Yang Fluidization, Solids Handling, and Processing
.pdfContents xiii
3 Heat Transfer in Fluidized Beds .......................................... |
153 |
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John C. Chen |
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1.0 |
INTRODUCTION ................................................................................ |
153 |
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2.0 |
BUBBLING DENSE FLUIDIZATION ............................................. |
154 |
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2.1 |
Hydrodynamic Characteristic ...................................................... |
154 |
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2.2 |
Heat Transfer to Submerged Surfaces ......................................... |
155 |
3.0 |
CIRCULATING FAST FLUIDIZATION .......................................... |
173 |
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3.1 |
Hydrodynamic Characteristics ..................................................... |
173 |
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3.2 |
Heat Transfer ................................................................................ |
178 |
NOTATIONS ................................................................................. |
201 |
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Subscripts ................................................................................. |
202 |
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REFERENCES ................................................................................. |
202 |
4 Gas Distributor and Plenum Design in Fluidized Beds ... |
209 |
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S.B. Reddy Karri and Ted M. Knowlton |
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1.0 |
INTRODUCTION ................................................................................ |
209 |
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2.0 |
TYPES OF GRIDS............................................................................... |
210 |
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2.1 |
Perforated Plates (Upwardly-Directed Flow) ............................. |
210 |
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2.2 |
Bubble Cap (Laterally-Directed Flow) ....................................... |
210 |
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2.3 |
Sparger (Laterally or Downwardly-Directed Flow) ................... |
211 |
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2.4 |
Conical Grids (Laterally-Directed Flow) .................................... |
211 |
3.0 |
GRID DESIGN CRITERIA ................................................................ |
212 |
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3.1 |
Jet Penetration ............................................................................... |
212 |
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3.2 |
Grid Pressure-Drop Criteria ......................................................... |
214 |
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3.3 |
Design Equations .......................................................................... |
215 |
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3.4 |
Additional Criteria for Sparger Grids .......................................... |
218 |
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3.5 |
Port Shrouding or Nozzle Sizing ................................................. |
219 |
4.0 |
PARTICLE ATTRITION AT GRIDS ................................................ |
220 |
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4.1 |
Attrition Correlation ..................................................................... |
222 |
5.0 |
EROSION ................................................................................. |
223 |
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6.0 |
EFFECTS OF TEMPERATURE AND PRESSURE ......................... |
223 |
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7.0 |
PLENUM DESIGN .............................................................................. |
223 |
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8.0 |
DESIGN EXAMPLES ......................................................................... |
225 |
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8.1 |
FCC Grid Design .......................................................................... |
225 |
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8.2 |
Polyethylene Reactor Grid Design .............................................. |
230 |
NOTATIONS ................................................................................. |
233 |
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REFERENCES ................................................................................. |
235 |
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5 Engineering and Applications of Recirculating |
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and Jetting Fluidized Beds ................................................... |
236 |
Wen-Ching Yang
1.0 INTRODUCTION ................................................................................ |
236 |
xivContents
2.0RECIRCULATING FLUIDIZED BEDS WITH A DRAFT TUBE . 237
2.1 |
Draft Tube Operated As A Fluidized Bed .................................. |
240 |
2.2 |
Draft Tube Operated As A Pneumatic Transport Tube ............. |
242 |
2.3 |
Design Example for a Recirculating Fluidized Bed |
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with a Draft Tube .......................................................................... |
257 |
2.4 |
Industrial Applications ................................................................. |
263 |
3.0 JETTING FLUIDIZED BEDS ............................................................ |
264 |
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3.1 |
Jet Penetration and Bubble Dynamics ......................................... |
265 |
3.2 |
Gas Mixing Around the Jetting Region ...................................... |
281 |
3.3 |
Solids Circulation in Jetting Fluidized Beds ............................... |
295 |
3.4 |
Fines Residence Time in Jetting Fluidized Beds ........................ |
315 |
3.5 |
Scale-up Considerations ............................................................... |
317 |
3.6 |
Applications ................................................................................. |
319 |
NOTATIONS ................................................................................. |
319 |
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Greek Letters ................................................................................. |
322 |
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REFERENCES ................................................................................. |
323 |
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6 Fluidized Bed Coating and Granulation ........................... |
331 |
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Richard Turton, Gabriel I. Tardos, and Bryan J. Ennis |
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1.0 INTRODUCTION ................................................................................ |
331 |
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2.0 COATING OF PARTICLES IN FLUIDIZED BEDS ....................... |
