UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Fluid mechanics of high velocity fluidised beds Brereton, Clive 1987

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1988_A1 B73.pdf [ 12.98MB ]
Metadata
JSON: 831-1.0058687.json
JSON-LD: 831-1.0058687-ld.json
RDF/XML (Pretty): 831-1.0058687-rdf.xml
RDF/JSON: 831-1.0058687-rdf.json
Turtle: 831-1.0058687-turtle.txt
N-Triples: 831-1.0058687-rdf-ntriples.txt
Original Record: 831-1.0058687-source.json
Full Text
831-1.0058687-fulltext.txt
Citation
831-1.0058687.ris

Full Text

FLUID MECHANICS OF HIGH VELOCITY FLUIDISED BEDS by CLIVE BRERETON B.A.Sc.(Hons.),The U n i v e r s i t y Of B r i t i s h Columbia,1982 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department Of Chemical E n g i n e e r i n g We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA December 1987 © C l i v e B r ereton, 1987 3 9 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6(3/81) ABSTRACT T h i s t h e s i s p r o j e c t s t u d i e d a number of aspects r e l a t i n g to the f l u i d , mechanics of c i r c u l a t i n g f l u i d i s e d beds. Stud i e s of the macrostructure of a 9.3 m high x .15 m d i a . r i s e r showed a strong dependence of one important macroscopic d e s c r i p t o r , the d e n s i t y p r o f i l e , upon the geometry of the g a s / s o l i d s e x i t and the l o c a t i o n of the s o l i d s r e t u r n . I t was found that abrupt e x i t s promoted i n e r t i a l s o l i d s s e p a r a t i o n from the conveying gas which generated strong i n t e r n a l c i r c u l a t i o n p a t t e r n s and high s l i p v e l o c i t i e s . M i c r o s t r u c t u r a l s t u d i e s , i n support of the m a c r o s t r u c t u r a l i n v e s t i g a t i o n , and using a needle capacitance probe, showed how the r a d i a l d e n s i t y p r o f i l e develops with height causing a gradual d e n s i t y decay. The s t r u c t u r e , c h a r a c t e r i s e d by an " i n t e r m i t t e n c y index," was s t r o n g l y r a d i a l l y non-uniform at a l l l o c a t i o n s i n the lower regions of the column with pronounced aggregation or c l u s t e r i n g at the highest d e n s i t i e s . However, the c l u s t e r - l i k e s t r u c t u r e s present at the base r a p i d l y gave way to a more d i l u t e core-annular type flow s l i g h t l y f u r t h e r up the column. T h i s r a d i a l l y non-uniform s t r u c t u r e was used to e x p l a i n a number of macroscopic phenomena. These i n c l u d e d the e f f e c t s of e x i t type, s o l i d s r e t u r n l o c a t i o n , secondary a i r - i i i -a d d i t i o n and gas mixing. The r e s u l t s of the v a r i o u s s t u d i e s , drawn together, allow f a s t f l u i d i s a t i o n to be d e f i n e d t e n t a t i v e l y with respect to i t s r e l a t i o n s h i p s to choking, pneumatic t r a n s p o r t , and other f l u i d i s a t i o n regimes. Separate s t u d i e s were performed to examine gas mixing and the t r a n s i t i o n to t u r b u l e n t f l u i d i s a t i o n . The gas r e s i d e n c e time d i s t r i b u t i o n was found to be s u b s t a n t i a l l y d i f f e r e n t from plug flow and could be c h a r a c t e r i s e d c r u d e l y by a two-zone model. The t u r b u l e n t t r a n s i t i o n was found to be gradual, but nonetheless a t r a n s i t i o n , although a developed t u r b u l e n t zone d i d not e x i s t u n t i l w e l l beyond t r a n s p o r t c o n d i t i o n s . - i v -TABLE OF CONTENTS Page ABSTRACT i LIST OF TABLES v i i LIST OF FIGURES v i i i ACKNOWLEDGEMENTS x x i 1. INTRODUCTION 1 1.1 I n i t i a l Concepts 1 1.2 H i s t o r i c a l and C u r r e n t I n d u s t r i a l P e r s p e c t i v e s 11 1.3 F a s t F l u i d i s a t i o n and D e n s i t y P r o f i l e s 23 1.4 O b j e c t i v e s of the P r e s e n t Study 52 2. APPARATUS 54 2.1 Design C o n s i d e r a t i o n s 54 2.2 The R i s e r Column 58 2.3 The G a s - S o l i d s S e p a r a t i o n System 63 2.4 Stor a g e and R e c i r c u l a t i o n Systems 69 2.5 Data Measurement and A c q u i s i t i o n 74 3. EXPERIMENTAL RESULTS 82 3.1 D e n s i t y P r o f i l e s and Entrainment Rates i n C i r c u l a t i n g F l u i d i s e d Beds - M a c r o s c o p i c A s p e c t s 82 3.1.1 C o n s i d e r a t i o n s r e g a r d i n g use of p r e s s u r e data 82 3.1.2 I n i t i a l s t u d i e s w i t h alumina 84 3.1.3 I n i t i a l s t u d i e s of the e x i t e f f e c t 95 3.1.4 E n t r a n c e e f f e c t s and more on e x i t e f f e c t s 100 - v -Page 3.1.5 Low velocity entrainment tests 110 3.1.6 The imposed pressure drop, a s i g n i f i c a n t influence on c i r c u l a t i n g bed structure? 116 3.1.7 Secondary a i r addition - impact upon c i r c u l a t i n g f l u i d i s e d bed density p r o f i l e s 120 3.2 Microstructural Aspects of the C i r c u l a t i n g Fluidised Bed 124 3.2.1 Scope of microstructural study 124 3.2.2 Design c r i t e r i a for a microstructural probe 124 3.2.3 Capacitance probes - a general description 127 3.2.4 Development of a capacitance probe for this study 130 3.2.5 Response and c a l i b r a t i o n of the capacitance probe 137 3.2.6 Experimental studies with the capacitance probe 148 3.2.7 Treatment of results from the microstructural investigation 151 4. DISCUSSION 160 4.1 Microstructural Results 160 4.1.1 Development of the gas and solids flow p r o f i l e s 160 4.1.2 Possible mechanisms for solids motion.. 166 4.1.3 Nature of the local solids flow structure 173 4.1.4 Analogies with low velocity regimes.... 183 4.1.5 Fast f l u i d i s a t i o n and the saturated carrying capacity 185 4.1.6 Fast f l u i d i s a t i o n and choking 191 4.1.7 Fast--fluidisation and c i r c u l a t i n g beds - d e f i n i t i o n s 195 4.1.8 Scale influences 199 4.1.9 The imposed pressure drop phenomenon... 203 4.2 Discussion of the Macrostructural Results and their Implications.... 210 4.2.1 Exit effects in c i r c u l a t i n g f l u i d i s e d beds 210 4.2.2 Effects of secondary air introduction and solids return location 219 - v i -Page 5. THE TRANSITION TO TURBULENT FLUIDISATION, A BRIEF EXPERIMENTAL AND CONCEPTUAL STUDY... 224 5.1 I n t r o d u c t i o n 224 5.2 A B r i e f H i s t o r y of Turbulent F l u i d i s a t i o n 225 5.3 Experimental Design 230 5.4 R e s u l t s and D i s c u s s i o n 235 6. AXIAL GAS MIXING IN A CIRCULATING FLUIDISED BED 253 6.1 I n t r o d u c t i o n 253 6.2 The Experimental Study 258 6-2.1 General c o n s i d e r a t i o n s 258 6.2.2 Design of sampling and i n j e c t i o n systems 259 6.2.3 Detector/sampling system c h a r a c t e r i s a t i o n 270 6.2.4 R i s e r c h a r a c t e r i s a t i o n 270 6.3 Data A n a l y s i s 274 6.4 R e s u l t s , D i s c u s s i o n and Modelling 286 7. SUMMARY AND CONCLUSIONS 302 8. RECOMMENDATIONS 305 NOMENCLATURE 307 REFERENCES 311 APPENDIX 1. Sample Output from Time S e r i e s A n a l y s i s Routine BMD: 02T 322 APPENDIX 2. E s t i m a t i o n of the F l u c t u a t i n g V e l o c i t y Component f o r A i r on the C e n t r e l i n e of a Single-Phase Pipe Flow (Ug =6.5 ra/s, Dia. = .152 m, NTP) 329 APPENDIX 3. Computation of Pseudo-Dispersion C o e f f i c i e n t s from F-Curve Data 331 - v i i -LIST OF TABLES Page Table 2.1 Transit time for sand p a r t i c l e s over a 300 mm section of the L -valve 78 Table 3.1 Properties of alumina used in high vel o c i t y f l u i d i s a t i o n studies 85 Table 3.2 Properties of Ottawa sand used in high velocity f l u i d i s a t i o n studies 96 Table 3.3 Results from entrainment tests at low velocity 115 Table 3.4 Pressure drops over the c i r c u l a t i n g f l u i d i s e d bed loop 118 Table 3.5 Techniques used for determining local solids hold-up and p a r t i c l e velocity 126 Table 5.1 References for turbulent f l u i d i s a t i o n studies and methods used to identify the turbulent t r a n s i t i o n 232 Table 6.1 Test conditions for dispersion measurements in the c i r c u l a t i n g f l u i d i s e d bed 275 - v i i i -LIST OF FIGDRES Page F i g u r e 1.1 Schematic diagram of a v e r t i c a l g a s - s o l i d t r a n s p o r t l i n e 2 Fi g u r e 1.2 Flow regimes f o r g a s - s o l i d flow a c c o r d i n g to Leung (1980) 4 Fi g u r e 1.3 Photograph of a f a s t f l u i d i s e d bed viewed through the w a l l 8 Fi g u r e 1.4 S l i p v e l o c i t i e s i n high v e l o c i t y f l u i d i s a t i o n a c c ording to Yerushalmi and Cankurt (1978) 9 Figu r e 1.5 Regime diagram f o r g a s - s o l i d c o n t a c t i n g a c c o r d i n g to Grace (1986). Ap i s the d i f f e r e n c e between p a r t i c l e and gas d e n s i t i e s 12 F i g u r e 1.6 A t y p i c a l c i r c u l a t i n g bed combustor ( K u l l e n d o r f and Andersson, 1985) 16 Fig u r e 1.7 C o n t r o l of a c i r c u l a t i n g bed combustor by v a r i a t i o n of heat t r a n s f e r r a t e to a membrane w a l l . Q represents the t o t a l heat a b s o r p t i o n , H Q the o v e r a l l heat t r a n s f e r c o e f f i c i e n t above the secondary a i r p o r t s , and p s e c t n e mean suspension d e n s i t y above the secondary a i r p o r t s 18 F i g u r e 1.8 Heat t r a n s f e r c o e f f i c i e n t s i n f a s t f l u i d i s a t i o n as a f u n c t i o n of suspension d e n s i t y and temperature (Kobro and Brereton, 1985) 22 Fig u r e 1.9 Density p r o f i l e s f o r f a s t f l u i d i s a t i o n ( L i and Kwauk, 1980) 25 F i g u r e 1.10 The L i and Kwauk (1980) model f o r d e n s i t y p r o f i l e s i n f a s t f l u i d i s e d beds 28 Figu r e 1.11 C o r r e l a t i o n s f o r parameters i n the L i et a l . (1982) d e n s i t y d i s t r i b u t i o n model 29 - i x -Page Fi g u r e 1.12 E f f e c t i v e c l u s t e r diameters i n high v e l o c i t y f l u i d i s e d beds (Yerushalmi et a l . , 1978) 36 F i g u r e 1.13 P l o t of voidage versus gas v e l o c i t y f o r f l u i d c r a c k i n g c a t a l y s t over a wide range of gas v e l o c i t y showing regime t r a n s i t i o n s (Avidan, 1980) 38 F i g u r e 1.14 Flow regimes observed i n v e r t i c a l gas-l i q u i d flow (Soo, 1982), and a flow p a t t e r n map (Hewitt and Roberts, 1969) 40 F i g u r e 1.15 R a d i a l s o l i d s f l u x , v e l o c i t y and d e n s i t y p r o f i l e s i n a r i s e r according to B i e r l et a l . (1980) 42 F i g u r e 1.16 C a t a l y s t d e n s i t y d i s t r i b u t i o n s over the c r o s s - s e c t i o n of a commercial r i s e r (Schuurmans, 1980) 46 F i g u r e 1.17 Gas v e l o c i t y p r o f i l e , c a t a l y s t d e n s i t y d i s t r i b u t i o n and s o l i d s f l u x p r o f i l e measured by van Breugel et a J . (1969-70) i n a 0.3 m d i a . r i s e r . . .TT.TT 48 F i g u r e 2.1 Schematic of the c i r c u l a t i n g f l u i d i s e d bed t e s t r i g . Numbers designate p r i n c i p a l pressure measurement l o c a t i o n s f o r loop pressure measurement s t u d i e s 57 F i g u r e 2.2 D e t a i l of the secondary a i r nozzles f o r the r i s e r column 60 F i g u r e 2.3 Diagram of pressure tap/probe port 62 F i g u r e 2.4 D e t a i l of a column support bracket 64 F i g u r e 2.5 Primary cyclone d e t a i l , a l l dimensions i n mm 66 F i g u r e 2.6 Secondary cyclone d e t a i l , a l l dimensions i n mm 67 F i g u r e 2.7 T e r t i a r y cyclone d e t a i l a l l dimensions i n mm 68 F i g u r e 2.8 M o d i f i e d b u t t e r f l y valve f o r s o l i d s c i r c u l a t i o n rate measurement, dimensions i n mm 72 - x -Page Fi g u r e 2.9 Ae r a t i o n p o i n t s on the L - v a l v e and a t y p i c a l o p e r a t i n g mode from Knowlton and Hirsan (1978). Dimensions i n mm 75 Fig u r e 2.10 A t y p i c a l pressure t r a c e f o r build-up of alumina on the b u t t e r f l y valve f o r a c i r c u l a t i o n r a t e measurement. A s t r a i g h t l i n e i s sketched to show the l i n e a r i t y of the b u i l d - u p 77 Fi g u r e 2.11 Manifold c o n s t r u c t i o n f o r d i f f e r e n t i a l pressure measurements showing how 14 r i s e r l o c a t i o n s are manifolded 80 Fig u r e 3.1 Scanning e l e c t r o n micrograph of alumina p a r t i c l e s . M a g n i f i c a t i o n 400 x 87 F i g u r e 3.2 C i r c u l a t i n g f l u i d i s e d bed as i n i t i a l l y c o n s t r u c t e d . Alumina could be c i r c u l a t e d i n t h i s short L-valve design with s i n g l e p o i n t a e r a t i o n 88 Fi g u r e 3.3 L o n g i t u d i n a l d e n s i t y d i s t r i b u t i o n s f o r alumina i n a c i r c u l a t i n g f l u i d i s e d bed, Ug = 5.4 m/s, G s = 18, 41, and 95 kg/m 2s 90 F i g u r e 3.4 L o n g i t u d i n a l d e n s i t y d i s t r i b u t i o n s f o r alumina i n a c i r c u l a t i n g f l u i d i s e d bed, U g = 4.3 m/s, G s = 21 and 42 kg/m 2s.... 92 Fi g u r e 3.5 L o n g i t u d i n a l d e n s i t y d i s t r i b u t i o n f o r alumina i n a c i r c u l a t i n g bed, Ug = 2.6 m/s, G s = 25 kg/m 2s 93 Figu r e 3.6 L o n g i t u d i n a l d e n s i t y d i s t r i b u t i o n s f o r alumina i n a c i r c u l a t i n g bed, G s approximately constant (- 20 kg/m 2s), U g = 2.6, 4.3 and 5.4 m/s 94 Fig u r e 3.7 L o n g i t u d i n a l d e n s i t y p r o f i l e s obtained f o r sand i n a c i r c u l a t i n g bed as the base appeared v i s u a l l y choked, gas v e l o c i t i e s between 3.7 and 9.2 m/s 99 Fi g u r e 3.8 Ris e r column c o n f i g u r e d to r e t u r n s o l i d s 1.98 m above the d i s t r i b u t o r p l a t e f o r entrance e f f e c t s t u d i e s 101 - x i -Page Figu r e 3.9 L o n g i t u d i n a l d e n s i t y p r o f i l e s f o r sand, Ug = 4.9 m/s, G s = 24 and 26 kg/m 2s, abrupt e x i t , s o l i d s r e t u r n at 1.98 m above the gas d i s t r i b u t o r 102 Fi g u r e 3.10 L o n g i t u d i n a l d e n s i t y p r o f i l e s f o r sand, U g = 6.1 m/s, G s = 35, 45, and 59 kg/m 2s, abrupt e x i t , s o l i d s r e t u r n at 1.98 m above the gas d i s t r i b u t o r 103 Fi g u r e 3.11 L o n g i t u d i n a l d e n s i t y p r o f i l e s f o r sand, Ug = 7.1 m/s, G s = 45 and 73 kg/in 2s, abrupt e x i t , s o l i d s r e t u r n at 1.98 m above the gas d i s t r i b u t o r 104 Figu r e 3.12 L o n g i t u d i n a l d e n s i t y p r o f i l e s f o r sand, U g = 8.1 m/s, G s = 66, 71, and 82 kg/m 2s, abrupt e x i t , s o l i d s r e t u r n at 1.98 m above the gas d i s t r i b u t o r 105 Fi g u r e 3.13 D e t a i l s of three e x i t s s t u d i e d f o r c i r c u l a t i n g bed a p p l i c a t i o n 106 F i g u r e 3.14 L o n g i t u d i n a l d e n s i t y p r o f i l e s f o r sand, U g = 7.1 m/s, G s = 36, 73, 93, and 116 kg/m 2s, smooth e x i t , s o l i d s r e t u r n 1.98 m above the gas d i s t r i b u t o r 108 Fi g u r e 3.15 L o n g i t u d i n a l d e n s i t y p r o f i l e s f o r sand, Ug = 7.1 m/s, G s = 73 kg/m 2s, smooth and abrupt e x i t s , s o l i d s r e t u r n 1.98 m above the gas d i s t r i b u t o r . T r i a n g l e s represent smooth e x i t p r o f i l e , c i r c l e s abrupt 109 Figu r e 3.16 L o n g i t u d i n a l d e n s i t y p r o f i l e s f o r sand, Ug = 7.1 m/s, G s = 73 kg/m 2s, abrupt and extended e x i t s , s o l i d s r e t u r n at 1.98 m above the gas d i s t r i b u t o r . T r i a n g l e s represent extended e x i t p r o f i l e , c i r c l e s abrupt I l l Fig u r e 3.17 Column c o n f i g u r a t i o n f o r 1.5 m/s entrainment t e s t s 113 (a) I n i t i a l c o n f i g u r a t i o n (b) F i n a l C o n f i g u r a t i o n F i g u r e 3.18 Pressure versus e l e v a t i o n p l o t s f o r a r i s e r with f l u i d i s e d and packed bed storage zones. Numbers r e f e r to l o c a t i o n s on F i g u r e 2.1 119 - x i i -Page Fi g u r e 3.19 Density p r o f i l e s measured i n c i r c u l a t i n g beds of sand at a t o t a l gas v e l o c i t y of 8.6 m/s and a s o l i d s c i r c u l a t i o n r a t e of 2 45 kg/m s with d i f f e r e n t primary to secondary (P/S) a i r r a t i o s . Secondary a i r i n troduced through opposed p o r t s . C i r c l e s , zero secondary a i r ; t r i a n g l e s , P/S = 1.36; squares, P/S = 0.83 122 F i g u r e 3.20 Density p r o f i l e s measured i n c i r c u l a t i n g beds of sand at a t o t a l gas v e l o c i t y of 8-5 m/s and a s o l i d s c i r c u l a t i o n r a t e of 45 kg/m s with d i f f e r e n t primary to secondary (P/S) a i r r a t i o s . Secondary a i r i n t r o d u c e d through s w i r l p o r t s . C i r c l e s , zero secondary a i r ; t r i a n g l e s , P/S = 1.39; squares, P/S = 0.85 123 F i g u r e 3.21 Block diagram of a capacitance probe system i l l u s t r a t i n g p r i n c i p a l system components 128 F i g u r e 3.22 V a r i a b l e s i n f l u e n c i n g the c a p a c i t a n c e of a c o a x i a l c y l i n d r i c a l c a p a c i t o r ( T i p l e r , 1976) 132 F i g u r e 3.23 A t y p i c a l simple needle capacitance probe 134 F i g u r e 3.24 A photograph of the f i n a l c apacitance probe design 136 F i g u r e 3.25 P l o t of the r e l a t i v e p e r m i t t i v i t y of uniform sand a i r suspensions according to Wiener (1912) 141 F i g u r e 3.26 Output from capacitance probe g r a d u a l l y immersed i n t o a f i x e d bed of sand showing l i n e a r i t y of voltage with immersion depth.. 143 F i g u r e 3.27 Comparison of r a d i a l l y averaged d e n s i t i e s obtained using an i n t e g r a t e d capacitance probe s i g n a l , and the same d e n s i t i e s c a l c u l a t e d from pressure drop measurements 145 Figure 3.28 Capacitance probe t r a v e r s i n g r i g mounted on a s e c t i o n of the c i r c u l a t i n g f l u i d i s e d bed 149 - x i i i -Page Fi g u r e 3.29 L o n g i t u d i n a l and r a d i a l d e n s i t y d i s t r i b u t i o n s i n a c i r c u l a t i n g bed of sand, Ug = 6.5 m/s, G s = 62 kg/m s. Al s o shown are r a d i a l d i s t r i b u t i o n s of the standard d e v i a t i o n of d e n s i t y f l u c t u a t i o n s 154 F i g u r e 3.30 L o n g i t u d i n a l and r a d i a l d e n s i t y d i s t r i b u t i o n s i n a c i r c u l a t i n g bed of sand, Ug = 6.5 m/s, G s = 48 kg/m 2s. Al s o shown are r a d i a l d i s t r i b u t i o n s of the standard d e v i a t i o n of d e n s i t y f l u c t u a t i o n s 155 F i g u r e 3.31 L o n g i t u d i n a l and r a d i a l d e n s i t y d i s t r i b u t i o n s i n a c i r c u l a t i n g bed of sand, U g = 6.5 m/s, G s = 42 kg/m 2s. Al s o shown are r a d i a l d i s t r i b u t i o n s of the standard d e v i a t i o n of d e n s i t y f l u c t u a t i o n s 156 F i g u r e 3.32 R a d i a l v a r i a t i o n s i n d e n s i t y f l u c t u a t i o n s , power s p e c t r a l d i s t r i b u t i o n of d e n s i t y f l u c t u a t i o n s , and autocovariance of d e n s i t y f l u c t u a t i o n s , Ug = 6.5 m/s, G s = 62 kg/m 2s, Z = 533 mm 157 Fi g u r e 3.33 Ra d i a l v a r i a t i o n s i n d e n s i t y f l u c t u a t i o n s , power s p e c t r a l d i s t r i b u t i o n of d e n s i t y f l u c t u a t i o n s , and autocovariance of d e n s i t y f l u c t u a t i o n s , Ug = 6.5 m/s, = 62 kg/m 2s, Z = 1448 mm 158 s F i g u r e 3.34 Ra d i a l v a r i a t i o n s i n d e n s i t y f l u c t u a t i o n s , power s p e c t r a l d i s t r i b u t i o n of d e n s i t y f l u c t u a t i o n s , and autocovariance of de n s i t y f l u c t u a t i o n s , Ug = 6.5 m/s, G„ = 62 kg/m 2s, Z = 2362 mm 159 Figure 4.1 V a r i a t i o n of l o c a l v e r t i c a l s u p e r f i c i a l gas v e l o c i t y with r a d i a l p o s i t i o n and height as c a l c u l a t e d by the modified Kozeny equation. Density p r o f i l e s are measured values at v e r t i c a l l o c a t i o n s of 0.533 m and 2.362 m f o r a gas v e l o c i t y of 6.5 m/s and a s o l i d s c i r c u l a t i o n r a t e of 62 kg/m 2s 165 - x i v -Page Figu r e 4.2 I m p l i c a t i o n s of a simple d i f f u s i o n a l model f o r s o l i d s motion f o r gas and s o l i d s d e n s i t y p r o f i l e s . Lower f i g u r e shows a t y p i c a l experimental r e s u l t , upper f i g u r e the requirements f o r " a d i f f u s i o n a l model to be c o n s i s t e n t 168 F i g u r e 4.3 Streamfunction p r o f i l e s i n a developing flow. The streamfunction i s p l o t t e d as a f u n c t i o n of r a d i u s f o r a uniform gas v e l o c i t y p r o f i l e and a p a r a b o l i c p r o f i l e showing how, as the p r o f i l e changes with height due to r e d i s t r i b u t i o n and decay of de n s i t y , there i s a bulk flow of gas towards the w a l l . Arrows j o i n p o i n t s of constant streamfunction showing the d i r e c t i o n of gas flow 170 F i g u r e 4.4 Int e r m i t t e n c y i n d i c e s as a f u n c t i o n of r a d i u s f o r f u l l y developed core-annular and " i d e a l c l u s t e r flow." 177 F i g u r e 4.5 Int e r m i t t e n c y index p l o t t e d as a f u n c t i o n of r a d i u s at three v e r t i c a l l o c a t i o n s i n a c i r c u l a t i n g bed of sand f o r Ug = 6.5 m/s, G 0 = 62 kg/m 2s 178 s F i g u r e 4.6 Int e r m i t t e n c y index p l o t t e d as a f u n c t i o n of r a d i u s at three v e r t i c a l l o c a t i o n s i n a c i r c u l a t i n g bed of sand f o r U = 6.5 m/s, G = 48 kg/m 2s 179 Figu r e 4.7 Inter m i t t e n c y index p l o t t e d as a f u n c t i o n of r a d i u s at three v e r t i c a l l o c a t i o n s i n a c i r c u l a t i n g bed of sand for Ug = 6.5 6.5 m/s, G s = 43 kg/m 2s 180 Figu r e 4.8 A d e p i c t i o n of a smooth e x i t r i s e r f o r i l l u s t r a t i o n of the concepts i n v o l v e d with flow s t r u c t u r e s above and below the sa t u r a t e d c a r r y i n g c a p a c i t y . To the r i g h t i s a t y p i c a l d e n s i t y p r o f i l e below s a t u r a t i o n 188 - XV -Page Figu r e 4.9 A schematic diagram showing s o l i d s f l u x e s i n a r i s e r o p e r a t i n g above the s a t u r a t e d c a r r y i n g c a p a c i t y but below choking. On the l e f t i s a schematic i n which arrows i n d i c a t e approximate d i r e c t i o n s of s o l i d s flow and show the development of the w a l l l a y e r . On the r i g h t i s a second diagram where the width of up and downflow arrows gives an idea of how up and downflow f l u x e s vary with height i n the u n i t to give a net p o s i t i v e f l u x 192 Fig u r e 4.10 A schematic showing the concept of choking i n a r i s e r as a p p l i e d i n t h i s t h e s i s , and as observed i n the o v e r a l l d e n s i t y p r o f i l e 194 F i g u r e 4.11 A schematic diagram showing a high v e l o c i t y r i s e r o p e r a t i n g at a s o l i d s c i r c u l a t i o n r a t e greater than choking. On the l e f t i s a schematic i n which arrows i n d i c a t e approximate d i r e c t i o n s of s o l i d s flow and show the development of the w a l l layer up to i t s maximum s t a b l e (choked) t h i c k n e s s . On the r i g h t a second diagram shows how up, down, and cross f l u x e s vary with height, and shows how the c r o s s - f l u x i s i n e q u i l i b r i u m i n the choked zone 196 Fig u r e 4.12 Fast f l u i d i s a t i o n d e f i n e d i n terms of a region of p o t e n t i a l gas v e l o c i t i e s and s o l i d s c i r c u l a t i o n r a t e s 198 Fig u r e 4.13 E x i s t e n c e of d i f f e r e n t flow regimes i n d i f f e r e n t height r i s e r s . In the l e f t hand r i s e r , which i s t a l l , at c i r c u l a t i o n r a t e s G s i and G S2 the r i s e r i s s u b s t a n t i a l l y choked and small changes i n the c i r c u l a t i o n rate do not cause a lar g e f r a c t i o n a l change i n the i n v e n t o r y . In the r i g h t hand r i s e r of the same diameter, which i s short, the same c i r c u l a t i o n r a t e s produce dramatic f r a c t i o n a l i n v e n t o r y changes. T h i s s i t u a t i o n , where changes i n c i r c u l a t i o n r a t e produce lar g e and c o n t r o l l a b l e changes i n o v e r a l l hold up, i . e . , where a f a s t f l u i d i s e d bed occupies the whole column, i s u t i l i s e d i n c i r c u l a t i n g f l u i d i s e d beds 200 - x v i -Page Figu r e 4.14 Density p r o f i l e f o r a l a r g e c i r c u l a t i n g f l u i d i s e d bed combustor (32 m high x 8 m dia.) i n f e r r e d from data provided by Wein and Felwor (1986). D i s c o n t i n u i t i e s i n gas v e l o c i t y are p o i n t s of a i r a d d i t i o n ; the g r a d i e n t r e f l e c t s a furnace expansion 202 Figure 4.15 The proposed form of a decay length versus diameter f u n c t i o n f o r f a s t f l u i d i s a t i o n based upon examination of data from small and l a r g e u n i t s 204 F i g u r e 4.16 A c o n v e n t i o n a l l a b o r a t o r y c i r c u l a t i n g bed r e c y c l e loop with a f u l l y f l u i d i s e d r e t u r n c o n t r o l l e d by a mechanical (e.g., s l i d e ) v a l ve 207 Figure 4.17 A p o s s i b l e e x p l a n a t i o n f o r the apparent i n f l u e n c e of imposed pressure drop upon r i s e r o p e r a t i o n . When the decay length i s short compared to the column height, small changes i n the e x i t d e n s i t y and e x t e r n a l c i r c u l a t i o n r a t e r e s u l t from lar g e changes i n the column invento r y (pressure drop). Hence, si n c e the pressure drop across the v a l v e i s a f u n c t i o n only of the s o l i d s c i r c u l a t i o n r a t e , according to the pressure balance, column pressure drop appears to depend upon r e t u r n l e g pressure drop 208 F i g u r e 4.18 A bubbling f l u i d i s e d bed i l l u s t r a t i n g the phenomenon of coexistence of s t a b l e s t a t e s at choking. The bubbling bed on the l e f t , charged with a wide range of i n v e n t o r i e s (medium and high are shown here), w i l l show coexi s t e n c e of dense and d i l u t e phases, and c i r c u l a t i o n at the choking f l u x , provided the s p e c i f i e d c o n d i t i o n s are met 211 Figure 4.19 Diagram showing how s o l i d s are separated i n e r t i a l l y by an abrupt e x i t promoting i n t e r n a l c i r c u l a t i o n 213 F i g u r e 4.20 Heat t r a n s f e r s u r f a c e l o c a t i o n s f o r d i f f e r e n t commercial combustor designs 217 - x v i i -Page Figu r e 4.21 V a r i a t i o n of s o l i d s f l u x e s i n a c i r c u l a t i n g f l u i d i s e d bed with s o l i d s r e t u r n some d i s t a n c e above the gas d i s t r i b u t o r . The d e n s i t y p r o f i l e on the l e f t hand si d e , t y p i c a l of the f a s t bed with e l e v a t e d s o l i d s r e t u r n , i s thought to be caused by up, down, and cross f l u x e s as shown on the right-hand s i d e . There i s a lower zone of zero s o l i d s f l u x , an upper zone of net upward f l u x , and a complex cross flow p a t t e r n , p a r t i c u l a r l y at the r e t u r n l o c a t i o n where downflowing s o l i d s are d i s p l a c e d from the wa l l i n t o the core. 222 Fi g u r e 5.1 Dimensionless pressure f l u c t u a t i o n s and o v e r a l l bed d e n s i t y p l o t t e d a gainst gas v e l o c i t y to i l l u s t r a t e the onset of the tu r b u l e n t t r a n s i t i o n , U c, and the f u l l y t u r b u l e n t s t a t e , Ufc (Turner 1978) 228 Figure 5.2 Traces of the d i f f e r e n t i a l pressure f l u c t u a t i o n , as i n d i c a t e d by transducer voltage, versus time i n seconds over a 400 mm s e c t i o n of a bed of sand at d i f f e r e n t gas v e l o c i t i e s a - 0.11 m/s, b - 0.19 m/s, c - 0.40 m/s, d - 0.57 m/s, e - 1.25 m/s, f - 2.14 m/s, g - 2.9 m/s, h - 3.9 m/s 236 F i g u r e 5.3 P l o t of apparent s o l i d s volume f r a c t i o n versus s u p e r f i c i a l gas v e l o c i t y f o r a f l u i d i s e d bed of sand i n a 0.152 m diameter r e a c t o r 239 Figure 5.4 P l o t of standard d e v i a t i o n of d i f f e r e n t i a l pressure f l u c t u a t i o n s over a 460 mm length of a f l u i d i s e d bed of sand versus s u p e r f i c i a l gas v e l o c i t y 240 Fi g u r e 5.5 P l o t of the standard d e v i a t i o n of d i f f e r e n t i a l pressure f l u c t u a t i o n s normalised w.r.t. mean d i f f e r e n t i a l pressure, over a 460 mm s e c t i o n of a f l u i d i s e d bed of sand, versus s u p e r f i c i a l gas v e l o c i t y 241 - x v i i i -Page Figure 5.6 P l o t of the maximum peak-to-peak pressure f l u c t u a t i o n over a 460 mm s e c t i o n of a f l u i d i s e d bed of sand versus s u p e r f i c i a l gas v e l o c i t y 242 Fig u r e 5.7 Absolute pressure f l u c t u a t i o n s i n a sl u g g i n g bed according to Kehoe and Davidson (1973) showing absolute pressure i s not a bimodal f u n c t i o n 244 Figure 5.8 Standard d e v i a t i o n of a d i f f e r e n t i a l pressure s i g n a l measured over a small length versus expansion f o r s l u g flow, showing a maximum de s p i t e no l o s s of the two phase nature 248 Figure 6.1 Tracer p r o f i l e s measured 50 mm upstream of a c e n t r e l i n e i n j e c t i o n p o i n t at d i f f e r e n t gas v e l o c i t i e s (Cankurt and Yerushalmi, 1978). C/Co i s the r a t i o of t r a c e r c o n c e n t r a t i o n at the measurement po i n t to the i n j e c t i o n c o n c e n t r a t i o n . The lower graph represents f a s t bed c o n d i t i o n s (Ug > 1.8 m/s). Turbulent f l u i d i s a t i o n e x i s t s between 0.6 m/s and 1.7 m/s 254 Figure 6.2 V a r i a t i o n of a x i a l d i s p e r s i o n c o e f f i c i e n t with gas v e l o c i t y i n passing from s l u g g i n g to t u r b u l e n t f l u i d i s a t i o n (Yerushalmi and Avidan, 1985). T r a n s i t i o n to turbulence r e p o r t e d l y occurs around 0.7 m/s 256 Figu r e 6.3 V a r i a t i o n of a x i a l P e c l e t number with gas v e l o c i t y (Yerushalmi and Avidan, 1985) 257 Figure 6.4 Tracer i n j e c t i o n system f o r gas RTD s t u d i e s 263 Fig u r e 6.5 Photograph of t r a c e r sampling and dete c t o r system f o r RTD s t u d i e s 265 Figure 6.6 E f f e c t of sampling rate through thermal c o n d u c t i v i t y c e l l upon detector d i s p e r s i o n . (Dead time removed from F-curves) 267 - x i x -Page F i g u r e 6.7 E f f e c t of thermal c o n d u c t i v i t y c e l l type upon d e t e c t o r d i s p e r s i o n showing how design m o d i f i c a t i o n s (new c e l l type d r i l l e d out) reduced d i s p e r s i o n . (Dead time removed from F-curves) 268 Fi g u r e 6.8 Test c o n f i g u r a t i o n to e s t a b l i s h d e t e c t o r l i n e a r i t y 271 F i g u r e 6.9 Graph of i n t e g r a t e d d e t e c t o r output versus i n j e c t i o n volume to demonstrate d e t e c t o r l i n e a r i t y 272 F i g u r e 6.10 Optimised d e t e c t o r F-curve response 273 F i g u r e 6.11 Combined r i s e r / d e t e c t o r F-curve response f o r a x i a l mixing determinations i n c i r c u l a t i n g beds of sand at Ug = 7.1 m/s. Abrupt e x i t , G s = 0, 37, 49, 60 kg/m 2s Smooth e x i t , G s = 0, 65, 41, 33, 43 kg/m 2s 276 F i g u r e 6.12a D e f i n i t i o n s of d e v i a t i o n v a r i a b l e s f o r transform Equation 6.1. 6.12b Procedure f o r i s o l a t i n g the column RTD from the i n d i v i d u a l step responses f o r the d e t e c t o r and detector column combinations using deconvolution. IFT represents i n v e r s e F o u r i e r transform 281 Fig u r e 6.13 Smoothed segmented F-curve responses s u i t a b l e f o r transforming (dead time has been removed) 283 Fig u r e 6.14 E-curves f o r the detector ( c i r c l e s ) and d e t e c t o r / r i s e r combination (squares) from the i n v e r s e transforms of the transformed step responses 285 Fi g u r e 6.15 E x t r a p o l a t i o n of the r e a l and imaginary components of the F o u r i e r transform of the r i s e r RTD beyond t h e i r r e gion of accuracy to approximate higher frequency components before i n v e r s i o n 287 - xx -Page Fi g u r e 6.16 Comparison of the experimental r i s e r / d e t e c t o r combination F-curve with the co n v o l u t i o n of c a l c u l a t e d r i s e r and d e t e c t o r RTD's subjected to a step i n p u t . Dead time has been removed. Comparison i s f a v o u r a b l e 288 F i g u r e 6.17 RTD f o r run Dis 3 computed by decon v o l u t i o n . Dead time removed 289 Figu r e 6.18 Two zone model f o r gas mixing i n a c i r c u l a t i n g f l u i d s e d bed. C a = c o n c e n t r a t i o n i n annulus, C c = c o n c e n t r a t i o n i n core, r c = core r a d i u s , R = column r a d i u s , k = mass t r a n s f e r ( c r o s s f l o w ) c o e f f i c i e n t 291 F i g u r e 6.19 Comparison of the RTD f o r the r i s e r f o r run Dis 3 with best f i t p r e d i c t i o n s of the two zone model. a - c o n t i n u i t y obeyed, r c = 0.059 m, k = 0.11 m/s b - c o n t i n u i t y r e l a x e d , r c = 0.059 m, k = 0.08 m/s, U c = 8.55 m/s 295 Fi g u r e 6.20 P l o t of pseudo v e s s e l d i s p e r s i o n number (D/UgL) f o r a x i a l mixing a g a i n s t pressure drop i n a c i r c u l a t i n g bed of sand, Ug = 7.1 m/s 297 Fi g u r e 6.21 V a r i a t i o n of the standard d e v i a t i o n of absolute pressure f l u c t u a t i o n s near the base of the c i r c u l a t i n g f l u i d i s e d bed with t o t a l pressure drop over the u n i t f o r d i f f e r e n t e x i t geometries, c i r c l e s represent abrupt e x i t , squares smooth 299 F i g u r e A3.1 F-curve response of system and d e t e c t o r p l o t t e d on normal p r o b a b i l i t y paper (Yu, 1985), ' (Ug = 3.5 m/s, G s = 30 kg/m s, alumina) 333 1. INTRODUCTION 1.1 I n i t i a l Concepts The h i s t o r y of c i r c u l a t i n g f l u i d i s e d beds has been s h o r t but t u r b u l e n t . C r e a t e d i n t h e e a r l y 1940s f o r c r a c k i n g o p e r a t i o n s , t h e y were g e n e r a l l y out o f f a v o u r f o r many p r o c e s s e s u n t i l t h e l a t e 1970s when a renewed i n d u s t r i a l and a c a d e m i c i n t e r e s t b r o u g h t them a new p r o m i n e n c e . S i n c e t h a t t i m e , d i s c u s s i o n s have been n e a r l y as t u r b u l e n t as t h e c o n t a c t o r s t h e m s e l v e s , and t h e r e has been l i t t l e c o n s e n s u s about what c o n s t i t u t e s a c i r c u l a t i n g f l u i d i s e d bed and how t h e y m i g h t be c h a r a c t e r i s e d . The o n l y agreement a p p e a r s t o be t h a t c i r c u l a t i n g , or f a s t , f l u i d i s a t i o n i s an e x c e l l e n t c o n t a c t i n g scheme f o r many g a s - s o l i d r e a c t i o n s . As i m p l i e d above, one o f t h e most d i f f i c u l t a s p e c t s o f w o r k i n g w i t h c i r c u l a t i n g f l u i d i s e d beds i s d e s c r i b i n g e x a c t l y what i s meant by t h e t e r m . F i g u r e 1.1 i l l u s t r a t e s a v e r t i c a l g a s - s o l i d s t r a n s p o r t l i n e . F o r t h e s o l i d s i t i s a c l o s e d l o o p i n w h i c h e n t r a i n e d m a t e r i a l i s r e t u r n e d t o t h e base of t h e u n i t t h r o u g h a c y c l o n e and a s t a n d p i p e . I f t h e u n i t i s c h a r g e d w i t h an i n v e n t o r y o f s o l i d p a r t i c l e s and t h e gas v e l o c i t y i s g r a d u a l l y r a i s e d f r o m z e r o t o a p p r o x i m a t e l y 10 m/s, t h e n a s e q u e n c e o f f l o w r e g i m e s w i l l be r e c o r d e d . A t low gas v e l o c i t i e s , f i r s t t o minimum f l u i d i s a t i o n , and t h e n t o s e v e r a l t i m e s t h i s v a l u e , t h e f a m i l i a r p a c k e d bed, - 2 -F i g u r e 1.1 Schema t i c d iag ram of a v e r t i c a l g a s - s o l i d t r a n s p o r t l i n e . - 3 -b u b b l e - f r e e f l u i d i z a t i o n (at the minimum f l u i d i z a t i o n p o i n t only, or over an extended range) and bubbling f l u i d i s a t i o n regimes w i l l be seen. At the h i g h e s t gas v e l o c i t i e s another f a m i l a r regime, d i l u t e phase pneumatic t r a n s p o r t i s observed. Between these two extremes the flow s t r u c t u r e s are l e s s c l e a r and l e s s well understood. Leung (1980) d e s c r i b e s the c o n v e n t i o n a l wisdom re g a r d i n g the d i f f e r e n t p o s s i b l e flow regimes f o r c o c u r r e n t g a s - s o l i d s flow i n terms of a flowchart ( F i g u r e 1.2). Two d i f f e r e n t types of behaviour may occur. In the f i r s t , the r i g h t hand branch of F i g u r e 1.2, i f the gas v e l o c i t y i s reduced at a constant s o l i d s c i r c u l a t i o n r a t e , there i s an abrupt t r a n s i t i o n from a d i l u t e to a dense phase system. This i s the phenomenon commonly known as choking, d e s c r i b e d i n d e t a i l by such authors as Yang (1975) and Smith (1978). In the second type of system there i s not such a sharp t r a n s i t i o n ; i n s t e a d , as the gas v e l o c i t y i s reduced from pneumatic t r a n s p o r t , the bed g r a d u a l l y enters a regime c a l l e d "non-slugging dense phase flow" (Leung, 1980) or f a s t f l u i d i s a t i o n (Yerushalmi and Cankurt, 1978), a s t a t e c h a r a c t e r i s e d by l o n g i t u d i n a l g r a d i e n t s i n the suspended s o l i d s c o n c e n t r a t i o n , vigorous backmixing of s o l i d s , and high g a s - s o l i d s l i p v e l o c i t e s , an e x c e l l e n t combination of c h a r a c t e r i s t i c s f o r g a s - s o l i d c o n t a c t i n g . T h i s i s the regime of p r i n c i p a l i n t e r e s t to t h i s study. - 4 -Dilute (lean) Phase Flow Fuzzy Transition Sharp Transition (Choking Transition) Non-slugging Dense Phase Flow Fuzzy Transition Slugging Dense Phase Flow Slugging Dense Phase Flow Sharp Transition Sharp Transition High Gas Velocity Transition from Fluidized Flow to Packed Bed Flow Packed Bed (Moving Bed) Flow Low Gas Velocity F i g u r e 1.2 Flow regimes f o r g a s - s o l i d flow a c c o r d i n g to Leung (1980). - 5 -An a l t e r n a t i v e way of approaching the f a s t f l u i d i s a t i o n regime i s by g r a d u a l l y i n c r e a s i n g the gas v e l o c i t y . T h i s g i v e s a somewhat d i f f e r e n t i n s i g h t i n t o the process. In a small diameter column with a p p r o p r i a t e l y s i z e d p a r t i c l e s , as the gas v e l o c i t y i s r a i s e d , f i r s t bubbling and then s l u g g i n g occur. These are w e l l documented. Less f a m i l i a r i s the t r a n s i t i o n which occurs as the v e l o c i t y i s r a i s e d through the s l u g g i n g regime, i . e . the t r a n s i t i o n to t u r b u l e n t f l u i d i s a t i o n . T h i s t r a n s i t i o n has r a i s e d much con t r o v e r s y and i s considered i n t h i s t h e s i s . For the purposes of t h i s i n t r o d u c t o r y s e c t i o n the t r a n s i t i o n may be d e f i n e d as a gradual breakdown of the two phase s t r u c t u r e of the b u b b l i n g and s l u g g i n g regimes, where a dense phase emulsion surrounds d i l u t e phase voids, to a c o n d i t i o n of i n c r e a s e d u n i f o r m i t y . In t h i s new " t u r b u l e n t " f l u i d i s e d s t a t e , bubbles as such no longer e x i s t (Yerushalmi and Cankurt, 1978), but the bed c o n s i s t s of r e f l u x i n g strands or packets of p a r t i c l e s where n e i t h e r a dense nor a d i l u t e phase can t r u l y be s a i d to be continuous. There are i m p l i c a t i o n s a s s o c i a t e d with the t u r b u l e n t regime that s c a l e s of phase c o n t i n u i t y are s m a l l , compared to bubbling and s l u g g i n g , and t h a t , c o n t a c t i n g between gas and s o l i d s i s improved because there i s l e s s tendency f o r gas to bypass the p a r t i c u l a t e s i n the form of bubbles or s l u g s . Although there i s some evidence f o r t h i s ( M a s s i m i l l a , 1973) the evidence i s f o r improved c o n t a c t i n g - 6 -r e l a t i v e to a system d e s c r i b e d by emulsion and bubble phases. The s t u d i e s to date do not completely support the i n i t i a l concept of t u r b u l e n t f l u i d i s a t i o n as a uniform suspension of aggregates i n gas with continuous breakdown and reforming. One study at l e a s t (Abed, 1983) prov i d e s evidence f o r strong r a d i a l non-uniformity i n small u n i t s . However, m i c r o s t r u c t u r a l d e t a i l s should not be allowed to confuse the b a s i c concept of t u r b u l e n t f l u i d i s a t i o n as a g e n e r a l l y more uniform s t a t e than i s found at immediately lower v e l o c i t i e s . One c h a r a c t e r i s t i c of the tur b u l e n t regime i s th a t , because of the apparent regrouping of p a r t i c l e s i n t o s t r a n d s or c l u s t e r s ( i n a time mean sense), s l i p v e l o c i t i e s i n the t u r b u l e n t regime may be an order of magnitude higher than the t e r m i n a l v e l o c i t y of an i n d i v i d u a l p a r t i c l e , and t h i s occurs without s u b s t a n t i a l entrainraent. Therefore the t u r b u l e n t regime can s t i l l be c h a r a c t e r i z e d as a s t a t i c regime with an i d e n t i f i a b l e bed surface, a l b e i t somewhat more d i f f u s e than at lower v e l o c i t i e s . As the s u p e r f i c i a l gas v e l o c i t y i s g r a d u a l l y r a i s e d beyond t u r b u l e n t f l u i d i s a t i o n , f a s t f l u i d i s a t i o n , or the c i r c u l a t i n g bed regime, i s entered from the low v e l o c i t y end. J u s t as the t r a n s i t i o n from slugging to t u r b u l e n t f l u i d i s a t i o n i s gradual, so t h i s entry to f a s t f l u i d i s a t i o n need not be dramatic. Rather, the rate of entrainment from - 7 -the t u r b u l e n t bed g r a d u a l l y becomes so high (> 15kg/m s) that, unless e n t r a i n e d m a t e r i a l i s co n t i n u o u s l y r e p l a c e d , the bed empties very r a p i d l y . Although a f a s t f l u i d i s e d bed i s v i s u a l l y very s i m i l a r to a t u r b u l e n t bed, at l e a s t i n i t s densest r e g i o n s , i t has some s u b s t a n t i a l l y d i f f e r e n t p r o p e r t i e s : ( i ) While the t u r b u l e n t bed has a d i f f u s e s u r f a c e s e p a r a t i n g the dense bed from a freeboard zone, the d e n s i t y p r o f i l e i n a c i r c u l a t i n g bed undergoes an even more gradual t r a n s i t i o n from dense to d i l u t e s t a t e s , and may not even c o n t a i n e i t h e r extreme. ( i i ) While a t u r b u l e n t bed has f a i r l y low s o l i d s entrainment, a f a s t f l u i d i s e d bed i s a t r a n s p o r t r e a c t o r . Therefore i t s s t r u c t u r e i s c h a r a c t e r i s e d not only by gas v e l o c i t y and s o l i d p r o p e r t i e s , but a l s o by the s o l i d s c i r c u l a t i o n r a t e . T h i s f i n a l dependence i s c r i t i c a l f o r many i n d u s t r i a l a p p l i c a t i o n s . L i k e the t u r b u l e n t f l u i d i s e d bed, the c i r c u l a t i n g bed when viewed through a transparent w a l l appears to c o n s i s t of many strands of r e f l u x i n g p a r t i c l e s c o n t i n u o u s l y c o a l e s c i n g and reforming. A photograph i s shown i n Figure 1.3. A l s o , l i k e the t u r b u l e n t bed, s l i p v e l o c i t i e s i n the dense regions of a c i r c u l a t i n g bed may exceed i n d i v i d u a l p a r t i c l e t e r m i n a l v e l o c i t i e s by an order of magnitude. This i s i l l u s t r a t e d i n Fi g u r e 1.4. Together these observations led to the development of t h e o r i e s f o r c i r c u l a t i n g f l u i d i s e d bed f l u i d - 8 -F i g u r e 1.3 Photograph of a f a s t f l u i d i z e d bed viewed through the w a l l . - 9 -S L I P V E L O C I T Y ; € ( m / s ) L. 195 146 I t 1 r i « 1 i i i i i SOLID RATE, 6, (Kg/m* s) FAST -19.5 O . I SOUDS*FCC FLUIDIZED W REGIME TRANSPORT VELOCITY TURBULENT REGIME ' 4 ^ /BREAKDOWN OF SLUGS _ % BUBBLING REGIME fm1 l * l I I I I 0 . 2 i-e 0 . 3 0 . 4 0 . 6 0 . 8 l . O ^ c h a n g e i n s c a l e F i g u r e 1.4 S l i p v e l o c i t i e s i n high v e l o c i t y f l u i d i z a t i o n according to Yerushalmi and Cankurt (1978). - 10 -mechanics based upon the e x i s t e n c e of st r a n d s , or c l u s t e r s of p a r t i c l e s , d i s p e r s e d u n i f o r m l y over the r e a c t o r c r o s s - s e c t i o n . Each c l u s t e r was assumed to behave l i k e a s i n g l e l a r g e r p a r t i c l e i n a time mean sense, although i t was e v i d e n t l y i n a continuous s t a t e of formation and d e s t r u c t i o n . I t was these l a r g e , " e f f e c t i v e agglomerates" which gave the f a s t bed i t s high s l i p v e l o c i t i e s and a number of p o t e n t i a l advantages: ( i ) The a b i l i t y to maintain r e l a t i v e l y dense beds of f i n e p a r t i c l e s at high v e l o c i t i e s , a l l o w i n g high throughput i n small c r o s s - s e c t i o n u n i t s . ( i i ) Intense backmixing of s o l i d s , promoting temperature u n i f o r m i t y . ( i i i ) The agglomerates are i n no sense c l o s e packed, and allow s u b s t a n t i a l c o n v e c t i v e throughflow. Therefore the s u r f a c e area of each i n d i v i d u a l p a r t i c l e remains a c t i v e . ( i v ) There are p o t e n t i a l c o n t r o l advantages to the c i r c u l a t i n g bed a s s o c i a t e d with the a b i l i t y to r a p i d l y change the r i s e r i n v e n t o r y by changing the e x t e r n a l c i r c u l a t i o n r a t e of s o l i d s . These f e a t u r e s , together with others, suggested that the c i r c u l a t i n g bed co u l d be an e f f e c t i v e medium f o r many r e a c t i o n s . Having placed f a s t f l u i d i s a t i o n i n a q u a l i t a t i v e hydrodynamic context, i t i s v a l u a b l e to see i t d e f i n e d - 11 -somewhat more q u a n t i t a t i v e l y . Regime diagrams have o f t e n been used f o r t h i s purposes, and F i g u r e 1.5 shows a proposed regime diagram due to Grace (1986a). Fast f l u i d i s a t i o n occupies a r e g i o n of l i m i t e d v e l o c i t i e s and p a r t i c l e s i z e s . The v e l o c i t y l i m i t s are imposed by l a c k of t r a n s p o r t at the lower end, and by o v e r l y d i l u t e suspensions at the uper end ( s l i p v e l o c i t y approaches t e r m i n a l v e l o c i t y ) . P a r t i c l e s i z e l i m i t a t i o n s , although i n d i c a t e d on t h i s regime diagram, are more tenuous. I t i s not c l e a r as yet whether very l a r g e p a r t i c l e s f o r f a s t f l u i d i s a t i o n (> 1.5 mm) can be contacted i n t h i s regime, and f i n e r p a r t i c l e s , f a l l i n g i n G e l d a r t ' s group C ( G e l d a r t , 1973) are c u r r e n t l y under study (Brereton et a l . , 1987). 