emulsion phase near the sphere. As shown by Kai et al. (1991), vd from thefalling-sphere method is about an order of magnitude smaller than from the bubble shape androtating cylinder viscometer methods. In addition, the effect of dense phase voidage is notincluded, although it is clear that vd decreases with increasing dense phase voidage (Bagnold,1954; Kai et a!., 1991).The transition from a laminar closed wake to a turbulent open wake depends on theReynolds number and hence on the dense phase viscosity. This transition occurs for ReBl30 forbubbles in liquids (Clift et a!., 1978). Such a criterion can be extended to gas-solids systems if thedense phase viscosity can be determined (Davidson et al., 1977; Clift et al., 1978). Table 3.782indicates that the Reynolds number corresponding to the maximum stable bubble size was usuallyhigher than 130. ‘While there is considerable scatter, not surprising given the difficulty inmeasuring DB,max and the approximate nature of the kinematic viscosity correlation, the resultssuggest that laminar closed wakes behind bubbles transform into turbulent open wakes at aboutthe same condition as where bubbles reach their maximum stable size.Table 3.7. Relationship between maximum stable bubble size and estimated bubbleReynolds number based on equations (3.4) and (3.5) which determinesthe nature of the following wake.Source 1 Particles D dp pp, DB, max ReBmaxm jim kg/rn3 mmMatsen (1973) Coke 0.60 26 2080 25 2470 2080 64 7470 2080 127 20990 2080 >152 >261Rowe and Catalyst 0.14 59 880 100 163MacGillivray (1980)Sun and Chen FCC 0.80 54 1800 110 182(1989) 64 1800 130 225Asaietal. (1990) FCC 0.20 64 1850 75 98To distinguish the Type I sharp transition from the Type II gradual transition, the bubblesize, bubble shape and the column size need to be considered. As bubbles grow, their wakes alsoincrease in size. Note that bubbles may be elongated and have stunted wakes when restricted bythe walls of the column (Clift et al., 1978). As a result, wakes following slugs are still laminar andclosed for ReD up to 500 (Campos and Carvalho, 1988). The ReB=13O criterion thereforerequires that the maximum stable bubble size be much smaller than the column diameter, as wellas that the wake be turbulent and open. This means that the Type I sharp transition should onlybe attainable in columns of sufficient size. Table 3.8 shows a comparison of the turbulenttransition mode observed using small particles and the ratio DB,max/D With DBmax estimated bysetting ReB,max= 130 where ReBmax and Vd are given by equations (3.4) and (3.5). It is seen that83the sharp transition was indeed observed for small particles ‘With DB,max/D generally smaller thanabout unity except the 51 mm diameter column result of Thiel and Potter (1977), while the TypeII transitions all correspond to higher values of this ratio.Table 3.8. Comparison of the type oftransition to turbulent fluidization With DB,max/Dpredicted on the basis ofReB,max=l3O.Author 1 Pp dp D DBmax/D TransitionkIm3 m mm mode*KehoeandDavidson 1100 22 100 0.75 I(1970) 2200 22 100 0.78 I2200 22 50 1.56 I1100 26 100 0.77 I1100 55 100 0.86 I1100 55 50 1.72 IIMassimilla (1973) 1000 50 156 0.54 IThiel and Potter 930 60 51 1.71 I(1977) 930 60 102 0.85 I930 60 218 0.40 ICrescitelli et a!. 940 60 152 0.56 I(1978) 1400 60 152 0.58 I1550 95 152 0.63 IYerushalmi and 1670 33 152 0.53 ICankurt (1979) 1070 49 152 0.55 I1450 49 152 0.57 IAbed (1984) 850 55 152 0.56 ISchnitzlein and 1400 59 152 0.58 IWeinstein (1988)MorietaL (1988) 729 56 50 1.68 II2400 78 50 1.88 IIKai (1991) 770 55 82 1.02 IGrace and Sun 1440 60 100 0.88 I(1991)Perales et al. 1715 80 92 1.02 I(1991)Horio et a!. (1992) 1000 60 200 0.44 I* I -- Type I sharp transition; II Type II gradual transition.84Based on these considerations, we postulate the following transition criterion: Transitionfrom bubbling to turbulent fluidization is postulated to occur when the bubble spacing becomesclose enough that following bubbles are strongly influenced by the wakes of leading bubbles. Ifthe bubble wakes at this transition point are turbulent and open (i.e. ReB> 130), the transition isthen expected to be sharp (denoted as Type I above). Otherwise, the transition is a gradualprocess (denoted above as Type II).3.3.1.2. Transition velocity of Type I systemsIn freely bubbling fluidized beds, the spatial distribution of bubbles develops in a nonuniform manner due to bubble coalescence (Grace and Harrison, 1968; Park et a!., 1969; Abed,1984; Asai et al., 1990). Most bubbles tend to rise where there is a net upflow of particles, whilebubbles are relatively scarce in regions where there is a substantial dowaflow of particles. Insmall three-dimensional colunms bubbles tend to migrate toward the centre due to wall effectsduring their motion upward (Matheson et al., 1949; Park et al., 1969). Bubbles in large diametervessels often rise in swarms (Whitehead, 1971). When bubbles in vertical alignment are closeenough, the rear bubble tends to be elongated; coalescence occurs when bubbles are close enoughthat the following one is strongly distorted and accelerated by the wake of the leading bubble(Clift and Grace, 1970). According to Clift and Grace (1970), the interaction between twovertically aligned equal-sized bubbles becomes particularly strong after the nose of the followingbubble closes to within one bubble diameter from the nose ofthe bubble ahead.Bubbles are expected to coalesce rapidly when the superficial gas velocity is increased sothat the spacing is such that following bubbles overlap the wake of leading bubbles. If the wakesofthe leading bubbles are turbulent, they will have a disruptive influence on the following bubbles.Bubbles may then break down into smaller voids due to the instability caused by turbulence, sothat it may become almost impossible to distinguish one void from its neighbours. In such a state,85the bed can be characterized as being in a state of “continuous coalescence - virtually a channelingstate with tongues of fluid darting in zig-zag fashion through the bed”, the description applied byKehoe and Davidson (1970) to turbulent fluiclization. Bubble coalescence also occurs whenbubbles with closed laminar wakes interact. However, little or no splitting is likely to occurbecause the closed laminar wakes cause minimal disturbances to bubbles which enter them(Crabtree and Bridgwater; 1971; Komasawa et al., 1980).As noted above, the transition velocity to turbulent fluidization has usually beendetermined based on the standard deviation of pressure fluctuations (see Table 3.1). Since U,defined as the point when the standard deviation of pressure fluctuations reaches a maximum, hasbeen widely interpreted as an indicator of transition to turbulent flow, the corresponding flowstructure ofbubbles needs to be explored as this point is approached.Consider an idealized schematic of equal-sized spherical-cap bubbles of diameter DB risingin vertical alignment as shown in Figure 3.18 where distortion of bubbles during interaction isneglected for simplicity. The distance from the lower surface of the sphere enclosing the leadingbubble to the upper surface of the following bubble on the axis is denoted by LB. For simplicity, itis assumed that (a) the bubble has a flat base with wake angle O; (b) the voidage in the wake isthe same as in the emulsion phase; and (c) there are no solids inside the bubbles (Chit and Grace,1970). It can then be shown from geometry that the vertical distance from the lower surface ofthe bubble to the bottom of the sphere for which the bubble forms the cap is given byhW=DB(1+COSOW)/2 (3.6)If an optical probe is located at the axis as shown in Figure 3.18, it should record avoidage of when exposed to dense phase and 1 in the bubble phase. The correspondingstandard deviation of signals can then be shown to be,86= J(D —hW)(LB +h)DB +LBIt is straightforward to show that this standard deviation reaches a maximum whenLB DB — 2h(3.7)(3.8)Figure 3.18. Schematic showing idealized picture of two equal-sized bubbles in vertical alignment.Taking the superficial gas velocity at which s is a maximum as U, one can calculate theseparation distance at U by combining equations (3.6) and (3.8). Figure 3.19 shows LB/DB at U,as a function of wake angle. In gas fluidized beds of Group A and B particles, the wake angle,O, generally ranges from 100 to 130 degrees for DB<l6Omm (Rowe and Partridge, 1965). It isseen that for wake angles from 90 to 120 degrees, the separation distance, LB, is always smallerthan 0. SDB, a value at which there is significant bubble-bubble interaction (Clifi and Grace, 1971).Therefore significant bubble-bubble interaction is expected when the superficial gas velocityreaches U.DB87Figure 3.19 further shows that the separation distance at U increases with increasingwake angle, 0w,. Because the wake angle increases with increasing particle size and density(Rowe and Partridge, 1965), the separation distance at U is larger for denser and larger particles.Coupled with the higher effective dense phase viscosities for larger particles (Grace, 1970), thissuggests a less “turbulent” flow pattern at U, for Group B and D particles. For smaller and lighterGroup A particles, however, significant bubble-bubble interaction is expected at U because LB atU is smaller than O.5DB.Figure 3.19. Dimensionless separation between successive bubbles at U=U as functions of wakeangle for 0.45. U is taken as condition where standard deviation of signalsfrom an optical probe located on the axis of the bubble path reaches a maximuniIn practice, optical probe tips cannot always be on the axis of bubble paths given therandom motion ofbubbles. An averaged separation distance therefore depends on the wake angleand bubble packing status. LB is then expected to be smaller than predicted in Figure 3.19.o. degrees88To predict the transition velocity to turbulent fluidization, a bubbling fluidized bed isdivided into two regions, one primarily occupied by bubbles and the other by the dense phase.According to the modified two-phase theory (Clift and Grace, 1985),GB =Y(UUmj)S (3.9)where Y1. Y is around 0.8 in bubbling systems of fine Group A particles (Baeyens and Geldart,1986). For Group B particles a correlation for Y was given by Baeyens (1986),Y 2. 27Ar -0.21 (3.10)From a mass balance on the bubble phaseGB8fiUBS (3.11)while the bubble rise velocity is given (Grace and Harrison, 1969) byUB=U—Umf+0.7l1f•b: (3.12)Combining equations (3.9), (3.11) and (3.12) givesU=Umf+0.7lkB.jii5:/(Y—E ) (3.13)At U, equation (13) becomes,U =U /(Y—6BC) (3.14)For Type I systems, bubble wakes are required to be open and turbulent at U0(i.e. ReB130). Bubbles are then assumed to reach their “maximum stable size” when ReB reaches 130 for afreely bubbling bed. Therefore,DBC 130vd/0.7lLJ)2I3 (3.15)Because bubbles are afready well deformed and interacting when U is reached, it isnecessary to base the corresponding bubble volume fraction on experimental evidence. Toestimate 6Bc’ all literature data on local and overall voidage and void phase volume fraction atU=U( from capacitance probes, optical fibre probes and absolute and differential pressurefluctuation measurements are listed in Table 3.9. In general, bubbles are larger and following89wakes proportionally smaller for larger particles (Rowe and Partridge, 1965), so that 6Bc tendsto be higher in systems with larger particles. Such a trend is evident when all available 6Bc data inTable 3.9 are plotted against Ar in Figure 3.20. It is seen that 6Bc ranges from 0.30 to 0.50.Given the scatter, only a linear fit is justified. A least squares fitting of the data with 95%confidence limits in Figure 3.20 leads toEBc — (0.30±0.06)Ar°°°°’5 (3.16)Substituting equations, (3.15) and (3.16) into equation (3.14), one obtains the expression for U0,U0 = +2.59Ar°°4v3/(Y—0.3Ar°°4 (3.17)with Y0.8 for Group A particles or estimated by equation (3.10) for Group B and D particles,while Vd is estimated by equation (3.5) for spherical particles.1.0 -0.8 - -• D Equation (3.16)0.2I I I I IicP 1o 102 102 1o4 id5ArFigure 3.20. Local and spatial average void phase volume fraction at U=U0 as a function of Ar.Op en symbols: local void phase volume fraction based on optical and capacitanceprobes; Solids symbols: spatial average void fraction based on differential pressurefluctuations. Absolute pressure fluctuation data have been omitted because, asshown in section 3.2, they give unreliable values of U0. Data sources are listed inTable 3.9.90Table 3.9. Local and overall time-average voidage and void phase volume fraction at Ufrom the literatureAuthor Column size d,, EBC P Method*mm p.m kg/rn3 kPaLanneau (1960) 100 70 2000 0.41 0.68 170 CP70 2000 0.41 0.68 520 CPAbed (1984) 152 54.8 850 0.36 0.62 100 CPLancia et al. (1988) 100 257 2650 0.41 0.68 100 CP700 2650 0.52 0.74 100 CPYang et al. (1990) 114 67 1480 0.39 0.67 100 OPAsai et aL (1990) 152 64 1850 0.28 0.61 100 OPTsukada et al. (1993) 100 46.4 1780 0.40 0.68 100 OP46.4 1780 0.35 0.65 350 OP46.4 1780 0.30 0.65 700 OPThiswork 102 60 1580 0.38 0.66 100 OPCanadaetaL (1978) 305x305 650 2480 0.51 0.73 100 DPF2600 2920 0.51 0.73 100Yenishalmi and 152 33 1670 0.55 0.87 100 DPFCankurt (1979) 49 1070 0.44 0.69 10049 1450 0.29 0.63 100268 2650 0.53 0.74 100Schnitzlein and 152 59 1450 0.38 0.66 100 APFWeinstein (1988)Morietal. (1988) 50 56 729 0.34 0.64 100 APF134 2400 0.60 0.78 100SunandChen(1989) 800 54 1800 0.31 0.62 100 APF800 64 1800 0.33 0.63 100Yang et aL (1990) 114 67 1480 0.40 0.67 100 APFLee andKim(1990) 100 362 2500 0.42 0.68 100 APFGraceandSun(1991) 102 60 1580 0.42 0.68 100 DPFHorio et al. (1992) 50 60 1000 0.51 0.73 100 APF106 2600 0.67 0.82 100Brereton and Grace 152 158 2480 0.31 0.62 100 DPF( 1992a)Chaouki (1992) 82 130 2650 0.25 0.59 100 DPFTsukada et al. (1993) 100 46.4 1780 0.42 0.68 100 APF46.4 1780 0.36 0.65 350 APF46.4 1780 0.36 0.65 700 APFSvenssonetal.(1993) 1420x1470 320 2600 0.31 0.62 100 DPFMeietal. (1993) 300 3180 1100 0.49 0.72 100 DPFThiswork 102 60 1580 0.27 0.60 100 DPF* APF- absolute pressure fluctuation measurements; DPF- cliflèrential pressure fluctuationmeasurements; CP- capacitance probe; OP- optical fibre probe.91To summarize, the transition from bubbling to turbulent fluidization can be estimated ascorresponding to the superficial velocity at which the separation distance between bubbles reachesa certain value. This transition is sharp (Type I transition) when bubbles at this transition pointhave turbulent open wakes (i.e. ReB>l30) and are much smaller than the column diameter.Otherwise, the transition is gradual (Type II transition).3.3.2. Experimental resultsTo test the above postulate, experiments were carried out in a 102 mm diameter columnusing the same FCC particles as in the experiments detailed in section 3.2. Differential pressurefluctuations were measured by differential pressure transducers, while local voidage fluctuationswithin the same bed interval were monitored with an optical fibre probe. Detailed information onthe experimental set-up were reported by Sun (1991), while details of the pressure and opticalfibre probes are provided in Chapter 2.Figure 3.21 shows local voidage fluctuations at r=O and r/R=0.8 as a function of localaverage voidage. All the data for r=O can be well correlated by a single curve, even though thedata were obtained with different solids recycle rates. The local average voidage, , at themaximum standard deviation of local voidage fluctuations is around 0.66, so that BC=(6C-,)/(l-6)=0.38. Figure 3.22 thrther shows that the skewness of local voidage fluctuations is close tozero at the same value of , suggesting that the probe tip was indeed covered alternatively andequally by the void phase and dense phase when the transition velocity U was reached.The cross-sectional average voidage at U from the differential pressure fluctuationmeasurements is found to be around 0.60 (see Figure 3.8), somewhat lower than the local voidageat the axis (0.66 at Figure 3.21), due to the lower local voidage near the wall (see Figure 3.23).When U is determined by plotting skewness of local voidage fluctuations against superficial gas920.45 —0.4Co.350>ti)ID0(00C(00.20.150.1 —0.4-30.4velocity, as in Figure 3.24, the transition velocity is then seen to occur at about UO. 7 mIs on theaxis and at about U=l.4 rn/s near the wall. This further indicates that U from the standarddeviation of differential pressure fluctuations corresponds to transition in the core region whenbubbles are closely spaced in that region.*‘: Valve 100% open,r=N+ Valve 100% open, rIR=0.8* Valve 50% open, rIR=0.0LI Valve 30% open, rIR=0.0I I I I0.5 0.6 0.7 0.8 0.9 1Local Time-Average VoidageFigure 3.21. Standard deviation of local voidage fluctuations from the optical probe as a functionof local time-average voidage.• Valve 100% open, rIRO.0+ Valve 100% open, rIRO.8* Valve 50% open, rIRO.0LI Valve 30% open, rIRO.032Co(0I:-2+0.5 0.6 0.7 0.8 0.9 1Local Time-Average VoidageFigure 3.22. Skewness ofvoidage fluctuations from the optical probe at z=O.28 m as a function oflocal time-average voidage.93Um!sFigure 3.23. Local time-average voidage at z0.28 m as a function of radial location andsuperficial gas velocity.Cl)U)0)U)U,mlsFigure 3.24. Skewness of local voidage fluctuations from optical probeof radial location and superficial gas velocity.at z0.28 m as a function0.500.0 02 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0210—1-2-30.0 02 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.094The turbulent regime appears to be a transition regime between the bubbling and fastfluidization regimes. In the bubbling regime a dense phase is the continuous phase with <0•3(see Table 3.9), while in a fast fluidized bed, gas forms the continuous phase in the core regionwhile dense structures persist to some extent, primarily in an annular region at the walls. Theturbulent regime is then the transition regime in which voids becomes dominant in the core region,eventually linking with each other to form a continuous phase and, developing gradually towardthe wall, constituting a core-annular flow structure. Such a continuous transition process issupported by the intermittency index of local voidage shown in Figure 3.25. As proposed byBrereton and Grace (1993), the intermittency index approaches zero for completely segregatedcore-annular flow and unity for a dispersion of clusters of voidage U in a solids-free gas. Notethat the intermittency index should also be unity for an ideal bubbling bed where there are emptyvoids in a dense phase of voidage With increased local voidage, the intermittency index isseen to decrease monotonically beyond a certain voidage of about 0.64. The decay ofintermittency index indicates a gradual development from well-defined bubbly flow to a core-annular flow structure.0.8ID>‘106020.4 0.5 0.6 0.7 0.8 0.9 1Local Time-Average VoidageFigure 3.25. Intermittency index from optical probe at z=0.28 m as a function of local voidage,radial position and solids return valve opening.H-H-• Valve 100% open, rIRO.0+ Valve 100% open, rIRO.8* Valve 30% open, rIRO.0Valve 50% open, rIRO.0953.3.3. Effect of gas and particle properties and column geometry on U3.3.3.1. Effect of particle propertiesIn the proposed model [equations (3.14) and (3.17)], the minimum fluidization velocityincreases with increasing particle size and density. The second term on the right hand side ofequation (3.17) also increases due to the increase of dense phase viscosity [see equation (3.5)]and the decrease of Y (Baeyens and Geldart, 1986) with increasing particle size and density. Uthus increases with particle size and density. Figure 3.26 shows a comparison of this model withthe literature data under ambient pressure and temperature conditions (see Table 3.1 for sourcesof data). There is seen to be reasonable agreement between the model and the literature data,although there is wide scatter. Accurate estimation of the effective dense phase viscosity isrequired to improve the present model.EDC.)DFigure 3.26. Effect of particle properties on transition velocity U based on literature U, data andthe proposed model. Data sources are listed in Table 3.1. Absolute pressurefluctuation data have been omitted because, as shown in section 3.2, they giveunreliable values ofU.Ar96Equation (3.17) also predicts that U varies with particle size distribution. For particles ofwide size distribution, the dense phase viscosity is lower than for particles of narrow sizedistribution (Matheson et al., 1949). This is also supported by the finding that bubbles are smallerfor particles of wide size distribution (Matsen, 1973; Sun, 1991). As a result, U is expected tobe smaller for wide PSD particles, in agreement with experimental findings (Grace and Sun,1991). Consistent with the experimental data of Judd and Goosen (1989), equation (3.15) alsopredicts that particles of irregular shape and rough surface give a higher U, because of smallerwake fraction (Rowe and Partridge, 1965) and higher dense phase viscosity (Grace, 1970).3.3.3.2. Effect of column size and static bed heightFor given particles, the column size is expected to have little effect on U so long as theratio of DB/D is much smaller than unity based on equation (3.17). This is consistent with theexperimental data of Cai (1989) which demonstrate that U does not vary with column diameterfor D>0. 1 m and Group A particles.Consistent with equation (3.17), static bed height seems to have little influence on U intall columns (e.g. H>l m) where fully developed bubbly flow is established in the upper region.This is supported by experimental data (Grace and Sun, 1991; Cai, 1989). In short beds of largeparticles (e.g. H/D<2), U determined from absolute pressure fluctuations tends to increase withstatic bed height (Canada et aL, 1978; Dunham et aL, 1993).3.3.3.3. Effect of axial and radial locationsFigure 3.27 shows transition velocity U data of Sun (1991) and this work obtained fromdifferential pressure fluctuation measurements. These show a small decrease in U with increasingheight. There is some evidence (e.g. Yates and Cheesman, 1992) that gas is progressively97transferred from the dense phase to the bubble phase with increasing height. This should lead tosome increase in Y, and this may account [see equation (3.17)] for the small decrease of U withincreasing z.1 2 Equation (3.19)• This work, Fj1,f =0.6 m+SUfl(1991),Hmf=O.7mDSun(1991),Hmfl.OmE I’0.8 Equation (3.17)- EEI. •0 ID 0.4-0 II0 0.2 0.4 0.6 0.8 1z,mFigure 3.27. Effect of axial location on the transition velocity U from the differential pressurefluctuation measurements for FCC particles used in this study.When the average bubble size is estimated for fine particles by the Darton et al. (1977)equationDB = 0. 54(U — Umj )°4(z +4)O8g_02 (3.18)the gas velocity, Ut’, required for bubbles to grow to DB can be calculated based on equations(3.14) and (3.18) as a function of z. After some algebra this givesU = Umf + 1.26 x io vj3 I (z + 4J)2 (3.19)This is shown for FCC particles used in this study by the broken line in Figure 3.27. The gasvelocity required for bubbles to grow to their maximum size is predicted to be much smaller than980.4 m/s at a level 0.2 m above the distributor, consistent with the present model where bubbles arenot only required to grow to have their wakes be open turbulent, but also required to be closeenough to trigger significant interaction.3.3.3.4. Effect of pressure and temperatureU has been found to decrease with increasing system pressure (Cai et a!., 1989; Tsukadaet aL, 1993) for Group A particles. As the pressure increases, the dense phase voidage, 5e’ hasbeen found to increase for fine Group A particles (Subzwari et al., 1978; Weimer and Jacob,1986). This must cause the dense phase viscosity to decrease (Bagnold, 1954; Kai et al., 1991).Dik is then expected to be reduced in pressurized systems. This is consistent with theexperimental finding that bubbles are smaller in high pressure systems (Subzwari et aL, 1978;King and Davidson, 1980). A decrease of U with increasing pressure would be predicted byequation (3.17) if the effect of pressure on the dense phase viscosity could be accounted forproperly.Cai et al. (1989) found that U, increased slightly with temperature in the range 20 to450 C. This was mainly attributed to a reduction in gas density. Kai et aL (1991), 011 the otherhand, used five different gases for one kind of fine particles and found that U decreased withincreasing gas phase viscosity, although the gas density also varied with the type of gas. Such adecrease in U is consistent with equations (3.14) and (3.17) because Vd and DBC decrease withincreasing temperature (Kai et al., 1991; Knowlton, 1992) for fine Group A particles.3.4. ConclusionStudies in a cylindrical column reveal that the transition velocity U is a strong function ofmeasurement method, while Uk depends on the solids recycle system and is therefore unsuitable99as a means of characterizing the particulate materiaL The transition velocity U0 from absolutepressure fluctuations tends to be lower than from differential pressure fluctuations. The valuedetermined from differential pressure fluctuations varies with axial location, being higher near thebottom than that near the top of the bed, suggesting that the transition takes place in the topregion first and develops downward. The standard deviation of voidage fluctuations from anoptical fibre probe also reaches a maximum with increasing U. The local voidage and apparentbed density depend on the nature of the unit. When solids return to the bottom of the column isrestricted, the slope ofthe voidage curve may undergo an abrupt change.The transition velocity, U0, also depends on how the data are interpreted. For absolutepressure fluctuations, the standard deviation normalized by the average local pressure reached amaximum at a lower gas velocity than the dimensional standard deviation, and decreased withheight. For differential pressure fluctuations, a higher transition velocity was obtained from thenormalized standard deviation. Skewness of absolute or differential pressure fluctuations doesnot appear to be a reliable indicator of flow regime transition.A mechanism for transition from bubbling to turbulent fluidization is proposed based onbubble-bubble interaction and coalescence. A relatively sharp transition to turbulent fluidizationtakes place when (i) the wake is open and turbulent (i.e. ReB> 130), (ii) the bubble size at U0 ismuch smaller than the column diameter and (iii) the dimensionless separation distance betweensuccessive bubbles approaches a certain value. The transition is gradual when the wake is closed,which occurs for larger or denser particles or where the maximum stable bubble size iscomparable with the column diameter.The proposed mechanism is reasonably consistent with experimental results obtained in acolumn of 102 mm diameter and with literature data for non-slugging systems. The measuredlocal voidage at U0 shows good agreement with values predicted based on the proposed100mechanism. This mechanism also successfully predicts the variation of U with particleproperties, measurement location and system pressure.101Chapter 4Type H Gradual Transition to Turbulent Fluidization4.1. IntroductionThe analysis in Chapter 3 showed that U, defined as the point where standard deviation ofdifferential pressure fluctuations or local voidage fluctuations reaches a maximum, is reachedwhen the gas bubble spacing or separation distance reaches a certain value which is dependent onthe dense phase viscosity. Such a mechanism successfully explains the type I sharp transition tothe turbulent fluidization regime in non-slugging systems which occurs due to significant bubble-bubble interaction. The purpose of this chapter is to clarify and predict the more gradual type IItransition which can occur in slugging systems and for shallow beds.According to Chapter 3, there are two kinds of type II transitions. One occurs in sluggingfluidized beds where the wakes ofbubbles of the size comparable to the column diameter are stillclosed or, in other words, the “maximum stable bubble size” is larger than the column diameter.The other one occurs in shallow fluidized beds where bubbles cannot grow to their maximumstable size before they erupt at the upper bed surface. In this study, the transition from sluggingto turbulent fluidization was investigated in the same 102 mm diameter column as used in the testsof Chapter 3 with a static bed height of 1 in. The same sand particles as used by Zhou et al.