333 |
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2.1 |
Introduction ................................................................................. |
333 |
2.2 |
Overview of Coating Process ....................................................... |
335 |
2.3 |
Microscopic Phenomena .............................................................. |
339 |
2.4 |
Modelling ................................................................................. |
344 |
2.5 |
Design Criteria .............................................................................. |
355 |
3.0 GRANULATION OF FINE POWDERS IN FLUIDIZED BEDS.... |
365 |
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3.1 |
Introduction ................................................................................. |
365 |
3.2 |
Microscopic Phenomena .............................................................. |
366 |
3.3 |
Granule Growth Kinetics ............................................................. |
380 |
3.4 |
Experimental Support and Theoretical Predictions .................... |
387 |
3.5 |
Granule Consolidation, Attrition and Breakage ......................... |
398 |
3.6 |
Modeling of Granulation Processes ............................................ |
406 |
3.7 |
Unwanted Aggregation in Fluidized Beds .................................. |
418 |
ACKNOWLEDGMENT ............................................................................. |
424 |
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NOTATIONS ................................................................................. |
424 |
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REFERENCES ................................................................................. |
429 |
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7 Attrition in Fluidized Beds and Pneumatic |
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Conveying Lines .................................................................... |
435 |
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Joachim Werther and Jens Reppenhagen |
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1.0 INTRODUCTION ................................................................................ |
435 |
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2.0 FACTORS AFFECTING ATTRITION ............................................. |
437 |
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2.1 |
Material Properties ....................................................................... |
438 |
2.2 |
Process Conditions ....................................................................... |
440 |
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Contents |
xv |
3.0 |
ASSESSMENT OF ATTRITION ....................................................... |
444 |
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3.1 |
Breakage and Selection Functions............................................... |
444 |
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3.2 |
Attrition Rate ................................................................................. |
445 |
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3.3 |
Friability Indices ........................................................................... |
446 |
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3.4 |
Grindability Indices ...................................................................... |
446 |
4.0 |
ATTRITION TESTS ............................................................................ |
447 |
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4.1 |
Friability Tests .............................................................................. |
447 |
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4.2 |
Experiments to Study Attrition Mechanisms .............................. |
448 |
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4.3 |
Test Equipment and Procedures .................................................. |
449 |
5.0 |
ATTRITION IN FLUIDIZED BED SYSTEMS ................................ |
455 |
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5.1 |
Sources of Attrition ...................................................................... |
455 |
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5.2 |
Attrition in the Overall Fluidized Bed System, |
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Continuous Processes ................................................................... |
473 |
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5.3 |
Steps to Minimize Attrition in Fluidized Beds ........................... |
475 |
6.0 |
ATTRITION IN PNEUMATIC CONVEYING LINES.................... |
478 |
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6.1 |
Modeling ................................................................................. |
480 |
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6.2 |
Parameter Effects .......................................................................... |
480 |
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6.3 |
Steps to Minimize Attrition in Pneumatic Conveying Lines ..... |
482 |
NOTATIONS ................................................................................. |
484 |
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Subscripts ................................................................................. |
485 |
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Greek Symbols ................................................................................. |
486 |
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REFERENCES ................................................................................. |
486 |
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8 Bubbleless Fluidization ......................................................... |
492 |
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Mooson Kwauk |
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1.0 |
INTRODUCTION ................................................................................ |
492 |
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2.0 |
FLUIDIZED LEACHING AND WASHING .................................... |
492 |
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2.1 |
Uniform Particles .......................................................................... |
496 |
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2.2 |
Mixed Particles ............................................................................. |
500 |
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2.3 |
Staged Fluidized Leaching (SFL) ................................................ |
502 |
3.0 |
BUBBLELESS GAS/SOLID CONTACTING .................................. |
502 |
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3.1 |
Bubbling Fluidization and G/S Contacting Efficiency .............. |
502 |
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3.2 |
Species of Bubbleless G/S Contacting ........................................ |
507 |
4.0 |
DILUTE RAINING FLUIDIZATION ............................................... |
508 |
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4.1 |
Raining Particles Heat Exchanger ............................................... |
508 |
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4.2 |