1.2 H i s t o r i c a l and Current Industrial Perspectives C i r c u l a t i n g f l u i d i s e d beds have arguably been known s i n c e the e a r l y 1940s when, as part of Standard O i l ' s e f f o r t s to develop a c a t a l y t i c c r a c k i n g process f o r o i l , Lewis and G i l l i l a n d (1950) examined gas s o l i d c o n t a c t i n g at v e l o c i t i e s between minimum f l u i d i s a t i o n and 3 m/s ( S q u i r e s , 1985). T h i s e a r l y r e s e a r c h l e d to the development of a commercial upflow c a t a l y t i c c r a c k e r which was placed on stream i n 1943; however, t h i s and other r i s e r c r a c k e r s soon l o s t favour because of o p e r a t i o n a l d i f f i c u l t i e s , n otably dust c o l l e c t i o n and s o l i d s i n v e n t o r y c o n t r o l (Turner, - 12 -d p - . A r ' / ' . ^ V s / / . * ] ' ' 3 Figure 1.5 Regime diagram f o r g a s - s o l i d contacting according to Grace (1986a). Ap i s the d i f f e r e n c e between p a r t i c l e and gas d e n s i t i e s . - 13 -1979). Therefore i n d u s t r y turned to the b u b b l i n g f l u i d i s e d bed as a standard f o r both c a t a l y t i c c r a c k i n g and r e g e n e r a t i o n , and these u n i t s p r o l i f e r a t e d u n t i l the e a r l y 1950s when S h e l l appears to have r e i n t r o d u c e d the concept of high v e l o c i t y c r a c k i n g (Rehbein e_t aJU , 1959). By t h i s time, with the i n t r o d u c t i o n of u l t r a - h i g h a c t i v i t y z e o l i t e c a t a l y s t s , which were both more durable and p e r m i t t e d s h o r t e r vapour phase r e s i d e n c e times, and with advances i n s o l i d s flow c o n t r o l systems, r i s e r c r a c k i n g c o u l d become a r e a l i t y . C u r r e n t l y i t i s the i n d u s t r y standard. Despite t h i s long h i s t o r y of upflow g a s - s o l i d c o n t a c t i n g o p e r a t i o n s i n the o i l i n d u s t r y , i n a regime which i s arguably f a s t f l u i d i s a t i o n , there was s u r p r i s i n g l y l i t t l e p u b l i s h e d r e s e a r c h on the s u b j e c t u n t i l the l a t e 1970s. P r i o r to t h i s there had been s u b s t a n t i a l work on pneumatic t r a n s p o r t , at very low suspended s o l i d s c o n c e n t r a t i o n s (oKO.Ol), and a l s o s u b s t a n t i a l work on the r e l a t e d phenomenon of choking, but the s t u d i e s tended to focus on m a i n t a i n i n g the former and a v o i d i n g the l a t t e r ; the r e g i o n of i n termediate gas v e l o c i t y and high suspension d e n s i t i e s , f a s t f l u i d i s a t i o n , had been l a r g e l y u n s t u d i e d . C o n t a c t i n g at i n t e r m e d i a t e gas v e l o c i t i e s , i n a context other than r i s e r c r a c k i n g , appears to have o r i g i n a t e d with Reh of L u r g i Chemie und Huttenteknik (Reh et al_. , 1980). L u r g i developed a f a s t f l u i d i s e d bed alumina c a l c i n e r and - 14 -from t h i s progressed i n t o combustion and other a p p l i c a t i o n s (Reh et^ a_l. , 1980). A large number of c i r c u l a t i n g bed processes are now under development i n c l u d i n g : ( i ) Gas c l e a n i n g p r o c e s s e s - u t i l i s i n g high mass t r a n s f e r c o e f f i c i e n t s and larg e a v a i l a b l e s u r f a c e fo r a d s o r p t i o n of HF, HG1 and S 0 2 from f l u e gases (Reh, 1985). ( i i ) Low pressure g a s i f i c a t i o n processes - f o r g a s i f i c a t i o n of low grade f u e l s such as wood waste to produce a gas s u i t a b l e f o r lime k i l n f i r i n g (Kobro and Stromberg, 1986). ( i i i ) P y r o l y s i s processes - to produce l i q u i d f u e l s from c o a l and other s o l i d carbonaceous f u e l s . ( i v ) M e t a l l u r g i c a l processes - i n c l u d i n g the ELRED process f o r p r e r e d u c t i o n of i r o n ore, and a s i m i l a r process f o r pr e r e d u c t i o n of l a t e r i t i c n i c k e l ores. Both processes d r a m a t i c a l l y reduce energy c o s t s f o r subsequent process steps ( H i r s c h et a l . , 1985) . Se v e r a l of these processes have been d r i v e n by the need to make economic, environmentally sound use of stocks of high sulphur, high ash, or s t r o n g l y caking c o a l s which have proved d i f f i c u l t to process using other techniques. The c i r c u l a t i n g bed presents a t u r b u l e n t c o n t a c t i n g medium minimising problems with caking and simultaneously p r o v i d i n g - 15 -the o p p o r t u n i t y f o r in-bed sulphur removal i n combustion proc e s s e s . T h i s may have removal e f f i c i e n c i e s approaching 90% at Ca:S r a t i o s as low as 1.5:1 (Reh et a l . , 1980). Success with combustion of these d i f f i c u l t to burn c o a l s has led to the use of a l a r g e number of other f u e l s i n c i r c u l a t i n g bed combustion u n i t s ; these i n c l u d e a n t h r a c i t e culms, high sulphur petroleum cokes formed as a byproduct of t a r sands p r o c e s s i n g , high moisture wood wastes, and even a dehydrated sewage sludge powder produced by the Carver G r e e n f i e l d process (Stromberg et a l . , 1985). Commercial u n i t s now o f f e r an extremely competitive technology f o r the new u n i t market, and lar g e numbers of u n i t s have been b u i l t i n Europe, Scandinavia, and more r e c e n t l y i n the United S t a t e s and Canada with c a p a c i t i e s as small as 2.5 MW-th (Stromberg et a l . , 1985) and as large as 100 MWe (Schweiger, 1985). The s p e c i f i c s of t h i s t h e s i s , notably the types of s o l i d s and the range of gas v e l o c i t i e s employed, have been d i r e c t e d s t r o n g l y towards the combustion a p p l i c a t i o n . While the general c o n c l u s i o n s remain v a l i d f o r a l l c i r c u l a t i n g bed t e c h n o l o g i e s , numerical values may be s p e c i f i c to the gas v e l o c i t i e s and s o l i d s types which were examined. A t y p i c a l c i r c u l a t i n g f l u i d i s e d bed combustor i s shown i n F i g u r e 1.6. I t o f f e r s the f o l l o w i n g advantages over a t r a d i t i o n a l p u l v e r i s e d or stoker f i r e d combustion system. - 16 -GAS HOT WATER STEAM LIMESTONE PRIMARY AIR 40-80% WATER /STEAM F i g u r e 1.6 A t y p i c a l c i r c u l a t i n g bed combustor ( K u l l e n d o r f and Andersson, 1985). - 17 -( i ) Decreased f u e l p r e p a r a t i o n c o s t s because of the a b i l i t y to burn high ash, high sulphur c o a l s i n rough crushed form - t y p i c a l l y minus 25 - 40mm. ( i i ) Decreased c o s t s , c a p i t a l and o p e r a t i n g , a s s o c i a t e d with removal of sulphur from the f l u e gas. In-bed d e s u l p h u r i s a t i o n can be accomplished u s i n g limestone or dolomite as a sorbent r a t h e r than r e q u i r i n g expensive f l u e gas d e s u l p h u r i s a t i o n equipment such as wet or dry scrubbers. ( i i i ) Decreased thermal and f u e l N0 X p r o d u c t i o n due to decreased o p e r a t i n g temperatures. A l l these advantages are a l s o o f f e r e d by more t r a d i t i o n a l bubbling f l u i d i s e d bed combustors; however, c i r c u l a t i n g f l u i d i s e d beds o f f e r f u r t h e r advantages s t i l l : ( i ) Improved turndown and m u l t i f u e l c a p a b i l i t y , without the need to p r o v i d e compartmentalised beds, by v i r t u e of the a b i l i t y to vary heat t r a n s f e r c o e f f i c i e n t s over a wide range (e.g. 50 - 250 W/m2K) through c o n t r o l of s o l i d s c i r c u l a t i o n r a t e . ( i i ) Simpler turndown and c o n t r o l p r a c t i c e s . ( i i i ) Improved u t i l i s a t i o n of in-bed sorbents f o r sulphur capture without e x t e r n a l ash c l a s s i f i c a t i o n , treatment and r e c y c l e loops. ( i v ) Lower NOx emissions than f o r bubbling beds by - 18 -v i r t u e of the a b i l i t y to stage a i r i n t r o d u c t i o n at two or even three l e v e l s . (v) Lower c o s t s f o r f u e l f e e d i n g systems s i n c e improved s o l i d s mixing decreases the number of feed p o i n t s r e q u i r e d . ( v i ) Fuel savings through improved combustion e f f i c i e n c y . ( v i i ) Smaller u n i t c r o s s - s e c t i o n s by v i r t u e of higher gas v e l o c i t i e s . To q u a l i f y these comments and present bubbling beds i n a f a i r p e r s p e c t i v e i t i s important to note that bubbling beds can provide e q u a l l y good sulphur capture and combustion e f f i c i e n c y as the best c i r c u l a t i n g u n i t s , p rovided that cyclone ash r e c y c l e loops are employed. A l s o , N0 X emissions can be reduced by secondary a i r a d d i t i o n . However, t h i s tends to take p l a c e at the expense of sulphur capture. Hence, bubbling bed technology competes s t r o n g l y with the c i r c u l a t i n g bed with the advantage of proven r e l i a b i l i t y and w e l l understood ash c h a r a c t e r i s t i c s . The p r i n c i p a l argument i n favour of a c i r c u l a t i n g bed i s then reduced to the s i m p l i c i t y of turndown and an improved m u l t i f u e l c a p a b i l i t y . I t i s not p o s s i b l e at t h i s stage to make an economic choice between the two i n a given s i z e range by a s s e s s i n g the r e l a t i v e c o s t s of a bubbling bed with ash r e c y c l e and a c i r c u l a t i n g u n i t . - 19 -The c i r c u l a t i n g f l u i d i s e d bed combustor makes use of the f o l l o w i n g p e r c e i v e d merits of f a s t f l u i d i s a t i o n : ( i ) Temperature u n i f o r m i t y due to i n t e n s i v e i n t e r n a l s o l i d s mixing. ( i i ) Intimate g a s - s o l i d c o n t a c t i n g by v i r t u e of high g a s - s o l i d s s l i p v e l o c i t i e s and no bubbles. ( i i i ) A b i l i t y to c o n t r o l heat t r a n s f e r c o e f f i c i e n t s by c o n t r o l of c i r c u l a t i o n r a t e s , and hence d e n s i t y p r o f i l e s . I t i s t h i s t h i r d p o i n t , which i s not e n t i r e l y d i v o r c e d from the f i r s t two, which has motivated much of the present study. T h i s has been d i s c u s s e d i n d e t a i l by Kobro and B rereton (1985) with the essence of the argument given below. Our a b i l i t y to c o n t r o l and to design c i r c u l a t i n g f l u i d i s e d bed combustors i s a d i r e c t f u n c t i o n of our a b i l i t y t o be a b l e to p r e d i c t heat t r a n s f e r and f l u i d mechanics. I f we c o n s i d e r the c o n t r o l or design o b j e c t i v e as being able to m aintain a d e s i r a b l e combustion temperature i n a r i s e r furnace chamber which has membrane wa l l s (water cooled heat t r a n s f e r s u r f a c e s ) f o r s i d e s , then the problem becomes one of c o n t r o l l i n g the amount of heat t r a n s f e r r e d i n t o these s u r f a c e s . T h i s i s shown i n F i g u r e 1.7. I d e a l l y t h i s should be accomplished without having to use excess a i r or f l u e gas r e c i r c u l a t i o n to remove heat from the combustion chamber s i n c e the f i r s t reduces the b o i l e r e f f i c i e n c y , and the - 20 -Q=H 0AAT Cooling • — Secondary Air Fixed Inventory C F B A Secondary Zone Density p Primary Air High U g - *High/9 e ( 7+High H Q Low Ug Low/9 s e c - *Low H Q gure 1.7 C o n t r o l of a c i r c u l a t i n g bed combustor by v a r i a t i o n of heat t r a n s f e r r a t e t o a membrane w a l l . Q r e p r e s e n t s the t o t a l heat a b s o r p t i o n , H Q the o v e r a l l heat t r a n s f e r c o e f f i c i e n t above the secondary a i r p o r t s , and P s e c the mean susp e n s i o n d e n s i t y above the secondary a i r ports - 21 -second i s mechanically and economically u n d e s i r a b l e . In order to maintain constant furnace temperature, independent of load or f u e l , then at low load, or f o r f i r i n g of high moisture f u e l s a small amount of heat removal i s necessary; at high load the converse h o l d s . T h i s i m p l i e s that s i n c e the d r i v i n g f o r c e i s f i x e d by furnace temperature, and the heat t r a n s f e r area i s f i x e d by design, load f o l l o w i n g r e q u i r e s "an a b i l i t y to vary the heat t r a n s f e r c o e f f i c i e n t to the furnace w a l l . The c i r c u l a t i n g bed p r o v i d e s p r e c i s e l y t h i s a b i l i t y . In t h i s d i s c u s s i o n , j u s t one type of c i r c u l a t i n g bed c o n t r o l w i l l be i l l u s t r a t e d t y p i f y i n g what i s c a l l e d a " f i x e d i n v e n t o r y u n i t " . T h i s i s s u f f i c i e n t f o r our purposes here; the reader i s r e f e r r e d to Kobro and Brereton (1985) f o r d i s c u s s i o n of a second u n i t type, the " v a r i a b l e i n v e n t o r y d e s i g n . " In a f i x e d i n v e n t o r y c i r c u l a t i n g f l u i d i s e d bed combustor there i s very l i t t l e hold-up i n the r e c y c l e l e g so s u b s t a n t i a l l y a l l of an i n i t i a l i n v e n t o r y of m a t e r i a l i s d i s t r i b u t e d between a dense primary zone and a l e s s dense high v e l o c i t y zone. The amount i n each depends upon the primary to secondary a i r s p l i t and the t o t a l gas v e l o c i t y , with F i g u r e 1.7 showing approximate d i s t r i b u t i o n s f o r two d i f f e r e n t gas v e l o c i t i e s r e p r e s e n t i n g f u l l and h a l f load c o n d i t i o n s . Now, F i g u r e 1.8 shows measured heat t r a n s f e r c o e f f i c i e n t s for a c i r c u l a t i n g bed b o i l e r (Kobro and - 22 -Brereton, 1985), i n d i c a t i n g that these are an approximately l i n e a r f u n c t i o n of suspension d e n s i t y over the measured range. I f these r e s u l t s are combined with the d e n s i t y d i s t r i b u t i o n s of F i g u r e 1.7, i t i s evident that, as long as heat t r a n s f e r s u r f a c e i s l o c a t e d p r i n c i p a l l y above the secondary a i r p o r t s , then the high v e l o c i t y , high load s c e n a r i o w i l l promote a higher o v e r a l l heat t r n a s f e r c o e f f i c i e n t . Hence there i s a n a t u r a l tendency f o r load c o n t r o l which may be f i n e - t u n e d by changes i n primary to secondary a i r s p l i t and other techniques. The n a t u r a l turndown of the c i r c u l a t i n g bed combustor which r e s u l t s from a decrease i n v e l o c i t y promoting a decrease i n s h a f t holdup, provides f o r extremely simple turndown p r a c t i c e . However, i t can only be u t i l i s e d i f a c c u r a t e p r e d i c t i o n s can be made of d e n s i t y p r o f i l e s and t h e i r v a r i a t i o n with v e l o c i t y and other o p e r a t i n g parameters. The d e n s i t y p r o f i l e s on a macroscopic l e v e l , and the mixing on a macro and microscopic l e v e l w i l l determine heat t r a n s f e r , temperature u n i f o r m i t y , furnace e x i t temperature and other parameters e s s e n t i a l to the c i r c u l a t i n g bed designer. 1.3 Fast F l u i d i s a t i o n and Density P r o f i l e s Up to t h i s point t h i s i n t r o d u c t i o n has focussed upon what i s meant by f a s t f l u i d i s a t i o n , where f a s t f l u i d i s e d beds have found a p p l i c a t i o n thus f a r , and why i t i s - 12,3 -F i g u r e 1.8 Heat t r a n s f e r c o e f f i c i e n t s i n f a s t f l u i d i s a t i o n as a f u n c t i o n of suspension d e n s i t y and temperature (Kobro and Brereton, 1985). - 24 -important to be able to c h a r a c t e r i s e the d e n s i t y p r o f i l e i n order to p r e d i c t how a f a s t f l u i d i s e d bed w i l l perform i n one p a r t i c u l a r i n s t a n c e - turndown of a CFB combustor. I t i s a l s o important to be able to p r e d i c t d e n s i t y p r o f i l e s i n other cases, f o r example, where c a t a l y t i c r e a c t i o n s occur. In these i n s t a n c e s , the c a t a l y s t d e n s i t y p r o f i l e along the r e a c t o r determines the gas s o l i d contact-time h i s t o r y and the extent of c o n t a c t i n g . It i s e s s e n t i a l to understand how and why t h i s w i l l change as the c a t a l y s t c i r c u l a t i o n r a t e i s changed. Because of i t s importance, the d e n s i t y p r o f i l e has r e c e i v e d c o n s i d e r a b l e a t t e n t i o n , both from the p o i n t of view of i t s macrostructure, and i t s m i c r o s t r u c t u r e . However, i t i s s t i l l not c l e a r how the d e n s i t y p r o f i l e forms, why i t takes c e r t a i n shapes, how i t i s a f f e c t e d by v a r i a t i o n s i n parameters such as p a r t i c l e s i z e and s o l i d s c i r c u l a t i o n r a t e , and how the m i c r o s t r u c t u r a l elements combine to form the macrostructure. Experimental s t u d i e s such as those conducted at CUNY (Yerushalmi and Cankurt, 1978; Turner, 1979; Weinstein e_t a l . , 1981; Weinstein £t al_. , 1983) and s i m i l a r s t u d i e s by L i and Kwauk (1980) show that d e n s i t y p r o f i l e s i n c i r c u l a t i n g f l u i d i s e d beds may g e n e r a l l y be d e s c r i b e d by an approximately "S" shaped p r o f i l e , Figure 1.9. They s t r e t c h from a high d e n s i t y asymptote at the base of the column, or - 25 -Sol ids IRON CONCENTRATE circulation, kg/M2 • sec top ALUMINA FCC CATALYST 16 PYRITE CINDER 4J .e 60 •H <U rc « bottom 1.0 O.ft 0.9 1.0 0.« V o i d a g e , F i g u r e 1.9 Density p r o f i l e s f o r f a s t f l u i d i s a t i o n ( L i and Kwauk, 1980). - 26 -at some imaginary p o i n t below the base, through an i n f l e c t i o n p o i n t , to what seems to be a low d e n s i t y asymptote at or beyond the top of the u n i t . More r e c e n t l y , s i m i l a r p r o f i l e s , or p o r t i o n s of t h i s c h a r a c t e r i s t i c shape have been found by Arena et a_l. (1985), Fusey et al_. (1985), Rhodes and G e l d a r t (1985) and Brereton and Stromberg (1985). D i f f e r e n t f a c t o r s have been found to i n f l u e n c e the s p e c i f i c d e t a i l s of the shape of the p r o f i l e . Many of these are i n c l u d e d i n a model by L i and Kwauk (1980) extended by L i et a l . (1982). The v a r i a b l e s i n c l u d e p a r t i c l e s i z e , p a r t i c l e d e n s i t y , gas d e n s i t y , gas v i s c o s i t y , gas v e l o c i t y , s o l i d s c i r c u l a t i o n r a t e , and more c o n t r o v e r s i a l l y , the "imposed pressure drop." T h i s l a s t parameter i s t r e a t e d at length i n a l a t e r s e c t i o n . The L i and Kwauk model t r e a t s the c i r c u l a t i n g f l u i d i s e d bed, and i n t e r p r e t s the voidage p r o f i l e i n terms of c l u s t e r s of p a r t i c l e s . The c h a r a c t e r i s t i c d e n s i t y p r o f i l e shape i s a s c r i b e d to a balance of " d i f f u s i v e " and "buoyancy" f o r c e s a c t i n g upon each c l u s t e r . Each p r o f i l e i s then c h a r a c t e r i s e d by the equation -1 (Z - Z.) (1.1) o where the f i t t e d constants e a > e* and Z± have a p h y s i c a l s i g n i f i c a n c e as shown i n F i g u r e 1.10. The terms e a and e* - 27 -have been c o r r e l a t e d by L i et al_. (1982) f o r a number of s o l i d s and a s i n g l e u n i t geometry, these c o r r e l a t i o n s being shown i n Fig u r e 1.11. Z Q was termed the c h a r a c t e r i s t i c l ength f o r the f a s t f l u i d i s a t i o n , and t h i s , and the l o c a t i o n of the i n f l e c t i o n marked by Z i were a l s o c o r r e l a t e d by L i e t a l . (1982). I n t e r p r e t a t i o n of the s t r u c t u r e of the c i r c u l a t i n g f l u i d i s e d bed i n terms of a uniform, or approximately uniform, d i s p e r s i o n of aggregates p r o v i d e s a simple way of i n t e r p r e t i n g c i r c u l a t i n g bed phenomena such as high s l i p v e l o c i t i e s (Yerushalmi et a_l. , 1978) and good g a s - s o l i d c o n t a c t i n g with no d i f f u s i o n a l r e s i s t a n c e w i t h i n c l u s t e r s (Wainright and Hoffman, 1974; DeLasa and Gau, 1973). The s t r u c t u r e corresponds very w e l l with v i s u a l o b s e r v a t i o n s through a w a l l and a l s o has some precedents i n other multiphase flows. These are considered below. The r a t i o n a l i s a t i o n process can begin by c o n s i d e r i n g s t a b i l i t y analyses on uniform f l u i d - s o l i d suspensions. Jackson (1971) performed such a l i n e a r s t a b i l i t y a n a l y s i s , v a l i d f o r small p e r t u r b a t i o n s , and r a t i o n a l i s e d the formation of bubbles i n bubbling f l u i d i s e d beds by showing that a uniform g a s - s o l i d suspension was unstable to voidage p e r t u r b a t i o n s . The concept was extended to hig h e r v e l o c i t i e s and more d i l u t e systems by Grace and Tuot (1979) who concluded that a l l homogeneous f l u i d - s o l i d systems, i n c l u d i n g l i q u i d - s o l i d systems, are unstable to such - 28 -Typical Voidage Distribution Proposed Physical Modal 4 DKNSB CUISTEHSl , volume fraction of dense clusters, f solids concn. in dense phase, 1 - £ & DILUTE CONTINUUM: volume fraction of dilute phase, 1 - f solids concn. in dilute phase, 1 - £* S E G R E G A T I O N F L U X D I P P U S I O N F L U X voidage t gas F i g u r e 1.10 The L i and Kwauk (1980) model f o r d e n s i t y p r o f i l e s i n f a s t f l u i d i s e d beds. - 29 -Re = s U'_ G F i g u r e 1.11 C o r r e l a t i o n s f o r parameters i n the L i e t a l . (1982) d e n s i t y d i s t r i b u t i o n model. ( R e ^ ~ ~ i s -the p a r t i c l e Reynold number based on the r e l a t i v e v e l o c i t y between gas and s o l i d . True v e l o c i t i e s , not s u p e r f i c i a l v e l o c i t i e s a re used i n the d e f i n i t i o n . Ar i s the Archimedes number.) - 30 -p e r t u r b a t i o n s and t h e r e f o r e may show a tendency toward se g r e g a t i o n i n t o m u l t i p l e phases. However, the r a t e of growth of the p e r t u r b a t i o n i n most l i q u i d systems i s s m a l l compared to the r a t e at which i t t r a v e l s through the system, so most p r a c t i c a l l i q u i d f l u i d i s e d systems appear homogeneous and s t a b l e to observers. Exceptions are systems such as leadshot i n water, with high d e n s i t y r a t i o s which can behave l i k e g a s - s o l i d bubbling f l u i d i s e d beds. Grace and Tuot's c o n c l u s i o n , that a l l f l u i d - s o l i d systems are unstable to voidage p e r t u r b a t i o n , i s important because i t e x p l a i n s the e x i s t e n c e of h e t e r o g e n e i t y . However, l i n e a r s t a b i l i t y analyses are l i m i t e d to t h i s c o n c l u s i o n ; they do not p r e d i c t the nature of the system which i s formed as a r e s u l t of i n s t a b i l i t y . The f i n a l form depends on n o n - l i n e a r processes governed by e n e r g e t i c and e n t r o p i c c o n s i d e r a t i o n s . T h e o r e t i c a l support f o r the concept of a c l u s t e r can be found i n a number of s t u d i e s . For example, Jayaweera et a l . (1964) found that spheres, r e l e a s e d i n c l o s e p r o x i m i t y to each other, and f a l l i n g through l i q u i d s at low Reynolds numbers, tended to c l u s t e r i n r e g u l a r a r r a y s due to a balance of hydrodynamic f o r c e s ; the c l u s t e r s had t e r m i n a l v e l o c i t i e s higher than the t e r m i n a l v e l o c i t i e s of the i n d i v i d u a l spheres. T h i s r e s u l t could a l s o be shown mathematically using the method of r e f l e c t i o n s and v i s c o u s f l u i d flow theory. - 31 -At higher Reynolds numbers Zenz and Othmer (1960) p o s t u l a t e d a "wake mechanism". Recognising that a laminar or t u r b u l e n t wake behind a s i n g l e p a r t i c l e c o n s t i t u t e s a reg i o n of low pressu r e , they t h e o r i s e d that "when the c o n c e n t r a t i o n of a d i l u t e suspension becomes so great, or the d i s t a n c e between p a r t i c l e s so s m a l l , that the wake behind a p a r t i c l e reaches the next downstream p a r t i c l e , the downstream p a r t i c l e w i l l f a l l i n t o the wake of the upstream p a r t i c l e , and thereby the two p a r t i c l e s w i l l present a l a r g e r composite or e f f e c t i v e diameter which the p r e v a l e n t f l u i d v e l o c i t y can then c e r t a i n l y not s u s t a i n , so that the p a r t i c l e s f a l l s t i l l f a r t h e r , g i v i n g r i s e to a s o r t of chain r e a c t i o n which c o l l a p s e s the e n t i r e bed." In t h i s i n s t a n c e , the wake mechanism i s seen as a means of e x p l a i n i n g a choking t r a n s i t i o n . An i d e n t i c a l e f f e c t can be p o s t u l a t e d to e x p l a i n the t r a n s i t i o n from d i l u t e phase t r a n s p o r t to f a s t f l u i d i s a t i o n at some c r i t i c a l s o l i d s l o a d i n g . Evidence f o r the wake e f f e c t i s c i t e d i n the work of Ford (1950) who dropped ch a i n s of v a r i o u s lengths through g l y c e r o l . Up to a c e r t a i n length a chain f e l l as a c o l l a p s e d mass, but beyond t h i s c r i t i c a l l e n g t h , where the chain length appeared to exceed the length of the wake formed by the f i r s t l i n k , the cha i n f e l l as a s t r a i g h t length s i n c e there was s u f f i c i e n t drag on the f i n a l l i n k s to extend i t . P l a u s i b l e t h e o r i e s such as the wake mechanism, - 32 -s u b s t a n t i a t e d by a l a r g e number of " s i g h t i n g s " of c l u s t e r s (Razumov et a l . , 1968; Reh, 1971; Y o u s f i and Gau, 1974; Turner, 1979; Kwauk, 1980), l e d to general acceptance of a c l u s t e r theory f o r f a s t f l u i d i s a t i o n and hence, t e n t a t i v e models f o r c l u s t e r s i z e s . A l l of these models were e m p i r i c a l i n nature using experimental data to hypothesise e f f e c t i v e c l u s t e r s i z e s ; hence none of them should be construed as v a l i d a t i n g a c l u s t e r theory, but simply as p r o v i d i n g values f o r parameters which can be used i n p r e d i c t i v e models. The b a s i s f o r most of the s t u d i e s was the Richardson-Zaki (1954) equation, an expansion versus v e l o c i t y c o r r e l a t i o n used widely and s u c c e s s f u l l y f o r uniform suspensions i n sedimentation and l i q u i d f l u i d i s a t i o n . The equation i s p u r e l y e m p i r i c a l and takes the form where Vj_ i s the modified s i n g l e p a r t i c l e t e r m i n a l v e l o c i t y , d i f f e r i n g f o r l i q u i d f l u i d i s a t i o n from the s e t t l i n g v e l o c i t y i n an i n f i n i t e medium by a column c o r r e c t i o n , U n (1.2) d l o g V = log V± + P (1.3) D - 33 -and 'n' i s a Richardson-Zaki (R-Z) exponent which v a r i e s with the s i n g l e p a r t i c l e f r e e f a l l Reynolds number d n = 4.65 + 20 ^ ( R e t < 0 , 2 ) d n =(4.4 + 18 Re" (0.2< Re t< 1) (1.5) n =(4.4 + 18 -gfi) R e " 0 , 1 (1 < Re t< 200) (1.6) n = 4.4 Re" 0* 1 (200 <Ret< 500) (1.7) n = 2.4 ( R e t > 5 0 0 ) (1*8) Some e a r l y work (Capes and Mc l l h i n n e y , 1968; Richardson and Davies, 1966; Godard and Richardson, 1968; Mogan et a l . , 1969) has suggested that t h i s equation could be a p p l i e d to p a r t i c u l a t e f l u i d i s e d g a s - s o l i d systems ( t y p i c a l l y group A s o l i d s j u s t above minimum f l u i d i s a t i o n , but below minimum bubbling, and high p r e s s u r e systems), but the values of the Richardson Zaki exponent 'n' were much l a r g e r than p r e d i c t e d by the Richardson-Zaki c o r r e l a t i o n , with values as high as 8.85 found by Godard and Richardson (1968) and a value of 32 found by Crowther and Whitehead (1978). Mogan et al_. (1970/71 and 1969) e x p l a i n e d t h i s phenomenon, and reduced the exponent i n the Richardson-Zaki (R-Z) c o r r e l a t i o n c l o s e to the normal range (2.4 - 4.65), by assuming that the system behaviour was dominated by the l a r g e s t cut of p a r t i c l e s i n the s i z e d i s t r i b u t i o n . When t h i s s i z e f r a c t i o n was used to c a l c u l a t e Vt an Ret, an R-Z index of 4.88 and an accurate expansion c o r r e l a t i o n were obtained. - 34 -However, Capes (1974) t r e a t e d Mogan's data somewhat d i f f e r e n t l y . U s i n g an approach which had been used to t r e a t f l o e f o r m a t i o n i n s e d i m e n t a t i o n ( M i c h a e l s and B o l g e r , 1962; S c o t t , 1968), Capes found t h a t the e xpansion c o r r e l a t i o n c o u l d a l s o be reduced t o the normal R-Z form by i n t r o d u c i n g an apparent voidage and an apparent t e r m i n a l v e l o c i t y . These c o u l d be c o n s i d e r e d as the voidage of the system w i t h the a g g r e g a t e s t r e a t e d as hard spheres, and an e f f e c t i v e a g g r e g a t e v e l o c i t y r e s p e c t i v e l y . U s i n g these "apparent v a l u e s " , e x c e l l e n t p r e d i c t i o n s of expansion r e s u l t e d , w i t h a s t a n d a r d d e v i a t i o n of p r e d i c t e d from observed v a l u e s 4% l e s s than u s i n g Mogan's approach. In a d d i t i o n , the R-Z i n d e x f e l l i n the range 3.0 t o 3.5, s a t i s f y i n g v a l u e s f o r a t e c h n i q u e which i s p h y s i c a l l y more p l a u s i b l e , by a n a l o g y w i t h l i q u i d systems, than Mogan's method. I t i s v a l u a b l e t o c o n s i d e r these e a r l y s t u d i e s of the use of the R i c h a r d s o n - Z a k i e x p r e s s i o n i n some d e t a i l because they are the f i r s t cases i n which a g g l o m e r a t i o n i s c o n s i d e r e d , a concept c e n t r a l t o the study of f a s t and t u r b u l e n t beds. A l s o i t i s i m p o r t a n t to note t h a t the a p p l i c a t i o n s are f o r p a r t i c u l a t e f l u i d i s a t i o n , c h a r a c t e r i s t i c of most l i q u i d f l u i d i s e d systems and o n l y v a l i d under c o n d i t i o n s of dense phase e x p a n s i o n . The u n i f o r m i t y i m p l i e d by those s t a t e s , a u n i f o r m i t y g e n e r a l l y c o n s i d e r e d n e c essary t o a p p l y the R-Z c o r r e l a t i o n , i s a l s o - 35 -i m p l i e d by a p p l y i n g the R-Z c o r r e l a t i o n to higher v e l o c i t y s t a t e s and i s suggestive of a perceived breakdown of the bubble and dense phase s t r u c t u r e of lower v e l o c i t y f l u i d i s a t i o n . Yerushalmi et al_. (1978) were the f i r s t authors to apply the R-Z e x p r e s s i o n to a c i r c u l a t i n g f l u i d i s e d bed. Using a concept s i m i l a r but not i d e n t i c a l to Capes (1974), they computed e f f e c t i v e c l u s t e r diameters which are shown i n F i g u r e 1.12 as a f u n c t i o n of voidage. Stromberg (1983) obtained s i m i l a r r e s u l t s using f o r c e balance techniques without a p p l i c a t i o n of an expansion c o r r e l a t i o n . Avidan (1980) proposed that a l l gas f l u i d i s a t i o n regimes, even bubbling and s l u g g i n g , could be c o r r e l a t e d by an R-Z type e x p r e s s i o n . He r e v e r t e d to the idea of l e t t i n g ' n ' exceed the o r i g i n a l Richardson-Zaki l i m i t s , and considered i t as a nonuniformity index which i n c r e a s e d with an i n c r e a s e d two phase c h a r a c t e r i n the system. The value of 'n' could be as high as 10 i n the s l u g g i n g regime but approached 4.5-5 i n developed t u r b u l e n t f l u i d i s a t i o n , a value which i s almost i d e n t i c a l to the R-Z value f o r homogeneous suspensions. Ut i n the o r i g i n a l Richardson-Zaki expression was r e p l a c e d by an e f f e c t i v e c l u s t e r t e r m i n a l v e l o c i t y , Vt*» found e x p e r i m e n t a l l y . The index 'n' was used to f i n d e f f e c t i v e c l u s t e r diameters and gave r e s u l t s which agreed f a v o u r a b l y with Yerushalmi et a l . (1978). - 36 -F i g u r e 1.12 E f f e c t i v e c l u s t e r d i a m e t e r s i n h i g h v e l o c i t y f l u i d i s e d beds ( Y e r u s h a l m i e t a l . , 1978). - 37 -F i g u r e 1.13 i l l u s t r a t e s the good f i t g i v e n by Avidan's approach f o r one f i n e - p a r t i c l e case. S t r a i g h t l i n e s on a p l o t of l o g i o e a g a i n s t l o g i o U show a c o n s t a n t R-Z i n d e x w i t h i n a regime, and d i s t i n c t breaks c l e a r l y d e l i n e a t e t r a n s i t i o n s . The method may not be v a l i d , however, f o r l a r g e r p a r t i c l e s (Canada et a_l, 1978), and Rhodes and G e l d a r t (1986) have suggested t h a t the t u r b u l e n t t r a n s i t i o n i n d i c a t e d by one such break may not be the same t r a n s i t i o n as has been observed by some o t h e r a u t h o r s . T h i s b r i e f d i s c u s s i o n shows how the concept of a g g r e g a t i o n has p r o l i f e r a t e d i n the h i g h v e l o c i t y f l u i d i s a t i o n l i t e r a t u r e . I t has f o c u s s e d upon m o d i f i c a t i o n s of t h e R i c h a r d s o n - Z a k i e x p r e s s i o n ; however, o t h e r e m p i r i c a l e x p r e s s i o n s have a l s o been developed. For example, Matsen (1982) uses c l u s t e r f o r m a t i o n as an i n t e g r a l p a r t of h i s e x p l a n a t i o n of a g e n e r a l i s e d g a s - s o l i d s f l o w regime diagram. In a l l c a s e s , though, the a u t h o r s appear t o have e n v i s a g e d the e x i s t e n c e of a c o n d i t i o n of r e l a t i v e u n i f o r m i t y c r e a t e d by a dynamic e q u i l i b r i u m where p a c k e t s of p a r t i c l e s undergo c o n t i n u o u s c o a l e s c e n c e and breakup but where, i n a time-average sense, the p a c k e t s can be t r e a t e d as porous assemblages. T h i s i s the c l u s t e r e x p l a n a t i o n of f a s t and t u r b u l e n t f l u i d i s e d bed phenomena. There are c o n v e n i e n t a n a l o g i e s between g a s - s o l i d and g a s - l i q u i d systems which are u s e f u l f o r v i s u a l i s i n g the - 38 -F i g u r e 1.13 P l o t of voidage versus gas v e l o c i t y f o r f l u i d c r a c k i n g c a t a l y s t over a wide range of gas v e l o c i t y showing regime t r a n s i t i o n s (Avidan, 1980). - 39 -v a r i o u s regimes which can e x i s t . F i g u r e 1.14 shows t h e f l o w regimes which are found i n v e r t i c a l g a s - l i q u i d f l o w t o g e t h e r w i t h a regime diagram i n d i c a t i n g phase b o u n d a r i e s as a f u n c t i o n of d i m e n s i o n a l gas and l i q u i d k i n e t i c energy p a r a m e t e r s . There are d i r e c t a n a l o g i e s between bubble and s l u g f l o w s i n the g a s - l i q u i d system, and b u b b l i n g and s l u g g i n g f l u i d i s a t i o n i n the g a s - s o l i d system. S i m i l a r l y , t u r b u l e n t f l u i d i s a t i o n i s v i s u a l l y comparable t o churn f l o w . D i s c o u n t i n g l o n g i t u d i n a l g r a d i e n t s and c o n s i d e r i n g a c l u s t e r approach then w i s p y - a n n u l a r f l o w would seem t o be a good analogue t o f a s t f l u i d i s a t i o n . P a r t i c u l a r l y i n a l a r g e d i a m e t e r system where the a r e a o c c u p i e d by t h e annulus would be a s m a l l f r a c t i o n of the t o t a l and the wispy c l u s t e r - l i k e c o r e would dominate. At t h i s p o i n t i t i s c o n v e n i e n t to i n t r o d u c e a second s c h o o l of t h i n k i n g w i t h r e g a r d t o c i r c u l a t i n g f l u i d i s e d bed hydrodynamics. A number of a u t h o r s might contend t h a t a n n u l a r g a s - l i q u i d f l o w i s a f a r s u p e r i o r analogue t o f a s t f l u i d i s a t i o n than w i s p y - a n n u l a r f l o w . C i t i n g e x p eriments which show pronounced r a d i a l g r a d i e n t s i n f a s t and even t u r b u l e n t f l u i d i s e d beds, w i t h s t r o n g e v i d e n c e f o r a s o l i d s boundary l a y e r , those a u t h o r s c o n t e s t the i d e a of c l u s t e r f o r m a t i o n and e x p l a i n many c i r c u l a t i n g bed phenomena u s i n g a c o r e - a n n u l a r model. - 40 -F i g u r e 1.14 Flow regimes observed i n v e r t i c a l g a s - l i q u i d f l o w (Soo, 1982), and a f l o w p a t t e r n map ( H e w i t t and R o b e r t s , 1969). - 41 -Strong r a d i a l g r a d i e n t s i n f a s t f l u i d i z e d beds were f i r s t noted by B i e r l et a_l (1980). Measurements made with a s o l i d s f l u x probe pointed upstream and downstream gave s o l i d s f l u x p r o f i l e s shown i n F i g u r e 1.15. When these were combined with s t a g n a t i o n pressure p r o f i l e s obtained from a momentum f l u x probe, they c o u l d be used to i n f e r p a r t i c l e v e l o c i t y p r o f i l e s and p a r t i c l e d e n s i t y p r o f i l e s i n both the upstream and downstream d i r e c t i o n s ; these are a l s o shown i n F i g u r e 1.15. The p a r t i c l e v e l o c i t y p r o f i l e s show a continuous r a d i a l g r a d a t i o n as do the s o l i d s f l u x p r o f i l e s . These are i n d i c a t i v e of l a r g e r a d i a l g r a d i e n t s i n the v e r t i c a l component of the gas v e l o c i t y . However, when the two are combined to generate a r a d i a l d e n s i t y p r o f i l e , t h i s shows a strong demarcation between an upflow core, with uniform suspension d e n s i t y , and an annulus which, on average, i s i n downflow. In terms of the type of s o l i d and range of gas v e l o c i t i e s , c o n d i t i o n s used by B i e r l et ajL. are d i r e c t l y comparable to those of Yerushalmi et a l . (1978). Both authors at some p o i n t s used c r a c k i n g c a t a l y s t s (dp32 = 50 um, Pp = 1100 kg/m ) and gas v e l o c i t i e s i n the range lm/s to 6m/s. However B i e r l et; a l . used only a 75 mm diameter r i s e r , whereas the s t u d i e s at CUNY were performed i n a 150 mm d i a . u n i t . Other f a c t o r s such as f i n e s content which can have a marked e f f e c t of f l u i d i s a t i o n c h a r a c t e r i s t i c s , p a r t i c u l a r l y dense phase v i s c o s i t y - 42 -CALCULATED DENSITY PROFILES (THIRTEEN FEET FROM ENTRANCE) CALCULATED PARTICLE VELOCITY PROFILES 2 /3 1 O 1/3 2 /3 (r/R) (r/R) Figure 1.15 Radial solids flux, velocity and density p r o f i l e s in a r i s e r according to B i e r l et a l (1980). - 43 -(Matheson et a l . , 1949) are a l s o l i k e l y to have been d i f f e r e n t , but would be u n l i k e l y to produce such gross m a c r o s t r u c t u r a l changes. D i s c u s s i o n of B i e r l ' s r e s u l t s would be incomplete without a l s o n o t i n g that X-ray techniques were used to c o n f i r m the core-annular flow s t r u c t u r e f i n d i n g , and that there was a tendency towards i n c r e a s e d homogeneity with i n c r e a s i n g height i n the d i r e c t i o n of flow. However, the i n c r e a s e d homogeneity was a l s o a s s o c i a t e d with decreased d e n s i t i e s , and a core-annular s t r u c t u r e remained. B i e r l ' s c o n c l u s i o n , that f a s t f l u i d i s e d beds c o n s i s t of dense a n n u l i surrounding d i l u t e cores, was not a new f i n d i n g i n the sense that no one had observed t h i s type of flow s t r u c t u r e p r e v i o u s l y . S t u d i e s of r i s e r s , g e n e r a l l y r e l a t e d to the p e t r o c h e m i c a l i n d u s t r y , had shown s i m i l a r s t r u c t u r e s i n both l a r g e and small u n i t s . However, these s t r u c t u r e s had been i n t e r p r e t e d as being c h a r a c t e r i s t i c of r i s e r s , and the c i r c u l a t i n g bed was considered as a t o t a l l y d i f f e r e n t flow regime due p r i n c i p a l l y to lower o p e r a t i n g v e l o c i t i e s . Yerushalmi and Cankurt (1978) express t h i s d i f f e r e n c e as f o l l o w s : "Demixing of the gas and c a t a l y s t i n the r i s e r r e a c t o r i s gross i n comparison with the f i n e - s c a l e demixing of the f a s t bed c o n d i t i o n . A probe t r a v e r s i n g the f a s t bed would pass every inch or so from a lean v o i d to a c l u s t e r or - 44 -s t r a n d of s o l i d , or v i c e versa. In c o n t r a s t , d e n s i t y contours across the r i s e r r e a c t o r r e v e a l extreme s o l i d s e g r e g a t i o n , high d e n s i t y zones most l i k e l y r e p r e s e n t i n g s o l i d f l o w i n g downward appear along the w a l l , while the core remains r e l a t i v e l y d i l u t e . E a r l y ideas that r i s e r s were e n t i r e l y d i f f e r e n t from c i r c u l a t i n g beds have r e c e n t l y been modified to accept the presence of s u b s t a n t i a l w a l l e f f e c t s , even i n c i r c u l a t i n g f l u i d i s e d bed o p e r a t i o n s . S t u d i e s by Weinstein et a l . (1985), Hartge et a l . (1985) and Brereton and Stromberg (1985) a l l show the presence of a r e l a t i v e l y dense s o l i d s annulus l a y e r i n CFB o p e r a t i o n s using X-ray a b s o r p t i o n , combinations of o p t i c a l probes and gamma ray a b s o r p t i o n , and c a p a c i t a n c e probes r e s p e c t i v e l y . However, i n each of these cases the core-annulus demarcation was l e s s pronounced than i n the B i e r l study. In view of these f i n d i n g s , the d i s t i n c t i o n s between r i s e r s and c i r c u l a t i n g f l u i d i s e d beds become l e s s c l e a r , l i m i t e d to q u a l i t a t i v e p e r c e p t i o n s r a t h e r than a d i s t i n c t regime t r a n s i t i o n . S p e c i f i c a l l y , a r i s e r would g e n e r a l l y be c h a r a c t e r i s e d by higher gas v e l o c i t i e s , and lower suspension d e n s i t i e s which l i m i t the degree of s o l i d s backmixing and permit, f o r example, a p p r e c i a b l e l o n g i t u d i n a l temperature g r a d i e n t s . Apart from an i n i t i a l a c c e l e r a t i o n region, one would a l s o expect approximately uniform l o n g i t u d i n a l pressure g r a d i e n t s i n a r i s e r column. These d i s t i n c t i o n s are d i s c u s s e d f u r t h e r i n Chapter 4. - 45 -However, the s i m i l a r i t i e s between r i s e r s and c i r c u l a t i n g beds are s u f f i c i e n t l y strong to j u s t i f y a d e t a i l e d review of r i s e r l i t e r a t u r e . Because of t h e i r use f o r c a t a l y t i c c r a c k i n g i n the o i l i n d u s t r y , a number of s t u d i e s have been made on commercial r i s e r i n s t a l l a t i o n s . Bartholomew and Casagrande (1957), Hunt et al_. (1957) , Saxton and Worley (1970) and Schuurmans (1980) have a l l presented c a t a l y s t d e n s i t y contours over c r o s s - s e c t i o n s of commercial r i s e r s ranging from 0.5 to 1.1m diameter. Neither Saxton and Worley (1970) nor Schuurmans (1980) i n d i c a t e the diameter of the r i s e r which they s t u d i e d except to say that they were of commercial s i z e . In a l l cases, gamma ray a b s o r p t i o n was used to d e t e c t the d e n s i t y contours and i n d i c a t e d strong s e g r e g a t i o n of c a t a l y s t toward the w a l l s . Figure 1.16 shows a r e s u l t from the Schuurmans paper i n d i c a t i n g d e n s i t i e s c l o s e to the w a l l up to four times higher than the c e n t r e l i n e value. In t h i s case there i s a l s o a d e f i n i t e t r a n s i t i o n from the core to the annulus r e g i o n . The r e s u l t s of Hunt et a l (1952) are very s i m i l a r to those of Schuurmans and provide c o n v i n c i n g evidence that the annulus can occupy a s u b s t a n t i a l f r a c t i o n of the u n i t , even i n a r e a c t o r which has a l a r g e diameter compared to t y p i c a l l a b o r a t o r y equipment. T h i s i s a v a l u a b l e i n s i g h t , which shows that the e f f e c t s observed i n l a b o r a t o r y experiments are not simply a r t i f a c t s of the small - 46 -2 Q o C A T A L Y S T DENSITY, k g / m 3 / / / " / / / lOOr- • / i # \ / • * / > # / • •1.0 0 1.0 R Figure 1.16 Catalyst density d i s t r i b u t i o n s over the cross-section of a commercial r i s e r (Schuurmans, 1980 ) . - 47 -equipment s i z e caused by l a r g e s u r f a c e area to volume r a t i o s with c o r r e s p o n d i n g l y l a r g e boundary l a y e r e f f e c t s . F i n a l l y , d e n s i t y contours presented by Saxton and Worley (1970) and Bartholomew and Casagrande (1957), show that core-annular phenomena may be i n f l u e n c e d by r e a c t o r i n t e r n a l s . In both cases the annulus i s d i s c o n t i n u o u s , breaking at one or more p o i n t s around the r i s e r c ircumference. Whether or not t h i s i s b e n e f i c i a l w i l l depend upon the nature of the process, but i n a l l i n s t a n c e s s t r u c t u r e s such as feed n o z z l e s , b a f f l e s , c a t a l y s t engagers and bends i n the r i s e r can have a marked e f f e c t upon the c a t a l y s t d e n s i t y d i s t r i b u t i o n . More fundamental work upon r i s e r s t r u c t u r e has been performed by van Breugel et a l . (1969-70) who measured upward and downward s o l i d s mass f l u x e s , and gas v e l o c i t y p r o f i l e s i n a 0.3 m ID u n i t . R e s u l t s are shown i n F i g u r e 1.17 f o r r i s e r t r a n s p o r t of 40 um alumina at a mean mass f l u x of 400 kg/m 2s and a s u p e r f i c i a l gas v e l o c i t y of 6.3 m/s. The study shows how the presence of s o l i d s can c r e a t e steep g r a d i e n t s i n what would normally be a t u r b u l e n t gas v e l o c i t y p r o f i l e f o l l o w i n g approximately the 1/7 power law. I f t h i s i s mirrored i n the lower v e l o c i t y CFB regime, then i t has dramatic i m p l i c a t i o n s f o r conversion i n systems where s e l e c t i v i t y i s an i s s u e , because i t i n t r o d u c e s a phenomenon e q u i v a l e n t to T a y l o r d i s p e r s i o n i n laminar flow. - 48 -F i g u r e 1.17 Gas v e l o c i t y p r o f i l e , and upward and downward s o l i d s f l u x p r o f i l e s measured by v a n - B r e u g e l e t a l . (1969-70) i n a 0 . 3 m d i a . r i s e r . — ' - 49 -It i s t h e r e f o r e important to gain a thorough understanding of the s o l i d phase f l u i d mechanics s i n c e these have an impact upon the gas phase behaviour. The van Breugel study a l s o provides u s e f u l c o n f i r m a t i o n of the q u a l i t a t i v e v a l i d i t y of s o l i d s f l u x p r o f i l e s determined i n the B i e r l et a l . study (1980). M o d e l l i n g of a core-annulus flow s t r u c t u r e can be undertaken from a more fundamental viewpoint than m o d e l l i n g of c l u s t e r flow. The st r o n g e r d e f i n i t i o n of the flow s t r u c t u r e , past research i n t o gas flow through g e o m e t r i c a l l y d e f i n e d porous media, and the a b i l i t y to wr i t e momentum balance equations on a we l l d e f i n e d annulus wall combine to make fundamental approaches tenable. Nakamura and Capes (1973) a p p l i e d both a core-annular flow model and a uniform flow model to pneumatic t r a n s p o r t data which they obtained with v a r i o u s s o l i d s i n a 76 mm diameter r i s e r . They s t u d i e d c o n d i t i o n s between choking and well developed pneumatic t r a n s p o r t i n what they c a l l e d the "in t e r m e d i a t e and t u r b u l e n t flow regimes". The core-annular flow model could not be s a i d to be s u p e r i o r to a uniform flow model except at gas v e l o c i t i e s c l o s e to the s i n g l e p a r t i c l e terminal v e l o c i t y where there i s c o n s i s t e n t l y a negative shear s t r e s s on the r i s e r wall because the p a r t i c l e s are on average i n downflow and the gas v e l o c i t y i s low. T h i s negative shear s t r e s s c o n d i t i o n may a l s o hold i n - 50 -fast f l u i d i s a t i o n where high suspended solids densities ensure downflow at the wall. One of the most inter e s t i n g conclusions of the Nakamura and Capes study was that a core annular flow model w i l l always predict a lower o v e r a l l pressure drop than a uniform flow model. This has important implications i f the structure i s constrained to minimise pressure drop. Shimizu (1965) presents a model for core-annular flow which i s considerably simpler than the model of Nakamura and Capes in one sense: i t assumes a gas velocity p r o f i l e , based upon a measured value of the centreline gas velocity, whereas Nakamura and Capes determine gas v e l o c i t i e s in the core and annular sections by combinations of momentum balances and the constraint that pressure drop i s minimised. Despite t h i s s i m p l i f i c a t i o n , the model i s more v a l i d for applications in many c i r c u l a t i n g bed cases because i t takes into account bulk transfer of solids from the core to the annulus. This in turn predicts a decaying density p r o f i l e while the Nakamura-Capes model i s only v a l i d for f u l l y developed flow. Both of the above models are written for s p e c i f i c scenarios where the authors have observed core-annular flow phenomena, and attempted to correlate their results in terms of a physically consistent solids flow pattern. In t h i s sense they are true core-annular models, which rely upon a - 51 -s p e c i f i c gas velocity p r o f i l e for annulus formation and where each term has a readily apparent physical meaning. Both models represent a useful and v a l i d starting p o i n t f o r any model of a c i r c u l a t i n g bed based upon a core-annulus conception, which might be used to show how this flow regime could explain certain c i r c u l a t i n g bed reaction and hydrodynamic phenomena. However, there also exist models which could be called general upflow/downflow models. These include van Deemter's "countercurrent flow model" (1967) and Staub's "turbulent flow model" (1979), both of which consider phases flowing i n d i f f e r e n t directions, but neither of which considers the sp a t i a l d i s t r i b u t i o n of the phases. Thus they could equally well be used for an appropriately conceived cluster flow as for a core annulus model. The Staub model i s a modification of van Deemter's model, which was written with low velocity regimes in mind. It replaces an e f f e c t i v e d i f f u s i o n c o e f f i c i e n t , used to express solids exchange between upflow and downflow phases, with a turbulent mixing length, and uses the Richardson-Zaki expression to represent expansion behaviour of both dense and d i l u t e phases. In summary, a number of models exist within the l i t e r a t u r e which with modifications could be applied to a c i r c u l a t i n g f l u i d i s e d bed which i s believed to consist of an upflowing dilute core and a descending dense annulus. - 52 -There i s strong evidence that this flow structure i s ch a r a c t e r i s t i c of both large and small diameter r i s e r reactors, which operate at higher gas v e l o c i t i e s than c i r c u l a t i n g beds, and there i s also strong evidence to show that there i s some form of denser wall region in c i r c u l a t i n g bed operations. However, i t i s not clear what kind of structures are present in a CFB core - whether i t i s d i l u t e or consists of a strongly backmixed cluster phase - or how core and annulus interact to produce the c h a r a c t e r i s t i c density p r o f i l e s and other phenomena associated with high ve l o c i t y f l u i d i s a t i o n . 1.4 Objectives of the Present Study At the outset of this study there was a need for understanding of c i r c u l a t i n g bed phenonmena at two levels, the macrostructural and microstructural. This understanding was required from a fundamental viewpoint to determine the natures of regimes and regime transitions, and from an applied viewpoint to improve design correlations for pressure drop and heat transfer c o e f f i c i e n t s . A better conceptual understanding of the c i r c u l a t i n g f l u i d i s e d bed regime, and a l l high velocity regimes, was also required to better comprehend the advantages and limitations of c i r c u l a t i n g beds as reactors. This in turn should lead to more r e l i a b l e scale-up and more cost eff e c t i v e units through improved predictive models. - 5 3 -With these three broad objectives as a background, more s p e c i f i c r e a l i s a b l e objectives were established: ( i ) To characterise how solids c i r c u l a t i o n rate and gas velocity affect the macrostructure of a c i r c u l a t i n g f l u i d i s e d bed unit. ( i i ) To establish what microstructural changes accompany changes in macrostructure. ( i i i ) To formulate a conceptual model of the c i r c u l a t i n g f l u i d i s e d bed which establishes how the c i r c u l a t i n g f l u i d i s e d bed f i t s into the pattern of the other regimes, including choking, and to ensure that this model i s consistent with available microstructural and macrostructural data from units of a l l sizes. In addition to this main focus upon the general f l u i d mechanics of the c i r c u l a t i n g bed regime, two smaller studies arose from the work. These were studies of gas mixing in the c i r c u l a t i n g bed regime, something which i s related cl o s e l y to the s o l i d phase flow structure, and breakdown from slugging to turbulent f l u i d i s a t i o n . These aspects are detailed in separate sections at the end of the thesis. 2 . APPARATOS 2.1 Design Considerations The experimental measurements i n the present study were conducted almost e x c l u s i v e l y on a s i n g l e c i r c u l a t i n g bed u n i t f a b r i c a t e d s p e c i f i c a l l y f o r t h i s work. T h i s s e c t i o n d e s c r i b e s the c o n s t r u c t i o n of t h i s u n i t and the accompanying i n s t r u m e n t a t i o n and data a c q u i s i t i o n systems. References to other p i e c e s of apparatus appear p e r i o d i c a l l y through the r e p o r t and r e l e v a n t dimensions of such u n i t s are given at the p o i n t of r e f e r e n c e . The c i r c u l a t i n g bed u n i t was designed with the f o l l o w i n g c r i t e r i a i n mind: ( i ) I t should be t a l l enough that a s u b s t a n t i a l p o r t i o n of the u n i t operates beyond the a c c e l e r a t i o n l e n g t h . Papers on pneumatic t r a n s p o r t (Shimizu elb a l . , 1978) show that t h i s could mean entry lengths g r e a t e r than 150 pipe diameters to achieve a t r u l y f u l l y developed flow s t a t e . However, i f "developed flow" i s taken to imply lengths greater than the apparent a c c e l e r a t i o n zone at the base of a CFB column, then the r e s u l t s of Weinstein et a l . (1981) suggest that a 152 mm ID column must be s u b s t a n t i a l l y longer than 2m. ( i i ) The u n i t must have as large a diameter as p o s s i b l e to make the r e s u l t s amenable to s c a l e up. - 55 -( i i i ) The u n i t should be designed to operate at s u p e r f i c i a l gas v e l o c i t i e s as low as 1 mm/s, which i s the minimum f l u i d i z a t i o n v e l o c i t y f o r a f i n e m a t e r i a l such as 50um d i a . f l u i d c r a c k i n g c a t a l y s t , and as high as 10 m/s, a t y p i c a l pneumatic t r a n s p o r t v e l o c i t y f o r a f i n e m a t e r i a l and only s l i g h t l y beyond the t y p i c a l o p e r a t i n g range of c i r c u l a t i n g bed combustion systems. These may use coarse i n e r t m a t e r i a l s up to 750 um d i a . . ( i v ) The un i t should be of the v a r i a b l e inventory type, with c o n t r o l l e d c i r c u l a t i o n of s o l i d s (Kobro and Brereton, 1985). T h i s i s more s u i t e d to fundamental r e s e a r c h than a f i x e d inventory u n i t which r e l i e s upon changes i n t o t a l s o l i d s inventory through c o n t r o l l e d a d d i t i o n and drainage to manipulate s o l i d s c i r c u l a t i o n independently of gas v e l o c i t y . (v) The u n i t should be transparent to permit v i s u a l o b s e r v a t i o n of the flow phenomena. ( v i ) The u n i t should be modular i n c o n s t r u c t i o n a l l o w i n g f l e x i b i l i t y i n geometric parameters such as height, e x i t type, and even u n i t diameter so that the e f f e c t of each upon c i r c u l a t i n g bed c h a r a c t e r i s t i c s can be determined. ( v i i ) Accommodation should be made to permit i n t r o d u c t i o n of the a i r at more than one l e v e l to simulate the f l u i d mechanics of combustion systems which operate with a i r staged at two, and sometimes three l e v e l s . - 56 -The design of the unit was constrained by the following factors: ( i ) A maximum unit height of 10 m, dictated by headroom in the laboratory. ( i i ) An a i r supply to the r i s e r of 10 Nm /min (324 scfm) available at a delivery pressure of 34 kPa (5 psig). Within the framework of these constraints a unit was designed which i s shown in Figure 2.1 and which comprises three basic sections: ( i ) An instrumented high velocity r i s e r , ( i i ) A solids separation system, ( i i i ) Solids storage and return systems. Under steady operating conditions in any of the transport regimes the c i r c u l a t i n g f l u i d i s e d bed t y p i c a l l y operates as follows: P a r t i c l e s are fed at a constant rate from the large diameter storage column, through an L-valve into the r i s e r at i t s base. The rate of solids flow i s controlled by varying the rate of aeration to the L-valve at one or more points. High velocity motive gas then carries the solids up the r i s e r , at the same rate at which they are supplied, and discharges them through an exit at the r i s e r top into the f i r s t of two cyclones. This f i r s t cyclone i s coaxial with the storage unit and following Yerushalmi et a l . (1976) has no cone. Hence large fluxes of s o l i d s , which might choke the conical exit of a more conventional ( - 57 -Exit R iser Column Secondary Air Tangential Opposed • Air Out Primary and Secondary Cyc lones Modif ied Butterfly Valve Storage Bed Bubbl ing (Storage) Bed Aerat ion L-Valve H.P. Air B lower Air F i g u r e 2.1 S c h e m a t i c o f t h e c i r c u l a t i n g f l u i d i s e d bed t e s t r i g . Numbers d e s i g n a t e p r i n c i p a l p r e s s u r e measurement l o c a t i o n s f o r l o o p p r e s s u r e measurement s t u d i e s . - 58 -c y c l o n e , can r a i n downwards i n t o the storage zone from where they begin f u r t h e r c i r c u l a t i o n c y c l e s . Gas and any s o l i d s which are not caught by the primary separator pass to a second cyclone of c o n v e n t i o n a l Stairmand high e f f i c i e n c y d e s i g n . T h i s r e t u r n s captured p a r t i c l e s to the storage zone through an e x t e r n a l , aerated r e c y c l e l i n e . Gas i s then d i s c h a r g e d e i t h e r to t e r t i a r y c y c l o n i c s e p a r a t o r s or to atmosphere. Each part of the c i r c u l a t i n g bed system i s now d e s c r i b e d s e p a r a t e l y . 