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A novel circulating fluidized bed Fusey, Isabelle 1985

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A NOVEL C I R C U L A T I N G F L U I D I Z E D BED by I S A B E L L E F U S E Y A T H E S I S SUBMITTED IN P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF A P P L I E D S C I E N C E S i n F A C U L T Y OF GRADUATE S T U D I E S CHEMICAL E N G I N E E R I N G We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e g u i r e d s t a n d a r d T H E U N I V E R S I T Y OF B R I T I S H COLUMBIA A u g u s t 2 6 , 1985 © I S A B E L L E F U S E Y , 1985 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 i t 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 i s understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of CW i / ^ . . •» The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date f W c , 2-9-ABSTRACT A novel type of circulating fluidized bed has been investigated and tested. While a conventional circulating fluidized bed unit consists of two vessels standing side by side - a fast bed operating at high gas velocity, and a slow bed which acts as a recycle vessel and operates at a much lower velocity - the novel design incorporates the two beds into a unique concentric arrangement. The inner column acts as the fast bed and the annular region acts as the slow bed. A baffle to separate the gas-solid mixture at the top of the inner column has been designed and tested. The baffle works reasonably well but design optimization is needed. Two types of air inlets for aeration of the insert have been tried: vertical and tangential. The vertical air inlet has been found to produce the highest solids circulation rates. Two types of solids have been investigated: polyvinyl chloride resin and cracking catalyst. The use of the heavier and smaller cracking catalyst particles resulted in higher circulation rates and greater solids hold-up in the inner column. The hydrodynamic behavior of the system has been studied using pressure and circulation flux measurements. The solids circulation flux, the axial pressure p r o f i l e , and the absolute pressure inside the system are generally a l l strong functions of air velocity in both the inner and outer sections, solids inventory, type of particle, and type of air i n l e t . Table of Contents ABSTRACT . . i i LIST OF TABLES . vi LIST OF FIGURES v i i i ACKNOWLEDGEMENT xiv INTRODUCTION ...1 1. FLUIDIZED BED REACTORS 4 1.1 Fluidization regimes 4 1.2 Fast fluidization .. '8 2 . THE NOVEL SYSTEM 13 2.1 Description 13 2.2 Advantages and disadvantages ..13 3. OTHER RECIRCULATING SYSTEMS 16 4. EXPERIMENTAL APPARATUS 22 4.1 Introduction .22 4.2 The columns 22 4.3 The baffle and cyclone 25 4.4 Aeration .........25 4.5 Pressure measurement 29 4.6 3olids circulation rate measurement 32 5. EXPERIMENTAL STRATEGY 37 5.1 Introduction .37 5.2 Independent variables 38 5.2.1 Air velocity 38 5.2.2 Bed materials .40 5.2.3 Inventory 44 5.2.4 Air inlet configuration 48 5.3 Dependent variables 48 i i i 5.3.1 Pressure 48 5.3.2 Circulation flux of solids 52 5.4 Experimental runs 52 RESULTS 55 6.1 Introduction 55 6.2 The unit in operation 55 6.2.1 Bed structure and flow pattern 55 6.2.2 Miscellaneous observations on operation ...60 6.3 Pressure profile 62 6.3.1 Introduction 62 6.3.2 Effect of inner air velocity 64 6.3.3 Effect of outer air velocity 67 6.3.4 Effect of inventory 70 6.3.5 Effect of solids properties 73 6.3.6 Effect of air inlet configuration 73 6.3.7 Pressure fluctuations 77 6.4 Solids circulation flux ...82 6.4.1 Introduction 82 6.4.2 Effect of inner velocity 83 6.4.3 Effect of solids inventory ..89 6.4.4 Effect of outer velocity ..92 6.4.5 Effect of solids properties ....92 6.4.6 Effect of air inlet configuration 98 DISCUSSION ..101 7.1 Introduction 101 7.2 Pressure drop 101 7.2.1 The concept of pressure drop balance .....101 iv 7.2.2 Contributions to pressure drop 104 7.2.3 Density profiles 105 7.2.4 Entrance effect 113 7.2.5 Pressure fluctuations -..........'.....119 7.3 Solids circulation rate ........119 7.4 Relationship between solids hold-up and flux ...129 7.4.1 Particle and s l i p velocities 129 7.4.2 Coupling effect ...130 7.4.3 Levelling off and dropping of solids rate 132 7.5 Comparison with literature data 136 7.6 Comparison with other circulating bed designs ..140 7.7 The tangential inlet 142 7.8 The baffle 144 CONCLUSION • 146 RECOMMENDATIONS FOR FURTHER STUDIES ..147 NOMENCLATURE 149 REFERENCES ..151 APPENDIX A: CALIBRATION OF AIR FLOW METERS ..155 APPENDIX B: MINIMUM FLUIDIZATION VELOCITY ...158 APPENDIX C: RAW DATA 163 APPENDIX D: PLOTS OF CHAPTERS 6 AND 7 182 APPENDIX E: CONTRIBUTIONS TO PRESSURE DROP ..205 APPENDIX F: VOIDAGE PROFILES ...207 APPENDIX G: STATISTICAL PROCEDURE 219 APPENDIX H: ERROR ANALYSIS ..225 v LIST OF TABLES TABLE TITLE PAGE 1.1 Studies in fast fluidization. 10 5.1 Dependent and independent variables. 39 5.2 Air flows and air velocities. 41 5.3 Inner-to-outer flow ratios. 42 5.4 Bed materials. 43 5.5 Size distribution for cracking catalyst. 45 5.6 Inventory levels. 46 5.7 Height of air inlet above the distributor 49 plate. 5.8 Position of pressure measurement points. 50 5.9 Experimental conditions investigated for PVC. 53 5.10 Experimental conditions investigated for 54 cracking catalyst. 6.1 Major trends. 56 6.2 Effect of solids type on gauge pressure and 75 pressure drop for medium inventory, U.=1.7 m/s, vertical inlet. I 6.3 Effect of air inlet configuration on gauge 78 pressure and pressure drop for PVC, low inventory, U^ =2.2 m/s. vi 0 6.4 Effect of air inlet configuration on gauge 80 pressure and pressure drop for cracking catalyst, high inventory, U^ =1.7 m/s. 6.5 Ratios of the circulation flux for cracking 97 catalyst to that for PVC. 6.6 Ratios of the circulation flux for a vertical 100 inlet to that for a tangential inlet. 7.1 Contributions to pressure drop for cracking 107 catalyst, D.»1.9n/s, U"o=0.034 m/s, high inventory, tangential inlet. 7.2 Approximate acceleration losses for cracking 118 catalyst, high inventory. 7.3 Empirical constants for the s t a t i s t i c a l 121 model. 7.4 Particle and s l i p velocities. 131 7.5 Effect of solid circulation flux on the 145 pressure drop across the baffle for cracking catalyst, tangential inlet. v i i LIST OF FIGURES FIGURE - TITLE PAGE 0.1 The novel circulating bed. 2 1.1 Fluidization regimes. 5 1.2 The relationship between pressure drop and 6 superficial gas velocity. 2.1 A conventional circulating fluidized bed. 14 3.1 A spouted bed with a draft tube. 17 3.2 Westinghouse recirculating bed. 19 3.3 Chambert's circulating bed. 20 4.1 Photograph of the apparatus. 23 4.2 The experimental apparatus. 24 4.3 The viewing ports and supports. 26 4.4 The baffle. 27 4.5 Photograph of the baffle. 28 4.6 The air inlet configurations. 30 4.7 The pressure probe. 31 4.8 The slide valve used to measure circulation 33 rates. 4.9 Photograph of the air inlets. 34 4.10 Photograph of the slide valve. 34 5.1 The relative locations of the bed surface, 47 air inlet, and insert. v i i i 5.2 Pressure measurement ports. 51 6.1 The solids flow pattern around the baffle. 59 6.2 Typical pressure profile for PVC, medium 63 inventory, U^ =1.7 m/s, UQ=0.046 m/s, vertical inlet. 6.3 Effect of inner gas velocity on insert axial 65 pressure profile for PVC, medium inventory, UQ=0.046 m/s, vertical i n l e t . 6.4 Effect of inner gas velocity on gauge 66 pressure and pressure drop for PVC, medium inventory, UQ=0.046 m/s, vertical inlet. 6.5 Effect of outer gas velocity on gauge 68 pressure and pressure drop for cracking catalyst, medium inventory, U\=1.7 m/s, vertical inlet. 