Experimental Verification ............................................................ |
512 |
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4.3 |
Baffling and Particles Distribution .............................................. |
515 |
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4.4 |
Pilot Plant Demonstration ............................................................ |
519 |
5.0 |
FAST FLUIDIZATION ....................................................................... |
523 |
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5.1 |
Longitudinal Voidage Distribution ............................................. |
525 |
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5.2 |
Regimes for Vertical G/S Systems .............................................. |
529 |
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5.3 |
Radial Voidage Distribution ........................................................ |
533 |
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5.4 |
Modeling Fast Fluid-bed Reactors .............................................. |
533 |
6.0 |
SHALLOW FLUID BEDS .................................................................. |
537 |
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6.1 |
Dynamics for the Distributor Zone.............................................. |
537 |
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6.2 |
Activated Solids Shallow Fluid Bed Heat Exchanger ................ |
537 |
xvi Contents
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6.3 |
Cocurrent Multistage Shallow Fluid Bed .................................... |
541 |
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6.4 |
The Co-MSFB as a Chemical Reactor ........................................ |
545 |
7.0 |
FLUIDIZATION WITH NO NET FLUID FLOW ............................ |
546 |
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7.1 |
Levitation of Discrete Particles .................................................... |
547 |
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7.2 |
Semi-Fluidization through Oscillatory Flow .............................. |
551 |
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7.3 |
Application to Pseudo Solid-Solid Reactions ............................. |
553 |
8.0 |
PARTICLES WHICH QUALIFY |
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FOR BUBBLELESS OPERATION ................................................... |
556 |
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8.1 |
Powder Characterization .............................................................. |
556 |
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8.2 |
Improving Fluidization by Particle Size Adjustment ................. |
562 |
9.0 |
WHY BUBBLING AND NOT PARTICULATE FLUIDIZATION 569 |
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9.1 |
The Energy-Minimized Multiscale (EMMS) Model .................. |
570 |
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9.2 |
Reconciling L/S and G/S Systems ............................................... |
573 |
10.0 |
EPILOGUE ................................................................................. |
576 |
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NOTATIONS ................................................................................. |
576 |
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REFERENCES ................................................................................. |
578 |
9 Industrial Applications of Three-Phase Fluidization |
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Systems ................................................................................... |
582 |
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Jack Reese, Ellen M. Silva, Shang-Tian Yang, |
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and Liang-Shih Fan |
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1.0 INTRODUCTION ................................................................................ |
582 |
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Part I: Smelting Reduction, Paper Processing, and |
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Chemical Processing ................................................................................. |
588 |
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2.0 SMELTING REDUCTION ................................................................. |
588 |
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2.1 |
Introduction ................................................................................. |
588 |
2.2 |
Principles of Smelting Reduction ................................................ |
590 |
2.3 |
Post-Combustion and Heat Transfer in SRF ............................... |
593 |
2.4 |
Slag Layer Behavior ..................................................................... |
599 |
2.5 |
Future of Smelting Reduction of Iron Ore .................................. |
603 |
3.0 PAPER PROCESSING ........................................................................ |
604 |
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3.1 |
Introduction ................................................................................. |
604 |
3.2 |
Chemical Pulping of Wood Chips ............................................... |
605 |
3.3 |
Pulp Bleaching and Flotation De-inking ..................................... |
609 |
4.0 CHEMICAL PROCESSING ............................................................... |
614 |
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4.1 |
Introduction ................................................................................. |
614 |
4.2 |
Hydrotreating/Hydrocracking Petroleum Intermediates ............ |
614 |
4.3 |
Fischer-Tropsch Synthesis ........................................................... |
619 |
4.4 |
Methanol Synthesis ...................................................................... |
621 |
Part II: Three-Phase Biofluidization ...................................................... |
623 |
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5.0 BIOLOGICAL APPLICATIONS OF THREE-PHASE |
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FLUIDIZATION ................................................................................. |
623 |
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5.1 |
Introduction ................................................................................. |
623 |
5.2 |
Applications ................................................................................. |
629 |
5.3 |
Bioparticles ................................................................................. |
637 |
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Contents |
xvii |
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5.4 |
Hydrodynamics ............................................................................. |
643 |
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5.5 |
Phase Mixing in a Three-Phase Reactor ..................................... |
647 |
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5.6 |
Mass Transfer................................................................................ |
648 |
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5.7 |
Modeling ................................................................................. |
651 |
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5.8 |