2.2 The Riser Column The c i r c u l a t i n g f l u i d i s e d bed r i s e r was c o n s t r u c t e d of 152 mm (6") ID 165 mm (6 1/2") OD cast transparent p o l y a c r y l i c tubing. I n d i v i d u a l flanged s e c t i o n s , i n m u l t i p l e s of 457 mm (18") lengths and i n l e t and e x i t s e c t i o n s , combined to give a maximum t o t a l column height of 9.3 m (366") which could be reduced i n 457 mm (18") increments to give a u n i t of d i f f e r e n t h e i g h t s . The a i r was i n t r o d u c e d i n t o the column through a p e r f o r a t e d p l a t e at the column base. This had 19% f r e e area and was formed from two 12.7 mm (1/2") t h i c k Dural Aluminium p l a t e s . The upper p l a t e was d r i l l e d with 6.3 mm (1/4") holes on a 12.7 mm (1/2") square p i t c h and the lower p l a t e with 7.9 mm (5/16") holes on i d e n t i c a l c e n t r e s . A 200 mesh s t a i n l e s s s t e e l screen could be sandwiched between the p l a t e s , f o r o p e r a t i o n i n the low v e l o c i t y regimes, reducing the e f f e c t i v e open - 59 -area to approximately 8% and e l i m i n a t i n g s o l i d s leakage i n t o the windbox. In the high v e l o c i t y f l u i d i z a t i o n s t u d i e s t h i s screen was g e n e r a l l y omitted because i t tended to plug both with f i n e s and tramp m a t e r i a l generated by slow d e t e r i o r a t i o n of the blower f i l t e r s . A i r could be s u p p l i e d to the r i s e r column from e i t h e r a compressor with a c a p a c i t y of 0.03 Nm3/s at 200 kPag (64 SCFM at 30 p s i g ) , or a S u t o r b i l t model 7 HV blower p r o v i d i n g 0.15 Nm3/s of a i r at 34 kPag (324 SCFM at 5 p s i g ) . A i r from the compressor was metered by one of three p a r a l l e l rotameters and entered the windbox through a s i d e p o r t ; compressor a i r provided gas v e l o c i t i e s up to 1.65 m/s i n the 152 mm diameter r i s e r . Blower a i r entered the windbox at i t s base through a l a r g e , 63.5 mm (2 1/2") d i a . , low pressure drop n o z z l e . I t was s u i t a b l e up to a maximum s u p e r f i c i a l gas v e l o c i t y of approximately 10 m/s. In a d d i t i o n to the primary a i r , i n t r o d u c e d at the base of the u n i t , a i r could a l s o be int r o d u c e d through secondary n o z z l e s . These n o z z l e s , l o c a t e d 762 mm (30") above the d i s t r i b u t o r i n Figure 2.1, are de p i c t e d i n d e t a i l i n Figu r e 2.2. T h i s l o c a t i o n i s a r b i t r a r y s i n c e they may be interchanged with any other s e c t i o n of the r i s e r to produce geometries of i n t e r e s t ; however, the c o n f i g u r a t i o n which i s shown gives a dense bed depth t y p i c a l of some i n d u s t r i a l combustion a p p l i c a t i o n s . Two s e t s of secondary a i r no z z l e s - 60 -Figure 2 .2 D e t a i l of the secondary a i r nozzles for the r i s e r column. - 61 -are available, both using a i r supplied by the Sutorbilt blower and metered using a sharp edged o r i f i c e . The upper nozzle set consists of four d i r e c t l y opposed 25.4 mm (1") dia. r a d i a l i n l e t s spaced at 90° intervals around the circumference. The lower nozzle set uses four i d e n t i c a l l y sized i n l e t s f i r i n g tangentially into the r i s e r . Both types of secondary a i r i n l e t find use commercially, although swirl a i r i s limited to small units. Additional features of the r i s e r section are the solids i n l e t tee, with a standard right angle tee construction permitting solids to flow freely from the L-valve into the r i s e r , and the e x i t . In Figure 2.1 this i s shown as an abrupt t r a n s i t i o n from the 152 mm (6") ID v e r t i c a l r i s e r to a 95.3 mm (3 3/4") ID horizontal exit. This exit has a centreline located 76 mm (3") below the r i s e r top. This was the most common of several exit geometries tested. Other exit geometries are described in Chapter 3. To allow measurement of s t a t i c and dynamic pressures at d i f f e r e n t points along the length of the r i s e r , and to permit insertion of various intrusive probes, access ports/pressure taps were located at 457 mm (18") i n t e r v a l s along the length of the r i s e r . The construction of these ports i s shown in Figure 2.3. For more specialised measurements, anticipated in the future, such as heat transfer probes and laser doppler signals, the cost of - 62 -COTTON WOOL SOLIOS FILTER 1/4 NPT TO CONNECT TO TUBE FITTING W A L L Figure 2.3 Diagram of pressure tap/probe port. - 63 -m o d i f i c a t i o n has been minimised by the use of the four interchangeable 457 mm (18") t e s t s e c t i o n s , any of which can be r e a d i l y replaced by a s p e c i a l i s e d i n s t r u m e n t a t i o n s e c t i o n without a f f e c t i n g the remainder of the column. The column i s supported s t r u c t u r a l l y at the base, and by support brackets d e t a i l e d i n F i g u r e 2.4 on each of the 1372 mm (54") lengths of r i s e r . The brackets provide support f o r the weight of the column, but are designed p r i n c i p a l l y to f i x the column r i g i d l y i n a h o r i z o n t a l plane while a l l o w i n g v e r t i c a l movement due to thermal expansion. 2.3 The Gas-Solids Separation System Gas and s o l i d s l e a v i n g the r i s e r pass through a short h o r i z o n t a l s e c t i o n of f l e x i b l e hosing and enter the modified primary cyclone. T h i s was c o n s t r u c t e d from a p i e c e of 8" Sch. 40 pipe, to allow c o n s i d e r a b l e e r o s i o n without r e q u i r i n g replacement. The body of the cyclone was extended to a length of 508 mm, compared with 300 mm f o r a standard Stairmand design, but the cone was omitted as noted above. This d e s i g n , s i m i l a r to that used by Yerushalmi et a l . (1976), serves the dual purpose of p e r m i t t i n g extremely h i g h s o l i d s f l u x e s , and a l l o w i n g a e r a t i o n a i r , provided to the storage zone and L - v a l v e , to pass upward and outward through the cyclone without unduly a f f e c t i n g the s o l i d s d i s c h a r g e . The m o d i f i c a t i o n s to the c o n v e n t i o n a l design do not appear to reduce the cyclone e f f i c i e n c y s i g n i f i c a n t l y , i t s capture - 64 -I I 'I IE H ll II •i .J M i> li I' li P L A T E W A S H E R C O L U M N B R A C K E T C O M P R E S S I O N SPRING HEX N U T 11/4 T U B U L A R S Q S T E E L S U P P O R T 3/8" B O L T F i g u r e 2.4 D e t a i l of a column support bracket. - 65 -e f f i c i e n c y t y p i c a l l y e x c e e d i n g 98% f o r the c o n d i t i o n s o f i n t e r e s t . D e t a i l s o f t h e c y c l o n e d e s i g n a r e shown i n F i g u r e 2.5. Gas from t h e f a s t bed and s t o r a g e u n i t l e a v e s t h e p r i m a r y c y c l o n e and p a s s e s t h r o u g h s e c o n d a r y , and sometimes t e r t i a r y c y c l o n e s e p a r a t o r s b e f o r e d i s c h a r g e t o a t m o s p h e r e . L i k e t h e p r i m a r y c y c l o n e the s e c o n d a r y c y c l o n e , shown i n F i g u r e 2.6, was f a b r i c a t e d from an 8" Sch. 40 s e a m l e s s s t e e l p i p e . However, t h i s c y c l o n e was o f more c o n v e n t i o n a l d e s i g n . A v a r i a b l e p i t c h g u i d e vane was l o c a t e d i n t h e i n l e t d u c t t o d i r e c t gas and s o l i d s towards t h e c y c l o n e w a l l and a l l o w the i n l e t v e l o c i t y t o be v a r i e d , t o enhance c o l l e c t i o n e f f i c i e n c y a t low gas f l o w r a t e s . T h i s had t o be used j u d i c i o u s l y s i n c e too h i g h a p r e s s u r e d r o p would c a u s e gas f l o w up the s o l i d s d i s c h a r g e l e g . Gas l e a v i n g t h e s e c o n d a r y c y c l o n e c o u l d be p a s s e d t o e i t h e r one o r two p a r a l l e l t e r t i a r y c y c l o n e s d i s c h a r g i n g i n t o a s t o r a g e h o p p e r . At low v e l o c i t i e s (< 4 m/s s u p e r f i c i a l v e l o c i t y i n t h e 152 mm r i s e r ) one such c y c l o n e was used and a t h i g h e r f l o w r a t e s two. These c y c l o n e s were o n l y n e c e s s a r y when a l u m i n a was used i n the c i r c u l a t i n g bed, b e c a u s e i t was f r i a b l e and tended t o b r e a k down o v e r t h e c o u r s e o f s e v e r a l days of o p e r a t i o n . The t e r t i a r y c y c l o n e s a r e d e t a i l e d i n F i g u r e 2.7. - 66 -203 102 GAS EXHAUST GAS/SOLIDS INLET ± K O SOLIDS EXHAUST MOUNTING FLANGE Figure 2.5 Primary cyclone d e t a i l , a l l dimensions i n mm. - 6 7 -GAS/SOLIDS INLET 8 T 203 h« H -•j 1271«-GAS EXHAUST [ 1 1 MOUNTING BRACKETS o 3 SOLIDS DISCHARGE Figure 2.6 Secondary cyclone d e t a i l , a l l dimensions in mm. - 68 -F i g u r e 2.7 T e r t i a r y cyclone d e t a i l , a l l dimensions i n mm. - 69 -2.4 Storage and Recirculation Systems S o l i d s captured by the primary cyclone s p i r a l downward through a 343 mm (13 1/2") ID 356 mm (14") OD p o l y a c r y l i c column onto a dense bed at the column base, from here they are fed by a p o l y a c r y l i c L-valve to the base of the r i s e r . The 356 mm (14") d i a . "storage column" c o n s i s t s of f i v e f l a n g e d s e c t i o n s , two of length 1372 mm (54"), the same length as the major s e c t i o n s of the r i s e r , and two of l e n g t h 1067 mm (42"). The f i f t h f langed s e c t i o n c o n t a i n s an impact flowmeter de s c r i b e d by B u r k e l l (1986). Approximately 1200 mm of the column i s f i l l e d with s o l i d s , c o n s t i t u t i n g a t o t a l i n v e n t o r y of nearly 320 kg, e x c l u s i v e of the L - v a l v e , when the u n i t i s f i l l e d with sand. The L-valve contains a f u r t h e r 180 kg of m a t e r i a l . The object of p r o v i d i n g such a high i n v e n t o r y was t h r e e f o l d . F i r s t l y i t provides f o r extremely s t a b l e o p e r a t i o n of the L-valve, s i n c e changes i n the i n v e n t o r y i n the r i s e r do not s u b s t a n t i a l l y a f f e c t the L-valve head. Secondly, i t permits measurement of the r e c i r c u l a t i o n r a t e u s i n g the " b u t t e r f l y valve technique" (Yerushalmi et_ al_. , 1976; B u r k e l l , 1985) which r e l i e s upon the a v a i l a b i l i t y of a large mass of f l u i d i s e d s o l i d s . T h i r d l y , i t allows expansion at a f u t u r e date to a l a r g e r r i s e r , up to 229 mm (9") i n diameter, without m o d i f i c a t i o n of the r e t u r n system. - 70 -The storage s e c t i o n may be run e i t h e r as a l o w - v e l o c i t y f l u i d i s e d or non-aerated zone. F l u i d i s a t i o n a i r provided by the compressor enters the storage zone through a p e r f o r a t e d p l a t e d i s t r i b u t o r at the column base. The d i s t r i b u t o r i s formed from two p i e c e s of Dural Aluminium p l a t e , each i s 12.7 mm (1/2") t h i c k , with 1.6 mm (1/ 16") and 3.2 mm (1/8") d i a . holes on a 12.7 mm (1/2") square p i t c h d r i l l e d through the upper and lower p l a t e s r e s p e c t i v e l y . These provide 1.2% open area. A 200 mesh s t a i n l e s s s t e e l screen i s sandwiched between the two p l a t e s to prevent s o l i d s from weeping i n t o the windbox. The v e r t i c a l standpipe of the L-valve i s c o n c e n t r i c with the storage zone and passes d i r e c t l y through both d i s t r i b u t o r p l a t e s and the windbox; i t i s se a l e d at each l o c a t i o n by an o - r i n g a l l o w i n g the L-valve to be moved v e r t i c a l l y but p r e c l u d i n g gas leakage. The f l u i d i z a t i o n a i r i s used f o r three purposes: ( i ) To i n c r e a s e the s o l i d s head on the L - v a l v e , making i t e a s i e r to generate high s o l i d s c i r c u l a t i o n r a t e s . ( i i ) To vary the "imposed pressure drop" across the c i r c u l a t i n g bed as def i n e d by Weinstein et a l . (1983) . ( i i i ) To permit c i r c u l a t i o n rate measurements. For c i r c u l a t i o n r a t e determinations, a f l u i d i s e d bed - 71 -storage zone i s used i n combination with a porous p l a t e , low pressure drop, modified b u t t e r f l y valve l o c a t e d between the middle two f l a n g e s i n the r e t u r n zone. When t h i s v a l v e ( F i g u r e 2.8) i s c l o s e d , f l u i d i s e d s o l i d s b u i l d up upon i t and are deplete d i n the re g i o n below (Yerushalmi et a_l. , 1976). However the t o t a l pressure head f o r s o l i d s c i r c u l a t i o n remains approximately constant. S o l i d s c i r c u l a t i o n r a t e can be measured by monitoring the r a t e of change of pressure drop between a p o i n t j u s t below the b u t t e r f l y v a l v e , and a second point approximately 1 metre above. When t h i s p r essure drop ( l e s s t h a t a c r o s s the v a l v e i t s e l f ) i s equated to the weight of s o l i d s per u n i t area, a c i r c u l a t i o n r a t e measurement can be obtained. Opening the b u t t e r f l y valve r e t u r n s the system to normal o p e r a t i o n ; i t must be opened before the lower bed l e v e l drops below the secondary cyclone r e t u r n l i n e , at which poin t gas bypasses p r e f e r e n t i a l l y up t h i s l i n e , both e l i m i n a t i n g f l u i d i s a t i o n above the b u t t e r f l y valve and reducing the secondary cyclone s e p a r a t i o n e f f i c i e n c y . L i k e the r i s e r column, the r e t u r n column i s supported both at the d i s t r i b u t o r and with brackets along i t s l e n g t h . A l s o l i k e the r i s e r column, i t may be reduced i n length by removal of d i f f e r e n t s e c t i o n s . The f i n a l element of the c i r c u l a t i n g f l u i d i s e d bed loop i s the L-valve, which c o n t r o l s the feed r a t e of s o l i d s i n t o F i g u r e 2.8 Mo d i f i e d b u t t e r f l y valve f o r rate measurement, dimensions s o l i d s i n mm. c i r c u l a t i o n - 73 -the r i s e r . L -valves have been examined e x t e n s i v e l y by Knowlton and Hirsan (1978) as feeders f o r pneumatic t r a n s p o r t l i n e s , and t h e i r use has been patented by Studsvik E n e r g i t e k n i k AB i n Sweden as c o n t r o l l e d r e c y c l e legs f o r c i r c u l a t i n g bed combustion systems. They can be c l a s s i f i e d as a type of p a r t i a l l y aerated s o l i d s flow v a l v e , using a small amount of a e r a t i o n to c o n t r o l the flow of a l a r g e mass of s o l i d s . 'Properly designed they a l s o provide a gas s e a l so that gas does not flow up the L-valve. The use of p a r t i a l a e r a t i o n c o n t r a s t s markedly with the f u l l y f l u i d i s e d flows which are used i n " f l u o s e a l " type arrangements. These are not designed to c o n t r o l the s o l i d s flow, unless used i n c o n j u n c t i o n with a mechanical valve, but they do provide a gas s e a l . Laboratory c i r c u l a t i n g f l u i d i s e d beds commonly show t h e i r c a t a l y t i c cracker h e r i t a g e by using f u l l y f l u i d i s e d s o l i d s r e t u r n s c o n t r o l l e d by a s l i d e v a l v e . Although t h i s has advantages f o r f i n e a e r a t a b l e m a t e r i a l s , which are reputed to be not e a s i l y c o n t r o l l e d using non-mechanical v a l v e s , the UBC c i r c u l a t i n g bed was designed to use the L-v a l v e concept. The r a t i o n a l e was mechanical s i m p l i c i t y and a d e s i r e to study the use of L-valves more f u l l y f o r f i n e p a r t i c l e a p p l i c a t i o n s . In the event that the L-valve would not f u n c t i o n p r o p e r l y using f i n e m a t e r i a l , the o p t i o n remained of i n s t a l l i n g a s l i d e valve i n the v e r t i c a l s e c t i o n of the r e c y c l e leg and p r o v i d i n g s u f f i c i e n t a e r a t i o n over - 74 -the remainder of the h o r i z o n t a l and v e r t i c a l s e c t i o n to e s t a b l i s h f u l l y f l u i d i s e d flow. For t h i s reason a l a r g e number of a e r a t i o n p o i n t s were provided around the r e c y c l e l e g . These are shown i n Figure 2.9, together with a diagram showing the t y p i c a l regime of flow f o r the r e c y c l e loop. M e c h a n i c a l l y , the L-valve was c o n s t r u c t e d from 152 mm (6") ID, 165 mm (6 1/2") OD cast a c r y l i c t ubing. The height of the v e r t i c a l s e c t i o n was 2438 mm (96") with the upper p o r t i o n p r o t r u d i n g approximately 75 mm i n t o the storage zone. A 711 mm (28") h o r i z o n t a l s e c t i o n was connected to the r i s e r feed tee using a neoprene sleeve which prevented t r a n s m i s s i o n of v i b r a t i o n s between the r i s e r and r e t u r n column. 2.5 Data Measurement and Acquisition C h a r a c t e r i s a t i o n of the macrostructure of the c i r c u l a t i n g f l u i d i s e d bed r e q u i r e s measurement of the pressure p r o f i l e along the u n i t at known values of r i s e r gas v e l o c i t y , s o l i d s c i r c u l a t i o n r a t e and r i s e r geometry. The techniques used are summarised below: ( i ) R i s e r S u p e r f i c i a l Gas V e l o c i t y - T h i s was measured using an o r i f i c e metre, f a b r i c a t e d to ASME standards, with i n t e r c h a n g e a b l e o r i f i c e s , and s u i t a b l e f o r gas v e l o c i t i e s g r e a t e r than 1.5 m/s. Rotameters c a l i b r a t e d with a dry t e s t meter were used at lower v e l o c i t i e s . - 75 6 0 0 0 Ib/hr S T A G N A N T S O L I D S R E G I O N R E T U R N C O L U M N F i g u r e 2.9 A e r a t i o n p o i n t s on the L-valve and a t y p i c a l o p e r a t i n g mode from Knowlton and H i r s a n (1978). Dimensions i n mm. - 76 -( i i ) S o l i d s C i r c u l a t i o n Rate - The s o l i d s c i r c u l a t i o n r a t e was measured e i t h e r using the b u t t e r f l y v a l ve technique, or by t r a c k i n g i n d i v i d u a l p a r t i c l e s i n the downflow l e g of the L-valve and assuming plug flow across the standpipe. B u r k e l l (1986) compared these techniques and showed that they could be used i n t e r c h a n g e a b l y provided that a c a l i b r a t i o n was made i n the l a t t e r case. The c a l i b r a t i o n constant was an apparent voidage f o r the moving bed used to c o r r e c t measured to mean r a d i a l v e l o c i t y . In ge n e r a l , the b u t t e r f l y valve was used f o r measurement of alumina c i r c u l a t i o n r a t e s , u s i n g a Disa type 51 D 20 c a p a c i t a t i v e pressure transducer to rec o r d the change of d i f f e r e n t i a l p ressure with time. T h i s transducer has in t e r c h a n g e a b l e diaphragms s u i t a b l e f o r d i f f e r e n t d i f f e r e n t i a l pressure ranges. P a r t i c l e t r a c k i n g was used f o r sand t r i a l s . The reason f o r using one technique i n the f i r s t case and a second i n the second i s r e l a t e d to the ease of i d e n t i f y i n g i n d i v i d u a l p a r t i c l e s . F i g u r e 2.10 shows a t y p i c a l pressure t r a c e f o r the b u i l d up of alumina with time on the b u t t e r f l y v a l v e ; Table 2.1 provi d e s a t a b u l a t i o n of t r a n s i t times f o r i n d i v i d u a l sand p a r t i c l e s over a designated 300 mm length of the L - v a l v e . The l i n e a r i t y of Figure 2.10 i n d i c a t e s that i t i s j u s t i f i a b l e to assume that i s o l a t e d c i r c u l a t i o n r a t e measurements using the modified b u t t e r f l y v a l ve do not a f f e c t the c i r c u l a t i o n i t s e l f . The low standard d e v i a t i o n of the repeated measurements of Table 2.1 shows that - 77 -F i g u r e 2.10 A t y p i c a l p r e s s u r e t r a c e f o r b u i l d - u p o f a l u m i n a on the b u t t e r f l y v a l v e f o r a c i r c u l a t i o n r a t e measurement. A s t r a i g h t l i n e i s s k e t c h e d t o show the l i n e a r i t y of t h e b u i l d - u p . - 78 -Table 2.1 T r a n s i t Times f o r P a r t i c l e s over a 300 mm V e r t i c a l S e c t i o n of the L-Valve Determined V i s u a l l y ' a T y p i c a l Result P a r t i c l e Number Time (s) 1 5.48 2 6.96 3 6.79 4 6.28 5 6.64 Average time 6.43 Standard d e v i a t i o n 0.587 - 79 -p a r t i c l e t r a c k i n g p r o v i d e s a s t r a i g h t f o r w a r d and r e p r o d u c i b l e method of determining c i r c u l a t i o n r a t e s when i n d i v i d u a l p a r t i c l e s are e a s i l y i d e n t i f i a b l e , ( i i i ) R i s e r Pressure P r o f i l e s - Pressure p r o f i l e s were determined using the pressure taps l o c a t e d at 457 mm (18") increments along the r i s e r length. Any 14 of these taps could be connected i n t o a system of two manifolds shown i n Figu r e 2.11. Hence d i f f e r e n t i a l pressures could be measured between any 2 adjacent p o i n t s t o generate the r i s e r p r e s s u r e p r o f i l e . Each manifold was connected i n t o one end of e i t h e r a manometer or the Disa c a p a c i t a t i v e pressure tranducer. Accurate pressure p r o f i l e d e termination demanded use of the transducer, together with a data logging system ( d e s c r i b e d below) to r e g i s t e r the v a r i a t i o n s i n output v o l t a g e with time. I n t e g r a t i o n of t h i s v o l t a g e s i g n a l then y i e l d e d an average value which c o u l d be converted i n t o a d i f f e r e n t i a l pressure using transducer c a l i b r a t i o n curves. L i n e a r i t y of these c a l i b r a t i o n s made the i n t e g r a t i o n / c o n v e r s i o n process s t r a i g h t f o r w a r d . Logging s i g n a l s i n t h i s manner was s u i t a b l e f o r determination of average pressure drops, but was not s u i t a b l e i n cases where t r a n s i e n t s were of i n t e r e s t , f o r example i n s t u d i e s of pressure f l u c t u a t i o n s r a t h e r than t h e i r mean values. In these cases s i g n a l s would be attenuated by the lengths of pressure l i n e s , and the valves - 80 -R iser 14 13 12 11 10 9 8 7 6 5 4 3 2 1 ~i ~ i i ""1 i i i - n i l " I L . I Pressure Transducer r 0 ± I 1 X H i xh-- C X r -- t X r --CXr -- C X r -- C X --00-- D x } -— C X r -- - t x j ---tx-- t x j -Manifolds I L _ _ _ Manometer F i g u r e 2.11 Manifold c o n s t r u c t i o n f o r d i f f e r e n t i a l pressure measurements showing how 14 r i s e r l o c a t i o n s are manifolded. - 81 -i n the m a n i f o l d . T h e r e f o r e , f o r t r a n s i e n t measurements, separate pressure l i n e s were set up and the transducer was l o c a t e d as c l o s e as p o s s i b l e to the pressure f l u c t u a t i o n source. The d a t a l o g g i n g system which was used to measure the time v a r i a t i o n s i n transducer output v o l t a g e , was used at a number of p o i n t s i n t h i s study to r e c o r d d i f f e r e n t v o l t a g e s i g n a l s . I t has been d e s c r i b e d i n d e t a i l by B u r k e l l (1986). The system c o n s i s t s of a Tecmar A/D, D/A programmable da t a l o g g i n g board o p e r a t i n g i n b i p o l a r mode and run i n c o n j u n c t i o n with an IBM XT computer. Operating i n t h i s f a s h i o n , with software presented by B u r k e l l (1986), the Tecmar board c o u l d a c q u i r e data i n the range + 12V to - 12V at r a t e s up to 30,000 p o i n t s per second. For l o g g i n g of p r e s s u r e s i g n a l s , sampling r a t e s of 100 p o i n t s per second and sampling d u r a t i o n s of 30 s were t y p i c a l l y used. - 82 -3. EXPERIMENTAL 3.1 Density P r o f i l e s and Entrainment Rates - Macroscopic  Aspects 3.1.1 C o n s i d e r a t i o n s r e g a r d i n g use of pressure data As noted i n Chapter 1, the macrostructure of c i r c u l a t i n g f l u i d i s e d beds has g e n e r a l l y been c h a r a c t e r i s e d by the v a r i a t i o n of suspended s o l i d s d e n s i t y with height along the column. I t i s important to be able to p r e d i c t d e n s i t y p r o f i l e s i f one i s to study the e v o l u t i o n of g a s - s o l i d c o n t a c t i n g i n any c i r c u l a t i n g bed system. T h i s c o n t a c t i n g h i s t o r y can a s s i s t i n p r e d i c t i o n s of conversion i n c a t a l y s t systems, and of carbon and p o l l u t a n t c o n c e n t r a t i o n s i n corabustors. On a more mechanical l e v e l , the i n t e g r a t e d suspended s o l i d s d e n s i t y w i l l p a r t i a l l y determine fan requirements, while i t s l o c a l value profoundly i n f l u e n c e s suspension-to-wall heat t r a n s f e r c o e f f i c i e n t s (Kobro and Brereton, 1985). Density p r o f i l e s are g e n e r a l l y i n f e r r e d from the gra d i e n t of the absolute pressure p r o f i l e , or from d i r e c t measurement of d i f f e r e n t i a l pressures over r e g u l a r i n t e r v a l s along a c i r c u l a t i n g bed. The pressure drop i s then a s c r i b e d t o t a l l y to the weight of the s o l i d s and f l u i d per u n i t area, ( i . e . to the h y d r o s t a t i c p r e s s u r e ) , assuming that a n e g l i g i b l e p o r t i o n i s accounted f o r by the combined e f f e c t s - 83 -of gas-wall f r i c t i o n , s o l i d s - w a l l f r i c t i o n , and s o l i d s a c c e l e r a t i o n . T h i s assumption, l e a d i n g to has been shown to be accurate to w i t h i n 10% by Turner f o r a 152 mm ID column used at CUNY (Turner, 1978). However Arena et a l . (1985) found that the e r r o r could be as high as 70% i n a s m a l l e r column (41 mm ID) at v e l o c i t i e s of 7 m/s. In t h i s study we have employed equation 3.1 s i n c e , i n a l l the runs of i n t e r e s t , f r i c t i o n a l gas pressure drops were small as were estimates of the two-phase flow f r i c t i o n a l p ressure drop. For the l a t t e r estimate, the c o r r e l a t i o n of Rose and Barnacle (1957) was a p p l i e d which, while admittedly crude, g i v e s a u s e f u l order of magnitude estimate of f r i c t i o n a l e f f e c t s . Using a value i n d i c a t e d by Soo (1982) f o r a f a c t o r t i n the Rose c o r r e l a t i o n , ( 1 0 _ l + ) , f r i c t i o n a l pressure drop was c a l c u l a t e d as e q u i v a l e n t to a s o l i d s hold up of 1.3 kg/m3. T h i s was f o r a s o l i d s f l u x of 70 kg/m 2s at a gas v e l o c i t y of 7 m/s i n a 150 mm d i a . column. An a d d i t i o n a l c a l c u l a t i o n shows that a suspension with a d e n s i t y of 100 kg/m , a c c e l e r a t e d or d e c e l e r a t e d between r e s t and 6 m/s over a 3 m d i s t a n c e , adds or s u b t r a c t s 15 kg/ra to the apparent d e n s i t y given by equation 3.1. Hence, e r r o r s may approach t h i s magnitude at entrances and e x i t s . - 84 -3.1.2 I n i t i a l s t u d i e s with alumina At the outset the i n t e n t i o n was simply to c h a r a c t e r i s e the p a r t i c u l a r CFB column i n which we were working, then to proceed r a p i d l y to study the m i c r o s t r u c t u r e of the flow. We d i d not a n t i c i p a t e f i n d i n g p r o f i l e s which were s i g n i f i c a n t l y d i f f e r e n t from those of e a r l i e r authors. I n i t i a l s t u d i e s were conducted with alumina as the c i r c u l a t i n g s o l i d . T h i s had a Sauter mean diameter of 64um, d e n s i t y of 3500 kg/m and a measured minimum f l u i d i s a t i o n v e l o c i t y of 10.5 mm/s. The complete s i z e d i s t r i b u t i o n , determined by a s i e v e a n a l y s i s , i s given i n Table 3.1. A scanning e l e c t r o n micrograph, Figure 3.1, shows that the alumina i s p o l y c r y s t a l l i n e with each c r y s t a l mass forming a c l o s e l y s p h e r i c a l p a r t i c l e . E a r l y attempts to o b t a i n r e p r o d u c i b l e d e n s i t y p r o f i l e s were u n s u c c e s s f u l . Our f i r s t experience, which used a column shown i n F i g u r e 2.1, showed that i t was not p o s s i b l e to o b t a i n high c i r c u l a t i o n r a t e s of the f i n e alumina using a customary L-valve with a s i n g l e a e r a t i o n p o i n t . High c i r c u l a t i o n r a t e s promoted a v i o l e n t s t i c k - s l i p flow i n the l a r g e 152 mm (6") d i a . L - v a l v e , although there had been no evidence of such behaviour i n a small 38 mm (1.5") d i a . t e s t v a l v e running at i d e n t i c a l downward s o l i d s v e l o c i t y . N either were there problems with flow i n the set-up of Fi g u r e 3.2 which had a s h o r t e r v e r t i c a l L s e c t i o n . The s i t u a t i o n was remedied by j u d i c i o u s a e r a t i o n around the - 85 -Table 3.1 Properties of Alumina Used in High Velocity F l u i d i s a t i o n Studies Property Value Mean P a r t i c l e Diameter, d 64 P um P a r t i c l e Density, p p 3,500 kg/m3 Bulk Density, 1,140 kg/m3 Loose Packed Voidage, eT *0.67 L P a r t i c l e Terminal Velocity, V t, 0.24 based on gas properties at 25°C m/s Archimedes Number 31 U „ Experimental 0.010 mf m/s Bulk Density at Minimum F l u i d i s a t i o n , 1,100 kg/m3 Bed Voidage at Minimum F l u i d i s a t i o n , em^ *0.69 Angle of Repose 30° •includes internal voids of p a r t i c l e s . Table 3.1 cont'd - 86 -S i z e A n a l y s i s Sieve P a r t i c l e Diameter Weight I n t e r v a l um F r a c t i o n 710-600 655 -600-500 550 -500-425 462.5 -425-355 390 -355-300 327.5 -300-250 275 -250-212 231 -212-180 196 -180-150 165 1.1 150-125 137.5 2.8 125-106 115.5 5.8 106-90 98 11.8 90-75 82.5 24.4 75-63 69 37.0 63-53 58 3.6 53-45 49 4.4 45-38 41.5 3.3 38-0 19 5.7 - 87 -F i g u r e 3.1 Scanning e l e c t r o n m i c r o g r a p h of alumina p a r t i c l e s . M a g n i f i c a t i o n 400 x. - 88 -Air Out Exi t R ise r Column Modif ied Butterf ly Valve Storage Bed Bubbl ing (Storage] Bed Aerat ion L-Valve Aerat ion Blower Ai r F i g u r e 3.2 C i r c u l a t i n g f l u i d i s e d bed as i n i t i a l l y c o n s t r u c t e d . A l u m i n a c o u l d be c i r c u l a t e d i n t h i s s h o r t L - v a l v e d e s i g n w i t h s i n g l e p o i n t a e r a t i o n . - 89 -L-valve s e a l . T h i s appeared to improve the flow c h a r a c t e r i s t i c s of the alumina, except i n the region of the corner which remained t o t a l l y deaerated. Under these circumstances a small amount of motive gas d i r e c t e d along the a x i s of the h o r i z o n t a l s e c t i o n of the L-valve, a e r a t i n g the corner s e c t i o n , provided e x c e l l e n t c o n t r o l , even at high c i r c u l a t i o n r a t e s . When the d e n s i t y p r o f i l e s were p l o t t e d f o r a number of steady runs, the r e s u l t s were somewhat s u r p r i s i n g . They are shown i n Figure 3.3 f o r a s e r i e s of three runs i n which gas v e l o c i t y was held s u b s t a n t i a l l y constant and the s o l i d s c i r c u l a t i o n r a t e v a r i e d over a wide range. In the lower h a l f of the column the p r o f i l e s behave as one would a n t i c i p a t e from r e s u l t s of previous authors. However, higher up the column, i n s t e a d of a continuous decay of de n s i t y or a steady d e n s i t y value, there i s a dramatic change i n the curvature of the p r o f i l e , with the d e n s i t y r i s i n g toward the top of the u n i t . In r e t r o s p e c t , these were l e s s s u r p r i s i n g because a s i m i l a r behaviour had been observed i n e a r l y work performed i n the column of F i g u r e 3.2. However, at that point i t had been a t t r i b u t e d to a lack of height and the height of the column had been extended. Three f u r t h e r runs were made with the alumina. These were at v e l o c i t i e s lower than the o r i g i n a l 4.8 m/s. The f i r s t two were at 3.8 m/s and at c i r c u l a t i o n r a t e s - 90 -O 5 6 -m on t-{/) Q > O m < x o 0 40 80 120 160 200 SUSPENDED SOLIDS DENSITY , kg/m3 F i g u r e 3.3 L o n g i t u d i n a l d e n s i t y d i s t r i b u t i o n s f o r alumina i n a c i r c u l a t i n g f l u i d i s e d bed, Ug = 5.4 m/s, G s = 18, 41, and 95 kg/m 2s. - 91 -e q u i v a l e n t to the higher v e l o c i t y cases. The f i n a l run was made at a s u p e r f i c i a l v e l o c i t y of 2.3 m/s at the hi g h e s t p e r m i s s i b l e c i r c u l a t i o n r a t e f o r t h i s v e l o c i t y , a value f o r t u i t o u s l y c l o s e to the lowest of the c i r c u l a t i o n r a t e s at the higher v e l o c i t i e s . The f a c t o r which l i m i t e d the c i r c u l a t i o n r a t e at 2.3 m/s was a v i o l e n t s l u g g i n g at the base of the column. T h i s "choking" behaviour could o c c a s i o n a l l y cause breakage at the flanged column j o i n t s . F i g u r e 3.4 i s a p l o t of d e n s i t y p r o f i l e s measured at a s u p e r f i c i a l v e l o c i t y of 3.8 m/s; Fig u r e 3.5 shows the f i n a l run at Ug = 2.6 m/s. L a s t l y , F i g u r e 3.6 i s a p l o t of the three runs made at constant s o l i d s c i r c u l a t i o n r a t e (« 20 kg/m 2s) but at d i f f e r e n t gas v e l o c i t i e s . Cursory examination of the d e n s i t y p r o f i l e s generated with alumina shows trends i n the lower h a l f of the column c o n s i s t e n t with p u b l i s h e d e a r l i e r data. For example, F i g u r e 3.5 shows the c h a r a c t e r i s t i c a c c e l e r a t i o n zone followed by a dense phase and a decaying d i l u t e f r eeboard. However, except at the lowest v e l o c i t y , there i s a dramatic e x i t e f f e c t which, at combinations of high gas v e l o c i t i e s and s o l i d s c i r c u l a t i o n r a t e s , can s t r e t c h to occupy the whole of the upper h a l f of the u n i t . T h i s p r e v i o u s l y unobserved e f f e c t demanded c o n s i d e r a b l e a t t e n t i o n s i n c e , i n a d d i t i o n to impacting upon commercial design, i t has i m p l i c a t i o n s r e g a r d i n g the nature of the d i l u t e phase. - 92 -0 20 40 60 80 KM) SUSPENDED SOLIDS DENSITY , kg/m3 F i g u r e 3.4 L o n g i t u d i n a l d e n s i t y d i s t r i b u t i o n s f o r alumina i n a c i r c u l a t i n g f l u i d i s e d bed, Ug = 4.3 m/s, G s = 21 and 42 kg/m 2s. - 93 -0 200 400 600 800 1000 SUSPENDED SOLIDS DENSITY , kg/m3 F i g u r e 3.5 L o n g i t u d i n a l d e n s i t y d i s t r i b u t i o n f o r alu m i n a i n a c i r c u l a t i n g bed, Ug = 2.6 m/s, G s = 25 kg/m 2s. - 94 -200 400 600 800 1000 SUSPENDED SOLIDS DENSITY , kg/m3 Figure 3.6 Longitudinal density d i s t r i b u t i o n s for alumina in a c i r c u l a t i n g bed, G s approximately constant (= 20 kg/m 2s), U g = 2.6, 4.3 and 5.4 m/s. - 95 -F u r t h e r experiments with alumina were not p o s s i b l e because of a p a u c i t y of m a t e r i a l . The alumina underwent a t t r i t i o n so that c o n s i d e r a b l e make-up was r e q u i r e d to maintain a constant s i z e d i s t r i b u t i o n . The column was t h e r e f o r e f i l l e d with Ottawa sand of 156 \im Sauter mean diameter, and a l l subsequent experiments were performed with t h i s m a t e r i a l . A f u l l l i s t i n g of the sand p r o p e r t i e s i s given i n Table 3.2. A f i n e sand was chosen because i t i s t y p i c a l of the bed m a t e r i a l used i n c i r c u l a t i n g f l u i d i s e d bed combustion systems. Also , the m a t e r i a l permits o p e r a t i o n at higher s u p e r f i c i a l gas v e l o c i t i e s (6 - 10 m/s) without the c i r c u l a t i o n r a t e requirements becoming e x c e s s i v e . 3.1.3 S t u d i e s of the e x i t e f f e c t To e s t a b l i s h that the e x i t e f f e c t was present with sand, as with alumina, a s e r i e s of "choked runs" was conceived. These were runs where the gas v e l o c i t y was s e t at r e g u l a r increments between 4 and 9 m/s, and at each gas v e l o c i t y the s o l i d s c i r c u l a t i o n r a t e was i n c r e a s e d u n t i l a "choked dense phase" was v i s i b l e 750 mm up the column. Because choking i s a contentious phenomenon i n the c i r c u l a t i n g bed and pneumatic t r a n s p o r t l i t e r a t u r e , i t was necessary to d e f i n e i t as a v i s u a l phenomenon for t h i s t e s t s e r i e s . However, i n a l l cases the v i s u a l appearance of a dense phase at the base of the column c o i n c i d e d with a - 96 -Table 3.2 P r o p e r t i e s of Ottawa Sand Used i n High V e l o c i t y F l u i d i s a t i o n S t u d i e s Property Value Mean P a r t i c l e Diameter, d 148 P um P a r t i c l e Density, p 2,650 p kg/m3 Bulk Density, 1,550 kg/m3 Loose Packed Voidage, e L 0.42 P a r t i c l e Terminal V e l o c i t y , V t, 0.99 based on gas p r o p e r t i e s at 25°C m/s Archimedes Number 290 Umf E x P e r i m e n t a i 0.021 m/s Bulk D e n s i t y at Minimum F l u i d i s a t i o n , 1,500 kg/m3 Bed Voidage at Minimum F l u i d i s a t i o n , 0.43 Angle of Repose 29° Table 3.2 cont'd - 97 -Size Analysis Sieve Interval P a r t i c l e Diameter vva Weight Fraction 710-600 655 0.1 600-500 550 0.2 500-425 462.5 0.3 425-355 390 0.7 355-300 327.5 1.4 300-250 275 0.9 250-212 231 12.7 212-180 196 11.5 180-150 165 31.5 150-125 137.5 22.4 125-106 115.5 8.9 106-90 98 4.6 90-75 82.5 2.9 .75-63 69 1.5 63-53 58 0.3 53-45 49 0.1 45-38 41.5 0.1 38-0 19 0.1 - 93 -s i t u a t i o n where a small i n c r e a s e i n c i r c u l a t i o n r a t e caused a dramatic r i s e i n the f a s t bed i n v e n t o r y . T h i s i s not intended to imply that the dense phase of the base of the r i s e r was s l u g g i n g , only that such a dense phase e x i s t e d . One r a t i o n a l e f o r running these "choked t e s t s " was that we wished to determine the l i m i t i n g d i l u t e phase s o l i d s hold up at each gas v e l o c i t y . I t was hoped that the column was s u f f i c i e n t l y long, and the entrance and e x i t lengths s u f f i c i e n t l y s hort, that t h i s would be reached over some' f r a c t i o n of the column le n g t h . The value of f i n d i n g the l i m i t i n g d e n s i t y lay i n the f a c t that t a l l , small diameter columns would presumably have such a d e n s i t y e x i s t i n g over much of t h e i r length i f a choked phase were allowed to form at t h e i r base. T h i s represents a l i m i t i n g p r a c t i c a l case f o r combustion processes i n such u n i t s , s i n c e fan power requirements would prevent much higher s o l i d hold-ups. The b e n e f i t s of higher c i r c u l a t i o n r a t e s would be s m a l l , p r o v i d i n g minimal a d d i t i o n a l o v e r a l l heat t r a n s f e r at high expense i n terms of pressure drop. The s i t u a t i o n f o r l a r g e diameter u n i t s , i s e n t i r e l y d i f f e r e n t s i n c e , as d i s c u s s e d i n Chapter 4 , decay lengths u s u a l l y exceed column lengths. F i g u r e 3 .7 shows s i x d e n s i t y p r o f i l e s obtained i n the choked t e s t s e r i e s . For sand, as f o r alumina, there i s a dramatic e x i t e f f e c t which i s enhanced by the higher v e l o c i t i e s of the sand runs. - 99 -0 1 1 1 ' 1 1 0 100 200 300 400 500 SUSPENDED SOLIDS DENSITY , kg/m3 F i g u r e 3.7 L o n g i t u d i n a l d e n s i t y p r o f i l e s obtained f o r sand i n a c i r c u l a t i n g bed as the base appeared v i s u a l l y choked, gas v e l o c i t i e s between 3.7 and 9.2 m/s. - 100 -The s i g n i f i c a n c e and the i m p l i c a t i o n s of the e x i t e f f e c t are noted i n subsequent s e c t i o n s of the t h e s i s . Here i t should be noted though that the nature of the choked phase v a r i e d c o n s i d e r a b l y with v e l o c i t y , from a s l u g g i n g type c o n d i t i o n with high c a r r y o v e r , at the low end, to a smooth r e f l u x i n g flow dominated v i s u a l l y by strands at the w a l l at the high end. 3.1.4 Entrance e f f e c t s , and more on e x i t e f f e c t s Prompted by the i n t e r e s t i n g d e n s i t y p r o f i l e s found at the e x i t of the column, the next set of experiments was aimed at determining whether entrance geometry i s a l s o s i g n i f i c a n t . For t h i s purpose the column was reassembled to re t u r n the s o l i d s 1.98 m above the gas d i s t r i b u t o r p l a t e . T h i s i s shown i n Figure 3.8. A d e t a i l e d set of t e s t s was then performed i n which the gas v e l o c i t y was v a r i e d from 4.9 to 8.1 m/s. Density p r o f i l e s were e s t a b l i s h e d f o r a number of c i r c u l a t i o n r a t e s at each gas flow. The complete set of p r o f i l e s i s shown i n Fi g u r e s 3.9 to 3.12. These p r o f i l e s demonstrate the important e f f e c t of gas v e l o c i t y upon e x i t , and, what i s e v i d e n t l y a s o l i d s entrance e f f e c t . The choice of e x i t geometry f o r the i n i t i a l design, shown i n d e t a i l i n Figure 3.13, was motivated by the d e s i r e to make the simplest p o s s i b l e t r a n s i t i o n from the c i r c u l a t i n g bed to the cyclone. The a c t u a l s i z i n g was then d i c t a t e d by pressure drop c o n s t r a i n t s which r e q u i r e d that - 101 -Air Out Primary and Secondary Cyc lones Modif ied Butterf ly Valve Storage Bed Bubbl ing (Storage) Bed Aerat ion L-Valve L-Valve J l ( * Aerat ion H . P . A i r F i g u r e 3.8 R i s e r column c o n f i g u r e d to r e t u r n s o l i d s 1.98 m above the d i s t r i b u t o r p l a t e f o r entr a n c e e f f e c t s t u d i e s . - 102 -0 100 200 300 400 500 SUSPENDED SOLIDS DENSITY , kg/m3 F i g u r e 3.9 L o n g i t u d i n a l d e n s i t y p r o f i l e s f o r sand, U g = 4.9 m/s, G s = 24 and 26 kg/m s, abrupt e x i t , s o l i d s r e t u r n at 1.98 m above the gas d i s t r i b u t o r . - 103 -O 5 6 go on Q Ui > O m < 0 150 300 450 600 750 SUSPENDED SOLIDS DENSITY , kg/m3 F i g u r e 3.10 L o n g i t u d i n a l d e n s i t y p r o f i l e s f o r ^ a n d , U g = 6.1 m/s, G s = 35, 45, and 59 kg/m s, a b r u p t e x i t , s o l i d s r e t u r n a t 1.98 m above the gas d i s t r i b u t o r . - 104 -0 100 200 300 400 500 SUSPENDED SOLIDS DENSITY , kg/m3 Figure 3.11 Longitudinal density p r o f i l e s for sand, U g = 7.1 m/s, G s = 45 and 73 kg/m2s, abrupt exit, s o l i d s return at 1.98 m above the gas di s t r i b u t o r . - 105 -9 -SUSPENDED SOLIDS DENSITY , kg/m3 F i g u r e 3.12 L o n g i t u d i n a l d e n s i t y p r o f i l e s for sand, Ug = 8.1 m/s, G s = 66, 71, and 82 kg/m 2s, abrupt e x i t , s o l i d s r e t u r n at 1.98 m above the gas d i s t r i b u t o r . - 106 -F i g u r e 3.13 D e t a i l s of t h r e e e x i t s s t u d i e d f o r c i r c u l a t i n g bed a p p l i c a t i o n . - 107 -the entrance v e l o c i t y to the cyclone be kept below approximately 20 ra/s at the maximum gas flow rate (9 m/s i n the 152 mm (6") r i s e r ) . The f i n a l r a t i o n a l i z a t i o n f o r the choice of s i z e was that at 7 m/s, a t y p i c a l c i r c u l a t i n g f l u i d i s e d bed combustor v e l o c i t y , the entrance v e l o c i t y to the cyclone i s 15 m/s, a l s o c o n s i s t e n t with c u r r e n t i n d u s t r i a l CFBC p r a c t i c e . However, i n d u s t r i a l u n i t s would g e n e r a l l y have a somewhat more gradual t r a n s i t i o n . F o l l o w i n g the i n i t i a l r e s u l t s , i n which c o n s i d e r a b l e s o l i d r e f l e c t i o n from the top end p l a t e could be observed v i s u a l l y , due to the i n a b i l i t y of s o l i d to f o l l o w the sha r p l y curved gas path i n t o the e x i t channel, we proposed that the e x i t e f f e c t could be a l t e r e d , and u l t i m a t e l y c o n t r o l l e d by the curvature of the e x i t geometry. T h e r e f o r e a second e x i t was designed which minimised r e f l e c t i o n and in c o r p o r a t e d a smooth t r a n s i t i o n v i a a long r a d i u s bend from the upflow column to the cyclone. Thi s e x i t i s a l s o shown i n F i g u r e 3.13 together with a t h i r d e x i t used l a t e r f o r comparative purposes. A s e r i e s of t e s t s was run with the smooth e x i t at a gas v e l o c i t y of 7.1 m/s and at c i r c u l a t i o n r a t e s from 36 to 116 kg/m s. These r e s u l t s , shown i n Figure 3.14, can be compared d i r e c t l y with the previous t e s t s made on the o l d e x i t and depicted i n Figure 3.11. The d i f f e r e n c e i s immediately apparent. With the new "zero r e f l e c t i o n e x i t " , which v i s u a l l y i t appeared to be, the d e n s i t y p r o f i l e - 108 -Legend 0 K K ) 2 0 0 3 0 0 4 0 0 5 0 0 SUSPENDED SOLIDS DENSITY , kg/m3 F i g u r e 3.14 L o n g i t u d i n a l d e n s i t y p r o f i l e s f o r sand. U g = 7.1 m/s, G s = 36, 73, 93, and 116 kg/m s, smooth e x i t , s o l i d s r e t u r n 1.98 m above the gas d i s t r i b u t o r . - 109 -Fi g u r e 3.15 L o n g i t u d i n a l d e n s i t y p r o f i l e s f o r sand, Ug = 7.1 m/s, G s = 73 kg/m s, smooth and abrupt e x i t s , s o l i d s r e t u r n 1.98 m above the gas d i s t r i b u t o r . T r i a n g l e s represent smooth e x i t p r o f i l e , c i r c l e s abrupt. - 110 -continues to decay from s o l i d s entrance to s o l i d s e x i t , t a k i n g on a form more s i m i l a r to p r o f i l e s presented i n the l i t e r a t u r e by previous workers. A s p e c i f i c comparison i s shown i n F i g u r e 3.15 which d e p i c t s d e n s i t y p r o f i l e s f o r two i d e n t i c a l gas v e l o c i t i e s and s o l i d s c i r c u l a t i o n r a t e s , but with the d i f f e r e n t e x i t s . T h i s f i g u r e shows that the e x i t e f f e c t i n f l u e n c e s the column through i t s e n t i r e t y , r i g h t from the gas entrance to the gas e x i t . A f i n a l experiment was conducted with top 3 of Figure 3.13, a s l i g h t v a r i a n t on the i n i t i a l e x i t design. The r e s u l t s obtained with t h i s v a r i a n t are p l o t t e d i n Figure " 3.16 together with r e s u l t s f o r almost i d e n t i c a l c o n d i t i o n s and the i n i t i a l abrupt e x i t geometry. The p r o f i l e s are s u b s t a n t i a l l y the same, although small d e v i a t i o n s between the two occur c l o s e to the s o l i d s r e t u r n tee. Hence there seems to be l i t t l e i n f l u e n c e of a l l o w i n g the s o l i d s an a d d i t i o n a l short d e c e l e r a t i o n d i s t a n c e above the e x i t o f f t a k e . 3.1.5 Low v e l o c i t y entrainment t e s t s A f t e r f i n d i n g such marked e f f e c t s of e x i t geometry upon what i s e f f e c t i v e l y " e n t r a i n e d " at high v e l o c i t y , we decided to i n v e s t i g a t e how s i g n i f i c a n t e x i t geometry could prove at much lower gas v e l o c i t i e s . Bubbling and t u r b u l e n t f l u i d i s e d bed entrainment data have been c o r r e l a t e d using a wide number of models which - I l l -F i g u r e 3.16 L o n g i t u d i n a l d e n s i t y p r o f i l e s f o r sand, Ug = 7.1 m/s, G s = 73 kg/m s, a b r u p t and e x t e n d e d e x i t s , s o l i d s r e t u r n a t 1.98 m above the gas d i s t r i b u t o r . T r i a n g l e s r e p r e s e n t e x t e n d e d e x i t p r o f i l e , c i r c l e s a b r u p t . - 112 -have grown i n complexity with time. I t i s not the purpose of t h i s t h e s i s to d i s c u s s these except to note that i t i s common f o r entrainment p r e d i c t i o n s from d i f f e r e n t c o r r e l a t i o n s to be r a d i c a l l y d i f f e r e n t . For example, Grace (1982) i n summarising some of the p e r t i n e n t l i t e r a t u r e notes that " v a r i a t i o n s of two orders of magnitude are not unusual." One of the f a c t o r s that changes widely from one experimental set-up to another i s the geometry of the e x i t ; hence a b r i e f attempt was made to determine whether geometric e f f e c t s could account f o r some of the d i s c r e p a n c i e s between d i f f e r e n t s t u d i e s and c o r r e l a t i o n s . An experiment was conducted at a gas v e l o c i t y of 1.5 m/s u s i n g the 156 um d i a . Sauter mean diameter Ottawa sand. This v e l o c i t y i s 1.5 times the c a l c u l a t e d t e r m i n a l v e l o c i t y of a s i n g l e p a r t i c l e of mean s i z e , s u f f i c i e n t to provide measurable entrainment i n r e l a t i v e l y b r i e f experiments, but not so high as to produce s u b s t a n t i a l m a t e r i a l l o s s i n our t a l l column. An i n i t i a l t e s t s e r i e s was run with the apparatus set up as shown i n Figure 3.17a. Here the s o l i d s r e t u r n and storage loops have been removed e n t i r e l y from the system, and the secondary a i r ports have been plugged f l u s h with the i n s i d e diameter of the column. The e n t r a i n e d s o l i d s were captured by a 178 mm diameter high e f f i c i e n c y Stairmand cyclone d i s c h a r g i n g i n t o a catch pot. They were returned to the system a f t e r each t e s t . - 113 -F i g u r e 3.17 Column c o n f i g u r a t i o n f o r 1.5 m/s e n t r a i n m e n t t e s t s ( a ) I n i t i a l c o n f i g u r a t i o n (b) F i n a l C o n f i g u r a t i o n - 114 -Examination of an absolute f i l t e r l o c a t e d i n the cyclone discharge l i n e showed that t h i s cyclone provided e f f e c t i v e l y 100% capture of the e n t r a i n e d m a t e r i a l at the gas v e l o c i t y employed. Des p i t e p r e c a u t i o n s designed to e l i m i n a t e p o i n t s f o r s o l i d s hold-up i n the system, and ensure accurate measurement of e n t r a i n e d m a t e r i a l , i n i t i a l r e s u l t s were i r r e p r o d u c i b l e . The v a r i a n c e between runs at the same c o n d i t i o n s and with the same e x i t was too high because of s a l t a t i o n i n the e x i t l i n e . To remedy t h i s , the system was r e c o n f i g u r e d to the set-up shown i n , F i g u r e 3.17b. T h i s i s i d e n t i c a l to Figure 3.17a except f o r the a d d i t i o n of a high pressure a i r source to one of the s w i r l a i r p o r t s . At the end of each t e s t s a l t a t e d s o l i d s were blown out of the e x i t duct i n t o the cyclone system by admitting a i r i n t o t h i s upper port f o r approximately f i v e minutes. With t h i s m o d i f i c a t i o n r e p r o d u c i b l e r e s u l t s could be obtained; these are shown i n Table 3.3. The entrainment r e s u l t s were analysed s t a t i s t i c a l l y u sing a T - t e s t to t e s t f o r equivalence of the two mean entrainment r a t e s . The r e s u l t s showed that the hypothesis of equal means can be r e j e c t e d at a confidence l e v e l between 90% and 95%; however, the d i f f e r e n c e i s not l a r g e , only 7% of the t o t a l entrainment. Therefore, although e x i t geometry can account f o r some small f r a c t i o n of the d i s c r e p a n c i e s i n v a r i o u s entrainment - 115 -Table 3.3 Results from Entrainment Tests at Low Velocity Gas Ve l o c i t y =1.5 m/s I n i t i a l Bed Height = 0.91 m Total Unit Height = 9.3 m Run Time (mins) Mass of Solids Entrained (kg) 5 5 5 5 0.68 0.74 0.77 0.74 5 5 5 5 0.74 0.80 0.80 0.80 Run Designation Exit Geometry l a l b l c Id Abrupt Abrupt Abrupt Abrupt 2a 2b 2c 2d Smooth Smooth Smooth Smooth - 116 -c o r r e l a t i o n s at t h i s r e l a t i v e l y modest s u p e r f i c i a l v e l o c i t y and i n a t a l l column, there must be other more s u b s t a n t i a l f a c t o r s . 