6.6 Effect of outer gas velocity on gauge 69 pressure and pressure drop for PVC, low inventory, U^ =1.7 m/s, vertical inlet. 6.7 Effect of bed inventory on insert axial 71 pressure profile for PVC, U^ =1.7 m/s, Uo=0.046 m/s, vertical i n l e t . i 6.8 Effect of bed inventory on gauge pressure and 72 pressure drop for PVC, U\ = 1.7 m/s, Uo=0.046 m/s, vertical inlet. ix Effect of solid type on insert axial pressure profile for medium inventory, TJ\ = 1.7 m/s, UQ=0.046 m/s, vertical inlet. Effect of height of inlet above the distributor plate on insert axial pressure profile for PVC, high inventory, TJ\=2.2 m/s, Uo=0.034 m/s, vertical inlet. Effect of air inlet configuration on insert axial pressure profile for cracking catalyst, medium inventory, U^ =1.7 m/s, Uo=0.046 m/s. Pressure fluctuations for cracking catalyst, medium inventory, Uo=0.034 m/s. (a) 0.3 m above the air inlet, (b) 0.3 m the below baffle. Typical solids circulation fluxes for PVC, medium inventory, U^ =1.7 m/s, Uo=0.046 m/s. Effect of inner and outer gas velocity on the circulation of PVC, medium inventory, vertical inlet. Effect of inner gas velocity and bed inventory on the circulation of PVC, Uo=0.046 m/s, vertical i n l e t . Effect of inner and outer gas velocity on the circulation of cracking catalyst, medium inventory, vertical inlet. 6.17 E f f e c t of inner gas v e l o c i t y and bed 88 inventory on the c i r c u l a t i o n of cracking c a t a l y s t , Uo=0.023 m/s, v e r t i c a l i n l e t . 6.18 E f f e c t of bed inventory and inner gas 90 ve l o c i t y on the c i r c u l a t i o n of PVC (Cross-plot of f i g . 6.15). 6.19 E f f e c t of outer gas v e l o c i t y and bed 91 inventory on the c i r c u l a t i o n of PVC, U^=2.4 m/s, v e r t i c a l i n l e t . 6.20 E f f e c t of bed inventory and inner gas 93 ve l o c i t y on the c i r c u l a t i o n of cracking c a t a l y s t (Cross-plot of f i g . 6.17). 6.21 E f f e c t of outer gas v e l o c i t y and bed 94 inventory on the c i r c u l a t i o n of cracking c a t a l y s t , U.=1.7 m/s, v e r t i c a l i n l e t . 6.22 E f f e c t of outer and inner gas v e l o c i t y on the 95 c i r c u l a t i o n of PVC (Cross-plot of f i g . 6.14). 6.23 E f f e c t of inner and outer gas v e l o c i t y on the 96 c i r c u l a t i o n of cracking c a t a l y s t (Cross-plot of f i g . 6.16). 6.24 E f f e c t of height of i n l e t above the 99 d i s t r i b u t o r plate on the c i r c u l a t i o n of PVC, high inventory, Uo=0.034 m/s, v e r t i c a l i n l e t . 7.1 Pressure drop " c i r c u i t " . 102 xi 7.2 Typical measured insert pressure profile for 106 cracking catalyst, high inventory, U^ =1.9 m/s, UQ=0.046 m/s, tangential inlet. 7.3 Density profile and fluidization regimes. 108 7.4 Voidage profile for cracking catalyst, 111 U\ = 1.7 m/s, Uo=0.046 m/s, vertical inlet. 7.5 Voidage profile for PVC, 1^ =1.7 m/s, 112 UQ=0.046 m/s, vertical inlet. 7.6 Effect of inner gas velocity on voidage 114 profile for cracking catalyst, high inventory, Uo=0.046 m/s, tangential inlet. 7.7 Effect of outer gas velocity on voidage 115 profile for cracking catalyst, high inventory, U\=1.7 m/s, tangential inlet. 7.8 Effect of inlet configuration on voidage 116 profile for cracking catalyst, high inventory, = 1-9 m/s, Uo=0.023 m/s. 7.9 F i t of the s t a t i s t i c a l model for PVC, 1.2.2 vertical i n l e t . 7.10 F i t of the s t a t i s t i c a l model for PVC, 123 tangential i n l e t . 7.11 Fit of the s t a t i s t i c a l model for cracking 124 catalyst, vertical inlet. 7.12 Fit of the s t a t i s t i c a l model for cracking 125 catalyst, tangential inlet. x i i 7.13 F i t of the s t a t i s t i c a l model for PVC. 126 7.14 Fit of the s t a t i s t i c a l model for cracking 127 catalyst. 7.15 F i t of the s t a t i s t i c a l model for the entire 128 data set. 7.16 Typical response of solid circulation flux to 133 a change in inner air velocity. 7.17 C r i t i c a l pressure points in the bed. 135 7.18 Mass solids loading ratio as a function of 137 inner and outer gas velocity for cracking catalyst, high inventory, vertical inlet. 7.19 Density profiles from published studies. 139 7.20 The Lurgi and Studsvik circulating beds. 141 x i i i ACKNOWLEDGEMENT I would like to express my thanks to the following individuals: Dr. J.R. Grace and Dr. J. Lim, for their support, guidance, and patience during the course of this work. Jim Burkell and Clive Brereton, for kindly helping solving various problems with the equipment. I would also like to thank the staff of the Chemical Engineering Workshop and Stores for their cooperation. Financial support from the Natural Sciences . and Engineering Research Council is gratefully acknowledged. xiv INTRODUCTION Fluidization has long been recognized as an attractive technique for contacting a gas with a large inventory of solid particles. Notwithstanding the numerous industrial uses of fluidization, i t s potential remains to be fu l l y exploited. In recent years, circulating beds have begun to capture an appreciable fraction of the market, especially for small, light, flaky and sticky particulate materials which are d i f f i c u l t to handle in bubbling beds. The work presented here is a study of the behavior of a novel circulating fluidized bed. A schematic diagram of the proposed unit is shown in figure 0.1. The system is characterized by a concentric arrangement. The solids travel up the insert and are returned to the outer slow bed via a baffle located on top of the insert. High velocity air is introduced at the bottom of the inner column, while air at a much lower velocity is introduced uniformly in the outer column. The geometry and the hydrodynamics of the system make i t compact, amenable to operation at elevated pressures, and suitable for retrofitting of existing cylindrical columns.- This geometry may be attractive, for example, for coal or low-quality fuel combustion or gasification. The specific objectives of the study were 1. To test the f e a s i b i l i t y of the concept. 2. To design and test a baffle which returns the solids from the fast bed to the slow bed. 1 2 Figure 0.1 The novel circulating bed. To test different air inlet geometries. To characterize the hydrodynamic behavior of the system using experimentally determined pressure and circulation rate data. 1. FLUIDIZED BED REACTORS 1 . 1 FLUIDIZATION REGIMES A gas fluidized bed is a gas-solid contacting device in which a gas is blown upwards through a bed of fine solid particles. Figure 1.1 gives a schematic representation of the different regimes of fluidization. These regimes are best discussed in terms of the relationship between gas superficial velocity and pressure drop across the bed shown in figure 1.2. When low velocity gas is introduced at the bottom of a packed bed, a pressure drop is created by the drag exerted on the particles by the gas. As the gas superficial velocity is increased, the pressure drop across the bed increases and when a velocity is reached at which the drag force equals the weight of the solids, the bed particles become suspended. Since in many respects the bed contents behave like a liquid, the bed is said to be fluidized. Increasing the gas velocity beyond the minimum fluidization velocity promotes the formation of bubbles which travel through the bed to i t s surface. In the bubbling regime a large portion of the gas travels in the form of bubbles, thus limiting mass and heat transfer between gas and solids. The pressure drop across the bed does not change significantly, but i t fluctuates errat i c a l l y . If the bed is long and narrow, that is i f bubbles can grow to a size of the order of the bed diameter, and i f the gas superficial velocity is high 4 J L A I R A I R A I R I. F I X E D 2. B U B B L I N G 3. S L U G G I N G 4. T U R B U L E N T 5. F A S T 6. D I L U T E F L U I D I Z E D T R A N S P O R T F i g u r e 1 . 