(1994) of Sauter mean diameter 215 urn and density 2640 kg/rn3 were used as bed materiaL Thetransition in shallow fluidized beds was studied using silica gel particles of mean diameter of 2 mmand density 1400 kg/rn3 with a static bed height of 0.05 in. Differential pressure fluctuations andlocal voidage fluctuations were measured by means of pressure transducers and an optical fibreprobe, respectively, in the same manner as for the previous tests with FCC particles. Thehydrodynamics around the transition velocity U, are explored in this chapter based on newexperimental results and literature data.1024.2. Transition to Turbulent Fluidization in Tall Slugging Fluidized Beds of Large Particles4.2.1. Transition velocitiesPressure fluctuations in tall slugging beds were studied by Kehoe and Davidson (1972a)using Group A and B particles. The fluctuations were related to slug length, the spacing betweenslugs and their rise velocity. With the assumption that slugs have uniform length and spacing (seeFigure 4.1), the pressure fluctuations at one location are shown in Figure 4.2. The standarddeviation of absolute pressure fluctuations, s, can thus be evaluated (Kehoe and Davidson,1972a). The results are shown in Figure 4.3, with dimensionless standard deviation expressed asa function of dimensionless superficial gas velocity, (UUmf)/U51, slug length, L8/D, and slugspacing, LT/D. It has been reported (Kehoe and Davidson, 1970; Thiel and Potter, 1977) that theinter-slug spacing ranges from 2 to 10 times D, and is insensitive to the variation of U. Therefore,it is expected that the standard deviation will be described by the constant slug spacing lines (seeFigure 4.3) with increasing superficial gas velocity. It is seen that the standard deviation ofabsolute pressure fluctuations caused by the passage of slugs increases with increasing superficialgas velocity due to the increase in slug length (see Figure 4.3). Therefore, a maximum valuecannot be reached ifthere is no limitation in slug length.When the contribution of the propagation of pressure waves generated at the bed surfaceis considered (Baeyens and Geldart, 1974; Noordergraaf et al, 1987), the absolute pressurefluctuations then originate both from slug passage and slug eruption at the upper surface.Noordergraaf et al. (1987) found that the maximum amplitude of absolute pressure fluctuations isproportional to the amplitude of surface height oscillations. The amplitude of surface heightoscillations in deep slugging beds can be estimated (Kehoe and Davidson, 1972b) by/XJI=(UUmf)LT/USi (4.1)where U31=0.351 (4.2)103Figure 4.1. Schematic diagram of gas slugs in deep slugging fluidized beds.UsitIDFigure 4.2. Pressure fluctuations due to slug passage at a location of fully developed sluggingfluidized beds. Adapted from Kehoe and Davidson (1972a).0 1 2 3104543ci)00.1Figure 4.3. Dimensionless standard deviation of absolute pressure fluctuations on the axis of afully slugging fluidized bed due to slug passage as a function of dimensionlesssuperficial gas velocity.As the superficial gas velocity increases with constant slug spacing, the surface height fluctuationsincrease, causing the amplitude of pressure fluctuations due to surface height fluctuations toincrease. The amplitude and standard deviation of absolute pressure fluctuations thenmonotonically increase. Therefore, the standard deviation of absolute pressure fluctuations doesnot reach a maximum until bed particles are entrained significantly, which only occurs when thesuperficial gas velocity is raised beyond Use, the velocity corresponding to significant solidsentrainment (see Chapter 5). Experimentally, in deep slugging fluidized beds (H up to 2 m),Cresciteffi (1978) and Judd and Goosen (1989) found that absolute pressure fluctuations did notreach a maximum for U>O.8 rn/s using Group A powders.In most gas-solids fluidized beds, H is no more than several meters. The slug length is(UUmf)/USI105then expected to be limited to a certain value (e.g. Ls<1OD according to Kehoe and Davidson,1970). It is seen in Figure 4.3 that the standard deviation of pressure fluctuations due to slugpassage decreases if the slug length is limited to a certain value, e.g. Ls<1OD. Correspondinglythe spacing between slugs, L-, decreases. The amplitude of pressure fluctuations due tooscillation of the bed surface height, as shown in Equation (4.1), also decreases. As a result, amaximum amplitude point appears in the standard deviation versus superficial gas velocity curve.The transition velocity, U, in such a case is expected to increase with increasing static bed heightand approaches Use when the static bed height is increased to such a value that bed particles arealready significantly entrained before the maximum slug length is reached (Rhodes and Geldart,1986a). Such a transition in shallow fluidized beds is discussed in detail in section 4.3 below.Differential pressure fluctuations arise mostly from the passage of gas slugs since pressurewaves from outside the measurement interval are ifitered (see Chapter 2). Figure 4.4 shows thepredicted standard deviation of differential pressure fluctuations due to slug passage as a functionof superficial gas velocity. As the superficial gas velocity increases, the slug length increaseswhile slug spacing remains constant. The standard deviation thus initially increases withincreasing superficial gas velocity. Eventually, the standard deviation reaches a maximum valuewhen the slug spacing reaches a certain value. The dimensionless velocity, (U-U1f)/5J, at thispeak point is seen to be approximately 1. When an optical fibre probe is used, the recorded solidfraction signals go to zero when exposed to the slug and go to one when exposed to the densephase. The standard deviation reaches a maximum value (0.5) when Ls=LT, as shown in Figure4.5. The dimensionless velocity at this point is predicted to be around 0.7, smaller than that fromthe differential pressure fluctuations.To veril3i the above analysis, experiments were carried out in a 102 mm diameter columnusing sand particles of mean diameter 215 tm. Figure 4.6 shows the standard deviation of localvoidage fluctuations measured by an optical fibre probe located on the axis. It is seen that a1060.90.80.7__0.6-j0)a) 0.50.40.3Figure 4.4. Predictedheight, L,C,)standard deviation of differential pressure fluctuations across a region ofas a function of superficial gas velocity in a fully slugging fluidized bed.10Figure 4.5. Predicted standard deviation of local voidage fluctuations at a point on the axis of afully slugging fluidized bed as a function of sup efficial gas velocity.0.2 -0.1(UU)/U1100.1 1(UU)/Us11070UVc’V(0(I)maximum value around 0.4 is reached for (U-U)/TJsil. The standard deviation of differentialpressure fluctuations measured between 0.20 and 0.28 m above the distributor are shown inFigure 4.7(a). The peak is seen to correspond to (U-Uu.)IUsi1.8, a higher value than in Figure4.6, consistent with the predictions in Figures 4.4 and 4.5, although the dimensionless superficialvelocities are higher in both cases. The standard deviation of differential pressure fluctuationsmeasured in the bottom developing flow region (rr0.030.20 m) shown in Figure 4.7(b), reachesa maximum at (U-U)/Usi3.4, higher than in the upper region [Figure 4.7(a)]. This can beexplained by the existence of a developing bubbly flow region near the distributor (Baeyens andGeldart, 1974). The information from this lower section is mainly a reflection of coalescingbubble flow, as shown in Figure 3.27 of Chapter 3. Table 4.1 shows some literature data obtainedin relatively deep slugging beds. It is seen that (Uc-Umi)/U51is around 0.8 from the local voidagefluctuation measurement and around 1.5 from the differential pressure fluctuation measurement, ingood agreement with the theoretical analysis.0.50.40.30.20.100 6Figure 4.6. Standard deviation of local voidage fluctuations from optical probe at z=0.28 m as afunction of dimensionless superficial gas velocity.1 2 3 4 5(U-Lf)/UsI1081.40-0>a)0VV(I)Cu0-04-,>a)0VV4-,(I)Figure 4.7. Standard deviation of differential pressure fluctuations as a function of dimensionlesssuperficial gas velocity measured between: (a) z=0.20 to 0.28 m, and (b) z=0.03 to0.20 m above the distributor.1.2I0.80.60.40.200 1 2 3 4 5 6(UUm/UsiI I I1.510.50LI(b)I I I0 1 2 3(U-U/Us4 5 6109Table 4.1. Summary of literature data on transition from slugging to turbulent fluidizationusing Group B and D particles in deep fluidized beds.Author D d,1, p, H1/D (U Umf) Methodmm jim kg/rn3 m/s U1Kehoe and 102 145 2600 >15 0.22 0.63Davidson (1972a)Lancia et aL 100 257 2650 5.0 0.19 0.54 CP(1988) 700 2650 5.0 0.30 0.86 CPChaouki (1992) 82 130 2650 7.3 0.30 0.96 CPThis work 102 215 2640 9.8 0.35 1.0 OPBrereton and 152 158 2480 —6.6 0.50 1.2 DPFGrace (1992)This work 102 215 2640 9.8 0.55 1.8 DPF* CP --- capacitance probe; OP --- optic fiber probe;DPF --- differential pressure fluctuation measurement.4.2.2 Flow patterns around the transitionLike gas bubbles in liquids, slugs may become unstable due to interaction with the wake ofthe preceding slug. For spherical-cap bubbles in liquids, the following wake becomes open andturbulent when ReB (UBDB/vd) is larger than about 130 (Clifi and Grace, 1985), a finding whichwas useful in analyzing the transition from bubbling to turbulent fluidization in fine particle non-slugging systems in Chapter 3. For slugs in liquids, Campos and Guedes de Carvaiho (1988)found that the wake length behind a slug is well correlated byL ID = 0.30 + 0.003486UD/ Vd (4.3)and the transition from a closed laminar wake to an open turbulent wake appears to occur whenReD (=USID/vd) becomes larger than about 500. if the column diameter and the effectivekinematic viscosity of the fluidized dense phase are known, ReD can then be estimated. In gas-solids fluidized beds, limited studies (see Grace, 1982) show that Vd ranges from about 0.0004 to0.0008 m2/s and increases with particle diameter. ReD = 0.35JD/ v, is then always smaller110than 450 in columns for D<0.3 m. The corresponding wake length based on equation (4.3) isthen smaller than 2D. The indication is that slugs in gas-solid slugging beds are always followedby closed laminar wakes.In gas-solids slugging fluidized beds, the spacing between slugs, LT, is around 2D in theupper developed region, especially for large particles (Kehoe and Davidson, 1972a). If significantslug-slug interactions are supposed to occur when following slugs enter the wake of the precedingslug, the same as in Chapter 3, then significant slug-slug interactions are not expected at Ubecause the wake length is smaller than the slug spacing. This is consistent with the experimentalfindings that slug-like flow behaviour persists at gas velocities much higher than u in sluggingfluidized beds of Group B and D particles (Brereton and Grace, 1992).4.3. Transition to Turbulent Flow in Shallow Fluidized Beds of Large ParticlesTo date, most studies with Group B and D particles have been carried out in smallcolumns of limited static bed height (H1f?D<2) with U0 based on absolute pressure fluctuationmeasurements (see Table 4.2). Beds of these particles are expected to exhibit coalescingbubble/slug flow (Kehoe and Davidson, 1970; Baeyens and Geldart, 1974) in columns shorterthan required for fully developed slug flow. The transition to “turbulent” flow in shallow bedstends to be different from that in deep slugging fluidized beds. For instance, an increase of U0with increasing static bed height does not occur in deep slugging beds (Canada et al., 1978;DunhametaL, 1993).In a shallow fluidized bed, the maximum amplitude or standard deviation of absolutepressure fluctuations has commonly been used to identify the transition to turbulent fluidization(e.g. Canada et aL, 1978; Satija and Fan, 1985b). Figure 4.8 shows the standard deviation ofabsolute pressure fluctuations as a function of superficial gas velocity in a shallow fluidized bed ofillTable 4.2. Summary of literature data on transition to turbulent fluidization in shallow fluidizedbeds of Group B and D particles with H{D2.Author D d p, H1/D U-U Method*mm urn kg/rn3 rn/sCanadaetal. 305x 650 2480 0.82 0.90 0.73 APF(1978) 305 2600 2920 0.82 2.00 0.73650 2480 1.31 1.40 -2600 2920 1.31 3.20 -SatijaandFan 102 1000 2767 2.0 2.24 - APF(1985b) 2320 3537 2.0 2.875500 3537 2.0 4.506900 3537 2.0 5.10Konoetal.(1986) 108 1000 2500 1.0 1.80 - APFChyang and 75 1410 2400 1.73 3.30 - APF2050 2400 1.73 3.103260 2400 1.73 3.60DunhametaL 203 242 7589 1.0 2.76 - APF(1993)** 1.5 3.122.0 3.222.5 3.50341 2632 1.0 1.501.5 1.642.0 1.902.5 1.993.0 1.963.5 2.18Meietal.(1993) 300 3180 1100 1.53 2.00 0.72 DPF3180 1190 1.53 2.087140 1190 1.53 3.143180 2600 1.53 3.50This work 102 2000 1400 0.05 0.27 - APF*AJ)F absolute pressure fluctuation measurement;DPF --- differential pressure fluctuation measurement.**Some data obtained with Hmi/D>2were also included.large round silica gel particles in this study. It is seen that the standard deviation reaches amaximum at U=1.05 mis. According to equations (2.21) and (2.22), the amplitude of absolutepressure fluctuations tends to increase monotonically with increasing superficial gas velocity for agiven static bed height. Since the bed particles were not entrained from the column when the112amplitude of pressure fluctuations reached a maximum, emptying of bed particles did not causethe drop in amplitude beyond the maximum point. To explain such a transition, one needs toestimate the maximum amplitude ofpressure fluctuations attainable in the system.10080/00:6 :8 to 1.2 1.4U, misFigure 4.8. Experimental standard deviation of absolute pressure fluctuations at z=0.01 m as afunction of superficial gas velocity for D’0. 102 in, H11=0.05 in, and silica gelparticles with d=2.0 mm,p13=1400 kg/rn3.In shallow fluidized beds with large particles, Noordergraaf et al. (1987) reported that theamplitude of absolute pressure fluctuations increased almost linearly with increasing superficialgas velocity and static bed height, and was proportional to the amplitude of surface heightfluctuations. This is also supported by experimental data for FCC obtained in our 50 mmdiameter column as shown in Figure 4.9 where the amplitude of absolute pressure fluctuationsincreases almost linearly with increasing static bed height for H,<0.2 in. The amplitude ofpressure fluctuations as a function of H (U-U) and particle and gas properties can beexpressed as,113P = q(Ar)(Hrnf ID)(UUmf) (4.4)(10-cL)-o0EE0.4E5 0.20Figure 4.9. Effect of static bed height on the maximum amplitude of absolute pressure fluctuationsfor FCC particles ofd.1,=60 jim, p,l58O kg/rn3 in the 50 mm diameter column. []:U=0.08 mis; •: U=0.04 mis.In a column filled with particles, the pressure measured near the distributor goes tominimum after a slug erupts at the surface (Baeyens and Geldart, 1974). The maximum pressurecorresponds to the condition when the dense bed expands to a maximum and is expected to beproportional to the static bed height. Figure 4.10 shows the maximum amplitude of absolutepressure fluctuations corresponding to the U point versus Ar at various static bed heights, wheredata sources are listed in Table 4.3. It is seen that the maximum amplitude normalized by p(’is a function of the static bed height and is lower than unity. The data in Figure 4.10can be correlated by an equation ofthe formP/[pp(1—Emf)gHmf]=Kl(1—K2IH f) (4.5)Least squares fitting results inK1=0.74 andK2=0.028. By assuming that U is reached when thenormalized amplitude of the absolute pressure fluctuations reaches a certain maximum value, i.e.11max’ the transition velocity u0 in a shallow bed can thus be predicted by combining equations(4.4) and (4.5). A semi-empirical equation is thus established of the form,Rec—Rem! =Pg(UcUmj)dp/ !ig=q1(Ar)q2HjID) (4.6)0.1 0.2 0.3 0.4 0.5 0.6 0.7H, m114Table 4.3. Summary of literature data on theshallow gas-solids fluidized beds.maximum amplitude of pressure fluctuations inSource D, mm H. m p, kg/rn3 d, mm p(1-E)gHCanada et aL (1978) 305 0.40 2920 2.6 0.750.75 2920 2.6 0.750.40 2480 0.65 0.650.75 2480 0.65 0.65Sadasivanetal.(1980) 200 0.18 2600 0.23 0.580.24 2600 0.23 0.63This work 102 0.05 1390 2.0 0.35a)a02 • I I • I0.0 0.1 02 0.3 0.4 0.5H, mFigure 4.10. Dimensionless maximum amplitude of absolute pressure fluctuations as a function ofstatic bed height.Equation (4.5)1.00.80.60.4115To evaluate the effect of gas and particle properties, the data of Satija and Fan (1985) andDunham et al. (1993) with H,jt)=2 (see Table 4.2) are plotted in Figure 4.11. Least squaresfitting of the data leads toRecRemj O.87Ar°45 (4.7)i04U)102101102Figure 4.11. (Re-Re) with H,JD=2 as a function of Ar based on data of Satija and Fan (1985)and Dunham et al. (1993).Figure 4.12 shows (Re-Re)/Ar°45 as a function of H,,1D. It is seen that (ReRe11-)/Ar°45increases with increasing H/D, but such an effect nearly disappears when H,JD>2.The experimental data in Figure 4.12 show wide scatter, probably due to the differentexperimental systems, measurement techniques and data processing methods. An approximate fitcan be obtained using an equation of the form(Re—Re,)/Ar°45=K3[l4(DIHmf)] (4.8)Least squares fitting results inK3=1.32 andK4=O.42.The flow pattern around the transition point has been observed visually by Canada et al.H../D=2Equation (4.7)Ar116(1978) and Chyang and Huang (1988), who reported that cyclic oscillations of their fluidized bedstended to disappear when U exceeds U0. In the present study, the dominant frequency determinedbased on the power spectrum analysis has also been found to disappear for U>U (=1.05 mIs).Visually it was observed also that cyclic flow tended to disappear for U>U, with all gasbubbles/slugs passing through the central region while particles descended along the wall. Uappears to correspond to an early stage of transition from bubbly/slug flow to well-establishedcore-annular flow.2.0Equation (4.8)123 4HdDFigure 4.12. (Re0-Re)/Ar°45as a function ofH/D based on data listed in Table 4.2.4.4. ConclusionTwo kinds of type II gradual transition exist in fluidized beds of Group B and D particles.When the bed is sufficiently deep where fully developed slug flow is established, the maximumamplitude of absolute pressure fluctuations is not reached until the bed particles becometransportable, i.e. the terminal velocity of single particles is reached. The transition velocity U0 in117such a case indicates a transition from slugging to core-annular flow. A U value much lowerthan the terminal velocity of single particles can be identified based on standard deviations ofdifferential pressure fluctuations or local voidage fluctuations. This value can be predicted by slugflow models and does not signify a transition to turbulent fluidization. In fluidized beds which aretoo shallow for bubbles to coalesce sufficiently to span the cross-section of the column, theamplitude of pressure fluctuations reaches a maximum at a certain gas velocity. The transitionvelocity U corresponding to a maximum of the standard deviation or the maximum amplitude ofabsolute pressure fluctuations then tends to increase with increasing static bed height as well aswith particle size and density, and can be correlated by equation (4.8).118Chapter 5Transition from Low Velocity fluidization to High Velocity Transport5.1. IntroductionThe puipose of this chapter is to explore the transition which occurs from a conditionwhere it is possible to distinguish an interface between a “bed” and a freeboard region to highervelocity conditions where there is no such distinct interface.Single phase vertical flow of gas can be either upward or downward. With the addition ofa solids phase, the particles can also travel up or down. Three flow modes exist: co-currentupflow, co-current downflow and counter-current flow with gas flowing upward [see Figure5.1(a)]. The termination of counter-current flow occurs when solids can no longer fall downward(i.e. at the flooding point) and some particles are carried up by the gas to form co-current flow.The lower limit of co-current upflow is set by the gas velocity at which the gas-solids suspensioncollapses and particles begin to drop out of the upflowing stream; below this point countercurrent flow becomes possible. For gas-solids co-current downflow, free-falling particles arealways accelerated by the gravity force before the drag force is balanced by the gravity force.When solids are introduced into the middle section of a vertical tube in which gas isflowing from bottom to top, both co-current upward flow and counter-current flow are possiblewhen the gas velocity is higher than the terminal velocity of single particles. As shown byWilhelm and Valentine (1951), at a low solids feed rate all injected particles are carried upwardgiving a co-current upward flow in the upper section. When the solids feed rate is increased tosuch an extent that the upward flow collapses due to saturation of solids entrainment, excessparticles fall downward and leave the tube from the bottom, so that there is counter-current flowin the lower section as well as co-current upward flow in the upper section. lIthe bottom of the119tube is restrained by a distributor which prevents particles from escaping from the system, afluidized bed forms in the bottom section of the tube [see Figure 5.1(b)]. Thus, two types of flowsystems can be distinguished, with the free system corresponding to transport operation as shownin Figure 5.1(a), while the bottom-restrained system corresponds to fluidized bed operation asindicated in Figure 5.1(b) (Lapidus and Elgin, 1957). A circulating fluidized bed can be operatedin either a co-current upward flow (pneumatic transport) mode or fast fluidization mode,depending on the gas velocity and solids circulation rate.co-uprd flow co-downverd flow counter-flow(a) Free systemsGas flow Solids flowbubbling bed fast fluidized bed pneumatic transport(b) Mechanically restrained systems (bottom restrained)Figure 5.1. Flow modes of gas-solids two-phase vertical transport systems.The lower limit of co-current upward flow, where the gas-solids suspension collapses andparticles drop out of the upflowing stream, has been referred to as the saturated carrying capacitypoint (see Chapter 6). The upper limit of counter-current flow is set by the flooding velocity(Wilhelm and Valentine, 1951; Lapidus and Elgin, 1957). The boundary between low velocity120batch fluidization and high velocity circulating fluidization in gas-solids systems is still not well-defined, although the transition may be considered to occur when significant numbers of particlesare entrained from the fluidized bed (Bi and Fan, 1992). Based on the measurement of thevariation of pressure drop gradient, (dP/dz), a transport velocity beyond which the sharp changeof pressure drop gradient with increasing solids circulation rate disappears was proposed byYerushalmi and Cankurt (1979) to quantif3i the transition to high velocity fast fluidization. Theexistence of such a transport velocity, however, was questioned by Rhodes and Geldart (1986b)and Scbnitzlein and Weinstein (1988).In this chapter, we describe experiments in a circulating fluidized bed apparatus toinvestigate solids entrainment behaviour. A systematic analysis is then carried out to seek anappropriate boundary between low velocity fluidization and high velocity fast fluidization. Thebehaviour around the transition is also explored based on experimental results obtained in thiswork as well as literature data.5.2. ExperimentsExperiments were conducted using a column of square 152x152 mm cross-section and 9.1mheight, shown schematically in Figure 5.2 equipped with multi-orifice type distributor plate offractional open area 17%. This CFB riser is connected to a 300 mm ID Plexiglas standpipe.Entrained particles are collected by two cyclones in series and returned to the standpipe. Thesolids circulation rate is controlled via an L-valve installed at the bottom of the standpipe andmeasured by timing the descent of identffiable particles at the wall of the transparent standpipe.Sand particles of mean diameter 215 tm and density 2540 kg/rn3were used as bed material.Pressure drops and differential pressure fluctuations were measured using sensitivepressure transducers (Omega PX 162). Differential pressures were measured at two locations,121I. 1•9Am0 D> -0(j)—000DDcDc-‘between 0.10 and 0.25 m and between 0.71 and 0.86 m above the distributor. Tubes of 0.3 mlength each having a dead volume of 4.2 cm3 were connected the pressure taps to the transducers.Local voidage fluctuations were measured by a reflection-type optical fibre probe which had a tipdiameter of 1.5 mm. The probe tip was always located at the wall 0.775 m above the distributor.This probe was calibrated using a fluidized suspension of the same particles in water. Signalsfrom both pressure transducers and the optical fibre probe were recorded simultaneously by adigital data logging system (DAS 8 board) at a frequency of 100 Hz for intervals of 40 s.5.3. Experimental Results and Discussion5.3.1. Termination of co-current fully suspended upflowFigures 5.3(a) and (b) show the apparent suspension density, obtained from the differentialpressure measurements at two sections of the riser as a function of solids circulation rate. It isseen that bed density initially increases gradually with increasing solids circulation rate at a givensuperficial gas velocity. Beyond a certain solids flux, the bed density increases sharply withincreasing solids flux, due to collapse of the utiiform suspension. Figure 5.3(c) shows the localdensity measured with the optical fibre probe at the wall of the riser, midway between thepressure ports used to obtain the differential measurements displayed in Figure 5.3(a). A sharpchange of slope is again obvious.Figures 5.4(a), (b) and (c) show the standard deviation of pressure and voidagefluctuations as a fimction of solids circulation rate for the same conditions as in Figure 5.3. It isseen that the standard deviation of pressure fluctuations also increases sharply with increasingsolids circulation rate as the suspension collapses to form a fluidized bed at the bottom. Thetransition condition thus corresponds to choking. The standard deviation of voidage fluctuations[Figure 5.4(c)] increases more smoothly than the standard deviation of pressure fluctuations123[Figures 5.4(a) and (b)], suggesting that the development of wall dense-phase structure occurssmoothly rather than abruptly.c)E0)-C’)Ca)4-,CU)0C’,E0)U)U)4-,CU)I0.0C’,E0)-IFigure 5.3. Apparent bed density as a function of solids circulation rate for four superficial gasvelocities: (a) from differential pressure transducer over interval from 0.71 to 0.86 m;(b) from differential pressure transducer over interval from 0.10 to 0.25 m; (c) fromoptical fibre probe at height 0.775 m. •: U=4.1 mis; +: U=4.8 mis; I]: U=5.7 m/s;x: U=6.6 m/s.0 5 10 15 20 25Solids Circulation Rate, kg/m2s1240C0CuVCCu4-’C,)Cu0C0CuVCu-oCCu4-,Cl,E-S0)-C04-,Cu>G)VCuVCCu4-’C’,25Figure 5.4. Standard deviation of differential pressure and voidage fluctuations as functions ofsolids circulation rate. (a) and (b) from differential pressure transducers; (c) fromoptical fibre probe. Probe locations, gas velocities and operating conditions are as inFigure 5.3.As discussed in Chapter 3, there is a strong relationship between fluidized bed fluctuationsand bed densities in bubbling and turbulent fluidized beds. Figures 5.5(a) and (b) show thestandard deviation of pressure fluctuations as a function of apparent density for the same height0 5 10 15 20Solids Circulation Rate, kg/m2s125interval as in Figures 5.3(a) and (b) and Figures 5.4(a) and (b) . It is seen that all pressurefluctuation data obtained at different gas velocities and different locations are well correlated by asingle line. The same applies to local voidage fluctuations as shown in Figure 5.5(c). Thefluctuations tend to increase with increasing solids concentration. The abrupt change in the slopeof the line in Figures 5.5(a) and (b) corresponds to collapse of the suspension. The apparentdensity at this transition point is around 30 to 40 kg/rn3. This finding supports speculation (Zenzand Otlimer, 1960; Smith, 1978) that there exists a saturation solids concentration beyond which auniform gas-solids suspension can no longer exist stably.In Figure 5.5(c), the standard deviation of local voidage fluctuations is seen to reach amaximum at a local density of about 400 kg/rn3, corresponding to a local voidage of around 0.85.Similar results were reported by Brereton and Grace (1993) from capacitance probemeasurements. To elucidate the phenomenon, the skewness of local voidage fluctuations isplotted in Figure 5.6(a) as a fimction of local voidage. It is seen that the skewness passes throughzero at a local density of about 450 kg/rn3, roughly the same value at which [see Figure 5.5(c)]the standard deviation reaches a maximuni In view of the bimodal probability distribution profileof local voidage signals from an optical fibre probe with one peak corresponding to the lean phaseand the other to the dense phase (see Chapter 2), the zero skewness suggests that the probe isexposed for half the time to the dense phase and for the other half to the lean phase. When theprobe is equally covered by the dense phase and dilute phase, the standard deviation reaches itsmaximum (Brereton, 1987). The intermittency index defined by Brereton and Grace (1993) isplotted in Figure 5.6(b). From its definition, the intermittency index should approach zero forcompletely separated core-annular flow and unity for a dispersion of clusters of voidage s in asolids-free gas. The intermittency index is seen to be close to zero for very dilute uniform flowand to increase steadily with increasing local particle concentration, suggesting the appearance ofrecurrent structures from uniform suspension flow. Beyond the level (s0.85) where both thestandard deviation and the intermittency index reach maxima and the skewness goes to zero, a126non-uniform structure can be considered to be well established, with the wall mostly covered byirregular streamers or clusters.50 100 200Local Density kg/rn3500 1,000Figure 5.5. Standard deviation of differential pressure and voidage fluctuations as a function ofapparent or local density. (a) and (b) from differential pressure transducers; (c) fromoptical fibre probe. Probe locations, operating conditions and gas velocities are as inFigure 5.3.220127Cl)Cl)ci)Cl)>.