3.1.6 The imposed pressure drop - a s i g n i f i c a n t i n f l u e n c e  on c i r c u l a t i n g bed s t r u c t u r e ? A lar g e number of parameters are known to i n f l u e n c e the d e n s i t y p r o f i l e i n a c i r c u l a t i n g f l u i d i s e d bed. These i n c l u d e the gas v e l o c i t y , s o l i d s c i r c u l a t i o n r a t e , gas and s o l i d s p h y s i c a l p r o p e r t i e s , and, as shown above, the u n i t geometry. A parameter which has r e c e i v e d r e l a t i v e l y l i t t l e a t t e n t i o n i s the so c a l l e d "imposed pressure drop" across the system. T h i s concept was introduced by Weinstein et a l • (1981) whose experiments appear to show that, f o r a given system at a f i x e d gas v e l o c i t y and s o l i d s c i r c u l a t i o n r a t e , an i n f i n i t e number of d e n s i t y p r o f i l e s can e x i s t depending upon the imposed pressure drop. Each p r o f i l e c o n t a i n s d i f f e r e n t f r a c t i o n s of s t a b l e dense and d i l u t e phases and a t r a n s i t i o n zone, the amount of each being determined by the need to balance the pressure drop over the r e t u r n l e g . With t h i s i n mind, a b r i e f s e r i e s of t e s t s was performed to examine the "imposed pressure drop" phenomenon. For the "imposed pressure drop" experiments the system was co n f i g u r e d as shown i n Fig u r e 2.1. The pressure drop was then measured over each p o r t i o n of the s o l i d s loop under the two sets of circumstances. In each case the gas - 117 -v e l o c i t y and s o l i d s c i r c u l a t i o n r a t e s were i d e n t i c a l . However, i n the f i r s t run the s o l i d s storage v e s s e l was maintained f u l l y f l u i d i s e d so that a pressure drop of +117 mm of mercury was imposed upon the loop. In c o n t r a s t , i n the second run no a e r a t i o n was s u p p l i e d to the s o l i d s storage v e s s e l and a pressure drop of only -1mm mercury was measured over the same bed. The r e s u l t s are shown i n ta b u l a r form i n Table 3.4 and as p l o t s of absolute pressure versus v e r t i c a l l e v e l i n Figu r e 3.18. From these r e s u l t s i t seems that there was no impact of the imposed pressure upon the r i s e r d e n s i t y p r o f i l e . In each case f o r a gas v e l o c i t y of 6.9 m/s and a s o l i d s c i r c u l a t i o n r a t e of 29 kg/m 2s the pressure drop over the r i s e r was 13 mm Hg. The pressure versus height diagrams i n d i c a t e what happened. In the same manner as f o r a mechanical c o n s t r i c t i o n , such as a s l i d e or b u t t e r f l y valve, the v e r t i c a l s e c t i o n of the L-valve acts as a pressure reducer f o r the gas. When the s o l i d s storage v e s s e l i s f l u i d i s e d , c r e a t i n g a high absolute pressure at the bubbling bed d i s t r i b u t o r , gas flows down the L-valve at a v e l o c i t y r e l a t i v e to the s o l i d s which produces a c o u n t e r b a l a n c i n g p r e s s u r e drop. On the c o n t r a r y , i n the absence of f l u i d i s a t i o n of the storage v e s s e l , the absolute pressure and gas flow are s u b s t a n t i a l l y reduced. The only impact upon the o p e r a t i o n of the u n i t was that, i n the l a t t e r case, - 118 -Table 3.4 Pressure Drops Over the C i r c u l a t i n g F l u i d i s e d Bed Loop Run C o n d i t i o n s : R i s e r Gas V e l o c i t y - 6.9 m/s S o l i d s C i r c u l a t i o n Rate - 29 kg/m 2s D i f f e r e n t i a l Pressure D e s i g n a t i o n Pressure Drop with F l u i d i s a t i o n A i r i n Storage Zone (cm H 20) Pressure Drop Without F l u i d i s a t i o n A i r i n Storage Zone (cm H 20) 1-2 17 .8 17 .8 2-3 32 .2 29.9 3-4 -159.7 1.4 4-5 65.6 -86 .0 5-1 48 .1 44.5 •Pressure Tap D e s i g n a t i o n ^ ar° i l l u s t r a t e d i n Fi g u r e 2.1. - 119 - T 1 1 1 1 1 1 1 r J 1 1 l 1 l l l l 0 40 80 120 160 Gauge Pressure (mmK^O) 10 8 6 © 4 X • r 1 1 1 1 1 r Packed Bed F i g u r e 3.18 0 40 80 120 160 Gauge Pressure (mm H2O) Pressure versus e l e v a t i o n p l o t s for a r i s e r with f l u i d i s e d and packed bed storage zones. Numbers r e f e r to l o c a t i o n s on Figure 2.1. - 120 -the L-valve a e r a t i o n had to be increased 15% to provide the necessary motive gas f o r the r e q u i r e d h o r i z o n t a l s o l i d s t r a n s p o r t . Our r e s u l t s i n d i c a t e d that f o r a given c i r c u l a t i n g bed system the gas v e l o c i t y and s o l i d s c i r c u l a t i o n r a t e uniquely determine the pressure p r o f i l e i n the r i s e r s e c t i o n . T h i s i s r a t i o n a l i s e d i n terms of the seemingly c o n t r a d i c t o r y r e s u l t of Weinstein e_t a_l. (1981) i n Chapter 4. 3.1.7 The impact of secondary a i r a d d i t i o n on c i r c u l a t i n g bed d e n s i t y p r o f i l e s I n d u s t r i a l c i r c u l a t i n g f l u i d i s e d bed combustion systems are c h a r a c t e r i s e d by a d d i t i o n of the f l u i d i s i n g a i r at more than one l o c a t i o n . For example, the L u r g i u n i t at Duisburg u t i l i s e s a i r i n t r o d u c t i o n at three v e r t i c a l l o c a t i o n s , primary a i r , secondary a i r and a t h i r d f r a c t i o n of a i r used f o r conveying of the feed (Wein and Felwor, 1986). Staged a i r promotes staged combustion, which reduces formation of both f u e l NOx and thermal NOx, and r e s u l t s i n formation of a lower v e l o c i t y higher d e n s i t y bed i n the lowest or primary zone. T h i s dense bed i s advantageous f o r mixing of h i g h l y r e a c t i v e f u e l s , and i s e s s e n t i a l f o r turndown purposes i n some "constant i n v e n t o r y " u n i t s (Kobro and Brereton, 1985). However, d e s p i t e i t s importance to p r a c t i c a l o p e r a t i o n , the e f f e c t of staged a i r i n t r o d u c t i o n upon c i r c u l a t i n g bed behaviour i s not we l l understood. - 1 2 1 -In a combustion system, depending upon the load, mean p a r t i c l e s i z e , and the f u e l type, the primary zone can operate i n a v a r i e t y of f l u i d i s a t i o n regimes. In t h i s study, t h i s regime was v a r i e d , while t o t a l gas v e l o c i t y was maintained constant by v a r y i n g the primary-to-secondary a i r s p l i t . T h i s i s equiv a l e n t i n an i n d u s t r i a l b o i l e r context to v a r y i n g the a i r s p l i t while m a i n t a i n i n g constant load. A s e r i e s of t e s t s was conducted with the u n i t set up as shown i n Figure 2.1. A i r entered the column at two v e r t i c a l l o c a t i o n s , the primary d i s t r i b u t o r and through four secondary p o r t s lo c a t e d 990 mm (39") f u r t h e r up the column. Both a v a i l a b l e methods of secondary a i r i n t r o d u c t i o n were t e s t e d , f i r s t l y the d i r e c t l y opposed p o r t s , and l a t e r the four t a n g e n t i a l h o r i z o n t a l ( s w i r l ) n o z z l e s . For each geometry the t o t a l gas v e l o c i t y and s o l i d s c i r c u l a t i o n r a t e s were maintained constant at 8.6 m/s and 45 kg/m 2s r e s p e c t i v e l y , and de n s i t y p r o f i l e s were recorded at each of three primary to secondary a i r s p l i t s . R e s u l t s from the d i f f e r e n t runs are shown i n Fi g u r e s 3.19 and 3.20. They are r a t i o n a l i s e d i n Chapter 4. - 122 -0 100 200 300 400 SUSPENDED SOLIDS DENSITY , kg/m3 Figure 3.19 Density p r o f i l e s measured in c i r c u l a t i n g beds of sand at a total gas velocity of 8.6 m/s and a solids c i r c u l a t i o n rate of 45 kg/m s with different primary to secondary (P/S) a i r rat i o s . Secondary a i r introduced through opposed ports. C i r c l e s , zero secondary a i r ; triangles, P/S = 1.36; squares, P/S = 0.83. - 123 -SUSPENDED SOLIDS DENSITY , kg/m3 F i g u r e 3.20 Density p r o f i l e s measured i n c i r c u l a t i n g beds of sand at a t o t a l gas v e l o c i t y of 8^5 m/s and a s o l i d s c i r c u l a t i o n r a t e of 45 kg/m s with d i f f e r e n t primary to secondary (P/S) a i r r a t i o s . Secondary a i r introduced through s w i r l p o r t s . C i r c l e s , zero secondary a i r ; t r i a n g l e s , P/S = 1.39; squares, P/S = 0.85. - 124 -3.2 Experimental Study of the Microstrueture of the  C i r c u l a t i n g F l u i d i s e d Bed 3.2.1 Scope The approach taken towards understanding the c i r c u l a t i n g f l u i d i s e d bed was f i r s t to study the macrosturcture, and how i t v a r i e d with key experimental v a r i a b l e s , then to t r y and r a t i o n a l i s e t h i s macroscopic behaviour by studying the m i c r o s t r u c t u r e . The combination of s t u d i e s leads to a conceptual model of the c i r c u l a t i n g bed. T h i s s e c t i o n of the t h e s i s d e s c r i b e s the development of a capacitance probe to study l o c a l suspended s o l i d s c o n c e n t r a t i o n . R e s u l t s from t e s t s with the f i n a l probe design are then presented. 3.2.2 Design c r i t e r i a f o r a m i c r o s t r u c t u r a l probe The m i c r o s t r u c t u r a l study of the c i r c u l a t i n g f l u i d i s e d bed was o r i g i n a l l y intended: ( i ) To determine the time averaged suspended s o l i d s c o n c e n t r a t i o n at v a r i o u s l o c a t i o n s . ( i i ) To determine the t i m e - v a r i a t i o n of the instantaneous l o c a l suspended s o l i d s c o n c e n t r a t i o n at the same p o i n t s . ( i i i ) To measure the l o c a l s o l i d s v e l o c i t y both on a time-mean and instantaneous b a s i s . - 125 -( i v ) To o b t a i n these measurements without d i s t u r b i n g e i t h e r the gas or the s o l i d s flow, i . e . the measurement d e v i c e should not i n f l u e n c e the measured s i g n a l . A l a r g e number of probes have been i n t r o d u c e d i n t o c i r c u l a t i n g and bubbling f l u i d i s e d beds with the o b j e c t i v e of determining v a r i o u s parameters (Grace and Baeyens, 1986). In a d d i t i o n , s e v e r a l n o n - i n t r u s i v e techniques have been used s p e c i f i c a l l y f o r the d e t e r m i n a t i o n of point-averaged suspended s o l i d s c o n c e n t r a t i o n . These techniques are summarised i n Table 3.5. Examination of t h i s t a b l e shows that of the v a r i o u s types of probes, the f i b r e o p t i c v a r i e t y developed by Oki et al_. (1980) i s one of the most promising; such a probe has the c a p a c i t y to measure most of the r e q u i r e d parameters both at low and high temperatures. U n f o r t u n a t e l y , the f i b r e o p t i c probe does not e a s i l y g ive the l o c a l d e n s i t y v a r i a t i o n s on an instantaneous b a s i s which are important to d i s t i n g u i s h between d i f f e r e n t hydrodynamic models; a l t e r n a t i v e o p t i o n s were t h e r e f o r e considered. Of these, the one that was best s u i t e d to our a p p l i c a t i o n was the c a p a c i t a n c e probe. P r o p e r l y c o n s t r u c t e d , i t appeared that t h i s could provide a c c u r a t e instantaneous measurements of l o c a l s o l i d s c o n c e n t r a t i o n . These would then be i n t e g r a t e d to y i e l d average l o c a l v a l u e s . It i s u n f o r t u n a t e that p a r t i c l e v e l o c i t y data cannot be obtained from such a probe. Table 3.5 Techniques Used f o r Determining Loc a l S o l i d s Hold-Up and P a r t i c l e V e l o c i t y (modified from Grace and Baeyans, 1986) Method A d d i t i o n of tagged t r a c e r p a r t i c l e s X or y-ray photography Impact of p a r t i c l e s on a piezo e l e c t r i c c r y s t a l T r a c k i n g of r a d i o a c t i v e p a r t i c l e s T r a c k i n g of r a d i o p i l l t r a c e r s T r a n s i t time of p a r t i c l e s viewed by o p t i c a l f i b r e l i g h t d e t e c t o r s Thermistor probe Capacitance probe I s o k i n e t i c and momentum f l u x probes Some References Ge l d a r t and C r a n f i e l d (1972) Weinstein et a l . (1985) B i e r l et aTT TT980) Heertjes et a l . (1970/71) U n et a l . (1980) Masson et ja l . (1978) Merry and Davidson (1973) Rao & Venkateswarku (1973) Ohki et a l . (1980) Glicksman and McAndrews (1985) Werther & Molerus (1973) Almstedt & Olsson (1982) B i e r l et a l . (1980) Q u a n t i t y ( i e s ) Measured S o l i d s c i r c u l a t i o n and v e l o c i t y ( i n s t a n t a n e o u s ) R a d i a l voidage d i s t r i b u t i o n (time mean) L o c a l s o l i d s v e l o c i t y ( i n stantaneous) L o c a l s o l i d s v e l o c i t y ( i n s t a n t a n e o u s ) L o c a l s o l i d s v e l o c i t y ( i n s t a n t a n e o u s ) L o c a l s o l i d s v e l o c i t y and hold-up (instantaneous v e l o c i t y , mean hold-up) L o c a l s o l i d s v e l o c i t y (time mean) L o c a l s o l i d s hold up L o c a l s o l i d s hold up (time mean) and s o l i d s f l u x (time mean upward and downward) - 127 -However, these data appeared to be the l e a s t important f o r i n i t i a l d i s c r i m i n a t i o n between the vari o u s models f o r c i r c u l a t i n g beds. 3.2.3 Capacitances probes - general d e s c r i p t i o n The techniques f o r measuring p o r o s i t y v a r i a t i o n s i n f l u i d i s e d beds u s i n g c a p a c i t a n c e probes have been i n continuous development s i n c e the p i o n e e r i n g work of Morse and B a l l o u (1951) soon a f t e r frequency modulation br o a d c a s t i n g made the b a s i c instrument components widely and cheaply a v a i l a b l e . T h e i r i n i t i a l probe was a p a r a l l e l p l a t e c a p a c i t o r with each p l a t e 13 mm square and separated by 10 mm. T h i s r e l a t i v e l y cumbersome design has s i n c e given way to t r u l y m i n i a t u r i s e d needle probes such as those of Werther and Molerus (1973) (2.3 mm needle length x 0.4 mm needle d i a . ) and even s u r f a c e probes such as those of F i t z g e r a l d (1976); however the b a s i c c i r c u i t r y of many probes are i d e n t i c a l , and only the improved s t a b i l i t y of modern t r a n s i s t o r i s e d components has allowed m i n i a t u r i s a t i o n and s u b s t a n t i a l gains i n probe performance. Most c a p a c i t a n c e probe systems c o n s i s t of three b a s i c components which are shown s c h e m a t i c a l l y i n Fig u r e 3.21. ( i ) The probe: T h i s i s made of two p a r t s , the support which, considered e l e c t r i c a l l y , i s a f i x e d system cap a c i t a n c e , and the measuring s e c t i o n i t s e l f , which i s t y p i c a l l y e i t h e r a - 128 -Probe 5 F M Signal Voltage Signal Variable Fixed Capacitance C Resonant Oscillating Circuit Demodulator F i g u r e 3.21 Block diagram of a capacitance probe system i l l u s t r a t i n g p r i n c i p a l system components. - 129 -pair of p a r a l l e l plates, or a needle protruding from the support. Either geometry forms a second, variable capacitance, in p a r a l l e l with the f i r s t . The probe i s inserted into the f l u i d i s e d bed with the measuring section located in the region of interest; changes of void fraction in this zone create changes in the d i e l e c t r i c constant which in turn a l t e r the system capacitance. Hence, capacitance becomes a continuous indicator of the solids loading in the region of the probe t i p . ( i i ) The resonant o s c i l l a t o r c i r c u i t : The capacitance probe forms part of a t r a n s i s t o r i s e d tuned o s c i l l a t i n g c i r c u i t whose o s c i l l a t i n g frequency varies as a function of the probe capacitance. In our case the o s c i l l a t o r was of the Clapp type, part of a commercially available transducer system marketted by Disa. Other types, e.g., the Hartley o s c i l l a t o r (Morse and Ballou, 1951) could also have been used. In each case the variation in capacitance at the probe t i p i s converted to a frequency modulation; this i s especially suitable for signal transmission since i t is sensitive neither to noise nor to attenuation. - 130 -( i i i ) The demodulating c i r c u i t : The frequency modulated s i g n a l must be demodulated to g i v e a v o l t a g e or c u r r e n t output p r o p o r t i o n a l to the s h i f t from the base frequency. This occurs i n a "reactance c o n v e r t e r " or frequency d i s c r i m i n a t o r c i r c u i t designed to give an output compatible with data-logging requirements. Although the system described above i s probably the most common type of capacitance probe set up, i t i s important f o r completeness to note that at l e a s t one other type of capacitance measurement device has worked s u c c e s s f u l l y . F i t z g e r a l d (1976) has used a f i x e d frequency source, and measured capacitance changes by c o u p l i n g the d i s c h a r g e from the c a p a c i t o r over h a l f of an A.C. c y c l e to a s u i t a b l y c o n s t r u c t e d c i r c u i t . 3.2.4 Development of a probe f o r t h i s study The capacitance probe developed f o r t h i s study was based upon a commercially a v a i l a b l e reactance conversion system, the Disa 51E01 reactance converter combined with a type 51E02 o s c i l l a t o r and 51E02 tuning plug. These components are designed f o r c a p a c i t a t i v e pressure transducers compatible f o r resonant tuning and frequency d i s c r i m i n a t i o n with the p l u g / o s c i l l a t o r / c o n v e r t o r combination. Given such a system, the design process f o r the probe - 131 -r e q u i r e s the manufacture of a u n i t with both f i x e d base capa c i t a n c e , and capacitance v a r i a t i o n s w i t h i n the s p e c i f i c a t i o n s of the c a p a c i t a t i v e pressure transducer l i n e . These are a t o t a l probe capacitance between zero and 30 pf, and a capacitance v a r i a t i o n , due to d i e l e c t r i c constant changes at the probe t i p , not to exceed 1 pf a c c o r d i n g to the r e f e r e n c e manual f o r the Disa type 51E01 reactance convertor. The v a r i a b l e s which i n f l u e n c e the capacitance of a c o a x i a l c y l i n d r i c a l c a p a c i t o r are shown i n Fi g u r e 3 . 2 2 and may be summarised by the equation 2ire DL C (3.2) *n{-} Fig u r e 3 . 2 3 shows a t y p i c a l probe design. The f i x e d c a p a c i t a n c e of the support can simply be d e s c r i b e d by the c o a x i a l c y l i n d r i c a l c apacitance model of Figure 3 . 2 2 with the inner " l i v e " wire t r e a t e d as the core and the outer grounded sheath as the s h e l l . The v a r i a b l e capacitance around the measurement t i p i s created by d i e l e c t r i c constant changes i n a much more complex f i e l d between the needle t i p and the f i n a l few m i l l i m e t r e s of grounded sheath. C a l c u l a t i o n s shown below i n d i c a t e that i n order to b u i l d an ac c e p t a b l e design with a base capacitance between 0 and 30 - 132 -Cylindrical capacitor con-sisting of an inner wire of radius a and a concentric outer shell of radius b. The electric field is calculated from Gauss' law using a cy-lindrical gaussian surface of radius r and length L, be-tween the conductors. 2nDeQL Figure 3.22 V a r i a b l e s i n f l u e n c i n g the capacitance of a co a x i a l c y l i n d r i c a l c apacitor ( T i p l e r , 1976). - 133 -pf, a number of r e s t r i c t i o n s apply. These are p a r t i c u l a r l y s i g n i f i c a n t i f the probe i s to be used subsequently f o r high temperature work (a p r e r e q u i s i t e f o r our study) because the i n s u l a t i n g ceramics i n such probes have high r e l a t i v e p e r m i t t i v i t y compared to p l a s t i c s or a i r ; t h i s r e s t r i c t s the length of probe 'L' which gives the maximum 30 pf c a p a c i t a n c e . Consider a probe to be c o n s t r u c t e d with a 0.75 mm d i a . l i v e wire i n a sheath with an ID of approximately 2 mm (3 mm OD). What would be the maximum probe length i f the i n s u l a t i n g m a t e r i a l i s a t y p i c a l ceramic with a r e l a t i v e p e r m i t t i v i t y of 6? A p p l i c a t i o n of Equation 3.2 i n d i c a t e s that a probe length of approximately 80 mm i s the maximum which could be t o l e r a t e d , an i n s u f f i c i e n t value f o r t r a v e r s a l across a column of diameter 152 mm. Therefore a p r a c t i c a l probe design must c o n s i s t of a small diameter sheath c l o s e to the measuring volume, to minimise flow d i s t u r b a n c e i n t h i s zone, expanding to a l a r g e r diameter sheath s e v e r a l centimetres away from the t i p . The l a r g e r diameter s e c t i o n can then be c o n s i d e r a b l y longer than 80 mm both by v i r t u e of the l a r g e r ID, and because the d i e l e c t r i c i s p a r t i a l l y a i r and p a r t i a l l y ceramic. The length can become v i r t u a l l y u n l i m i t e d by using s u f f i c i e n t l y large diameter sheathing away from the measurement p o i n t . However, the r e l a t i v e length gain begins to decrease with i n c r e a s i n g diameter, - 134 -LIV/E NEEDLE UJIRE 0.7S mm DIA GROUNDED SHEATH 3 mm DIA GROUNDING LUIRE COAX COUPLING TEFLON INSULATION Dimensions i n mm F i g u r e 3.23 A t y p i c a l simple needle capacitance probe. - 135 -because of the nature of the l o g a r i t h m i c term i n the denominator of Equation 3.1. F i n a l l y , i t should be noted that i t i s v a l u a b l e to minimise the length of the smaller diameter sheath to improve the probe's r i g i d i t y . Changes i n the geometry of the probe due to i m p e r c e p t i b l e bending under s t a t i c and dynamic f o r c e s can produce capacitance changes of the same order of magnitude as those r e s u l t i n g from changes i n the d i e l e c t r i c constant around the t i p . S t r u c t u r a l i n t e g r i t y i s t h e r e f o r e an important part of the probe d e s i g n . S e v e r a l probes were f a b r i c a t e d over the course of t h i s study, each smaller than the previous, u n t i l f i n a l l y a s a t i s f a c t o r y compromise between m i n i a t u r i s a t i o n and r i g i d i t y was obtained. The f i n a l probe i s shown i n F i g u r e 3.24. The probe sheath i s c o n s t r u c t e d from 3.2 mm (1/8") OD 2.2 mm (0.85") ID 316 s t a i n l e s s s t e e l tubing at the measurement end. T h i s i s press f i t t e d i n t o a 6.4 mm (1/4") OD bushing to i n c r e a s e the sheath diameter at a d i s t a n c e of 35 mm (1 3/8") from the probe t i p , so that the remainder of the sheath can be f a b r i c a t e d from 6.4 mm (1/4") OD, 4.6 mm (0.180") ID s t a i n l e s s s t e e l t ubing. The l i v e probe component i s a r i g i d , s i n g l e strand, s t a i n l e s s s t e e l , 1 mm (0.025") d i a . wire, p r o t r u d i n g 6 mm (3/16") from the sheath at the probe t i p . I t runs along the sheath a x i s i n s u l a t e d from the sheath by a s i n g l e , continuous, magnesium oxide - 136 -gure 3.24 A photograph of the f i n a l c a p a c i t a n c e probe d e s i g n . - 137 -thermocouple i n s u l a t o r . The wire i s held r i g i d i n the i n s u l a t o r , and the i n s u l a t o r i s held r i g i d i n the 3.2 mm (1/8") OD sheath using "Omegatite" high temperature ceramic thermocouple cement. L a s t l y , to provide a convenient e l e c t r i c a l connection at the non-measurement end, a 6.3 mm (1/4") tube to 3.2 mm (1/8") female NPT compression f i t t i n g was modified to accept a BNC connector; t h i s was made compatible with the RF connection of the Disa tuning plug u s i n g a BNC-to-RF t r a n s i t i o n a l f i t t i n g . 3.2.5 Response and c a l i b r a t i o n of the c a p a c i t a n c e probe In order to study the t r a n s i e n t responses i n a c i r c u l a t i n g f l u i d i s e d bed, the measuring and d a t a l o g g i n g i n s t r u m e n t a t i o n should be capable of responding at f r e q u e n c i e s s i g n i f i c a n t l y higher than the f r e q u e n c i e s observed i n the system. The D i s a reactance c o n v e r s i o n system i s capable of measuring s i g n a l s up to a frequency of 100 KHz, because of the extremely high resonant frequency band employed i n the o s c i l l a t i n g c i r c u i t (4.5 - 5.5 MHz). Therefore the f r e q u e n c i e s which we are i n t e r e s t e d i n f o r c i r c u l a t i n g bed measurements, three orders of magnitude lower than the 100 KHz cut o f f frequency, do not pose a measurement problem. A l s o , s i n c e the capacitance probe has no moving p a r t s , there are n e i t h e r mechanical lags nor h y s t e r e s i s to l i m i t the frequency response at the measurement s i t e . - 138 -The e l e c t r o n i c output from the reactance converter i s a D.C. v o l t a g e between +6V and -6V, corresponding r e s p e c t i v e l y to +lpf and -1 pf v a r i a t i o n s i n the probe ca p a c i t a n c e . T h i s s i g n a l i s i d e a l f o r logging on the IBM-XT computer using a Tecmar A/D i n t e r f a c e with twelve b i t c o n v e r s i o n . The program used f o r logging the capacitance probe s i g n a l i s i d e n t i c a l to the program used f o r logging s i m i l a r s i g n a l s from the high s e n s i t i v i t y pressure transducer attached t o the same reactance c o n v e r t e r . As noted i n S e c t i o n 2.5, where the b a s i c measurement systems were int r o d u c e d , t h i s program can log up to 30,000 p o i n t s per second, 2 orders of magnitude f a s t e r than the process requirements. Having e s t a b l i s h e d that the capacitance probe system i s capable of measuring i n the d e s i r e d frequency range (assumed to be 0-100 Hz u n t i l f u r t h e r i n f o r m a t i o n became a v a i l a b l e ) , the next steps were to determine ( i ) that the probe could generate a r e p r o d u c i b l e s i g n a l , ( i i ) that the s i g n a l could be c a l i b r a t e d a gainst the v o i d f r i c t i o n i n the measurement zone, ( i i i ) that the probe d i d not i n t e r f e r e s i g n i f i c a n t l y with the f l u i d mechanics i n the measurement volume. ( i ) S i g n a l r e p o d u c i b i l i t y : In order to e s t a b l i s h s i g n a l r e p r o d u c i b i l i t y , and a s s i s t i n developing a c a l i b r a t i o n , the capacitance probe was f i r s t t e s t e d i n packed and bubbling beds. The packed bed t e s t simply c o n s i s t e d of immersing the probe t i p i n a - 139 -packed bed'of sand, moving i t around, and then removing i t . T h i s e s t a b l i s h e d that the s i g n a l was r e p r o d u c i b l e s i n c e i t c o n s i s t e n t l y a t t a i n e d one constant value i n a packed bed, and another i n a i r . In a d d i t i o n , the dynamic f o r c e s caused by moving the probe around did not appear to d e f l e c t the probe t i p s i g n i f i c a n t l y . T e s t s i n bubbling beds provided c o n f i r m a t i o n of the packed bed r e s u l t . In a t y p i c a l t r a c e , the probe s i g n a l f e l l to a c o n s i s t e n t d i l u t e phase value each time a bubble passed the probe t i p before r e t u r n i n g to i t s dense phase va l u e . ( i i ) Probe c a l i b r a t i o n : The problem of probe c a l i b r a t i o n can only be r e s o l v e d a f t e r a number of experiments. I t i s f i r s t u s e f u l to e s t a b l i s h that the output from the reactance converter i s a l i n e a r f u n c t i o n of the capacitance i n the measurement zone and t h e r e f o r e a l i n e a r f u n c t i o n of the d i e l e c t r i c constant. F o r t u n a t e l y t h i s i s a f e a t u r e of the reactance converter design. T h e o r e t i c a l l y then, by e s t a b l i s h i n g a r e l a t i o n s h i p between the d i e l e c t r i c constant of the g a s - s o l i d suspension and the s o l i d s l o a d i n g , and assuming that the s o l i d s are u n i f o r m l y d i s p e r s e d over the probe volume, i t i s p o s s i b l e to e s t a b l i s h a probe c a l i b r a t i o n . This problem has been - 140 -t r e a t e d by Bakker and H e e r t j e s (1959) who e s t a b l i s h e d that the f u n c t i o n due to Weiner (1912) gives the best approximation to the true d i e l e c t i c constant versus voidage curve. where: D = r e l a t i v e p e r m i t t i v i t y of u n i f o r m l y d i s p e r s e d mixture Di = r e l a t i v e p e r m i t t i v i t y of the d i s c o n t i n o u s phase D 2 = r e l a t i v e p e r m i t t i v i t y of the continuous phase e = voidage T h i s r e l a t i o n s h i p i s p l o t t e d i n F i g u r e 3.25 f o r a sand/air system, (D\ = 7, D 2 = 1) showing that although the f u n c t i o n i s s l i g h t l y n o n - l i n e a r i n the region e = 0 to e = 0.35, i t i s c l o s e to l i n e a r over the region of i n t e r e s t f o r f l u i d i s a t i o n s t u d i e s (e = 0.5 to e = 1.0). Our own experiments confirmed t h i s l i n e a r i t y over a narrow range. The probe t i p was immersed i n absolute a l c o h o l and uniform suspensions of f i n e p o l y t h y l e n e powder were maintained by vigorous a g i t a t i o n . Reactance converter output was then p l o t t e d as a f u n c t i o n of s o l i d s hold up to confirm a l i n e a r dependence of d i e l e c t r i c constant upon voidage, at l e a s t i n the narrow region e = 0.97 to e = 1.0. D + 2D2 (3.3) - 141 -F i g u r e 3.25 P l o t of the r e l a t i v e p e r m i t t i v i t y o f u n i f o r m sand a i r s u s p e n s i o n s a c c o r d i n g t o Wiener (1912) . - 142 -A second c a l i b r a t i o n experiment i s shown i n F i g u r e 3.26. The probe t i p was immersed to v a r i o u s a c c u r a t e l y measured depths i n a packed bed of f i n e sand. Reactance converter output was then p l o t t e d as a f u n c t i o n of immersed depth. The r e s u l t , analogous to a r e s u l t of Werther and Molerus (1973) when a probe was dipped i n t o cyclohexane, i n d i c a t e s f i r s t that the probe f i e l d does not extend more than approximately 1 mm beyond the end of the probe t i p , and second that the v a r i a t i o n of probe output i s l i n e a r with submergence. Combining these r e s u l t s with the f a c t that the d i e l e c t r i c constant of the uniform suspension v a r i e s l i n e a r l y with s o l i d s hold-up, one i s led to conclude that the probe f i e l d i s e s s e n t i a l y c y l i n d r i c a l and that the capacitance change i s f a i r l y i n s e n s i t i v e to the d i s t r i b u t i o n of s o l i d s w i t h i n the f i e l d volume. The l a t t e r r e s u l t i s u s e f u l because i t i s no longer necessary to assume u n i f o r m l y d i s t r i b u t e d s o l i d s to c a l c u l a t e the mean s o l i d s hold up. The preceding d i s c u s s i o n e s t a b l i s h e s both t h e o r e t i c a l and experimental j u s t i f i c a t i o n s f o r c a l i b r a t i n g a needle c a p a c i t a n c e probe by f i r s t measuring the probe output i n a i r , then i n a packed bed of the m a t e r i a l of i n t e r e s t whose s o l i d s f r a c t i o n i s known. Intermediate probe outputs are then converted to s o l i d s f r a c t i o n s by l i n e a r i n t e r p o l a t i o n s . In c oncluding the comments on c a l i b r a t i o n i t must be s t a t e d that a l i n e a r i n t e r p o l a t i o n procedure has been - 143 -F i g u r e 3.26 Output from c a p a c i t a n c e p r obe g r a d u a l l y immersed i n t o a f i x e d bed of sand showing l i n e a r i t y o f v o l t a g e w i t h immersion d e p t h . - 144 -commonly used f o r capacitance probe c a l i b r a t i o n (e.g. Abed, 1983; Carotenuto e_t a l . , 1974). However l i t t l e a t t e n t i o n has been given to j u s t i f i c a t i o n , or to the problem of where the s o l i d s l i e i n the measurement zone; i t was necessary to r e s o l v e both these i s s u e s before commencing time-consuming experiments. I t should a l s o be noted that i t was p o s s i b l e to check the probe c a l i b r a t i o n procedure when the runs were f i n a l l y made. R a d i a l d e n s i t y p r o f i l e s i n t e g r a t e d over the column c r o s s - s e c t i o n gave d e n s i t i e s which corresponded w e l l with mean bulk d e n s i t i e s d e r i v e d from pressure drop measurements. This comparison i s i l l u s t r a t e d i n F i g u r e 3.27. ( i i ) R e l i a b i l t y of probe data: R e l i a b i l i t y of data taken by the capacitance probe r e q u i r e s that the probe not i n t e r f e r e s i g n i f i c a n t l y with the hydrodynamics i n the measurement volume. T h i s problem has been i n v e s t i g a t e d by Rowe and Masson (1981), but only f o r measurement of bubble parameters i n gently bubbling beds. They found that immersed probes can i n t e r f e r e s u b s t a n t i a l l y and tend to both deform the shape, and a l t e r the r i s e v e l o c i t y of bubbles i n t h e i r v i c i n i t y . The degree of d i s t u r b a n c e was, s u r p r i s i n g l y , not n e c e s s a r i l y a f u n c t i o n of probe s i z e , and a " r e l a t i v e l y massive probe caused l i t t l e d i s t u r b a n c e . " - 145 -0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 D e n s i t y From C a p a c i t a n c e Probe (kg/nr*) Figure 3.27 Comparison of r a d i a l l y averaged d e n s i t i e s obtained using an integrated capacitance probe s i g n a l , and the same d e n s i t i e s c a l c u l a t e d from pressure drop measurements. - 146 -Of the nine probes t e s t e d by Rowe and Masson e i g h t were supported v e r t i c a l l y and one was supported h o r i z o n t a l l y l i k e the probe used i n t h i s study. The v e r t i c a l probes were found to be p r e f e r a b l e f o r measurement of bubble phase parameters because "the h o r i z o n t a l l y supported probe d e c e l e r a t e s the bubbles markedly and promotes s p l i t t i n g . " U n f o r t u n a t e l y there has not been any s i m i l a r work r e l a t i n g to c i r c u l a t i n g f l u i d i s e d beds; nor i s i t l i k e l y to be forthcoming s i n c e the x-ray techniques which Rowe a p p l i e d , are not s u i t e d to the complex and f i n e r s c a l e flow s t r u c t u r e s i n c i r c u l a t i n g beds. Therefore, at present the optimum geometry of probes f o r c i r c u l a t i n g beds remains an u n c e r t a i n and p o t e n t i a l l y c ontentious i s s u e and even a n o n - i n t r u s i v e technique such as l a s e r doppler anemometry does not n e c e s s a r i l y provide a s o l u t i o n . A f t e r r e j e c t i n g a large f r a c t i o n of the s i g n a l because of i n a b i l i t y to penetrate the s o l i d s boundary l a y e r , there i s a strong p r o b a b i l i t y that the remaining s i g n a l w i l l be biased h e a v i l y towards measurement of d i l u t e phase c h a r a c t e r i s t i c s . T h i s would occur because when a packet of p a r t i c l e i s pa s s i n g through and around the very small measuring volume, the measurement volume i n general w i l l be s h i e l d e d and no s i g n a l w i l l be r e g i s t e r e d . Hence, there i s no i d e a l way to design a probe f o r , or to make l o c a l measurements i n a c i r c u l a t i n g bed. Probes - 147 -must be d e s i g n e d t o c a u s e m i n i m a l i n t e r f e r e n c e and even t h e n the r e s u l t s must be t r e a t e d w i t h a p p r o p r i a t e p r u d e n c e . In our c a s e , p h y s i c a l c o n s t r a i n t s d i c t a t e d t h a t the probe had t o e n t e r from t h e s i d e o f t h e column and c o u l d n o t be bent e i t h e r upward o r downward s i n c e t h i s would p r e v e n t o n - l i n e r e moval r e q u i r e d f o r r e g u l a r m a i n t e n a n c e . A l s o , w h i l e i t i s l o g i c a l t o measure b u b b l e r i s e v e l o c i t i e s w i t h a downwards d i r e c t e d p r o b e , t h e d i r e c t i o n o f s o l i d s f l o w i n t h e c i r c u l a t i n g bed changes i n b o t h a time-mean s e n s e w i t h p o s i t i o n , and i n an i n s t a n t a n e o u s sense w i t h t i m e . S i n c e a downward f a c i n g p r o b e would c e r t a i n l y d i s t u r b measurement o f downward moving s o l i d s , and an upward f a c i n g p r o be upward moving s o l i d s , the h o r i z o n t a l l y d i r e c t e d p r o be a p p e a r s t h e most a c c e p t a b l e compromise. R a d i a l s o l i d s movement w i l l c e r t a i n l y be a f f e c t e d , but by m e a s u r i n g o v e r t h e n e a r r a d i u s , s i n c e r a d i a l p a r t i c l e f l u x e s a r e p r i m a r i l y from t h e c e n t e r l i n e . t o the w a l l , t h e s e e f f e c t s s h o u l d be m i n i m i s e d . When c o n s i d e r i n g the s i z e and geometry o f t h e probe a n e e d l e probe was p r e f e r r e d o v e r a p a r a l l e l p l a t e p r o b e b e c a u s e i t does not i n h i b i t c i r c u m f e r e n t i a l movement t h r o u g h the p r obe volume. The probe was made as s m a l l as p o s s i b l e b e c a u s e , a l t h o u g h a l a r g e p r o b e d i d not d i s t u r b b u b b l e s , a s m a l l m e a s u r i n g volume i s d e s i r a b l e t o i d e n t i f y f i n e r s c a l e d e m i x i n g , and a l a r g e h o r i z o n t a l probe would l i k e l y d i s t u r b t h e f l o w s t r u c t u r e i n a c i r c u l a t i n g bed. - 148 -3.2.6 Experimental s t u d i e s with the c a p a c i t a n c e probe In order to o b t a i n r e l i a b l e c apacitance t r a c e s the probe i t s e l f must be r i g i d , as noted i n s e c t i o n 3.2.4. In f a c t the whole of the tuned c i r c u i t , from the probe t i p to the o s c i l l a t o r , must be clamped r i g i d l y , s i n c e any geometric v a r i a t i o n s , such as the bending of a c o a x i a l c able, produce measurable capacitance changes. To ensure t h i s s t a b i l i t y while the probe i s t r a v e r s e d from one s i d e of the column t o the other,the t r a v e r s i n g r i g shown i n F i g u r e 3.28 was c o n s t r u c t e d . A s e r i e s of t e s t s was then conducted to examine the decay of d e n s i t y along the column. The t e s t s e r i e s examined three c o n d i t i o n s i n d e t a i l . S p e c i f i c a l l y , the column was set up as shown i n Figure 2.1, and, f o r a constant gas v e l o c i t y of 6.5 m/s, the s o l i d s c i r c u l a t i o n was set at three r a t e s . At each c i r c u l a t i o n r a t e the v a r i a t i o n of the capacitance probe s i g n a l was recorded at seven r a d i a l p o s i t i o n s from the near w a l l to the c e n t r e l i n e , at each of three d i f f e r e n t v e r t i c a l l o c a t i o n s , 533 mm, 1448 mm and 2362 mm (21", 57" and 93") from the d i s t r i b u t o r . At each p o s i t i o n the s i g n a l was logged f o r 30s at a sampling frequency of 100 p o i n t s per second; i t was c o n d i t i o n e d with a Rockland model 442 dual h i / l o f i l t e r set f o r a low pass frequency of 100 Hz to remove spurious high frequency noise. Under these logging c o n d i t i o n s the Nyquist frequency i s 50 Hz, so that meaningful data can be obtained - 149 -F i g u r e 3.28 C a p a c i t a n c e probe t r a v e r s i n g r i g mounted on a s e c t i o n of the c i r c u l a t i n g f l u i d i s e d bed. - 150 -up to t h i s frequency l i m i t . F i n a l l y , i n a d d i t i o n to logging the s i g n a l d i g i t a l l y , i t was recorded i n analogue form on an EMI model SE 6150 Mark 2 u l t r a v i o l e t o s c i l l a g r a p h . T h i s has the merit of p e r m i t t i n g immediate o b s e r v a t i o n of the s i g n a l to check that the probe i s f u n c t i o n i n g p r o p e r l y ; i t a l s o permits q u a l i t a t i v e e v a l u a t i o n of the s i g n a l s without p r o c e s s i n g of the d i g i t i z e d data. Only one d i f f i c u l t y was encountered during the c a p a c i t a n c e probe t e s t s . T h i s was that, d e s p i t e a l l p r e c a u t i o n s , the probe b a s e l i n e tended to s h i f t as the probe was t r a v e r s e d across the column. The need to s e a l the probe on a purged compression f i t t i n g ( F i g u r e 3.28), although i d e a l f o r keeping sand o f f the bearing s u r f a c e r e q u i r e d f o r t r a v e r s i n g , creates a d e f l e c t i o n on the probe unless p e r f e c t alignment can be obtained. Numerous attempts to achieve p e r f e c t alignment were u n s u c c e s s f u l , so that a b a s e l i n e at each p o i n t had to be taken as the mimimum capacitance probe s i g n a l over each s p e c i f i c measurement p e r i o d . T h i s assumes i n e f f e c t that, at some time i n the 30 s sampling i n t e r v a l there w i l l be a zero, or i n s i g n i f i c a n t hold up i n the measurement volume; v i s u a l l y t h i s appeared to be the case, even at the w a l l . It was not p o s s i b l e to make a b a s e l i n e c o r r e c t i o n by e s t a b l i s h i n g a b a s e l i n e at each point i n an empty column because the capacitance probe i s a l s o temperature - 151 -s e n s i t i v e . S o l i d s c i r c u l a t i o n c o o l s the gas, which i s preheated by the blower, and a l t e r s the b a s e l i n e s l i g h t l y . Although one can c o r r e c t f o r t h i s by measuring temperature i n the measurement volume, and f o r pure a i r i n the windbox, the complexity i s not warranted. T h i s procedure was adopted on s e v e r a l occasions, but the r e s u l t was i n d i s t i n g u i s h a b l e from that obtained i f the minimum s i g n a l was assumed to represent 100% voidage. One l i m i t a t i o n of adopting t h i s assumption i s that s o l i d s loadings on the c e n t r e l i n e are measured with lower percentage accuracy than at the w a l l , s i n c e a small absolute e r r o r causes higher p r o p o r t i o n a l e r r o r . However, the general c o n c l u s i o n s regarding flow s t r u c t u r e and d i f f e r e n t i a t i o n between the flow regimes remain v a l i d . 3.2.7 Treatment of r e s u l t s from the m i c r o s t r u c t u r a l  i n v e s t i g a t i o n Before r e s u l t s could be computed from capacitance probe measurements, i t was necessary to show that s i g n a l s from the capacitance probe are both s t a t i o n a r y and e r g o d i c . T h i s was shown according to the c r i t e r i a of Bendat (1971) r e q u i r i n g that d i f f e r e n t s e c t i o n s of the same time h i s t o r y have means and v a r i a n c e s no d i f f e r e n t than e x p l i c a b l e through sampling v a r i a n c e . I t e s t a b l i s h e s that the data can be analysed using values from a s i n g l e continuous s i g n a l ; - 152 -there i s no i m p l i c a t i o n that the s i g n a l does not possess p e r i o d i c components. The s i g n a l from each l o c a t i o n was analysed to give the f o l l o w i n g data: ( i ) The mean s o l i d s d e n s i t y ( i i ) The standard d e v i a t i o n of the s o l i d s d e n s i t y about the mean ( i i i ) The power spectrum and autocovariance f u n c t i o n of the s o l i d s d e n s i t y . The f i r s t two parameters can be computed r e a d i l y by a r i t h m e t i c o p e r a t i o n s upon the 3000 d i s c r e t e data p o i n t s generated f o r each run (30 s of data at 100 p o i n t s per second), so t h i s a n a l y s i s was performed upon the IBM-XT microcomputer. The power s p e c t r a and autocovariance f u n c t i o n s are more complex; these were computed by uploading the data to the mainframe computer and making use of the software package BMD:02T. A sample output from t h i s package i s presented i n Appendix 1. The r e s u l t s from the m i c r o s t r u c t u r a l s t u d i e s can be summarised i n Figures 3.29 to 3.34. The f i r s t three of these show the l o n g i t u d i n a l voidage v a r i a t i o n at each of the three c o n d i t i o n s s t u d i e d . These are combined with the p l o t s of the r a d i a l v a r i a t i o n s i n the mean and standard d e v i a t i o n of the voidage at the three v e r t i c a l l o c a t i o n s which were considered. The f i n a l three f i g u r e s each c o n c e n t r a t e on a s p e c i f i c r a d i a l d i s t r i b u t i o n f o r the high - 153 -c i r c u l a t i o n r a t e run, and show three curves f o r each of the seven measurement volumes: ( i ) A tr a c e of the d e n s i t y f l u c t u a t i o n with time, ( i i ) The power s p e c t r a l d i s t r i b u t i o n of the d e n s i t y f l u c t u a t i o n s , ( i i i ) The autocovariance of the d e n s i t y f l u c t u a t i o n s . HEIGHT ABOVE DISTRIBUTOR . m c CD M & a. o p- tr1 CD H- 01 3 0 II p> iQ <Tt O CO p-r+ >< cn rt tr to H-£ n r t X O I—' H - LQ, 0 c o l-h 3 P> to rt cn H-3 rt O Hi L Q C i r t n t r n o rt C P) rt H-O 3 cn CD cu 01 fD O & Pi H-ii) tn O pi rt t-h (-• pi O 3 5 cn QJ a. 3 p> CD P> h{ pj 3 3 PJ cn CD CD H . L Q rt < H-P> rt H-O o Hi p> a II P) <Tl M • U l cn H-W rt H H-tr rt H-O cn Point D e n s i t y ( k g / m 3 ) o o ro o o co o o o o O O CD O O O o S t a n d a r d Dev ia t ion Of D e n s i t y F l u c t u a t i o n s ( k g / m 3 ) - S'ST -HEIGHT ABOVE DISTRIBUTOR . m p-cQ 0 CD o O. CD P-3 cn cn rt P- I"! C+ H-c »-h rt I—1 P-C O o rt cn d PJ O rt t-h P-O rt 3 tr cn CD cn rt PJ & ft) »-{ Oi O. (D < P-PJ rt P-O 3 O i-ti Q P- t-1 cn 3 O 3 II QJ p-O co p-i-S X O \ P> PJ g pj | _ i NJ rt cn P- PJ • 3 3 cQ p. rt 0 O. P-3> cr n H (D PJ cn Oi Oi o P-o PJ cn Hi pj 0 cn O. 3 PJ CD 3 3 3 OJ cn pj •» p-H rt ro O K ; cQ i-{ Oi PJ II P-01 cn p- <Tt rt PJ • ^ P U l H -cr 3 c \ rt cn P-- o 3 cn 3 O i - O — O -o cn *< 3 CT O |-c (V m X en W a O w lO " i * Point D e n s i t y ( k g / m 3 ) cn o o CD O o o o O L I O ( o — o CO C n O ^ CO to 00 CO c/> ~< 3 cr o_ X 2. CQ' IT S t a n d a r d Deviat ion Of Dens i ty F l u c t u a t i o n s (kg/m 3 ) - SSI -HEIGHT ABOVE DISTRIBUTOR . m P -iQ 0 P . CD CO P-rt a a O CD P-Cn 3 cn rt II n P- 4^ 0 rt X O P - L Q 0 o H- tr1 3 O pj i£) p-o p-n Ml h-1 0 O rt C p) rt p-O 3 cn rt d p-3 P> 3 P> rort cn p- p> 3 3 tr CD Cb Oi P-Oi i-i P) cn rt P) 3 Oi p) l-i Oi P) l-t OJ ro CD P) Oi CD 3 < P-P) rt cn P> 3 Oi cn - p-rt P> O. p- <y\ II P- P> O 3 O i-h Oi P-cn rt ii P-tr 0 rt p-O 3 cn Point D e n s i t y ( k g / m 3 ) to co A cn o> -vi o o o o o o o o o o o o t>no to 3 cr o S3 o 2 co 6i O A " S3 oo co X °. to" 3" S t a n d a r d Dev ia t ion Of D e n s i t y F l u c t u a t i o n s ( k g / m 3 ) CO o o o o cn O o X to —• o 2. O -N CO i rO CO CO - 9QT -Distance From Wall, mm Z = 5 3 3 rnm 8 13 2 3 33 43 53 0-2 04 06 0-8 1-0 Time ,s 0.5 1.0 1.5 TIME LAG (») 4 ( FREQUENCY (H>) Figure 3.32 Radial v a r i a t i o n s i n density f l u c t u a t i o n s , power spectral d i s t r i b u t i o n of density fluct u a t i o n s , and autocovariance of density fluct u a t i o n s , U = 6.5 m/s, G g = 62 kg/m s Z = 533 mm. 8 - 157 -Distance From Wall, mm Z =1448 m m 8 13 23 33 43 53 Time ,s 10 1.5 TIME LAG (i) Figure 3.33 Radial v a r i a t i o n s i n density f l u c t u a t i o n s , power s p e c t r a l d i s t r i b u t i o n of density f l u c t u a t i o n s , and autocovariance of density fl u c t u a t i o n s , U =6.5 m/s, G = 62 kg/m s, Z = 1448 mm. g s - 158 -Distance From Wall, mm Z = 2362 mm 8 13 23 33 43 53 T i m e ,s 1.0 TIME LAG (t) Figure 3.34 Radial v a r i a t i o n s i n density f l u c t u a t i o n s , power spectral d i s t r i b u t i o n of density f l u c t u a t i o n s , and autocovariance of density f l u c t u a t i o n s , U = 6.5 m/s, G g = 63 kg/m s, Z — 2362 mm. - 159 -- 160 -4. DISCUSSION 4.1 Microstructural Results 4.1.1 Development of Gas and Solids Flow P r o f i l e s The objective of the microstructural study of the c i r c u l a t i n g f l u i d i s e d bed was to develop a picture of how s o l i d s d i s t r i b u t e themselves longitudinally and r a d i a l l y in a r i s e r , and to explain these d i s t r i b u t i o n s . Figures 3.29, 3.30 and 3.31 show the variation of the time-mean r a d i a l loading d i s t r i b u t i o n with height for the different c i r u l a t i o n rates. The figures are very similar in appearance to results presented by Hartge et a l . (1985) and Weinstein et aJ. (1985) obtained using a f i b r e optic probe and X-ray absorption respectively. The results confirm a r a d i a l d i s t r i b u t i o n of density which increases from the centreline to the wall, without a sharp demarcation between core and annular regions. The longitudinal and r a d i a l density p r o f i l e s for the three cases allow one to propose a gross flow pattern for solids in the important region of decaying solids concentration. One potential explanation for this decay in solids concentration i s that solids move from an upflowing zone in the centre of the r i s e r to a downflowing zone at the r i s e r wall where they cascade downward in sheets towards the base of the column. - 1 6 1 -It appears that there are two levels to the problem of elucidating the flow structures in a c i r c u l a t i n g f l u i d i s e d bed. The f i r s t i s i d e n t i f i c a t i o n of the gas and solids flow patterns. The second i s attempting to explain how the two intera c t to produce the driving forces for changes in gas and so l i d s d i s t r i b u t i o n s as the two p r o f i l e s develop. In view of the limited number, and type, of measurements which could be attained in this study, i t i s not possible to es t a b l i s h conclusively what happens at either l e v e l . However, i t i s possible to postulate some possible mechanisms, and suggest directions for future research. Our own measurements have examined the so l i d s phase exclusively, and are limited to findings about the d i s t r i b u t i o n of that phase. It i s not possible to esta b l i s h , for example, the direction of s o l i d s flow at a point either on an instantaneous, or time-mean basis using a single capacitance probe. However, the solids flow pattern suggested e a r l i e r , proposing a developing p r o f i l e with net s o l i d s upflow in a low density central zone and net downflow near to the r i s e r walls, i s a l o g i c a l extension of the observed density p r o f i l e s for the following reasons: ( i ) It i s supported by visual obervations of the wall region. ( i i ) It i s consistent with results for steady state r i s e r flows obtained by other authors (e.g. van - 162 -Breugel, 1969-70; Monceaux et al_. , 1985) who measured downflow at the wall using mass flux probes. ( i i i ) It can be rationalised by a simple f l u i d mechanic explanation presented below. An increased understanding of the solids p r o f i l e development can be gained by postulating what happens to the gas phase. The experimental solids r a d i a l density p r o f i l e s were taken at different heights and s i m p l i f i e d models were applied to estimate the v e r t i c a l component of gas v e l o c i t y at each location. If i t i s assumed that the r a d i a l pressure gradient i s very much smaller than the longitudinal over a given cross-section, then the v e r t i c a l gas velocity can be estimated provided that a pressure drop-voidage-gas v e l o c i t y relationship i s known. In practice, there i s no such suitable relationship; the solids aggregation phenomena and complex solids c i r c u l a t i o n patterns render conventional correlations inapplicable in a s t r i c t sense. However, i f the s i m p l i f i c a t i o n i s made that s l i p v e l o c i t i e s are substantially higher than s o l i d v e l o c i t i e s , so that the gas v e l o c i t y approximates the s l i p velocity and conventional forms of pressure drop vs voidage correlations are applied, then some insight can be achieved. Three different forms of correlation were used, based upon the Kozeny (1927), Burke-Plummer (1928), and - 163 -Richardson-Zaki (1954) equations. Each suggests a d i f f e r e n t form f o r the pressure drop-voidage dependence which can be used to c a l c u l a t e the gas v e l o c i t y p r o f i l e s , a l b e i t with the o r i g i n a l constant i n each equation r e p l a c e d by a f i t t e d constant whose magnitude i s f i x e d to give the c o r r e c t t o t a l gas v e l o c i t y . For example, the Kozeny equation g i v e s Ap = 150 nil (1 - e ) 2 ( 4 > 1 ) Al A 2 3 d e P Now imposing the c o n d i t i o n of constant pressure gradient suggests that l o c a l v e r t i c a l v e l o c i t y v a r i e s with l o c a l voidage i n the f o l l o w i n g manner. ,_v3 U ( r ) = K {—^12 ,} (4.2) ( l - e ( r ) ) 2 E v a l u a t i n g K to give the c o r r e c t mean v e l o c i t y gives T J * { £ ( R > 3 2 } R 2 U ( r ) = e ( r > (4-3) 0 rR, e ( r ) J , . ( l - e ( r ) ) The value of t h i s approach i s not that q u a n t i t a t i v e r e s u l t s w i l l be v a l i d , s i n c e one does not expect equations to be s t r i c t l y a p p l i c a b l e , but simply that i t demonstrates mathematically what one expects i n t u i t i v e l y , i . e . that s t r o n g r a d i a l g r a d i e n t s i n s o l i d s d e n s i t y are l i n k e d to - 164 -s t r o n g r a d i a l g r a d i e n t s i n gas v e l o c i t y . The approach a l s o suggests another i n t u i t i v e l y l o g i c a l r e s u l t which i s that v e r t i c a l changes i n the r a d i a l s o l i d s d e n s i t y p r o f i l e are matched by simultaneous changes i n the r a d i a l d i s t r i b u t i o n of gas v e l o c i t y , and that the q u a l i t a t i v e nature of these changes i s the same f o r each of the v o i d a g e - v e l o c i t y c o r r e l a t i o n s . For each case the gas v e l o c i t y p r o f i l e becomes f l a t t e r with i n c r e a s i n g height along the column as the r a d i a l l y averaged s o l i d d e n s i t y decays. F i g u r e 4.1 shows how the c e n t r e l i n e maximum decreases and the w a l l v e l o c i t y g r a d u a l l y i n c r e a s e s to match the more uniform r a d i a l s o l i d s d i s t r i b u t i o n i n one such case. Here the c e n t r e l i n e gas v e l o c i t y i s estimated as 26 m/s at the column base (4 times the mean s u p e r f i c i a l gas v e l o c i t y ) . T h i s i s s i m i l a r to the magnitude found by B i e r l et a l . (1980). A s i m i l a r , but u s u a l l y l e s s pronounced behavior i s e v i d e n t i n the estimated development of the gas v e l o c i t y p r o f i l e i n most i n s t a n c e s . However, some anomalies can occur i n the lower part of the bed when the c e n t r e l i n e d e n s i t y decays p r o p o r t i o n a l l y f a s t e r than that at the w a l l . In t h i s case an i n i t i a l r e d i s t r i b u t i o n of gas from w a l l to c e n t r e l i n e can be p r e d i c t e d f o r c e r t a i n voidage versus v e l o c i t y dependencies. A l s o , i t should be noted that t h i s approach does not enforce the n o - s l i p c o n d i t i o n at the w a l l , a c o n d i t i o n which may be important i n the true p r o f i l e development. 