1 F l u i d i z a t i o n reg imes . 6 ONSET OF FAST FLUIDIZATION INCREASING PARTICLE FLUX MINIMUM FLUIDIZATION VELOCITY SUPERFICIAL VELOCITY F i g u r e 1 . 2 T h e r e l a t i o n s h i p b e t w e e n p r e s s u r e d r o p a n d s u p e r f i c i a l g a s . v e l o c i t y . 7 enough, slugs form and periodically travel up the column. This is the slugging regime. Upon further increase of the gas velocity the bed enters the turbulent regime. The gas-solid system now assumes a more homogeneous character - the bubbles disappear and the pressure fluctuations decay after having reached a maximum. At the same time, the flux of particles entrained above the bed increases significantly. Further increasing the gas velocity can lead to the fast fluidized regime. The most v i s i b l e characteristics of fast fluidization are the disappearance of the bed surface, a drastic increase in solids entrainment, and the agitated, disorderly motion of the particles. Many of the particles travel in clusters that continuously form and disintegrate as they travel upwards or downwards. The mean s l i p velocity (the relative velocity between the gas and the solid) is greater than the particle terminal velocity - a fact thought to reflect the formation of clusters with terminal velocities greater than for single particles. The pressure drop not only depends on gas velocity but also on solid circulation rate. Feeding more solids to a bubbling bed raises the bed height but does not change the bed density, significantly, while feeding more solids to a fast fluidized bed increases it s density. The pressure drop increases with solids circulation rate and tends to decrease with gas velocity. 8 A further increase in gas velocity leads to dilute phase transport (pneumatic, conveying). The solid concentration is low, the s l i p velocity is of the order of the particle terminal velocity, few clusters exist, and there is very l i t t l e solids backmixing. The pressure drop increases with gas velocity because of the predominant effect of wall f r i c t i o n . 1.2 FAST FLUIDIZATION So far most of the industrial applications of fluidization have been based on the bubbling fluidized bed. However, the advantages of fast fluidization over bubbling fluidization are now more clearly appreciated and f u l l exploitation of i t s great industrial potential has begun. Lurgi Chemie und Huttentechnik GmbH of West Germany was the f i r s t company to use fast fluidization on a commercial basis in a process for calcining aluminium hydroxide (Reh, 1971). The advantages of fast fluidization include: 1. higher gas treating capacity per unit surface area, 2. more efficient contact between the gas and the solids, 3. handling of cohesive, light, or flaky solids, 4. ease of scale-up. These advantages are added to: 1. ease of solid handling, 2. high gas-solid and bed-surface heat transfer, 3. temperature uniformity, which are a l l characteristic of conventional fluidized beds. 9 The degree of interest in the First International Conference On Circulating Fluidized Beds to be held in Halifax during November 1985 illustrates the considerable appeal of this recent technological development. The interest in fast fluidization has triggered a number of research projects both in industry and academic institutions. The variety and extent of the work done is briefly summarized in table 1.1. While not comprehensive, table 1.1 l i s t s the main subjects addressed by the different workers. Much of the fundamental work has been done by Yerushalmi, Weinstein and colleagues at the City College of New York. In recent years studies have begun to appear from a number of other groups including Li and colleagues in China. Leung (1980) and Matsen (1982) have tried to develop a criterion to differentiate fast fluidization from pneumatic conveying. Most of the work so far has been preliminary or descriptive in nature. The industrial uses of fast fluidized beds include ore roasting, solids drying, catalytic cracking, and calcination. Perhaps one of the most promising developments lie s in combustion of coal or of low quality fuels. Fast fluidization combustion has many advantages. It allows for simpler fuel pretreatment, a reduced number of feed points, easier turndown, reduced NOx emissions, and improved sulphur removal. Moreover, these advantages may be combined with those of pressurized combustion. The latter include a more compact combustion unit, lower pollutant emissions, and the T a b l e 1.1 S t u d i e s In f a s t f l u i d i z a t i o n . S u b j e c t Speci f i c s G e n e r a l advantages G e n e r a l a p p l i c a t i o n s Hydrodynamics D e l i n e a t i o n of f a s t f l u i d i z e d regime and bed s t r u c t u r e C l u s t e r f o r m a t i o n ; c o r r e l a t i o n to determine a r e p r e s e n t a t i v e c l u s t e r diameter Gas backmlxing Mathematical model and e m p i r i c a l c o r r e l a t i o n s to p r e d i c t a x i a l v o idage p r o f i l e A x i a l v o i d a g e p r o f i l e and energy l o s s e s I n f l u e n c e of imposed p r e s s u r e drop ( i . e . amount of s o l i d s 1n r e t u r n l e g ) on s o l i d s hold-up and a x i a l v o idage p r o f i l e R e f e r e n c e Yerushalmi et a l . , 1976 Yerushalmi and Cankurt, 1978 Reh et a l . . 1980 Yerushalmi et a l . , 1976 Yerushalmi and Cankurt, 1978 Yerushalmi et a l . , 1978 Yerushalmi and Cankurt, 1979 B i e r l e t a l . , 1980 Yerushalmi et a l . , 1978 Cankurt and Y e r u s h a l m i , 1978 L i and Kwauk, 1980 L i e t a l . , 1984 Stromberg, 1981 W e i n s t e i n et a l . , 1981 W e i n s t e i n , G r a f f , et a l . , 1984 I n f l u e n c e of p a r t i c l e d e n s i t y on s o l Ids hold-up and a x i a l v o i d a g e p r o f i l e W e i n s t e l n . M e l l e r , et a l . . 1984 C a l c i n a t i o n Combust 1on R a d i a l voidage p r o f i l e L u r g i c i r c u l a t i n g bed Advantages over c o n v e n t i o n a l f l u i d i z e d beds Overview of i n d u s t r i a l p r o j e c t s S t u d s v l k combustion b o i l e r W e i n s t e l n , Shao, and Wasserzug, 1984 Reh, 1971 Reh e t a l . , 1980 Schwieger, 1985 Schwieger, 1985 Stromberg, 1981 Stromberg, 1982 L u r g i c i r c u l a t i n g bed b o i l e r Reh et a l . , 1980 P y r o f l o w * c i r c u l a t i n g f l u i d i z e d bed Engstrom and Y i p , 1982 combustion b o i l e r B a t t e l l e mult ( s o l i d f l u l d i zed-bed. Nack et a l . . 1980 combustion p r o c e s s 12 possibility of power generation by expanding the flue gas in a gas turbine. A number of industrial processes - Lurgi (Reh et a l . , 1981), Pyropower Corp.(Engstrom and Yip, 1982; Sahagian, 1984), Studsvik Energiteknik AB (Stromberg, 1982), Battelle (Nack et a l . , 1980) - that apply the circulating-bed concept to combustion of coal and other solid fuels have already been developed. There is also increasing interest in applying circulating beds to endothermic reactions (including gasification) and to other non-catalytic gas-solid reactions. 