‘C.)ci).4-,4-,E1U).4-’C1,000Figure 5.6. (a) Skewness and (b) intermittency index from optical fibre probe as a function oflocal density at wall. Conditions and gas velocities are as in Figure 5.3(c).5.3.2. Onset of significant entrainmentSolids entrainment in fluidized beds operated at low and intermediate gas velocities hasbeen well documented (Geldart, 1986). Entrainment at higher velocities has also been reported inrecent years (e.g., Yerushalmi et aL, 1978; Gao et aL, 1991). Almost all entrainment data showthe same characteristics as in Figure 5.7 where the Type A choking velocity, UCA, defined as thesupefficial gas velocity at which uniform suspension collapses and particles start to accumulate in20 30 50 100 200 500Local Density, kg/rn3128the bottom of the column (detailed discussion is given in Chapter 6), determined in the presentstudy are plotted as a function of solids circulation rate. In low velocity bubbling fluidized beds,entrained particles are mainly ejected into the freeboard by wakes of bubbles erupting at the bedsurface. The solids entrainment rate increases sharply with increasing superficial gas velocity(Geldart, 1986), while the solids holdup in the upper freeboard region also increases withincreasing superficial gas velocity (Nazemi et aL, 1974), in agreement with the decreasing slope ofthe curve at low gas velocities in Figure 5.7. Beyond a certain gas velocity, bubbles no longerexist due to the absence of a dense fluidized bed. Entrainment then mainly depends on thecarrying-ability of the gas phase. In a gas-solids transport system, solids flux and gas velocity atType A choking points are related byUCAG3= PP(l ECA)(6CA(1)E0DFigure 5.7. Type A choking velocity as a function of solids circulation rate.(5.1)0 5 10 15 20 25G5, kg/m2s129As indicated by Figures 5.5(a) and (b), the apparent bed density is independent of gas velocity andsolids circulation rate when the suspension collapses, i.e. 6CA is constant at UCA. A linearrelationship between (I and Type A choking velocity UCA in the high velocity range withconstant in Figure 5.7 suggests that U11 in Equation (5.1) approaches a constant value, whichcan be determined from the intercept and slope of the linear portion of the curve. This criticalvelocity, which we designate Use, can be considered to be a hindered terminal velocity or apparentterminal velocity of bed particles, because the entrainment of single particles is initiated when thesuperficial gas velocity reaches the terminal settling velocity, while Use can be considered tocorrespond to the onset of significant entrainment for the assembly ofparticles.The critical velocity Use can also be determined in a batch operated fluidized bed bymeasuring solids entrainment or the time required to empty all bed particles. In a fluidized bedhaving a given inventory of particles, W0, the time required to blow out all bed particles (so-called emptying-time) is related to the solids entrainment rate byT= (5.2)G3Awhere (I is the entrainment flux, corresponding to the solids circulation flux in a circulatingfluidized bed measured at the exit of the column and A is the cross-sectional area of the riser. Acurve similar to that in Figure 5.7 can be obtained if the emptying time T is measured at eachgiven gas velocity and the data are plotted as l/T versus superficial gas velocity. Asdemonstrated in Figure 5.8 using the data ofPerales et al. (1991), Use can then be determined.5.3.3. Critical velocity, UseAll Use and saturation voidage, 6cA’ values determined by using available literature resultsbased on the entrainment method defined above are listed in Table 5.1. For comparison, thecolumn dimensions and operating conditions are also indicated. This allows the effects of130operating conditions (e.g. pressure and temperature), column dimensions (bed diameter andheight) and particle properties (mean particle size and density, particle size distribution), as well asother parameters like solids inventory and solids feed system to be evaluated.3Cl)E2D0 0.01 0.02 0.0311T 1/s0.04 0.05Figure 5.8. Reciprocal ofbed emptying time as a function of superficial gas velocity based on thedata ofPerales et al. (1991) for FCC particles, d,=80 jim, p,=l’7l5 kg/rn3.Solids entrainment rates in conventional fluidized beds have been reported to be affectedby bed diameter (Lewis et al., 1962). Column diameter may therefore have some effect on Use.Due to stronger suspension-wall ffiction, the saturated solids entrainment rate is expected to belower for smaller diameter risers than for large columns. However, the effect on the criticalvelocity appears to be minor as evidenced by Figure 5.9 where experimental data from Table 5.1with relatively tall risers (I.e. Ilo>5 .5 m) are plotted as a function ofp13d,, and column diameter. Itis seen that the critical velocity hardly varies as the column diameter increases at least for thelimited range of 20 to 200 mm.131Table 5.1. Critical velocity and saturation voidage data in order of reducing column diameter.1(a) Ambient pressure and temperature dataAuthor 11o D dp pp Use 6CA( m) (mm) (jim) (kg/rn3) (m/s)ChangandLouge(1992) 7.0 200 234 1440 4.0 0.94367 7400 2.4 0.995Baietal. (1987) 9 186 94 1546 1.6 0.932187 703 1.6 0.967Zhang et a!. (1990) 6.4 186 384 681 1.9 -62 1006 0.8 -Yerushalmi et al. (1978) 8.4 152 33 1670 1.4 -49 1070 0.9 0.970Yerushalmi and Cankurt 8.4 152 49 1450 1.3 0.976(1979)Rhodes and Geldart 6.6 152 42 1020 1.3 0.981(1986b) 64 1800 1.3 0.98738 1310 1.0 0.985Schnitzlein and 8.4 152 59 1450 1.4 0.967Weinstein (1988)Thiswork 9.1 152x152 212 2640 2.8 0.990Zhangetal. (1985) 8 115 220 732 1.9 -Satija et aL (1985) 6.5 102 155 2446 - 0.994245 2446 - 0.996Bi et aL (1991) 6.4 102 325 660 1.8 0.984Takeuchietal. (1986) 5.5 100 57 1050 1.4 0.944Hiramaetal.(1992) 5.5 100 54 750 0.8 0.975Perales et aL (1991) 2.9 92 80 1715 1.4 -ChenetaL (1980) 8 90 54 3160 2.0 0.98881 3090 2.6 0.98558 1780 1.2 0.98156 3050 2.0 0.987Dry and Christensen 7.2 90 71 1370 1.3 0.960(1988)Gao et al. (1991) 8.4 90 62 1020 0.75 0.97482 1780 1.5 0.982205 760 1.5 0.975132Table 1(a) (continued)Capes and 9.1 76 256 7510 5.5 0.999Nakamura (1974) 535 7510 10.4 0.9971200 7850 14.5 0.9982340 7700 17.1 0.9951080 2470 16.1 0.9791780 2900 11.1 0.9852900 2860 10.4 0.9971780 1085 9.3 0.9973400 911 7.2 0.997Yerushalmietal. (1976) 7.6 76 49 1070 1.5 -Kato et al. (1989) 3 66 61 1700 0.6 0.969Drahosetal.(1988) 2.23 55 120 2550 1.6 0.994200 2550 1.7 0.998Yousfi and Gao 6 50 118 2470 2.0 -(1974) 143 2470 2.2 -183 2470 1.6 -290 1060 2.5 -Horio et aL (1992) 2.4 50 60 1000 0.6 0.921Zenz (1949) 1.2 44.5 168 2098 1.5 0.980587 2483 3.1 0.979930 2643 3.4 0.9841676 1089 2.7 0.940Lewisetal.(1949) 3 31.8 40 2483 1.3 0.955100 2483 1.6 0.938280 2483 2.5 0.927SunandYang 6 30 165 794 1.7 -(1990) 325 794 1.9 -85 1487 1.7 -MoketaL (1989) 9 20 210 2620 2.6 0.982Table 1(b) High pressure data ofKnowlton and Bachovchin (1976).H0 D dp Pp Pg Use(m) (mm) (rim) (kg/rn3) (kg/rn3) (mis)15 76 245 3909 11.9 2.4245 3909 21.5 2.0245 3909 35.6 1.9889 1259 5.9 4.8889 1259 11.7 2.8889 1259 18.7 2.5889 1259 37.6 2.0889 1259 53.5 1.6133430.6Figure 5.9. Effect of pd and column diameter on Use based on data sources in Table 5.1(a).Column height may also affect Use. The solids entrainment rate in a fluidized bed isgenerally considered not to vary with axial location above some height, called the TransportDisengaging Height (TDH). Below the TDH, however, the solids entrainment rate increases withdecreasing height. Therefore, solids entrainment in a riser much shorter than the TDH is higherthan in a taller column. Hence, Use is expected to be lower in a shorter riser. This is seen clearlyin Figure 5.10 where Use values obtained from risers ofheight less than 3 m are significantly lowerthan those from relatively tall risers (IIo>5.5 m). The critical velocity appears to be insensitive tocolumn height only for tall risers.In relatively tall risers, the solids feed system has little effect on Use because it has littleeffect on solids entrainment, as reflected in the experimental results of Gao et al. (1991) and Baiet al. (1992). The data of Gao et al. (1991) fhrther indicate that solids inventory has negligibleinfluence on Use.B D=152-200mmx D=90-ll5mmL D=54-76mm+ D20-32 mm+2>< L><IL00 0.1 0.2 0.3 0.4 0.5kg/rn213443.532.521.510.500.02Figure 5.10. Effect of and column height on Use based on data sources listed in Table 5.1(a).The effect of pressure and temperature in gas-solids flow systems can be evaluated basedon their effects on solids entraimment. The solids entrainment rate increases with increasingsystem pressure (May and Russell, 1953; Chan and Knowlton, 1984; Tsukada et al., 1993). Usethen decreases as pressure increases as seen in Table 5.1(b). Direct evidence of the iiifluence oftemperature is lacking. For small particles where the terminal velocity of single particles isinversely proportional to the gas viscosity, Knowlton (1992) found that entrainment increasedwith increasing temperature. For coarse particles (d>0. 7 mm) where the terminal velocity ofsingle particles is more strongly affected by the gas density, Choi et al. (1993) reported thatentrainment decreased with increasing temperature. One may thus infer that Use, similar to U,decreases for fine particles and increases for coarse particles with increasing temperature.It is likely that Use increases with increasing particle size and density. In addition, particlesize distribution (PSD) may have some influence. In gas-solids fluidized beds, the solidsPd kg/rn21 2135entrainment rate has been found to be proportional to the fine particle content (Geldart, 1986).Use is thus expected to be lower for particles having higher fines content. In addition, in thepresence of fine particles, coarse particles can be entrained at lower gas velocity because theterminal velocity is greatly reduced by the interaction between fine and coarse particles (Geldartand Pope, 1983; Satija and Fan, 1985a). Use for coarse particles is therefore expected to bereduced by the presence of fines.To summarize, Use should not depend on column dimensions and geometry (ie. riserheight, riser diameter, solids feed device) or on solids inventory when large diameter, tall risersare used. Use, like U, can thus be considered to characterize the bed materiaL Figure 5.11shows all Use data in Table 5.1(a) obtained in risers of D>75 mm and IIo>5.5 m plotted indimensionless form. The boundaries between Groups A and B and between B and D particles, asdetermined by Grace (1986), are also included in Figure 5.10. Tn general, Use is seen to be muchhigher than Ut for Group A particles, somewhat higher than Ut for Group B particles, and almostthe same for Group D particles. One implication is that large particles can be transportedsignificantly just beyond the terminal velocity due to the absence of interparticle forces, while fineparticles cannot be significantly transported until U>>U due to lateral segregation, interp articleforces and clustering behaviour. The ratio (Use/Ut) can thus be taken as an indicator of the extentof lateral particle segregation and interparticle forces. Note that the point where Use/Ut=lcorresponds closely to the BD boundary. The data in Figure 5.11 can be best fitted byRese (1.53 ± 0. 05)Ar 0.50±0.03 (53)with 95% confidence limits. The correlation coefficient for equation (5.3) is 0.987.5.3.4. Saturation concentration of fully suspended gas-solids flowA saturation concentration of gas-solids upward transport was first proposed by Zenz(1949) based on experiments in a 44.5 mm diameter conveyor and an argument that the wake of aleading particle interacts strongly with a following particle when the spacing between them is136‘unFigure 5.11. Rese=pgUsedp/i.ig as a function of Ar based on data from sources listed in Table5.1(a), and compared with terminal Reynolds number.reduced beyond a certain value. Yousfl and Gau (1974) also derived a criterion for the maximumsolids fraction based on a stability analysis of a conveyed suspension subjected to smalldisturbances. Arguing that the rise velocity of a bubble should not exceed the velocity ofpropagation of a change in voidage, Smith (1978) proposed a criterion for the limiting porosity ofpneumatic transport. Extending Jackson’s linear instability analysis of dense beds of solidsparticles to dilute transport systems, Grace and Tuot (1979) showed that all systems are unstableto the growth of voidage waves. The growth distances increase dramatically as the voidageapproaches 1, suggesting that stable uniform suspension flow only exists for low solids loadings.Recently, Zenz and Othmer (1992) related the critical volume fraction of gas-solids flow to liquid-vapour equilibrium, with the dense phase corresponding to the liquid and the saturation lean phaseto the vapour. The saturation concentration, analogous to the vapour pressure, tends to beconstant for a given gas-solids system.Ar137CC.)cICBased on the slopes of entrainment curves and equation (5.1), solids holdups at Type Achoking points, which correspond to the maximum attainable solids fraction in a transport line,have been evaluated and are listed in Table 5.1(a). The data for columns of D>50 mm and H0>6m are plotted against Ar in Figure 5.12. Although the data are quite scattered, it can be seen thatthe saturation solids fraction decreases with increasing particle size andlor density. For largeparticles the saturation solids fraction is lower than 0.02. Suspensions of line Group A particles,however, can operate with solids fraction higher than 0.05. This suggests that conventional lean-phase pneumatic transport lines with Groups B and D particles can only be operated with 6>0.98,while dilute conveying of line Group A particles can be carried out with voidages as low as 0.95before the suspension collapses.0.080.060.040.020Figure 5.12. Saturation volumetric solids fraction corresponding to Use plotted as a function ofAr. Data sources are listed in Table 5.1(a).1 102Ar1061385.4. Transport VelocityAccording to Yerushalmi and Caukurt (1979), a critical solid circulation rate may existwhere a sharp change in the pressure gradient takes place when the solids circulation rate is variedat a constant gas velocity (see Figure 5.13). As the gas velocity increases beyond a certain point,the sharp change in the pressure gradient disappears. The gas velocity at this critical point is thendefined as the transport velocity Utr, which is said to denote the onset of the fhst fluidizationregime. This transport velocity differs from Use determined from the methods described above.For example, in Figure 5.7, Use is seen to be approximately 2.7 mIs, while the transport velocity,Utr, based on Figure 5.3 is higher than 6.6 mIs based on the definition in Figure 5.13; significantlyhigher than Use. This is also shown in Table 5.2 where the transport velocity Utr is comparedwith the critical velocity Use for the same system.0’(1)0Figure 5.13. Definition of transport velocity based on Yerushalmi and Cankurt (1979).139Table 5.2. Summary oftransport velocity data.Author Particles 1 D 1 dp p Use Utrj (mm) j (gm) (kgAn3) (mis) (mis)Yerushalmi and FCC 152 49 1070 0.90 1.37Cankurt (1979) HFZ-20 49 1450 1.50 2.10H-alumina 103 2460 - 3.85Chenetal. (1980) FCC 90 58 1780 - 1.8Alumina 54 3160 - 2.0Alumina 81 3090 - 2.6Iron ore 56 3050 - 2.0Iron ore 105 4510 - 4.0KwauketaL (1986) FCC 300 58 1780 1.25 1.85LietaL(1992) FCC 90 54 930 - 2.50Horio etal. (1992) FCC 50 60 1000 0.55 1.10Sand 106 2600 - 4.5Bietal. (1991) Polyethylene 102 325 660 1.60 2.25AdanezetaL (1993) Sand 170 100 2600 - 3.15Given that some researchers (Rhodes and Geldart, 1986b; Schnitzlein and Weinstein,1988) found it difficult to identilj such a transition point, the transport velocity seems to dependon the column geometry and measurement method. Pressure gradient proffles reported byYerushalmi and Cankurt (1979) were also different when measured at different axial locations.Over the bottom 0.3 in, the sharp change of pressure gradient against the solids circulation ratetended to disappear when the gas velocity exceeded 1.5 mIs for FCC particles; such a change inthe pressure gradient is not clear, however, over an interval of 0.9 m beginning 2 m above thedistributor. To circumvent the arbitrary choice of the transport velocity, Horio et al. (1992)calculated the maximum [8(dP / dz) / 8G] at each given gas velocity and plotted it against thesuperficial gas velocity. This parameter is expected to decrease with increasing superficial gasvelocity, with the variation becoming gradual for U>Utr.In a fluidized bed, the pressure drop is proportional to solids concentration when ffictionand acceleration effects are neglected, i.e. dP/dzp( 1-)g. A sudden change in pressure dropthen corresponds to a sudden change in bed voidage within the measuring interval. Consider a140circulating fluidized bed as shown in Figure 5.14(a), with a dense bed ofvoidage Ed at the bottomand a dilute-phase of voidage 8cA in the upper section. At the given gas velocity, the suspensioncollapses at the choking point (see Figure 5.3) and a sudden jump of solids concentration app ears.The collapsed dense section in the bottom develops upward and passes the lirst and the secondpressure taps as the solids circulation rate is further increased. Correspondingly, the pressuredrop increases steadily until the dense phase passes the upper tap location. As shown in Figure5.14(b), the maximum gradient of [8(dP / dz)/ aG3] can be approximated by________Pg(ECA Ed) (5.4)8G ) AG3 Uwhere AG is the solids circulation rate required to raise the dilute-dense interface from thebottom to the top pressure tap, which can be expressed (Kunii and Levenspiel, 1990) asAG3 = (G30 —G:)exp[—a(H —z—L)] (5.5)GCA________________________N P(1 -E)gb2=constantH0____bAG(a) (b)Figure 5.14. (a). Schematic of voidage in CFB riser and (b) simplified estimation ofMax[8(dP / dz)/ aG31.141The solids flux right above the dense-dilute interface, 1so, can be estimated by the correlation ofWen and Chen (1982),G0 = 7.68 x 10’°7tD2Dp5g°(U — Umf )2.5 / (5.6)where DB is the diameter of bubbles erupting at the upper surface. For FCC type particles, themaximum stable bubble size is around 0.1 m (see Chapter 3). Therefore, the bubble size at gasvelocities higher than U can be considered to be about 0.1 m for FCC type particles. Forslugging systems with large particles, DB can be estimated as equivalent to the column diameter.The saturated solids flux, G*, can be estimated by the equation ofBi and Fan (1991),G:OOo345(U/1f_)L45A194 (5.7)Substituting equations (5.5) to (5.7) into equation (5.4), one obtains,(8(dP/dz) P(EcAEd) (58)L r3G — [B1(U— Urnj )2.5 —BU22’45]exp[—a(H0—z — L)]withB1 = 7.68x l0’°7tD2D3p5g°/i (5.9)andB2 0.00345pgAr’’(gdp)° (5.10)It is seen that [ô(dP / dz) / 8G] is a function of the measuring location, z, the separationdistance L between the two pressure ports, the decay constant, a, and the superficial gas velocity,as well as gas and particle properties. Figures 5.15(a) to (d) shows the variation of[(dP / dz) / ãG3J with the superficial gas velocity predicted by equation (5.8) for typical FCCparticles. Here d is estimated from the equation of King (1989),6d =(U+l)/(U+2) (5.11)ECA is taken as 0.99 based on Figure 5.12 for Group A particles. The decay constant, a, isconsidered to obey, aU=constant (Lewis et al., 1962; Kuini and Levenspiel, 1990) with theconstant from 2 to 4 I depending on particle properties. The transport velocity determined142according to the method proposed by Yerushalnii and Cankurt (1979) and Hono et al. (1992) isexpected in Figure 5.15(a) to be higher when the pressure drop is measured at the lower sectionof the riser. Figure 5.15(b) shows that the transport velocity increases with column height.Figure 5.15(c) indicates that the transport velocity tends to be higher from pressure drops oversmaller separation distances. In equation (5.7), particle properties are mainly reflected throughthe decay constant. In fluidized beds, it has been found that decay constant, a, increases withparticle diameter and density (Kunii and Levenspiel, 1990). Figure 5.15(d) shows that thetransport velocity increases with increasing decay constant.The above analysis indicates that a transition does occur in axial solids concentrationproliles with increasing superficial gas velocity. The transport velocity, Utr, indicates a transitionof axial voidage proffles in the riser, analogous to the “critical point” in the phase diagram(Matsen, 1982; Klinzing, 1986). Below this velocity, a distinct interface exists between the topdilute region and the bottom dense region when a sufficient solids circulation rate can be ensured.Beyond this velocity, there is a continuous gradation of suspension density, and the variation ofvoidage with height tends to be relatively smooth. However, such a transition relies on themeasurement method and the way the data are interpreted. To ensure success in determining thetransport velocity, it is recommended that the pressure drop be measured near the bottom of theriser between two pressure taps separated by a small distance, and that the data be processed as inFigures 5.13 and 5.14. Since it is more difficult to determine Uft and solids entrainment rate at Utris much higher than at Use, it is recommended that Use be used to define the transition fromturbulent fluidization to solids transport operation or fast fluidization.5.5. ConclusionThe Type A choking velocity sets the boundary between co-current upward pneumaticconveying and the collapsed flow mode of circulating fluidized beds, often called fast fluidization.1431x1OZrna=Um=1Om1’z2I=04m5()U,rn/s28x10z6Xi04x102xlO 1x1042 2sxio3z6x1O4xiO dO62 2 z 2 2 z I8x103 6x1O 4x10 0 8x10 6x16 4x103 2x103 aH0mH010ma=21Um1,z=Om6U,rn/sa=O.5/Urn1a=MJrn1z=Om=5ma=2!UrnH08L=1ma=2/um1,z0mL=3\___H0_5m(c)I23456U,rn/sUrn/sFigure5.15.Predictedmaximumpressuregradientasafunctionofsuperficialgasvelocity.