165 0 20 40 60 76 Distance From Wall (mm) 0 20 40 60 76 Distance From Wall (mm) F i g u r e 4.1 V a r i a t i o n of l o c a l v e r t i c a l s u p e r f i c i a l gas v e l o c i t y w i t h r a d i a l p o s i t i o n and h e i g h t as c a l c u l a t e d by the m o d i f i e d Kozeny e q u a t i o n . D e n s i t y p r o f i l e s a r e measured v a l u e s a t v e r t i c a l l o c a t i o n s of 0.533 m and 2.362 m f o r a gas v e l o c i t y of 6.5 m/s and a s o l i d s c i r c u l a t i o n r a t e o f 62 kg/m 2s. - 166 -To summarise, estimation of v e r t i c a l velocity p r o f i l e s using a variety of voidage-velocity correlations, shows that the points of highest velocity on a r a d i a l p r o f i l e are characterised by the lowest densities, and visa versa. The same computations suggest that the gas velocity p r o f i l e may develop with height from a strongly curved p r o f i l e in the high density zone at the base of the unit to a more uniform p r o f i l e in the lower density regions at greater heights. 4.1.2 Possible mechanisms for s o l i d s movement The calculations of Section 4.1.1 imply changes in the gas velocity p r o f i l e with height, but in themselves they do not approach the complex problem of why such changes take place, i . e . why do solids redistribute themselves and why does the high overall density at the base of the unit tend to decrease with height? We suggest that t h i s i s at least p a r t i a l l y due to a natural tendency for solids to move into the low gas ve l o c i t y region close to the wall generated by the no s l i p condition which must exist at this point. Solids w i l l f a l l downward once in t h i s low velocity region, and, unless they are reentrained, the cross-sectional mean density w i l l decay with height. It i s possible to postulate a number of mechanisms to account for ra d i a l s o l i d s motion. It is clear that r a d i a l movement i s not a simple d i f f u s i o n a l process based upon a - 167 -s o l i d s d e n s i t y d r i v i n g f o r c e . If t h i s were the case then s o l i d s at the base of the column would tend to d i f f u s e inward from regions of high d e n s i t y to the lower d e n s i t y c e n t r e l i n e . A p r o f i l e with high c e n t r e l i n e d e n s i t y decaying towards the downflow sink at the wall would be p r e d i c t e d f u r t h e r up the column, combined with a complicated gas v e l o c i t y p r o f i l e showing a c e n t r e l i n e minimum. T h i s i s i l l u s t r a t e d i n F i g u r e 4.2. A more a t t r a c t i v e concept at f i r s t glance i s to c o n s i d e r the d r i v i n g f o r c e f o r s o l i d s motion again i n terms of a d i f f u s i o n a l movement, but with the d r i v i n g f o r c e as the d e n s i t y i n excess of the s a t u r a t i o n c a r r y i n g c a p a c i t y , or choking d e n s i t y , p r e v a l e n t at the l o c a l c o n d i t i o n s . T h i s i n turn might be considered as a measure of the tendency f o r the system to agglomerate ( c l u s t e r ) , and an a p p r o p r i a t e l y d e f i n e d r a d i a l c l u s t e r gradient could be i n t r o d u c e d . T h i s would represent a p l a u s i b l e model f o r those who l i k e to consider the c i r c u l a t i n g bed i n terms of a g g l o m e r a t e - l i k e s p e c i e s . However, i t would r e q u i r e a s u b s t a n t i a l r e t h i n k i n g of c u r r e n t ideas r e g a r d i n g trends i n s a t u r a t e d c a r r y i n g c a p a c i t i e s with v e l o c i t y , s i n c e , to e x p l a i n d i f f u s i o n a l t r a n s p o r t from regions of low d e n s i t y to high would r e q u i r e lower choking c o n c e n t r a t i o n s at high v e l o c i t y than at low. Current choking c o r r e l a t i o n s such as those of Matsen (1982) suggest t h a t , at l e a s t on the macroscopic l e v e l , and hence by i n f e r e n c e on the m i c r o s c o p i c , the opposite i s t r u e . - 168 -High density Density gradient for causing down- diffusional flux to wall Gas Velocity or Solids Density Form of density profile required to justify simple diffusional model Gas Velocity Solids Density Gas Velocity or Solids Density Typical form of density I profile R _ o Radius Figure 4.2 I m p l i c a t i o n s of a simple d i f f u s i o n a l model for s o l i d s motion f o r gas and s o l i d s d e n s i t y p r o f i l e s . Lower f i g u r e shows a t y p i c a l experimental r e s u l t , upper f i g u r e the requirements f o r a d i f f u s i o n a l model to be co n s i s t e n t . - 169 -Matsen f i n d s : a ch = 0.0003 U /V t < 1.29 (4.4) = 1.26 x 10"** (U /V t) 3.41 , U /V.> 1.29 ' g' t (4.5) a ch where, a c h = s o l i d s volume f r a c t i o n f o r choking Ug = s u p e r f i c i a l gas v e l o c i t y (m/s) Vt = s o l i d s t e r m i n a l v e l o c i t y (m/s) R e j e c t i o n of these mechanisms f o r t r a n s f e r of m a t e r i a l to the w a l l prompts examination of more complex f e a t u r e s of the gas flow and s p e c i f i c a l l y of how the gas v e l o c i t y p r o f i l e develops with h e i g h t . I f one c o n s i d e r s the gas v e l o c i t y p r o f i l e as developing from an approximately p a r a b o l i c shape at the base of the column to a s u b s t a n t i a l l y f l a t t e r p r o f i l e higher up, and p l o t s the s t r e a m l i n e s f o r the flow development, i t i s apparent that there i s a small r a d i a l c o n v e c t i v e gas flow over the t r a n s i t i o n h e i g h t . T h i s i s i l l u s t r a t e d i n F i g u r e 4.3. Crude estimates of the p o t e n t i a l r a d i a l v e l o c i t y components i n v o l v e d , which were based on changes i n the stream f u n c t i o n between p a r a b o l i c and f l a t p r o f i l e s over a d i s t a n c e of 1 m, suggest values of the order of 0.12 m/s at some p o i n t s on the r a d i a l c r o s s s e c t i o n . Therefore some p o r t i o n of the r a d i a l l y outward s o l i d s t r a n s f e r may be due to c o n v e c t i v e gas flow r a t h e r than to d i f f u s i v e mixing processes. I f t h i s i s c o r r e c t then the nature of any subsequent modelling processes would be - 170 -T 1 1 " 1 1 r Distance From Wall (mm) Figure 4.3 Streamfunction p r o f i l e s i n a developing flow. The streamfunction i s p l o t t e d as a f u n c t i o n of radius f o r a uniform gas v e l o c i t y p r o f i l e and a pa r a b o l i c p r o f i l e showing how, as the p r o f i l e changes with height due to r e d i s t r i b u t i o n and decay of density, there i s a bulk flow of gas towards the w a l l . Arrows j o i n points of constant streamfunction showing the d i r e c t i o n of gas flow. - 171 -s u b s t a n t i a l l y a l t e r e d . For comparative purposes i t i s v a l u a b l e to note that r a d i a l convective v e l o c i t y components of approximately 0.13 m/s compare with a t y p i c a l dimensional r a d i a l turbulence i n t e n s i t y (r.m.s. v e l o c i t y f l u c t u a t i o n ) of approximately 0.1 m/s on the c e n t r e l i n e of a si n g l e - p h a s e gas flow at Ug = 6.5 m/s (Appendix 2 ) . However there i s st r o n g evidence that the l a t t e r i s l i k e l y to be reduced s u b s t a n t i a l l y by the presence of s o l i d s (Soo, 1982). Thus, c o n v e c t i v e r a d i a l flows could generate s o l i d s f l u x e s of at l e a s t the same order of magnitude as t u r b u l e n t s o l i d s d i f f u s i o n due to gas turbulence. A second p o t e n t i a l mechanism, which could r e i n f o r c e the c o n v e c t i v e flow of s o l i d s , i s an e f f e c t i v e d i f f u s i o n a l movement caused by r a d i a l v a r i a t i o n s i n gas turbul e n c e i n t e n s i t y . T h i s i s not a true d i f f u s i o n a l motion because s o l i d s are d r i v e n up a de n s i t y g r a d i e n t , r e l y i n g upon non-continuum e f f e c t s i n the s o l i d s phase. I n t u i t i o n suggests that a strong r a d i a l gradient of s o l i d s d e n s i t y i s l i k e l y to generate a strong r a d i a l g r a d i e n t i n gas turbulence i n t e n s i t y , p a r t i c u l a r l y i t s r a d i a l component which i s l i k e l y to be l e s s i n f l u e n c e d than the v e r t i c a l by the p r i m a r i l y up and down s o l i d s motion. If the r a d i a l component of turbulence i s damped by the presence of s o l i d s , then the almost l i n e a r v e l o c i t y p r o f i l e s of van-Breugel (1969-70) would suggest higher r a d i a l turbulence i n t e n s i t i e s - 172 -on the c e n t r e l i n e than i n the wa l l r e g i o n , although the gas shear i s approximately constant over the r a d i a l c r o s s s e c t i o n . T h i s i s a d i f f e r e n t s i t u a t i o n to s i n g l e phase flow where a high shear r a t e near the wa l l c r e a t e s a weak maximum i n the r a d i a l t u r b u l e n t i n t e n s i t y (Hinze, 1959). Now i f s o l i d s are considered to f o l l o w the gas phase tur b u l e n c e , a l b e i t with phase la g s due to drag e f f e c t s , the gr a d i e n t i n turbulence i n t e n s i t y n a t u r a l l y c r e a t e s a s o l i d s motion from the high i n t e n s i t y to the low i n t e n s i t y zone, with c o l l e c t i o n of p a r t i c l e s at the wall enhanced by i n e l a s t i c c o l l i s i o n . In summary, the experimental s t u d i e s using the cap a c i t a n c e probe show str o n g r a d i a l n o n - u n i f o r m i t i e s i n the d e n s i t y d i s t r i b u t i o n of the s o l i d s . T h i s , combined with v i s u a l evidence of downflow at the w a l l l a y e r and r e s u l t s of other authors i n steady r i s e r flows, suggest that decay of the d e n s i t y p r o f i l e with height may be due to a r a d i a l l y non-uniform s t r u c t u r e . I t appears that r a d i a l movement of s o l i d s from an upflowing core to downflowing annulus r e s u l t s i n a d e n s i t y which decays with height, with the movement perhaps accounted f o r by co n v e c t i v e gas flow and r a d i a l g r a d i e n t s i n turbulence i n t e n s i t y . T h i s p o t e n t i a l mechanism f o r decay does not preclu d e other types of s o l i d s motion. For example, decay may a l s o occur i n the core due to agglomeration of s o l i d s i n t o c l u s t e r s , with t h e i r subsequent downward motion due to - 173 -i n c r e a s e d e f f e c t i v e mass. A l s o , movement of s o l i d s towards the w a l l may be aided by e l e c t r o s t a t i c f i e l d s as i n developed pneumatic t r a n s p o r t (Soo et a_l. , 1964). However, the s t r o n g r a d i a l n o n - u n i f o r m i t i e s do suggest a predominantly core-annular s t r u c t u r e . U n f o r t u n a t e l y i t i s not p o s s i b l e to v e r i f y these ideas with the r e s u l t s of the present study; the mechanics of r a d i a l gas and s o l i d s flow, and t u r b u l e n t f l u c t u a t i o n g r a d i e n t s must remain c o n j e c t u r e u n t i l e f f e c t i v e measurement techniques f o r these parameters become a v a i l a b l e . 4.1.3 Nature of the l o c a l s o l i d s flow s t r u c t u r e To gain a b e t t e r understanding of the l o c a l nature of the two phase flow, i n a d d i t i o n to the p r o f i l e s of l o c a l d e n s i t y , which i n d i c a t e the time-averaged behaviour at a p o i n t i n the column, i t i s a l s o important to examine the instantaneous behaviour. T h i s i s r e f l e c t e d i n the time t r a c e s of d e n s i t y , shown i n F i g u r e 3.32 - 3.34, and more q u a n t i t a t i v e l y i n the standard d e v i a t i o n of the d e n s i t y about i t s mean value. F i n a l l y , the p e r i o d i c i t y of d e n s i t y f l u c t u a t i o n s i s r e f l e c t e d i n the autocovariance and a u t o s p e c t r a l d e n s i t y f u n c t i o n s . The time t r a c e of the p o i n t d e n s i t y shows dramatic changes with height. For the highest c i r c u l a t i o n r a t e at the lowest measurement p o i n t (« 533 mm above the d i s t r i b u t o r ) , the c e n t r e l i n e d e n s i t y f l u c t u a t e s d r a m a t i c a l l y - 174 -between values as high as 1200 kg/m and as low as 20-40 kg/m . The upper value represents a d e n s i t y c l o s e to the loose packed bed d e n s i t y of 1325 kg/m3 showing that the bed s t r u c t u r e at t h i s p o i n t has a strong two phase, c l u s t e r - l i k e c h a r a c t e r . However, both mean and peak d e n s i t i e s decay r a p i d l y with height along the c e n t r e l i n e as these agglomerates appear to break up and/or d i f f u s e to the w a l l r e g i o n . 914 mm above the f i r s t measurement p o i n t the l o c a l bulk d e n s i t y has decayed from 150 to b a r e l y 30 kg/m 3, and the s t r u c t u r e has given way to a much more homogeneous c e n t r e l i n e flow with o c c a s i o n a l smaller and l e s s dense packets of p a r t i c l e s passing through the probe volume. A f u r t h e r 914 mm up the column b r i n g s remarkably l i t t l e change i n the c e n t r e l i n e flow s t r u c t u r e as the l o c a l d e n s i t y appears to have decayed to a constant d e n s i t y which may be a s s o c i a t e d with a s a t u r a t e d c a r r y i n g c a p a c i t y , as d i s c u s s e d below. In order to compare p r o f i l e s on a more q u a n t i t a t i v e b a s i s , g i v i n g more i n s i g h t i n t o the two phase s t r u c t u r e of the system, i t i s u s e f u l to examine r a d i a l p r o f i l e s of the standard d e v i a t i o n . Those are shown i n F i g u r e s 3.29, 3.30 and 3.31. Although these provide a q u a n t i t a t i v e measure of the v a r i a b i l i t y of the l o c a l d e n s i t y , the curves are not e a s i l y i n t e r p r e t e d because d e n s i t y a l s o v a r i e s from poin t to p o i n t . Not s u r p r i s i n g l y , the standard d e v i a t i o n of d e n s i t y f l u c t u a t i o n s decreases from wall to c e n t r e l i n e , f o l l o w i n g the time-mean d e n s i t y d i s t r i b u t i o n . - 175 -To provide a more v a l i d comparator of the two-phase nature of the flow at d i f f e r e n t p o i n t s , an i n t e r m i t t e n c y index may be de f i n e d as: Standard D e v i a t i o n of D e n s i t y I n t e r m i t t e n c y = Y = F l u c t u a t i o n s a t a ^Y e ^ P o : f - n t p  y Y Standard D e v i a t i o n of Density F l u c t u a t i o n s f o r f u l l y segregated Two Phase Flow with I d e n t i c a l Mean d e n s i t y as at P o i n t P (4.6) The denominator i n t h i s e xpression i s d e r i v e d by c o n s i d e r i n g the f u l l y segregated or " i d e a l " two phase system as i n t e r m i t t e n t l y composed of s o l i d s - f r e e voids and loose packed regions as i n the well-known two phase theory commonly assumed to apply f o r bubbling f l u i d i s e d beds at low gas v e l o c i t i e s (Davidson and H a r r i s o n , 1963). T h i s does not imply that t h i s i s an optimum form of c o n t a c t i n g , only that the d e n s i t y can have only one of two values, zero or the d e n s i t y of a loose packed bed. At high v e l o c i t i e s t h i s flow s t r u c t u r e represents " i d e a l c l u s t e r flow" where s o l i d s are segregated i n t o loose packed c l u s t e r s of dense phase and the probe f i n d s i t s e l f e i t h e r i n these or i n gas at any i n s t a n t . The standard d e v i a t i o n of d e n s i t y f l u c t u a t i o n s f o r t h i s flow can be computed a n a l y t i c a l l y f o r any average l o c a l d e n s i t y and does not depend upon the s i z e or frequency of c l u s t e r s . I t can be shown to be: - 176 -o = p h J ^ ( 1 " p / p L } ( 4 * 7 ) 3 where p = l o c a l average s o l i d s holdup (kg/m ) 3 P L = hold-up of- s o l i d s i n loose packed bed (kg/m ) a = standard d e v i a t i o n of s o l i d s hold-up (kg/m ). T h i s i s a u s e f u l n o r m a l i s i n g f a c t o r f o r l o c a l standard d e v i a t i o n because i t i s a l s o the maximum p o s s i b l e standard d e v i a t i o n f o r a p a r t i c u l a r l y l o c a l d e n s i t y . T h e r e f o r e the i n t e r m i t t e n c y index v a r i e s between zero and u n i t y r e p r e s e n t i n g the extremes of p e r f e c t l y homogeneous and f u l l y segregated (non-homogeneous) flows. As an example of the p o s s i b l e i n t e r p r e t a t i o n of t h i s index, c o n s i d e r the extremes of f u l l y developed core-annular and i d e a l c l u s t e r flow, F i g u r e 4.4. Core-annular flow, d e s p i t e the step change i n d e n s i t y at some r a d i u s , has a uniform i n t e r m i t t e n c y index of zero over the whole c r o s s - s e c t i o n , w hile p e r f e c t c l u s t e r flow has a constant index of u n i t y . The i n t e r m i t t e n c y i n d i c e s have been c a l c u l a t e d and p l o t t e d f o r each of the measured p r o f i l e s . These p l o t s are shown i n F i g u r e s 4.5 to 4.7 f o r the three c i r c u l a t i o n f l u x e s . The index p r o f i l e s f o r the highest c i r c u l a t i o n r a t e case ( F i g u r e 4.5) give s some i n t e r e s t i n g i n s i g h t s i n t o the - 177 -C L U S T E R I N G C O R E - A N N U L A R c l u s t e r s a n n u l u s c o r e Intermittency Index V Radius Radius F i g u r e 4 . 4 I n t e r m i t t e n c y i n d i c e s as a f u n c t i o n of f o r f u l l y d e v e l o p e d c o r e - a n n u l a r and " c l u s t e r f l o w . " r a d i u s i d e a l - 178 -0.7 0 6 0 5 0-1 1—"o^o •—1—r •f Symbol Height ( O 0 533 • 1-448 A 2.362 • • 2 0 4 0 O i J I L 0 6 0 7 6 D i s t a n c e F r o m W a l l ( m m ) F i g u r e 4.5 I n t e r m i t t e n c y index p l o t t e d as a f u n c t i o n of r a d i u s at three v e r t i c a l l o c a t i o n s i n a c i r c u l a t i n g bed of sand f o r U g = 6.5 m/s, G s = 62 kg/m 2s. - 179 -F i g u r e 4.6 I n t e r m i t t e n c y index p l o t t e d as a f u n c t i o n of ra d i u s at three v e r t i c a l l o c a t i o n s i n a c i r c u l a t i n g bed of sand fo r U g = 6.5 m/s, G s = 48 kg/m 2s. - 180 -0.7 0 6 0 5 x <D •g 0 4 o § 0-3 E I 0 2 c 0-1 ~ i 1 1 1 1 r Symbol Height (m) O 0-533 • 1.448 A 2.362 J i i i * • • 0 20 40 60 76 Distance From Wall (mm) F i g u r e 4.7 I n t e r m i t t e n c y i n d e x p l o t t e d as a f u n c t i o n o f r a d i u s a t t h r e e v e r t i c a l l o c a t i o n s i n a c i r c u l a t i n g bed o f sand f o r Ug = 6.5 m/s, G s = 43 kg/m 2s. - 181 -nature of the o v e r a l l d e n s i t y p r o f i l e development. At the lowest p o i n t , d e s p i t e the strong r a d i a l g radient of d e n s i t y , the i n t e r m i t t e n c y index remains s u b s t a n t i a l l y constant over the c r o s s - s e c t i o n ; there i s a weak maximum approximately halfway between the w a l l and the c e n t r e l i n e . The high value of approximately 0.65 i n d i c a t e s a very inhomogeneous flow with i n t e r m i t t e n t packets of dense and d i l u t e phase. The near constancy of the index over the c r o s s - s e c t i o n confirms what i s seen on the instantaneous time t r a c e s of d e n s i t y , i . e . , c l u s t e r - l i k e bodies over the whole c r o s s - s e c t i o n . However, 914 mm higher up the column the p i c t u r e i s d r a m a t i c a l l y d i f f e r e n t . A r a p i d decay i n the c e n t r e l i n e inhomogeneity i s evident, presumably due to c l u s t e r breakdown and conv e c t i v e t r a n s p o r t to the wall r e g i o n . The inhomogeneity i n c r e a s e s towards the w a l l along the path of the agglomerate t r a n s p o r t and reaches a maximum of 0.47 i n the w a l l r e g i o n , 20mm from the w a l l i t s e l f . Thus, the inhomogeneity at the wall remains high, although i t too has decayed from i t s value at the column base with the o v e r a l l decrease i n d e n s i t y . F i n a l l y at the highest l e v e l of measurement, the index, together with the d e n s i t y , appears to have reached a constant value along the c e n t r e l i n e . However, inhomogeneity continues to decay i n the v i c i n i t y of the w a l l as the p r o f i l e continues to r e c t i f y towards i t s f i n a l f u l l y developed shape. I t i s important to r e a l i s e - 182 -that the f i n a l shape of the p r o f i l e i s d i c t a t e d by the e x i t geometry, a f a c t which i s r a t i o n a l i s e d i n terms of a conceptual model i n S e c t i o n 4.1.5. The other p r o f i l e s of inhomogeneity vary i n a s i m i l a r manner, except that they lac k the i n i t i a l near-constancy of the i n t e r m i t t e n c y index at the lowest l e v e l . T h i s i s probably due to lower s o l i d s c i r c u l a t i o n r a t e s and hence lower i n i t i a l suspension d e n s i t i e s i n these l a t t e r cases p r e c l u d i n g the need f o r a pronounced i n i t i a l c l u s t e r i n g . The f i n a l aspect of the s t a t i s t i c a l study of the c a p a c i t a n c e probe s i g n a l s i s r e l a t e d to s i g n a l p e r i o d i c i t y . While the mean values i n d i c a t e d time-averaged d e n s i t i e s and the inhomogeneity index gave i n f o r m a t i o n about the d i s t r i b u t i o n of d e n s i t y between d i f f e r e n t p e r c e i v e d phases, a complete p i c t u r e of the flow s t r u c t u r e r e q u i r e s knowledge of p e r i o d i c i t y of phase renewal. T h i s i s e s p e c i a l l y important f o r heat t r a n s f e r s t u d i e s . The power s p e c t r a and autocovariance f u n c t i o n s f o r c a p a c i t a n c e probe s i g n a l s from each p o i n t of one run were shown i n F i g u r e s 3.32-3.34. They are remarkable p r i m a r i l y f o r showing very l i t t l e p e r i o d i c i t y , even where there i s a r e l a t i v e l y inhomogeneous flow s t r u c t u r e - at the base of the column and the w a l l s . Although the power s p e c t r a show weak peaks i n some of these t r a c e s , the general f i n d i n g i s that at these gas v e l o c i t i e s renewal takes p l a c e f a i r l y randomly - 183 -with a power spectrum s i m i l a r to the spectrum seen f o r wide band noise (Bendat, 1980). T h i s suggests a d i f f e r e n t form of modelling of heat t r a n s f e r processes than at low v e l o c i t i e s where, f o r small p a r t i c l e s , renewal r a t e s govern the heat t r a n s f e r c o e f f i c i e n t , and where these r a t e s are well d e f i n e d by bubble processes. A s t a t i s t i c a l approach would be more v a l i d i n t h i s high v e l o c i t y s c e n a r i o . 4.1.4 Analogies with low v e l o c i t y regimes The conceptual model proposed f o r s o l i d s movement i n the decay zone of the c i r c u l a t i n g bed bears strong analogy with some d e s c r i p t i o n s and models of freeboard flow i n lower v e l o c i t y bubbling systems. C l u s t e r s t r u c t u r e s i n the freeboard of bubbling f l u i d i s e d beds appear to have been observed as e a r l y as 1962 by Lewis et aJ.. (1962). These authors d e s c r i b e s o l i d s " p r o j e c t i l e s " with d e n s i t i e s approximately that of the dense phase and a l s o "groups or streamers of p a r t i c l e s at a higher c o n c e n t r a t i o n " (than the d i s p e r s e phase), "but at a c o n c e n t r a t i o n much lower than the dense phase." They a l s o d e s c r i b e the disengaging a c t i o n of the freeboard zone as "due to the t r a n s p o r t of upward moving s o l i d s by t u r b u l e n t eddies to areas i n the d i s p e r s e phase f a v o r a b l e to downflow," i n c l u d i n g "streamers" and "regions of low gas v e l o c i t y near the column w a l l . " Lewis e_t a l . proposed a model f o r the freeboard based upon mechanistic - 184 -c o n s i d e r a t i o n s of s o l i d s upflow and downflow. However, the model does not consider s p a t i a l d i s t r i b u t i o n s of upward and downward f l u x e s . In subsequent work the concept of m u l t i p l e phases, i n c l u d i n g agglomerates thrown i n t o the freeboard from noses and wakes of bubbles, has been common i n c o n s i d e r a t i o n of e l u t r i a t i o n data. For example, K u n i i and L e v e n s p i e l (1969) proposed a model i n c o r p o r a t i n g three phases and s o l i d s t r a n s f e r between each. The three phases were a gas stream with completely d i s p e r s e d s o l i d s , p r o j e c t e d agglomerates moving upward, and descending agglomerates. Given the apparent s i m i l a r i t y between p h y s i c a l s t r u c t u r e i n c i r c u l a t i n g f l u i d i s e d beds and freeboard, one might expect to be able to apply freeboard models to the c i r c u l a t i n g bed with l i t t l e m o d i f i c a t i o n . U n f o r t u n a t e l y t h i s does not appear to be completely the case. Being one-dimensional, these e a r l y freeboard models are unable to p r e d i c t the complex r a d i a l motion of s o l i d s evident i n the c i r c u l a t i n g bed. L a t e r models (e.g., Horio jet a l . , 1980, 1985) which develop the two dimensional nature of the freeboard, and c o n s i d e r p a r t i c l e movement i n t o a descending wall zone should be b e t t e r . The drawback to a c t u a l a p p l i c a t i o n of these models to a c i r c u l a t i n g bed i s t h a t , although they represent r e a l i s t i c s o l i d s movement mechanisms, (e.g., Horio et a l . (1980) propose a r a d i a l s o l i d s movement due to - 185 -turbulence i n t e n s i t y g r a d i e n t s ) , the models are subsequently s i m p l i f i e d to give a well mixed core and a well mixed annulus. This may be v a l i d i n the bubbling bed where the freeboard turbulence generated by d i s s i p a t i o n of the energy of "ghost bubbles" g i v e s r i s e to a c l e a r demarcation between core and annular zones with f a i r l y constant p r o p e r t i e s . I t may a l s o be v a l i d i n the more d i l u t e s e c t i o n of the c i r c u l a t i n g bed r i s e r towards the top. However, i n the high d e n s i t y r e g i o n of a c i r c u l a t i n g bed, the s t r u c t u r e v a r i e s c o n t i n u o u s l y with r a d i u s , with no c l e a r core-annular demarcation, and a true two-dimensional model i s probably needed to represent the s o l i d s f l u x e s . Nonetheless, a two zone (well-mixed core, w e l l mixed annulus) model r e p r e s e n t s a u s e f u l s t a r t i n g point f o r a mechanistic model of the f a s t bed decay zone, provided that the nature of the t u r b u l e n t s t r u c t u r e i s modified to remove the c h a r a c t e r i s t i c bubble frequency and r e p l a c e i t with something more a p p r o p r i a t e to high v e l o c i t y c o n d i t i o n s . Such a model i s used with some success to d e s c r i b e gas mixing i n Chapter 6. 4.1.5 Fast f l u i d i s a t i o n and the s a t u r a t e d c a r r y i n g c a p a c i t y The capacitance probe t e s t s and pressure p r o f i l e s were used to develop a conceptual model f o r the l o c a l s o l i d s flows i n a c i r c u l a t i n g f l u i d i s e d bed. With i n t r o d u c t i o n of the concept of s a t u r a t e d c a r r y i n g c a p a c i t y , t h i s can be - 186 -extended i n t o more general ideas which help to e x p l a i n c i r c u l a t i n g bed macroscopic behaviour. For the purposes of t h i s d i s c u s s i o n we c o n s i d e r that there i s a maximum s t a b l e suspension d e n s i t y f o r g a s - s o l i d s flow i n a t a l l t r a n s p o r t l i n e at a given gas v e l o c i t y . I f the r a d i a l l y averaged s o l i d s d e n s i t y exceeds t h i s c r i t i c a l v alue then, when s o l i d s t r a n s p o r t processes such as t u r b u l e n t d i f f u s i o n cause p a r t i c l e s to move i n t o the w a l l l a y e r , they are s u f f i c i e n t l y numerous to modify the gas boundary l a y e r such that there i s a bulk p a r t i c l e downflow. Consequently the mean d e n s i t y decays. However, i f the r a d i a l l y averaged suspension d e n s i t y i s l e s s than, or equal to the c r i t i c a l d e n s i t y , the gas boundary l a y e r i s penetrated s u f f i c i e n t l y o f t e n by t u r b u l e n t gas eddies that any p a r t i c l e s tending to f a l l downward, due to average boundary l a y e r v e l o c i t i e s lower than t e r m i n a l v e l o c i t i e s , are r e e n t r a i n e d and, on the average, move upwards. It can be argued that s t a t i s t i c a l l y every p a r t i c l e w i l l e v e n t u a l l y reach the w a l l zone and has some f i n i t e , although small p r o b a b i l i t y of f a l l i n g without reentrainment so that e v e n t u a l l y , i n a s u f f i c i e n t l y t a l l v e r t i c a l pipe, complete disengagement would occur. Whether or not an i n f i n i t e l y t a l l pipe could s u s t a i n pneumatically conveyed s o l i d s i s an academic question not l i k e l y to be r e s o l v e d by experiment. P r o f i l e s i n t a l l but f i n i t e columns do appear to approach - 187 -l i m i t i n g values so that non-zero s a t u r a t e d c a r r y i n g c a p a c i t i e s appear to be reasonable f o r p r a c t i c a l purposes, j u s t as the concept of a t r a n s p o r t disengaging height (TDH), beyond which s o l i d f l u x i s independent of height, has been u s e f u l i n studying entrainment and freeboard phenomena. Note that the concept of s a t u r a t e d c a r r y i n g c a p a c i t y d e f i n e d here does not imply anything about the s t r u c t u r e of the s a t u r a t e d flow. I t only i m p l i e s that both the time-mean gas and s o l i d s v e l o c i t y and c o n c e n t r a t i o n s should be " f u l l y developed" or s t a b l e . I f the e x i s t e n c e of a s a t u r a t e d c a r r y i n g c a p a c i t y i s accepted, v e r t i c a l g a s - s o l i d two phase flows can be d i v i d e d i n t o two d i s t i n c t l y d i f f e r e n t types, those with s o l i d s c i r c u l a t i o n r a t e s lower than t h i s c a p a c i t y , and those where i t i s higher. To i l l u s t r a t e the d i f f e r e n c e s , consider a g a s - s o l i d flow i n the r i s e r of F i g u r e 4.8 which has a very smooth g r a d u a l l y curved e x i t , s i m i l a r to the e x i t No. 2 used i n t h i s study (see Chapter 3). T h i s e x i t i s assumed to have gradual enough curvature that there are no i n e r t i a l s e p a r a t i v e f o r c e s a c t i n g on p a r t i c l e s approaching i t . Hence p a r t i c l e s which t r a v e l upward through plane a-a' leave the r e a c t o r , and no p a r t i c l e s pass downward through t h i s plane. The only other notable f e a t u r e of t h i s r i s e r i s a height to diameter r a t i o of approximately 50, a s i m i l a r value to that used i n t h i s study. - 188 -EXIT PLANE SOLIDS FEED SMOOTH EXIT PROMOTING ZERO SOLIDS REFLECTION ACROSS PLANE A-A X 10 DEVELOPED FLOW ZONE REGION OF SOLIDS ACCELERATION, REDISTRIBUTION, AND BACKFLOW DENSITY GAS IN SCHEMATIC OF A SMOOTH EXIT RISER TYPICAL DENSITY PROFILE FOR TRANSPORT BELOW THE SATURATED CARRYING CAPACITY F i g u r e 4.8 A d e p i c t i o n of a smooth e x i t r i s e r f o r i l l u s t r a t i o n of the concepts i n v o l v e d with flow s t r u c t u r e s above and below the s a t u r a t e d c a r r y i n g c a p a c i t y . To the r i g h t i s a t y p i c a l d e n s i t y p r o f i l e below s a t u r a t i o n . - 189 -G a s - s o l i d s flows i n t h i s r i s e r , where the c i r c u l a t i o n r a t e i s lower than the s a t u r a t e d c a r r y i n g c a p a c i t y , are r e l a t i v e l y s t r a i g h t f o r w a r d . They are t y p i f i e d by p r o f i l e s 1 and 2 of Figure 3.14 r e p r e s e n t i n g s o l i d s c i r c u l a t i o n r a t e s of 36 kg/m 2s and 73 kg/m 2s r e s p e c t i v e l y at the p r e v a i l i n g gas v e l o c i t y of 7.1 m/s. For each of these p r o f i l e s , a le n g t h of approximately 2 m above the s o l i d s i n j e c t i o n p o i n t i s c h a r a c t e r i s e d by g r a d i e n t s i n the apparent suspension d e n s i t y caused by: ( i ) G r a d u a l l y decreasing s l i p v e l o c i t i e s as the s o l i d s are a c c e l e r a t e d to t h e i r f i n a l v e l o c i t y . ( i i ) L o c a l c i r c u l a t i o n p a t t e r n s as the s o l i d s are r e d i s t r i b u t e d from an i n i t i a l d i s t r i b u t i o n imposed by the r e t u r n system to a s t a b l e r a d i a l p a t t e r n . ( i i i ) Apparent d e n s i t y i n c r e a s e s due to a c c e l e r a t i v e pressure drop. E v e n t u a l l y , however, a s t a b l e p r o f i l e i s reached which i s c h a r a c t e r i s e d by constant suspension d e n s i t y , w i t h i n the accuracy l i m i t s of the measurement system ( ± 5 kg/m 3). V i s u a l l y one sees o c c a s i o n a l strands of p a r t i c l e s f a l l i n g down the wall over the region corresponding to these " s t a b l e " p r o f i l e s , but the strands are r a p i d l y r e e n t r a i n e d and do not s u r v i v e . Now consider the s c e n a r i o when s o l i d s are in t r o d u c e d i n t o the r i s e r at a r a t e g r e a t e r than the s a t u r a t e d c a r r y i n g - 190 -c a p a c i t y f o r the gas v e l o c i t y and column i n q u e s t i o n . In order to obtain a l o n g i t u d i n a l p r o f i l e which remains i n v a r i a n t with time, the rate at which s o l i d s leave the r e a c t o r must become equal to t h e i r feed r a t e . T h i s must take plac e although the d e n s i t y tends to decay to i t s c r i t i c a l value given s u f f i c i e n t h e i g h t . The s i t u a t i o n i s r e s o l v e d when a d e n s i t y i s e s t a b l i s h e d at the e x i t which i s gr e a t e r than c r i t i c a l , a scenario which occurs when there are s u f f i c i e n t s o l i d s i n the r i s e r that the e x i t becomes l o c a t e d i n a zone where d e n s i t y i s c o n t i n u i n g to decay with h e i g h t . P r o f i l e s 3 to 5 of Figure 3.14 i l l u s t r a t e t h i s 2 2 e f f e c t at c i r c u l a t i o n r a t e s of 93 kg/m s and 116 kg/m s r e s p e c t i v e l y , each s u c c e s s i v e p r o f i l e r e q u i r i n g a higher d e n s i t y at the e x i t plane to s a t i s f y the imposed c i r c u l a t i o n r a t e . To c l a r i f y what i s happening i n these i n s t a n c e s , i t i s e s s e n t i a l to r e l a t e macrostructure to the m i c r o s t r u c t u r a l s o l i d s c i r c u l a t i o n . Consider the s i t u a t i o n when the r i s e r i s running at, or j u s t below the s a t u r a t i o n c a r r y i n g c a p a c i t y , and a small i n c r e a s e i s made i n the r a t e at which s o l i d s are fed to the r i s e r . According to our m i c r o s t r u c t u r a l understanding of the i n t e r n a l s o l i d s movement, and our understanding of s a t u r a t i o n c a r r y i n g c a p a c i t y , these a d d i t i o n a l s o l i d s w i l l g r a d u a l l y d i f f u s e , or move c o n v e c t i v e l y , towards the wall where they begin to - 191 -form a downflowing s o l i d s wall l a y e r . Hence there i s no instantaneous e f f e c t upon output at the top of the r i s e r . However, as the newly formed downflowing l a y e r reaches the r i s e r base and s o l i d s feed p o i n t , the downflowing s o l i d s are f o r c e d i n t o the r i s e r core where they combine with f r e s h upflowing m a t e r i a l . The r e s u l t i n g higher d e n s i t y upflow core decays over a g r e a t e r length, r e i n f o r c i n g the w a l l l a y e r and i n t e r n a l c i r c u l a t i o n even f u r t h e r , a reinforcement process which continues u n t i l the developing upflow zone has the r e q u i r e d d e n s i t y at the r i s e r e x i t . The net r e s u l t of the change, shown i n F i g u r e 4.9, i s the development of an i n t e r n a l c i r c u l a t i o n p a t t e r n , where there i s a net constant u p f l u x g r e a t e r then the s a t u r a t e d c a r r y i n g c a p a c i t y . T h i s s i t u a t i o n , a l s o portrayed by Rhodes and G e l d a r t (1985), i s d r a m a t i c a l l y d i f f e r e n t than that f o r t r a n s p o r t below the s a t u r a t i o n c a r r y i n g c a p a c i t y s i n c e the whole column now operates as a developing p r o f i l e . 4.1.6. Fast f l u i d i s a t i o n and choking Small increments i n the s o l i d s c i r c u l a t i o n r a t e beyond the s a t u r a t i o n c a r r y i n g c a p a c i t y can be accommodated i n the way d e s c r i b e d above, with a developing p r o f i l e extending from the base of the column to i t s e x i t . However, i f the c i r c u l a t i o n r a t e i s i n c r e a s e d beyond some value, c a l l e d the "choking f l u x " i n t h i s d i s c u s s i o n , a dense phase with s t a b l e - 192 -DOWNFLOW UPFLOW CORE F i g u r e 4.9 A s c h e m a t i c d i a g r a m showing s o l i d s f l u x e s i n a r i s e r o p e r a t i n g above t h e s a t u r a t e d c a r r y i n g c a p a c i t y but below c h o k i n g . On the l e f t i s a s c h e m a t i c i n which a r r o w s i n d i c a t e a p p r o x i m a t e d i r e c t i o n s o f s o l i d s f l o w and show the development o f t h e w a l l l a y e r . On the r i g h t i s a s e c o n d d i a g r a m where th e w i d t h o f up and downflow a r r o w s g i v e s an i d e a of how up and downflow f l u x e s v a r y w i t h h e i g h t i n t h e u n i t t o g i v e a net p o s i t i v e f l u x . - 193 -d e n s i t y appears at the base of the column. St a b l e d e n s i t y here i m p l i e s a suspended"solids c o n c e n t r a t i o n which does not vary a p p r e c i a b l y with height, as i l l u s t r a t e d i n Figure 4.10. P r o f i l e 5 of Fi g u r e 3.14 begins to show t h i s f e a t u r e i n our own work. A s t a b l e d e n s i t y region i s a l s o shown c l e a r l y i n the r e s u l t s of L i and Kwauk (1980) reproduced i n F i g u r e 1.9. Dense phase formation occurs when the r e q u i r e d c i r c u l a t i o n rate n e c e s s i t a t e s s u f f i c i e n t d e n s i t y at the column e x i t , that, with a c o n v e n t i o n a l decay p r o f i l e , the d e n s i t y at the column base exceeds a c r i t i c a l "choking" v a l u e . To s a t i s f y the high e x i t d e n s i t y requirement, a s t a b l e dense phase forms to whatever height i s necessary f o r the normal decay process to give the r e q u i r e d imposed c i r c u l a t i o n r a t e . T h i s process gives r i s e to the c h a r a c t e r i s t i c 's' shaped p r o f i l e s of f a s t f l u i d i s a t i o n d e s c r i b e d by the model of L i and Kwauk (1980) and observed e x p e r i m e n t a l l y by Weinstein et al_. (1980) at high s o l i d f l u x e s . A p o s s i b l e m i c r o s t r u c t u r a l e x p l a n a t i o n of t h i s choking phenomenon i s a s s o c i a t e d with the development of the downflowing s o l i d s w a l l l a y e r . As the imposed s o l i d c i r c u l a t i o n r a t e i s g r a d u a l l y i n c r e a s e d , then the process of s o l i d s movement toward the w a l l and downflow cre a t e t h i c k e r and denser wall l a y e r s at the base of the u n i t . E v e n t u a l l y , the l a y e r may be s u f f i c i e n t l y t h i c k , and the rate of gas - 194 -saturated carrying capacity increasing stable dense phase choking Density F i g u r e 4.10 A schematic showing the concept of choking i n a r i s e r as a p p l i e d i n t h i s t h e s i s , and as observed i n the o v e r a l l d e n s i t y p r o f i l e . - 195 -flow through the core s u f f i c i e n t l y high, that a s u b s t a n t i a l amount of s o l i d s are s t r i p p e d from the wa l l r e g i o n . At t h i s p o i n t a dynamic e q u i l i b r i u m can be conceived between the s t r i p p i n g process and the growth process r e s u l t i n g i n s t a b l e gas and s o l i d s flow p a t t e r n s . T h i s s c e n a r i o , a l s o conceived by B r i e n s and Bergougnou (1986), i s i l l u s t r a t e d i n F i g u r e 4.11. The build-up of d i f f e r e n t amounts of t h i s " s t a b l e " phase to give d i f f e r e n t d e n s i t i e s at the r e a c t o r e x i t then becomes a very l o g i c a l and r e a d i l y explained s c e n a r i o . In t h i s d i s c u s s i o n choking has been d e f i n e d as the appearance of dense phase at the base of the t r a n s p o r t l i n e . T h i s i s a d e f i n i t i o n which i s c o n s i s t e n t with the gene r a l concept of choking as a p p l i e d to pneumatic t r a n s p o r t systems where, at some s o l i d s c i r c u l a t i o n r a t e , the incremental pressure drop r e q u i r e d f o r a small increment i n the c i r c u l a t i o n r a t e i n c r e a s e s r a p i d l y . It does not imply anything about the nature of the dense phase formed, f o r example that i t should be s l u g g i n g or produce l a r g e p r e s s u r e f l u c t u a t i o n s . 4.1.7 Fast f l u i d i s a t i o n and c i r c u l a t i n g beds - d e f i n i t i o n s D i l u t e phase t r a n s p o r t and choked flow represent two important extreme s t a t e s f o r a g a s - s o l i d s flow. In any r i s e r where the length r e q u i r e d f o r the s o l i d s d e n s i t y to decay from choked to d i l u t e i s much s h o r t e r than the r i s e r - 196 -DOWNFLOW WALL LAYER UPFLOW CORE Solids layer with zero thickness J Developing solids layer Fully developed solids layer has maximum stable thickness • choked zone tttt WW Turn around at base Net external solids flux Exit plane, upf low only due to zero reflection Solids I f e e d a t ^-s^ r—' external flux F i g u r e 4.11 A schematic diagram showing a high v e l o c i t y r i s e r o p e r a t i n g at a s o l i d s c i r c u l a t i o n r a t e g r e a t e r than choking. On the l e f t i s a schematic i n which arrows i n d i c a t e approximate d i r e c t i o n s of s o l i d s flow and show the development of the w a l l l a y e r up to i t s maximum s t a b l e (choked) t h i c k n e s s . On the r i g h t a second diagram shows how up, down, and cross f l u x e s vary with height, and shows how the c r o s s - f l u x i s i n e q u i l i b r i u m i n the choked zone. - 197 -i t s e l f , then the r i s e r w i l l operate i n e i t h e r a d i l u t e , or s u s b s t a n t i a l l y choked mode. Below the s a t u r a t i o n c a r r y i n g c a p a c i t y i t w i l l be the former, and above i t can be the l a t t e r . For such a r i s e r , f a s t f l u i d i s a t i o n e x i s t s over a range of s o l i d s c i r c u l a t i o n r a t e s from a lower value, where the s a t u r a t e d c a r r y i n g c a p a c i t y i s exceeded, to an upper value where a s t a b l e dense phase f i l l s the e n t i r e column. Between these l i m i t s there i s a region i n the r i s e r with a s u b s t a n t i a l v e r t i c a l d e n s i t y g r a d i e n t from a lower d e n s i t y value, needed to assure the imposed s o l i d s f l u x at the e x i t , to a higher value, corresponding to the choked phase d e n s i t y , lower down. Fast f l u i d i s a t i o n corresponds to t h i s t r a n s i t i o n a l ( d e n s i t y decay) region and can only e x i s t above some minimum gas v e l o c i t y where the rate of decay of d e n s i t y i s s u f f i c i e n t l y low to promote vigourous s o l i d s motion w i t h i n the zone. T h i s i s i l l u s t r a t e d i n Figure 4.12. An i n t e r e s t i n g c o r o l l a r y of t h i s d e f i n i t i o n of f a s t f l u i d i s a t i o n i s that there i s an important d i s t i n c t i o n between f a s t f l u i d i s a t i o n and the c i r c u l a t i n g f l u i d i s e d bed. The l a t t e r i m p l i e s a c o n f i g u r a t i o n and op e r a t i n g c o n d i t i o n s p r o v i d i n g f o r vigorous s o l i d s r e f l u x i n g and s u b s t a n t i a l e x t e r n a l c i r c u l a t i o n r a t e s , with l o c a l d e n s i t i e s v a r y i n g i n a gradual manner with height as the c i r c u l a t i o n rate i s v a r i e d . The l a s t f e a t u r e w i l l only be seen i f there i s l i t t l e or no choked phase present, i . e . , i f most or a l l - 198 -R E G I O N O F F A S T F L U I D I S A T I O N B O U N D A R I E S SOMEWHAT A R B I T R A R Y I I MINIMUM G I V E H I G H C I R C U L A T I O N U 6 T O 1 U Q A T W H I C H I M I N I M U M G F O R , R E F L U X I N G S S T R O N G MAXIMUM R E A S O N A B L E D E N S I T Y C A N O C C U R A T P R A C T I C A L G_ 1 LOW U g D E N S E P H A S E I S B U B B L I N G OR S L U G G I N G D E C A Y Z O N E I S V E R Y S H O R T MEDIUM U g D E N S E P H A S E IS T U R B U L E N T D E C A Y Z O N E O F I N T E R M E D I A T E L E N G T H H I G H U g D E N S E P H A S E I S V E R Y T U R B U L E N T D E C A Y Z O N E I S O F S U B S T A N T I A L L E N G T H W I T H V I G O R O U S R E F L U X I N G V . H I G H U g D E N S E P H A S E D O E S NOT FORM D E C A Y Z O N E I S A N A C C E L E R A T I O N Z O N E G s S A T I S V E R Y LOW AND R E A C T O R I S S U B S T A N T I A L L Y C H O K E D 6 S S A T 1 8 • I N T E R M E D I A T E / A L A R G E P A R T O F T H E R E A C T O R I S S T I L L C H O K E D F i g u r e 4.12 Fast f l u i d i s a t i o n d e f i n e d i n terms of a region of p o t e n t i a l gas v e l o c i t i e s and s o l i d s c i r c u l a t i o n r a t e s . - 199 -of the the column operates i n the f a s t regime. Hence, although f a s t f l u i d i s a t i o n i s a regime dependent on c i r c u l a t i o n r a t e s and gas v e l o c i t i e s , e f f e c t i v e o p e r a t i o n of a c i r c u l a t i n g bed depends a l s o upon the geometry of the u n i t . If the height of the u n i t s u b s t a n t i a l l y exceeds the height of the decay l e n g t h , then a small i n c r e a s e i n c i r c u l a t i o n r a t e above the s a t u r a t i o n c a r r y i n g c a p a c i t y w i l l c r e a t e a s u b s t a n t i a l l y choked r e a c t o r with a f a s t f l u i d i s e d regime occupying some f r a c t i o n of the top p o r t i o n . However, in a short r e a c t o r a f u l l y c i r c u l a t i n g bed meeting the above c r i t e r i a would be formed. T h i s i s shown i n Figure 4 . 1 3 . The d i s t i n c t i o n between the two i s not j u s t academic because i t impacts upon c o n t r o l l a b i l i t y of the c i r c u l a t i n g bed: i t i s d e s i r a b l e to have a gradual change of hold-up with c i r c u l a t i o n r a t e f o r c o n t r o l purposes, and i t may o f t e n be d e s i r a b l e to avoid a build-up of choked phase because of the high pressure drop which r e s u l t s . I t i s a l s o important to r e a l i s e that measurement of " t r a n s p o r t v e l o c i t y " (Yerushalmi and Cankurt, 1979 ) may be u n i t - s p e c i f i c because of height c o n s i d e r a t i o n s , and t h e r e f o r e the bounds of the f a s t f l u i d i s a t i o n regime i t s e l f , measured by e x t e r n a l methods, are a f f e c t e d . 4 . 1 . 8 S c a l e i n f l u e n c e s The notion that height can i n f l u e n c e our a b i l i t y to operate a c i r c u l a t i n g bed i s very important when c o n s i d e r i n g - 200 -Tall Riser Region of fast fluidisation Choked region Exit plane Short Riser si Exit plane Region of fast fluidisation Density Density gure 4.13 E x i s t e n c e of d i f f e r e n t flow regimes i n d i f f e r e n t height r i s e r s . In the l e f t hand r i s e r , which i s t a l l , at c i r c u l a t i o n r a t e s Gsi and G S2 the r i s e r i s s u b s t a n t i a l l y choked and small changes i n the c i r c u l a t i o n rate do not cause a l a r g e f r a c t i o n a l change i n the in v e n t o r y . In the r i g h t hand r i s e r of the same diameter, which short, the same c i r c u l a t i o n r a t e s produce dramatic f r a c t i o n a l inventory changes. T h i s s i t u a t i o n , where changes i n c i r c u l a t i o n r a t e produce large and c o n t r o l l a b l e changes i n o v e r a l l hold up, i . e . , where a f a s t f l u i d i s e d bed occupies the whole column, i s . u t i l i s e d i n c i r c u l a t i n g f l u i d i s e d beds - 201 -r e s u l t s from l a b o r a t o r y s c a l e u n i t s which may have l a r g e h e i g h t - t o diameter r a t i o s . However, f o r i n d u s t r i a l s c a l e o p e r a t i o n s there i s s t r o n g evidence that the i n c r e a s e d diameter r e s u l t s i n p r o p o r t i o n a l l y i n c r e a s e d decay l e n g t h s . F i g u r e 4.14 i s the d e n s i t y p r o f i l e from one such u n i t , a 32 m high, 8 m diameter combustor which operates at a gas v e l o c i t y of 6.4 m/s and a temperature of approximately 850°C (Wein and Felwor, 1986). E v i d e n t l y the decay length f o r t h i s u n i t i s g r e a t e r than the 32 m height of the r i s e r , as compared with decay lengths of the order of 4.5 m i n our own u n i t o p e r a t i n g at a s i m i l a r gas v e l o c i t y and s o l i d s f l u x ( P r o f i l e 3 of F i g u r e 3.14). Although there could be some i n f l u e n c e of temperature here, the r e s u l t s of Stromberg (1982) show l i t t l e e f f e c t of temperature upon d e n s i t y p r o f i l e s . I t i s p o s s i b l e to r a t i o n a l i z e longer decay lengths f o r l a r g e r diameter u n i t s based upon the s o l i d s movement model developed e a r l i e r . S o l i d s must t r a v e l longer d i s t a n c e s from the core r e g i o n to the annulus to reach a downflow zone i n l a r g e r diameter columns. If the slope of the v e l o c i t y p r o f i l e , the i n i t i a l s o l i d s d i s t r i b u t i o n , and t u r b u l e n c e i n t e n s i t i e s remain constant as the column diameter i s i n c r e a s e d , then one would a n t i c i p a t e a l i n e a r dependence of decay length upon diameter. U n f o r t u n a t e l y , there are few - 202 -G a s V e l o c i t y ( m / s ) 0 2 4 6 8 1 0 I 1 1 1 1 1 5 0 0 D e n s i t y ( k g / m 3 ) F i g u r e 4.14 D e n s i t y p r o f i l e f o r a l a r g e c i r c u l a t i n g f l u i d i s e d bed combustor (32 m h i g h x 8 m d i a . ) i n f e r r e d from d a t a p r o v i d e d by Wein and F e l w o r ( 1 9 8 6 ) . D i s c o n t i n u i t i e s i n gas v e l o c i t y a r e p o i n t s of a i r a d d i t i o n ; the g r a d i e n t r e f l e c t s a f u r n a c e e x p a n s i o n . - 203 -data showing the e f f e c t s of r e a c t o r s c a l e . Simple v i s u a l comparison of l o n g i t u d i n a l d e n s i t y p r o f i l e s suggests that decay lengths i n c r e a s e on average somewhat l e s s than l i n e a r l y with diameter, a r e s u l t which f i n d s some support by analogy with the work of Avidan (1980) who suggests that s o l i d s a x i a l d i f f u s i v i t i e s i n the t u r b u l e n t regime vary approximately l i n e a r l y with diameter at low diameter and then become approximately constant. Taking the a x i a l d i f f u s i v i t y as a measure of a mean turbulence i n t e n s i t y over a c r o s s - s e c t i o n , and r e c o g n i s i n g that t h i s i s a l s o r e s p o n s i b l e f o r r a d i a l s o l i d s motion, suggests that the decay length w i l l vary l i n e a r l y with diameter i n a l a r g e v e s s e l , but l e s s than l i n e a r l y i n a small one. This i s i l l u s t r a t e d i n Fi g u r e 4.15. 