Scale Up ................................................................................. |
653 |
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5.9 |
Process Strategy ............................................................................ |
655 |
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5.10 |
Novel Reactors .............................................................................. |
657 |
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5.11 |
Economics ................................................................................. |
661 |
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5.12 |
Summary ................................................................................. |
662 |
ACKNOWLEDGMENT ............................................................................. |
663 |
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NOTATIONS ................................................................................. |
663 |
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REFERENCES ................................................................................. |
664 |
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10 Dense Phase Conveying ......................................................... |
683 |
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George E. Klinzing |
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1.0 |
INTRODUCTION ................................................................................ |
683 |
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2.0 |
ADVANTAGES OF DENSE PHASE CONVEYING ...................... |
693 |
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3.0 |
BASIC PHYSICS ................................................................................. |
695 |
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4.0 |
PULSED PISTON FLOWS ................................................................. |
698 |
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5.0 |
VERTICAL FLOW SYSTEMS .......................................................... |
706 |
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6.0 |
BOOSTERS ................................................................................. |
708 |
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NOTATIONS ................................................................................. |
709 |
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Greek ................................................................................. |
709 |
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Subscripts ................................................................................. |
710 |
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REFERENCES ................................................................................. |
710 |
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11 Design Considerations of Long-Distance Pneumatic |
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Transport and Pipe Branching ............................................ |
712 |
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Peter W. Wypych |
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1.0 |
INTRODUCTION ................................................................................ |
712 |
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2.0 |
LONG-DISTANCE PNEUMATIC CONVEYING ........................... |
713 |
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2.1 |
Product Characterization and Classification ............................... |
714 |
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2.2 |
Blow Tank Design ........................................................................ |
733 |
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2.3 |
Conveying Characteristics ........................................................... |
738 |
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2.4 |
Pressure Drop Prediction.............................................................. |
741 |
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2.5 |
Stepped-Diameter Pipelines ......................................................... |
747 |
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2.6 |
Valves ................................................................................. |
748 |
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2.7 |
Pipeline Unblocking Techniques ................................................. |
751 |
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2.8 |
General Considerations ................................................................ |
752 |
3.0 |
PIPE BRANCHING ............................................................................. |
753 |
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3.1 |
Dust Extraction ............................................................................. |
754 |
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3.2 |
Flow Splitting ................................................................................ |
760 |
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3.3 |
Pressure Loss ................................................................................ |
766 |
NOTATIONS ................................................................................. |
767 |
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REFERENCES ................................................................................. |
769 |
xviii Contents
12 Cyclone Design ...................................................................... |
773 |
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Frederick A. Zenz |
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1.0 |
INTRODUCTION ................................................................................ |
773 |
2.0 |
REQUIRED DESIGN DATA ............................................................. |
774 |
3.0 |
CORRELATING FRACTIONAL COLLECTION EFFICIENCY .. |
775 |
4.0 |
EFFECT OF SOLIDS LOADING ...................................................... |
778 |
5.0 |
CYCLONE LENGTH .......................................................................... |
778 |
6.0 |
CONES, DUST HOPPERS AND EROSION .................................... |
780 |
7.0 |
CYCLONE INLET AND OUTLET CONFIGURATIONS.............. |
781 |
8.0 |
THE COUPLING EFFECT ................................................................. |
785 |
9.0 |
PRESSURE DROP .............................................................................. |
787 |
10.0 |
SPECIAL CASES ................................................................................ |
788 |
11.0 |
BED PARTICLE SIZE DISTRIBUTION |
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AND CYCLONE DESIGN ................................................................. |
791 |
12.0 |
CENTRIFUGAL VERSUS CENTRIPETAL CUT POINT |
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PARTICLE SIZE ................................................................................. |
793 |
13.0 |
CYCLONE DESIGN EXAMPLES .................................................... |
794 |
14.0 |
ALTERNATE APPROACH TO SOLVING EXAMPLE B ............. |
804 |
15.0 |
ALTERNATE APPROACH TO SOLVING EXAMPLE C ............. |
809 |
16.0 |
DIPLEG SIZING AND CYCLONE PRESSURE BALANCE ......... |
812 |