(a)Effectofaxiallocation;(b)Effectofcolumnheight;(c)Effectofseparationdistancebetweenthetwotapsusedfordifferentialpressuremeasurement;(d)Effectofdecayconstant,a.FCCparticleswithcL,=6Orim, p,1500kg/rn3fluidizedbyairat20°Cand100kPainacolumnofD=0.15niA critical velocity, Use, is defined based on the solids entrainment versus gas velocity curve.Conventional fluidized beds equipped with cyclones and diplegs have generally been operated atU<Use. Circulating fluidized beds, on the other hand, are often operated beyond the criticalvelocity iii order to achieve high solids circulation rates. The critical velocity, like the terminalvelocity of single particles, is a function of particle properties, increasing with mean particle sizeand density. Raising the absolute pressure reduces the critical velocity, while raising temperaturemay increase or decrease the critical velocity, depending on particle size and density. Columndiameter and height influence the critical velocity little so long as a sufficiently tall column is used.The saturation concentration corresponding to Type A choking tends to be higher for fineparticles. In conventional transport lines with large particles, the saturation concentration rarelyexceeds 0.02.The transport velocity, Utr, defined by Yerushalimi and Cankurt (1979), corresponds to atransition of axial voidage profiles in the riser. Below this velocity, a distinct interface existsbetween a top dilute region and a bottom dense region at a high solids circulation rate. AboveUtr, the variation of voidage with height becomes relatively smooth. Utr is a function ofmeasurement location and separation distance between two pressure taps, as well as gas andparticle properties.145Chapter 6Types of Choking in Vertical Pneumatic Systems6.1. IntroductionWhen gas flows vertically upward through a bed of solid particles, the batch operationmode with a distinct bed surface is replaced by pneumatic transport when the gas velocity exceedsthe critical velocity Use (see Chapter 5). In the opposite direction, stable operation ofconventional pneumatic transport ceases when the gas velocity is reduced below the chokingvelocity (Leung, 1980; Reddy Karry and Knowlton, 1991; Bi and Fan, 1991). The fastfluidization regime is believed to lie between the lower velocity fluidization regimes (bubbling,slugging and turbulent fluidization) and the pneumatic transport regime. Such a fast fluidizationregime is, however, still not well delined, in large measure due to poor understanding of chokingphenomena (Grace, 1986; Bi and Fan, 1991). A proper knowledge of choking would aid inunderstanding the mechanisms which govern hydrodynamic regime transitions and in bridging thegap between conventional fluidizationldense-phase transport and pneumatic transport. Theobjective in this chapter is to clarif’ different definitions of choking employed in the literature andto explain the relevance of choking to regime transitions in fluidization and solids transport.6.2. Initiation of Choking6.2.1. Choking defmitionsThe term “choking” has generally been used to describe a phenomenon which occurs whenthere is an abrupt change in the behaviour of a gas-solids conveying system. A number ofdefinitions and criteria have been developed to describe and predict choking. For a tall verticalriser in which solid particles are being conveyed at a given rate and the gas velocity is graduallyreduced, Zenz and Othiner (1960) defined choking as the point at which slugging occurred to146such an extent that extremely unsteady flow conditions ensued. In a similar approach, Yousfl andGau (1974) defined choking as occurring when solid plugs extend over the entire pipecross-section. The choking point, therefore, has been characterized by the formation ofslugs/plugs and severe instability. Such an unsteady transition, which we ll refer to as “classicalchoking” or Type C choking, was determined by Zenz (1949), Lewis et aL (1949), Ormiston(1969), Drahos et al. (1988), Mok et al. (1989) and Bi et al. (1991).Based on such a definition, choking has been found to depend on the properties of bothgas and solid particles as well as on the size and geometry of the column which contains the flowsystem (Zenz, 1949; Yousfi and Gau, 1974). For large particles, choking was observed to resultin slugging; for some others slugging does not come into play. To clarii\y a system as slugging ornon-slugging, criteria have been proposed based on instability analysis of uniform suspensionflow (Yousfl and Gau, 1974), stability of slugs (Yang, 1976), and the propagation of continuitywaves (Smith, 1978). For large units with small particles, when the maximum stable bubble size ismuch smaller than the column diameter, slugging is not encountered due to the absence of slugs.The second type of choking, which has been called “premature choking” (Reddy Karri andKnowlton, 1991), results from equipment (blower or standpipe) limitations. No slugging appears,but the system becomes inoperable. This unstable condition may be due to the inability of theblower to provide sufficient pressure head to support all of the particles in suspension (Zenz andOthmer, 1960) plus the head losses through the gas distributor, riser exit, cyclone, etc.. Withblowers characterized by reducing volumetric delivery at increasing delivery pressure, Doig andRoper (1963) and Leung et al. (1971) analyzed such an instability process as shown in Figure 6.1.The solid lines represent the pressure head at the bottom of the conveyor versus gas flow-ratecharacteristics, while the dashed lines are characteristics of the blower. For a fixed solids flowrate, there are two possible operating points, A and B, with point B inherently unstable. A smallreduction in the gas flow rate at B would result in an increase in the pressure drop, resulting in a147further decrease in the gas flow rate and eventual blockage of the conveyor. For Group B and Dparticles, the analyses of Bandrowski and Kaczmarzyk (1981) and Matsumoto et a!. (1982) showa similar instability when the blower characteristic curve intercepts the conveying systemcharacteristic curve tangentially. The gas velocity at this critical point is generally higher than theslugging-type (or classical) choking velocity and can be reduced toward the latter by making theblower characteristic curve steeper (compare AB and A’B’ in Figure 6.1). In gas-liquid cocurrent upflow systems, a flow “excursion” instability, similar to that in gas-solids systems, canresult from the interaction between pump and conveyor characteristics (Ishii, 1982).EzDCl)Cl)ci)0Figure 6.1. Operational instability due to insufficient pressure head supplied by gas blower.Another type of “premature choking” can occur at higher gas velocity than that of classicalchoking in circulating fluidized beds. Upflow risers are generally directly coupled withdowncomers which return entrained particles to the bottom region of the risers. A pressurebalance between the riser and downcomer is required to maintain the system under steadyoperation. If the gas velocity is decreased at a given solids circulation rate, a critical state may bereached at which steady operation at a given solids flux becomes impossible; this instability occursbecause solids cannot be fed to the riser at the prescribed rate, although slugging may not comeU, rn/s148into play at this point (Knowlton and Bachovchin, 1976; Takeuchi et al., 1986; Bai et al., 1987;Bader et al., 1989; Hirama et aL, 1992). This critical condition depends on solids inventory in thestandpipe, with lower critical velocity for higher solids inventory (Hirama et al., 1992; Gao et aL,1991). This mode of instability can be circumvented by increasing the solids inventory orstandpipe height, or, alternatively, by uncoupling the riser and downcomer, e.g. by utilizing ascrew feeder as solids feeding system. Such a critical condition is caused by an inappropriatepressure balance between the riser and downcomer. Such an instability again results from theinteraction between auxiliary equipment, in this case the solids return and/or feed device, and theconveyor. Again, the instability needs to be distinguished from classical choking. We call themequipment-limited modes of choking, Type B or “Blower-/standpipe-induced choking”.The third use of the term choking relates to solids refluxing at the wall of an upward flowcolumn causing accumulation of particles in the lower regions . Chang and Louge (1992) calledthis third mode “incipient choking”. However, we introduce the term “Accumulative choking” or,Type A choking, to give a better description of the flow pattern transition at this point. Matsen(1982) attributed this mode of choking to an abrupt change in voidage. Such a stepwise changein voidage or pressure drop was also adopted as the mechanism of choking by Yerushalmi andCankurt (1979), Satija et al. (1985), Conrad (1986), Brereton (1987), Rhodes (1989) and Day etal. (1990). The stepwise change in average bed voidage can be thither attributed to formation ofa dense bed at the bottom of the conveyor. From the viewpoint of solids conveying, this point hasbeen referred to as the minimum transport velocity of the transport line (Thomas, 1962; Matsen,1982), because the solids circulation rate at this point is the maximum attainable at a given gasvelocity without accumulation. The solids circulation rate at this point therefore appears to be the1 Note that the accumulation must occur at the bottom of the riser for this type of choking to occur. The increasein solids concentration at the top of a riser with a constricted exit (e.g. Brereton and Grace, 1994) penetrates alimited distance downward and does not constitute choking.149same as the saturation carrying capacity (Zenz and Weil, 1958; Wen and Chen, 1982; Matsen,1982; Li et al., 1992).Capes and Nakamura (1973) defined choking as the condition under which internal solidscirculation begins, with solids moving downward at the pipe wall and upward in the central core.This internal solids circulation may be related to the formation of particle clusters or streamers,but is not necessarily accompanied by a sudden increase in solids concentration or pressure drop(Leung, 1980; Matsumoto et aL, 1987; Drahos et aL, 1988; Rhodes, 1989). Instead, it has beenfound that internal solids circulation occurs right after the gas velocity is reduced to reach theminimum pressure drop point (see Figure 6.1) (Leung, 1980; Matsumoto et aL, 1987; Drahos etal., 1988). This velocity is, in turn, analogous to the minimum pressure drop point identffied inhorizontal transport lines, which coincides with the saltation velocity where particles drop out ofthe suspension and slide along the bottom of the pipe (Thomas, 1962; Matsumoto et al., 1975;Wirth and Molerus, 1986; Geldart and Ling, 1992). For vertical flow, the velocitiescorresponding to both the minimum pressure drop and the onset of clustering appear to besomewhat higher than the velocity when particles start to accumulate at the riser bottom (Bi andFan, 1991).Other definitions of choking have also been proposed. For example, Briens andBergougnou (1986) assumed that choking occurs when the annular region at which particles flowdownward grows to occupy 25% of the total pipe cross-sectional area, i.e. rc/R=O. 866. Thechoice of 25% is arbitrary, especially when one considers that the area occupied by the annularregion varies with axial position. This choking condition also does not correspond to any unstablecondition, given that there is evidence that a circulating fluidized bed can operate in a stablemanner with the annular solids dowuflow region occupying as much as 50% of the cross-sectionalarea (Rhodes, 1989; Horio et aL, 1988; Bader et al., 1989).150It is unlikely that such differing definitions could give consistent results. As shown below,this is indeed the case when one attempts to correlate choking data based on data from authorswho have utilized different criteria and definitions to define the choking condition.6.2.2. Choking classificationAs pointed out by Capes and Nakamura (1973), choking is not a single clear-cutphenomenon; instead the term is used to denote a whole range of instabilities. The discrepancy inchoking definitions and determinations must play an important role in the scatter of data and lackof clarity regarding choking (Yerushalmi and Cankurt, 1979; Yang, 1983; Conrad, 1986; Rhodes,1990). However, most investigators have proposed new correlations to fit literature data based ondifferent and conflicting definitions. Punwani et al. (1976) compared various choking velocitycorrelations with available experimental data and found that the Yousfi and Gnu (1974) equationgave the best prediction of the experimental data of Zenz (1949), Lewis et aL (1949) andOrmiston (1969), while seriously underestimating the data of Capes and Nakamura (1973). Thecorrelations of Yang (1975) and Punwani et al. (1976) most accurately predict the data of Capesand Nakamura (1973), but overestimate other data. A comparison by Chong and Leung (1986)showed that the Yousfi and Gau (1974) equation fitted the choking data better for Geldart GroupA and B particles, while the Yang (1975, 1983) equation was recommended for Group Dparticles. Aware of the differences for different kinds of particles, Day et al. (1990) treated theslip factor in their model equations in such a way that different correlations were evaluated fordifferent particle categories according to a particle mean size. However, no one has evaluated theequations based on the differences in the definitions of what constitutes choking and the differingassumptions.Table 6.1 lists all available choking definitions found in the open literature andcorresponding regime transition definitions obtained in gas-solids vertical upflow systems for the151purpose of comparison and classification. All the definitions can be classified into the threecategories described above, depending on the phenomena observed and definitions of chokingemployed. Type C or classical choking corresponds to the occurrence of slug flow and inherentsevere instability. Type B or blower-/standpipe-induced choking corresponds to a marginalinstability condlition in which the bed collapses, either because an inadequate pressure balance isbuilt up in the whole unit so that solids cannot be fed to the riser at the prescribed rate, or becausethe blower can no longer provide the pressure drop required to support the materiaL Type A oraccumulative choking is characterized by the appearance of a dense bed at the bottom of the riser,stepwise changes in bed voidage and pressure drop, and solids dowuflow at the wall.The most popular choking correlations of Leung et al. (1971), Yousfl and Gau (1974),Yang (1975, 1983), Punwani et a!. (1976), Matsen (1982), as well as the recent equation of Biand Fan (1991), all listed in Table 6.2, are compared with the literature data in Table 6.3.Calculated root mean square relative deviations (RMS) in the predicted choking velocities aregiven in Table 6.4. It can be seen that for the Type C choking velocity, the Yousfl and Gaucorrelation, evaluated from the experimental data of Lewis et aL (1949), Zenz (1949) andOrmiston (1969) as well as their own data, gives the best prediction. All other equationsoverestimate the experimental data. All of the data used to derive this condition corresponded totransition to slug flow; the other definitions of choking should all give higher values.The Type B choking velocity, mainly resulting from the restriction of the pressure balancein the whole system, is found to be somewhat higher than the prediction of the Yousfl and Gau(1974) equation, but lower than the prediction of Bi and Fan (1991), Yang (1975, 1983) andPunwani et aL (1976). None of these equations gives good predictions of this transition velocity,as can be seen in Table 6.4. It appears that the Type B choking condition generally occursbetween the Type C or classical choking and Type A or accumulative choking conditions.Deviations are generally higher, not surprising in view of the fact that blower characteristics and152Table 6.1. Summary of choking definitions(a). Classical (Type C) choking definitionAuthor [ DefinitionZenz (1949) slugging occurs to such extent that stable operation ceasesLewis et al. (1949) termination of steady operation due to slug formationOrmiston (1965) bed collapses into slugging stateYousfi and Gau (1974) solids slugs extend over the entire pipe cross-sectionDrahos et al. (1988) formation of slugging dense bedMok et al. (1989) transport line is pluggedBi et al. (1991) slugging occurs to such extent that stable operation ceasesChang and Louge loud banging noises and shaking of the riser resulting from the(1992) passage of slugs(b). Blower-/standpipe-induced (Type B) choking definitionsAuthor DefinitionKnowlton and solids flux can no longer be maintained at the prescribed rateBachovchin (1976)Bandrowski et aL system becomes unstable due to the gas blower being unable to(1981) support the transport lineMatsumoto et al. (1982) substantial transport of solids becomes impossible because the gasblower cannot support the transport lineTakeuchi et aL (1986) solids flux can no longer be maintained at the prescribed rateBai et al. (1987) solids flux can no longer be maintained at the prescribed rateBader et al.(1988) steady operation at the given solids flux becomes impossibleSchnitzlein and maximum solids flux attainable at a given gas velocityWeinstein (1988)Gao et al. (1991) same as Schnitzlein and WeinsteinHorio et al. (1992) same as Schnitzlein and WeinsteinFlirama et al. (1992) solids flux can no longer be maintained at the prescribed rate153(c). Accumulative (Type A) choking definitionsAuthor DefinitionYenishalmi and Cankurt stepwise change in pressure drop(1979)Matsen (1982) stepwise change in bed voidage due to the formation of clusters ofparticlesYang (1983) slight decrease of transport velocity at the same solids rate willincrease the pressure drop in the transport line exponentially, whichprovides a demarcation between the dilute-phase pneumatictransport and the fast fluidization regimeSatija et a!. (1985) step change in bed voidageChong and Leung stepwise transition from dilute-phase uniform suspension to dense-(1986) phase non-uniform suspensionTakeuchi et aL (1986) difference in density between top and bottom ofthe column startsto appearConrad (1986) termination ofuniform suspension flowBrereton (1987) solids start to accumulate in the bottom of the riserDrahos et aL (1988) particles start to accumulate at the bottom of the column due to theimbalance between the solids feed rate and the transport capacityof the gasRhodes (1989) sudden increase in solids concentration and amplitude ofpressurefluctuationDay et al. (1990) axial voidage variation appears at the inlet ofthe columnChang and Louge suspension collapse and a denser region starts to form at the(1992) bottom ofthe riserLi et aL (1992) sudden change in flow structure from dilute-phase to dense-phasetransport; the velocity corresponds to the saturation carryingcapacity ofthe system154Table 6.2. Choking velocity correlations used in the comparison155Table 6.3. Summary of experimental studies on choking velocity(a). Classical (Type C) choking velocityReference Solids d p D H0 type ofim kg/rn3 mm m feederZenz (1949) salt 168 2098 44.5 1.2 hopperGB 587 2483 44.5sand 930 2643 44.5rape seed 1676 1089 44.5Lewis et al. GB 40 2483 31.8 3.0 hopper(1949) GB 100 2483 31.8GB 280 2483 31.8Ormiston (1969) sand 120 2659 25.4 5.5 hoppersand 151 2659 25.4sand 225 2659 25.4sand 265 2659 25.4Yousfi and Gau sand 118 2470 50 6.0 fluidized bed(1974) sand 143 2470 50sand 183 2470 50PE 290 1060 50Drahos et al. phosphate 120 2550 55 2.23 screw feeder(1988) phosphate 200 2550 55MoketaL(1989) sand 210 2620 20 9.0 fluidizedbedBietaL (1991) PE 325 660 102 6.4 standpipe,Dd/D=lt GB - glass beads; PE - polyethylene156(b). Blower-/standpipe-induced (Type B) choking velocityReference Solids d p D H0 type ofjim kg/rn3 mm m feederKnowlton and siderite 157 2384 76.2 15.0 standpipeBachovchin lignite 363 747 76.2(1976)Bandrowski et a!. sand 400 2500 20 hopper(1981)Matsumoto et aL GB 1030 2500 20 5.6 hopper(1987) GB 1960 2500 20GB 2970 2500 20Takeuchietal. FCC 57 1050 100 5.5 standpipe,(1986) Dd/D=2.0Bai et aL (1987) FCC 94 1646 186 8.4 standpipe,silicagel 187 703 186 Dd/D=1.6silicagel 603 790 186silicagel 1041 1303 186coal 939 2200 186sand 78 2660 186sand 652 2660 186Bader et al. Catalyst 76 1714 305 12.2 standpipe,(1988) Dd/D1Schnitzlein and FCC 59 1450 152 8.4 standpipe,Weinstein (1988) Dd/D=2.2Gao et aL (1991) FCC 62 1020 90 8.4 standpipe,Catalyst 82 1780 90 DdLD=2.2Horio et a!. FCC 60 1000 200 1.6 standpipe,(1992) Sand 106 2600 200 1.6 Dd/D=2.0ITirama et al. FCC 54 750 100 5.5 standpipe,(1992) FCC 69 930 100 DdID=2.0157(c). Accumulative (Type A) choking velocityReference Solids d1, D H0 type ofurn kg/rn3 mm m feederYerushalmi and FCC 49 1070 152 8.5 standpipeCankurt (1979) HFZ-20 49 1450 152Chenetal.(1980) ironore 105 4510 90 9.0 standpipealumina 81 3090 90iron ore 56 3050 90FCC 58 1780 90Satijaetal. sand 155 2446 102 6.5 standpipe(1985) sand 245 2446 102Takeuchi et al. FCC 57 1050 100 5.5 standpipe(1986)Bi(1988) FCC 48 1450 186 8.4 standpipesand 31 2650 186silicagel 140 760 186silicagel 280 760 186Drahos et al. phosphate 120 2550 55 2.23 screw(1988) feederMok et al. (1989) sand 210 2620 20 9.0 fluidizedbedBietaL (1991) PE 325 660 102 6.5 standpipeChang and Louge plastic grit 234 1440 200 7.0 standpipe(1992) steel grit 67 7400 200 7.0158Table 6.4. Comparison between experimental data and choking predictions(a). Classical (Type C) choking velocitydata source No. of RMS relative deviation of experimental datattdatait 2 3 r4 5 6Zenz (1949) 18 0.768 5.625 0.298 0.926 0.866 1.22Lewis et aL (1949) 21 0.385 1.277 0.083 0.264 0.262 0.768Ormiston (1969) 12 0.294 1.808 0.098 0.244 0.193 1.174Drahos et al. (1988) 13 0.323 0.974 0.063 0.224 0.211 0.299Moketal.(1989) 6 0.236 1.635 0.104 0.117 0.211 0.299BietaL (1991) 4 0.460 0.932 0.053 0.216 0.058 0.166total 74 0.470 3.126 0.160 0.490 ] 0.456 0.905t 1, 2, 3, 4, 5, 6 correspond to equations ito 6 in Table 6.2.11Rivis = ZIUch,ctd 1ch,exp2 1/2Ch,exp159(b). Blower-/standpipe-induced (Type B) choking velocitydata source No. of RMS relative deviation of experimental data• data1 2 3 4 5 6Knowlton and 24 0.660 0.583 0.872 0.647 0.634 0.602Bachovchin(1976)Bandrowski et aL 2 0.536 1.626 0.711 0.285 0.360 0.090(1981)Matsumoto et al. 12 0.082 3.73 1 0.542 0.126 0.102 0.360(1982)TakeuchietaL 6 0.437 0.798 0.063 0.633 0.277 0.139(1986)Bai et al. (1987) 38 0.446 2.5 12 0.265 0.499 0.406 0.570Bader et al. (1988) 3 0.494 0.805 0.597 0.563 0.369 0.090Schnitzlein and 6 0.447 0.8 14 0.392 0.252 0.08 1 0.332Weinstein (1988)Gao et aL (1991) 62 0.427 0.478 0.244 0.362 0.266 0.171Hono et aL (1992) 17 0.539 0.5 19 0.459 0.485 0.372 0.292Hirama et al. 4 0.434 0.811 0.472 1.03 0.861 0.23 1(1992)total 174 0.457 1.563 0.436 0.475 0.380 0.388160(c). Accumulative (Type A) choking velocitydata source No. of RMS relative deviation of experimental datadata1 2 3 4 5 6Yerushalmi and 5 0.818 0.874 0.230 0.226 0.235 0.112Cankurt (1979)Chen et aL (1980) 12 0.755 0.555 0.472 0.378 0.245 0.165Satija et aL (1985) 4 0.524 0.523 0.430 0.207 0.285 0.291TakeuchietaL 7 0.581 0.838 0.244 0.258 0.178 0.118(1986)Drahos et al. (1988) 5 0.595 0.058 0.348 0.35 1 0.410 0.094Bi(1988) 15 0.571 0.638 0.533 0.144 0.304 0.488Mok et aL (1989) 9 0.440 0.733 0.428 0.369 0.406 0.299Biet al. (1991) 4 0.540 0.556 0.192 0.050 0.174 0.267ChangandLouge 10 0.578 0.371 0.444 0.316 0.362 0.200(1992)total 71 0.576 j 0.439 0.390 0.266 ] 0.292 0.240external standpipe conditions, not included in the correlations, played important roles for thesedata.The Type A choking velocity is sometimes also called the minimum transport velocity ofthe conveyor. The solids circulation rate at this point corresponds to the saturation carryingcapacity (Zenz and Weil, 1958; Wen and Chen, 1982; Sciazko et al., 1991). Table 6.4(c) showsthat the Yang (1975, 1983) equation gives satisfactory agreement with the literature data, whilethe Bi and Fan (1991) equation, which was based on most of these data, predicts these data mostaccurately. The Yousfi and Gau (1974) equation is found to underpredict the data.161To summarize, three distinct types of choking initiation mechanisms have been identified.The lowest (Type C or classical) results in severe slugging in the transport line; the second (TypeB or blower-/standpipe-induced) depicts an instability resulting from gas blower-conveyorinteraction anchor solids feeder-conveyor interaction in the system; the third (Type A oraccumulative) denotes a transition from a condition when all particles are traveling upwards withlittle or no axial variation to a mode where there is solids downflow at the wall and accumulationof a dense phase at the bottom. For practical applications, the most undesirable condition in acommercial system is the instability of operation. It is therefore practical to consider the classicalchoking as the lowest critical choking transition, while Type B choking may occur first whenthere are blower or standpipe limitations. Accumulative choking, corresponding to the onset of adense region at the riser bottom, should not be confused with the other two transitions whichrepresent operational limitations. With decreasing gas velocity, Type A choking occurs first,followed by Type B (when applicable due to blower or feeder limitations) or otherwise by Type Cchoking for slugging systems.6.3. Choking PredictionsMany equations have been developed to predict the choking velocity based on differentassumptions (Marcus et al., 1990). The correlation of Leung et al. (1971) was obtained byassuming that at choking the slip velocity between gas and particles is equal to the free-fall orterminal velocity of single particles, and that the choking voidage is equal to 0.97. In the equationof Yang (1975) the slip velocity was also assumed to equal the terminal velocity of singleparticles, while the solids-to-tube wall ffiction factor was taken as a constant (0.01, estimatedfrom experimental data of Hariu and Moistad, 1949). The choking data of Capes and Nakamura(1973) were used to validate the modeL However, it was found that another constant ffictionfactor, 0.04, had to be used to fit other choking data. To correlate other literature data, Yang(1983) later modified the friction factor to be dependent on the ratio of gas and solids densities;162Punwani et al. (1976), 011 the other hand, modified the choking friction factor of Yang (1975) byincluding a gas density effect to fit the high pressure choking data of Knowlton and Bachovchin(1976). The equations of Yousfl and Gait (1974) and Knowlton and Bachovchin (1976) arepurely empirical. The former was derived from the experimental data of Zeiiz (1949), Lewis et al.(1949), Ormiston (1969) and Yousfi and Gau (1974) in which choking was defined by the slugflow condition; the latter was obtained by correlating the only high pressure choking data, i.e.those ofKnowlton and Bachovchin (1976), in which the riser was coupled with a downcomer andthe particles were of wide size distributions.No single equation can be used to predict all three types of choking velocities. Hence,separate approaches for predicting the onset of each type of choking are required.6.3.1. Accumulative choking velocity, UCAThe minimum transport velocity, which corresponds to the accumulative choking velocity,UCA, is an important parameter for pneumatic transport and for particle entrainment in thefreeboard. From the pneumatic transport point of view, it sets the minimum superficial gasvelocity required to fully suspend a given flux of solid particles without accumulation in the wholetransport line. UCA is related to the solids elutriation rate from the top of the bed. A number ofcorrelations have been proposed to calculate the entrainment from fluidized beds operated atrelatively low gas velocities (U<1 mis) (e.g. see Wen and Chen, 1982; Geldart, 1986) or atsomewhat higher gas velocities (U<4 mis) (e.g. Zenz and Weil, 1958; Sciazko et al., 1991).However, there are no correlations which can be reliably extended to the high velocity range.When the gas velocity is reduced to below the accumulative choking point, some particlescan no longer be fully suspended. The dilute-phase transport therefore collapses and a dense bedforms at the bottom of the riser. It is important to understand why the dilute suspension to163collapse at this transition point. Yang (1975) suggested that the solids-wall fiction approaches aconstant (0.01) at this transition point based on the data of Hariu and Moistad (1949). Matsen(1982) attributed the collapse to the formation of particle clusters. Louge et al. (1991), on theother hand, postulated that it occurs when the particle weight overcomes gas shear in a globalmomentum balance. Day et al. (1990) modeled this choking process as corresponding to no axialvoidage variation at the inlet of the riser, reflecting the absence of particle accumulation at thebottom of the riser when the gas velocity exceeds the accumulative choking velocity. Until themechanism of suspension collapse is understood, it is recommended that the Yang (1975, 1983)and Bi and Fan (1991) equations, both of which are based on the accumulative choking definitionandlor experimental data, be used to predict this velocity.6.3.2. Blower-/standpipe-induced choking velocity, UCB6.3.2.1. Conveyor-blower interactionCentriffigal blowers are characterized by reducing volumetric delivery with increasingdelivery pressure. For a blower of given power, there is a maximum gas velocity correspondingto a given pressure head (Wen and Galli, 1971). The typical pressure drop versus gas flow ratecharacteristic curves are generally provided by the supplier for a given gas blower. The criticalcondition can thus be determined as indicated in Figure 6.1 (Doig and Roper, 1963; Leung et al.,1971; Bandrowski and Kaczmarzyk, 1981; Matsumoto et al., 1982; Dry and La Nauze, 1990).6.3.2.2. Conveyor-feeder interactionIn a conveyor accompanied by a solids return device, such as a standpipe in a circulatingfluidized bed, a pressure balance is reached between the riser and the standpipe when the particlesin the downcomer are fluidized (Kwauk et al., 1986; Yang, 1989; Rhodes and Geldart, 1987).Key components of a typical CFB unit are the riser, a downcomer, a solids control valve, and a164gas-solids separator/cyclone (see Figure 6.2). For a given solids inventory, solids circulation rateand superficial gas velocity, the pressure head at the bottom of the riser, r, and at the bottom ofthe downcomer, d, are each predetermined when the unit is under steady operation. Thepressure drop across the solids control valve, AP, is thus adjusted to be equal to dr•However, when the solids control valve has been completely opened, a further increase in r Oilreducing superficial gas velocity makes smaller than the fully open valve pressure drop,APo. The system then cannot remain at steady state at the prescribed solids circulation rate.Such a process is illustrated in Figure 6.3. The solid line represents the characteristic curve of r•The dashed lines represent the maximum available pressure head from the downcomer, Pd-zXPVO.As gas velocity is reduced toward UCB, the pressure drop across the control valve is adjusted tomeet the requirement for pressure balance in the whole ioop, i.e., v1?d4r. However, beyond aH0LELoFigure 6.2. A typical circulating fluidized bed system. L0 is the height of the dense bed in thedowncomer when all the particles are stored there.165certain point, the pressure drop across the solids control valve cannot be fhrther reduced, eitherbecause the valve has been completely opened or because the aeration air no longer has anyeffect. In this case, either the gas velocity in the riser needs to be raised to maintain the bed understeady operation at the prescribed solids circulation rate or the solids circulation rate sharplydecreases while the gas velocity remains the same. The former corresponds to the maximumsolids circulation rate identified by Schnitzlein and Weinstein (1988), Gao et al. (1991) and Horioet al. (1992), while the latter represents the critical condition identified by Takeuchi et aL (1986)and Bai et aL (1987). Such an instability analysis is carried out next and compared with theexperimental data ofHirama et aL (1992) and Gao et aL (1991).zICl)U)U)0Figure 6.3. Operational instability due to imbalance of pressures at the base of riser anddowncomer.