2. THE NOVEL SYSTEM 2.1 DESCRIPTION Figure 2.1 shows a typical conventional fast fluidized, or circulating, bed. It basically consists of two columns: the fast bed and the accompanying standpipe which acts both as a recyle path and as a feeding vessel. Most or a l l of the gas and the feed solids are introduced at the bottom of the fast bed. The entrained solids are sent from the fast bed to the standpipe through one or more cyclones. A comparison of Figures 0.1 and 2.1 shows that in the novel circulating bed, f i r s t studied by Mounce (1983) and investigated further in the present work, the parall e l arrangement of the conventional system has been transformed into a concentric arrangement. The baffle which returns the solids coming from the fast bed (the tubular insert) to the slow bed acts as a primary cyclone. 2.2 ADVANTAGES AND DISADVANTAGES The geometry of the novel system adds several advantages to the attractive characteristics of conventional fast fluidized beds: 1. The compact arrangement minimizes floor requirements and is easier to pressurize. 2. Retrofitting of existing bubbling fluidized beds can be readily accomplished by adding an insert. 3. If the insert i s made of heat transfer tubes, heat 13 Figure 2 . 1 A conventional circulating fluidized bed. 15 transfer can be enhanced since heat is transferred both from the fast and the slow bed, i.e. from the complete periphery of the tubes. Likely disadvantages include maintenance problems, erosion of the baffle, and less direct and precise control of the solid circulation rate. 3. OTHER RECIRCULATING SYSTEMS Because of its geometry, the system under study is in some respects similar, notwithstanding major differences, to a family of axially symmetric physical systems which have been used to promote solids circulation. Internal circulation can be induced in a fluidized bed by inserting a draft tube and providing selective aeration. The resulting density gradient, coupled with the f l u i d i t y of the particulate material, causes the particles to circulate. This basic concept of solids circulation allows for much f l e x i b i l i t y in the design and operation of such a system. Design parameters such as the diameter ratio of the insert and outer bed, height of the insert above the distributor plate, and air distributor configuration can be arranged in a number of ways. The operating parameters of greatest importance are the inventory of solids and the air velocities. The draft tube can be entirely submerged in the bed or i t can extend above the bed surface. The flow in the draft tube can be in the bubbling, slugging, turbulent fluidization, fast fluidization, or dilute phase transport regime. The particles in the outer annular region can f a l l freely under gravity, or descend as a moving packed bed or as a dense phase fluidized bed. A number of units using the solid recirculation concept have been developed. Many of these systems are now referred to as spout-fluid beds. A typical spout-fluid bed with a draft tube is shown schematically in figure 3.1. The draft 16 17 Figure 3.1 A spouted bed with a draft tube. 18 draft tube may be impermeable or permeable. The " f l u i d l i f t solid recirculator" reported by Buchanan and Wilson (1965) is a spouted bed f i t t e d with a draft tube above the nozzle. Since then, many variations of the spouted-bed-with-a-draft-tube bed concept have been studied (Descamps et a l . , 1971; Mann and Crosby, 1975; Khoe and Van Brakel, 1980; Khoe and Van Brakel, 1983; C l a f l i n and Fane, 1983). Recirculating units have been applied to coating and mixing. A draft tube in a fluidized bed combustor has also been used to reduce the elutriation of fines (Judd and Weihack, 1983). The fines entrained upward are disengaged and carried downward by the particles descending in the annular region. LaNauze and Davidson (1975) studied a system in which a draft tube, submerged in a fluidized bed, is operated in the bubbling or slugging regime.- In the recirculating system developed by the Westinghouse group (Yang and Keairns, 1975; 1978; 1983) shown in figure 3.2, the solids are conveyed in dilute flow up a draft tube submerged in an aerated bed. Figure 3.3 shows another version of a circulating system (Chambert, 1978). Air is fed at the bottom of a fluidized bed f i t t e d with an insert made of a series of vertical heat-exchange surfaces. The air-solids mixture is separated at the top of the insert by a baffle which imparts tangential motion. A number of the studies cited above have investigated the effect of separation distance between the bottom of the draft tube and the distributor plate and of air velocity on PH AIR Figure 3 . 2 Westinghouse recirculating bed. 20 INSERT TOP VIEW OF SEPARATOR F i g u r e 3.3 Chambert's c i r c u l a t i n g bed. 21 gas bypassing characteristics and solids circulation rates. However, conclusions are not directly applicable to this project because of the different design and operating parameters. A major difference is found in the air distribution system. Comparing figures 3.1, 3.2, and 3.3 to figure 0.1 shows that the concentric circulating fluidized bed studied here seems to be the only recirculating unit in which the air sent to the draft tube does not f i r s t travel through some part of the outer bed. 4. EXPERIMENTAL APPARATUS 4.1 INTRODUCTION The equipment used in the present work was f i r s t investigated by Mounce (1983) in a preliminary study which established that fast fluidization could be maintained in the given geometry. A number of modifications were made to improve the operation of the preliminary system: use of a simpler baffle with a lower pressure drop, extension of the length above the baffle, aeration of the solids returning from the secondary cyclone, modification of the cyclone solids outlet, use of a more reliable method for obtaining pressure profiles, addition of a tangential inlet, and installation of new supports (also acting as viewing ports) for the insert. • A photograph of the apparatus used appears in figure 4.1. Its chief features are described below. 4.2 THE COLUMNS The experimental set-up, illustrated in figure 4.2, consists of two concentric cylindrical plexiglass columns with separate air distributors and a gas-solid separating baffle. The outer column has an outer diameter of 0.20 m (8 in), an inner diameter of 0.19 m (7.5 in), and is 2.1 m high. The insert has an outer diameter of 0.10 m (4 in), an inner diameter of 0.09 m (3.5 in), and is 1.5 m high. The insert is installed concentrically in the 22 F i g u r e 4.1 Photograph of the a p p a r a t u s . to co 24 Figure 4.2 The experimen tal apparatus. 25 outer column, with its base 0.18 m (7 in) above the distributor plate. The four supports for the inner column, shown in figure 4.3, also act as viewing ports allowing for direct observation of the interior of the insert without having the view obscured by particles f a l l i n g in the annular outer column or adhering to the outer wall. 4.3 THE BAFFLE AND CYCLONE The baffle which separates the gas-solid mixture at the top of the insert is shown in figures 4.4 and 4.5. It consists of an assemblage of 6 evenly-spaced curved blades which impart a tangential horizontal motion to the gas. The baffle has an outside diameter of 0.165 m (6.5 in), and an inside diameter of 0.09 m (3.5 in). Each blade is a 0.025 m (1 in) high 90° sector of a 0.133 m (5.5 in) c i r c l e . The conical top of the baffle prevents the accumulation of solids. A cyclone collects the solids not captured by the baffle and returns them to the outer bed. Aeration at the bottom of the return line prevents plugging. The return line has an inner diameter of 0.025 m (1 in). 