4.1.9 The imposed pressure drop phenomenon The argument of Weinstein et a_l. (1983) that an i n f i n i t e number of f a s t f l u i d i s e d bed pressure p r o f i l e s can e x i s t at any combination of gas v e l o c i t y and c i r c u l a t i o n r a t e , and that which i s found depends upon the need to s a t i s f y the "imposed drop" i s an important academic i s s u e . I t i s l e s s important p r a c t i c a l l y as shown below. Weinstein argues that a given pressure drop over the r e t u r n l e g of a c i r c u l a t i n g system i s matched by an a p p r o p r i a t e d i s t r i b u t i o n - 204 -Figure 4.15 The proposed form of a decay length versus diameter func t i o n for f a s t f l u i d i s a t i o n based upon examination of data from small and large u n i t s . - 205 -of dense phase, d i l u t e phase and decay length i n the r i s e r column with the hold-up i n dense and d i l u t e phases f u n c t i o n s of the gas v e l o c i t y and s o l i d s c i r c u l a t i o n r a t e . When attempting to apply t h i s model to design of a system u s i n g an L-valve i n the r e t u r n l e g , there i s an immediate d i f f i c u l t y . Weinstein et a_l. (1983) s t a t e that the r i s e r p r essure drop a d j u s t s to match the r e c y c l e loop, while f o r design of L-v a l v e s , Knowlton and Hirsan (1978) s t a t e t hat the L-valve a d j u s t s to the needs of the r i s e r s i d e . Our own experimental r e s u l t s support the l a t t e r , ( S e c t i o n 3.1.6), with the r i s e r pressure drop a unique f u n c t i o n of gas v e l o c i t y and s o l i d s c i r c u l a t i o n r a t e . A p o s s i b l e e x p l a n a t i o n f o r the apparent anomaly l i e s i n the d i f f e r e n t c o n s t r u c t i o n s of the u n i t s and general i n a b i l i t y to make s u f f i c i e n t l y accurate c i r c u l a t i o n r a t e d e t e r m i n a t i o n s . Two elements are key to t h i s e x p l a n a t i o n . The f i r s t i s that when a column operates i n what we have c a l l e d choke flow, with a f u l l y developed dense phase i n the lower r e g i o n s , then, because of the approximately e x p o n e n t i a l decay of d e n s i t y i n the freeboard, small changes i n c i r c u l a t i o n r a t e c l o s e to the s a t u r a t e d c a r r y i n g c a p a c i t y can produce s u b s t a n t i a l changes i n the d e n s i t y p r o f i l e . T h i s i s a r e f l e c t i o n of the f a c t that a l a r g e change i n t o t a l hold-up i s r e q u i r e d to produce a small change i n the hold-up at the e x i t plane. The second element i s r e l a t e d to - 206 -the r e c y c l e system and the need f o r a pressure balance around the c i r c u l a t i n g bed loop. A t y p i c a l c i r c u l a t i n g bed r e c y c l e loop, shown i n Figure 4.16, i s f u l l y f l u i d i s e d with a b u t t e r f l y valve or s l i d e valve f o r c o n t r o l . Now c o n s i d e r the s i t u a t i o n when a constant valve s e t t i n g i s maintained, the equipment i s loaded with a given i n v e n t o r y of s o l i d s , and the u n i t i s s t a r t e d . E v e n t u a l l y i t w i l l e q u i l i b r a t e at some c i r c u l a t i o n r a t e where the pressure drop over the r e c y c l e and r i s e r s i d e s are balanced and where the pressure drop over the s o l i d s c o n t r o l valve i s r e l a t e d to the s o l i d s f l u x . T h i s s c e n a r i o has been modelled by Rhodes and G e l d a r t (1986b). If the t o t a l inventory i s now i n c r e a s e d , then p r o v i d e d that the r e a c t o r i s t a l l compared to the decay length, a new pressure balance w i l l be e s t a b l i s h e d at almost i d e n t i c a l c i r c u l a t i o n r a t e because of the f i r s t element. Under these circumstances the pressure drop over the s o l i d s c o n t r o l valve remains almost constant with the f r e s h s o l i d s d i s t r i b u t i n g themselves between r i s e r and r e c y c l e to pr o v i d e an equal i n c r e a s e i n pressure drop i n each l e g . T h i s i s i l l u s t r a t e d i n Fig u r e 4.17. I t would take an extremely s e n s i t i v e c i r c u l a t i o n r a t e measurement to d i s t i n g u i s h the inc r e a s e d c i r c u l a t i o n r a t e of the higher i n v e n t o r y system, although such an i n c r e a s e has occurred. T h i s i s a p o s s i b l e cause f o r the f i n d i n g s of Weinstein et a l . (1983). Although there i s l i t t l e d i f f e r e n c e between the theory presented here and the theory of Weinstein et a l . f o r many - 207 -Riser i Mechanical Valve Return Leg High Velocity Air Sufficient air for fluidisation <hpair< F i g u r e 4.16 A c o n v e n t i o n a l l a b o r a t o r y c i r c u l a t i n g bed r e c y c l e loop with a f u l l y f l u i d i s e d r e t u r n c o n t r o l l e d by a mechanical (e.g., s l i d e ) v a l v e . - 208 -Small change in G s Short decay length c f . column height Density Pressure Balance: APt column AR valve' AP. return! return2 = 0 F i g u r e 4.17 A p o s s i b l e e x p l a n a t i o n f o r the apparent i n f l u e n c e of imposed pressure drop upon r i s e r o p e r a t i o n . When the decay length i s short compared to the column height, small changes i n the e x i t d e n s i t y and e x t e r n a l c i r c u l a t i o n r a t e r e s u l t from large changes i n the column inventory (pressure drop). Hence, since the pressure drop across the valve i s a f u n c t i o n only of the s o l i d s c i r c u l a t i o n r a t e , according to the pressure balance, column pressure drop appears to depend upon return leg pressure drop. - 209 -p r a c t i c a l purposes, there i s an important academic d i s t i n c t i o n . Here we p o s t u l a t e that at any gas v e l o c i t y and s o l i d s f l u x there i s only a s i n g l e unique s t a b l e s t a t e . T h i s i s d i l u t e phase below the saturated c a r r y i n g c a p a c i t y and dense phase above. Only at the s a t u r a t e d c a r r y i n g c a p a c i t y can two phases c o e x i s t . However, Weinstein et a l . propose that i n f a s t f l u i d i s a t i o n there are two s t a b l e phases f o r many d i f f e r e n t s o l i d s c i r c u l a t i o n r a t e s at the same gas v e l o c i t y . Such a theory r e q u i r e s some f a c t o r such as the imposed pressure drop to determine phase d i s t r i b u t i o n s i n a r i s e r whereas, a s i n g l e steady s t a t e theory does not. Our own theory i s very s i m i l a r to that of Rhodes and Gel d a r t (1985, 1986b) who a l s o p o s t u l a t e that f a s t f l u i d i s a t i o n i s a high v e l o c i t y freeboard phenomenon and model i t as such. Some confusion can a r i s e when ap p l y i n g the unique s t a b l e s t a t e theory to s i t u a t i o n s without c l o s e c o n t r o l over r e c i r c u l a t i o n , or with f l u o s e a l type r e t u r n s . A bubbling bed r e t u r n i n g m a t e r i a l through a cyclone d i p l e g would be a t y p i c a l example. In t h i s case the c i r c u l a t i o n r a t e must be e s t a b l i s h e d by i t e r a t i o n so that a pressure balance i s achieved over r e a c t o r and r e t u r n legs. However, the d e n s i t y p r o f i l e i s s t i l l a unique f u n c t i o n of the c i r c u l a t i o n r a t e and gas v e l o c i t y . In many such cases, p a r t i c u l a r l y i n r e a c t o r s which are t a l l compared to the decay length, then - 210 -the s t a b l e c i r c u l a t i o n r a t e would be equal to the s a t u r a t e d c a r r y i n g c a p a c i t y , the one s i t u a t i o n where we hypothesize that two s t a b l e s t a t e s can e x i s t and where in v e n t o r y (or imposed pressure drop) would i n f l u e n c e the r i s e r p r o f i l e . T h i s i s shown i n Figure 4.18. U n f o r t u n a t e l y , i t i s extremely d i f f i c u l t to show c o n c l u s i v e l y whether or not two s t a b l e s t a t e s can e x i s t i n a r e a c t o r other than at the choking f l u x . E x i t phenomena c r e a t i n g i n t e r n a l r e c i r c u l a t i o n may crea t e the appearance of a s t a b l e d i l u t e phase d e n s i t y , when the same d e n s i t y would undergo f u r t h e r decay i n a smooth e x i t column. D e f i n i t i o n s of s t a b i l i t y become c r u c i a l i n t h i s i n s t a n c e so the d i s c u s s i o n so f a r has considered only the n o n - r e f l e c t i v e e x i t . 4.2 Macrostructural Results and t h e i r Implications 4.2.1 E x i t e f f e c t s i n c i r c u l a t i n g f l u i d i s e d beds The strong e f f e c t of e x i t geometry upon c i r c u l a t i n g f l u i d i s e d bed d e n s i t y p r o f i l e s was shown i n Figure 3.15. T h i s f i g u r e compares two p r o f i l e s obtained at i d e n t i c a l gas v e l o c i t y and s o l i d s c i r c u l a t i o n rate but with two d i f f e r e n t e x i t c o n f i g u r a t i o n s . Examining the two p r o f i l e s shows that the e x i t geometry i s important because i t can i n f l u e n c e the d e n s i t y p r o f i l e , not j u s t i n the immediate v i c i n i t y of the - 211 -• • V »• * j o ° o o © ° stable dilute phase TDH stable dense phase Density Unit with medium inventory Density Unit with high inventory stable dilute phase TDH stable dense phase Two stable states form when: column height > TDH+ dense phase height and circulation rate is not controlled F i g u r e 4.18 A bubbling f l u i d i s e d bed i l l u s t r a t i n g the phenomenon of coex i s t e n c e of s t a b l e s t a t e s at choking. The bubbling bed on the l e f t , charged with a wide range of i n v e n t o r i e s (medium and high are shown here), w i l l show coex i s t e n c e of dense and d i l u t e phases, and c i r c u l a t i o n at the choking f l u x , provided the s p e c i f i e d c o n d i t i o n s are met. - 212 -e x i t , but throughout the column. In the case th i s constitutes a distance of 9.4 m, or 60 equivalent diameters. Either measure i s s i g n i f i c a n t on an i n d u s t r i a l scale i f the phenomenon i s found to also occur in large equipment. Visual observations indicate the nature of the exit e f f e c t . They indicate an i n e r t i a l separation of sol i d s from gas at the top of the abrupt exit column as the gas i s accelerated and simultaneously forced to turn in a short radius. The separation phenomenon i s shown in Figure 4.19; l i k e cyclonic separation i t i s highly velocity dependent. Separated solids cascade downwards along the wall, adding to the t o t a l density of the suspension; some are reentrained, but some continue downward to influence the p r o f i l e at a distance tens of diameters below the exit. The second and th i r d exits which were tested, which can be denoted as "smooth" and "extended" respectively, give p r o f i l e s which support the idea of the abrupt exit acting as an i n e r t i a l separator. The second exit was designed to minimise separation of solids from the gas. It has a more gradual curvature than the f i r s t combined with a gradual area reduction. There was no visual evidence of this exit causing separation, and the continuous decay of suspended soli d s density with height also suggests that this may be the case. F i n a l l y , s l i p v e l o c i t i e s calculated from Figure - 213 -Crossf lowing solids layers on roof I Gas streamlines Solids streamlines F i g u r e 4.19 Diagram showing how s o l i d s a r e s e p a r a t e d i n e r t i a l l y by an a b r u p t e x i t p r o m o t i n g i n t e r n a l c i r c u l a t i o n . - 214 -3.14 f o r t h i s e x i t approach the t e r m i n a l v e l o c i t y at the top of the column. This i s also i n d i c a t i v e of small amounts of r e f l e c t i o n . The "extended" e x i t , shown in Figure 3.13, was c o n s t r u c t e d b e l i e v i n g that i f p a r t i c l e s or c l u s t e r s , which were separated i n e r t i a l l y , were given time to d e c e l e r a t e i n an e xtension s e c t i o n , and then a c c e l e r a t e downward before encountering the gas e x i t , t h e i r higher downward v e l o c i t i e s might reduce reentrainment. T h i s might lead to higher d e n s i t i e s and s l i p v e l o c i t i e s than f o r e x i t No. 1. In p r a c t i c e , the p r o f i l e s were n e a r l y i d e n t i c a l f o r the two cases, but the reason i s not a b s o l u t e l y c l e a r . In t h i s small geometry i t seems that much of the i n e r t i a l s e p a r a t i o n r e s u l t s i n separated s o l i d s ending up i n a w a l l r e g i o n , and that much of the downflow f l u x i s due to downflow i n an annular zone. The r e s u l t f o r both e x i t s i s a downflowing wall l a y e r with s i m i l a r s t r u c t u r e , and hence s i m i l a r reentrainment c h a r a c t e r i s t i c s . A d i f f e r e n c e might be observed i n a l a r g e u n i t where separated s o l i d s are l e s s l i k e l y to t r a v e l a l l the way to the w a l l . The importance of the e x i t e f f e c t can be d i s c u s s e d on two l e v e l s : ( i ) Impact upon d e n s i t y p r o f i l e c o r r e l a t i o n s and modelling ( i i ) Impact upon design. The importance of the e x i t e f f e c t upon d e n s i t y c o r r e l a t i o n s i s that the nature of any p r e d i c t i v e equations must r e f l e c t some c h a r a c t e r i s t i c of the e x i t geometry, which can i n f l u e n c e even the b a s i c shape of the p r o f i l e . T h i s i n t r o d u c e s an a d d i t i o n a l degree of d i f f i c u l t y i n t o the problem because a complex boundary c o n d i t i o n enters i n t o any mathematical d e s c r i p t i o n of the f l u i d mechanics. I t a l s o makes decay equations, such as those of L i and Kwauk (1980) and Stromberg (1982), u n s u i t a b l e i n cases where the d e n s i t y i n c r e a s e s at the top of the r e a c t o r , and subj e c t to c o r r e c t i o n even i n cases where i t does not s i n c e l i m i t i n g d e n s i t i e s appear to be a f f e c t e d . Most s i g n i f i c a n t l y , i t i m p l i e s that the simple f l u i d mechanical model upon which the L i and Kwauk model i s based i s not s u i t a b l e f o r a l l geometric c o n f i g u r a t i o n s . A simple method which could be used to d e s c r i b e e x i t e f f e c t s , and which i s v a l u a b l e f o r i l l u s t r a t i v e purposes i s to c o n s i d e r each e x i t geometry as being c h a r a c t e r i s e d by a r e f l e c t i o n c o e f f i c e n t , a. T h i s could i d e a l l y vary from °° to 0 and would be de f i n e d as f o l l o w s : - 216 -p e = Suspension d e n s i t y at e x i t l e v e l Ug = S u p e r f i c i a l gas v e l o c i t y V-t = S i n g l e p a r t i c l e t e r m i n a l v e l o c i t y G s = S o l i d s c i r c u l a t i o n r a t e A high value of a i m p l i e s a high e x i t s l i p v e l o c i t y p o t e n t i a l l y due to c l u s t e r i n g and/or r e f l e c t i o n . It i s not p o s s i b l e to separate the two, and both imply a high degree of i n t e r n a l mixing, making a a measure of the r a t i o of i n t e r n a l to e x t e r n a l c i r c u l a t i o n r a t e s . At the other extreme, an a value of zero r e p r e s e n t s the c o n d i t i o n of no e x i t r e f l e c t i o n with an undisturbed pneumatic t r a n s p o r t stream l e a v i n g the column. In t h i s case, promoted by smooth e x i t s , the s l i p v e l o c i t y i s approximately equal to the t e r m i n a l v e l o c i t y . The p o t e n t i a l value of the parameter a, the r e f l e c t i o n c o e f f i c i e n t , i s apparent when c o n s i d e r i n g the s u i t a b i l i t y of any e x i t f o r a given design s i t u a t i o n . For example, i n c i r c u l a t i n g f l u i d i s e d bed combustion systems d i f f e r e n t designs u t i l i s e d i f f e r e n t l o c a t i o n s f o r d i f f e r e n t f r a c t i o n s of the heat t r a n s f e r s u r f a c e . F i g u r e 4.20 shows how t h i s s u r f a c e may be e i t h e r i n s i d e the c i r c u l a t i n g bed combustor, or o u t s i d e i n the r e t u r n loop, depending upon the c o n t r o l and turndown philosophy. The f i g u r e a l s o shows how the f r a c t i o n of heat exchange s u r f a c e i n the combustor can vary from u n i t y i n some designs to zero i n others, with others - 217 -Convection Pass Heat removal fraction - F3 Optional Fluid Bed Heat Exchanger Heat removal fraction - F2 Design Type F1 F2 F3 Reference Ahlstrom/Pyropower 0.5 0.0 0.5 Engstrom et al.(1985) B a t t e l l e - R l l e y 0.0 0.5 0.5 Jones et al.(1982) Lurgi/CE 0.0-0.5 0.0-0.5 0.5 Reh et a l . (1980) Studsvik/B&W 0.5 0.0 0.5 Stromberg (1982) F i g u r e 4.20 Heat t r a n s f e r s u r f a c e l o c a t i o n s f o r d i f f e r e n t commercial combustor d e s i g n s . - 218 -s t i l l o p e r a t i n g at an intermediate p o i n t . The optimum s e l e c t i o n of e x i t c o n f i g u r a t i o n i n each case i s d i c t a t e d by the r e l a t i v e amounts of i n t e r n a l and e x t e r n a l c i r c u l a t i o n r e q u i r e d f o r e f f e c t i v e o p e r a t i o n . In a u n i t with no e x t e r n a l heat exchange an e x i t geometry with maximum r e f l e c t i o n c o e f f i c i e n t should be s e l e c t e d tending to maximise i n t e r n a l mixing while minimising e x t e r n a l c i r c u l a t i o n and the cost of r e c y c l e loops. However, u n i t s with e x t e r n a l heat t r a n s f e r s u r f a c e r e q u i r e d i f f e r e n t c o n s i d e r a t i o n s . In these cases the e x t e r n a l c i r c u l a t i o n r a t e must be s u f f i c i e n t l y high to permit the r e q u i r e d amount of e x t e r n a l heat t r a n s f e r . On the other hand, i t i s s t i l l d e s i r a b l e to maintain s u b s t a n t i a l i n t e r n a l mixing to e s t a b l i s h temperature u n i f o r m i t y w i t h i n the combustor. Hence intermediate r e f l e c t i o n c o e f f i c i e n t would appear to be optimum. S i m i l a r l i n e s of t h i n k i n g suggest d i f f e r e n t optimum e x i t c o n f i g u r a t i o n s f o r other c i r c u l a t i n g bed chemical pr o c e s s e s . For example i n c a t a l y t i c c r a c k i n g or f l a s h p y r o l y s i s , where plug flow of s o l i d s i s d e s i r a b l e , a zero r e f l e c t i o n e x i t might be most s u i t a b l e although, as shown l a t e r , t h i s may a d v e r s e l y a f f e c t gas d i s p e r s i o n . In summary, v a r y i n g the geometry of a c i r c u l a t i n g f l u i d i s e d bed e x i t presents an opportunity to vary the r e l a t i v e amounts of i n t e r n a l and e x t e r n a l c i r c u l a t i o n i n the - 219 -u n i t . T h i s i n turn i n f l u e n c e s the s o l i d s mixing, the pressure drop f o r a given c i r c u l a t i o n r a t e , and the g a s - s o l i d s mass and heat t r a n s f e r c h a r a c t e r i s t i c s . I f , as appears l i k e l y , the same phenomena occur i n large s c a l e u n i t s , the e x i t geometry can be "customized" f o r a given s e r v i c e , at l e a s t with respect to the s o l i d s flow c h a r a c t e r i s t i c s , producing RTD's approximating plug flow at one extreme and mixed flow at the other. 4.2.2 E f f e c t s of secondary a i r i n t r o d u c t i o n and s o l i d s  r e t u r n l o c a t i o n L i k e the e x i t e f f e c t , phenomena a s s o c i a t e d with secondary a i r i n t r o d u c t i o n , and r e t u r n of s o l i d s high above the d i s t r i b u t o r , can be explained i n terms of the r a d i a l l y non-uniform s t r u c t u r e of the c i r c u l a t i n g bed. I n t r o d u c t i o n of secondary a i r with d i r e c t l y opposed p o r t s leads to graphs of l o n g i t u d i n a l d e n s i t y p r o f i l e s f o r d i f f e r e n t primary to secondary a i r s p l i t s at constant t o t a l v e l o c i t y as shown i n Figure 3.19. The p r o f i l e s are c h a r a c t e r i s e d by a continuous decay i n d e n s i t y from the primary d i s t r i b u t o r to where the e x i t e f f e c t becomes e v i d e n t . There appears to be a s l i g h t d i s c o n t i n u i t y i n the slope of the de n s i t y p r o f i l e at the secondary a i r p o r t s . As one would a n t i c i p a t e , lower primary v e l o c i t y promotes higher primary zone d e n s i t y , but at the top of the r e a c t o r the - 220 -p r o f i l e s are i d e n t i c a l . The p r o f i l e s can be explained by c o n s i d e r i n g two r i s e r s on top of one another j o i n e d at the secondary a i r ports by an upflowing core and downflowing annular exchange of s o l i d s . The p r o f i l e s obtained with s w i r l ( t a n g e n t i a l entry) secondary a i r are remarkably d i f f e r e n t , F i g u r e 3.20. In these cases there i s a d i s c o n t i n u i t y i n the grad i e n t of the d e n s i t y p r o f i l e and a high d e n s i t y zone where the secondary a i r i s i n t r o d u c e d . V i s u a l l y i t was apparent that the d i f f e r e n c e was caused by the tendency f o r the s w i r l secondary a i r to pi c k up annulus p a r t i c l e s by v i r t u e of the high angular v e l o c i t i e s , f o r c i n g the downflowing l a y e r upward ag a i n s t i t s e l f , and i n t o the centre of the r e a c t o r where i t was r e e n t r a i n e d . Thus, while the downflowing s o l i d s annulus could cascade between the opposed p o r t s , p e r m i t t i n g both core and annular s o l i d s to be exchanged between the upper and lower zones, the s w i r l a i r prevented the l a t t e r . F o r c i n g the annular s o l i d s to turn around i n t h i s manner promotes a high d e n s i t y r e g i o n at the base of what e f f e c t i v e l y becomes a separated zone. It was not p o s s i b l e to determine whether the s w i r l a i r had a s u b s t a n t i a l c y c l o n i c e f f e c t , tending to i n t e n s i f y the core-annulus phenomena of f a s t f l u i d i s a t i o n . One might a n t i c i p a t e decreased decay lengths due to increased rates of s o l i d s t r a n s f e r to the wall area. However, when s w i r l a i r - 221 -i s i n t roduced i n the secondary mode, promoting reentrainment, i t i s not p o s s i b l e to compare decay lengths i n a meaningful way with the conv e n t i o n a l a i r d i s t r i b u t i o n . If the s w i r l a i r was used as primary a i r a v a l i d comparison co u l d be made s i n c e s o l i d s w i l l be r e e n t r a i n e d at t h i s l o c a t i o n by the d i s t r i b u t o r i r r e s p e c t i v e of the type of a i r i n t r o d u c t i o n . I n t r o d u c t i o n of s o l i d s some d i s t a n c e above the d i s t r i b u t o r p l a t e i s i n some ways l i k e s w i r l a i r i n t r o d u c t i o n . Both a f f e c t the normal exchange of s o l i d s between upper and lower bed zones. By r e t u r n i n g the r e c y c l e d s o l i d s high up i n the column, two separate zones are formed. T h i s can be seen i n Figures 3.9 to 3.12. The lower bed has no net v e r t i c a l f l u x of s o l i d s , analogous to the s i t u a t i o n of t o t a l f l u x i n a d i s t i l l a t i o n column. S o l i d s are fed by annular downflow from the upper s e c t i o n , f a l l down the w a l l , and change d i r e c t i o n at the base of the u n i t . An i n t e r n a l c i r c u l a t i o n p a t t e r n appears to be e s t a b l i s h e d j u s t as i n a co n v e n t i o n a l c i r c u l a t i n g bed, with a c h a r a c t e r i s t i c decay of d e n s i t y with height due to r a d i a l t r a n s f e r . A l i k e l y p i c t u r e of how the upward and downward s o l i d s f l u x e s vary with height i s shown i n Figure 4.21. Above the s o l i d s r e t u r n port a second zone i s formed which i s more conv e n t i o n a l than the lower zone i n the sense that there i s a net v e r t i c a l f l u x of s o l i d s . T h i s f l u x , and the - 222 -DOWNFLOW UPFLOW CORE LAYER | Gas in Figure 4.21 Variation of solids fluxes in a c i r c u l a t i n g f l u i d i s e d bed with solids return some distance above the gas di s t r i b u t o r . The density p r o f i l e on the l e f t hand side, typical of the fast bed with elevated s o l i d s return, i s thought to be caused by up, down, and cross fluxes as shown on the right-hand side. There i s a lower zone of zero so l i d s flux, an upper zone of net upward flux, and a complex crossflow pattern, p a r t i c u l a r l y at the return location where downflowing solids are displaced from the wall into the core. - 223 -f a c t t h at r e t u r n i n g s o l i d s d i s t u r b the downflowing annulus, f o r c i n g s o l i d s to the core, c o n t r i b u t e to the high d e n s i t i e s at the base of t h i s upper zone. - 224 -5. THE TRANSITION TO TURBULENT FLUIDISATION - A BRIEF STUDY 5.1 Introduction In a d d i t i o n to p r o v i d i n g an op p o r t u n i t y to study the f l u i d mechanics of f a s t f l u i d i s e d beds, the design of the c i r c u l a t i n g bed u n i t a l s o allows o p e r a t i o n at low f l u i d i s a t i o n v e l o c i t i e s i n the bubbling and s o - c a l l e d t u r b u l e n t regimes. Examination of the l i t e r a t u r e r e v e a l s widely d i f f e r i n g views about the nature of the t u r b u l e n t regime i n p a r t i c u l a r , and i t s r e l a t i o n s h i p to the s l u g g i n g regime and to choking. Notably, while authors such as Avidan (1980) and Yong et a_l. (1986) suggest that the t u r b u l e n t regime corresponds to a s t a b l e suspension of p a r t i c l e c l u s t e r s , Rhodes and Ge l d a r t (1986a) contend that, although t u r b u l e n t f l u i d i s a t i o n may occur i n t h i s manner i n la r g e beds of f i n e power c a t a l y s t s , the t u r b u l e n t f l u i d i s a t i o n observed by many authors i s not a regime t r a n s i t i o n but a t r a n s f e r of s o l i d s to a r e f l u x i n g f r eeboard zone. Our own work i n t h i s area had two o b j e c t i v e s . The f i r s t was to i d e n t i f y what low v e l o c i t y regimes e x i s t f o r the 169 pm diameter sand used during most of t h i s i n v e s t i g a t i o n , and to i d e n t i f y whether or not there i s a dramatic t r a n s i t i o n between these low v e l o c i t y regimes and the c i r c u l a t i n g bed s t a t e . The second was to c r i t i c a l l y - 225 -examine the regime t r a n s i t i o n l i t e r a t u r e i n the l i g h t of our own r e s u l t s . 5.2 A Br i e f History of Turbulent F l u i d i s a t i o n The f i r s t o b s e r v a t i o n of a t r a n s i t i o n from a bubbling or s l u g g i n g f l u i d i s e d bed to a more homogeneous suspension i s g e n e r a l l y a t t r i b u t e d to Lanneau (1960). However, there are r e f e r e n c e s to a smooth d i s p e r s e phase f l u i d i s a t i o n i n a t r a n s p o r t l i n e , at v e l o c i t i e s somewhere beyond s l u g g i n g , as e a r l y as 1949 (Zenz, 1949). T h i s paper mentions voidages i n the range 0.9-1.0, and the f a c t that the movement of p a r t i c l e s becomes "extremely t u r b u l e n t " , o b s e r v a t i o n s which suggest that Zenz observed at l e a s t G e l d a r t ' s t u r b u l e n t t r a n s i t i o n . D e s p i t e these e a r l y o b s e r v a t i o n s of an apparently more homogeneous s t a t e , which i n Lanneau's case went as f a r as d e f i n i n g a hete r o g e n e i t y index and making d e t a i l e d c a p a c i t a n c e probe measurements, no f u r t h e r l i t e r a t u r e appeared f o r another decade u n t i l Kehoe and Davidson (1971), studying s l u g g i n g beds, observed that at high v e l o c i t i e s t h i s regime breaks down i n t o "a s t a t e of continuous coalescence - v i r t u a l l y a c h a n n e l l i n g s t a t e with tongues of f l u i d d a r t i n g i n a z i g zag f a s h i o n through the bed." They c a l l e d t h i s the " t u r b u l e n t regime" to d i s t i n g u i s h i t from bubbling or s l u g g i n g and to imply a very d i f f e r e n t - 226 -modus operandi compared to the well ordered s l u g g i n g s t a t e -It i s important to reproduce t h i s e a r l y d e s c r i p t i o n of the t u r b u l e n t bed to i n d i c a t e what t u r b u l e n t f l u i d i s a t i o n i s intended to imply, i . e . , a regime d i s t i n c t from s l u g g i n g with f i n e r s c a l e higher frequency inhomogeneities. The regime t r a n s i t i o n seems intended to imply a r e o r d e r i n g of the bed s t r u c t u r e to a new s t a t e , s t a b l e i n the same sense that a bubbling or s l u g g i n g bed i s s t a b l e , and d i s t i n c t from a freeboard s t r u c t u r e which i s unstable i n the sense that voidage i n c r e a s e s with h e i g h t . Whether or not t h i s i s i n f a c t what was observed w i l l be l e f t unanswered at t h i s p o i n t . The work by Kehoe and Davidson (1971) was followed by o b s e r v a t i o n s of t u r b u l e n t f l u i d i s a t i o n by other workers. M a s s i m i l l a (1973) e s t a b l i s h e d that the t u r b u l e n t regime, whatever i t s nature, o f f e r s b e t t e r c o n t a c t i n g than the s l u g g i n g regime by v i r t u e of a breakdown of the two phase s t r u c t u r e . Studying the c a t a l y t i c o x i d a t i o n of propylene, M a s s i m i l l a found that two phase models, s u i t a b l e f o r s l u g flow, d r a m a t i c a l l y u n d e r p r e d i c t t u r b u l e n t bed c o n v e r s i o n . Capacitance probe s i g n a l s gave some i n d i c a t i o n of the nature of the t r a n s i t i o n , suggesting s l u g breakdown and coalescence, but there i s no i n d i c a t i o n i n t h i s study that a high degree of u n i f o r m i t y was obtained. Carotenuto et a l . (1974) and C r e s c i t e l l i et a l . (1975) pro v i d e a c l e a r e r i n s i g h t i n t o the nature of the t u r b u l e n t - 227 -t r a n s i t i o n . Both authors examined capacitance probe s i g n a l s from beds of f i n e s o l i d s (< 300 ym dia.) and show that the t r a n s i t i o n to t u r b u l e n t f l u i d i s a t i o n can be i d e n t i f i e d with an i n c r e a s e d p r o b a b i l i t y of l o c a l d e n s i t i e s o c c u r r i n g which are intermediate between those dense and d i l u t e phases found i n bubbling and s l u g g i n g beds. T h e i l and P o t t e r (1977) presented experimental data and o b s e r v a t i o n s on flow t r a n s i t i o n s from s l u g g i n g to t u r b u l e n t f l u i d i s a t i o n . These i n i t i a l papers led to a more focussed study of t u r b u l e n t f l u i d i s a t i o n at CUNY (Turner, 13 78; Avidan, 1980). Turner (1978) in t r o d u c e d the concept of using pressure f l u c t u a t i o n s , r a t h e r than capacitance probe s i g n a l s , to i d e n t i f y the onset of the t u r b u l e n t regime. Dimensionless pressure f l u c t u a t i o n s (peak to peak a b s o l u t e p r e s s u r e d i v i d e d by average t o t a l bed and freeboard pressure drop) were p l o t t e d a gainst gas v e l o c i t y . T h i s r a t i o was found to r i s e to a peak and then decrease. The peak was s a i d to s i g n i f y the onset of the t u r b u l e n t t r a n s i t i o n , and f u l l y t u r b u l e n t f l u i d i s a t i o n was s a i d to e x i s t when the r a t i o a t t a i n a constant value. Figure 5.1 i s a t y p i c a l p l o t of t h i s r a t i o taken from Turner's work with the symbols U c and Uk introduced to denote the onset of the t r a n s i t i o n and the f u l l y t u r b u l e n t s t a t e r e s p e c t i v e l y . Avidan (1980) s t u d i e d the p r o p e r t i e s of the t u r b u l e n t regime, notably bed expansion, and d e f i n e d a t r a n s i t i o n - 228 -SOLIDS *HFZ- 20 G A S V E L O C I T Y U (m/$) F i g u r e 5.1 D i m e n s i o n l e s s p r e s s u r e f l u c t u a t i o n s and o v e r a l l bed d e n s i t y p l o t t e d a g a i n s t gas v e l o c i t y t o i l l u s t r a t e t h e o n s e t o f the t u r b u l e n t t r a n s i t i o n , U c , and the f u l l y t u r b u l e n t s t a t e , Uk ( T u r n e r 1978). - 229 -based on a dramatic change i n slope of a Richardson-Zaki (1954) p l o t , ( l o g e vs. log U). Avidan v i s u a l i s e d a t u r b u l e n t bed composed of a uniform d i s p e r s i o n of c l u s t e r s i n gas, and s i z e s were computed f o r c l u s t e r s based on an approach proposed by Capes (1974) u t i l i s i n g a modified Richardson-Zaki e x p r e s s i o n . These s i z e s ( e q u i v a l e n t c l u s t e r s diameters of the order of 4 mm i n the t u r b u l e n t regime) are s i m i l a r to s i z e s computed by Yerushalmi et a l . (1978) using a d i f f e r e n t approach. S o l i d s mixing was c o r r e l a t e d using an a x i a l d i f f u s i v i t y , which i n i t s e l f i s s u g g e s t i v e of a much more homogeneous random s t r u c t u r e than one f i n d s i n the bubbling or s l u g g i n g regimes; two phase, multi-parameter mixing models such as those of Davidson and H a r r i s o n (1963) or K u n i i and L e v e n s p i e l (1969) are t y p i c a l l y used i n these lower v e l o c i t y regimes. P o s s i b l y because of the r e l a t i v e ease with which the p r e s s u r e measurements can be made, a number of subsequent authors have followed Turner i n i d e n t i f y i n g a decrease i n some form of pressure f l u c t u a t i o n with the onset of t u r b u l e n t f l u i d i s a t i o n . These i n c l u d e Canada et a l . (1978), and Yong et aJ. (1986). Rhodes and G e l d a r t (1986a) have questioned the v a l i d i t y of using pressure f l u c t u a t i o n s alone as a t u r b u l e n t t r a n s i t i o n c r i t e r i o n . They suggest that a decrease i n pressure f l u c t u a t i o n s does not i n r e a l i t y denote a - 230 -fundamental r e s t r u c t u r i n g of the bed to a new regime with a s t a b l e c l u s t e r suspension. Rather, they argue that the pressure s i g n a l which they observed can be ex p l a i n e d simply by c o n s i d e r i n g the i n c r e a s i n g t r a n s f e r of m a t e r i a l to the freebo a r d , and hence the decreasing bed l e v e l , with i n c r e a s i n g s u p e r f i c i a l gas v e l o c i t y . In a separate paper (G e l d a r t and Rhodes, 1985), they a l s o argue a g a i n s t a s t a b l e suspension of c l u s t e r s on the grounds that s l i p v e l o c i t y data, used e x t e n s i v e l y to support c l u s t e r theory, can a l s o be e x p l a i n e d by r a d i a l n o n - u n i f o r m i t i e s i n the t u r b u l e n t regime. These have been found e x p e r i m e n t a l l y by Abed (1983). To summarise, at the time when we made our t u r b u l e n t t r a n s i t i o n measurements, there was a body of e x i s t i n g l i t e r a t u r e a v a i l a b l e and two apparently c o n f l i c t i n g t h e o r i e s which sought to e x p l a i n the reported o b s e r v a t i o n s . I t seemed d e s i r a b l e to design an experiment which at best would r e s o l v e the d i f f e r e n c e s between the two t h e o r i e s , or at l e a s t c l a r i f y what happens i n our own system. 5.3. Experimental Design The low v e l o c i t y f l u i d i s a t i o n experiments were conducted with the equipment set up as shown i n Fi g u r e 3.8. The changes i n c o n f i g u r a t i o n were necessary because, when i n i t i a l t e s t s were run with the s o l i d s returned to the base - 231 -of the u n i t , the L-valve tended to discharge s o l i d s i f the column was run i n the sl u g g i n g mode. With the column set up with a r e t u r n p o i n t above the bed l e v e l , leakage was no problem and a small c o n t r o l l e d s o l i d s flow could be maintained through the L-valve to match the e l u t r i a t i o n r a t e . The r e q u i r e d c i r c u l a t i o n at each gas v e l o c i t y was determined by a t r i a l and e r r o r process i n which the c i r c u l a t i o n was i n c r e a s e d u n t i l a d e s i r e d a b s o l u t e p r e s s u r e was a t t a i n e d i n the windbox. T h i s pressure was a measure of the bed in v e n t o r y under c o n d i t i o n s where the f r a c t i o n a l pressure drop f o r gas flow through the d i s t r i b u t o r and cyclones was small ( t y p i c a l l y 0.5 kPa and 0.2 kPa r e s p e c t i v e l y ) compared to the d i f f e r e n t i a l pressure over the bed of s o l i d s of approximately 9 kPa. Table 5.1 t a b u l a t e s the work to date on t u r b u l e n t f l u i d i s a t i o n . P a r t i c u l a r a t t e n t i o n has been given to the method by which the t u r b u l e n t t r a n s i t i o n was i d e n t i f i e d , e s p e c i a l l y when t h i s i n v o l v e d measurement of pressure f l u c t u a t i o n s . The t a b l e shows that Turner (1978) and Canada et a l . (1978) both r e l a t e d regime t r a n s i t i o n s to a b s o l u t e pressure f l u c t u a t i o n s which, depending upon the author, may or may not have been made dimensionless by d i v i s i o n by the o v e r a l l column pressure drop. On the other hand, Yong et a l . (1986) and Rhodes and G e l d a r t (1986a) both used d i f f e r e n t i a l pressure f l u c t u a t i o n s between a p o i n t i n - 232 -Table 5.1 References f o r Turbulent F l u i d i s a t i o n S t u d i e s and Methods Used to I d e n t i f y the Turbulent T r a n s i t i o n Reference Technique(s) Used Lanneau (1960) Capacitance probe s i g n a l s used to c a l c u l a t e a heterogeneity index equal to the mean l o c a l d e v i a t i o n of bed d e n s i t y about the l o c a l average d e n s i t y . Heterogeneity maximised i n the s l u g g i n g regime. Kehoe & Davidson (1971) Capacitance probe s i g n a l s and X - r a y photographs used to i n f e r breakdown of the s l u g g i n g regime. M a s s i m i l l a (1973) Capacitance probe s i g n a l s and d e v i a t i o n of bed expansion data from s l u g flow theory used to i n f e r breakdown of the s l u g g i n g regime. Carotenuto et a l . (1974) P r o b a b i l i t y d e n s i t y f u n c t i o n s f o r c a p a c i t a n c e probe s i g n a l s were p l o t t e d and found to become unimodal at t r a n s i t i o n . T h i e l & P o t t e r (1977) Turner (1979) Canada et a l . (1975) V i s u a l o b s e r v a t i o n of breakdown of slugs. Measurement of manometer pressure f l u c t u a t i o n s between the base of the bed and the top of the freeboard give p l o t s of peak to peak f l u c t u a t i o n s d i v i d e d by t o t a l bed pressure drop which showed maxima at the "beginning of the t r a n s i t i o n to t u r b u l e n c e . " E f f e c t i v e l y an absolute pressure f l u c t u a t i o n . As per Turner (1978), but using a pressure transducer rather than a manometer. C r e s c i t e l l i jet a l (1978) Loss of p e r i o d i c i t y of a u t o c o r r e l a t i o n f u n c t i o n of capacitance probe s i g n a l s and gradual decrease i n absolute pressure f l u c t u a t i o n s used to s i g n i f y breakdown. Table 5.1 Cont'd - 233 -Reference Technique(s) Used Avidan (1980) Abed (1983) Change i n slope of Richardson - Zaki p l o t , ( l o g e vs log u) used to i d e n t i f y t r a n s i t i o n . V i s u a l determination of bed height gave e. Changes i n the vari a n c e and skewness of the p r o b a b i l i t y d e n s i t y f u n c t i o n s of capacitance probe s i g n a l s at d i f f e r e n t r a d i i used to i n f e r t r a n s i t i o n . S a t i j a & Fan (1985) Yong et a l . (19861 Rhodes & G e l d a r t (1986a) Absolute pressure f l u c t a t i o n s measured by transducers were monitored above the bed, and the t u r b u l e n t t r a n s i t i o n d e f i n e d as the p o i n t where there was a zero p r o b a b i l i t y of zero p r e s s u r e . I d e n t i f i e d the beginning of the t u r b u l e n t t r a n s i t i o n using d i f f e r e n t s t a t i s t i c a l manipulations of d i f f e r e n t i a l pressure f l u c t u a t i o n data measured with t r a n s d u c e r s . These were c a l l e d a "nonuniformity c o e f f i c i e n t i n the time domain" and a "nonuniformity c o e f f i c i e n t i n the frequency domain. D i f f e r e n t i a l pressure f l u c t u a t i o n s measured using manometers used to i n f e r a " p s e u d o - t r a n s i t i o n " to t u r b u l e n c e . - 234 -the bed and a second p o i n t , j u s t above the d i s t r i b u t o r , to i d e n t i f y what i s presumably the same t r a n s i t i o n . As shown below, i t i s not c l e a r that these two techniques are i d e n t i c a l . In t h i s study a s l i g h t l y d i f f e r e n t approach was taken; d i f f e r e n t i a l pressures were measured between two p o i n t s 460 mm apart, with the lower p o i n t l o c a t e d 230 mm above the d i s t r i b u t o r p l a t e . T h i s set-up was considered p r e f e r a b l e to measurement of absolute pressure because i n t e g r a t i o n of the d i f f e r e n t i a l pressure s i g n a l would give a measure of the bed voidage and more importantly e s t a b l i s h whether or not the upper bed surface had f a l l e n below the upper pressure tap. I t i s important to note, however, that mean bed voidage cannot be estimated at a l l a c c u r a t e l y i n the s l u g g i n g regime by t h i s method because of a c c e l e r a t i o n and d e c e l e r a t i o n e f f e c t s (Kehoe and Davidson, 1973). T h i s i s shown c l e a r l y i n the r e s u l t s . With t h i s experimental design a s e r i e s of experiments was performed i n which the s u p e r f i c i a l gas v e l o c i t y was g r a d u a l l y r a i s e d from 0.05 m/s to 4 m/s, stopping at r e g u l a r i n t e r v a l s to make measurements. At each measurement v e l o c i t y i t was f i r s t e s t a b l i s h e d that dense phase covered the upper pressure tap and that e l u t r i a t i o n r a t e s and r e t u r n r a t e s were i n balance at a wind box pressure of 10 kPa. T h i s corresponded to a loose packed bed height of 850 mm of - 235 -s o l i d s . Pressure f l u c t u a t i o n s were logged over the measurement s e c t i o n using the Disa high s e n s i t i v i t y pressure t r a n s d u c e r (with a 0.2 mm diaphragm) connected to the IBM-XT through the Tecmar board. Each s i g n a l was logged f o r 60 s at a sampling r a t e of 100 p o i n t s per second and was recorded s i m u l t a n e o u s l y i n analogue format on the UV chart r e c o r d e r . 5.4. Results and Discussion Each data f i l e obtained from the low v e l o c i t y f l u i d i s a t i o n s t u d i e s was i n t e g r a t e d to o b t a i n the apparent mean s o l i d s hold-up, and then analysed to o b t a i n the standard d e v i a t i o n . The r e s u l t s could then be combined with v i s u a l o b s e r v a t i o n s of the experiments to gain some i n s i g h t s i n t o the behavior of the system. F i g u r e s 5.2a-h are t r a c e s of the d i f f e r e n t i a l pressure s i g n a l f o r the bed f o r s e l e c t e d cases over the o p e r a t i n g range. Beside each f i g u r e i s a d e s c r i p t i o n of what was observed i n the column at the time when the t r a c e was recorded. At v e l o c i t i e s up to approximately 1 m/s the behaviour of the f l u i d i s e d bed i s e x a c t l y as one would a n t i c i p a t e ; bubbling gives way to s l u g g i n g at 0.12 m/s and from here to approximately 1 m/s both the d i f f e r e n t i a l pressure s i g n a l s and v i s u a l o bservations are c o n s i s t e n t with the s l u g g i n g regime. At higher v e l o c i t i e s there i s evidence of some - 236 -> CO W T-1 T w a. 0-11 m/s VIGOROUS BUBBLING, VERGING ON SLUGGING C > 5 1 0 1 5 2 0 V 6 -4-2 -b. 0-19 m/s DEVELOPED SLUGGING WITH CLEAR TWO PHASE STRUCTURE AND STRONG PERIODICITY 0 5 1 0 ' 1 5 " 2 0 ' T w V 6 -4-2 -1 i c- 0-40 m/s AGAIN, DEVELOPED SLUGGING WITH CLEAR TWO PHASE STRUCTURE 0 5 " 1 0 " 1 5 2 0 ' T r Vi 6 -d. 0-57 m/s SOME VISUAL EVIDENCE FOR A SMALL AMOUNT OF SLUG BREAKDOWN 0 2 4 6 8 1 0 T F i g u r e 5-2 Traces of the d i f f e r e n t i a l p r e s s u r e f l u c t u a t i o n , as i n d i c a t e d by t r a n s d u c e r v o l t a g e , v e r s u s time i n seconds over a 400 mm s e c t i o n of a bed of sand at d i f f e r e n t gas v e l o c i t i e s a - 0.11 m/s, b - 0.19 m/s, c - 0.40 m/s, d - 0.57 m/s, e - 1.25 m/s, f - 2.14 m/s, g - 2.9 m/s, h - 3.9 m/s - 237 -6 8 1 0 T e. 1-25 m/s IRREGULAR INTERMITTENT PERIODS OF A MORE UNIFORM NATURE, VISUALLY LIKE FAST FLUIDISATION f. 2-14m/s INCREASINGLY REGULAR PERIODS OF UNIFORMITY WITH INCREASED LENGTH, BUT STILL PERIODIC SLUGGING 9. 