(a) Model equationsIn a typical circulating fluidized bed shown in Figure 6.2, if the pressure at the outlet ofthe gas-solids separator/cyclone is taken as zero, the pressure head at the bottom of the riser, r,and at the bottom of the downcomer, d, can be calculated by:F,. = (6.1)U, rn/s166=p(i— mf )gL0 — [p(l— e)gH + p(i— E)gLJ +—‘ (6.2)where H0 is the riser height and LEis the equivalent length of the exit (between riser and cyclone)section, with e and E being the corresponding voidages. The first term in equation (6.1) comesfrom the pressure drop in the riser, and the rest from the pressure drops across the cyclone (APe),that due to solids to wall ffiction (APfS) and solids acceleration (APac). In equation (6.2), thepressure head at the bottom of the downcomer, d’ is obtained by first subtracting solids holdupsin the riser and the exit pipe sections from the total solids inventory (first term), and then addingthe pressure drops due to solids-to-wall ffiction (-APfS’) and solids acceleration (APac’).In the riser, the pressure drops due to solids acceleration and ffiction are not significant atlow solids circulation rates but need to be considered at high solids circulation rates. As a firstapproximation, APac can be estimated by:G2AP = 0.5—- (6.3)ppSeveral correlations are available for particle-wall ffiction (see Leung, 1980). In the presentanalysis, the Kono and Saito (1969) equation is adopted:APft = 0.057g(H+L) (6.4)APac’ and /XPfs, can be estimated from similar equations.The pressure drop across the cyclone can be approximated by:AP =-PgU2 (6.5)where c, the ffiction coefficient, is chosen as 50 (Rhodes and Geldart, 1987).167Assuming that the slip velocity is equal to the particle terminal velocity in the exit section,the voidage above the riser exit can be estimated by:= G (6.6)p(U—U)This equation has been justified in laboratory-scale CFB risers with solids circulation rate up to600 kg!m2s(Kunii and Levenspiel, 1990). In commercial risers, the slip velocity could be higherthan the terminal velocity of single particles (Matsen, 1976). Appropriate estimation of the slipvelocity, however, has not been provided. Since U is much higher than Ut, the small differencebetween Ut and the actual slip velocity should not cause significant error in the calculation.The difference between r and d is the pressure drop available for the solids flow controlvalve, i.e.:=(6.7)For slide valves and similar valves where the solids flow is controlled by changing the openingarea, the pressure drop across the control valve and solids flux can be estimated (Jones andDavidson, 1965; Rudolph et al., 1991) as:= 1 G8 (6.8)2CPp(lEmj) DID8where Cd is a constant ranging from 0.69 to 0.8, D is the equivalent diameter of the open area ofthe control valve and D is the inside diameter of the discharge pipe. When the valve is filly op en,tP is designated L\P.Under steady state operation, AP is adjusted to be equal to AP0 by varying the open areaof the control valve (or the aeration flow for non-mechanical valves) to provide a given solidsfeed rate at a given superficial gas velocity. When the control valve has been completely open,the system cannot remain at steady state at the prescribed solids circulation rate unless AP,0<AP.168The situation is illustrated in Figure 6.3. The mean bed voidage under the critical condition canbe obtained by combining equations (6.1), (6.2), (6.7) with the criterion AP0=A , at the criticalpoint to give:(1—Emf)LO _(1_EE)LE(__)2— (AI +AI +APfi +A—A1’+A))1 —p1,g69-- H0 1+(D/Dd)2} ( . )After substituting(1-SE), M AP, APft, AP, AP’ and APfi’ using equations (6.3), (6.4),(6.5), (6.6) and (6.8), there are three unknowns, i.e. , G and UCB. Another relationshipbetween the three unknowns is needed to determine the Type B choking velocity, UCB, for agiven solids circulation rate, (is, or the critical solids circulation rate for a given superficial gasvelocity. Several approaches have been explored to relate average bed voidage, superficial gasvelocity and solids circulation rate. Kato et al. (1989) and Zhang et al. (1990) gave correlationsbased on their own experimental data. Such correlations, however, tend to be unit-dependent. Aone-dimensional diflüsion model was proposed by Kwauk et al. (1986). Core-annular modelswere proposed by Bai et al. (1988) and Senior and Brereton (1992). However, several modelparameters need to be fitted to use these models due to the lack of data.Another kind of model (Rhodes and Geldart, 1987; Yang, 1988; Bolton and Davidson,1988; Kunii and Levenspiel, 1990) extends particle entrainment models for conventional fluidizedbeds to circulating fluidized beds. The only parameter needed with this approach is the decayconstant, a. Since it is much simpler, this approach is adopted here.The one-dimensional entrainment model of Kunii and Levenspiel (1990) is adopted in thiscalculation. The bed average voidage is expressed as:1—s = — 5d +1— — (1— ‘---)(s— d) (6.10)aI-J H0where, Hd is the height of the bottom dense region, given by:169Hd = H0_in(E6d) (6.11)a EEEwhere , the saturated voidage far from the exit of the column, can be approximated by:*6 = 1— (6.12)p(U-U)Substituting equation (6.11) into equation (6.10), we obtain:1—e = (1_Ed)+_F(EE_Ed)_(e*_ed)1n[6:) (6.13)aH[The saturation carrying capacity, G*, is estimated using the correlation of Bi and Fan(1991) (equation 6 in Table 6.2). The voidage in the bottom dense region, Ed, ranges from about0.75 to 0.85. For fine particle systems, the equation of King (1989) [equation (5.9)] is used forestimation. The decay constant, a, is an important parameter. In bubbling fluidized beds, Wenand Chen (1982) suggested a value of 4 rn’, while a range of 2 to 6 rn’ has generally beenreported in the literature. Kunii and Levenspiel (1990) collected a wide range of literature datafor high velocity fluidized beds and found that a varies from 0.3 to 2.5 ur’. The value tends to bea function ofparticle properties, but is relatively insensitive to column diameter and superficial gasvelocity at high gas velocities. Rhodes and Geldart (1987) found that a = 0.5 nr1 best fitted theirexperimental data obtained in a riser of 8 m height and 0.15 m diameter using fine aluminaparticles at gas velocities higher than Use. A similar value, a = 0.47 rn1-, was suggested by Boltonand Davidson (1988) for a 0.15 rn diameter column and FCC particles. For fine particle systems,a value ofa0.5 m4 seems reasonable and is used in the present model.Once a relationship among bed average voidage, superficial gas velocity and solidscirculation rate has been established, the critical point at which stable operation of the circulatingfluidized bed system becomes impossible can be predicted by following an iterative procedure:For a given solids circulation rate, a critical gas velocity is first assumed. Bed average voidage is170then calculated from equations (6.9) and (6.13), separately. if the two values differ, a new gasvelocity is assumed and the calculation repeated until 6 calculated from the two equations differby less than a pre-set error. This gas velocity is then taken as the critical velocity correspondingto a given solids circulation rate. For a given superficial gas velocity, the critical solids circulationrate can be estimated in a similar way. Where both gas velocity and solids circulation rate havebeen determined experimentally at the critical point, s can be predicted directly from equation(6.9), together with equations (6.3) to (6.6) and (6.8).(b) Model verification and predictionModel predictions are first tested against the data of Hirama et aL (1992) obtained underso-called critical conditions. In their tests, the lowest possible superficial gas velocities (criticalvelocities) for proper operation of their system were determined experimentally for several solidscirculation rates. Corresponding mean solids holdups were also measured at these criticalconditions. To compare, the mean solids holdup at this critical point is calculated from thepredictive model described above. Column geometry parameters and operating conditions appearin Table 6.5. The maximum open area of the valve is assumed to be equal to the area of thedischarge pipe. Cd=O.7Sand LE=l.O m are chosen in the simulation. The mean solids holdups atthese critical points can then be readily calculated using equations (6.1) through (6.9).Table 6.5 shows the results. There is excellent agreement between predicted andmeasured bed mean voidages for the solids circulation rates tested, i.e. 10 and 80 kg!m2s. Thissuggests that the so-called critical conditions determined experimentally by Hirama et al. (1992)result from the instability of the whole unit due to pressure imbalance.The model is further validated through comparison with the data of Gao et al. (1991),where the static bed height in the downcomer is specified. Gao et al. determined the critical171velocities following the procedure of Schnitzlein and Weinstein (1988) in which a maximum solidscirculation is reached at a given gas velocity when the solids control valve is completely opened.Bed structure parameters and particle properties are listed in Table 6.6. However, the meansolids holdups in the riser were not reported. Hence, equations (6.10) to (6.13) are used toestimate . Figures 6.4 to 6.6 compare model predictions with Cd again taken as 0.75 and LEtaken as 1 m and experimental data. Good agreement is obtained for all types ofparticles.Table 6.5. Comparison of experimental data of Hirama et aL (1992) with modelpredictionsD=lOOmm Dp200mm Dç=SOmmH0=5.5mParticles L0 G UCB CB, exp 6CB, calm kg/m2s misHA54 1.1 10 1.17 0.917 0.922d, = 54 im 2.7 10 0.75 0.783 0.806p1, = 750 kg/rn3FCC69 1.1 80 2.94 0.934 0.93 1d1, = 69 tm 2.7 80 2.19 0.835 0.813p=93Okg/mTable 6.6. Bed parameters and particle properties used by Gao et al. (1991)D=90mm Dd=200mm Dç5OmmH0 = 8.4 mParticles Pb d1, L0kg/rn3 kg/rn3 im mFCC 1020 529 62 1.93,3.10,4.04Catalyst 1780 1049 82 1.53,2.23,2.64Silica gel 760 465 205 1.80,2.66,3.59172200160U)E 120C804008060U8, rn/s6Figure 6.4. Comparison of model predictions (shown by the lines) with the experimental data ofGao et al. (1990) for FCC particles.140120100I40200Uc5, ni/sFigure 6.5. Comparison of model predictions (shown by the lines) with the experimental data ofGao et al. (1990) for catalyst particles.0 1 2 3 41 2 3 4173140L01.8m L=2.66m Lo=a5gm120 -100LI’60 ‘02345 6U, rn/sFigure 6.6. Comparison of model predictions (shown by the lines) with the experimental data ofGao et al. (1990) for silica gel particles.From the foregoing analysis, it is clear that the maximum solids circulation ratecorresponding to the critical operating condition in a CFB unit is strongly affected by the unitgeometry. Total solids inventory also affects the critical operating conditions. In light of thepressure balance between the riser and the downcomer, more particles stay in the riser when totalsolids inventory is increased, as reflected in equation (6.9). To maintain a higher riser solidsholdup for a given gas velocity, Gs must then be increased, as indicated by equations (6.11) to(6.13). Equation (6.9) shows that the standpipe-to-riser diameter ratio, the ratio of the static bedheight in the standpipe to the riser height, and the opening of the solids control valve all play veryimportant roles.For a typical laboratory-scale circulating fluidized bed using typical FCC particles, Figures6.7 to 6.10 give a set of model predictions showing the influence of unit geometry and total solidsinventory to the maximum solids circulation rate before instability occurs. For comparison, theType A choking velocity from the Bi and Fan (1991) equation and the Type C choking velocityfrom the Yousfi and Gau (1974) equation, which was found by Teo and Leung (1984) to be themost accurate correlation for Group A particles, are also plotted. As expected, the maximum174solids circulation rate increases with increasing solids inventory (Figure 6.7), with increasingstandpipe diameter (Figure 6.8) or with increasing open area of solids control valve (Figure 6.9).These figures suggest that the maximum solids circulation rate first increases rapidly withincreasing gas velocity due to the significant gain in the saturation carrying capacity of the gasphase. However, beyond a certain gas velocity, the increase of solids circulation rate slows down,as the solids circulation starts to be restricted by the solids feeding system. Pressure loss due toparticle-wall ffiction also reduces the available pressure head for particle transportation.Eventually, the solids circulation curve is seen to merge with the Type A choking curve. Thesolids feeding system is thus more important when the unit is operated at a high gas velocitywhere increasing U can only slightly increase solids circulation because the maximum (I is nolonger sensitive to the gas velocity. To achieve a higher solids circulation rate, a better measure isto increase the pressure available for solids feeding by adding more particles and/or reduce thepressure loss through the solids control valve and the gas-solids separator.U, rn/sFigure 6.7. Predicted effect of solids inventory on the maximum solids circulation rate for p,=1500 kg/m3,d=60 p,m, I1=l0 m, L0=5 m, D=Dd=D=DV=0.15 m, Cd=O.75 LE=lin. Dotted line is the Type A choking velocity predicted by Bi and Fan (1991);dashed line is Type C choking velocity predicted by Yousfi and Gau (1974).Cl)2,0001.0005002001005020100 2 3 4 5 6 7 8 9 101752,0001,000500Coa)200-( 100502010U, rn/sFigure 6.8. Predicted effect of standpipe size on the solids circulation rate for constant L0 andH0. Conditions and broken curves as in Figure 6.7.U,m/sFigure 6.9. Predicted effect of solids control valve on. the solids circulation rate for constant L0and H0. Conditions and broken curves as in Figure 6.7.Figure 6.9 shows that solids circulation rate is affected less by the solids control device atlow solids circulation rates, while the control valve provides an important regulation function athigh (1g. From the proper regulation point of view, the open ratio of the valve needs to be kept0 I 2 3 4 5 6 7 8 9 102,0001,000600Cl)C) 200(5 1005020100 1 2 3 4 5 6 7 10176under 50% to have a significant control capability at low (i5. The maximum available solidscirculation rate is then lower than expected with the control valve fully opened.Figure 6.10 indicates the effect of system pressure on the critical choking velocity whereany variation of decay constant and dense phase voidage with pressure has been neglected. Thecritical velocity is predicted to decrease with increasing pressure, in agreement with theexperimental results of Knowlton and Bachovchin (1976). Such a decrease is mainly due to theincrease of saturated entrainment rate with increasing pressure as observed by Chan andKnowlton (1984). A more accurate evaluation of the influence of system pressure requiresfurther information on the effects ofpressure on the decay constant and dense phase voidage.Figure 6.10. Effect ofpressure on the solids circulation rate. Conditions as in Figure 6.7.It should be noted that the accuracy of the model depends on the accuracy of theequations adopted, i.e., equations (6.3) to (6.6) and equations (6.10) to (6.13), some of whichmay not hold in larger scale commercial systems. More accurate correlations can be incorporatedinto the model as they become available in the future.2,0001,000U) 5000) 2001005020100 2 3 4 5 6 7 8 9U, rn/s101776.3.3. Classical choking velocity,Classical choking occurs as the gas velocity is reduced when slug flow commences to suchan extent that stable operation as a dilute suspension becomes impossible (Zenz 1949). In a batchsystem, bubble or slug behaviour is dependent on the superficial gas velocity. In a continuoussystem, on the other hand, bubble or slug behaviour depends on the relative motion between gasand solids phase rather than the superficial gas velocity. The apparent relative velocity atchoking, often called a “slip velocity”, is— (6.14)p(l—In a fluidized bed with increasing gas flow, the most unstable condition should occur around thevelocity U which corresponds to the maximum standard deviation of pressure fluctuations.Above the Type A choking velocity, UCA, bed particles become transportable, and the absence ofa dense bed prevents the formation of gas bubbles.Reported classical choking velocity data of Zenz (1949), Lewis et al. (1949), Ormiston(1969), Yousfl and Gau (1974), Mok et aL (1989) and Bi et al. (1991) are plotted as Re5cversus Ar in Figure 6.11. For comparison, Reynolds numbers corresponding to U [equation(3.3)], Use [=UCA-G8CA6CA/p(l-CA)] [equation (5.3)] and the terminal velocity of singleparticles (Grace, 1986) are also plotted. It is seen that most experimental Type C choking data liebetween Re and Rese. Uscc usually lies between U to Use depending on particle properties andunit structure. Until more experimental data are generated and the classical choking mechanism ismore clearly understood, the Yousfl and Gau (1974) equation, equation 3 in Table 6.2 can beused to estimate 11cc1781,000 10,000 100,000ArFigure 6.11. Reynolds number based on slip velocity at classical choking point as a function ofArchimedes number compared with Reynolds number based on U, Use and particleterminal velocity.6.4. Slugging versus Non-Slugging SystemsNot all systems are capable of slugging. If the particles are relatively small or the riserdiameter is relatively large, void diameters do not approach the riser diameter due to splitting.Under these circumstances, there can be no transition to slug flow and the system can be said tobe a non-slugging system (Zenz 1949; Yousfi and Gau 1974; Yang 1976; Leung 1980). Althoughclassical choking cannot occur in such systems, types B and A choking can still occur.Several different criteria proposed to distinguish slugging from non-slugging systems arelisted in Table 6.7. Since they are based on different concepts and since there is considerableuncertainty regarding the mechanism of bubble splitting and factors which control maximum void1,00050020010050• Zenz(1949)LI Lewis et al. (1949)+ Ormiston(1969)>< Yousfi and Gau (1974)• Moketal.(1989)o Bietal.(199l)20105211 10 100Ret for single particles based on Grace (1986)179Table6.7.Criteriafordistinguishingsluggingandnon-sluggingsystemsAuthorsProposedmechanismEquationsforsluggingCommentsYousfi andGao(1974)StabilityofupwardflowofauniformU:2140NoallowanceforwallunboundedsuspensiongdeffectsYang(1975)SlugstabilitybasedonHarrisonetal.U:0.35Basedonbubblesplitting(1961)equationgDfromrearGeldart(1977)Slugstabilitybasedonempiricalu>03evidencegD whereU’isbasedonparticlesofdiameter2.7d.Smith(1978)SlugspostulatedtonotbeabletoriseU6’’n(1>0.41fasterthanporositywavesGuedesdeCarvaihoSlugstabilitybasedonamodifiedPg!1g1)°5>(Basedonbubblesplitting(1981)Harrisonetal.(1961)equation(p0.66)fromrearsize, none of the equations is widely accepted. For example, several of the criteria in Table 6.7are based on the concept of bubble splitting from the rear, whereas there is considerable evidence(e.g. Rowe and Partridge 1965; Clifi and Grace 1972; Upson and Pyle 1973) that splitting occursfrom the front. Improved understanding is needed before there are reliable methods to distinguishslugging from non-slugging systems.6.5. Relationship between Choking and Flow Regime TransitionsThe provision of a standpipe which allows particles to be returned to the bottom of theriser makes a circulating fluidized bed system capable of being operated from conventionalfluidization (bubbling, slugging) right through to pneumatic transport. A circulating fluidized bedis, however, generally operated in the so-called fast fluidization regime which is usuallycharacterized by a denser region at the bottom of a riser and a more dilute region above with nosharp interface between these two regions. With increasing gas velocity, the transition from fastfluidization to pneumatic transport corresponds to the saturation carrying point, minimumtransport velocity or accumulative choking velocity, beyond which all particles are transported upthe riser, with no particle accumulation at the bottom. The termination of fast fluidization whenreducing gas flow to dense-phase transport is commonly said to be demarcated by the chokingvelocity. Clearly this must be one ofthe other choking velocities (Type B or Type C).Figure 6.12 gives a flow chart showing the possible flow regimes and regime transitions ingas-solids cocurrent upward flow systems. The boundary between dilute-phase flow and fastfluidization is set by the Type A or accumulative choking velocity or minimum transport velocity.The transition from fast fluidization to the dense-phase flow regimes depends on particleproperties and the physical equipment, since the transition corresponds to one of three conditions- Type B or blower-!standpipe-induced choking, Type C or classical choking, or (for non-sluggingsystems) U. When there are blower andlor solids feeder limitations, the fast fluidization regime181terminates to an inoperable regime at the Type B choking velocity. For a slugging system, fastfluidization may transform to slugging dense-phase flow at the Type C choking velocity. In non-slugging systems where classical choking does not exist, if sufficient pressure heads are providedby both the gas blower and the solids feeder, then steady bubbling dense-phase flow operation canbe realized (Yousfi and Gau 1974; Hirama et al. 1992). Transition from fast fluidization to non-slugging dense-phase flow occurs gradually in such a case. Some characteristic is then needed todefine the boundary between these two regimes. This transition can be considered to occur whenthe bottom dense region lulls the entire riser as the gas velocity is reduced at a fixed solids flowrate. Figure 6.11 suggests that choking may occur between U0 and Use, involving a transition to adense phase flow. As a first estimate, one can also use U0 to quantifj this transition.Decreasing superficial gas velocity with G5 = constant[-phaseflol Ucc Slugging systemsI D,max >O.6D Classical choking(Type C)Inoperable1. blower induced______________UCB Fast L UcA Pneumatic2. standpipe induced Blower-/standpipe- •-j fluidization cumuIatjve transportinduced choking gU G, (Type B) (Type A)Non-slugging udense-phase flow . Non-slugging systemsDB,max <O.6D Gradual transitionFigure 6.12. Flow chart showing the transitions between dense-phase transport, fast fluidizationand pneumatic transport with decreasing gas flow at constant solids flux.1826.6. ConclusionThree different types of choking have been identified. Type A (accumulative) chokingoccurs as gas velocity is reduced for all systems when local refluxing (downward motion) ofparticles occurs to such an extent that a dense region is fonned at the bottom. Type B (blower-Istandpipe-induced) choking takes place when either the blower is incapable of providing sufficientpressure head to maintain all the particles in suspension or when the standpipe which returnssolids to the base of the riser is incapable of supplying the required flow of particles. Such aninstability has been successfully predicted by a simple analysis based on the pressure balance overthe whole loop. This type of choking can be avoided by proper design of the blower andstandpipe and by maintaining an adequate inventory of solids, or by uncoupling the riser and thesolids feed system. Type C (classical) choking occurs only for slugging systems, i.e. systemswhere bubbles can grow to a size comparable with the riser internal diameter. In this case, severeslugging occurs as gas velocity is reduced for a conveyed suspension. The three types aresummarized in Table 6.8.The boundary between fast fluidization and pneumatic transport is set by the Type Achoking velocity/minimum transport velocity, while the transition from fast fluidization toslugging dense-phase flow is demarcated by the Type C or Type B choking velocities, whicheveris greater. The transition from fast fluidization to non-slugging dense-phase flow for smallparticles in large diameter units where voids cannot grow to fill the column occurs when thebottom dense region occupies the whole riser. Two flow regimes may be present in the bottomdense region of the riser, depending on particle properties and the physical nature of the blower,standpipe and riser. For small particles in large diameter units, slugging and classical choking donot exist. However, for large particles in small diameter units, slug-like structures can occurperiodically in the bottom dense region, causing the transition between dense-phase conveyingand fast fluidization to be gradual diffuse rather than abrupt.183Table6.8.Summaryoftypesofchoking00TypeManifestationMeansofavoidanceorPredictionrestrictionsA-AccumulativeSomeparticlesbegintomoveNoneYang(1975,1983)orBidownward,i.e.refluxingbegins,andaandFan(1991)densephaseformsatthebottomB-Blower-/standpipe-CatastrophicshutdownasblowerisLargerblower,increasedMatsumotoetal.(1982) asinducedincapableofmaintainingfloworassolidsinventory,tallerinFigure6.1forblowerstandpipeisincapableofsupplyingstandpipeoruncouplinginduced;Modelin6.3.2.2.enoughsolidstobalancethesolidsfeedsystemforstandpipe-inducedentrainmentC-ClassicalSevereslugginginadensephasebeginsNotanoutcomefornon-YousfiandGau(1974)sluggingsystems,i.e.ifriserdiameterissignificantlylargerthanlargestvoidsChapter 7Flow Regime Diagrams of Gas-Solid Fluidization and Upward Transport7.1. IntroductionThe purpose of this chapter is to combine the material presented in previous chapters withother work in the literature to provide more coherent flow regime maps governing fluidizationand solids transport.Various attempts have been made to plot flow regime maps for gas-solid suspensions. Inan early study, Zenz (1949) proposed a flow diagram in which both dense fluidization and cocurrent pneumatic flow regimes are indicated, but the “turbulent” region around which bothslugging and choking are present was not delineated. A similar flow regime map was proposedby Yerushalmi et a!. (1976) in which bed voidage was plotted against superficial gas velocity toshow the transitions among the packed bed, bubbling bed, turbulent fluidization and fastfluidization regimes. The regime map developed by Li and Kwauk (1980) also plotted voidageagainst superficial gas velocity. Squires et al. (1985) expanded such a map to include thepneumatic transport regime and choking points, and this was further modified by Rhodes (1987).The transition from low velocity to high velocity fluidization is, however, still poorlycharacterized. Grace (1986) extended and modified the approach of Reh (1971) to propose aunified regime diagram based on literature data to show the operating ranges of conventionalfluidized beds, spouted beds, circulating beds and transport systems. The transition from lowvelocity to high-velocity fluidization was not clearly delineated, although some data available atthat time were plotted to indicate the onset of turbulent fluidization.Following another approach, Leung (1980), Klinzing (1981) and Yang (1983) proposedflow regime maps of gas-solids transport in which superficial gas velocity was plotted against185solids flux, with gas-solid transport divided into dense phase flow and dilute phase flow regimes.The termination of pneumatic transport to dense phase fluidization was again unclear. Takeuchiet al. (1986) proposed a flow map based on their experimental findings to define the boundaries offast fluidization. This flow regime map was modified by Bi and Fan (1991) to include thetransition from heterogeneous dilute flow to the homogeneous dilute flow regime. Hirama et al.