4.4 AERATION Two independent air feed systems - one for the insert and the other for the outer column - provide aeration to the unit. 2 6 / / / / / / / / 0 04 m / / / v / / / / ^ ^ V ^ ^ V / / / E to o / / / / / / / / \ \ \ v ^ s. v / / / / / \ \ \ \ 7^ As E o OUTER COLUMN WALL INSERT WALL F i g u r e 4.3 The viewing p o r t s and supports. 2 7 TO CYCLONE i BOTTOM P L A T E OUTER COLUMN B A F F L E TOP CIRCULAR BLADE INSERT BOTTOM P L A T E CIRCULAR BLADE F i g u r e 4 . 4 T h e b a f f l e . 28 29 For the outer column, air comes from the main department compressor. The distributor consists of a 0.0125 m thick plexiglass plate with 0.0016 m (1/16 in) holes on a 0.01 m (3/8 in) square pitch. The open area represents approximatively 2% of the total area. A fine-mesh wire screen covers the plate to prevent backflow of solids. The air flow is measured with rotameters (calibration in Appendix A). Air from a 10 psig blower is brought to the insert via a 0.038 m ID (1.5 in) copper pipe. The height of the top of the inlet pipe above the distributor plate can be varied from 0 to 0.4 m. Two air inlet configurations (vertical and tangential), shown in figures 4.6 and 4.9, were investigated. For the vertical inlet, the air simply enters as a jet through the top of the 0.038 m pipe. For the tangential inlet, the inlet pipe is bent so that i t is off-center and is sealed at the top. The air then enters tangentially through a 0.063 m high, 0.012 m wide channel which follows the curvature of the inner column. The air flow is measured with a 0.025 m (1 in) or i f i c e plate meter (calibration in Appendix A). 4.5 PRESSURE MEASUREMENT Time-mean pressures are measured with water manometers. Pressure taps are located every 0.15 m along the outer column. The pressure in the insert is determined using the probe inserted from-above as shown in figure 4.7. The probe 30 TANGENTIAL VERTICAL OUTER COLUMN INNER COLUMN TANGENTIAL INLET PLAN VIEW OF TANGENTIAL INLET Figure 4.6. The air inlet configurations. 31 TO WATER MANOMETER TO CYCLONE B A F F L E INSERT H OUTER BED PRESSURE PROBE Figure 4.7 The pressure probe. 32 is simply a 2.1 m long, 0.006 m OD (1/4 in) stainless steel tube with a 90° bend near the bottom. The end is covered with a porous steel plug to prevent entry of particles. The top of the tube is connected to a water manometer. The probe can be moved up and down so as to obtain an axial pressure pr o f i l e . Since the tube contains a 90° bend and enters off-center, radial pressure profiles can also be obtained by rotating the tube. Pressure fluctuations are studied using a DISA capacitive pressure transducer system. Components of this system include a DISA 51E01 reactance converter, 51D20 low pressure transducer, 51E02 oscillator, and a 51E03 tuning plug. The pressure signal from the pressure probe is s p l i t in two: one component goes directly into one port of the diff e r e n t i a l pressure transducer while the other component is fed to a large reservoir. The container, acting as a surge tank, dampens the fluctuations. The averaged constant pressure signal coming from the reservoir is fed to the other port of the pressure transducer. In this manner, the pressure fluctuations are recorded relative to the average pressure. The analog output from the reactance converter is connected to a chart recorder (Gould, Brush 220). 4.6 SOLIDS CIRCULATION RATE MEASUREMENT Figure 4.8 and 4.10 show the slide valve used for measuring solids circulation rates. It consists of two halves, each made of a piece of wire screen connected to a 33 • F L A N G E O U T E R C O L U M N I N N E R C O L U M N R O D PLAN VIEW O U T E R C O L U M N I N N E R C O L U M N F L A N G E M O V A B L E P L A T E FRONT VIEW F i g u r e 4 . 8 T h e s l i d e v a l v e u s e d t o m e a s u r e c i r c u l a t i o n r a t e s . F i g u r e 4.9 Photograph of the a i r i n l e t s . F i g u r e 4 . 1 0 Photograph of the s l i d e v a l v e . 35 metal frame and a rod. The wire screen allows the gas to tr a v e l through the valve when closed. When the valve i s open i t does not obstruct the annular region in any way. When the valve i s closed (accomplished by pushing the rods in) the annular region between the two columns i s blocked and the f a l l i n g s o l i d s accumulate on the valve. The sol i d s c i r c u l a t i o n rate can be obtained by measuring the time required for the height of s o l i d s to reach a c e r t a i n l e v e l . While t h i s fast and simple way of obtaining c i r c u l a t i o n rates i s si m i l a r to methods employed by e a r l i e r workers (Yerushalmi et a l . , 1976; B i e r l et a l . , 1980), i t does have some drawbacks. F i r s t , i t disturbs the flow pattern and the pressure p r o f i l e in the outer column. Second, estimating the height of the upper surface of the accumulating s o l i d s on the valve i s not always easy. Third, the density of the bed of s o l i d s on the valve i s not known accurately. The method has however been found to be quite reproducible. For each run, f i v e measurements are taken, and the average c a l c u l a t e d . The measurement i n t e r v a l i s kept as short as possible to minimize interference e f f e c t s . The density of the accumulated s o l i d s i s taken to be that of the bed of so l i d s in the outer column, which i s obtained from pressure measurements. Since the s o l i d s above the closed valve are observed to bubble, and since the bubbling a c t i v i t y increases with outer a i r v e l o c i t y , i t seems reasonable to assume that the density above the closed valve i s the same as the density of the bed below i t . Thus measuring the rate 36 of r i s e of the bed surface above the valve i s equivalent to measuring the rate of descent of the bed surface below the valve. Both methods were t r i e d and the r e s u l t s found to be comparable. Although there i s a tendency for the c i r c u l a t i o n fluxes determined by measuring the rate of accumulation above the valve to be s l i g h t l y higher (at most 1 0 % ) , that method was adopted because the apparatus design c h a r a c t e r i s t i c s make i t considerably easier to use. 5. EXPERIMENTAL STRATEGY 5.1 INTRODUCTION A number of design and operation parameters may influence the behavior of the novel fluidized bed. The most important are liste d below: Design parameters: 1 . Separating baffle (geometry and height). 2. Air inlet configuration. 3. Distance between the bottom of the insert and the distributor. 4. Distance between the top of the insert and the top of the outer column. 5. Diameter ratio of the insert and the outer column. Operating parameters: 1. Air velocity introduced to the insert (expressed as a superficial velocity based on the inner column area). 2. Air velocity introduced in the outer column (expressed as a superficial velocity based on the outer column area). 3. Bed inventory of solid particles. 4. Solids properties (density, mean size, size distribution, shape). A l l experiments were carried out with air at essentially atmospheric pressure and temperature. Gas properties could 37 38 also play an important role. The behaviour of the column may be characterized by a number of variables: 1. Pressure drop or fluctuation. 2. Solids hold-up in the insert. 3. Solids circulation velocity. 4. Amount of air passing from the outer column into the insert or in the reverse direction. 5. Entrainment rate of particles into the secondary cyclone. It is desirable not only to evaluate the effect of each operation or design parameter on the performance of the bed but also to gain an understanding of the coupling effects that may exist between different parameters. Not a l l design parameters were investigated in this study. The baffle, the insert/outer column diameter ratio, and the distance above and below the insert were fixed. Furthermore, transfer of gas between the inner and outer columns and entrainment were not studied systematically. Table 5.1 l i s t s the dependent and independent variables that were examined. 