NOTATIONS ................................................................................. |
814 |
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REFERENCES ................................................................................. |
815 |
13 Electrostatics and Dust Explosions in Powder Handling .... |
817 |
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Thomas B. Jones |
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1.0 |
INTRODUCTION ................................................................................ |
817 |
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2.0 |
CHARGING OF SOLID PARTICLES .............................................. |
818 |
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2.1 |
Triboelectrification ....................................................................... |
819 |
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2.2 |
Charge Relaxation ........................................................................ |
823 |
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2.3 |
Induction Charging of Particles ................................................... |
824 |
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2.4 |
Electrostatic Fields and Potentials ............................................... |
825 |
3.0 |
FLUIDIZED BED ELECTRIFICATION .......................................... |
829 |
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3.1 |
Background ................................................................................. |
829 |
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3.2 |
More Recent Work ....................................................................... |
832 |
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3.3 |
Beneficial Effects of Electric Charge .......................................... |
836 |
4.0 |
ESD DUST IGNITION HAZARDS ................................................... |
836 |
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4.1 |
Basics of Suspended Solids Ignition ........................................... |
837 |
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4.2 |
Types of Discharges .................................................................... |
841 |
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4.3 |
Charge Dissipation ....................................................................... |
850 |
5.0 |
ESD HAZARDS IN FLUIDIZED BED SYSTEMS ......................... |
854 |
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5.1 |
Hazards Associated with Fluidization ......................................... |
855 |
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5.2 |
Hazards in Peripheral Equipment and Processes ........................ |
857 |
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5.3 |
Other Nuisances and Hazards ...................................................... |
863 |
6.0 |
CONCLUSION ................................................................................. |
864 |
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ACKNOWLEDGMENT ............................................................................. |
866 |
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REFERENCES ................................................................................. |
867 |
Index .............................................................................................. |
872 |
1
Fluidized Bed Scale-up
Leon R. Glicksman
1.0INTRODUCTION
Although fluidized beds have been used extensively in commercial operations such as fluidized bed combustors and fluid catalytic cracking, engineers are still faced with uncertainties when developing new commercial designs. Typically, the development process involves a laboratory bench scale unit, a larger pilot plant, and a still larger demonstration unit. Many of the important operating characteristics can change between the different size units. There is a critical problem of scale-up: how to accurately account for the performance changes with plant size to insure that a full size commercial unit will achieve satisfactory performance. In addition, it would be helpful if the smaller units could be used to optimize the commercial plant or solve existing problems.
One discouraging problem is the decrease in reactor or combustor performance when a pilot plant is scaled up to a larger commercial plant. These problems can be related to poor gas flow patterns, undesirable solid mixing patterns and physical operating problems (Matsen, 1985). In the synthol CFB reactors constructed in South Africa, first scale-up from the pilot plant increased the gas throughput by a factor of 500. Shingles and McDonald (1988) describe the severe problems initially encountered and their resolution.
1
2 Fluidization, Solids Handling, and Processing
In some scaled up fluidized bed combustors, the lower combustion zone has been divided into two separate subsections, sometimes referred to as a “pant leg” design, to provide better mixing of fuel and sorbent in a smaller effective cross section and reduce the potential maldistribution problems in the scaled up plant.
Matsen (1985) pointed out a number of additional problem areas in scale-up such as consideration of particle size balances which change over time due to reaction, attrition and agglomeration. Erosion of cyclones, slide valves and other components due to abrasive particles are important design considerations for commercial units which may not be resolved in pilot plants.
If mixing rates and gas-solid contacting efficiencies are kept constant between beds of different size, then thermal characteristics and chemical reaction rates should be similar. However, in general, the bed hydrodynamics will not remain similar. In some instances, the flow regime may change between small and large beds even when using the same particles, superficial gas velocity and particle circulation rate per unit area. The issue of scale-up involves an understanding of these hydrodynamic changes and how they, in turn, influence chemical and thermal conditions by variations in gas-solid contact, residence time, solid circulation and mixing and gas distribution.
There are several avenues open to deal with scale-up. Numerical models have been developed based on fundamental principals. The models range from simple one-dimensional calculations to complex multidimensional computational fluid dynamics solutions. There is no doubt that such first principal models are a great aid in synthesizing test data and guiding the development of rational correlations. In a recent model evaluation, modelers where given the geometry and operating parameters for several different circulating beds and asked to predict the hydrodynamic characteristics without prior knowledge of the test results (Knowlton et al. 1995). None of the analytical or numerical models could reliably predict all of the test conditions. Few of the models could come close to predicting the correct vertical distribution of solid density in the riser and none could do it for all of the test cases! Although it is tempting to think that these problems can be solved with the “next generation of computers,” until there is general agreement and thorough verification of the fundamental equations used to describe the hydrodynamics, the numerical models will not stand alone as reliable scale-up tools.