(1992), on the other hand, tried to extend such a diagram to the transition from high-velocity tolow-velocity fluidization, but the transition was again not fully defined.In this chapter, unified flow regime diagrams are proposed based on experimental findingspresented in the previous chapters to show the relationship between flow regimes for both gas-solid fluidization and co-current upward transport.7.2. Flow Regimes in Gas-Solid Fluidized BedsIn a gas-solid fluidized bed, it has long been understood that fixed bed flow transforms tofluidized bed flow at U For fine particle systems, bubbles appear at Umb, while slugs start toform at Urns. The transition to the turbulent fluidization regime is generally assumed to occur atU. The termination of batch operation of fluidized beds is marked by significant entrainment ofbed particles beyond Use where particles can no longer be maintained in the column unlessentrained particles are captured and returned to the bed efficiently. Such a flow transition processis depicted in Figure 7.1. In large diameter columns and/or where small particles are used, theslugging regime may be bypassed altogether. Only small transient voids appear in the turbulentregime between U and Use.A flow regime diagram consistent with the above picture is shown in Figure 7.2. In thisdiagram, the dimensionless parameters U (=Re/Arh’3)and d,* (ArlI3) suggested by Grace(1986) are used as axes. The equation of Grace (1982) modified from the Wen and Yu186correlation (1966) is chosen for the calculation ofURemj = J27.22 +O.O4O8Ar —27.2 (7.1)corresponding to the point where the standard deviation of differential pressure fluctuationsreaches a maximum, is based on equation (3.3). The critical velocity Use is defined as the pointwhere solids begin to be entrained significantly (Chapter 5), setting an upper limit on conventionalfluidized bed operation. The Use line in Figure 7.2 is based on equation (5.3).Particulate Ifluidization fl D13,max<O.66D____Bubbling____Slugging____Turbulent SignificantFixed bedJ u fluidization Urns u Lidization entrainmentIncreasing gas velocityFigure 7.1. Flow chart showing regime transitions in gas-solid fluiclized beds.Since the transition velocity Urns depends on the column diameter, not included in thedimensionless coordinates, Urns cannot be plotted on this diagram. For fine Group A particles,the minimum bubbling velocity can be estimated by the Geldart and Abrahamsen (1978)dimensional correlation,U = (7.2)Pgwhich again cannot be included on the diagram.7.3. Flow Patterns in Gas-Solid Vertical Transport LinesA gas-liquid column can be operated under continuous conditions in which liquid iscontinuously fed to the bottom and overflows from the top. In a gas-solid system, such atransport operation can also be achieved if both gas and solids are supplied at sufficient rates to187DIIAr113Figure 7.2. Flow regime map for gas-solids fluidization. Heavy lines indicate transition velocities,and the regions indicated by light lines are the typical operating ranges of bubblingfluidized beds and turbulent fluidized beds.I1 10 102188the bottom of the column, with gas and solids also leaving continuously at the top. Ideally, theflow patterns of the transport line are completely determined by the relative velocity between thegas and the particle phase (i.e. by the slip velocity) rather than the superficial gas velocity.Analogous to gas-liquid upward transport, the flow patterns are depicted in Figure 7.3. At a fixedsolids flux, a transport line may experience bubbly flow, slug flow and the turbulent flow regimebefore achieving the pneumatic transport regime. A particulate flow regime may also exist forfine Group A particles. The slug flow regime may be bypassed for large diameter columns.Figure 7.3. Flow chart showing regime transitions in gas-solids upward transport lines. VVmb, Vms, V, VCA and V are defined by equations (7.3) to (7.8).The pneumatic transport regime has been studied extensively (Marcus et al., 1990), whilerelatively few studies have been reported on dense phase transport (Conrad, 1986), possiblybecause it is relatively difficult to maintain dense phase flow under stable operation. Unlikepneumatic transport above the Type A choking velocity where particles are fully suspended in thegas, particles in dense phase transport are pushed up the column, requiring a relatively high gaspressure and a high feed rate of particles. When the gas blower is unable to provide sufficientpressure head or solids cannot be fed to the riser at the required rate, stable operation of densephase flow becomes impossible due to Type B choking (see Chapter 6). In some cases, eventhough sufficient blower pressure and solids feeding are provided, it is impossible to achieveD,<O.66DIncreasing gas velocity ((3 =constant)189dense phase transport due to severe slugging, i.e. to Type C or “classical choking” (see Chapter6).In solids transport systems, the transition velocity depends on the relative velocity betweenthe two phases. Ideally, the minimum fluidization velocity, V113 can be estimated byG6v. = u + (7.3)p(’— Smj)Similarly, the minimum bubbling velocity can be predicted byv =u + G58, (74)ml) ml)where Umb can be calculated from equation (7.2). The velocity V which marks the onset ofturbulent flow can be estimated byG5c (75)p(’— s)where is approximately 0.65 in non-slugging systems and 0.75 in slugging systems (see Chapter3), while the minimum transport velocity or the Type A choking velocity, VCA, is predicted byVCA = Use + GSEcA (7.6)PP(lEcA)The bed voidage at this transition point, ECA, ranges from 0.96 to 0.99, depending on particleproperties as shown in Figure 5.12. For fine Group A particles, RCA’ as shown in Figure 5.12, isaround 0.96. For large Group B and Group D particles, ECA is around 0.99.The minimum pressure-drop point denotes the transition from dispersed to aggregate flowconditions, as recognized by Leung (1980) and Klinzing (1981). Accurate quantitativedetermination of this transition is made difficult by the uncertainty of the solid ffiction factor andsolid acceleration term in the momentum balance equations. As a first approximation, the Bi and190Fan (1991) correlationVmp = 1O.1(gd)°7(G3/p )O.31O().139 Ar°2’ (7.7)is used for the calculation.The minimum slugging velocity in a slugging system can be estimated byG8s (7.8)p(1— 8,,,)where Urns can be estimated by an equation due to Stewart and Davidson (1967)U,,, = Urn! +0.071f (7.9)while Ems is estimated to be about 0.55 if the slug volume fraction is taken to be 1/6 (Stewart andDavidson, 1967). However, in columns of large diameter, such a slug flow regime does not exist.The region between V and Vrnb then all belongs to the bubbly flow regime.Based on the above considerations, a flow regime diagram, Figure 7.4, similar to Figure7.2, can be produced with Ar as the abscissa axis and V, defined as= V[p / gpg(pp —pg)]”3—8) [Pg / gpg(pp — Pg)]”3 (7.10)as the ordinate. Since both the minimum slugging velocity, Vms, and the minimum pressure dropvelocity, Vmp depend on column diameter, they cannot be included in this diagram. For a batchoperated fluidized bed with given particles, the flow pattern is determined by the superficial gasvelocity only. For (3=0, Figure 7.4 becomes the same as Figure 7.2 because V*=U*. Figure 7.4can thus be considered as a generalized flow regime diagram. In a solids transport system withgiven particles, the flow pattern depends on both the superficial gas velocity and the solidscirculation rate. To determine the flow pattern under given operating conditions, both Ar and V”need to be calculated and then be located on Figure 7.4 to determine the flow pattern.191-Ic>IIIAr113Figure 7.4. Idealized flow regime map for gas-solids upward transport. Heavy lines indicatetransition velocites, and the region indicated by thin lines is the typical operatingrange ofbubbly flow.1 10 102192The map in Figure 7.4 is idealized with no equipment-related restrictions. In circulatingfluidized beds and transport risers, dense phase operation below V is difficult to realize due tolimitations in gas blowers and solids feed devices. In real systems, stable operation of dense phasetransport may terminate at the Type B choking velocity andJor at the Type C choking velocity(see Chapter 6). This is clearly demonstrated in Figure 7.5 where three possible flow transitionroutes with decreasing superficial gas velocity at a fixed solids circulation rate are included. Thereverse transition route in Figure 7.3 can be realized only in systems with no equipment-relatedrestrictions and with no classical choking occurring.Figure 7.5. Flow chart showing regime transitions in circulating fluidized beds and transportrisers with decreasing gas flow.A circulating/fast fluidized bed is generally operated in the region between the Type A andthe Type B or C choking velocities and with the gas velocity close to the minimum pressuregradient point, Vmp. It can be considered to cover both the turbulent flow and the core-annulardilute flow regimes, as indicated in Figure 7.5. A fast fluidization regime is usually characterizedby a concentration profile consisting of a dense bottom region and dilute top region. Such acombination is similar to what is found in the turbulent flow regime bounded in Figure 7.5 by theDecreasing superficial gas velocity (G = constant)CFB Circulating Fluidized BedsFFB Fast Fluidized Beds193Type B or C choking velocities and the Type A choking velocity. In most cases, it is impossibleto operate a circulating fluidized bed under dense phase transport conditions because insufficientsolids can be provided from the standpipe owing to pressure imbalance between the riser anddowncomer.Figures 7.6(a) and (b) are modified maps for typical circulating fluidized beds andtransport riser operation with (I5/p as the abscissa and V/Ui as the ordinate. In this map theclassical choking velocity is obtained from the equation ofYousfl and Gau (1974) [equation (3) inTable 6.2], while VCA is estimated using the equation of Bi and Fan (1991) [equation (6) in Table6.2]; the boundary between homogeneous flow and core-annular flow is derived from equation(7.7). It is seen in Figure 7.6(a) that the fast fluidization regime for FCC is very narrow atsuperficial gas velocities less than Use, indicating that there is a sharp transition from core-annulardilute-phase flow to dense phase fluidization due to the lower solids carrying ability of the gas atlow gas velocities. As a result, a fast fluidization regime can only be realized at gas velocitiesgreater than Use. Comparing Figures 7.6(a) for fine Group A particles and Figure 7.6(b) forGroup B particles, it is seen that the core-annular dilute-phase flow regime becomes narrower forlarger particles. A core-annular dilute-flow regime should not exist for Group D particles,because the suspension collapses to form a dense region at the bottom as soon as a core-annularstructure is established due to the formation of particle streamers in the near wall region. This isconsistent with Chapter 5 where we have seen that Use is almost the same as U for large Group Dparticles.Table 7.1 summarize key characteristics of different high velocity fluidization regimes. Atypical transition process with decreasing gas velocity is indicated in Figure 7.6(a) by line a-b-c-de-f At a constant solids circulation rate, the transport line is operated in the homogeneous diluteflow regime without lateral solids segregation at gas velocities higher than that corresponding topoint b. Particle streamers do not form near the column wall. Particle streamers start to form due19480I•14(b)Vmp70(a)\0’-12Vc60--10-e0\50-8-VCA00005;30Ucc20 10 0 0.000.050.100.150.200.250.300.000.050.100.150.200.250.30G5Ip1rn/sGIprn/sFigure7.6.Practicalflowregimemapsforgas-solidsupwardtransportinthepresenceofrestrictionsfor (a)FCCparticles,cI,,6Otm,1500kg/rn3,D=0. 1m;(b)Sandparticles,d=200im,p,=26OOkg/rn3,D=0. Iin.to the particle-wall interaction when the gas velocity is reduced to point b, and the core-annularstructure develops as the gas velocity is reduced from point b to point c. The axially uniformsuspension collapses at point c with a collapsed dense phase forming in the bottom and a core-annular flow persisting in the upper section. The transport line becomes unstable when the gasvelocity is decreased to point d, due either to type B or to type C choking. The solids circulationrate can then no longer be held constant when the superficial gas velocity is further decreasedbelow point d. As a result, the solids circulation rate drops along line d-e. Eventually, the solidscirculation rate reaches G*, the saturated carrying capacity or the saturated entrainment rate. Afurther decrease in gas velocity causes the operation to travel along the entrainment curve (ie.line e-f) because particles can only be entrained by the gas, as in a conventional fluidized bed.Table 7.1. Key characteristics of the turbulent fluidization, fast fluidization and dilute phasetransport regimes.Characteristic Turbulent Fast Core-annular Homogeneousfluidization fluidization dilute transport dilute transportGas velocity range Uc<U<Use Use<U<VCA VCA<U<Vmp U>Vmpor VCh<USolids flux range GqGc* Gc>Gc* Gq<Gc* Gs<<Gs*Overall voidage e=0.6-0. 8 e0. 8-0.95 6=0.95-0.99 e>0.99Axial particle High High Low NonegradientsRadial particle Moderate High High lowgradientGas-solids slip Low High LowvelocityParticle backmixing High High Low None1967.4. ConclusionUnified flow regime maps are presented for gas-solids fluidized beds and gas-solidsupward transport lines. For conventional gas-solids fluiclization operation (i.e., G5O), the flowregimes include the fixed bed, bubbling bed, slugging bed and turbulent bed regimes. Beyond Useparticles are significantly entrained from the fluidized bed, and it is impossible to operate understeady conditions with very low G5 and appreciable solids concentrations. For gas-solids verticaltransport operation, solids flux must be incorporated in the flow regime diagrams. The flowregimes then include dilute-phase transport, turbulent flow, slug/bubbly flow, delayed bubbly flowand packed bed flow. hi practical operation of circulating fluidized beds and transport risers,operation below the turbulent regime is usually impossible due to equipment-induced restrictions.Practical flow regime maps are then proposed with V/Ui plotted against G5/p and with the flowregimes including homogeneous dilute flow without appreciable lateral and axial gradients ofvoidage, core-annular dilute phase flow when there are appreciable lateral gradients but smallaxial gradients, and fast fluidization or turbulent fluidization where both lateral and axial gradientsare significant.The flow regimes in conventional fluidized beds and dilute-phase transport have beenstudied quite extensively and are relatively clear. Transitions in dense-phase transport linesrequire further study using transport lines capable ofbeing operated under extreme conditions, i.e.at high solids fluxes and densities.197Chapter 8Conclusions and Recommendations8.1. Conclusions of This WorkExperiments in a 50 mm diameter column show that forced oscillations can be establishedin a gas-solids fluidized bed when a disturbance of similar frequency is supplied to the bed. Suchoscillations interfere with the propagation of compression waves in fluidized beds. As a result,the amplitude of pressure waves can be attenuated or amplified during their propagation. Thefindings suggest that the attenuation cannot be predicted based only on viscous dissipation or gas-solids relative fluctuations. This can be explained by the interaction between particles and the factthat forced oscillations of fluidized beds are coupled with propagating pressure waves.Pressure waves propagate in fluidized beds at speeds of order 10 mIs. The velocity tendsto be higher when the bed is de-fluidized. The propagation velocity of pressure waves in gas-solids fluidized beds can be well predicted by pseudo-homogeneous compressible wave theoryand by separated flow compressible wave theory. When the gas velocity is less than U boththeories fail to predict the dramatic increase of wave velocity with decreasing gas velocity,probably due to a change in the form of waves as particle-particle contacts cause the gas-solidsmixture to lose its compressibility. Pressure waves may then propagate as elastic waves, whichpropagate at higher velocity in a porous medium, rather than as compressible waves.The existence of pressure waves affects measurement of fluidized bed fluctuations. Dueto the interference from propagating waves, absolute pressure (single-point) measurements do notprovide localized signals. Pressure waves can be filtered to a reasonable extent by usingdifferential pressure measurements of appropriate spacing. Optical fibre probes register localvoidage fluctuations mainly caused by passage of voids. Even with appropriate spacing,198differential pressure measurements do not provide the same information as optical fibre probesbecause of much larger measurement volumes and because of different dependencies of proberesponse on bubble size.Studies in a cylindrical column reveal that the transition velocity U is a strong function ofmeasurement method, while Uk depends on the solids recycle system and is therefore unsuitableas a means of characterizing hydrodynamics in the column. U from absolute pressurefluctuations tends to be lower than from differential pressure fluctuations, and the transitionvelocity is independent of axial location. U from differential pressure fluctuations varies withaxial location, being higher near the bottom than near the top of the bed. The standard deviationof voidage fluctuations from an optical fibre probe also reaches a maximum with increasing U.The local voidage and apparent bed density depend on the nature of the unit. When solids returnto the bottom of the column is restricted, the slope of the voidage curve may undergo an abruptchange.The transition velocity, U, also depends on how the data are interpreted. For absolutepressure fluctuations, the standard deviation normalized by the average local pressure reached amaximum at a lower gas velocity than the dimensional standard deviation, while the peak velocitydecreased with height. For differential pressure fluctuations, a higher transition velocity wasobtained from the normalized standard deviation. Skewness of absolute or differential pressurefluctuations does not appear to be a reliable indicator offlow regime transition.A mechanism for transition from bubbling to turbulent fluidization is proposed based onbubble-bubble interaction and coalescence. The sharp transition to turbulent fluidization (denotedType I) is considered to take place when (i) the wake is open and turbulent (i.e. ReB> 130), (ii) theseparation distance between successive bubbles approaches a certain value (e.g. LB/DB<O. 5) and(iii) the bubble size at U is much smaller than the column diameter (i.e. ReB IO.66D > 130). The199transition is gradual (Type II) when the wake is closed, which occurs for larger or denser particlesor where the maximum stable bubble size is comparable with the column diameter. The proposedmechanism is consistent with experimental results obtained in this study and with literature data.The measured local voidage at U shows good agreement with the value predicted based on theproposed mechanism. This mechanism also successililly predicts the variation of transitionvelocity U with measurement location and system pressure.Two kinds of transitions exist in fluidized beds of large particles. When the bed issufficiently deep, the maximum amplitude of absolute pressure fluctuations is not reached until thebed particles are significantly entrained. The transition velocity U in such case corresponds totransition from slugging to core-annular flow. However, a transition velocity much lower than theterminal velocity of single particles can be identified corresponding to the maximum amplitude ofdifferential pressure fluctuations or local voidage fluctuations. This transition point can be wellpredicted by slug flow models and does not correspond to transition to turbulent fluidization. Inshallow fluidized beds, the growth of bubbles/slugs is limited by the depth of the dense region.The amplitude of pressure fluctuations then goes to a maximum at a certain gas velocity. Thetransition velocity U corresponding to the maximum amplitude of pressure fluctuations increaseswith increasing static bed height.A critical velocity, Use, is defined based on the characteristics of the solids entrainmentversus gas velocity curve. Conventional fluidized beds equipped with cyclones and diplegs havegenerally been operated below this critical velocity. Circulating fluidized beds, on the other hand,are often operated beyond the critical velocity in order to achieve a high solids circulation rate.The transport velocity, defined by Yerushalnii and Cankurt (1979), represents a transition ofaxial voidage proffles in the riser. Below this velocity, a distinct interface exists between the topdilute region and the bottom dense region when a sufficient rate of solids circulation can beensured. Above this velocity, the interface becomes relatively diffuse. This transport velocity is a200function of measurement location and the separation distance between the pair of pressure tapsover which the pressure drop is measured.Three different types of choking have been identified. Type A (accumulative) chokingoccurs as the superficial gas velocity is reduced for all systems when local refluxing (downwardmotion) ofparticles begins to such an extent that a dense region is formed at the bottom. Type B(blower-/standpipe-induced) choking takes place when either the blower is incapable of providingsufficient pressure head to maintain all the particles in suspension or when the standpipe whichreturns solids to the base of the riser is incapable of supplying the required flow ofparticles. Suchan instability is successfully predicted by a simple analysis based on the pressure balance over thewhole unit ioop. The analysis further shows that this type of choking can be avoided by properdesign of the blower and standpipe and by maintaining an adequate inventory of solids or byuncoupling the riser and the solids feed system. Type C (classical) choking occurs only forslugging systems, i.e. systems where bubbles can grow to a size comparable with the riser internaldiameter. In this case, severe slugging occurs as the superficial gas velocity is reduced for aconveyed suspension.Unified flow regime maps are presented for gas-solids fluidized beds and gas-solidsupward transport lines. For conventional gas-solids fluidization operation (i.e., G50), the flowregimes include the lixed bed, bubbling bed, slugging bed and turbulent bed regimes. Beyond Useparticles are significantly entrained from the fluidized bed and it is impossible to operate understeady conditions with very low G5 and appreciable solids concentrations. For gas-solids verticaltransport operation, solids flux must be incorporated in the flow regime diagrams. The flowregimes then include dilute-phase transport, turbulent flow, slug/bubbly flow, delayed bubbly flowand packed bed flow.201In practical operation of circulating fluidized beds and transport risers, operation belowthe turbulent flow regime is commonly impossible due to equipment-induced restrictions.Practical flow regime maps are proposed with V/Ut plotted against 11p with the flow regimesincluding homogeneous dilute flow without appreciable lateral and axial gradients of voidage,core-annular dilute phase flow where there are appreciable lateral gradients but small axialgradient, and fast fluidization or turbulent fluidization when there are both lateral and axialgradients. The boundary between fast fluidization and pneumatic transport is set by the Type Achoking velocity, while the transition from fast fluidization to slugging dense-phase flow isdemarcated by the Type C or Type B choking velocity, whichever is greater. The transition fromfast fluidization to non-slugging dense-phase flow for small particles in large diameter units wherevoids cannot grow to liii the column occurs when the transition velocity V is reached.8.2. Recommendations for Future Work1. The attenuation of pressure waves and bed oscillations need to be further studied byconsidering gas-solids motion in gas-solids fluidized beds as a non-linear or chaotic process.2. Flow regimes in conventional fluidized beds and dilute-phase transport have been studiedquite extensively and are relatively clear. Transitions in dense-phase transport lines requirefurther study using transport lines capable of being operated under extreme conditions, i.e.high solids flux and density.3. Although the bounds of the turbulent/fast fluidization regime in line particle systems can bewell delineated by U0 and UCA, the gas and particle flow patterns in this regime are stillunclear. To develop a reactor model, the local flow structure still needs to be studied.4. One of the important characteristics of gas-solids fluidized beds is the liquid-like flowbehaviour of the dense phase. This character has been recognized and used to analyze someaspects of fluidized bed behaviour such as the bubble motion, particle elutriation and apparent202viscosity of the dense phase. The similarity between flow patterns in gas-solids fluidized bedsand gas-liquid vertical flow lines needs to be studied more extensively.203NomenclatureA amplitude ofpressure oscillations, Pacross-sectional area of column, m2Ar =Archimedesnumber, pg(pp—pg)dg/Azo amplitude of the first peak ofpressure oscillations at location z0, PaA21 = amplitude of the first peak ofpressure oscillations at location z1, PaA0 = amplitude ofthe first peak ofpressure oscillations, PaA1 = amplitude of the second peak ofpressure oscillations, Paa = decay constant, rn1B = constant used in Table 6.7 given by Carvallio (1981)Bf = density ratio {=PgE / [p (1— e) + PgE] }B1 = parameter defined by equation (5.9)B2 = parameter defined by equation (5.10)C = sound velocity in air (=330 mIs)Cd = coefficient defined in equation (6.8)C = specific heat ofparticles, J/kgKD = column diameter, mDB = bubble diameter, mDBmax = maximum stable bubble diameter, mDd = standpipe diameter, mD = solids discharge pipe diameter, mD5 = diameter of a slug, mD = equivalent diameter ofthe open area of the control valve, mD0 = equivalent diameter ofthe open area of the control valve in full open, md,1, = mean particle size, jimd1* = dimensionless parameter (=Ar”3)204E energy ofpressure waves, N.mEb = elasticity ofporous mateiial,N/m2E = elasticity ofnon-porous material, N/rn2f = frequency, liz’fw pressure