5.2 INDEPENDENT VARIABLES 5.2.1 AIR VELOCITY The outer velocity is obtained by dividing the air flow as measured with the rotameter by the outer column 39 Table 5.1 Dependent and independent variables. Varied Parameters Range Inner velocity 1.4 - 3.5 m/s Outer velocity 0.013 - 0.108 m/s. Bed materials cracking catalyst* polyvinyl chloride resin* Inventory 0.4 - 0.8 m Air inlet configuration vertical tangential Height of inner air inlet 0.18 - 0.34 m Measured Quantities Range Axial and radial profiles of time mean (gauge) pressure in inner column 0.36 - 4.64 kPa Pressure fluctuation in inner column Axial profile of time mean (gauge) pressure in outer column 0.24 - 6.69 kPa Solids circulation flux 0.8 - 36.7 kg/m2s (PVC) 3.3 - 71.7 kg/m2s (cracking catalyst) * For properties see Table 5.4 below. 40 cro s s - s e c t i o n a l area (0.0285 in 2), and the inner v e l o c i t y by d i v i d i n g the a i r flow as measured with the o r i f i c e plate meter by the insert c r o s s - s e c t i o n a l area (0.0062 m 2). S t r i c t l y speaking the term flow should be substituted for the term v e l o c i t y . Only in the absence of net gas transfer are the two quantities equivalent. However, the v e l o c i t y concept i s adopted here because i t s use i s more common in the f l u i d i z a t i o n l i t e r a t u r e , because the a i r does not appear to bypass from the i n s e r t into the outer column, and because the amount of a i r fed to the outer bed i s s i g n i f i c a n t l y lower than the amount of a i r fed to the i n s e r t . Table 5.2 gives the a i r flows and a i r v e l o c i t i e s used, while table 5.3 gives the values of inner-to-outer a i r flow r a t i o s for d i f f e r e n t combinations that were tested. The lower l i m i t for the outer- a i r flow was chosen to be the flow at which the outer bed i s just below the minimum f l u i d i z a t i o n state. This point was determined by observation. The upper l i m i t for the inner a i r flow was chosen to be the flow at which the s o l i d s entrainment rate in the cyclone i s s i g n i f i c a n t . 5.2.2 BED MATERIALS Two types of p a r t i c l e s were studied: a polyvinyl chloride r e s i n (PVC) and a cracking c a t a l y s t (CC). Their respective properties are l i s t e d in table 5.4. For PVC, the p a r t i c l e s i z e was obtained from the manufacturer. Consistent values could not be obtained eit h e r with a sieving method or 41 Table 5.2 Air flows and air velocities. Column Flow (m3/s) Velocity (m/s) Inner 0.0087 1 .4 0.0106 1 .7 0.0118 1.9 0.0137 2.2 0.0149 2.4 0.0161 2.6 0.0168 2.7 0.0180 2.9 0.0192 3.1 0.0205 3.3 Outer 0.00036 0.013 0.00066 0.023 0.00097 0.034 • 0.00132 0.046 0.00159 0.056 0.00209 0.073 0.00308 0. 108 42 Table 5.3 Inner-to-outer flow ratios. Outer veloc ity, m/s Inner 0.013 0.023 0.034 0.046 0.056 velocity, m/s 1 .4 24.2 13.1 8.9 6.6 5.5 1 .7 29.4 15.9 10.9 8.0 6.7 1.9 32.8 17.8 12.1 9.0 7.4 2.2 38.0 20.6 14.1 10.4 8.6 2.4 41 .5 22.4 15.3 11.3 9.4 2.6 44.9 24.3 16.6 12.3 10.2 2.7 46.7 25.2 17.2 12.7 10.6 2.9 50. 1 27.1 18.5 13.7 1 1 .4 - 3.1 53.6 29.0 19.8 14.6 12.1 , 3.2 55.3 29.9 20.4 15. 1 12.5 3.3 57.0 30.8 21 .1 15.6 12.9 43 T a b l e 5.4 Bed m a t e r i a l s . P r o p e r t y C r a c k i n g c a t a l y s t PVC Shape round i r r e g u l a r M a t e r i a l d e n s i t y , kg/m 3 2500 1400 P a r t i c l e d e n s i t y pp, kg/m 3 2000 1 400 B u l k d e n s i t y p D , kg/m 3 930 650 Mean p a r t i c l e s i z e , ixm 60 119 Ujjif- c a l c u l a t e d , m/s 0.0029 0.0081 Umf e x p e r i m e n t a l , m/s 0.0052 0.0087 T e r m i n a l v e l o c i t y , m/s 0.10 0.23 Archimedes number 4.4 20.2 S u p p l i e r G u l f r e f i n e r y • B.F. G o o d r i c h 44 a particle size image analyzer. The size distribution for the cracking catalyst powder is given in table 5.5; The mean diameter was determined using a particle size image analyzer. The random loose-packed bulk density was measured by pouring a weighed amount of particles into a graduated cylinder and recording the volume. The values measured agree exactly with the numbers provided by the suppliers. The PVC particle density was supplied by the manufacturer. An accurate value for the particle density of the porous cracking catalyst could not be obtained. The material density was found to be 2500 kg/m3, and a reasonable particle density of 2000 kg/m3 was assumed. The minimum fluidization velocity was calculated using Grace's modification of Wen and Yu's correlation (Grace, 1982). The minimum fluidization velocity was also determined experimentally using pressure drop data. Calculations and experimental results are reported in Appendix B. 5.2.3 INVENTORY For each type of particles, three inventory levels were used. The inventory level represents the amount of particles contained in the bed. The inventory level can be determined indirectly by determining the average height of the bed surface in the outer column. Table 5.6 gives the approximate amounts of particles that were used for the different runs, and figure 5.1 shows a comparative picture of the respective locations of the bed surface for the three inventories used Table 5.5 Size distribution for cracking catalyst. Mean diameter, Lim Percent by number 2.9 2 8.8 0 14.7 1 20.5 4 26.4 1 1 32.2 16 38. 1 25 44.0 14 49.8 1 1 55.7 9 61.5 2 67.4 3 73.2 1 79.1 0 85.0 1 90.8 0 Table 5.6 Inventory levels. Inventory Height of outer bed (m) Approximate amount of PVC (kg) Approximate amount of CC (kg) low 0.37 8 1 1 medium 0.60 12 18 high 0.76 16 25 47 O ro CO CM e CD JL JL HIGH I N V E N T O R Y MEDIUM INVENTORY LOW INVENTORY gure 5.1 The r e l a t i v e l o c a t i o n s of the bed s u r f a c e , a i r i n l e t , and i n s e r t . 48 (referred to as low, medium and high), the height of the air inlet, and the bottom of the insert. 5.2.4 AIR INLET CONFIGURATION The different types of inlet are described in chapter 4. The effect of the height of the insert air inlet above the distributor plate was only established for a high inventory of PVC particles with a vertical air inlet. The three heights tested are l i s t e d in table 5.7. The rest of the experiments were conducted with the air inlet 0.28 m (11 in) above the distributor, and 0.10 m (4 in) above the bottom of the insert. 5.3 DEPENDENT VARIABLES 5.3.1 PRESSURE Details on the pressure measurement probe are given in chapter 4. Table 5.8 and figure 5.2 give the position of each point, in the insert and the outer column, where the pressure was measured. Pressure fluctuations were recorded for a medium inventory of cracking catalyst with a vertical inlet. The outer velocity was fixed at 0.034 m/s, and the inner velocity was varied form 0.6 to 2.6 m/s. The fluctuations were recorded at two different points in the column: 0.3 m above the air inlet, and 0.3 m below the baffle (i.e. positions 3 and B respectively). The measuring probe was 49 Table 5.7 Height of a i r i n l e t above the d i s t r i b u t o r plate Inlet Height above d i s t r i b u t o r (m) Height above bottom of insert (m) low middle high 0.18 0.28 0.34 0.00 0.10 0.16 50 Table 5.8 Position of pressure measurement points. Column Point Height above distributor plate (m) Inner 1 0.25 2 0.41 3 0.56 4 0.71 5 0.86 6 1 .02 7 1.17 8 1 .32 9 1 .47 10 1 .63 Outer 1 1 0.05 12 0.20 13 0.66 1 4 1 .57 51 F i g u r e 5.2 P r e s s u r e measurement p o r t s . 