On the other hand, there is a blizzard of empirical and semiempirical correlations which exist in the fluidized bed literature to predict
Fluidized Bed Scale-up |
3 |
fluid dynamic behavior. In addition there are probably a large number of proprietary correlations used by individual companies. The danger lies in extrapolating these relations to new geometric configurations of the riser or inlet, to flow conditions outside the range of previous data, or to beds of much different sizes. Avidan and coauthors in a 1990 review of FCC summed up the state of the art: “basic understanding of complex fluidization phenomena is almost completely lacking. While many FCC licensors and operators have a large body of in-house proprietary data and correlations, some of these are not adequate, and fail when extrapolated beyond their data base.” (Avidan, et al., 1990.)
As a example, consider the influence of mean particle size. In the early work on bubbling fluidized bed combustors, attempts were made to use relations from the classic fluidization literature which had concentrated on FCC applications with much smaller particles. In many cases, it was discovered that the relationships for small particles gave erroneous results for combustors with much larger particles. For example, the two phase theory equating the excess gas velocity above minimum fluidization to the visible bubble flow was shown to be severely distorted for large particle systems. Jones and Glicksman (1985) showed that the visible bubble flow in a bubbling bed combustor was less than one fifth of uo-umf. In other cases even the trends of the parametric behavior were changed. Heat transfer to immersed surfaces in fine particle bubbling beds increased strongly with a decrease in the mean particle size. For large particle beds, the heat transfer, in some instances, decreased with a decreased particle diameter.
Another approach to scale-up is the use of simplified models with key parameters or lumped coefficients found by experiments in large beds. For example, May (1959) used a large scale cold reactor model during the scale-up of the fluid hydroforming process. When using the large cold models, one must be sure that the cold model properly simulates the hydrodynamics of the real process which operates at elevated pressure and temperature.
Johnsson, Grace and Graham (1987) have shown one example of verification of a model for 2.13 m diameter industrial phthalic anhydride reactor. Several bubbling bed models gave good overall prediction of conversion and selectivity when proper reaction kinetics were used along with a good estimate of the bubble size. The results were shown to be quite sensitive to the bubble diameter. The comparison is a good check of the models but the models are incomplete without the key hydrodynamic data. In this case, the bubble size estimates were obtained from measurements of overall bed density in the reactor.
4 Fluidization, Solids Handling, and Processing
As Matsen expresses it, after over a half a century of scale-up activity in the chemical process industry, “such scale-up is still not an exact science but is rather a mix of physics, mathematics, witchcraft, history and common sense which we call engineering.” (Matsen, 1995.)
A complete treatment of scale-up should include the models, numerical calculation procedures and experimental data designers need to carry out successful scale-up from small size beds to commercial units. This would involve a large measure of the existing fluidized bed research and development effort; clearly, such a task is beyond the scope of a single chapter. Since changes in the bed size primarily influence scale-up through changes in the bed hydrodynamics, one focus of this chapter is on experimental results and models which deal explicitly with the influence of bed diameter on hydrodynamic performance for both bubbling and circulating fluidized beds. The changes in the bed dynamics will, in turn, impact the overall chemical conversion or combustion efficiency through changes in the particle-to-gas mass transfer and the heat transfer from the bed to immersed surfaces or the bed wall. Several examples of this influence are also reviewed.
The second focus of this chapter is on the use of small scale experimental models which permit the direct simulation of the hydrodynamics of a hot, possibly pressurized, pilot plant or commercial bed. By use of this modeling technique, beds of different diameters, as well as different geometries and operating conditions, can be simulated in the laboratory. To date, this technique has been successfully applied to fluidized bed combustors and gasifiers. Derivation of the scale modeling rules is presented for a variety of situations for gas solid fluidized beds. Verification experiments and comparisons to large scale commercial systems are shown. Rules for the use of this experimental modeling technique for FCC operations as well as for the simulation of bed-to-solid surface heat transfer are also given.
2.0REACTOR MODELING: BED DIAMETER INFLUENCE
In this section, representative results are reviewed to provide a prospective of reactor modeling techniques which deal with bed size. There probably is additional unpublished proprietary material in this area. Early studies of fluidized reactors recognized the influence of bed diameter on conversion due to less efficient gas-solid contacting. Experimental studies were used to predict reactor performance. Frye et al. (1958) used