wave frequency, HzfB = frequency ofbubble motion, HzG = dimensionless quantity given by pgIp0Ug = acceleration due to gravity, rn/s2GB = bubble phase volume flux, m3/s= solids circulation rate or solids entrainment flux, kg/m2s= saturation carrying capacity, kg/m2sGo = solids entrainment rate right above the dense-dilute interface of a fluidized bed, kg/rn3Gs,cc = solids circulation rate at classical choking condition, kg/m2sH bed height, mH0 = colunm height, m= height ofbottom dense region in the riser, mH = static bed height, m= vertical distance from the lower surface of the sphere enclosing the bubble to theboundary between the wake and the bubble, mk = wave number, 1/rnkg thermal conductivity of gas, W/mKconstant used in equations (4.5) and (4.8) (il to 4)L = spacing between two pressure probes, mL0 height ofthe dense bed in the downcomer when all the particles are stored there, mLB separation distance between two succesive bubbles, mLE = equivalent length of the horizontal pipe between the riser exit and the cyclone, rnLE’ length between the cyclone and the dilute-dense interface in the downcomer, m205L5 = length of slugs, mT = spacing between successive slugs, mL = wake length behind a slug, mm = soffids-to-gas volumetric flow rate ratio (=G5/pU)N = number of data pointsn = the Richardson and Zaki constant, (-)P(t) instantaneous pressure, PaPB(t) = pressure signals caused by bubbles motion, Pa= pressure head available from gas blower, N/rn2= pressure at the bottom ofthe standpipe, N/rn21max maximum amplitude ofpressure fluctuations, Pa= pressure at the bottom ofthe riser, N/rn2Pw(t) = pressure waves, PaR = radius ofthe column, rnr = distance from the bubble centre, or from the axis of the column, rnr0 = radius of the core region, mRB = radius ofbubble, rnReB bubble Reynolds number based on UB, PgUBDB /ReB,max= bubble Reynolds number corresponding to teh mximurn size, PgUBDB,m. / ItgRe0 = Reynolds number based on U0, PgUjdp / ItgReD = Reynolds number based on UB and D, PgUBD / tgRek = Reynolds number based on Uk, PgUkdp /Jtg= Reynolds number based on Up5Ud / J1gRe5 ccReseRetRet= Reynolds number based on Us,cc, PgUs,ccdp/iig= Reynolds number based on Use, PgUsedp /= Reynolds number based on the terminal velocity of single particles, PgUtdp / Jtg= Reynolds number based on the transport velocity Utr, PgUtxdp / tg206S = cross-sectional area of the column, m2S0 open area of a single nozzle on the distributor in equation (2.21), m2s = standard deviation ofpressure fluctuations, PaT = bed emptying time, st =time,st = period offorced oscillation of fluiclized bed, sU = superficial velocity of gas supplied via distributor, rn/sU = dimensionless gas velocity, {p / [g(p — pg )tg]}”3UUB bubble rise velocity, misU = superficial gas velocity corresponding to maximum standard deviation ofpressurefluctuations, misU superficial gas velocity required to bring bubbles to their maximum stable size, m/stransition velocity from fast fluidization to non-slugging dense-phase flow regimes atwhich the dense bed develops to occupy the whole riser, rn/sUCA = Type A or accumulative choking velocity or minimum transport velocity, misUCB, UCB’ = Type B or premature choking velocity at which the operation becomes unstable dueto the interactions between gas blower and riser or between solids feeder and riser, mis= Type C or classical choking velocity at which slugging commences to such an extentthat stable operation becomes impossible, misUch = choking velocity, m/sUch, cal calculated choking velocity, m/sUch, exp experimentally determined choking velocity, misUd0 = minimum velocity of dilute conveying, mislJ = superficial velocity of gas supplied to the fluidized bed from a bubble injector located inthe upper section of the column based on the bed cross-sectional area, m/sUk = superficial gas velocity corresponding to minimum or leveling off of standard deviationofpressure fluctuations, mis207Umb =minimum bubbling velocity, rn/sU = minimum fluidization velocity, misUrns = minimum slugging velocity, misU, superficial gas velocity ofthe pressure probe, misU5 = velocity of surface waves, mis= apparent slip velocity between gas and solids at classical choking condition, misUse = onset velocity of significant solids entrainment, rn/sU5li = slip velocity, misUs = slug rise velocity, m/sUsj = rise velocity of an isolated slug, misU = terminal settling velocity of single particles, rn/sU’ = terminal settling velocity based on particles of 2.7d, rn/sUtr = transport velocity ofparticles, rn/sUw wave propagation velocity, misUW,exp experimentally determined wave velocity, m/sUW,cal = calculated wave velocity, misV = dimensionless velocity defined by equation (7.10)VB = volume ofbubble, m3V = transition velocity to turbulent flow in transport line, misVCA = Minimum transport velocity in transport line, mis (=UCA)Vrnb minimum bubbly flow velocity in transport line, rn/sVmf = minimum fluidzed flow velocity in transport line, m/sVms = minimum slug flow velocity in transport line, misVrnp = minimum pressure-drop velocity demarcating the transition from homogeneous flow toheterogeneous flow, misV = volume of the wake, m3W1 = solids inventory (i=0, 1, 2, 3), kg208Y = ratio of actual bubble flow rate to value predicted by simple two-phase theoryz height above distributor, mZ = critical height as defined in equation 8 of Table 3.4, mGreek symbolsa =coefficient defined asy =constant(1.4)Y12, max maximum cross-correlation coefficient of two series of signals= solids circulation rate required to raise the dilute-dense interface from the bottom of theriser to the upper pressure tap, as defined in Figure 5.14, kg!mm2s.AP(t) = instantaneous differential pressure signals, N/rn2pressure drop available for the solids flow control valve, N/rn2APac = pressure drop due to solids acceleration in the riser, N/rn2LPac = pressure drop due to solids acceleration in the standpipe, N/rn2= amplitude of differential pressure signals from bubble motion, N/rn2APB(t) = differential pressure signals from bubble motion, N/rn2APc = pressure drop across the cyclone, N/rn2APfs = pressure drop due to gas-solids mixture to wall friction in the riser, N/rn2APfs = pressure drop due to gas-solids mixture to wall friction in the standpipe, N/rn2= pressure drop across the measuring probe, N/rn2= pressure drop across solids control valve, N/rn2= pressure drop across solids control valve when the control valve is completely opened,N/rn2= amplitude ofpressure waves registered by differential pressure measurements, N/rn2APw(t) = pressure waves registered by differential pressure measurements, N/rn2= volume of solids displaced because of cfrifi per unit volume ofbubble209= volume of solids carried by the wake per unit volume ofbubble= dimensionless resistance coefficient defined by equation (3.1) and (6.5)6 = voidage6* = voidage at the upper dilute region of the riser6]3 = volume fraction occupied by bubbles6Bc = volume fraction occupied by bubbles at U=U= overall voidage at U=U6cA = overall voidage at Type A choking point6cB = overall voidage at Type B choking point6cc = overall voidage at Type C choking point6ch = overall voidage at choking point= voidage at the bottom dense region of the riser= voidage at the exit ofthe riser= voidage ofthe dense phase6mb = voidage at minimum bubbling velocity= voidage at minimum fluidization velocity8ms voidage at minimum slugging velocity= void fraction ofporous materialparameter in equation (4.4), a function of gas and particle properties= parameter in equation (4.6), a fhnction of gas and particle propertieswake angle defined as the angle from nose ofbubble to edge ofbase, degreeso = angle offvertical axis of symmetry, degrees= wavelength, meffective dynamic viscosity of dense phase, kg/nisLg = gas viscosity, kg/ins!1g20 = gas viscosity at 20 oC, kg/nis= liquid viscosity, kg/rn. s210vd effective kinematic viscosity of the dense phase, m2/sVg = kinematic viscosity of gas, m2Is= decay factor ofharmonic oscillation defined in equation (4), 1/s= longitudinal decay factor ofpressure disturbance defined in equation (9), 1/rnp density, kg/rn3Pe = dense phase density, kg/rn3Pg = gas density, kg/rn3Pg20 = gas density at 20 °C, kg/rn3Pi = liquid density, kg/rn3Pm = cross-sectional average density, kg/rn3= particle density, kg/rn3= skeleton density of solid, kg/rn3amplitude decay time, sTf dynamic relaxation time ofparticles, senergy decay time (2t), s= thermal relaxation time ofparticles, s= angular frequency ofwaves (=2itf), 1/s211ReferencesAbed, R., “The characterization of turbulent fluid-bed hydrodynamics,” Fluidization IV, D. Kuniiand R. Toei eds., Engineering Foundation, New York, pp. 137-144, 1984.Abrahamsen, A.R and D. Geldart, “Behaviour of gas-fluidized beds of fine powders, Part I.Homogeneous expansion,” Powder Technoi, 26, 35-46, 1980.Adanez, J., L.F. de Diego and P. Gayan, “Transport velocities of coal and sand particles,” PowderTechnol., 77, 61-68, 1993.Akagawa, K., T. Sakaguchi, T. Fujii, M. Sugiyams, T. Yamsguchi and Y. Ito, “Shock phenomenain bubble and slug flow regimes,” Two-Phase Flow Dynamics, A.E. Bergles and S. Ishigaieds., Hemisphere Publishing Corporation, New York, pp.2l’7-238, 1981.Aizabrani, A.A. and M.M. Noor Wali, “A study of pressure drop fluctuations in a gas-solidsfluidized bed,” Powder Technol., 76, 185-189, 1993.Asai, M., M. Nakajima, R. Yamazaki and G. limbo, “Flow structure in transition regime to aturbulent fluidized bed,” Proc. 3rd China-Japan Fluidization Conference, M.Kwauk and M.Hasatani eds., Science Press, Beijing, pp.265-274, 1990.Avidan, A.A. and J. Yerushalnñ, “Bed expansion in high velocity fluidization,” Powder Technol.,32, 223-232, 1982.Bader, K, J. Findlay and T.M. Knowlton, “Gas/solid flow patterns in a 30.5-cm-diametercirculating fluidized bed,” Circulating Fluidized Bed Technology II, J.F. Large and P. Basueds., Pergamon Press, Oxford, pp. 123-128, 1988.Baeyens, J. and D. Geldart, “Solids mixing,” Chapter 4 in Gas Fluidization Technology, D.Geldart ed., J. Wiley & Sons, pp.97-112, 1986.Baeyens, J. and D. Geldart, “An investigation into slugging fluidized beds,” Chem. Eng. Sci., 29,255-265, 1974.Bagnold, R.A., “Experiments on a gravity-free dispersion of large solids spheres in a Newtonianfluid under shear,” Proc. R. Soc. Lond., A225, 49-63, 1954.212Bai, D.R., Y. Jin, Z.Q. Yu, “A two-channel flow model of circulating fluidized beds,”Fluidization-88: Science and Technology, M. Kwauk and D. Kunii eds., Science Press,Beijing, pp. 155-161, 1988.Bai, D.R, Y. Jin, Z.Q. Yu and W.H. Yao, “A study on the performance characteristics of thecirculating Fluidized Bed,” Chem. Reac. Eng. and Technol., (in Chinese), 3, 24-32 1987.Bai, D.R., Y. Jin, Z.Q. Yu and J.X. Zhu, “The axial distribution of the cross-sectionally averagedvoidage in fast fluidized beds,” Powder TechnoL, 71, 5 1-58, 1992.Baird, M.H.I. and A.J. Klein, “Spontaneous oscillation of a gas-fluidized bed,” Chent Eng. Sci.,28, 1039-1048, 1973.Bandrowski, J. and G. Kaczmarzyk, “Some aspects of the operation and design of verticalpneumatic conveying,” Powder Technol., 28, 25-33, 1981.Baskakov, A.P., V.G. Tuponogov and N.F. Filippovsky, “A study of pressure fluctuations in abubbling fluidized bed,” Powder Technol., 45, 113-118, 1986.Bi, H.T., “Study on fast fluidized bed heat transfer,” M.S. thesis, Tsinghua University, Beijing,China, 1988.Bi, H.T. and L.-S. Fan, “Regime transitions in gas-solid circulating fluidized beds,” Paper lflOle,AIChE Annual Meeting, Los Angeles, Nov. 17-22, 1991.Bi, H.T., P.J. Jiang and L.-S. Fan, “Hydrodynamic behaviour of the circulating fluidized bed withlow density polymer particles,” Paper #lOld, AIChE Annular Meeting, Los Angeles, Nov.17-22, 1991.Bi, H.T. and L.-S. Fan, “On the existence of turbulent regime in gas-solid fluidization,” AIChE J.,38, 297-301, 1992.Biswas, J. and L. S. Leung, “Applicability of choking conelations for fast-fluid bed operation,”Powder Technol., 51, 179-180, 1987.Bolton, L.W. and J.F. Davidson, “Recirculation of particles in fast fluidized risers,” CirculatingFluidized Bed Technology II, P. Basu and J.F. Large eds., Pergamon Press, Toronto, pp. 139-153, 1988.213Brereton, C.M.H., “Fluid mechanics of high velocity fluidized beds,” Ph.D. thesis, University ofBritish Columbia, Vancouver, 1987.Brereton, C.M.H. and J.R. Grace, “The transition to turbulent fluiclization,” Cheni Eng. Res.Des., 70, 246-251, 1992.Brereton, C.M.H. and J.R. Grace, “Microstructural aspects of the behaviour of circulatingfluidized beds,” Chem. Eng. Sci, 48, 2565-2572, 1993.Brereton, C.M.H. and J.R Grace, “End effects in circulating fluidized bed hydrodynamics,”Circulating Fluiclized Bed Technology IV, A. Avidan ed., in press, 1994.Briens, C.L. and M.A. Bergougnou, “New model to calculate the choking velocity of monosizeand multisize solids in vertical pneumatic transport lines,” Can. J. Chem. Eng., 64, 196-204,1986.Broadhurst, T.E. and H.A. Becker, “Measurement and spectral analysis ofpressure fluctuations inslugging beds,” Fluidization Technology, VoL2, D.L.Keairns ed., Hemisphere PublishingCorp., Washington, pp.63-84, 1976.Cai, P., “The transition of flow regime in dense phase gas-solid fluidized bed,” Ph.D. thesis,Tsinghua University, Beijing, China, 1989.Cai, P., Y. Jin, Z.Q. Yu and C. Z. Zhou, “Measurement of the transmissive velocity of elasticwaves in gas-solid fluidized bed,” J. Chem. Eng. Chinese Universities, 1, 87-90, 1986.Cai, P., S.P. Chen, Y. Jin, Z.Q. Yu and Z.W. Wang, “Effect of operating temperature andpressure on the transition from bubbling to turbulent fluidization,” AIChE Symp. Ser.,85(270), 37-43, 1989.Cai, P., Y. Jin, Z.-Q. Yu and Z.-W. Wang, “Mechanism of flow regime transition from bubblingto turbulent fluidization,” AIChE J., 36, 955-956, 1990.Campos, J.B.L.M. and J.R.F. Guedes de Carvalho, “An experimental study of the wake of gasslugs rising in liquids,” J. Fluid Mech., 196, 27-37, 1988.214Canada, G.S., M.H. McLaughlin and F.W. Staub, “Flow regimes and void fraction in gasfluidization of large particles in beds without tube banks,” AIChE Synip. Ser., 74(176), 14-26, 1978.Capes, C.E. and Nakamura, K. “Vertical pneumatic conveying: an experimental study withparticles in the intermediate and turbulent flow regimes,” Can. J. Chem. Eng., 51, 31-38,1973.Carstensen, E.L. and L.L. Foldy, “Propagation of sound through a liquid containing bubbles,” J.Acoust. Soc. Amer., 19, 481-501, 1947.Chan, LH. and T.M. Knowlton, “The effect of pressure on entrainment from bubbling gasfluidized beds,” Fluidization IV, D. Kunu and R. Toei eds., Engineering Foundation, NewYork, pp.2W3-290, 1984.Chang, H. and M. Louge, “Fluid dynamic similarity of circulating fluidized beds,” PowderTechnol., 70, 259-270, 1992.Chaouki, J., Ecole Polytechnique, Montreal, Private communication, 1992.Chen, B.Y.; Y. Li, F. Wang, Y. Wang and M. Kwauk, “Studies on fast fluidization,” Cliem.Metallurgy (in Chinese), (5), 30-3 8, 1980.Chirone, K, L. Massiniilla and S. Russo, “Bubble-free fluidization of a cohesive powder in anacoustic field,” Chem. Eng. Sci., 48, 41-52, 1993.Choi, J.H., J.E. Son and S.D. Kim, “Solids entrainment in fluidized bed combustors,” J. Chem.Eng. Japan, 22, 597-606, 1993.Chong, Y.O. and L.S. Leung, “Comparison of choking velocity correlations in vertical pneumaticconveying,” Powder Technol., 47, 43-50, 1986.Chyang, C.- S. and W. -C. Huang, “Characteristics of large particle fluidization,” J. Chinese Inst.Chem. Eng., 19, 81-89, 1988.Clark, N.N. and C.M. Atkinson, “Amplitude reduction and phase lag in fluidized-bed pressuremeasurements,” Chem. Eng. Sci., 43, 1547-1557, 1988.215Clark, N.N., E.A. McKenzie Jr. and M. Gautam, “Differential pressure measurements in aslugging fluidized bed,” Powder Technol., 67, 187-199, 1991.Clifi, R., “An Occamist review of fluidized bed modeling,” AIChE Symp. Ser., 89(296), 1-17,1993.Clifi, K and J.R. Grace, “Bubble interaction in fluiclized beds,” AIChE Symp. Ser., 66(105), 14-27, 1970.Clifi, K and J.K Grace, “Coalescence of bubbles in fluidized beds,” AIChE Symp. Ser., 67(116),23-33, 1971.Clifi, K and J.K Grace, “The mechanism of bubble break-up in fluidized beds,” Chem. Eng. Sci,27, 2309-23 10, 1972Clift, K, J.K Grace and M.E. Weber, “Stability of bubbles in fluidized beds,” Ind. Eng. Chem.Fundam., 13, 45-5 1, 1974.Clift, K, J.K Grace and V. Sollazzo, “Continuous slug flow in vertical tubes,” Trans. ASME Ser.C: J. Heat Transfer, 96, 371-376, 1974.Clifi, K, J.K Grace and M.E. Weber, Bubbles, Drops and Particles Academic Press, New York,1978.Clifi, K and J.K Grace, “Continuous bubbling and slugging,” Chapter 3 in Fluidization, J.F.Davidson, K Clift and KC. Darton eds., Academic Press, London, pp.73-132, 1985.Conrad, K, “Dense-phase pneumatic conveying: A review,” Powder TechnoL, 49, 1-35, 1986.Contractor, KM. and J. Chaouki, “Circulating fluidized bed as a catalytic reactor,” CirculatingFluiclized Bed Technology ifi, P. Basu, M. Horio and M. Hasatani eds., Pergamon Press,Toronto, pp.39-48, 1991.Crabtree, JR. and J. Bñdgwater, “Bubble coalescence in viscous liquids,” Chem. Eng. Sci., 26,839-85 1, 1971.Crescitelli, S., G. Donsi, G. Russo and K Clifi, “High velocity behaviour of fluidized beds: slugsand turbulent flow,” Chisa Conference, Prague, pp. 1-11, 1978.216Darton, R.C., RD. Lanauze, J.F. Davidson and D. Harrison, “Bubble growth due to coalescencein fluidized beds,” Trans. Instn. Chem. Engrs., 55, 274-280, 1977.Davidson, J.F., Symposium on fluidization - discussion, Trans. Instn. Chem. Engrs., 39, 23 0-232,1961.Davidson, J.F., Rapporteur’s report, Tripartite Chem. Eng. Conf Synip. on Fluidization,Montreal, Inst. of Chem. Engrs., London, p.3, 1968.Davidson, J.F., “The two-phase theory of fluidization: Successes and opportunities,” AIChESymp. Series, 87(281), 1-12, 1991.Davidson, J.F., D. Harrison and J.R.F. Guedes de Carvaiho, “On the liquid like behaviour offluidized beds,” Annu. Rev. Fluid Mech., 9, 5 5-86, 1977.Daw, C.S. and J.S. Halow, “Modelling deterministic chaos in gas fluidized beds,” AIChE Symp.Ser., 88(289), 61-69, 1992.Day, J.Y., H. Littman and M.H. Morgan ifi, “A new choking velocity correlation for verticalpneumatic conveying,” Chem. Eng. Sci, 45, 355-360, 1990.DeKee, D., P. J. Carreau and K Mordarski, “Bubble velocity and coalescence in viscoelasticliquids,” Cheni Eng. Sci., 41, 2273-2283, 1986.Didwania, A.K. and G.M. Homsy, “The stability of the propagation of sharp voidage fronts,”Fluidization, J.R. Grace and J.M. Matsen eds., Plenum Press, pp. 109-116, 1980.Doig, I.D. and G.H. Roper, “The minimum gas rate for dilute-phase solids transportation in a gasstream,” Australian Chem. Eng., 1, 9-19, 1963.Drahos, J., J. Cermak, R. Guardani and K Schugerl, “Characterization of flow regime transitionin a circulating fluiclized bed,” Powder Technol., 56, 4 1-48, 1988.Dry, R.J. and I.N. Christensen, “Periodic density-inversion effects in a high-velocity fluidizedbed,” Chem. Eng. Sci., 43, 73 1-733, 1988.Dry, R.J. and RD. La Nauze, “Combustion in fluidized beds,” Chem. Eng. Prog., 86, 31-47,1990.217Dunham, G.E., M.D. Mann and N.S. Grewal, “Dependence of transition to turbulent fluidizationon static bed depth in a fluidized bed,” 4th Tnt. Conf on Circulating Fluidized Beds,Somerset, PA, Aug. 1-5, 1993.Epstein, P.S. and R.R. Carhardt, “The absorption of sound in suspensions and emulsions,” 3.Acoust. Soc. Am., 25, 553-565, 1953.Fan, L.T., T.-C. Ho, S. Hiraoka and W.P. Walawender, “Pressure fluctuations in a fluidized bed,”AIChE J., 27, 388-396, 1981.Fan, L.T., T.-C. Ho and W.P. Walawender, “Measurements of the rise velocities ofbubbles, slugsand pressure waves in a gas-solid fluidized bed using pressure fluctuation signals,” AIChE J.,29, 33-39, 1983.Fan, L.T., T.C. Ho, N. Yutani and W.P. Walawender, “Statistical study of the frequency of freebubbling in a shallow gas-solid fluidized bed,” Fluidization VI, D. Kunii and R. Toei eds.,Engineering Foundation, New York, pp. 1-3-1, 1984.Filla, M., L. Massimilla, D. Musmarra and S. Vaccaro, “Propagation velocities of disturbancesoriginated by gas jets in fluidized beds,” IUTAM Symp. on Mechanics of Fluidized Beds,Stanford Univ., July 1-4, 1991.Gao, S., G. Thao, S. Qiu, and W. Ma, “Solid circulating rate in fast fluidized bed,” Proc. 3rdChina-Japan Conference on Fluidization, M. Kwauk and M. Hasatani eds., Science Press,Beijing, pp.’76-85, 1991.Geldart, D., “Types of gas fluidization,” Powder Technol., 7, 185-195, 1973.Geldart, D., “Gas Fluidization,” short course, University ofBradford, 1977.Geldart, D., “Particle entrainment and carryover,” Chapter 6 in Gas Fluidization Technology, D.Geldart ed., John Wiley & Sons, New York, pp. 123-153, 1986.Geldart, D. and A.R. Abrahamsen, “Homogeneous fluidization of fine powders using variousgases and pressures,” Powder Technol., 19, 133-136, 1978.Geldart, D. and D.J. Pope, “Interaction of fine and coarse particles in the freeboard of a fluidizedbed,” Powder Technol., 34, 95-97, 1983.218Geldart, D. and M.J. Rhodes, “From minimum fluidization to pneumatic transport- a criticalreview of the hydrodynamics,” Circulating Fluidized Bed Technology, P. Basu ed., PergamonPress, Toronto, pp.21-31, 1986.Geldart, D. and S.J. Ling, “Saltation velocities in high pressure conveying of fine coal,” PowderTechnol., 69, 157-162, 1992.Geldart, D. and H.Y. Xie, “The use of pressure probes in fluidized beds of Group A powders,”Fluidization VII, O.E. Potter and D.J. Nicklin eds., Engineering Foundation, New York,pp.’749-756, 1992.Grace, J.R., “The viscosity of fluidized beds,” Can. J. Chem. Eng., 48, 30-33, 1970.Grace, J.R., “Fluidized bed hydrodymanics,” Chapter 8.1 in the Handbook of Multiphase Flow, G.Hetsroni ed., Hemisphere, Washington, 1982.Grace, J.R. “Contacting modes and behaviour classification of gas-solid and other two-phasesuspensions,” Can. J. of Chem. Eng., 64, 353-363, 1986.Grace, J.R., “High-velocity fluidized bed reactors,” Chem. Eng. Sci., 45, 1953- 1966, 1990.Grace, J.R., “Agricola aground: characterization and interpretation of fluidization phenomena,”AIChE Symp. Ser., 88(289), 1-16, 1992.Grace, JR. and D. Harrison, “The distribution of bubbles within a gas-fluidized bed,” I.Chem.E.Symp. Ser.,No.30,pp.105-ll3, 1968.Grace, J.R. and D. Harrison, “The behaviour of freely bubbling Fluidized beds,” Chem. Eng. Sci.,24, 497-508, 1969.Grace, J.R. and G. Sun, “Influence ofparticle size distribution on the performance of fluidized bedreactors,” Can. J. Chem. Eng., 69, 1126-1134, 1991.Grace, J.R. and J. Tuot, “A theory for cluster formation in vertically conveyed suspensions ofintermediate density,” Trans. I. Chem. Engrs., 57, 49-54, 1979.Gregor, W. and H. Rumpf “Velocity of sound in two-phase media,” Tnt. J. Multiphase Flow, 1,753-769, 1975.219Gregor, W. and H. Rumpf “The attenuation of sound in gas-solid suspension,” Powder Technol.,15, 43-5 1, 1976.Grolmes, M.A. and H.K. Fauske, “Propagation characteristics of compression and rarefactionpressure pulses in one-component vapor-liquid mixtures,” Nuclear Eng. Des., 11, 137-142,1968.Guedes de Carvaiho, J.R.F., “The stability of slugs in fluidized beds of fine particles,” ClientEng. Sci., 36, 1349-1356, 1981.Halder, P.K, A. Datta and R. Cliattopadhyay, “Mass transfer considerations in a turbulentfluidized bed,” Proc. 11th Tnt. Fluidized Bed Combustion Conference, E.J. Anthony ed.,pp. 1223-1227, 1993.Hariu, O.H. and M.C. Moistad, “Pressure drop in vertical tubes in transport of solids by gases,”In Eng. Chem., 41, 1148-1157, 1949.Harrison, D., J.F. Davidson and J.W.de Kock, “On the nature of aggregative and particulatefluidization,” Trans. Instn. Client Engrs., 39, 202-211, 1961.Harrison, D. and J.R. Grace, “Fluidized beds with internal baffles,” Chaper 13 in Fluidization, J.F.Davidson and D. Harrison eds., Academic Press, London, pp.599-626, 1971.He, Y.L., C.J. Lim, J.R. Grace, J.-X. Thu and S.Z. Qin, “Measurements of voidage profiles inspouted beds,” Can. J. Client Eng., 72,229-234, 1994.Henry, RE., M.A. Grolmes and H.K Fauske, “Propagation velocity of pressure waves in gas-liquid mixtures,” Co-Current Gas-Liquid Flow, E. Rhodes and D.S. Scott eds., Plenum Press,New York, pp. 1-17, 1969.Hiby, J.W., “Periodic phenomena connected with gas-solid fluidization,” Proc. mt. Symp. onFluidization, A.A.H. Drinkenburg ed., Netherlands University Press, Amsterdam, pp.99-109,1967.Hirama, T., H. Takeuchi and T. Chiba, “Regime classification of macroscopic gas-solid flow in acirculating fluidized-bed riser,” Powder Technol., 70, 2 15-222, 1992.220Hong, S.C., KJ. Oh, C.S. Choi and D.S. Doh, “Statistical analysis of the pressure fluctuations ina gas-solid fluidized bed,” Proc. 1st Asian Conference on Fluidized-Bed and Three-PhaseReactors, pp.22-33, 1988.Horio, M., “Hydrodynamics of circulating fluidization -- present status and research needs,”Circulating Fluidized Bed Technology ifi, P. Basu, M. Horio, and M. Hasatani eds.,Pergamon Press, Oxford, pp.3-14, 1991.Horio, M., K. Morishita, 0. Tachibana and N. Muruta, “Solid distribution and movement incirculating fluidized beds,” Circulating Fluidized Beds Technology II, P. Basu and J.F. Largeeds., Pergamon Press, Oxford, 1988.Horio, M., H. Ishui and M. Nishimuro, “On the nature of turbulent and fast fluidized beds,”Powder Technol., 70, 239-246, 1992.Hosny, N.M., “Forces on tubes in a fluiclized bed,” Ph.D. thesis, University of British Columbia,1982.Ishii, H., T. Nakajima and M. Horio, “The structure of flow fields in circulating fluidized-beds,”Proc. 1st Asian Conference on Fluidized-Bed and Three-Phase Reactors, pp. 139-146, 1988.Ishui, M., “Wave phenomena and two-phase flow instability,” Chapter 2.4 in Handbook ofMultiphase Systems, G. Hetsroni ed., Hemisphere Publishing Co., New York, 1982.Jackson, R., “Fluid mechanic theory,” Chapter 3 in Fluidization, J.F. Davidson and D. Harrisoneds., Academic Press, New York, pp.65-119, 1971.Jiang, P.J. and L.