52 along the axis of the column for these measurements. 5.3.2 CIRCULATION FLUX OF SOLIDS The circulation flux of the solids is the product of the solids hold-up in the insert and of the average solids velocity. In this study, the solids circulation rate was determined directly according to the method described in chapter 4. The circulation flux i s obtained by dividing the rate (mass per unit time) by the cross-sectional area of the insert. The solids hold-up can be inferred from pressure drop measurements, providing some assumptions are made, as discussed in section 7.2. 5.4 EXPERIMENTAL RUNS The experimental tree in table 5.9 and 5.10 gives the conditions and quantities measured for a l l experimental runs that were performed. Reproducibility of the data was found to be satisfactory and no hysteresis was observed. A simple error analysis is given in Appendix H. Table 5.9 Experimental conditions Investigated for PVC. Inventory Inlet I n l e t height Outer vel . Inner v e l o c i t y , m/s (m) cm/s 2 3 1 .4 1 .7 1 .9 2 2 2 4 2 7 3 4 1 .4 1 .7* 1 .9 2 2 2 4 2 7 4 6 1 .4 1 .7* 1 .9* 2 2* 2 .4 2 7 ve r t . 5 6 1 .4 1 .7* 1 .9 2 2* 2 4 2 7 low 7 3 1 .4 1 .7* 1 .9* 2 2* 2 4 2 7 10 8 1 4 1 .7* 1 .9 2 2* 2 4 2 7 5 6 1 4 1 .7* 1 .S 2 2* 2 4 2.6 2 7 tang. 0.28 7 3 1 .4 1 .7* 1 .9* 2 2* 2 4* 2.6 2 7* 10 8 1 A 1 .7* 1 .9 2 2* 2 4 2.6 2 7 2 3 1 4 1 7* 1 9 2 2* 2 4 2.6 2 7 2 9 3 1 3.2 3 4 1 4 1 .7* 1 9 2 2* 2 4 2.6 2 7 2 9 3 1 vert. 4 6 1 4* 1 7* 1 .9* 2 2* 2 4* 2.6 2 7 med ium 5 6 1 4 1 7* 1 9 2 2* 2 4 2.6* 2 7 5 6 1 4 1 7* 1 9 2 2* 2 4 tang. 7 3 1 4* 1 7* 1 9* 2 2* 2 4* 10 8 1 4 1 7* 1 9 2 2* 2 4 2 3 1 4 1 7 1 9 2 2 2 4 2.6 2 7 2 9 3 1 3 4 1 4 1 7 1 9 2 2* 2 4 2.6 2 7 0. 18 4 6 1 4 1 7 1 9 2 2* 2 4 2.6 5 6 1 4 1 7 1 9 2 2* 2 4 2.6 2 3 1 4 1 7 1 9 2 2 2 4 2.6 2 7 2 9 3 1 3 4 1 4 1 7 1 9 2 2* 2 4 2.6 2 7 2 9 high vert. 0.28 4 6 1 4 1 7* 1 9 2 2* 2 4 2.6 2 7* - 5 6 1 4 1 7 1 9 2 2 2 4 2.6 2 7 2 3 1 7 1 9 2 2* 2 4 2 7 2 9 3. 1 3 4 1 7 1 9 2 2* 2 4 2.6 2 7 2 9 3 1 0. 34 4 6 1 7 1 9 2 2 2 4 2.6 2 7 5 6 1 7 1 9 2 2 2 4 2.6 * pressure p r o f i l e taken OJ T a b l e 5 . 1 0 E x p e r i m e n t a l c o n d i t i o n s i n v e s t i g a t e d f o r c r a c k i n g c a t a l y s t . I n v e n t o r y I n l e t O u t e r cm v e l . , / s I nner ve1oc1ty , m/s 1 . 3 1 . 4 i 7* 1 .9 2 . 2 2 .4* 2 . 6 2 . 7 2 . 3 i . 4 i 7* i .9 2 . 2 2 . 4 * v e r t . 3 . 4 1 . 4 1 7* i .9 2 . 2 2 . 4 * 4 .6 1 . 4 * i 7* 1 . 9 * 2 . 2 * 5 . 6 i . 4 * 1 7* 1 . 9 * 2 . 2 1 ow 1 . 3 1 . 4 1 7* 1 9 2 . 2 * 2 . 4 2 . 6 2 . 7 2 . 3 1 . 4 1 7* 1 9 2 . 2 * 2 .4 t a n g . 3 .4 1 . 4 i 7* 1 9 2 . 2 * 4 .6 1 . 4 1 7* 1 9* 2 . 2 * 5 6 1 4 1 7* 1 9 2 . 2 * 1 . 3 1 4 1 7* 1 9 2 . 2 2 . 4 * 2 . 3 1 4 1 7* 1 9 2 . 2 * v e r t . 3 3 .4 .4 1 4 t 0 7* 6 - 2 . 6 * * 1 9* 2 . 2 4 .6 1 4* 1 7* 1 9* 2 . 2 med i um 5 .6 1 * 4 1 7* 1 9 1 . 3 1 4 1 7* 1 9 2 . 2 * 2 3 1 4 1 7* 1 9 2 . 2 * t a n g . 3 4 1 4 1 7* 1 9 2 2* 4 6 1 4* 1 7* 1 9* 2 2* 5 6 1 4 1 7* 1 9* 2 2 1 3 1 4 1 7* 1 9 2 2* 2 3 1 4 1 7* 1 9* 2 . 2 v e r t . 3 4 1 * 4 1 7* 1 9 2 2 4 6 1 4* 1 7* 1 9 5 6 1 4* 1 7* 1 9 h i g h 1 3 t 4 1 7* 1 9* 2 2 2 3 1 4 i 7* 1 9* 2 2 t a n g . 3 4 1 4 1 7* 1 9* 2 2 4 6 1 4* 1 7* i * 9 2 2* 5 6 1 4 1 7* 1 9* 2 2 * p r e s s u r e p r o f i l e t a k e n * * p r e s s u r e f l u c t u a t i o n s measured 6. RESULTS 6.1 INTRODUCTION An exhaustive compilation of the data collected can be found in Appendix C. In this chapter, the main findings are highlighted and summarized in a qualitative way, while a more quantitative analysis of the data can be found in Chapter 7. The major trends reported in table 6.1 are examined in more detail in the rest of this chapter. A l l the tables in the chapter were compiled by rearranging the data contained in Appendix C. For pressure measurements, the raw data were recorded in centimeters of o i l or of water and then converted to kilopascals (kPa). For the solids circulation rate measurements, the raw data were recorded following the method described in chapter 4, and then converted to fluxes in kg/m2s. The conversion procedures are outlined in Appendix C. The data which appear in graphical form are tabulated in Appendix D. 6.2 THE UNIT IN OPERATION 6.2.1 BED STRUCTURE AND FLOW PATTERN Two different zones make up the outer column: the dense fluidized bed at the bottom, and the freeboard region above the bed surface. In the freeboard, the particles separated by the baffle f a l l down in straight paths onto the bed surface. The dense bed is in the bubbling regime. The 55 T a b l e 6.1 Major t r e n d s A c t i o n E f f e c t on s o l i d s f l u x E f f e c t on AP a c r o s s i n s e r t E f f e c t on AP a c r o s s o u t e r column I n c r e a s e i n n e r v e l o c i t y I n c r e a s e D e c r e a s e Not a p p r e c i a b l e I n c r e a s e o u t e r v e l o c i t y I n c r e a s e Not a p p r e c i a b l e Not a p p r e c i a b l e I n c r e a s e i n v e n t o r y I n c r e a s e I n c r e a s e I n c r e a s e Change from PVC t o CC I n c r e a s e I n c r e a s e I n c r e a s e Change from v e r t i c a l t o t a n g e n t i a l i n l e t D e crease Not a p p r e c i a b l e Not apprec i a b l e R a i s i n g l e v e l of i n n e r gas i n l e t D ecrease D e c r e a s e Not a p p r e c i a b l e 57 b u b b l i n g a c t i v i t y depends on t h e o u t e r v e l o c i t y and on t h e bed m a t e r i a l . At t h e l o w e s t o u t e r v e l o c i t y , t h e bed appears t o be below the minimum f l u i d i z a t i o n s t a t e . The a i r v e l o c i t y r e q u i r e d t o f l u i d i z e t h e a n n u l a r r e g i o n i s s i g n i f i c a n t l y h i g h e r than the minimum f l u i d i z a t i o n v e l o c i t y d e t e r m i n e d i n an o r d i n a r y c y l i n d r i c a l column ( c f t a b l e 5.4). The o u t e r a i r v e l o c i t y must be a t l e a s t 0.03 m/s f o r PVC and 0.015 m/s f o r c r a c k i n g c a t a l y s t t o f l u i d i z e t h e o u t e r bed. As t h e o u t e r v e l o c i t y i n c r e a s e s , t h e s i z e , s p e e d , and c o n c e n t r a t i o n of bu b b l e s i n c r e a s e . When PVC i s use d , the b u b b l e s t e n d t o be f a i r l y l a r g e and a r e seen t r a v e l l i n g a l o n g t h e w a l l . I n c o n t r a s t , when the bed i s f i l l e d w i t h c r a c k i n g c a t a l y s t , t h e bu b b l e s a r e s m a l l e r and i n g e n e r a l do not t r a v e l a l o n g t h e w a l l . T h e i r p r e s e n c e i s d e t e c t e d i n t h e form of shadows o r dark r e g i o n s moving up i n the bed. The bed s u r f a c e o s c i l l a t e s up and down because of t h e b u b b l i n g a c t i v i t y . The e r u p t i n g b u b b l e s a t t h e bed s u r f a c e meet t h e s t e a d y f l o w of f a l l i n g p a r t i c l e s . I n t e r n a l c i r c u l a t i o n i n t h e dense bed i s e v i d e n t : a l o n g t h e w a l l , t h e p a r t i c l e s t r a v e l downward i n a s t i c k - s l i p m o t i o n . The s t r u c t u r e of t h e bed i n t h e upper p o r t i o n of t h e i n s e r t can be i n f e r r e d t h r o u g h t h e v i e w i n g p o r t s . However, when c r a c k i n g c a t a l y s t i s used, a t h i n l a y e r of f i n e p a r t i c l e s c o a t s t h e i n n e r w a l l of the i n s e r t and makes i t i m p o s s i b l e t o see a n y t h i n g . When PVC i s used, t h e p a r t i c l e s can be seen, but i t i s c e r t a i n l y not easy t o c h a r a c t e r i z e t h e f l o w m o t i o n of t h e g a s - s o l i d m i x t u r e . F i r s t , t he windows 58 a r e s m a l