2-9 m/s CONTINUOUS SOLIDS ADDITION REQUIRED AT A LOW RATE, FURTHER INCREASED UNIFORMITY h.3-9 m/s SUBSTANTIAL ENTRAINMENT, MOSTLY UNIFORM, BUT STILL SOME SLUGGING CHARACTER - 238 -s l u g s breaking down; per i o d s are observed between w e l l developed slugs during which the pressure transducer r e g i s t e r s smaller f l u c t u a t i o n s of higher frequency. These p e r i o d s corresponded v i s u a l l y to times when s o l i d s seemed t o be cascading downwards along the w a l l s , between s l u g s , i n p a t t e r n s very s i m i l a r to those found i n the higher v e l o c i t y c i r c u l a t i n g regime. These s i g n a l s p e r s i s t e d up to the hi g h e s t s u p e r f i c i a l gas v e l o c i t y s t u d i e d i n these t e s t s , 4.0 m/s, with the f r a c t i o n of time corresponding to what we s h a l l c a l l " t u r b u l e n c e " g r a d u a l l y i n c r e a s i n g with i n c r e a s i n g s u p e r f i c i a l v e l o c i t y . At the highest v e l o c i t y s u b s t a n t i a l entrainment was o c c u r i n g , with measured c i r c u l a t i o n r a t e s g r e a t e r than 12 kg/m 2s. However, a p e r i o d i c component, which was v i s u a l l y i d e n t i c a l to s l u g g i n g , was s t i l l e v i d ent i n the pressure t r a c e d e s p i t e the f a c t that t h i s was the low end of the c i r c u l a t i n g regime. V e l o c i t i e s had to exceed 5 m/s before a s t a b l e dense phase could be e s t a b l i s h e d which covered both pressure taps and showed no sl u g g i n g tendency. The r e s u l t s are a l s o p l o t t e d as graphs of apparent s o l i d s hold up, s o l i d s hold-up standard d e v i a t i o n , normalised standard d e v i a t i o n , and peak to peak pressure f l u c t u a t i o n versus gas v e l o c i t y i n Fi g u r e s 5.3 to 5.6 r e s p e c t i v e l y . The f i r s t graph, Figure 5.3, i s important because i t i n d i c a t e s that the mean pressure drop i s a smooth f u n c t i o n of gas v e l o c i t y c o n f i r m i n g , what i s observed - 239 -0 1 2 Superficial Gas Velocity (m /s ) F i g u r e 5.3 P l o t of apparent s o l i d s volume f r a c t i o n versus s u p e r f i c i a l gas v e l o c i t y f o r a f l u i d i s e d bed of sand i n a 0.152 m diameter r e a c t o r . - 240 -(0 a. o — — a 2 (0 TJ C 3 (0 4-> a) 0 1 2 Superf ic ia l Gas Velocity ( m / s ) F i g u r e 5.4 P l o t of standard d e v i a t i o n of d i f f e r e n t i a l pressure f l u c t u a t i o n s over a 460 mm length of a f l u i d i s e d bed of sand versus s u p e r f i c i a l gas v e l o c i t y . - 241 -0-8 0 6 c o .2 '> o Q "a c CO c o 0-4 0-2 0 1 1 1 1 1 o o o o o ° o o o o o o o -o -o o - o -o _ 1 1 1 1 1 0 1 2 Superf ic ia l Gas Velocity ( m / s ) F i g u r e 5.5 P l o t of the standard d e v i a t i o n of d i f f e r e n t i a l pressure f l u c t u a t i o n s normalised w.r.t. mean d i f f e r e n t i a l pressure, over a 460 mm s e c t i o n of a f l u i d i s e d bed of sand, versus s u p e r f i c i a l gas v e l o c i t y . - 242 -0 1 2 Superf ic ia l Gas Velocity ( m / s ) F i g u r e 5.6 P l o t of the maximum peak-to-peak pressure f l u c t u a t i o n over a 460 mm s e c t i o n of a f l u i d i s e d bed of sand versus s u p e r f i c i a l gas v e l o c i t y . - 243 -v i s u a l l y , that the bed l e v e l has not dropped below the upper pressure tap. In d i s c u s s i n g the r e s u l t s of t h i s study i t i s important to r e a l i s e that the v a r i o u s methods used to i n d i c a t e a t u r b u l e n t t r a n s i t i o n are not n e c e s s a r i l y i d e n t i c a l ; t h e i r s u i t a b i l i t y w i l l depend upon what one envisages the t r a n s i t i o n to be. I f the t r a n s i t i o n i s seen as being a t r a n s i t i o n to a s t a b l e c l u s t e r suspension, then c a p a c i t a n c e probe s i g n a l s are i d e a l t r a n s i t i o n i n d i c a t o r s . The s i g n a l can be analysed both f o r i t s p r o b a b i l i t y d e n s i t y f u n c t i o n and i t s a u t o c o r r e l a t i o n which should s h i f t from a c h a r a c t e r i s t i c bimodal p.d.f. with a w e l l defined low frequency i n the s l u g g i n g regime to a more unimodal p.d.f. with a l e s s w ell d e f i n e d , higher frequency autospectrum i n the t u r b u l e n t s t a t e . T h i s r e s u l t has been demonstrated by Carotenuto et aJ. (1974) f o r a f l u i d c r a c k i n g c a t a l y s t of 60 um s u r f a c e mean diameter and by C r e s c i t e l l i et a J . (1978) f o r a Ludox c a t a l y s t of s i m i l a r diameter. I n t e r p r e t a t i o n of a b s o l u t e pressure s i g n a l s i s much more complicated. For example, consider the a b s o l u t e p r e s s u r e s i g n a l at a p o i n t i n a f r e e l y s l u g g i n g bed. This has been developed t h e o r e t i c a l l y by Kehoe and Davidson (1974) assuming that pressure waves from slugs above the measurement point are e f f e c t i v e l y damped. The s i g n a l , i l l u s t r a t e d i n Figure 5.7, i s seen to r i s e and f a l l i n what i s approximately a t r i a n g u l a r waveform; pressure r i s e s as - 244 -Absolute pressure f l u c t u a t i o n s i n a s l u g g i n g bed according to Kehoe and Davidson (1973) showing absolute pressure i s not a bimodal f u n c t i o n . - 245 -the s l u g goes by and subsequently f a l l s back. If a p r o b a b i l i t y d e n s i t y f u n c t i o n i s c a l c u l a t e d f o r such a waveform, i t does not y i e l d a bimodal f u n c t i o n , d e s p i t e the stro n g two phase c h a r a c t e r s of the system. Hence, i n t e r p r e t a t i o n of the s i g n a l s i s l i m i t e d to observ a t i o n s of the maximum pressure f l u c t u a t i o n , or the standard d e v i a t i o n of f l u c t u a t i o n s , which do not have unambiguous i n t e r p r e t a t i o n s . In t h i s study, as noted e a r l i e r , and i n s i m i l a r f a s h i o n to the s t u d i e s of Yong ejt a_l. (1986) and Rhodes and G e l d a r t (1986a) , a d i f f e r e n t i a l r a ther than an absolute pressure s i g n a l was measured. Here, the pressure drop was measured over a 460 mm s e c t i o n of bed beginning 230 mm above the d i s t r i b u t o r . In Yong's case, the measurement was made from j u s t above the d i s t r i b u t o r to the middle of the u n i t , while i n the Rhodes and G e l d a r t experiments a 100 mm i n t e r v a l j u s t above the d i s t r i b u t o r was used. The merit of measuring d i f f e r e n t i a l pressure f l u c t u a t i o n s i s that they should be r e l a t i v e l y i n s e n s i t i v e to what happens above the measurement zone, p a r t i c u l a r l y i n deep beds, because such downstream f l u c t u a t i o n s e q u a l l y a f f e c t the upper and lower taps and hence c a n c e l . T h e r e f o r e , the d i f f e r e n t i a l pressure s i g n a l i s a time t r a c e of the s o l i d s hold-up between the two taps, combined with a c c e l e r a t i o n a f f e c t s , which tends towards a true measurement - 246 -of the hold-up as e i t h e r the tap s e p a r a t i o n tends to zero or i n f i n i t y . The statement r e g a r d i n g s e n s i t i v i t y to downstream f l u c t u a t i o n s might only f a i l to be true when there are r e l a t i v e l y few s o l i d s above the upper pressure tap, such as i n a number of the Rhodes and G e l d a r t experiments. In these cases r e l a t i v e pressure f l u c t u a t i o n amplitude i n c r e a s e d by a f a c t o r of 10.6 as the height of the bed s u r f a c e above the upper tap v a r i e d from 100 to 450 mm. For deeper beds t h e r e i s s t r o n g evidence ( F i a c c o and S t a f f i n , 1967; Kehoe and Davidson, 1973) that bed height does not a f f e c t even the a b s o l u t e pressure f l u c t u a t i o n s . In the l a t t e r study the authors were able to p r e d i c t absolute pressure f l u c t u a t i o n s i n t h e i r own s l u g g i n g beds and those of F i a c c o and S t a f f i n very w e l l using a model which d i s r e g a r d e d upstream e f f e c t s assuming that they were damped out. In our own s t u d i e s the bed s u r f a c e was c o n s i s t e n t l y over 400 mm above the upper pressure tap i n the developed s l u g flow and t u r b u l e n t regimes. The preceeding d i s c u s s i o n shows that there are d i f f e r e n c e s between absolute and d i f f e r e n t i a l p r essure f l u c t u a t i o n s . Below we show th a t , unless c e r t a i n p r e c a u t i o n s are taken, i t i s not c l e a r that a decrease i n the amplitude of e i t h e r c l e a r l y s i g n i f i e s the beginning of a true hydrodynamic t r a n s i t i o n . One way to i l l u s t r a t e t h i s i s to c o n s i d e r Figure 5.8. T h i s shows that the standard - 247 -Point Density Fluctuations In An ' Ideal ' Two-Phase System F i g u r e 5.8 Standard d e v i a t i o n of a d i f f e r e n t i a l pressure s i g n a l measured over a small length versus expansion f o r slug flow, showing a maximum despite no l o s s of the two phase nature. - 248 -deviation of a d i f f e r e n t i a l pressure signal, measured with closely spaced pressure taps, w i l l reach a maximum at some ve l o c i t y where the slug length i s equal to the slug spacing, even i f there i s no breakup whatsoever of the slug structure. Another possible means of obtaining a peak in fluctuation amplitude, i f this amplitude was measured using a simple manometer, would be to have a slug frequency close to the natural frequency of the manometer. Under these circumstances a resonant peak would be seen, again without a true breakdown of the two phase structure. Our measurements avoided the major points of contention. S p e c i f i c a l l y , they were made at the base of a deep bed which should eliminate the problem of a pressure flu c t u a t i o n signal which varies with the weight of s o l i d s above the measurement taps. Also, a high s e n s i t i v i t y , rapid response transducer was used which allows a complete trace of the fluctuation to be made. This permitted us to establish not only the maximum fluctuation, but also the state of the bed between the peaks. F i n a l l y the pressure transducer eliminates any p o s s i b i l i t y of measurement system resonance, the resonant frequency of the transducer being of the order of 2 kHz. The graphs can now be examined in d e t a i l . F i r s t l y , compare Figures 5.4 and 5.6, graphs of peak-to-peak pressure fluctuations and the standard deviations of the same - 249 -f l u c t u a t i o n s . I t i s apparent that, from the v e l o c i t y at which developed s l u g g i n g i s e s t a b l i s h e d ( « 130 mm/s) to 3 m/s, where there i s a s u b s t a n t i a l entrainment, there i s no drop i n the amplitude of pressure f l u c t u a t i o n s . However, although the peak-to-peak f l u c t u a t i o n remains unchanged, the frequency and r e g u l a r i t y of these high amplitude f l u c t u a t i o n s d i m i n i s h e s , so that the standard d e v i a t i o n of the pressure f l u c t u a t i o n s decreases g r a d u a l l y over the same v e l o c i t y range. The pressure t r a c e s bear out what one sees v i s u a l l y : There are p e r i o d s of turbulence i n t e r s p e r s e d between pe r i o d s of w e l l developed s l u g g i n g , somewhat analoguous to the i n t e r m i t t e n c y found i n a developing t u r b u l e n t flow of a s i n g l e phase f l u i d . Whether or not these data support the notion of a t u r b u l e n t t r a n s i t i o n depends s t r o n g l y upon d e f i n i t i o n , although very s i m i l a r behavior can be seen i n some t r a c e s from M a s s i m i l l a (1973), Canada ert a_l. (1978) and Carotenuto et a l • (1974). In our view a t r a n s i t i o n does occur i n the measurement volume but not i n the sense i m p l i e d e i t h e r by Turner (1978), Avidan (1980), or Rhodes and G e l d a r t (1986a). A t r a n s i t i o n to a s t a b l e c l u s t e r suspension with low entrainment i s d e f i n i t e l y not a p p l i c a b l e , but n e i t h e r i s t h e r e a p s e u d o - t r a n s i t i o n which depends upon a decreased o v e r l y i n g bed mass to cause decreased peak-to-peak o s c i l l a t i o n s . The l a t t e r undoubtably occurs i n the upper - 250 -p a r t of the bed, and at high enough v e l o c i t y would work downward to the measurement zone, but by using a deep bed t h i s e f f e c t was circumvented. What i s seen i s a gradual l o s s of the two phase c h a r a c t e r i n p e r i o d s of i n t e r m i t t e n c y . However, a s l u g g i n g component remains u n t i l w e l l i n t o what i s c o n v e n t i o n a l l y termed f a s t f l u i d i s a t i o n . T urbulent f l u i d i s a t i o n f o r t h i s system i s t h e r e f o r e not a simply c h a r a c t e r i z e d regime with steady p r o p e r t i e s . Instead, i t denotes a range of gas v e l o c i t i e s between s l u g flow and smooth t r a n s p o r t flow and has intermediate and i n t e r m i t t e n t c h a r a c t e r with b u r s t s of " t u r b u l e n c e " i n t e r s p e r s e d with p e r i o d s of s l u g - l i k e l a r g e amplitude f l u c t u a t i o n s , the former becoming dominant as the gas v e l o c i t y i s i n c r e a s e d . It i s notable that t h i s p i c t u r e i s c o n s i s t e n t with X-ray o b s e r v a t i o n s of Rowe et a l . (1980). In concluding t h i s s e c t i o n , a number of p o i n t s should be r e i t e r a t e d . Whether or not a t r a n s i t i o n occurs from s l u g g i n g to turbulence depends s t r o n g l y upon both semantics and the measurement technique. Peak-to-peak f l u c t u a t i o n s alone are not i n d i c a t i v e of a t r a n s i t i o n ; however, time t r a c e s and standard d e v i a t i o n measurements show that breakdown i s o c c u r r i n g . Secondly i t i s e s s e n t i a l to heed the work of Rhodes and G e l d a r t (1986a). The t r a n s i t i o n which they observe w i l l occur under many circumstances because r e l a t i v e l y shallow beds are used. However, t h i s i s - 251 -not a r e a l i n d i c a t o r of a breakdown of the two phase ch a r a c t e r i n the sense i m p l i e d by Yerushalmi and Cankurt (1978). F i n a l l y , the r e s u l t s of t h i s study are s p e c i f i c both to the equipment and to the s o l i d p a r t i c l e s used. There i s some evidence i n favour of a t u r b u l e n t t r a n s i t i o n to a homogeneous low entrainment bed i n beds of f i n e s o l i d s ( C r e s c i t e l l i et a l . , 1978; M a s s i m i l l a , 1973), and l i k e l y i n any u n i t where the bed s i z e i s s e v e r a l times the maximum s t a b l e bubble s i z e so that s l u g g i n g i s precluded. Under these circumstances Grace (1986b) has noted that the maximum bed voidage at which a s t a b l e bubbling bed can s u r v i v e i s l i m i t e d by c l o s e packing of the bubbles, l e a d i n g to an upper l i m i t on o v e r a l l bed voidage of approximately 0.7. Higher gas flows would n a t u r a l l y r e s u l t i n a di s c o n t i n u o u s s o l i d phase and a s i t u a t i o n e q u i v a l e n t to t u r b u l e n t f l u i d i s a t i o n . T h i s i s an approach which demands more a t t e n t i o n because i t p o i n t s towards a number of parameters which could i n f l u e n c e the " t u r b u l e n t t r a n s i t i o n " . One of these i s the e f f e c t i v e p a r t i c u l a t e phase v i s c o s i t y which i n turn i s s t r o n g l y i n f l u e n c e d by p a r t i c l e shape f a c t o r and f i n e s content (Matheson et aJ., 1949). T h i s might e x p l a i n the widely d i f f e r e n t t r a n s i t i o n behaviour found by C r e s c i t e l l i et a l . (1978) f o r two v i r t u a l l y i d e n t i c a l m a t e r i a l s , Ludox c a t a l y s t , dp = 60 ym p p = 1400 kg/m3, and a f l u i d c r a c k i n g c a t a l y s t dp = 60 ym p p = 940 kg/m 3. The former showed - 252 -dramatic breakdown to turbulence, without slug formation, while the la t t e r broke down slowly from slugging, in a fashion apprarently similar to the breakdown observed in this study. - 253 -6. AXIAL GAS MIXING IN A CIRCULATING FLUIDISED BED 6.1 Introduction E a r l y d i s c u s s i o n about the b e n e f i t s of c i r c u l a t i n g f l u i d i s e d bed technology focussed upon a number of i t s p e r c e i v e d merits f o r g a s - s o l i d c o n t a c t i n g (Yerushalmi et a l . , 1976). Among these was a reported small amount of gas backmixing r e l a t i v e to other f l u i d i s e d regimes by v i r t u e of the high gas v e l o c i t i e s employed. Gas backmixing i s of p a r t i c u l a r i n t e r e s t i n c e r t a i n chemical p r o c e s s i n g a p p l i c a t i o n s where product s e l e c t i v i t y may be s t r o n g l y i n f l u e n c e d by the r e s i d e n c e time d i s t r i b u t i o n of the gas. In these cases i t i s g e n e r a l l y d e s i r a b l e f o r the gas r e s i d e n c e time d i s t r i b u t i o n to approach plug flow. P r e v i o u s s t u d i e s of gas backmixing i n f a s t bed systems appear to r e i n f o r c e the p e r c e i v e d notion of the CFB as a near plug flow c o n t a c t o r . Both Cankurt and Yerushalmi (1978) and Yang e_t al_. (1983) found that when helium t r a c e r was i n j e c t e d c o n t i n u o u s l y at the c e n t r e l i n e of a c i r c u l a t i n g bed, and a r a d i a l helium c o n c e n t r a t i o n p r o f i l e was measured s e v e r a l centimetres upstream, there were no t r a c e s of helium except at the w a l l . T h i s suggested that there was n e g l i g i b l e p h y s i c a l backmixing except i n a wall l a y e r , which seemed to occupy a small f r a c t i o n of the r e a c t o r c r o s s - s e c t i o n . Cankurt and Yerushalmi's r e s u l t s , shown i n F i g u r e 6.1, d i f f e r e d from data obtained i n the somewhat - 254 -U(m/s) -7.6 -6.1 -2.5 0 2.5 5.1 7.6 Distance From Centre (cm) F i g u r e 6.1 Tracer p r o f i l e s measured 50 mm upstream of a c e n t r e l i n e i n j e c t i o n point at d i f f e r e n t gas v e l o c i t i e s (Cankurt and Yerushalmi, 1978). C/Co i s the r a t i o of t r a c e r c o n c e n t r a t i o n at the measurement point to the i n j e c t i o n c o n c e n t r a t i o n . The lower graph represents f a s t bed c o n d i t i o n s (Ug > 1.8 m/s). Turbulent f l u i d i s a t i o n e x i s t s between 0.6 m/s and 1.7 m/s. - 255 -lower v e l o c i t y t u r b u l e n t regime. A dramatic change i n the upstream wall c o n c e n t r a t i o n was found to occur f o r steady c e n t r e l i n e t r a c e r i n j e c t i o n at the t r a n s p o r t v e l o c i t y . At the lower v e l o c i t i e s Yerushalmi and Avidan (1985) note a decrease i n the a x i a l d i s p e r s i o n c o e f f i c i e n t i n passing from s l u g g i n g to t u r b u l e n t f l u i d i s a t i o n ( F i g u r e 6.2) with an approximately l i n e a r dependence of a x i a l P e c l e t number on v e l o c i t y , ( F i g u r e 6.3). In the t u r b u l e n t regime the data could be modelled e f f e c t i v e l y using a simple co u n t e r c u r r e n t two-phase model (Yerushalmi, 1986). While the f a s t regime continued to show an i n c r e a s e i n P e c l e t number, even beyond that i n t u r b u l e n t f l u i d i s a t i o n , a two-phase model no longer seemed a p p r o p r i a t e , apparently due to i n s u f f i c i e n t gas backmixing. U n f o r t u n a t e l y , although Cankurt and Yerushalmi (1978) and Yang et aA. (1983) demonstrate that p h y s i c a l downflow only occurs near the w a l l i n f a s t f l u i d i s a t i o n , not i n the i n t e r i o r of the r i s e r , they do not i n d i c a t e what s o r t of magnitude of t u r b u l e n t d i s p e r s i o n c o e f f i c i e n t might be expected; nor do they demonstrate that downflow at the w a l l i s s m a l l . Therefore some measurements of a c t u a l gas r e s i d e n c e time d i s t r i b u t i o n s were undertaken i n t h i s work i n an attempt to q u a n t i f y the mixing phenomena. - 256 -F i g u r e 6.2 V a r i a t i o n of a x i a l d i s p e r s i o n c o e f f i c i e n t with gas v e l o c i t y i n passing from s l u g g i n g to t u r b u l e n t f l u i d i s a t i o n (Yerushalmi and Avidan, 1985). T r a n s i t i o n to turbulence r e p o r t e d l y occurs around 0.7 m/s. - 257 -F i g u r e 6.3 V a r i a t i o n of a x i a l P e c l e t number with gas v e l o c i t y (Yerushalmi and Avidan, 1985). - 258 -6.2 The Experimental Study 6.2.1 General c o n s i d e r a t i o n s One of the simplest and most common methods of measuring resid e n c e time d i s t r i b u t i o n s i n flow systems i s to i n j e c t a t r a c e r i n t o the f l u i d e n t e r i n g the system i n a puls e with a known waveform; the c o n c e n t r a t i o n h i s t o r y of the t r a c e r i s then monitored at the system e x i t , and the re s i d e n c e time d i s t r i b u t i o n can be i n f e r r e d from the e x i t and i n l e t waveforms. The t r a c e r must s a t i s f y c e r t a i n c r i t e r i a i n order to be s u i t a b l e f o r use i n such a t e s t ; i t must: ( i ) Be r e a d i l y d e t e c t a b l e , p r e f e r a b l y i n r e a l time. ( i i ) Mix i n t i m a t e l y with the flowing f l u i d so that the RTD of the t r a c e r i s r e p r e s e n t a t i v e of the bulk f l u i d . ( i i i ) E i t h e r have p h y s i c a l p r o p e r t i e s i d e n t i c a l to the flowing f l u i d , so that i t may re p l a c e part of the flow i n g f l u i d when i t i s i n j e c t e d , or be present i n a small enough c o n c e n t r a t i o n that the bulk f l u i d p r o p e r t i e s are u n a f f e c t e d . For flow of a i r at high v e l o c i t i e s through the c i r c u l a t i n g f l u i d i s e d bed s e v e r a l gaseous t r a c e r s , hydrogen, helium and carbon d i o x i d e were considered. A l l of these could be detected at low c o n c e n t r a t i o n s i n a i r i n r e a l time using a cheap, commerically a v a i l a b l e , thermal c o n d u c t i v i t y - 259 -d e t e c t o r salvaged from an o l d gas chromatograph. However, only the helium could be used i n small enough q u a n t i t i e s that the bulk flow p r o p e r t i e s were u n a f f e c t e d at an acc e p t a b l e s i g n a l - t o - n o i s e r a t i o i n the de t e c t o r (Yu, 1986). The t r a c e r f l o w r a t e s r e q u i r e d f o r e i t h e r hydrogen or carbon d i o x i d e were too high f o r t h i s study (> 2% t o t a l flow) where the extreme s e n s i t i v i t y of the thermal c o n d u c t i v i t y c e l l cannot be used, because m o d i f i c a t i o n s and high throughflow c r e a t e noise due to flow f l u c t u a t i o n s through the c e l l ; these r e s u l t from pressure p u l s a t i o n s i n the r i s e r column. Ther e f o r e helium t r a c e r was employed together with a thermal c o n d u c t i v i t y c e l l f o r d e t e c t i o n . The only cause f o r concern was that the molecular weight of helium was so much smal l e r than that of a i r that there might be s i g n i f i c a n t t r a c e r s e g r e g a t i o n at the i n j e c t i o n p o i n t due to buoyancy. Care was taken to minimise t h i s by j u d i c i o u s design of the i n j e c t i o n system. 6.2.1 Sampling and i n j e c t i o n systems In order to design s u i t a b l e t r a c e r i n j e c t i o n and withdrawal systems f o r the c i r c u l a t i n g bed, i t i s important to understand the mixing processes which occur at e i t h e r end of the u n i t , and to a p p r e c i a t e how these a f f e c t the i n t e r p r e t a t i o n of the r e s u l t s i n any subsequent models. S p e c i f i c a l l y , i f the o b j e c t i v e of the experiment i s to - 260 -determine true r e s i d e n c e time d i s t r i b u t i o n s , r a t h e r than to c h a r a c t e r i s e the system i n terras of the best f i t to a s i n g l e o r m u l t i parameter model, then the boundaries should be c l o s e d so that t r a c e r gas cannot d i f f u s e e i t h e r out of or i n t o the system. Stated a l t e r n a t i v e l y , a l l flow across the system boundaries should be e n t i r e l y c o n v e c t i v e . Because the c i r c u l a t i n g bed i s non-uniform r a d i a l l y there are a l s o a d d i t i o n a l problems: ( i ) Tracer must be i n j e c t e d i n such a way that i t i s i n i t i a l l y d i s t r i b u t e d with a uniform c o n c e n t r a t i o n at each r a d i a l p o s i t i o n immediately upstream of the entrance. ( i i ) Gas l e a v i n g the v e s s e l must e i t h e r be sampled i s o k i n e t i c a l l y across the e x i t duct, to give a t r u e instantaneous p o i n t average t r a c e r c o n c e n t r a t i o n , or a mixing cup must be developed to give t h i s same instantaneous average. I f a l l of the above c o n s t r a i n t s can be s a t i s f i e d , then i t i s p o s s i b l e to generate accurate RTD data. To ensure that the t r a c e r enters the column u n i f o r m l y d i s p e r s e d i n the e n t e r i n g gas, i t was i n j e c t e d i n t o the windbox at the mouth of the gas entry n o z z l e . The flow i s very t u r b u l e n t at t h i s p o i n t ensuring r a p i d mixing. Although an e r r o r i s i n t r o d u c e d i n t o the residence time d i s t r i b u t i o n i n t h i s way, by adding the windbox RTD to that of the column, t h i s e r r o r i s small (mean reside n c e time i n - 261 -the windbox l e s s than 2% of the o v e r a l l mean residence time) . Windbox i n j e c t i o n a l s o e l i m i n a t e s the problem of having to use m u l t i p o i n t i n j e c t i o n e i t h e r immediately below or immediately above the d i s t r i b u t o r p l a t e with a r a t e at each p o i n t p r o p o r t i o n a l to the l o c a l gas v e l o c i t y . R e p r e s e n t a t i v e sampling across the e x i t duct to p r o v i d e a mixing cup point average gas c o n c e n t r a t i o n was not a problem. Both the smooth and abrupt e x i t s converge from a 152 mm (6") column i n s i d e diameter to a 100 mm (4") e x i t duct which i s compatible with the cyclone entrance. T h i s c o n t r a c t i o n a c t s as an e x c e l l e n t r a d i a l mixer at the high Reynolds number (»100,000) used i n the mixing experiments. T h e r e f o r e , r a d i a l p r o f i l e s i n t r a c e r c o n c e n t r a t i o n at the r i s e r e x i t are e l i m i n a t e d at the point of c o n t r a c t i o n , and a s i n g l e sampling l o c a t i o n , placed as c l o s e as p o s s i b l e to the e x i t , gives a mixing cup average. The p h y s i c a l design of the i n j e c t o r i s d i c t a t e d by the need to produce an input helium pulse with a r e p r o d u c i b l e waveform. In i t s t h e o r e t i c a l l y simplest form t h i s i s a D i r a c d e l t a , or u n i t impulse f u n c t i o n ; the response curve which i s measured f o r t h i s impulse i s the residence time d i s t r i b u t i o n f o r the combined windbox/riser/sensor system. In p r a c t i c e , however, i t was not p o s s i b l e to approximate a d e l t a helium input f o r t h i s system, because t h i s would r e q u i r e the i n t r o d u c t i o n of a s u b s t a n t i a l amount - 262 -of helium i n a time which was short compared to the 1.3 s res i d e n c e time i n the r i s e r . T h i s could not be accomplished without d i s t u r b i n g the flow; t h e r e f o r e we chose a step change i n helium input, from a constant flow at time 0~ to no-flow at time 0 +. E s s e n t i a l l y instantaneous s h u t - o f f c o u l d be obtained using a s o l e n o i d v a l v e , and t h i s was p r e f e r a b l e to instantaneous i n t r o d u c t i o n because there was a rotameter i n the helium l i n e which would o s c i l l a t e u n s t a b l y when the s o l e n o i d was opened i m p u l s i v e l y . The only problem with the step input i s that the mathematical a n a l y s i s of the r e s u l t s i s more complex because t h i s form of pulse has no F o u r i e r transform. In r e t r o s p e c t i t would have been p r e f e r a b l e to use a s i n g l e c y c l e squarewave input of length approximately equal to the r e a c t o r r e s i d e n c e time. The helium i n j e c t o r system i s shown s c h e m a t i c a l l y i n Fig u r e 6.4. Note the proximity of the s o l e n o i d to the di s c h a r g e n o z z l e so that when the s o l e n o i d i s c l o s e d , there i s minimal r e s i d u a l helium i n the nozzle to d i f f u s e slowly i n t o the system and blunt the sharpness of the step p u l s e . The sampling and d e t e c t o r systems are c o n s i d e r a b l y more complex than the i n j e c t o r and were the s u b j e c t of a c o n s i d e r a b l e development e f f o r t . The system complexity r e s u l t s from: ( i ) The s o l i d s l o a d i n g i n the e x i t i n g gas stream ( i i ) The short r e s i d e n c e times f o r the gas i n the c i r c u l a t i n g bed. - 263 -Riser Distributor Solenoid Valve •130m rn 4 mm Windbox In H e F i g u r e 6.4 T r a c e r i n j e c t i o n s y s t e m f o r gas RTD s t u d i e s . - 264 -The f i r s t f a c t o r n e c e s s i t a t e s that any sample stream be put through an absolute f i l t e r before c o n t a c t i n g the d e l i c a t e f i l a m e n t s of a thermal c o n d u c t i v i t y d e t e c t o r . The second f a c t o r makes the design of the sampling system and the d e t e c t o r more complex because of the need to minimise the gas residence time i n t h i s system. Long r e s i d e n c e times promote d i s p e r s i o n i n the det e c t o r system which can mask the d i s p e r s i o n phenomena i n the column. The f i n a l sampling-system/detector design i s shown i n Figu r e 6.5. I t c o n s i s t s of a 60 ym s i n t e r e d metal f i l t e r welded onto a 6.3 mm (1/4" OD), 4.6 mm (.180") ID, 40 mm length s t a i n l e s s s t e e l tube. This i s f i t t e d i n turn i n t o the sample side of a modified Bowmac thermal c o n d u c t i v i t y c e l l . The design r e s u l t s from a s e r i e s of experiments i n which f i l t e r pore s i z e , sampling tube length, sampling r a t e , and c o n d u c t i v i t y c e l l design were a l l v a r i e d i n order to minimise sampling system d i s p e r s i o n . Each v a r i a b l e had some e f f e c t , the most notable being f i l t e r pore s i z e ( t e s t e d at 15 ym and 60 ym l e v e l s ) sampling r a t e ( t e s t e d at 1667 mm3/s, 3333 mm3/s and 5000 mm3/s l e v e l s ) and c o n d u c t i v i t y c e l l design. The decrease i n d i s p e r s i o n with an increased f i l t e r pore s i z e i s r a t i o n a l , while the need to vary the l a s t two parameters at a l l i s a r e f l e c t i o n of the f a c t that the thermal c o n d u c t i v i t y c e l l was being used i n a s e r v i c e f o r - 265 -F i g u r e 6.5 Photograph of t r a c e r s a m p l i n g and d e t e c t o r system f o r RTD s t u d i e s . - 266 -which i t was not intended. In normal gas chromatography o p e r a t i o n , recommended f l o w r a t e s through such a c e l l are i n the range 416 - 833 mm3/s so that heat t r a n s f e r from the f i l a m e n t i s to an e s s e n t i a l l y stagnant gas and small f l o w r a t e v a r i a t i o n s do not a f f e c t the c e l l s t a b i l i t y . A l s o , the gas fo l l o w s a convoluted high pressure drop path through the c e l l not designed to minimise d i s p e r s i o n s i n c e t h i s w i l l not a f f e c t i n t e g r a t e d peak areas. However, i n our a p p l i c a t i o n we r e q u i r e minimum d i s p e r s i o n and high flowrates,* t h e r e f o r e the gas flo w r a t e was inc r e a s e d to 4167 mm3/s i n normal runs, and a c e l l design chosen which, with minor m o d i f i c a t i o n , allowed s t r a i g h t throughflow. F i g u r e s 6.6 and 6.7 show that these changes improve the c e l l o p e r a t i o n d r a m a t i c a l l y . Figure 6.6 i l l u s t r a t e s the e f f e c t of sampling upon the response to a step change i n t r a c e r c o n c e n t r a t i o n i n the gas flowing i n t o the f i l t e r . F i g u r e 6.7 shows how changing the c e l l from a convoluted Beckman design to a modified Bowmac u n i t ( d r i l l e d out to improve throughflow) i s a l s o e f f e c t i v e i n minimising d i s p e r s i o n . A f t e r making such s u b s t a n t i a l m o d i f i c a t i o n s to the c o n s t r u c t i o n and ope r a t i n g c o n d i t i o n s of the thermal c o n d u c i v i t y c e l l , i t was necessary to e s t a b l i s h that the output of the c e l l b ridge remained l i n e a r with helium c o n c e n t r a t i o n . T h i s i s the usual case f o r thermal - 267 -F i g u r e 6.6 E f f e c t of s a m p l i n g r a t e t h r o u g h t h e r m a l c o n d u c t i v i t y c e l l upon d e t e c t o r d i s p e r s i o n . (Dead t i m e removed from F - c u r v e s ) . - 268 -modified original 0 5 Time(s) 10 15 F i g u r e 6.7 E f f e c t o f t h e r m a l c o n d u c t i v i t y c e l l t y p e upon d e t e c t o r d i s p e r s i o n showing how d e s i g n m o d i f i c a t i o n s (new c e l l t y p e d r i l l e d o u t ) r e d u c e d d i s p e r s i o n . (Dead time removed from F - c u r v e s ) . - 2 6 9 -c o n d u c t i v i t y c e l l s , but may be a f f e c t e d by changing the heat t r a n s f e r mode to give a s u b s t a n t i a l c onvective component. To t e s t f o r t h i s l i n e a r i t y the c e l l was c o n f i g u r e d as shown i n F i g u r e 6.8 and d i f f e r e n t volumes of helium were i n j e c t e d i n t o the mixing tee f o r a constant c a r r i e r gas flow of 4167 mm /s and a bridge c u r r e n t of 150 mA. The c e l l output curve f o r each c o n d i t i o n was then i n t e g r a t e d ensuring that, f o r the l a r g e s t volume of helium i n j e c t e d , the output peak corresponded to a c o n c e n t r a t i o n higher than the c o n c e n t r a t i o n s proposed f o r the t r a c e r t e s t s . F i n a l l y a graph of the peak area (mV.s) was p l o t t e d a gainst the helium volume i n j e c t e d ( F i g u r e 6.9), and the l i n e a r i t y of t h i s p l o t was taken as proof of l i n e a r i t y of c e l l output (mV) with c o n c e n t r a t i o n over the r e q u i r e d range. This i s shown by Yu (1986) • The study to t h i s point had developed an i n j e c t i o n system, and a sensor which e x h i b i t e d d i s p e r s i o n approximately equal i n magnitude to the d i s p e r s i o n i n the column. T h i s was adequate f o r the experiments to be performed since sensor/sampling system d i s p e r s i o n can be acounted f o r e f f e c t i v e l y using mathematical techniques, provided that i t i s of a lower or comparable order of magnitude to the d i s p e r s i o n which i s to be measured. - 270 -6.2.3 Detector/sampling system c h a r a c t e r i s a t i o n To e l i m i n a t e detector/sampling system d i s p e r s i o n from the combined r i s e r / d e t e c t o r / s a m p l i n g system response r e q u i r e s measurement of the de t e c t o r RTD. T h i s was obtained by i n s e r t i n g the i n j e c t i o n lance immediately upstream of the d e t e c t o r and making a step change i n helium t r a c e r flow. The a i r flow was constant at a s u p e r f i c i a l v e l o c i t y of 7.1 m/s i n the r i s e r , the v e l o c i t y used i n subsequent experiments, and the sampling r a t e was 4166 mm3/s. Output v o l t a g e from the bridge was a m p l i f i e d 100 times using a CRC " A m p l i v o l t " DC a m p l i f i e r and recorded both i n analogue form on the u l t r a v i o l e t chart recorder and i n d i g i t a l format on the computer. A c t i v a t i o n of the s o l e n o i d , which shut o f f the helium flow, t r i g g e r e d an event marker on the UV r e c o r d e r , p e r m i t t i n g computation of mean re s i d e n c e times. The F-curve response obtained under these c o n d i t i o n s i s shown i n Figure 6.10. 6.2.4 R i s e r c h a r a c t e r i s a t i o n The i n i t i a l c h a r a c t e r i s a t i o n t e s t s led to a s e r i e s of experiments at a constant s u p e r f i c i a l gas v e l o c i t y of 7.1 m/s and at d i f f e r e n t s o l i d s c i r c u l a t i o n r a t e s . Two d i f f e r e n t e x i t c o n f i g u r a t i o n s were s t u d i e d to e s t a b l i s h whether these cause d i f f e r e n t amounts of gas mixing by v i r t u e of c r e a t i n g d i f f e r e n t i n t e r n a l s o l i d s mixing p a t t e r n s . A summary of the t e s t c o n d i t i o n s appears i n Table - 271 -sample tee for pulse helium injection r - r £ b o sample stream ^>hpair)>-conductivity cell reference stream F i g u r e 6.8 Test c o n f i g u r a t i o n to e s t a b l i s h detector l i n e a r i t y . - 272 -Volume Of He Injected (mm3) F i g u r e 6 .9 Graph of i n t e g r a t e d d e t e c t o r output versus i n j e c t i o n volume to demonstrate detector l i n e a r i t y . - 273 -Time (s) F i g u r e 6.10 Optimised d e t e c t o r F-curve response. - 274 -6.1; the column c o n f i g u r a t i o n f o r the abrupt and smooth e x i t s i s shown i n F i g u r e 2.1. Each t e s t c o n s i s t e d of making a step change i n t r a c e r flow as f o r the d e t e c t i o n c h a r a c t e r -i s a t i o n ; the output curves are shown i n F i g u r e 6.11. When the column has a smooth e x i t , runs Dis 4 to Dis 7, the F-curve i s l e s s smooth than f o r a t e s t at i d e n t i c a l t o t a l column pressure drop with an abrupt e x i t . T h i s i s caused by lar g e pressure f l u c t u a t i o n s i n the smooth e x i t case r e s u l t i n g from choking at the base of the column. The pressure f l u c t u a t i o n s cause flow v a r i a t i o n s through the sensor, which are manifested i n turn as v o l t a g e v a r i a t i o n s i n the thermal c o n d u c t i v i t y bridge due to the high c o n v e c t i v e component of heat t r a n s f e r . The pressure f l u c t u a t i o n s themselves formed the b a s i s of a f u r t h e r study d e t a i l e d below. 6.3 Data A n a l y s i s D i s p e r s i o n data can be analysed most e a s i l y i f the amount of d i s p e r s i o n i n both the r i s e r and d e t e c t o r i s r e l a t i v e l y small (D/UL < 0.02). In t h i s case ( L e v e n s p i e l , 1972) the shapes of C and F curves are i n s e n s i t i v e to the nature of the boundary c o n d i t i o n s . The C curves both f o r the d e t e c t o r alone and the d e t e c t o r / r i s e r combination are then approximately Gaussian, and the d i s p e r s i o n i n the r i s e r can be r e a d i l y computed from the d i f f e r e n c e i n the v a r i a n c e s of these two response curves. Table 6.1 Test C o n d i t i o n s f o r D i s p e r s i o n Measurements i n the C i r c u l a t i n g F l u i d i s e d Bed Run D e s i g n a t i o n Top Geometry Gas V e l o c i t y (m/s) S o l i d s Flux i n R i s e r (kg/m s) T o t a l R i s e r P r e s s u r e Drop (mm Hg) DisO Abrupt 7.1 0 0 D i s l Abrupt 7.1 37 24 Dis2 Abrupt 7.1 49 50 Dis3 Abrupt 7.1 60 72 Dis4 Smooth 7.1 0 0 Dis5 Smooth 7.1 65 27 Dis6 Smooth 7.1 41 12 Dis7 Smooth 7.1 33 7 Dis8 Smooth 7.1 43 17 - 276 -Ug = 71 m/s Gs = 0 kg/m 2s Smooth Exit F=0 Ug=7.1m/S G s =65kg/m 2 s Smooth Exit F=0 Ug=71m/s G s = 4 1 kg/m 2s Smooth Exit F=0 Ug = 7-1 m/s G s = 33kg/m 2 s Smooth Exit F=0-Ug = 7-1 m/s G s= 43 kg/m 2 s Smooth Exit F=0 r 0 I 3 - F » 1 4 T F « 1 F = 1 F=1 T 4 T " 4 F i g u r e 6.11 Combined r i s e r / d e t e c t o r F-curve response f o r a x i a l mixing determinations i n c i r c u l a t i n g beds of sand at Ug = 7.1 m/s. Abrupt e x i t , G s = 0, 37, 49, 60 kg/nTs 65. 41 Smooth e x i t , G s = 0, (Time i n seconds) 33, 43 kg/nTs Cont. - 277 -Ug =7-1 m/s G s = 0 kg/m 2s / Abrupt Exit / ~ "r -1 F:0 i 1 0 1 2 I 3 4 T Ug =7-1 m/s Gs=37 kg/m 2s Abrupt Exit / F = 0 ^ — ~ 1 i 0 1 I 2 i 3 4 T Ug =71 m/s G s =49kg/m 2 s Abrupt Exit > F=1 F=0 ^ — ^ ^ / ^ " ^ 6 * i 3 4 T Ug =71 m/s Gs=61 kg/m 2s Abrupt Exit / - v - F - 1 F = 0 • i 0 1 • 2 1 3 4 T - 278 -U n f o r t u n a t e l y , although the mixing i n the d e t e c t o r can be c r u d e l y approximated by a s m a l l - d i s p e r s i o n d i s p e r s e d plug flow model, as shown by the near l i n e a r i t y of the F-curve response when i t i s p l o t t e d on normal p r o b a b i l i t y graph paper, the same i s not true f o r the combined response curves. Even the former curve shows d i s p e r s i o n c o n s i d e r a b l y higher than the recommended maximum f o r the Gaussian approximation. Therefore r i g o r o u s treatment of the t r a c e r data r e q u i r e s more complex techniques, e i t h e r to f i t the data with a d i s p e r s i o n c o e f f i c i e n t f o r l a r g e d i s p e r s i o n , or, i f t h i s i s u n s u i t a b l e , to generate residence time d i s t r i b u t i o n s from which other models can be d e r i v e d . In the former case, a best f i t d i s p e r s i o n c o e f f i c i e n t i s f i r s t generated f o r the d e t e c t o r , minimising the sum of squares between the measured F-curve and a t h e o r e t i c a l curve generated by a f i n i t e d i f f e r e n c e model. The same technique i s then a p p l i e d to the r i s e r / d e t e c t o r combination generating a second b e s t - f i t d i s p e r s i o n c o e f f i c i e n t f o r the r i s e r and u t i l i s i n g the r e s u l t s of the f i r s t part f o r the d e t e c t o r . In the l a t t e r case i t i s not necessary to assume a model f o r the system. Instead, the combined s i g n a l and the d e t e c t o r s i g n a l are deconvoluted using F o u r i e r transform techniques to generate the true r i s e r RTD. The RTD can then be f i t t e d using a model a p p r o p r i a t e to i t s shape and the known p h y s i c a l c h a r a c t e r i s t i c s of the system. - 279 -Of the two techniques, the f i r s t has the advantages of r e l a t i v e s i m p l i c i t y and the a b i l i t y to handle noisy data, such as the data generated with the smooth e x i t . The second i s s u p e r i o r i n that there i s no i m p l i c i t assumption that the mixing i s d i s p e r s i v e i n nature, an assumption that may be f a r from t r u e , e s p e c i a l l y f o r large d i s p e r s i o n when other models o f t e n provide b e t t e r p h y s i c a l r e p r e s e n t a t i o n s . The eventual data a n a l y s i s used two techniques. The f i r s t was a non-rigorous simple a n a l y s i s based upon a pseudo-dispersion c o e f f i c i e n t , which permitted r a p i d comparison of data. The second technique was a r i g o r o u s e v a l u a t i o n of the RTD f o r a s i n g l e case using the F o u r i e r t r a n s f o r m techniques. ( i ) Non-rigorous a n a l y s i s : The graphs of the response curves on normal p r o b a b i l i t y paper followed a Gaussian d i s t r i b u t i o n c l o s e l y from an F value of approximately 0.05 to 0.7. T h e r e f o r e a pseudo d i s p e r s i o n c o e f f i c i e n t could be c a l c u l a t e d f o r any F curve i g n o r i n g the. remainder of the d i s t r i b u t i o n . T h i s c a l c u l a t i o n i s i l l u s t r a t e d i n Appendix 3. E f f e c t i v e l y i t ignores the extended t a i l of the response curve, which could have a s u b s t a n t i a l i n f l u e n c e upon s e l e c t i v i t y . However, the p s e u d o - d i s p e r s i o n c o e f f i c i e n t i s a u s e f u l number f o r comparison of mixing under d i f f e r e n t c o n d i t i o n s , and i t s trends lead to q u a l i t a t i v e c o n c l u s i o n s . - 280 -( i i ) Rigorous RTD computation: Rigorous computation of the RTD f o r a pulse t e s t r e q u i r e s deconvolution of the F curves f o r the d e t e c t o r and the r i s e r / d e t e c t o r combination. Under simpler circumstances t h i s i n v o l v e s computing the F o u r i e r transforms of both responses, d i v i s i o n of the two transforms, and i n v e r s i o n of the r e s u l t i n g transform to y i e l d the RTD. However, n e i t h e r response has a f i n i t e F o u r i e r t r a n s f o r m s i n c e the pulse does not r e t u r n to zero; t h e r e f o r e t r a n s f o r m a t i o n s are r e q u i r e d before the data can be t r e a t e d . Luyben (1973) shows that i f a process has a t r a n s f e r f u n c t i o n G(iw) i n the frequency domain, and i s subjected t o a step type pulse Q(t) to give a time domain output x ( t ) , then the t r a n s f e r f u n c t i o n , G(iw), i s given by — • r°° * /... -iwt ,. x - IW J x ( t ) e dt G(iw) = ^ (6.1) Q - iw J Q ( t ) e w x dt where x, x , Q and Q are d e f i n e d i n F i g u r e 6.12a. Convolu t i o n theory shows that i f Q(t) i s the response of the d e t e c t o r to an a r b i t a r y step input I ( t ) , and i f x ( t ) i s the response of the r i s e r / d e t e c t o r combination to the same a r b i t r a r y input, then G(iw) i s the frequency response of the r i s e r , and G(t) i s the time response to an impulse - 281 -a. b. Ttt) Step Change x l t ) 1 RTD=R1 Column * ( • Sensor C4 Measured output RTD=R2 T(t) > Transform according to Tliwh x - iwj x*|tlexp(-iwt)dt 7^ and take IFT A T(t) • R1 R1 .R2 A. T(t) t For the sensor alone T(t) * L A R2 From the transformed step responses for the isolated detector,R2, and detector-column combination, R1*R2, deconvolution gives: R 1 = | R 1 » R 2 I * J _ R2 F i g u r e 6.12a D e f i n i t i o n s o f d e v i a t i o n v a r i a b l e s f o r t r a n s f o r m E q u a t i o n 6.1. 6.12b P r o c e d u r e f o r i s o l a t i n g t h e column RTD from t h e i n d i v i d u a l s t e p r e s p o n s e s f o r t h e d e t e c t o r and d e t e c t o r column c o m b i n a t i o n s u s i n g d e c o n v o l u t i o n . IFT r e p r e s e n t s i n v e r s e F o u r i e r t r a n s f o r m . - 282 -f o r c i n g f u n c t i o n ; i . e . G(t) i s the residence time d i s t r i b u t i o n . T h i s i s i l l u s t r a t e d i n Figure 6.12b, showing that deconvolution of the transformed combination and transformed d e t e c t o r responses i s s u f f i c i e n t to generate the r i s e r RTD. P r a c t i c a l a p p l i c a t i o n of Equation 6.1 i s complicated by measurement noise and the f a c t that the F o u r i e r transforms are not b a n d - l i m i t e d . T h i s makes accurate computation of the magnitude and phase angle of the transform i n c r e a s i n g l y i n a c c u r a t e as the Nyquist frequency i s approached. The problem of noise was minimised by smoothing the output response curves from the U.V. recorder manually, and u s i n g manually d i g i t i s e d v e r s i o n s to generate the d i s c r e t e F o u r i e r transforms. T h i s i s p h y s i c a l l y e q u i v a l e n t to removing high frequency f l u c t u a t i o n s , caused by pressure p u l s a t i o n s , using a low pass f i l t e r . Smoothed and segmented v e r s i o n s of the d e t e c t o r response, and the response f o r run Dis 3, are shown i n Figure 6.13. The problem that the transforms are not b a n d - l i m i t e d was solved by using a s p e c i a l F o u r i e r transform subroutine, POLFT, a v a i l a b l e i n the UBC computer l i b r a r y and e s p e c i a l l y s u i t e d to non-band-limited f u n c t i o n s to avoid a l i a s i n g . T h i s r o u t i n e gave what appeared, and were l a t e r shown to be, accurate transforms and i n v e r s e transforms of the i n d i v i d u a l response f u n c t i o n s G(iw) = x - iw J°° x * ( t ) e " l w t dt - 283 -i i i 1 1 1 1 0 1 2 3 4 5 6 Figure 6.13 Smoothed segmented F-curve responses s u i t a b l e for transforming (dead time has been removed). - 284 -and G(iw) = Q - iw Q Q*(t) e ~ l w t dt. These are i n d i v i d u a l l y e q u i v a l e n t to the transforms of the d e r i v a t i v e s of the F curves, i . e . the E curves f o r the d e t e c t o r / r i s e r combination and d e t e c t o r , and can be r e c o g n i s e d as such i n the time domain, Fi g u r e 6.14. However, although the i n d i v i d u a l transforms are s u f f i c i e n t l y a c c u rate to generate u s e f u l RTD's when they are i n v e r t e d * , the r e s u l t becomes i n a c c u r a t e at high frequency i f they are d i v i d e d . T h i s occurs because both r e a l and imaginary components of both transforms approach zero at high frequency, and the r e s u l t of the d i v i s i o n becomes extremely s e n s i t i v e to small absolute e r r o r s i n e i t h e r transform. Once t h i s problem was recognised, a good approximation to the F o u r i e r c o e f f i c i e n t s of the quotient at high frequency c o u l d be obtained by e x t r a p o l a t i n g the r e a l and imaginary •Whenever a F o u r i e r transform was i n v e r t e d , i t was assumed that the i n v e r s e transform (the RTD) was r e a l . Under these circumstances the second h a l f of the F o u r i e r c o e f f i c i e n t s are the complex conjugates of the f i r s t h a l f . I f there i s any noise, t h i s w i l l not occur n a t u r a l l y when the data are manipulated i n any way (e.g., d i f f e r e n t i a t i o n i n the time domain which i s e q u i v a l e n t to m u l t i p l i c a t i o n by 'iw' i n the frequency domain). Therefore the c o n d i t i o n was enforced. - 285 -UJ Time (s) Figure 6.14 E-curves for the detector ( c i r c l e s ) and d e t e c t o r / r i s e r combination (squares) from the inverse transforms of the transformed step responses. - 286 -p a r t s from where they are accurate, at low frequency, to high frequency where both r e a l and imaginary p a r t s approach zero. Both components appear to approach zero r a p i d l y , F i g u r e 6.15, so a l i n e a r e x t r a p o l a t i o n appeared to s u f f i c e . F i n a l l y , when the transform, c o r r e c t e d i n t h i s manner, i s i n v e r t e d , then the r e s u l t i s an RTD f o r the r i s e r alone. To e s t a b l i s h the accuracy of the RTD obtained i n t h i s manner, i t was convoluted with the d e t e c t o r response and the r e s u l t was compared with the combined response f u n c t i o n as shown i n F i g u r e 6.16. T h i s comparison i s favourable, h e l p i n g to e s t a b l i s h the v a l i d i t y of the approach. 6.4 Results, Discussion and Modelling A r i g o r o u s RTD determination was made f o r run Dis 3. The r e s u l t i n g RTD i s shown i n Figure 6.17. Although the t e s t s of Cankurt and Yerushalmi (1978) and Yang (1983) are v a l i d i n i n d i c a t i n g very l i t t l e upstream d i s p e r s i o n , our r e s u l t s i n d i c a t e that these e a r l y r e s u l t s would give a f a l s e impression of the t o t a l amount of mixing i f a p p l i e d to our r i s e r . D i s p e r s i o n can be s u b s t a n t i a l at the high suspension d e n s i t y of run Dis 3 which averages 100 kg/m over the t o t a l column l e n g t h . A plug flow approximation to the r e s i d e n c e time d i s t r i b u t i o n could give large e r r o r s i n conversion and s e l e c t i v i t y . The RTD of Figure 6.17 i s not s u i t a b l e f o r d e s c r i p t i o n u s i n g a d i s p e r s i o n model. The large standard d e v i a t i o n - 287 -1.6 0.8 t 1.2 c o c o a £ o o LL >» mm CO c 5S CO E ? 0.4 CO "co <D Re Im x-1 O • TRANSFORM EXTRAPOLATION REQUIRED IN THIS AREA BECAUSE SUBSTANTIAL ERRORS RESULT FROM DIVISION OF SMALL NUMBERS FREQUENCY = (0.1 SECONDS)(ADDRESS-1) 4 8 1^ 16 ? 0 P o i n t A d d r e s s In D i s c r e t e F T Extrapolation of the real and imaginary components of the Fourier transform of the r i s e r RTD beyond their region of accuracy to approximate higher frequency components before inversion. Figure 6.15 - 288 -Time (s) F i g u r e 6.16 Comparison of the experimental r i s e r / d e t e c t o r combination F-curve with the c o n v o l u t i o n of c a l c u l a t e d r i s e r and d e t e c t o r RTD's subjected to a step input. Dead time has been removed. Comparison i s f a v o u r a b l e . - 289 -T i 1 1 1 1 1 r I 1 1 1 I I I I L 0 1 2 3 4 T i m e (s) Figure 6.17 RTD for run Dis 3 computed by deconvolution. Dead time removed. - 290 -about the mean would require a small axial Peclet number, but this i s inconsistent with the small amount of forward dispersion. A more appropriate model, e.g. a two-phase model, similar in form to the model applied by Yerushalmi (1986) in the bubbling and turbulent regimes, would appear to be needed. In applying the two phase model to the fast bed regime, the two phases which are assumed are a core of constant cross-section through which a l l of the gas passes, and a stagnant annulus; this i s i l l u s t r a t e d in Figure 6.18. Both the core and annular regions are assumed to be well mixed r a d i a l l y . While this representation i s obviously a tremendous s i m p l i f i c a t i o n of the true flow structure, there are a number of factors which support modelling the system in this way: ( i ) Radial density d i s t r i b u t i o n s measured in Section 3.2.6 show a flow structure with core and annular sections where, at the f a i r l y low densities prevailing over much of the column (< 50 kg/m3), the density i s distributed quite uniformly r a d i a l l y to within approximately 20 mm of the wall. ( i i ) B i e r l et a l . (1980) indicate that r a d i a l gas mixing within a core region i s rapid at high solids fluxes, supporting the approximation of a well mixed core zone. - 291 -R<«-AZ Each Zone Well Mixed Radially 1 / \ C c i u 9 Stagnant Annulus Plug Flow Core F i g u r e 6.18 Two zone model f o r gas mixing i n a c i r c u l a t i n g f l u i d s e d bed. C a = c o n c e n t r a t i o n i n annulus, C c = c o n c e n t r a t i o n i n core, r c = core r a d i u s , R = column r a d i u s , k = mass t r a n s f e r ( c r o s s f l o w ) c o e f f i c i e n t . - 292 -( i i i ) Separate experiments, i n which t r a c e r was i n j e c t e d c o n t i n u o u s l y at the w a l l , and measured at p o i n t s on the wall upstream and downstream, showed that gas flow at the wa l l was p e r i o d i c a l l y up and down f o r s o l i d s loadings greater than 30 kg/m 3. With l i t t l e i n f o r m a t i o n a v a i l a b l e , s i m p l i c i t y suggested modelling the annular zone as stagnant. ( i v ) A gas flow model of t h i s type, although not r e q u i r i n g interchange between core and annular r e g i o n s , has been used s u c c e s s f u l l y by B r i e n s and Bergougnou (1986) f o r a choking model, (v) The model i s s i m i l a r to the freeboard model of Horio et al_. (1985), d i s c u s s e d i n S e c t i o n 4.1.4, which was r a t i o n a l i s e d at that point as being q u i t e s u i t a b l e f o r the d i l u t e regions of a c i r c u l a t i n g bed. Weaknesses of the two zone model are: ( i ) I t i s uns u i t e d to d e s c r i b i n g the spread i n residence times caused by s u b s t a n t i a l v e l o c i t y g r a d i e n t s i n the high d e n s i t y region at the base of the bed and perhaps over a s u b s t a n t i a l f r a c t i o n of i t s length, ( i i ) As a p p l i e d i n t h i s study, the two zone model i s c h a r a c t e r i s e d by two parameters: a c r o s s f l o w - 293 -c o e f f i c i e n t and the f r a c t i o n a l area occupied by the annulus. S i n g l e best f i t parameters are generated which optimise the f i t of the model over the e n t i r e column. However, i n p r a c t i c e , these parameters almost c e r t a i n l y vary with height along the column according to l o c a l c o n d i t i o n s . The equations f o r the two-zone model are given below, with d e f i n i t i o n s of the v a r i o u s symbols given i n F i g u r e 6.18. 