- S. Fan, “Hydrodynamics of circulating fluidized bed with coarse particles,”AIChE Annual Meeting, Miami Beach, Florida, Nov. 1992.Jin, Y., Z.Q. Yu, Z.W. Wang and P. Cai, “A criterion for transition from bubbling to turbulentfluidization,” Fluidization V, K Ostergaard and A Sorensen eds., Engineering Foundation,New York, pp.289-296, 1986.Johnsson, F., A. Svensson and B. Leckner, “Fluidization regimes in circulating fluidized bedboilers,” Fluidization VII, O.E. Potter and D.J. Nicklin eds., Engineering Foundation, NewYork, pp.4’7l-478, 1992.221Jones, B.R.E. and D.L. Pyle, “On stability, dynamics, and bubbling in fluidized beds,” Chem. Eng.Prog. Symp. Ser., 67(116), 1-10, 1971.Jones, D.R.M. and J.F. Davidson, “The flow of particles from a fluidized bed through an orifice,”Rheol. Actã, 4, 180-186, 1965.Joshi, J.B. and Y.T. Shah, “Hydrodynamic and mixing models for bubble column reactors,” CheniEng. Comni, 11, 165-199, 1981Judd, M.R. and R. Goosen, “Effects of particle shape on fluidization characteristics of fineparticles in the freely and turbulent regimes,” Fluidization VI, J.R. Grace, LW. Shemilt andM.A. Bergougnou eds., Engineering Foundation, New York, pp. 4 1-48, 1989.Kage, H., N. Iwasaki and Y. Matsuno, “Frequency analysis of pressure fluctuation as a fluidizedbed diagnosis method,” J. Chem. Eng. Japan, 24, 76-8 1, 1991.Kage, H., N. Iwasaki and Y. Matsumo, “Frequency analysis ofpressure fluctuation in plenum as adiagnostic method for fluidized beds,” AIChE Symp. Ser., 89 (296), 184-190, 1993.Kai, T. and S. Furusaki, “Behaviour of fluidized beds of small particles at elevated temperatures,”J. Cheni Eng. Japan, 18, 113-118, 1985.Kai, T., M. Murakami, K.I. Yamasaki and T. Takahashi, “Relationship between apparent bedviscosity and fluidization quality in a fluidized bed with fine particles,” J. Chem. Eng. Japan,24, 494-500, 1991.Kaneo, Y., N. Yutani and M. Horio, “Pressure fluctuations in fluidized bed and freeboard,” Proc.1st Asia Conference on Fluidized-Bed and Three-Phase Reactors, pp. 14-21, 1988.Kang, W.K, J.P. Sutherland and G.L. Osberg, “Pressure fluctuations in a fluidized bed with andwithout screen cylindrical packings,” md. Eng. Cheni Fundani, 6, 499-504, 1967.Karplus, H.B., “The velocity of sound in a liquid containing gas bubbles,” Report C00-248,Illinois Inst. Technol., June 11, 1958.Kato, K, K Tamara, S. Arita, C. Wang and T. Takarada, “Particle holdup in a fast fluidized bed,”J. Chem. Eng. Japan, 22, 130-136, 1989.222Kehoe, P.W.K. and J.F. Davidson, “Continuously slugging fluidized beds,” Chemeca ‘70, Inst. ofCheni Eng. Symp. Ser., No.33, Butterworths, Australia, pp.9’7-1i6, 1970.Kehoe, P.W.K. and J.F. Davidson, “Pressure fluctuations in slugging fluidized beds,” AIChESymp. Ser.; 69(128), 34-40, 1972a.Kehoe, P.W.K. and J.F. Davidson, “The fluctuation of surface height in freely slugging fluidizedbeds,” AIChE Symp. Ser., 69(128), 41-48, 1972b.King, D.F., “Estimation of dense bed voidage in fast and slow fluidized beds of FCC catalyst,”Fluidization VI, J.R. Grace, L.W. Shemilt and M.A. Bergougnou eds., EngineeringFoundation, New York, pp.1-6, 1989.King, D.F. and D. Harrison, “The bubble phase in high-pressure fluidized beds,” Fluidization, J.R.Grace and J.M. Matsen eds., Plenum Press, pp. 101-108, 1980.King, D.F., F.R.G. Mitchell and D. Harrison, “Dense phase viscosities of fluiclized beds atelevated pressure,” Powder Technol., 28, 55-58, 1981.Klinzing, G.E., “Gas-solid transport,” McGraw-Hill, New York, 1981.Knowlton, T.M., “Pressure and temperature effects in fluid-particle systems,” Fluidization VII,O.E. Potter and D.J. Nicklin eds., Engineering Foundation, New York, pp.2’7-46, 1992.Knowlton, T.M. and D.M. Bachovchin, “The determination of gas-solids pressure drop andchoking velocity as a function of gas velocity in a vertical pneumatic conveying line,”Fluidization Technol., Vol. 1, D.L. Keairns ed., Hemisphere, Washington D.C., pp.253-282,1976.Kobayashi, M., D. Ramaswami and W.T. Brazelton, “Pulsed-bed approach to fluidization,” Chem.Eng. Prog. Symp. Ser., 66(105), 47-57, 1970.Kok, J.B.W., “Propagation velocity and rate of attenuation of surface waves on a homogeneouslyfluiclized bed,” IUTAM Symp. on Mechanics of Fluidized Beds, Stanford University, July 1-4, 1991.Komasawa, I., T. Otake and M. Kamojima, “Wake behaviour and its effect on interaction betweenspheñcal-cap bubbles,” J. Chem. Eng. Japan, 13, 103-109, 1980.223Konno, H. and S. Saito, “Pneumatic conveying of solids through straight pipes,” J. Cheni Eng.Japan, 2, 211-217, 1969.Kono, H.O., C.-C. Huang and M. Xi, “Stochastic and transient forces prevailing in fluiclized beds- basic understanding on attrition and erosion,” Fluidization VI, J.R. Grace, L.W. Shemilt andM.A. Bergougnou eds., Engineering Foundation, New York, pp. 597-604, 1989.Kunii, D. and 0. Levenspiel, “Entrainment of solids from fluidized beds: I. Hold-up of solids inthe freeboard, II. Operation of fast fluidlized beds,” Powder Technol., 61, 193-205, 1990.Kunii, D. and 0. Levenspiel, “Fluidization engineering,” Butterworth-Heinemann, Boston, MA,2nd edition, 1991.Kwauk, M., N. Wang, Y. Li, B. Chen and Z. Shen, “Fast fluidization at 1CM,” CirculatingFluidized Bed technology, P. Basu ed., Pergamon Press, Oxford, pp.13-62, 1986.Lancia, A., R. Nigro, G. Volpiceffi and L. Santoro, “Transition from slugging to turbulent flowregimes in fluidized beds detected by means of capacitance probes,” Powder Technol., 56,49-56, 1988.Lanneau, KP., “Gas-solids contacting in fluidized beds,” Trans. Instn. Chem. Engrs, 38, 125-137,1960.Lapidus, L. and J.C. Elgin, “Mechanics of vertical-moving fluidized systems,” ATChE J., 3, 63-68,1957.Leckner, B., “Heat transfer in circulating fluidized bed boilers,” Circulating Fluidized BedTechnology ifi, P. Basu, M. Horio andM. Hasatani eds., Pergamon Press, Toronto, pp.27-38, 1991.Lee, G. S. and S.D. Kim, “Pressure fluctuations in turbulent fluidized beds,” J. Cheni Eng. Japan,21, 5 15-521, 1988.Lee, G.S. and S.D. Kim, “Bed expansion characteristics and transition velocity in turbulentfluidized beds,” Powder Technol., 62, 207-2 15, 1990.Leu, L.-P. and C.-W. Lan, “Measurement of pressure fluctuations in two-dimensional gas-solidsfluidized beds at elevated temperatures,” J. Chem. Eng. Japan, 23, 555-562, 1990.224Leu, L.-P., J.-W. Huang and B.-B. Gua, “Axial pressure distribution in turbulent fluiclized beds,”Proc. 2nd Asian Conference on Fluidized-Bed and Three-Phase Reactors, pp.71-79, 1990.Leung, L.S., “Vertical pneumatic conveying: a flow regime diagram and a review of chokingversus non-choking systems,” Powder TechnoL, 25, 185-190, 1980.Leung, L.S., RJ. Wiles and D.J. Nicklin, “Correlation for predicting choking flowrate in verticalpneumatic conveying,” md. Eng. Chem. Process Des. Dev., 10, 183-189, 1971.Lewis, W.K., E.R. Gilliland and W.C. Bauer, “Characteristics of fluiclized particles,” md. Eng.Chem., 41, 1104-1117, 1949.Lewis, W.K, E.R. Gilliland and P.M. Lang, “Entrainment from fluidized beds,” AIChE Symp.Ser., 58 (38), 65-78, 1962.Li, J., M. Kwauk and L. Reh, “Role of energy minimization in gas-solid fluidization,”Fluidization VII, O.E. Potter and D.J. Nicklin eds., Engineering Foundation, New York,1992.Li, Y. and M. Kwauk, “The dynamics of fast fluidization,” Fluidization, J.R. Grace and J.M.Matsen eds., Plenum, New York, pp.5Y7-544, 1980.Lirag, R.C. and H. Littman, “Statistical study of the pressure fluctuations in a fluidized bed,”AIChE Symp. Ser., 67(116), 11-22, 1971.Lischer, J. and M.Y. Louge, “Optical fibre measurements of particle concentration in densesuspension: calibration and simulation,” Applied Optics, 31, 5106-5113, 1992.Little, W.J.G., “Pulsation phenomena in fluidized bed boilers,” Proc. 9th Intern. Conference onFluidized Bed Combustion, J.P. Mustonen ed., American Soc. Mech. Eng., New York,pp.561-566, 1987.Littman, H. and G.A.J. Homolka, “Bubble rise velocities in two-dimensional gas-fluidized bedsfrom pressure measurements,” AIChE Symp. Ser., 66(105), 37-46, 1970.Littman, H. and G.A.J. Homolka, “The pressure field around a two-dimensional gas bubble in afluidized bed,” Chem. Eng. Sci., 28, 223 1-2243, 1973.225Louge, M.Y. and M. Opie, “Measurements of the effective dielectricpermittivity of suspensions,”Powder Technol., 62, 85-94, 1990.Louge, M.Y., E. Mastorakos and J.T. Jenkins, “The role of particle coffisions in pneumatictransport,” J. Fluid Mech., 231, 345-356, 1991.Main, I.G., “Vibration and Waves in Physics,” Third edition, Cambridge University Press, 1993.Marcus, RD., L.S. Leung, G.E. Klinzing and F. Rizk, “Flow regimes in vertical and horizontalconveying,” Chapter 5 in Pneumatic Conveying of Solids, Chapman and Hall, New York,pp. 159-191, 1990.Martin, C.S. and M. Padmanabhan, “Pressure pulse propagation in two-component slug flow,” J.Fluids Engineering, 101, 44-52, 1979.Massimilla, L., “Behavior of catalytic beds of line particles at high gas velocities,” AIChE Symp.Ser., 69(128), 11-12, 1973.Matsen, T.M., “Evidence of maximum stable bubble size in a fluidized bed,” AIChE Symp. Ser.,69(128), 30-33, 1973.Matsen, T.M., “Some characteristics of large solids circulation systems,” Fluidization Technology,Vol.2, D.L. Keairns ed., Hemsphere Publishing Corp., Washington, pp. 135-141, 1976.Matsen, T.M., “Mechanisms of choking and entrainment,” Powder Technol., 32, 21-33 1982.Matsui, G., “Pressure wave propagation in a gas-liquid plug-train system,” Two-Phase FlowDynamics, A.E. Bergles and S. Ishigai eds., Hemisphere Publishing Corporation, New York,pp.185-200, 1981.Matsui, G., “Identification of flow regimes in vertical gas-liquid two-phase flow using differentialpressure fluctuations,” Tnt. J. Multiphase Flow, 10, 711-720, 1984.Matsumoto, S., S. Harada, S. Saito and S. Maeda, “Saltation velocity for horizontal pneumaticconveying,” J. Chem. Eng. Japan, 8, 33 1-333, 1975.Matsumoto, S., H. Sato, M. Suzuki and S. Maeda, “Prediction and stability analysis of choking invertical pneumatic conveying,” J. Chem. Eng. Japan, 15, 440-445, 1982.226Matsumoto, S. and M. Marakawa, “Statistical analysis of the transition of the flow pattern invertical pneumatic conveying,” mt. J. Muitiphase Flow, 13, 123-129, 1987.Matheson, G.L., W.A. Herbst and P.H. Holt, “Characteristics of fluid-solid systems,” md. Eng.Chein, 41, 1099-1104, 1949.Matthews, P.W., “Vibrations and Waves,” Northbum Printers, Bumaby, Canada, 1978.May, W.G. and F.R. Russell, “High pressure fluidization,” Presented at New Jersey Section ofA.C.S. Meeting-in-Miniature, 1953.Mecredy, R.C. and L.J. Hamilton, “Propagation of acoustic waves in two-phase two-componentmedia,” Trans. Amer. NucL Soc., 12, 833, 1969.Mei, J.S., J.M. Rockey, W.F. Lawson E. H. Robey, “Flow regime transitions in fluidized beds ofcoarse particles,” Proc. 11th Tnt. Fluidized Bed Combustion Conference, E.J. Anthony ed.,pp. 1225-1232, 1991.Mei, J.S., J.M. Rockey and E.H. Robey, “Effects of particle properties on fluidizationcharacteristics of coarse particles,” Presented at 4th Tnt. Conf on Circulating Fluidized Beds,Somerset, PA, Aug. 1-5, 1993.Miyazaki, K. and Y. Fujii, “Vapor explosions and pressure waves,” Two-Phase Flow Dynamics,A.E. Bergies and S. Ishigai eds., Hemisphere Publishing Corporation, New York, pp.285-310, 1981.Mok S.L.K, Y. Molodtsof J.F. Large and M.A. Bergougnou, “Characterization of dilute anddense-phase vertical upflow gas-solid transport based on average concentration and velocitydata,” Can. J. Chem. Eng., 67, 10-16, 1989.Mori, S., 0. Hashimoto, T. Haruta, K Mochizuki, W. Matsutani, S. Hiraoka, I. Yamada, T.Kojima and K. Tuji, “Turbulent fluidization phenomena,” Circulating Fluidized BedTechnology U, P. Basu and J.F. Large eds., Pergamon Press, Toronto, pp. 105-112, 1988.Mori, S., K Kato, E. Kobayashi and D. Liu, “Particle hold-up and its transport velocity incirculating fluidized bed,” Proc. 3rd China-Japan Conference on Fluidization, eds. M. Kwaukand M. Hasatani, Science Press, Beijing, pp.86-94, 1991.227Musmana, D., S. Vaccaro, M. Filla and L. Massimilla, “Propagation characteristics of pressuredisturbances originated by gas jets in fluidized beds,” Tnt. J. Multiphase Flow, 18, 965-976,1992.Musters, S.M.P. and K Rietema, “The effect of interparticle forces on the expansion of ahomogeneous gas-fluidized bed,” Powder TechnoL, 18, 23 9-248, 1977.Nakajima, M., M. Harada, M. Asai, R. Yamazaki and G. Jimbo, “Bubble fraction and voidage inan emulsion phase in the transition to a turbulent fluidized bed,” Circulating Fluiclized BedTechnology II, P. Basu and J.F. Large eds., Pergamon Press, Toronto, pp.’79-84, 1988.Nakoryakov, V.E., V.V. Kuznetsov, V.E. Dontsov and P.G. Markov, “Pressure waves ofmoderate intensity in liquid with gas bubbles,” mt. J. Multiphase Flow, 16, 74 1-749, 1990.Nazemi, A., M.A. Bergougnou and C.G.J. Baker, “Dilute phase hold-up in a large gas fluidizedbed,” AIChE Symp. Ser., 70 (141), 98- 102, 1974.Needham, D.J., “Surface waves on a homogeneously fluidized bed,” J. Eng. Math., 18, 259-271,1984.Nishihara, H. and I. Michiyoshi, “Acoustic velocity and attenuation in an air-water two-phasemedium,” Two-Phase Flow Dynamics, A.E. Bergies and S. Ishigai eds., HemispherePublishing Corporation, New York, pp.201-216, 1981.Nishikawa, K, K Sekoguchi and T. Fukano, “Characteristics of pressure pulsation in upwardtwo-phase flow,” Co-current Gas-liquid Flow, E. Rhodes and D.S. Scott eds., Plenum Press,New York, pp.18-46, 1969.Noordergraaf I.W., A. Van Dijk and C.M. Van Den Bleek, “Fluidization and slugging in large-particle systems,” Powder Technol., 52, 59-68, 1987.Nowak, W., M. Hasatani and M. Derczynski, “Fluidization and heat transfer of fine particles in anacoustic field,” AIChE Symp. Ser., 89(196), 137-149, 1993.Ormiston, KM., “Slug flow in fluidized beds,” Ph.D. thesis, Cambridge University, 1969. (datafrom Leung et al., 1971).228Otake, T., S. Tone, K. Nakao and Y. Mitsuhashi, “Coalescence and breakup of bubbles inliquids,” Chem. Eng. Sci., 32, 377-383, 1977.Park, W.H., W.K Kang, C.E. Capes and G.L. Osberg, “The properties of bubbles in fluidized bedof conducting particles as measured by an electroresistivity probe,” Chem. Eng. Sci., 24, 851,1969.Perales, J.F., T. Coil, M.F. Llop, L. Puigjaner, J. Amaldos and J. Casal, “On the transition frombubbling to fast fluidization regimes,” Circulating Fluidized Bed Technology ifi, P. Basu, M.Horio and M. Hasatani eds., Pergamon Press, Toronto, pp.73-’78, 1991.Punwani, D.V., M.V. Modi and P.B. Tarman, “A generalized correlation for estimating chokingvelocity in vertical solids transport,” Presented at International Powder Bulk Solids Handlingand Processing Conference, Chicago, 1976.Qin, S. and G. Liu, “Application of optical fibers to measure and display of fluidized systems,”Fluidization’82: Science and Technology, M. Kwauk and D. Kunii eds., Science Press,Beijing, China, pp.2S8-26’7, 1982.Ramayya, A.V., S.P. Venkateshan and A.K Kolar, “Comments on The analysis of pressurefluctuations in a two-dimensional fluidized bed,” Powder Technol., 68, 287-291, 1991.Reddy Karri, S.B. and T.M. Knowlton, “A practical definition of the fast fluidization regime,”Circulating Fluidized Bed Technology ifi, P. Basu, M. Horio, and M. Hasatani eds.,Pergamon Press, Oxford, pp.6’7-’72, 1991.Reh, L., “Fluid bed processing,” Chem. Eng. Progr., 67, 58-63, 1971.Rhodes, M.J., “The upward flow of gas/solid suspensions. Part 2: a practical quantitative flowregime diagram for the upward flow of gas/solid suspensions,” Chem. Eng. Res. Des., 67, 30-37, 1989.Rhodes, M.J., “Pneumatic conveying,” Chapter 7 in Principles of Powder Technology, M.J.Rhodes ed., John Wiley & Sons, New York, pp 143-170, 1990.Rhodes, M.J. and D. Geldart, “The hydrodynamics of re-circulating fluidized beds,” CirculatingFluidized Bed Technology, P. Basu ed., Pergamon Press, Oxford, pp.193-200, 1986a.229Rhodes, M.J. and D. Geldart, “Transition to turbulence?” Fluidization V, K Ostergaard and A.Sorensen eds., Science Foundation, New York, pp.281-288, 1986b.Rhodes, M.J. and D. Geldart, “A model for the circulating fluidized bed,” Powder Technol., 53,155-162, 1987.Rietema, K and S.M.P. Musters, “The effect of interparticle forces on the expansion of ahomogeneous gas-fluidized bed,” Proc. Tnt. Symp. on Fluidization and Its Applications,Toulouse, Oct. 1-5, pp.28-40, 1973.Rowe, P. N. and B.A. Partridge, “An X-ray study of bubbles in fluidized beds,” Trans. Tnstn.Chem. Engrs., 43, 157-171, 1965.Rowe, P.N. and H.J. MacGillivary, “The structure of a 15 cm diameter gas fluidized bed operatedat up to 1 m/s and seen by X-rays,” Fluidization, J.R. Grace and J.M. Matsen ed., Plenum,New York, pp.545-553, 1980.Roy, R., “Pressure fluctuations and scale-up in fluidized beds,” Ph.D. thesis, University ofCambridge, U.K., 1989.Roy, R. and J.F. Davidson, “Similarity between gas-fluidized beds at elevated temperature andpressure,” Fluidization VI, J.R. Grace, L.W. Shemilt and M.A. Bergougnou eds., EngineeringFoundation, New York, pp.293-300, 1989.Roy, K, J.F. Davidson and V.G. Tuponogov, “The velocity of sound in fluidized beds,” CheriiEng. Sci., 45, 3233-3245, 1990.Rudolph, V., Y.O. Chong and D.J. Nicklin, “Standpipe modelling for circulating fluidized beds,”Circulating Fluidized Bed Technology ifi, P. Basu, M. Horio, and M. Hasatani eds.,Pergamon Press, Oxford, pp.49-64, 1991.Ryzhkov, A.F. and E.M. Tolmachev, “Selection of optimal height for vibrofluiclized bed,” Theor.Found. Chem. Eng., 17, 140-147, 1983.Sadasivan, N., D. Barreteau and C. Laguerie, “Studies on frequency and magnitude offluctuations ofpressure drop in gas-solid fluidized beds,” Powder Technol., 26, 67-74, 1980.230Satija, S. and L.- S. Fan, “Characteristics of slugging regime and transition to turbulent regime forfluidized beds of large coarse particles,” AIChE J., 31, 1554-1562, 1985a.Satija, S. and L.- S. Fan, “Terminal velocity of dense particles in the multisolid pneumatictransport bed,” Chem. Eng. Sci., 40, 259-267, 1985b.Satija, S., J.B. Young and L.-S. Fan, “Pressure fluctuations and choking criterion for verticalpneumatic conveying of fine particles,” Powder Technol., 43, 257-271, 1985.Sclmitzlein, M.G. and H. Weinstein, “Flow characterization in high-velocity fluidized beds usingpressure fluctuations,” Chem. Eng. Sci., 43, 2605-2614, 1988.Schugel, K., M. Merz and F. Fetting, “Ermittlung der Dicliteverteilung in gasdurchstromtemFliessbettsystemen durch Rontgenstrahlen”, Chem. Eng. Sci., 15, 39-74, 1961.Sciazko, M., J. Bandrowski and J. Raczek, “On the entrainment of solid particles from a fluidizedbed,” Powder Technol., 66, 33-39, 1991.Senior, R.C. and C.M.H. Brereton, “Modelling of circulating fluidized bed solid flow anddistribution,” Chem. Eng. Sci., 47, 281-296, 1992.Seo, Y.C. and RH. Park, “Pressure and void fluctuations in a two-dimensional fluidized bed,”Proc. 1st Asia Conference onFluidized-Bed and Three-Phase Reactors, pp. 1-13, 1988.Shorokhod, V.V., “Electrical conductivity, modulus of elasticity, and viscosity coefficients ofporous bodies,” Powder Metallurgy, 6, 188-200, 1963.Sitnai, D., “Utilization of the pressure differential records from gas fluidized beds with internalsfor bubble parameters determination,” Chem. Eng. Sci., 37, 1059-1066, 1983.Sitnai, D., D.C. Dent and A.B. Whitehead, “Bubble measurement in gas-solid fluidized beds”,Chem. Eng. Sci., 36, 1583, 1981.Smith, T.N., “Limiting volume fractions in vertical pneumatic transport,” Chem. Eng. Sci, 33,745-749, 1978.Son, J.E., J.H. Choi and C.KLee, “Hydrodynamics in a large circulating fluidized bed,”Circulating Fluidized Bed Technology II, P. Basu and J.F. Large eds., Pergamon Press,Toronto, pp.113-120, 1988.231Squires, A.M., M. Kwauk and A.A. Avidan, “Fluid beds: at last, challenging two entrenchedpractices,” Science, 230, 1329-1337, 1985.Staub, F.W. and G.S. Canada, “Effect of tube bank and gas density on flow behavior and heattransfer in fluidized beds,” Fluidization, J.F. Davidson and J.H. Harrison eds., CambridgeUniversity Press, pp.339-344, 1978.Stewart, P.S.B. and J.F. Davidson, “Slug flow in fluidized beds”, Powder Technol., 1, 61-80,1967.Subzwa4, M.P., R. Chit and D.L. Pyle, “Bubbling behaviour of fluidized beds at elevatedpressures,” Fluidization, J.F. Davidson and D. Harrison eds., Cambridge Press, pp.50-53,1978.Sun, G.L., “Influence of particle size distribution on the performance of fluidized bed reactors,”Ph.D. thesis, University ofBritish Columbia, 1991.Sun, G.L. and G. Chen, “Transition to turbulent fluidization and its prediction,” in Fluidization VI,JR. Grace, L.W. Shemilt and M.A. Bergougnou eds., Engineering Foundation, New York,pp.33-44, 1989.Sun, G.L. and J.R. Grace, “Effect of particle size distribution in different fluidization regimes,”AIChE 1., 38, 7 16-722, 1992.Sun, J., M.M. Chen, and B.T. Chao, “On the fluctuation motions due to surface waves in gasfluidized beds,” Proc. 1st World Conference on Experimental Heat Transfer, Fluid Mechanicsand Thermodynamics, RK. Shah, E.N. Ganic and K.T. Yang eds., Elsevier, New York,p.1310, 1988.Sun, J.K. and G.L. Yang, “Studies on flow regimes of circulating fluidized beds,” Proc. 5thNational Fluidization Conference, Tsinghua University Press, Beijing, pp.86-89, 1990.Svensson, A., F. Johnsson and B. Leckner, “Fluid-dynamics of the bottom bed of circulatingfluidized bed boilers,” Proc. 12th Tnt. Conf on Fluidized Bed Combustion, L.N. Rubow ed.,ASME, Vol.2, pp.887-897, 1993.232Takeuchi, H., L. Hirama, T. Chiba, J. Biswas and L.S. Leung, “A quantitative regime diagram forfast fluidization,” Powder Technol., 47, 195-199, 1986.Tamarin, A.I., “The origin of selfexcited oscillation in fluidized beds,” mt. Cheni Eng., 4, 50-54,1964.Taylor, P.A., M.H. Lorenz and M.R. Sweet, “Special analysis of pressure noise in a fluidizedbed,” Fluidization and Its Applications, Cépadues Editions, Toulouse, France, pp.90-98,1973.Teo, C.S. and L.S. Leung, “Vertical flow of particulate solids in standpipes and risers,” Chapterii in Hydrodynamics of Gas-Solids Fluidization, eds. N.P. Cheremisnoff and P.N.Cheremisnoff Gulf Publishing Company, Houston, pp.470-1984.Thiel, W.J. and O.E. Potter, “Slugging in fluidized beds,” md. Eng. Cheni Fundaim, 16, 242-247,1977.Thomas, D.G., “Transport characteristics of suspensions: part VT, minimum transport velocity forlarge particle size suspensions in round horizontal pipes,” AIChE J., 8, 373-378, 1962.Tsukada, M., D. Nakanishi and M. Horio, “The effect of pressure on the phase transition frombubbling to turbulent fluidization,” Tnt. J. Multiphase Flow, 19, 27-34, 1993.Tutu, N.K, “Pressure fluctuations and flow pattern recognition in vertical two phase gas-liquidflows,” Tnt. J. Multiphase Flow, 8, 443-447, 1982.Tutu, N.K., “Pressure drop fluctuations and bubble-slug transition in a vertical two phase air-water flow,” hit. J. Multiphase Flow, 10, 211-216, 1984.Upson, P.C. and D. L. Pyle, “The stability of bubbles in fluidized bed,” Fluidization and ItsApplications, Cépadues Editions, pp.207-222, Toulouse, France, 1973.Verloop, J. and P.M. Heertjes, “Shock waves as a criterion for the transition from homogeneousto heterogeneous fluidization”, Chem. Eng. Sci., 25, 825-832, 1970.Verloop, J. and P.M. Heertjes, “Periodic pressure fluctuations in fluidized beds,” Chem. Eng. Sci.,29, 1035-1042, 1974.Waffis, G.B., “One-dimensional two-phase flow,” McGraw-Hill, New York, 1969.233Weimer, A.W. and K.V. Jacob, “On bed voidage and apparent dilute phase hold-up in highpressure-turbulent fluidized beds of fine powders,” Fluidization V, K Ostergaard and ASorensen eds., Science Foundation, New York, pp.313-320, 1986.Wen, C.Y. and Y.H. Yu, “A generalized method for predicting the minimum fluiclizationvelocity,” AIChE J., 12, 6 10-612, 1966.Wen, C.Y. and A.F. Galli, “Dilute-phase systems,” Chapter 16 in Fluidization, J.F. Davidson andD. Hamson eds., Academic Press, New York, pp.6’77-’7lO, 1971.Wen, C.Y. and L.H. Chen, “Fluidized bed freeboard phenomena: entrainment and elutriation,”AIChEJ.,28, 117-128, 1982.Werther, J. and 0. Molerus, “The local structure of gas fluidized beds: II. The spatial distributionofbubbles,” Jut. J. Multiphase Flow, 1, 103-122, 1973.Wilhelm, RH. and S. Valentine, “The fluidized bed,” hid. Eng. Cheni, 43, 1199-1203, 1951.Winter, 0., “Density and pressure fluctuations in gas fluidized beds,” ATChE J., 14, 426-434,1968.Wirth, K-E. and 0. Molerus, “Critical solids transport velocity in horizontal pipelines,” Chapter15 in Encyclopedia of Fluid Mechanics, Volume 4, N.P. Cheremisnoff ed., Gulf PublishingCompany, Houston, pp.471-484, 1986.Whitehead, A.B. “Some problems in large-scale fluidized beds,” Chapter 19 in Fluidization, J.F.Davidson and D. Harrison eds., Academic Press, New York, pp.’78l-8l4, 1971.Wong, H.W. and M.H.I. Baird, “Fluidization in a pulsed gas flow,” Chem. Eng. J., 2, 104-113,1971.Yang, W.C., “A mathematical definition of choking phenomenon and a mathematical model forpredicting choking velocity and choking voidage,” AIChE J., 21, 10 13-1021, 1975.Yang, W.C., “A criterion for fast fluidization,” Paper #E5, 3rd Intern. Conf on PneumaticTransport, April 7-11, Bedford, England, 1976.Yang, W.C., “Criteria for choking in vertical pneumatic conveying lines,” Powder TechnoL, 35,143-150, 1983.234Yang, W. C., “Mechanistic models for transitions between regimes of fluidization,” AIChE J., 30,1025-1027, 1984.Yang, W.C., “A model for the dynamics of a circulating fluidized bed loop,” Circulating FluidizedBed technology II, J.F. Large and P. Basu eds., Pergamon Press, Oxford, pp.181-191, 1988.Yang, W.C., and D.C. Chitester, “Transition between bubbling and turbulent fluiclization atelevated pressure,” AIChE Symp. Series, 84(262), 10-21, 1988.Yang, Y.R., S.X. Rong, G. Chen and B.C. Chen, “Flow regimes and regime transitions inturbulent fluidized beds,” Chem. Reaction Eng. and Technol.(in Chinese), 6, 9-16, 1990.Yates, J.G. and D.J. Cheesman, “Voidage variations in the regions surrounding a rising bubble ina fluidized bed,” AIChE Symp. Ser., 88(289), 34-3 9, 1992.Yerushalnii, J., D.H. Turner and A.M. Squires, “The fast fluidized bed,” hid. Eng. Chem. ProcessDes. Dev., 15, 47-5 1, 1976.Yerushahni, J., N.T. Cankurt, D. Geldart and B. Liss, “Flow regimes in vertical gas-solid contactsystems,” AIChE Symp. Ser., 174(176), 1-12, 1978.Yerushalnii, J. and N.T. Canlcurt, “Further studies of the regimes of fluidization,” PowderTechnol., 24, 187-205, 1979.Yousfi, Y. and G. Gau, “Aerodynamique de l’écoulement vertical de suspensions concentrêesgaz-solides- I. Regimes d’écoulement et stabilité aerodynamique,” Chem. Eng. Sci, 29,1939-1946, 1974.Zemz, F.A., “Two-phase fluidized-solid flow,” hid. Eng. Chem., 41, 280 1-2806, 1949.Zenz, F.A. and N.A. Weil, “A theoretical-empirical approach to the mechanism of particleentrainment from fluidized beds,” AIChE J., 4, 472-479, 1958.Zenz, F.A. and D.F. Othmer, “Fluidization and fluid-particle systems,” Reinhold Publishing Co.,New York, 1960.Zenz, F.A. and D.F. Othmer, “The saturation dilute-phase concentration of matter,” Chem. Eng.Comm., 116, 89-96, 1992.235Zhang, KY., D.B. Chen and G.L. Yang, “Study on pressure drop of fast fluidized beds,” Proc. 1stChina-Japan Conference on Fluidization, M. Kwauk and D. Kunii eds., Science Press,Beijing, pp. 148-157, 1985.Zhang, KY., G.H. Luo, J.S. Liu and G.L. Yang, “Study on pressure drop of fast fluidized beds,”Chem. Reac. Eng. Technol., 6, 24-28, 1990.Thao, X. and G.L. Yang, “Critical turbulent velocity for fluidized beds with baffles,” Proc. 3rdChina-Japan Fluidization Conference, M. Kwauk and M. Hasatani eds., Science Press,Beijing, pp. 196-201, 1990.Thou, J., J.R. Grace, S. Qin, C.H.M. Brereton, C.J. Lim and J.-X. Thu, “Voidage prollies in acirculating fluidized bed of square cross-section,” Chem. Eng. Sci. (in press), 1994.236Appendix 1. Determination of Void Phase Volume FractionFigure A. 1 shows traces recorded by the optical fibre probe for six different superficial gasvelocities. It is seen that there exist distinct two phases, a void phase corresponding to lowamplitude signals, and a dense phase corresponding to high amplitude signals. Such distinct void-dense phase traces give a bimodal distribution of probability function as shown in Figure A.2. Todetermine the volume fraction ofvoid phase and dense phase, an amplitude threshold must be set.It is seen that some small amplitude signals from small voids are superimposed on large amplitudesignals from large voids, contributing to the probability count in the intermediate amplitude range.One possibility is to set the middle point, i.e., (l-e)/(l-E)=O.5, as the distinguishing boundary.This seems to be justified when the bed is operated at low gas velocities where the dense phaseexpands very little and solids content in voids is small. When dense phase expansion and solidscontent in voids are taken into account, the dividing point may differ from the middle point. Asecond way to divide the void and dense phases is to set the boundary at the minimum probabilitypoint. This compensates somewhat for dense phase expansion and solids contained in voids. Thedisadvantage of this method is that determination of the minimum point becomes difficult whenthere is a flat region between the two peaks. In the present analysis the minimum point methodhas been used to determine void volume fraction. When a flat region appears, the middle point ofthe flat region is used as the cut point.Figure A.3 shows the void phase volume fraction from the two methods. The trend fromboth methods is identical, although the “middle point cut” method generally gives lower voidphase volume fraction than the “minimum point cut” method.237(1(a)(b(C)(d)(e)(f)4Figure A. 1. Traces from optical fibre probe on the axis of the bed with FCC particles for z=O.28m, r/R0.O. (a) U0.086 mis; (b) Ur=O.40 m; (c) U=O.80 mis; (d) U=1.15 mis; (e)U=l.50 mis; (f) U=l.72 rn/s.0 2Time, S238(l-E)/(l-s) (l-6)/(1-,)Figure A.2. Typical probability distribution function ofvoidage fluctuations from optical probe onthe axis for z=O.28 m, r/R=O.O.0.68 B040.2U, rn/sFigure A.3. Local void phase volume fraction from two interpretation methods as a function ofsuperficial gas velocity and radial location of the probe for z=O.28 iiiI I0.800 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2239

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