9C 9, 3C °_ + £K ( c _ c ) + rj c = 0 (6.2) 3t r v c a' c 3Z v ' c 8 C a 2 k r c a c (C - C ) = 0 (6.3) 9 t (R 2 - r ) C a c Note that the voidage i s assumed to be approximately u n i t y i n both core and annulus r e f l e c t i n g the o v e r a l l low d e n s i t y . These equations were solved, with the i n i t i a l c o n d i t i o n of an impulse a d d i t i o n of t r a c e r to the base of the column, using an e x p l i c i t f i n i t e d i f f e r e n c e r o u t i n e to give residence time d i s t r i b u t i o n s f o r v a r i o u s c o n d i t i o n s of c r o s s f l o w and annulus area. The p r e d i c t i o n s of the two zone model with best f i t parameters are compared with the measured residence time - 294 -d i s t r i b u t i o n in Figure 6.19; two results are shown. The f i r s t result i s the best solution which could be obtained i f a continuity condition was imposed, i . e . UgirR2 = U c l r r c 2 (6.4) A better result could not be obtained because the requirement that the tracer begins to appear at approximately 1 second demands a small annulus which i s not conducive to a large spread in residence time. By removing the continuity requirement, but in doing so compromising the model somewhat, the second result was obtained which shows excellent agreement with the experimental result. The agreement i s actually enhanced by some numerical dispersion in the numerical solution causing some apparent forward dispersion which would not be evident with a more accurate numerical scheme. Hence the simple core annular model, with a stagnant annulus, i s not a p a r t i c u l a r l y good representation of mixing patterns in the c i r c u l a t i n g bed. However, i t is substantially better than a plug flow approximation or a simple dispersion model and i s a useful st a r t i n g point for further developments. Major improvements in the model can be visualised by inclusion of dispersion in the core and annulus and/or vel o c i t y gradients in one or both zones. Any one of these could increase the amount of backmixing without compromising - 295 -Time (s) Figure 6.19 Comparison of the RTD for the r i s e r f or run Dis 3 with best f i t p r e d i c t i o n s of the two zone model• a - c o n t i n u i t y obeyed, r c = 0.059 m, k = 0.11 m/s b - c o n t i n u i t y relaxed, r c = 0.059 m, k = 0.08 m/s, U c = 8.55 m/s - 296 -the c o n t i n u i t y c o n d i t i o n . In a d d i t i o n , the model should be r e w r i t t e n to account f o r l o c a l c o n d i t i o n s , which as shown below are very important, r a t h e r than using lumped c o e f f i c i e n t s to d e s c r i b e the performance of the whole column. A d e t a i l e d r e s i d e n c e time d i s t r i b u t i o n a n a l y s i s was only performed f o r run Dis3. Other gas mixing data were analysed i n terms of the pseudo-dispersion c o e f f i c i e n t and compared on t h i s b a s i s . F i g u r e 6.20 i s a graph of t h i s c o e f f i c i e n t p l o t t e d a g a i n s t the t o t a l column pressure drop f o r runs DisO through to Dis7, where gas v e l o c i t y was he l d constant and t o t a l pressure drop and column e x i t geometry were v a r i e d . The pseudo-dispersion c o e f f i c i e n t i n c r e a s e s w i t h i n c r e a s i n g mean s o l i d s suspension d e n s i t y f o r both of the e x i t s which were employed. Increased mean hold-up appears to i n c r e a s e the suspension d e n s i t y i n the v i c i n i t y of the wal l as de s c r i b e d i n Chapter 4, which i n turn i s r e f l e c t e d i n i n c r e a s e d gas downflow and backmixing. More s u r p r i s i n g i s the dramatic e f f e c t of the e x i t type upon the d i s p e r s i o n c o e f f i c i e n t at constant mean hold-up. The smooth e x i t r e s u l t s i n a dramatic i n c r e a s e i n a x i a l d i s p e r s i o n r e l a t i v e to the abrupt design under c o n d i t i o n s of i d e n t i c a l t o t a l hold-up. T h i s o b s e r v a t i o n could have important i m p l i c a t i o n s f o r general r i s e r r e a c t o r design. In S e c t i o n 4.2 i t was - 297 -20 Total Pressure Drop (mm Hg) F i g u r e 6.20 P l o t of pseudo v e s s e l d i s p e r s i o n number (D/UgL) f o r a x i a l mixing against pressure drop i n a c i r c u l a t i n g bed of sand, Ug = 7.1 m/s. - 298 -e s t a b l i s h e d that the e x i t design could be used to c o n t r o l r a t i o s of i n t e r n a l - t o - e x t e r n a l c i r c u l a t i o n , d i f f e r e n t types of c o n t a c t o r r e q u i r i n g d i f f e r e n t r a t i o s f o r optimum performance. It i s now c l e a r that the e x i t design a l s o i n f l u e n c e s the gas mixing, a f a c t o r which i n turn a f f e c t s o v e r a l l r e a c t o r performance. In an e f f o r t to understand the impact of e x i t geometry upon d i s p e r s i o n , measurements were made of absolute pressure f l u c t u a t i o n s i n the r i s e r 533 mm above the d i s t r i b u t o r u s ing the D i s a c a p a c i t a t i v e pressure transducer f o r d i f f e r e n t t o t a l pressure drops over the column. The gas v e l o c i t y was held constant at 7.1 m/s. F i g u r e 6.21 shows the standard d e v i a t i o n of the pressure f l u c t u a t i o n s p l o t t e d a gainst the t o t a l r i s e r pressure drop and i l l u s t r a t e s a dramatic d i f f e r e n c e between c o n d i t i o n s at the base of the column f o r the two e x i t s . In the smooth e x i t case the standard d e v i a t i o n r i s e s very r a p i d l y to a high value a s s o c i a t e d with a choked dense phase forming at the base of the column. However, when the abrupt e x i t i s used, there i s a very much more uniform d i s t r i b u t i o n of s o l i d s over the column at a given t o t a l pressure drop, with a lower standard d e v i a t i o n of pressure f l u c t u a t i o n s . These o b s e r v a t i o n s appear to be r e l a t e d to the net gas phase mixing. The upward and downward movements of s o l i d s , which appear to be p r i m a r i l y r e s p o n s i b l e f o r the pressure - 299 -gure 6.21 V a r i a t i o n of the standard d e v i a t i o n of a bsolute pressure f l u c t u a t i o n s near the base of the c i r c u l a t i n g f l u i d i s e d bed with t o t a l pressure drop over the u n i t for d i f f e r e n t e x i t geometries, c i r c l e s represent abrupt e x i t , squares smooth. - 300 -f l u c t u a t i o n s , a l s o generate s u b s t a n t i a l gas mixing. Although t h i s mechanism i s not completely c o n s i s t e n t with the two zone model of mixing developed e a r l i e r , which assumes r a d i a l t r a n s f e r processes to be responsible f o r mixing, the defects of the two zone model were noted, and t h i s r e s u l t i s c o n s i s t e n t with the defects. However, independent of the v a l i d i t y of the two-zone model, pressure f l u c t u a t i o n s can be r a t i o n a l i s e d as a means for generating d i s p e r s i o n , and i t appears that the r e l a t i o n s h i p i s non-linear under the c o n d i t i o n s studied here. Large f l u c t u a t i o n s at the base of the smooth e x i t column, caused by the build-up of the choked dense phase, create large d i s p e r s i o n , perhaps because they remain undamped — there are few s o l i d s above to provide a damping e f f e c t . On the other hand, with the abrupt e x i t , s o l i d s are w e l l d i s t r i b u t e d , c r e a t i n g damping of pressure f l u c t u a t i o n s which remain at t h e i r l o c a l l e v e l r e l a t e d to l o c a l s o l i d s motion. Gas mixing i s e v i d e n t l y a subject which requires considerably more a t t e n t i o n . This p r e l i m i n a r y study has r a i s e d some i n t e r e s t i n g i s s u e s : ( i ) I t i s c l e a r that gas may not be close to plug flow i n a c i r c u l a t i n g bed. ( i i ) E x i t geometry can s u b s t a n t i a l l y a f f e c t gas mixing because of i t s impact upon hydrodynamics. - 301 -( i i i ) A two-zone model, modified to i n c l u d e a phase v e l o c i t y f o r the annulus or with other c o r r e c t i o n s , may be a v i a b l e s t a r t i n g p o i n t f o r a workable gas mixing model which i s c o n s i s t e n t with s o l i d s flow p a t t e r n s , p a r t i c u l a r l y i f the model i s a p p l i e d to the more d i l u t e regions of a f a s t bed. - 302 -7. SUMMARY AND CONCLUSIONS In summarising the r e s u l t s of t h i s t h e s i s we consider elements of the I n t r o d u c t i o n and examine how our views have been modified by the present experiments. At the outset of the study i t was c l e a r that small scale c i r c u l a t i n g beds are inf l u e n c e d by the w a l l where a layer of high density s o l i d s forms, but i t was unclear what the nature of core was, how dramatic was the t r a n s i t i o n between core and annulus, and to what extent agglomeration accounted for many c i r c u l a t i n g bed p r o p e r t i e s . Our r e s u l t s , the measurements of r a d i a l d e n s i t y p r o f i l e s and the development of an int e r m i t t e n c y index, suggest that the w a l l i s s u b s t a n t i a l l y responsible f o r the c h a r a c t e r i s t i c density decay p r o f i l e s . Comparison with density p r o f i l e s from large u n i t s suggests that t h i s may a l s o hold on scale-up. The r e s u l t s confirm strong r a d i a l v a r i a t i o n s i n density i n our 152 mm d i a . u n i t , with the character of the time-mean r a d i a l density p r o f i l e , and the instantaneous f l u c t u a t i o n s i n density, changing markedly with height and average s o l i d s loading. High loadings at the base of the vessel produced a strong two phase character, or i n t e r m i t t e n c y , even on the c e n t r e l i n e of r i s e r , which i s suggestive of aggregate formation. Also the power spectrum was i n d i c a t i v e of a f a i r l y random s e r i e s of - 303 -aggregate formation and d e s t r u c t i o n processes of the type i m p l i e d i n the c l u s t e r models of high v e l o c i t y f l u i d i s a t i o n . However, t h i s two phase character on the c e n t r e l i n e r a p i d l y gives way to a more homogeneous s t r u c t u r e higher up the reactor as the s o l i d s d ensity decays. We suggest that combinations of r a d i a l convective gas flows and turbulence i n t e n s i t y gradients may be responsible f o r r e c t i f i c a t i o n of the s o l i d s p r o f i l e s to the more t y p i c a l l y core-annular s t r u c t u r e found sev e r a l metres above the s o l i d s r e t u r n , and have defined f a s t f l u i d i s a t i o n as the decay zone where the r e c t i f i c a t i o n process takes place. From t h i s p e r s p e c t i v e , neither a core-annular model nor a c l u s t e r model can adequately be used conceptually to describe a c i r c u l a t i n g bed. However, i n view of the apparent importance of the r a d i a l nonuniformity to describe many f a s t f l u i d i s e d bed phenomena, v a r i a n t s of core-annular models may be p r e f e r a b l e i n many circumstances. The d e f i n i t i o n of a f a s t f l u i d i s e d bed as the density r e c t i f i c a t i o n region between asymptotic l i m i t s of choked dense and d i l u t e phases d e l i n e a t e s f a s t f l u i d i s a t i o n from the c i r c u l a t i n g f l u i d i s e d bed. We consider that f a s t f l u i d i s a t i o n may e x i s t as a region of an otherwise choked r e a c t o r whereas a c i r c u l a t i n g bed, with the property of c o n t r o l l a b i l i t y , can only e x i s t when f a s t f l u i d i s a t i o n occurs over most of i t s length. Hence, we would dispute the - 304 -d i s t i n c t i o n between choking and non-choking systems from a fundamental standpoint based upon s o l i d s and gas p r o p e r t i e s . However, an operator may observe choking i n a system with large height-to-diameter r a t i o when a dense phase of some nature, bubbling, slugging or t u r b u l e n t ^ w i l l almost f i l l the reactor at a c r i t i c a l s o l i d s f l u x . The phenomena of choking, the saturated c a r r y i n g c a p a c i t y , e x i t e f f e c t s and gas mixing may a l l be explained based on r a d i a l non-uniformity o r i g i n a t i n g at the w a l l . In the f i r s t two cases t h i s leads i n d i r e c t l y to the idea of a unique s t a b l e s t a t e f o r a given gas v e l o c i t y and s o l i d s f l u x , other than at the choking f l u x i t s e l f ; i n the l a s t two cases r a d i a l nonuniformity provides one p l a u s i b l e explanation f o r trends and p h y s i c a l e f f e c t s . E x i t s were found to have a s u b s t a n t i a l i n f l u e n c e on both the gas and s o l i d f l u i d mechanics, and gas mixing s t u d i e s showed RTD's s u b s t a n t i a l l y d i f f e r e n t from plug flow. F i n a l l y , the turbulent t r a n s i t i o n was studied and found to be a gradual t r a n s i t i o n to a more homogeneous s t a t e . However,substantial dense phase homogeneity was not achieved u n t i l w e l l i n t o a transport regime. - 305 -8. RECOMMENDATIONS The D i s c u s s i o n and Summary s e c t i o n s of t h i s t h e s i s are t e n t a t i v e i n t h e i r c o n c l u s i o n s because i n s u f f i c i e n t data were a v a i l a b l e to e i t h e r v a l i d a t e or d i sprove many of the i d e a s . Hence, the recommendations focus p r i m a r i l y upon extensions of the present work, to expand the e x i s t i n g data base and to design experiments which c o n t r o l f a c t o r s now known to i n f l u e n c e c i r c u l a t i n g f l u i d i s e d beds. The recommendations are: ( i ) To make use of f i b e r o p t i c technology to determine r a d i a l and v e r t i c a l components of v e l o c i t y f o r p a r t i c l e s at d i f f e r e n t l o c a t i o n s i n the u n i t . These data should help to determine what c i r c u l a t i o n p a t t e r n s are e s t a b l i s h e d w i t h i n the f a s t f l u i d i s e d bed and choked r e g i o n s , and e s t a b l i s h more concrete decay mechanisms, ( i i ) To vary the height of the c i r c u l a t i n g bed at UBC and hence to e s t a b l i s h the v a l i d i t y of the choking arguments with t h e i r dependence upon height to diameter r a t i o s , ( i i i ) To vary the diameter of the c i r c u l a t i n g bed under otherwise constant c o n d i t i o n s and to e s t a b l i s h the v a r i a t i o n of decay length with length to diameter r a t i o . - 306 -( i v ) To perform a l l t e s t s under c o n d i t i o n s where the e x i t can be r e a d i l y c h a r a c t e r i s e d ( p r e f e r a b l y smooth) and where the s o l i d s feed can a l s o be c h a r a c t e r i z e d . The cu r r e n t feed geometry i s very u n s u i t a b l e f o r v a l i d a t i n g mathematical d e s c r i p t i o n s of the CFB because the manner i n which s o l i d s are fed does not give a known i n i t i a l d i s t r i b u t i o n , (v) To examine the p o s s i b i l i t y of c h a r a c t e r i s a t i o n of e x i t s using a r e f l e c t i o n c o e f f i c i e n t , and the s i g n i f i c a n c e of e x i t e f f e c t s i n l a r g e u n i t s , ( v i ) To examine the impact of s w i r l a i r upon decay length under c o n t r o l l e d c o n d i t i o n s where i t can be introduced as the primary a i r f o r the system, ( v i i ) To f u r t h e r the s t u d i e s and modelling of the gas mixing phenomena to produce more r e a l i s t i c models and c o e f f i c i e n t s v a l i d f o r l o c a l use i n larg e s c a l e systems. - 307 -N O M E N C L A T U R E A Area f o r heat t r a n s f e r m Ar Archimedes number d 3 ( p (p -p ) / P 2 ) P g P g a L i v e wire r a d i u s f o r ca p a c i t a n c e probe m b Sheath inner r a d i u s f o r cap a c i t a n c e probe m C Capacitance of c o a x i a l c y l i n d r i c a l f c a p a c i t o r C a Tracer c o n c e n t r a t i o n i n annulus mol/m3 C c Tracer c o n c e n t r a t i o n i n core mol/m D Diameter of c y l i n d r i c a l column m D R e l a t i v e p e r m i t t i v i t y D A x i a l d i s p e r s i o n c o e f f i c i e n t m/s dp Mean p a r t i c l e diameter m dp32 Sauter mean p a r t i c l e diameter m E Response to u n i t impulse f o r c i n g f u n c t i o n F Response to u n i t step f u n c t i o n G s S o l i d s c i r c u l a t i o n f l u x kg/m 2s g A c c e l e r a t i o n due to g r a v i t y m/s 2 H Q O v e r a l l heat t r a n s f e r c o e f f i c i e n t W/m K k Mass t r a n s f e r ( c r o s s f l o w ) c o e f f i c i e n t m/s L T o t a l length m 1 Length c o o r d i n a t e m n Richardson-Zaki index p Pressure Q Heat t r a n s f e r r a t e W - 308 -R Radius of c y l i n d r i c a l column m Re Reynolds number r c Radius of core m t Time s U L o c a l f l u i d v e l o c i t y m/s U c S u p e r f i c i a l f l u i d v e l o c i t y i n core m/s Ug S u p e r f i c i a l gas v e l o c i t y i n column m/s U m f Minimum f l u i d i s a t i o n v e l o c i t y m/s U z L o c a l v e r t i c a l component of f l u i d m/s v e l o c i t y U' Turbulent f l u c t u a t i n g v e l o c i t y component m/s TJ S u p e r f i c i a l f l u i d v e l o c i t y i n column m/s V i M o d i f i e d p a r t i c l e t e r m i n a l v e l o c i t y m/s V r S i n g l e p a r t i c l e t e r m i n a l v e l o c i t y m/s w Frequency H z Z Height c o o r d i n a t e m Z Q Decay length d e f i n e d by L i and Kwauk m (1980 ) Zj[ I n f l e c t i o n p o i n t height d e f i n e d by L i m and Kwauk ( 1980 ) a R e f l e c t i o n c o e f f i c i e n t a S o l i d s volume f r a c t i o n a c h S o l i d s volume f r a c t i o n at choking Y In t e r m i t t e n c y index E Average voidage i n a c r o s s s e c t i o n of a column e(r) Local voidage at radiu s r - 309 -e a L i m i t i n g d i l u t e phase voidage e Q P e r m i t t i v i t y of f r e e space N/m2 e* L i m i t i n g dense phase voidage y V i s c o s i t y of gas Pa.s p Gas d e n s i t y p e Suspended s o l i d s d e n s i t y at e x i t plane kg/m 3 P L Loose packed bed d e n s i t y kg/m pp P a r t i c l e / d e n s i t y kg/m 3 Psusp Suspended s o l i d s d e n s i t y averaged kg/m3 over cross s e c t i o n o p L o c a l time mean suspended s o l i d s d e n s i t y kg/m 0 Standard d e v i a t i o n 1 P r a n d t l mixing length m S u b s c r i p t s - ( l e t t e r s ) a Annulus c Core c C l u s t e r ch Choking e E x i t g or G Gas i M o d i f i e d with column c o r r e c t i o n L L i q u i d mf Minimum f l u i d i s a t i o n o O v e r a l l p P a r t i c l e - 310 -s S o l i d s sec Above secondary a i r ports t Terminal z V e r t i c a l component S u b s c r i p t s - (numbers) 0 Free space ( p e r m i t t i v i t y ) REFERENCES Abed, R. (1983). The c h a r a c t e r i s a t i o n of t u r b u l e n t f l u i d - b e d hydrodynamics, Proceedings of the IV I n t e r n a t i o n a l Conference on F l u i d i z a t i o n , paper 2-5, Kashikojima, Japan. Almstedt, A.E., and Olsson, E. (1982). Measurements of bubble behaviour i n a p r e s s u r i z e d f l u i d i z e d bed burning c o a l using capacitance probes, Proc. 7th I n t e r n . F l u i d i z e d Bed Combustion Conf., 89-98, P h i l a d e l p h i a . Arena, U., Cammarota, A., and P i s t a n e , L. (1985). High v e l o c i t y f l u i d i z a t i o n behaviour of s o l i d s i n a l a b o r a t o r y s c a l e c i r c u l a t i n g bed, i n " C i r c u l a t i n g f l u i d i z e d bed technology," 119-126, P. Basu ed., Pergammon Press, Toronto. Avidan, A.A. (1980). Bed expansion and s o l i d mixing i n high v e l o c i t y f l u i d i z e d beds, Ph.D. d i s s e r t a t i o n , C i t y U n i v e r s i t y of New York, New York. Bakker, P.J., and H e e r t j e s , P.M. (1959). P o r o s i t y d e termination i n f l u i d i s e d beds. B r i t i s h Chemical E n g i n e e r i n g , 524-529, October. Bartholomew, R.N., and Casagrande, R.M. (1957). Measuring s o l i d s c o n c e n t r a t i o n i n f l u i d i z e d systems by gamma ray a b s o r p t i o n , Ind. and Engng. Chem., V o l . 49, No. 3, 428-431, March. Bendat, J.S. (1971). Random data: a n a l y s i s and measurement procedures, I n t e r s c i e n c e - W i l e y , New York. Bendat, J.S. (1980). Engineering a p p l i c a t i o n s of s p e c t r a l a n a l y s i s , I n t e r s c i e n c e - W i l e y , New York. B i e r l , T.W., Gajdos, L . J . , Mclver, A.E., and McGovern, J . J . (1980). S t u d i e s i n support of r e c i r c u l a t i n g bed r e a c t o r s f o r the p r o c e s s i n g of c o a l , DOE r e p o r t Ex-C-76-01-2449, J u l y . B r e r e t o n , C., Chaouki, J . , Grace, J.R., Legros, R., and Yeung, J . (1987). Hydrodynamic behaviour of a s i l i c a a e r o g e l powder i n a c i r c u l a t i n g f l u i d i s e d bed, Presented at 37th Canadian Chemical E n g i n e e r i n g Conference, Montreal, Quebec. Brereton, C., and Stromberg, L. (1985). Some aspects of the f l u i d dynamic behavour of f a s t f l u i d i z e d beds, i n " C i r c u l a t i n g f l u i d i z e d bed technology," P. Basu ed., 133-144, Pergammon Press, Toronto. - 312 -B r i e n s , C.L., and Bergougnou, M. (1986). A new model to c a l c u l a t e the choking v e l o c i t y o i monosize and m u l t i s i z e s o l i d s i n v e r t i c a l pneumatic t r a n s p o r t , Can. J . Chem. Eng., V o l . 64, 196-204, A p r i l . Burke, S.P., and Plummer, W.B. (1928). Ind. Eng. Chem., V o l . 20, 1196. B u r k e l l , J . (1986). S o l i d s c i r c u l a t i o n r a t e measurements i n c i r c u l a t i n g f l u i d i z e d beds. M.A.Sc. T h e s i s , UBC, Vancouver. Canada, G.S., McLaughlin, M.H., and Staub, F.W. (1978). Flow regimes and voi d f r a c t i o n d i s t r i b u t i o n i n gas f l u i d i z a t i o n of large p a r t i c l e s i n beds without tube banks, A.I.Ch.E.Symp.Ser., V o l . 74, No. 176, 14-26. Cankurt, N.T., and Yerushalmi, J . (1978). Gas backmixing i n high v e l o c i t y f l u i d i z e d beds, i n " F l u i d i z a t i o n , " Proceedings of the Second E n g i n e e r i n g Foundation Conference, J.F. Davidson and D.L. Keairns eds., 387-392, Cambridge U n i v e r s i t y P r e s s , Cambridge. Capes, C.E. (1974). P a r t i c l e agglomeration and the value of the exponent n i n the Richardson-Zaki equation, Powder Techo l . , V o l . 10, 303-306. Capes, C.E., and mcllh i n n e y . (1968). The p s e u d o - p a r t i c u l a t e expansion of screen-packed g a s - f l u i d i z e d beds, A.I.Ch.E.J., V o l . 14, No. 6, 917. Carotenuto, L., C r e s c i t e l l i , S., and Donsi, G. (1974). High v e l o c i t y behaviour of f l u i d i z e d beds; c h a r a c t e r i s a t i o n of regimes, Ing. Chim. I t a l . , V o l . 10, No. 12, 185-193. C r e s c i t e l l i , S., Donsi, G., and C l i f t , R. (1978). High v e l o c i t y behaviour of f l u i d i z e d beds; slugs and t u r b u l e n t flow, Proceedings of Chisa Conference, Prague, Aug. Crowther, M.E., and Whitehead, J.C. (1978). In " F l u i d i z a t i o n , " J.F. Davidson and D.L. Keairns eds., 65-70, Cambridge U n i v e r s i t y Press, London. Davidson, J.F., and H a r r i s o n , D. (1963). F l u i d i s e d p a r t i c l e s , Cambridge U n i v e r s i t y Press, Cambridge. DeLasa, H., and Gau, G. (1973). Influence des agregats sur le rendement d'un reacteur a t r a n s p o r t pneumatique, Chem. Eng. S c i . , V o l . 28, 1875-1884. - 313 -Engstrom, F., Osakeyhtio, A.A., and Sahagian, J . (1985). Operating experience with c i r c u l a t i n g f l u i d i z e d bed b o i l e r s , i n " C i r c u l a t i n g f l u i d i z e d bed technology," P. Basu ed., Pergammon Press, Toronto. F i o c c o , R.J., and S t a f f i n , H.K. (1967). Paper presented at 61st N a t i o n a l Am. I n s t . Chem. Engrs. Meeting. F i t z g e r a l d , T. (1976). Report to EPRI, CS 1476, S e c t i o n 8, Bubble Measurement Instrumentation. Ford, T.F. (1950). Chem. Eng. News, V o l . 28, 1300. Fusey, I., Lim, C.J., and Grace, J.R. (1985). Fast f l u i d i z a t i o n i n a c o n c e n t r i c c i r c u l a t i n g bed, i n " C i r c u l a t i n g f l u i d i z e d bed technology," 409-416, P. Basu ed., Pergammon P r e s s , Toronto. G e l d a r t , D. (1972). The e f f e c t of p a r t i c l e s i z e and s i z e d i s t r i b u t i o n on the behaviour of g a s - f l u i d i z e d beds, Powder Technol., V o l . 6, 201-205. G e l d a r t , D. (1973). Types of g a s - f l u i d i z a t i o n , Powder Technol., V o l . 7, 285-292. G e l d a r t , D. , and C r a n f i e l d , R.R. (1972). The gas f l u i d i z a t i o n of l a r g e p a r t i c l e s , Chem. Eng. J . , V o l . 59, 638-639. G e l d a r t , D. , and Rhodes, M.J. (1985). From minimum f l u i d i z a t i o n to pneumatic t r a n s p o r t - a c r i t i c a l review of the hydrodynamics, i n " c i r c u l a t i n g f l u i d i z e d bed technology," P. Basu, ed., Pergammon Press, Toronto. Glicksman, L.R., and McAndrews, G. (1985). The e f f e c t of bed width on the hydrodynamics of l a r g e p a r t i c l e f l u i d i z e d beds, Powder T e c h o l . , V o l . 42, 159-167. Goddard, K., and Richardson, J.F. (1968). The behaviour of bubble f r e e f l u i d i z e d beds, p r e p r i n t s , The T r i p a r t i t e Chem. Eng. Conf., Montreal. Grace, J.R. (1982). F l u i d i z e d bed hydrodynamics, S e c t i o n 8.1 i n "Handbook of multiphase systems," G. H e t s r o n i ed., McGraw H i l l , New York. Grace, J.R. (1986a). C o n t a c t i n g modes and behaviour c l a s s i f i c a t i o n of g a s - s o l i d and other two-phase suspensions, Can. J . Ch.E., V o l . 64, 353-363. - 314 -Grace, J.R., and Baeyans, J . (1986). Instrumentation and experimental techniques, i n "Gas f l u i d i z a t i o n technology," D. G e l d a r t ed., John Wiley and Sons, C h i c h e s t e r . Grace, J.R. and Tuot, J . (1979). A theory f o r c l u s t e r formation i n v e r t i c a l l y conveyed suspensions of intermediate d e n s i t i e s , Trans. I . Chem. E., V o l . 57, 49-54. Hartge,E.U., L i , Y., and Werther, J . (1985). A n a l y s i s of the l o c a l s t r u c t u r e of the two-phase flow i n a f a s t f l u i d i z e d bed, i n " C i r c u l a t i n g f l u i d i z e d bed technology," P. Basu ed., 153-160, Pergammon P r e s s , Toronto. H e e r t j e s , P.M., Verloop, J . , and Willems, R. (1970/71). The measurement of l o c a l mass flow r a t e s and p a r t i c l e v e l o c i t i e s i n f l u i d - s o l i d s flow," Powder Technol., V o l . 4, 38-40. Hewitt, G.F. (1982). L i q u i d - g a s systems, Chapter 2 i n "Handbook of multiphase systems," G. H e t s r o n i ed., McGraw H i l l , New York. Hewitt, G.F., and Roberts, D.N. (1969). S t u d i e s of two-phase flow p a t t e r n s by simultaneous X-ray and f l a s h photography, Report AERE-M2159, UKAEA, Ha r w e l l . Hinze, J.O. (1959). Turbulence, McGraw H i l l , New York. H i r s c h , M., Janssen, K., and Serbent, H. (1985). The c i r c u l a t i n g f l u i d i s e d bed as a re a c t o r f o r chemical and m e t a l l u r g i c a l processes, i n " C i r c u l a t i n g f l u i d i s e d bed technology," P. Basu ed., 329-340, Pergammon Press, Toronto. Horio, M., Shibata, T., Kadoguchi, K., and Muchi, I . (1985). Behaviour of e n t r a i n e d p a r t i c l e s i n the freeboard, Proceedings of 2nd Japan China f l u i d i z a t i o n conference. Horio, M. , T a k i , A., Hsieh, Y.S., and Muchi, I . (1980). E l u t r i a t i o n and p a r t i c l e t r a n s p o r t through the freeboard of a g a s - s o l i d f l u i d i s e d bed, i n " F l u i d i z a t i o n , " J.R. Grace and J.M. Matsen eds., Plenum Press, New York. Hunt, R.H., B i l e s , W.R. , and Reed, C O . (1957). Find c a t a l y s t d e n s i t y with i s o t o p e s , Petroleum R e f i n e r , V o l . 36, No. 4, 179-182, A p r i l . - 315 -Jackson, R. (1971). Chapter 3 i n " F l u i d i z a t i o n , " J.F. Davidson and D. H a r r i s o n eds., Academic press, London. Jayaweera, K.O.L.F., Mason, B.J., and Slack, G.W. (1964). The behaviour of c l u s t e r s of spheres f a l l i n g i n a vis c o u s l i q u i d , Part 1, Experiment, J . F l u i d Mech., V o l . 20, part 1, 121-128. Jones, 0., and Seber, E.C. (1982). I n i t i a l o p e r a t i n g experience at Conoco's south Texas m u l t i - s o l i d s FBC steam generator, Proceedings of 7th I n t e r n a t i o n a l Conference on F l u i d i z e d Bed Combustion, V o l . 1, 381-389, Pennsylvania. Kehoe, P.W.K., and Davidson, J.F. (1971). I n s t . Chem. Eng. (London) Symp. Ser., V o l . 33, 97. Kehoe, P.W.K., and Davidson, J.F. (1973). P r e s s u r e f l u c t u a t i o n s i n s l u g g i n g f l u i d i z e d beds, AIChE Symp. Ser., V o l . 69, No. 128, 34-40. Knowlton, T.M., and Hi r s a n , I. (1978). L - v a l v e s c h a r a c t e r i z e d f o r s o l i d s flow, Hydrocarbon P r o c e s s i n g , 149-156, March. Kobro, H., and Brereton, C. (1985). C o n t r o l and f u e l f l e x i b i l i t y of c i r c u l a t i n g f l u i d i s e d beds i n " C i r c u l a t i n g f l u i d i z e d bed technology," P. Basu ed., 263-272, Pergammon, Toronto. Kobro, H., and Stromberg, L. (1986). Studsvik E n e r g i t e k n i k , Nykoping, Sweden, Personal Communication. Kozeny, J . (1927). S i t z b e r , Akad. Wiss. Wien, Math-naturw. K l . ( A l t . H a ) ; V o l . 136, 271. K u l l e n d o r f , A., and Andersson, S. (1985). A general review of combustion i n c i r c u l a t i n g f l u i d i z e d beds, i n " C i r c u l a t i n g f l u i d i z e d bed technology," P. Basu ed., Pergammon Pr e s s , Toronto. K u n i i , D., and L e v e n s p i e l , 0. (1969). Entrainment and e l u t r i a t i o n from f l u i d i z e d beds, J o u r n a l of Chemical En g i n e e r i n g of Japan, V o l . 2, No. 1, 84-88. K u n i i , D., and L e v e n s p i e l , 0. (1969). F l u i d i z a t i o n E ngineering, John Wiley and Sons Inc., New York. Lanneau, K.P. (1960). G a s - s o l i d c o n t a c t i n g i n f l u i d i z e d beds, Trans. Ins t n . Chem. Engrs., V o l . 38, 125-143. - 316 -Leung, L.S. (1980). The ups and downs of g a s - s o l i d flow -a review, i n " F l u i d i z a t i o n , " J.R. Grace and J.M. Matsen, eds., Plenum Press, New York. L e v e n s p i e l , 0. (1972). Chemical r e a c t i o n e n g i n e e r i n g , John Wiley and Sons Inc., New York. Lewis, W.K., and G i l l i l a n d , E.R. (1950). U.S. patent No. 2,498,088. Lewis, W.K., G i l l i l a n d , E.R., and Lang, P.M. (1962). Entrainment from f l u i d i s e d beds, Chem. Eng. Prog. Symp. Ser., V o l . 58, No. 38, 65-78. L i , Y., Chen, B., Wang, F., and Wang, Y. (1982). Hydrodynamic c o r r e l a t i o n s f o r f a s t f l u i d i z a t i o n , Proceedings of the f i r s t China-Japan symposium on f l u i d i s a t i o n , 124-134, Hangzhou, China. L i , Y., and Kwauk, M. (1980). The dynamics of f a s t f l u i d i s a t i o n , i n " F l u i d i z a t i o n , " J.R. Grace and J.M. Matsen, eds., 537-544, Plenum Press, New York. L i n , J.S., Chen, M.M., and Chao, B.T. (1985). A novel r a d i o a c t i v e t r a c k i n g f a c i l i t y f o r measurement of s o l i d s motion i n gas f l u i d i z e d beds, A.I.Ch.E.J., V o l . 31, 465-473. Luyben, W.L. (1973). Process modeling, s i m u l a t i o n , and c o n t r o l f o r chemical engineers, McGraw H i l l , New York. M a s s i m i l l a , L. (1973). Behaviour of c a t a l y t i c beds of f i n e p a r t i c l e s at high v e l o c i t i e s , AIChE Symp. Ser., V o l . 69, No. 128, 11-13. Masson, H., J o f f r a n d , R., and Dang Tran, K. (1978). I n t e r n . Cong, on Mixing i n the Chemical I n d u s t r i e s , Mons. Matheson, G.L., Herbst, W.A., and Ho l t , P.H. ( I I ) . (1949). C h a r a c t e r i s t i c s of f l u i d - s o l i d systems, I n d u s t r i a l and Engng. Chem., V o l . 41, No. 6, 1099-1104, June. Matsen, J.M. (1982). Mechanisms of choking and entrainment, Powder Technol., V o l . 31, 21-33. Merry, J.M.D., and Davidson, J.F. (1973). G u l f s t r e a m c i r c u l a t i o n i n shallow f l u i d i z e d beds, Trans. I n s t n . Chem. Engrs., V o l . 51, 361-368. - 317 -Michaels, A.S., and Bolger, J.C. (1962). S e t t i n g rates and sediment volumens of f l o c u l a t e d k a o l i n suspensions, Ind. Eng. Chem. Fundara., V o l . 1, 24. Mogan, J.P., Taylor, R.W., and Booth, F.L. (1969). A method of p r e d i c t i o n of the p o r o s i t i e s of high-pressure gaseous f l u i d i z a t i o n systems, Can. J . Chem. Eng., V o l . 47, 126-130. Mogan, J.P., Taylor, R.W., and Booth, F.L. (1970/71). The value of the exponent n i n the Richardson and Zaki equation for f i n e s o l i d s f l u i d i z e d with gases under pressure, Powder Technol., V o l . 4, 286-289. Morse, R.D., and B a l l o u , CO. (1951). The u n i f o r m i t y of f l u i d i z a t i o n - i t s measurement and use, Chem. Eng. Progress, V o l . 47, No. 4, 199-204. Nakamura, K., and Capes, C.E. (1973). V e r t i c a l pneumatic conveying: a t h e o r e t i c a l study of uniform and annular p a r t i c l e flow models, Can. J . Ch.E., V o l . 51, 39-46. Oki, K., Ishi d a , M., and S h i r a i , T. (1980). The behaviour of j e t s and p a r t i c l e s near the gas d i s t r i b u t o r i n a three-dimensional f l u i d i z e d bed, i n " F l u i d i z a t i o n , " J.R. Grace and J.M. Matsen eds., 421-428, Plenum Press, New York. Rao, V.L., and Venkateswarku, D. (1973). Determination of v e l o c i t i e s and flow patterns of p a r t i c l e s i n mass flow hoppers, Powder Technol., V o l . 7, 263-265. Razumov, I.M., M a n s h i l i n , V.V., Terekhov, N.I., and Agafonov, A.V. (1968). Questions i n the aerodynamics of chemical r e a c t o r s with concurrent motion of the gas and l i q u i d phases, Translated from Khimiya i Tekhnologiya a T o p l i v i Masel, No. 9, 28-33, September. Reh, L. (1985). The c i r c u l a t i n g f l u i d bed reactor - a key to e f f i c i e n t g a s / s o l i d processing, i n " C i r c u l a t i n g f l u i d i z e d bed technology," P. Basu ed., 105-118, Pergammon Press, Toronto. Reh, L., Schmidt, H.W., Daradiraes, G., and Peterson, V. (1980). C i r c u l a t i n g f l u i d bed combustion, an e f f i c i e n t energy technology for energy supply and environmental p r o t e c t i o n , Proc. Inst . Energy I n t e r n a t i o n a l Conference on F l u i d i s e d Bed Combustion, pp. VI-2-1, VI-2-11. Rehbein, C.A., M i t c h e l l , W.A., and Wilson, R.A. (1959). O i l Gas J . , V o l . 25, 108. - 318 -Richardson, J.F., and Davies, L. (1966). Gas interchange between bubbles and the continuous phase i n a f l u i d i z e d bed, Trans. I n s t . Chem. Engrs., V o l . 44, 293. Richardson, J.F., and Za k i , W.N. (1954). Sedimentation and f l u i d i z a t i o n : P a r t I, Trans. Inst n . Chem. Engrs., V o l . 32, 35-53. Rhodes, M.J., and G e l d a r t , D. (1985). The hydrodynamics of r e c i r c u l a t i n g f l u i d i z e d beds, i n " C i r c u l a t i n g f l u i d i z e d bed technology," P. Basu ed., 193-200, Pergammon Press, Toronto. Rhodes, M.J., and G e l d a r t , D. (1986a). T r a n s i t i o n t o turbulence i n " F l u i d i z a t i o n V," K. Ostergaard and A. Sorensen eds., E n g i n e e r i n g Foundation, New York. Rhodes, M.J., and G e l d a r t , D. (1986b). A model f o r the r e c i r c u l a t i n g f l u i d i z e d bed, presented at annual AIChE meeting, Miami, December. Rose, H.E., and Barnacle, H.E. (1957). Flow of suspensions of non-cohesive s p h e r i c a l p a r t i c l e s i n p i p e s , Engineer, June 14, 898-901, June 21, 939-941. Rowe, P.N., and Masson, H. (1980). F l u i d i z e d bed bubbles observed simultaneously by probe and X-rays," Chem. Eng. S c i . , V o l . 35, 1443-1447. Rowe, P.N., and Masson, H. (1981). I n t e r a c t i o n of bubbles with probes i n gas f l u i d i z e d beds, Trans. I. Chem. E., V o l . 59, 177-185. Saxton, A.L., and Worley, A.C. (1970). Modern c a t a l y t i c - c r a c k i n g design. The O i l and Gas J o u r n a l , V o l . 68, No. 20, 82-99, May 18. S c h l i c t i n g , H. (1979). Boundary Layer Theory, McGraw-hill, New York. Schuurmans, H.J.A. (1980). Measurements i n a commercial c a t a l y t i c c r a c k i n g u n i t , Ind. Eng. Chem. Process Des. Dev., V o l . 19, No. 2, 267-271. Schwieger, R. (1985). F l u i d i z e d - b e d b o i l e r s achieve commercial s t a t u s worldwide, Power Magazine, February, 51-516. S c o t t , K.J. (1968). Thickening of calcium carbonate s l u r r i e s , Ind. Eng. Chem. Fundam. V o l . 7, 484. - 319 -S h i m i z u , A., E c h i g o , R., Hasegawa, S., and H i s h i d a , M. ( 1 9 7 8 ) . E x p e r i m e n t a l s t u d y on the p r e s s u r e d r o p and e n t r y l e n g t h of t h e g a s - s o l i d s u s p e n s i o n f l o w i n a c i r c u l a r t u b e , I n t . J . M u l t i p h a s e Flow, V o l . 4, 53-64. S h i m i z u , M., M i z u h a t a , Y., and N o r i y e s h i , M. ( 1 9 6 5 ) . S o l i d l o a d i n g i n d i l u t e - p h a s e f l u i d i z e d beds, Kagaku Kogaku ( a b r i d g e d e d n . ) , V o l . 3, No. 1, 14-18. S m i t h , T.N. ( 1 9 7 8 ) . L i m i t i n g volume f r a c t i o n s i n v e r t i c a l p n e u m a t i c t r a n s p o r t , Chem. Eng. S c i . , V o l . 33, 745-749. Soo, S.L. ( 1 9 8 2 ) . P n e u m a t i c c o n v e y i n g , C h a p t e r 7 i n "Handbook of m u l t i p h a s e s y s t e m s , " G. H e t s r o n i e d . , McGraw H i l l , New Y o r k . Soo, S.L., T r e z e k , G.J., D i m i c k , R.C., and H a h n s t r e i t e r , G.F. ( 1 9 6 4 ) . C o n c e n t r a t i o n and mass f l o w d i s t r i b u t i o n s i n a g a s - s o l i d s u s p e n s i o n , I. and E.C. F u n d a m e n t a l s , V o l . 3, No. 2, 98-106. S t a u b , F.W. ( 1 9 7 9 ) . S o l i d s c i r c u l a t i o n i n t u r b u l e n t f l u i d i z e d beds and h e a t t r a n s f e r t o immersed t u b e banks, T r a n s a c t i o n s o f t h e ASME, J o u r n a l o f H e a t T r a n s f e r , V o l . 101, 391-396, A u g u s t . S t r o m b e r g , L. ( 1 9 8 2 ) . F a s t f l u i d i z e d c o m b u s t i o n o f c o a l , p r e s e n t e d a t 7 t h I n t . C o n f e r e n c e on F l u i d i z e d Bed C o m b u s t i o n , P h i l a d e l p h i a , O c t o b e r . S t r o m b e r g , L. ( 1 9 8 3 ) . P e r s o n a l c o m m u n i c a t i o n , S t u d s v i k E n e r g i t e k n i k AB, N y k o p i n g , Sweden. S t r o m b e r g , L., K o b r o , H., B r e r e t o n , C., M o r r i s , T., and W a l k e r , D.J. ( 1 9 8 5 ) . The f a s t f l u i d i z e d bed - a t r u e m u l t i f u e l b o i l e r , p r e s e n t e d t o t h e e i g h t h i n t e r n a t i o n a l c o n f e r e n c e on f l u i d i z e d - b e d c o m b u s t i o n , H o u s t o n , T e x a s . S q u i r e s , A. ( 1 9 8 5 ) . The s t o r y of f l u i d c a t a l y t i c c r a c k i n g , the f i r s t c i r c u l a t i n g bed, i n " C i r c u l a t i n g f l u i d i z e d bed t e c h n o l o g y , " P. Basu ed., Pergammon P r e s s , T o r o n t o . T h i e l , W.J., and P o t t e r , O.E. ( 1 9 7 7 ) . S l u g g i n g i n f l u i d i z e d beds, I n d . Eng. Chem. Fundam., V o l . 16, No. 2, 242-247. T i p l e r , P.A. ( 1 9 7 6 ) . P h y s i c s , Worth P u b l i s h e r s I n c . , New Y o r k , New Y o r k . T u r n e r , D.H.L. ( 1 9 7 9 ) . T u r b u l e n t and f a s t f l u i d i z a t i o n , Ph.D. D i s s e r t a t i o n , C i t y U n i v e r s i t y o f New Y o r k . - 320 -van Breugel, J.W., S t e i n , J.J.M., and de V r i e s , R.J. (1969-70). I s o k i n e t i c sampling i n a dense g a s - s o l i d s stream, Proc. Instn. Mech. Engrs., V o l . 184, Pt. 3C, 18-23. van Deemter, J . J . (1967). The counter-current flow model of a g a s - s o l i d s f l u i d i z e d bed, i n "Proceedings of the i n t e r n a t i o n a l symposium on f l u i d i z a t i o n , " A.A.H. Drinkenburg ed., 334-347, Netherlands U n i v e r s i t y Press, Amsterdam. Wainwright, M.S., and Hoffman, T.W. (1974). The o x i d a t i o n of o-xylene i n a t r a n s p o r t e d bed r e a c t o r , Advances i n Chemstry, V o l . 133, No. 51, 669-685. Wein, W., and Felwor, P. (1986). C i r c u l a t i n g f l u i d i z e d bed combustion, ZAWSF, f i r s t power s t a t i o n a p p l i c a t i o n i n the HKWI of the Stadtwerke Duisburg AG, Proceedings of VDI conference, " F l u i d i z e d bed combustion (FBC) assessment-concepts-perspectives, 155-170, 3rd - 5th June, Essen. Weiner, 0. (1912). Abhandl, Sachs, Ges. Wiss. Math. Phys. NI., V o l . 32, 509. Weinstein, H., Avidan, A.A., Jean-Louis, J . , and M e l l e r , M. (1981). A x i a l v a r i a t i o n s i n a t r a n s p o r t e d high v e l o c i t y f l u i d i z e d bed, presented at the f a l l annual meeting of the A.I.Ch.E., New Orleans, LA, November. Weinstein, H., G r a f f , R.A., M e l l e r , M., and Shao, M.J. (1983). The i n f l u e n c e of the imposed pressure drop ac r o s s a f a s t f l u i d i s e d bed, Proceedings of the IV i n t e r n a t i o n a l f l u i d i z a t i o n conference, Kashikojima, Japan. Weinstein, H., Shao, M., and S c h n i t z l e i n , M. (1985). R a d i a l v a r i a t i o n i n s o l i d d e n s i t y i n high v e l o c i t y f l u i d i z a t i o n , i n " C i r c u l a t i n g f l u i d i z e d bed technology," P. basu ed., 201-206, Pergammon Pr e s s , Toronto. Werther, J . , and Molerus, 0. (1973). The l o c a l s t r u c t u r e of gas f l u i d i z e d beds - I. A s t a t i s t i c a l l y based measuring system, Int. J . Multiphase Flow, V o l . 1, 103-122. Yang, W.C. (1975). A mathematical d e f i n i t i o n of choking phenomenon and a mathematical model for p r e d i c t i n g choking v e l o c i t y and choking voidage, A.I.Ch.E.J., V o l . 29, 1013-1015. - 321 -Yang, G. , Huang, Z. , and Zhao, L. (1983). R a d i a l gas d i s p e r s i o n i n a f a s t f l u i d i z e d bed, Proceedings of the IV i n t e r n a t i o n a l conference on f l u i d i z a t i o n , Kashikojima, Japan. Yerushalmi, J . (1986). High v e l o c i t y f l u i d i z e d beds, i n "Gas f l u i d i z a t i o n technology," D. G e l d a r t ed., Chapter 7, John Wiley and Sons, C h i c h e s t e r . Yerushalmi, J . , and Avidan, A.A. (1985). H i g h - v e l o c i t y f l u i d i s a t i o n , i n " F l u i d i z a t i o n , second e d i t i o n , " J.F. Davidson, R. C l i f t and D. H a r r i s o n eds., Chapter 7, Academic Press, London. Yerushalmi, J . , and Cankurt, N.T. (1978). H i g h - v e l o c i t y f l u i d beds, Chemtech., September, 564-572. Yerushalmi, J . , and Cankurt, N.T. (1979). Further s t u d i e s of the regimes of f l u i d i z a t i o n , Powder Technol., V o l . 24, 187-205. Yerushalmi, J . , Cankurt, N.T., G e l d a r t , D., and L i s s , B. (1978). Flow regimes i n v e r t i c a l g a s - s o l i d contact systems, A.I.Ch.E. Symp., Ser., No. 176, V o l . 74, 1-13. Yerushalmi, J . , Turner, D.H., and Squires, A.M. (1976). The f a s t f l u i d i z e d bed, Ind. Eng. Chem., Process, Des. Dev., V o l . 15, No. 1, 47-53. Yong, J . , Yu, Z., Wang, Z., and Ping, C. (1986). A c r i t e r i o n f o r t r a n s i t i o n from bubbling to tu r b u l e n t f l u i d i s a t i o n , i n " F l u i d i z a t i o n V," K. Ostergaard and A. Sorenson eds., Engineering Foundation, New York. Y o u s f i , Y., and Gau, G. (1974). Aerodynamique de l'ecoulement v e r t i c a l de suspensions concentrees g a z - s o l i d e s - I. Regimes d'ecculement et s t a b i l i t e aerodynamique, Chem. Eng. S c i . , V o l . 29, 1939-1946. Yu, J . (1986). A x i a l gas d i s p e r s i o n i n a c i r c u l a t i n g f l u i d i z e d bed, B.A.Sc T h e s i s , UBC Dept. of Chemical E n g i n e e r i n g , Vancouver. Zenz, F.A. (1949). Two-phase f l u i d - s o l i d flow, I n d u s t r i a l and Engineering Chemistry, V o l . 41, No. 12, 2801-2806. Zenz, F.A., and Othmer, D.F. (1960). F l u i d i z a t i o n and f l u i d - p a r t i c l e systems, Rheinhold P u b l i s h i n g Corp., New York. - 322 -APPENDIX 1 Sample Output from Computer Program BMP:02T B M O O 2 T - A U T 0 C O V A R I A N C E A N D P O W E R S P E C T R A L A N A L Y S I S - R E V I S E D J U N E 1 9 . 1 9 7 2 H E A L T H S C I E N C E S C O M P U T I N G F A C I L I T Y . U C L A P R O B L E M N U M B E R T R 9 A I N P U T D A T A T O B E P R I N T E D O U T I N P U T S E R I E S T O B E P L O T T E D O U T - - . -0 E T R E N D I N 8 P R E W H I T E N I N G V A L U E O F C O N S T A N T C U S E D I N T H E P R E W H I T E N I N G T R A N S F O R M A T I O N Z ( T ) - X ( T * 1 ) - C X ( T ) - - - 0 . 0 N U M B E R O F S E R I E S • 1 N U M B E R O F O A T A P O I N T S - 1 0 0 0 I N U M B E R O F L A G S C H O S E N - 5 0 03 to N U M B E R O F S E L E C T I O N C A R D S - 1 £ 0 U S E P R E V I O U S D A T A I C O N S T A N T T I M E I N T E R V A L • 0 . 0 2 0 0 0 S E C O N D N U M B E R O F V A R I A B L E F O R M A T C A R D S • 1 V A R I A B L E F O R M A T I S (F12.7) L A G ( S E C O N O ) A U T O C O V A R I A N C E O F S E R I E S 1 0 . 0 0 . 0 2 0 0 0 . 0 4 0 0 0 . 0 6 0 0 O . O B O O 0 . 1 0 0 0 0 . 1 2 0 0 O . 1 4 0 0 0 . 1 6 0 0 O . 1 8 0 0 0 . 2 0 0 0 O . 2 2 0 0 0 . 2 4 0 0 0 . 2 6 0 0 0 . 2 8 0 0 0 . 3 0 0 0 O . 3 2 0 0 0 . 3 4 0 0 0 . 3 6 0 0 0 . 3 B 0 0 0 . 4 0 0 0 0 . 4 2 0 0 0 . 4 4 0 0 0 . 4 6 0 0 0 . 4 8 0 0 0 . 5 0 0 0 0 . 5 2 0 0 0 . 5 4 0 0 0 . 5 6 0 0 0 . 5 8 0 0 0 . 6 0 0 0 0 . 6 2 0 0 0 . 6 4 0 0 0 . 6 6 0 0 0 . 6 8 0 0 0 . 7 0 0 0 0 . 7 2 0 0 0 . 7 4 0 0 0 . 7 6 0 0 0 . 7 8 0 0 0 . 8 0 0 0 0 . 8 2 0 0 0 . 8 4 0 0 0 . 8 6 0 0 0 . 8 8 0 0 0 . 9 0 0 0 0 . 9 2 0 0 0 . 9 4 0 0 0 . 9 6 0 0 0 . 9 8 0 0 1 . 0 0 0 0 1 7 7 4 3 . 6 1 1 4 5 0 . 3 8 2 8 8 . 9 8 6 6 5 9 . 9 6 5 7 1 0 . 3 2 5 3 1 8 . 3 6 4 4 7 8 . 5 2 3 8 3 1 . 0 8 3 2 0 9 . 4 3 2 4 0 6 . 8 4 2 0 8 8 . 1 3 1 9 5 6 . 5 9 1 1 7 4 . 1 7 9 6 9 . 8 2 8 7 0 8 . 4 0 1 7 7 8 . 5 1 8 9 3 4 . 6 0 9 5 6 4 . 5 3 1 3 9 8 . 9 1 0 2 4 5 . 3 6 7 2 2 2 . 4 1 4 1 0 2 . 7 8 1 - 2 1 9 . 1 8 7 - 8 3 3 . 4 5 8 - 1 2 1 8 . 9 3 - 1 1 4 1 . 9 7 - 9 1 6 . 9 2 7 - 7 8 1 . 0 7 2 - 9 8 1 . 0 1 1 - 1 1 4 0 . 3 8 - 9 3 0 . 2 0 7 - 5 8 7 . 9 6 2 - 8 8 0 . 8 3 9 - 8 2 9 . 6 6 6 - 1 2 2 4 . 4 5 - 1 1 2 1 . 9 9 - 1 1 4 6 . 6 3 - 5 4 6 . 2 9 5 - 3 5 . 6 1 7 0 - 3 9 1 . 1 9 3 - 6 1 2 . 8 8 1 - 3 7 6 . 4 8 3 - 3 3 0 . 8 0 8 - 7 1 6 . 0 4 5 - 5 9 7 . 0 5 9 - 4 6 3 . 2 3 5 - 3 6 1 . 0 0 0 - 6 7 2 . 6 0 5 - 4 5 1 . 5 6 7 6 8 . 4 0 8 7 - 2 2 1 . 2 6 9 G R A P H O F A U T O C O V A R I A N C E F U N C T I O N O F S E R I E S 1 P L O T T E D A G A I N S T T I M E U P T O A L A O O F 1 . 0 0 0 0 S E C O N D 2 0 0 0 . 0 0 0 6 0 0 0 . 0 0 0 1 0 0 0 0 . 0 0 0 1 4 0 0 0 . 0 0 0 1 8 0 0 0 . 0 0 0 0 . 0 4 0 0 0 . 0 0 0 8 0 0 0 . 0 0 0 1 2 O 0 0 . O 0 0 1 6 0 0 0 . 0 0 0 . • . . . .+ . . . .+ . . . .+ . . . .+ . . . .+ . . . .+ . . . .+ . . . .+ . . . . • . . . .+ . . . .+ . . . .+ . . . .+ . . . . • . . . . * • . . . .+ . . . .+ . . . .+ . . . .+ . - 0 . 0 - 0 . 0 2 0 - 0 . 0 4 0 - 0 . 0 6 0 - 0 . 0 8 0 -o.too 1 2 0 1 4 0 1 6 0 1 8 0 - 0 . 2 0 0 - 0 . 2 2 0 - O . 2 4 0 - O . 2 6 0 - O . 2 8 0 . 3 0 0 . 3 2 0 . 3 4 0 . 3 6 0 . 3 8 0 . 4 0 0 . 4 2 0 . 4 4 0 . 4 6 0 . 4 8 0 . 5 0 0 . 5 2 0 . 5 4 0 . 5 6 0 . 9 8 0 . 6 0 0 . 6 2 0 . 6 4 0 . 6 6 0 . 6 8 0 . 7 0 0 - 0 . 7 2 0 - 0 . 7 4 0 . 7 6 0 . 7 8 0 . 8 0 0 . 8 2 0 . 8 4 0 . 8 6 0 . 8 8 0 - 0 . 9 0 0 • - 0 . 9 2 0 - 0 . 9 4 0 - 0 . 9 6 0 - 0 . 9 8 0 - 1 . 0 0 0 • - 0 . 0 - 0 . 0 2 0 - O . 0 4 0 - 0 . 0 6 0 - 0 . 0 8 0 - O . 1 0 0 - O . - O . - 0 . - O . - O . - O . - O . - O . - O . - O . . 1 2 0 . 1 4 0 . 1 6 0 . 1 8 0 . 2 0 0 . 2 2 0 . 2 4 0 . 2 6 0 . 2 8 0 . 3 0 0 - 0 . 3 2 0 - 0 . 3 4 0 - 0 . 3 6 0 - 0 . 3 8 0 - 0 . 4 0 0 - 0 . 4 2 0 - 0 . 4 4 0 - 0 . 4 6 0 - 0 . 4 8 0 - 0 . 5 0 0 - 0 . 5 2 0 - 0 . 5 4 0 - 0 . 5 6 0 - 0 . 5 8 0 - 0 . 6 0 0 - 0 . 6 2 0 - 0 . 6 4 0 - 0 . 6 6 0 - 0 . 6 8 0 - 0 . 7 0 0 - 0 . 7 2 0 - O . 7 4 0 - 0 . 7 6 0 - 0 . 7 8 0 - 0 . 8 0 0 - 0 . 8 2 0 - 0 . 8 4 0 - 0 . B 6 0 - 0 . 8 8 0 - 0 . 9 0 0 - 0 . 9 2 0 - 0 . 9 4 0 - O . 9 6 0 - 0 . 9 8 0 - l . O O O 00 2 0 0 0 . 0 0 0 6 0 0 0 . 0 0 0 1 0 0 0 0 . 0 0 0 1 4 0 0 0 . 0 0 0 1 8 0 0 0 . 0 0 0 0 . 0 4 0 0 0 . 0 0 0 8 0 0 0 . 0 0 0 1 2 0 0 0 . 0 0 0 1 6 0 0 0 . 0 0 0 FREQUENCY (CYCLES/SECOND) POWER SPECTRAL ESTIMATES OF SERIES 1 0.0 780.2102 0.500 825.6116 1 .000 706.3047 1 .500 448.7271 2.000 313.6892 2.500 270.6157 3.000 218.6600 3.500 158.8460 4.000 116.6621 4.500 1tO.8536 5.000 133.2542 5.500 117.364 1 6. OOO 100.4470 6. SOO 101.1807 7.000 95 .08351 7. SOO 92 .33142 8.000 83 .73883 8.500 70 .81042 9.000 88 .69572 9.500 93 .05856 to.000 66 . 18443 10.500 SO .28069 11.000 50 .96480 1 1 .500 50 .74872 12.000 50 .61479 12.500 45 . 30302 13.000 52 .12030 13.500 47 .39372 14.000 39 .26118 14.500 41 .44556 15.000 34.03842 15.600 32 .89920 16.000 31 .51137 16.500 28 .52795 17.000 27. .24739 17.500 29. .98529 18.000 36. 88815 18 .500 40. 94727 19.000 37. 36729 19.500 37. 59845 20.000 31 . 02040 20. BOO 25. 02356 21 .000 25. 48636 21 .500 27. 85072 22.000 27. 36684 22.500 32. 53157 23.000 28. 86046 23.500 23. 25368 24.000 24. 94315 24.500 23. 90150 23.000 20. 87764 THE CHECK SUM OF POWER SPECTRAL ESTIMATES IS 17743.30 AND SHOULD BE 17743.64 THE DIFFERENCE IS-O.3476563 G R A P H O F T H E P O W E R S P E C T R A L E S T I M A T E S O F S E R I E S 1 A G A I N S T F R E Q U E N C Y ( C V C L E S / S E C O N D ) 1 0 0 . 0 0 0 3 0 0 . 0 0 0 5 0 0 . 0 0 0 7 0 0 . 0 0 0 9 0 0 . 0 0 0 0 . 0 2 0 0 . 0 0 0 4 0 0 . 0 0 0 6 0 0 . 0 0 0 8 0 0 . 0 0 0 . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + . . . . + ' . . . . + . . . . * . - . . * - . . . + . . . . + . . . . 4 . . - 0 . 0 - O . 5 0 0 - 1 . 0 0 0 - 1 . 5 0 0 - 2 . 0 0 0 - 2 . 5 0 0 - 3 . 0 0 0 - 3 . 5 0 0 - 4 . 0 0 0 - 4 . 5 0 0 - 5 . 0 0 0 - 5 . 5 0 0 - 6 . 0 0 0 - 6 . 5 0 0 - 7 . 0 0 0 - 7 . 5 0 0 - 8 . O O O - 8 . 5 0 0 - 9 . 0 0 0 - 9 . 5 0 0 - 1 0 . 0 0 0 - 1 0 . 5 0 0 - 1 1 . 0 0 0 - 1 1 . 5 0 0 - 1 2 . 0 0 0 - 1 2 . 5 0 0 - 1 3 . 0 0 0 - 1 3 . 5 0 0 - 1 4 . 0 0 0 - 1 4 . 5 0 0 - 1 5 . 0 0 0 - 1 5 . 5 0 0 - 1 6 . 0 0 0 - 1 6 . 5 0 0 - 1 7 . 0 0 0 - 1 7 . 5 0 0 - 1 8 . 0 0 0 - 1 8 . 5 0 0 - 1 9 . 0 0 0 - 1 9 . 5 0 0 - 2 0 . 0 0 0 - 2 0 . 5 0 0 - 2 1 . 0 0 0 - 2 1 . 5 0 0 - 2 2 . 0 0 0 - 2 2 . 5 0 0 - 2 3 . 0 0 0 - 2 3 . 5 0 0 - 2 4 . 0 0 0 - 2 4 . 5 0 0 - 2 5 . 0 0 0 - 0 . 0 - O . 5 0 0 - 1 . 0 0 0 - 1 . 5 0 0 - 2 . 0 0 0 - 2 . 5 0 0 - 3 . 0 0 0 - 3 . 5 0 0 - 4 . 0 0 0 - 4 . 5 0 0 - 5 . O O O - 5 . 5 0 0 - 6 . 0 0 0 - 6 . 5 0 0 - 7 . O O O - 7 . 5 0 0 - 8 . 0 0 0 - 8 . 5 0 0 - 9 . 0 0 0 - 9 . 5 0 0 - 1 0 . 0 0 0 - 1 0 . 5 0 0 - 1 1 . O O O - 1 1 . 5 0 0 - 1 2 . 0 0 0 - 1 2 . 5 0 0 - 1 3 . O O O - 1 3 . 5 0 0 - 1 4 . 0 0 0 - 1 4 . 5 0 0 - 1 5 . 0 0 0 - 1 5 . 5 0 0 - 1 6 . O O O - 1 6 . 5 0 0 - 1 7 . 0 0 0 - 1 7 . 5 0 0 - 1 8 . 0 0 0 - 1 8 . 5 0 0 - 1 9 . O O O - 1 9 . 5 0 0 - 2 0 . 0 0 0 - 2 0 . 5 0 0 - 2 1 . 0 0 0 - 2 1 . 5 0 0 - 2 2 . 0 0 0 - 2 2 . 5 0 0 - 2 3 . 0 0 0 - 2 3 . 5 0 0 - 2 4 . 0 0 0 - 2 4 . 5 0 0 - 2 5 . 0 0 0 bo 1 0 0 . 0 0 0 3 0 0 . 0 0 0 5 0 0 . 0 0 0 7 0 0 . 0 0 0 9 0 0 . 0 0 0 0 . 0 2 0 0 . 0 0 0 4 0 0 . 0 0 0 6 0 0 . 0 0 0 8 0 0 . 0 0 0 POWER SPECTRAL ESTIMATES OF SERIES 1 PLOTTED IN A LOG SCALE AGAINST FREQUENCY (CYCLES/SECONO) -0 -O - 1 - 1 -2 -2 -3 -3 -4 -4 -S -9 -6 -6 -7 -7 -8 -8 -9 -9. -10. -10. -11. -11. -12. -12. -13. -13. -14. - 14 . - 15. - 15. - 16. 16 . 17 . 17 . 18. 18 . t9. 19. 20. 20 21 . 2 1 . 22. 22. 23. 23. 24. 24 . 25 . 0 50O .000 . 500 .000 .500 .000 .500 .000 .500 OOO .500 .000 .500 .000 .500 • .000 .500 .000 .500 .000 • .500 .000 .500 .000 . .500 < 000 . 500 . 000 . 500 . 000 < 500 . OOO . SOO . OOO . 500 * 000 . 500 . 000 . 500 . 000 • 500 . 000 . 500 . 000 . 500 • 000 . 500 . 000 . 500 . 000 + 3 6 0 0 4.400 5.200 6.000 6.800 3.200 4.000 4.800 5.600 6.400 ..+....•....+....+....+....+....•....+....•....+....•....+....+....+....+....+....+....•....+. • + -2 . -2 . -3. -3 . -4 . -4 . -5. -0 .0 -O. 500 -1 . OOO -1 .500 000 500 .000 500 000 500 .000 -5.500 -6.000 -6.500 -7.000 -7. SOO -8.000 -8.500 " -9.000 -B.500 -10.000 -10.500 -11.000 -11.500 -12.000 -12.500 -13.000 -13.500 -14.000 -14.500 -15.000 -15.500 -16.000 -16.500 - 17.000 - 17.500 -18.000 -18.500 -19.000 -19.500 -20.000 -20.500 -2 1.OOO -21.500 -22.000 -22.500 -23.000 -23.500 -24.000 -24.500 -25.000 w to oo . . + . . . . • . . , . • . . . . + . . . . + . . . . + . . . . + . . . . • . . . . + . . . . + . . . . • . . . . • . . . . + . . . . + . . . . - « . . . . . + . . . . • . 3.600 4.400 5.200 6.000 6.800 4.000 4.800 S.600 6.400 - 329 -APPENDIX 2 E s t i m a t i o n of the F l u c t u a t i n g V e l o c i t y Component f o r A i r  on the C e n t r e l i n e of a Single-Phase Pipe Flow (Ug = 6.5 m/s, D = .152 m, NTP) Assuming P r a n d t l ' s mixing length theory to hold f o r the r e l a t i v e l y i s o t r o p i c turbulence on the c e n t r e l i n e of a pipe we w r i t e At the p r e v a i l i n g Reynolds number, 66,000, both the 1/7 power low and the r e s u l t of Nikuradse hold approximately ( S c h l i c t i n g , 1979). The l a t t e r s t a t e s that f o r smooth pipes the mixing length i s dependent on diameter and r a d i a l p o s i t i o n , but independent of Reynolds number over a wide range of Reynolds numbers. On the pipe c e n t r e l i n e 2i/D = 0.14. The 1/7 power law g i v e s ( U ' ( r ) ) 2 = £ 2( (A2.1) U z ( r ) (A2.2) U c where n = 7 and where U c i s the c e n t r e l i n e v e l o c i t y given - 330 -by XT ~ (n + l ) n ( 2 n + 1) (A2.3) S u b s t i t u t i n g U g = 6.5 m/s, n = 7 gives U = 7.96 m/s and 7 ? 5 6 - = <S> ' (A2.4) Now d i f f e r e n t i a t i n g gives dU ( r ) 1 -6/7 - f r — = 7 7177- * < 7 ' 9 6 > < A 2 ' 5 > and s e t t i n g r = R = .076 m gives dU ( r ) i 7 Q 6 , \T = j ( J T ^ ) = 14.96 m/s2 (A2.6) F i n a l l y , s u b s t i t u t i n g i n t o A2.1, ( U ' ( r ) ) a - M 5 2 4 ) 2 ( 0 . 1 4 ) 2 (14.96) 2 (2") and U 1 ( r ) = 0 .16 m/s. - 331 -APPENDIX 3 Computation of Pseudo-Dispersion C o e f f i c i e n t s from F-Curve Data The F-curves can be des c r i b e d approximately by a normal d i s t r i b u t i o n i n the range F = 0.1 to F = 0.7 (Yu, 1985); t h i s i s shown i n F i g u r e A3.1 below i n which the F-curve response f o r a t y p i c a l run i s p l o t t e d on normal p r o b a b i l i t y paper. Assuming the remainder of the response to f o l l o w a normal d i s t r i b u t i o n gives the standard d e v i a t i o n f o r t h i s d i s t r i b u t i o n as: c ( d e t e c t o r & r i s e r ) = t ( F = * ? i g " i t ( F = ' 1 ) (A3.1) s i n c e there are 1.91 standard d e v i a t i o n s between the 10th and 70th p e r c e n t i l e s of a normal d i s t r i b u t i o n . Making the same assumptions f o r the de t e c t o r alone allows the v a r i a n c e i n r esidence times due to r i s e r d i s p e r s i o n to be c a l c u l a t e d as: 2 2 2 a ( r i s e r ) = a ( d e t e c t o r + r i s e r ) - a"1 ( d e t e c t o r ) (A3.2) F i n a l l y , f o l l o w i n g L e v e n s p i e l (1972), the 'vess e l d i s p e r s i o n number" i s r e l a t e d to the va r i a n c e by: - 332 -/ D v _ a ( r i s e r ) {JTL) ~ ~=2 g 2t where t i s the mean ves s e l residence number i s the inverse of the "vessel (A3.3) time. The a x i a l Peclet d i s p e r s i o n number." - 333 -99.9 1 1 i i i i i G G 7 OUTLET 95 98 95 So eo < 0°° .0 G p HELIUM IN TO 63 SO to 20 / O G / G / G / -O 20 / G / 10 G / -s / ~ G / -2 f i i i i .25 2-ZS >hi3 l i 3 I O U IZ-13 /*X3 /t-2_J T I M E • s e c Figure A3.1 F-curve response of:system and d e t e c t o r p l o t t e d on normal p r o b a b i l i t y paper (Yu, 1985), (Ug = 3.5 m/s, G s = 30 kg/m s, alumina). 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0058687/manifest

Comment

Related Items