l and o n l y a l l o w a c a u t i o u s guess t o be made about the o v e r a l l bed s t r u c t u r e . Second, t h e r e i s v i g o r o u s s o l i d s movement wh i c h i s not e a s i l y c h a r a c t e r i z e d , a l t h o u g h t h e v o i d a g e seems r a t h e r h i g h . I t i s i m p o s s i b l e t o see i f t h e v o i d a g e i s g r e a t e r i n t h e c o r e than a t t h e w a l l . The p a r t i c l e s seem t o t r a v e l i n l o o s e s h o r t - l i v e d p a c k e t s . Some p a r t i c l e s shoot up w h i l e o t h e r f a l l down. The bed s t r u c t u r e i s v i s u a l l y s i m i l a r t o t h e f r e e b o a r d a c t i v i t y above a v i o l e n t l y b u b b l i n g bed. F i g u r e 6.1 r e p r e s e n t s an a t t empt t o d e s c r i b e what happens i n t h e v i c i n i t y of t h e b a f f l e . The g a s - s o l i d s m i x t u r e comes out h o r i z o n t a l l y t h r o u g h t h e s i x s i d e o p enings of t h e b a f f l e . Most of the p a r t i c l e s f a l l down i n the a n n u l a r r e g i o n w h i l e some p a r t i c l e s a r e e n t r a i n e d by the gas i n t h e r e g i o n above the b a f f l e . There, th e g a s - s o l i d m i x t u r e t r a v e l s i n a s w i r l i n g p a t h , as' though i n a c y c l o n e . A l t h o u g h most of t h e p a r t i c l e s f a l l back down i n t o t h e gap between th e b a f f l e and t h e o u t e r w a l l where t h e y i n t e r m i x w i t h t h e f l o w coming from t h e b a f f l e o p e n i n g s , some p a r t i c l e s remain t r a p p e d f o r l o n g p e r i o d s i n a c i r c u l a t i n g m o t i o n above the b a f f l e . O t h e r s a r e c a r r i e d over t o t h e c y c l o n e . The a i r v e l o c i t y i n t h e i n s e r t c o n t r o l s t h e r e l a t i v e amounts of p a r t i c l e s f a l l i n g back i n the a n n u l a r r e g i o n , s w i r l i n g i n t h e r e g i o n above t h e b a f f l e , and e s c a p i n g t o t h e c y c l o n e . As the i n n e r gas v e l o c i t y i s i n c r e a s e d , t h e p r e s s u r e i n the u n i t i n c r e a s e s a l o n g w i t h t h e c i r c u l a t i o n of t h e s o l i d s f a l l i n g back i n the a n n u l a r r e g i o n . However, t h e r e i s a F i g u r e 6.1 The s o l i d s f l o w p a t t e r n around the b a f f l e . 60 maximum i n n e r v e l o c i t y , r e f e r r e d t o here as t h e f l o o d i n g v e l o c i t y , above which the system cannot be o p e r a t e d p r o p e r l y . I f the i n n e r v e l o c i t y i s above t h i s l e v e l , t h e bed b e h a v i o r changes d r a s t i c a l l y : t h e h o l d - u p of s o l i d s above the b a f f l e i n c r e a s e s p r e c i p i t o u s l y , t h e c y c l o n e l o a d i n g i n c r e a s e s , the c i r c u l a t i o n r a t e of the s o l i d s down the a n n u l a r r e g i o n d e c r e a s e s , and the p r e s s u r e i n s i d e i n c r e a s e s s i g n i f i c a n t l y . In the v i c i n i t y of t h i s c r i t i c a l p o i n t , o n l y a s m a l l increment i n v e l o c i t y i s s u f f i c i e n t t o t r i g g e r a major b e h a v i o r change i n t h e system. No m e a n i n g f u l measurements can be ta k e n when t h e bed i s i n t h e f l o o d i n g s t a t e . The system tends t o be i n an unsteady s t a t e because t h e r e i s an a c c u m u l a t i o n of s o l i d s i n t h e c y c l o n e r e t u r n l i n e . 6.2.2 MISCELLANEOUS OBSERVATIONS ON OPERATION Because the a i r i n l e t t o t h e i n s e r t has an open end, i t i s n e c e s s a r y t o t a k e c e r t a i n p r e c a u t i o n s t o a v o i d t h e a c c u m u l a t i o n of s o l i d s i n the a i r l i n e . To s t a r t up t h e u n i t , t h e gate v a l v e which c o n t r o l s the a i r f l o w t o the i n s e r t i s g r a d u a l l y opened u n t i l t he s o l i d s s t a r t t o c i r c u l a t e . A i r i s then s u p p l i e d t o the a n n u l a r r e g i o n . To shut t h e u n i t o f f , the p r o c e d u r e i s r e v e r s e d . F i r s t , t h e a i r f l o w t o the o u t e r column i s t u r n e d o f f , and t h e a i r f l o w t o t h e i n s e r t i n shut o f f o n l y when t h e s o l i d s have s t o p p e d c i r c u l a t i n g . 61 The h i g h v e l o c i t y and c e n t r i f u g a l motion cause e l e c t r o s t a t i c c h a r g e s t o d e v e l o p . The e f f e c t i s more s e v e r e when PVC p a r t i c l e s a r e used. Moreover, t h e PVC p a r t i c l e s have a n a t u r a l tendency t o s t i c k t o g e t h e r and do not f l o w e a s i l y . At low i n n e r v e l o c i t i e s , l i t t l e p i l e s of s o l i d s form on t h e bottom p l a t e of the b a f f l e between each b l a d e . H i g h e r a i r f l o w s p r e v e n t t h e s o l i d s from s e t t l i n g . I t was a l s o o b s e r v e d t h a t t h e s o l i d p a r t i c l e s t e n d t o f i l l t h e space j u s t under th e moving h a l v e s of t h e s l i d e v a l v e used t o measure s o l i d s c i r c u l a t i o n r a t e s . The v a l v e must be t a k e n a p a r t and c l e a n e d p e r i o d i c a l l y . Not o n l y would t h i s a c c u m u l a t i o n of s o l i d s a f f e c t the t r u e i n v e n t o r y l e v e l , but a l s o i t h i n d e r s the m otion of t h e s l i d i n g p a r t s . O v e r a l l , t h e a c c u m u l a t i o n of s o l i d s i n the v a l v e and on the b a f f l e i s e s t i m a t e d t o be a t most 5% of t h e t o t a l i n v e n t o r y of s o l i d s . A f t e r r o u g h l y 100 h o u r s of o p e r a t i o n w i t h PVC p a r t i c l e s , no s i g n of e r o s i o n c o u l d be d e t e c t e d . A f t e r a c omparable amount of time w i t h c r a c k i n g c a t a l y s t , on t h e o t h e r hand, the r e g i o n on t h e i n n e r w a l l of t h e o u t e r column where t h e p a r t i c l e s s e p a r a t e d by the b a f f l e impinge was f o u n d t o have a d u l l e r a p pearance. The b l a d e s of the b a f f l e , however, remained smooth and s h i n y . S i g n s of a b r a s i o n were a l s o o b s e r v e d on t h e a i r i n l e t p i p e : the e x t e r i o r s u r f a c e of t h e p o r t i o n of t h e copper p i p e which e x t e n d s i n t h e i n s e r t was more p o l i s h e d t h a n the r e s t of the p i p e . 62 6.3 PRESSURE PROFILE 6.3.1 INTRODUCTION A t y p i c a l p r e s s u r e p r o f i l e i s shown i n f i g u r e 6.2, where the h e i g h t i s g i v e n on t h e o r d i n a t e and the p r e s s u r e minus the a t m o s p h e r i c p r e s s u r e on the a b s c i s s a . The p r o f i l e s a r e g i v e n f o r a medium i n v e n t o r y of PVC, a e r a t e d w i t h an o u t e r a i r v e l o c i t y of 0.046 m/s, and an i n n e r a i r v e l o c i t y of 1.7 m/s t h r o u g h a v e r t i c a l i n l e t . The l i n e marked w i t h t h e s o l i d c i r c l e s t r a c e s the p r e s s u r e p r o f i l e i n the a n n u l a r r e g i o n . The s h a r p break i n t h e p r e s s u r e c u r v e o c c u r s a t the bed s u r f a c e . Below t h e bed s u r f a c e , t h e s u b s t a n t i a l and c o n s t a n t p r e s s u r e g r a d i e n t r e f l e c t s a u n i f o r m bed d e n s i t y . Between the bed s u r f a c e and th e t o p of t h e column, the p r e s s u r e d r o p i s n e g l i g i b l e (0.02 kPa a t m o s t ) . The l i n e w i t h t h e open c i r c l e s r e p r e s e n t s t h e p r e s s u r e p r o f i l e i n t h e i n s e r t . The change i n p r e s s u r e a l o n g the i n s e r t i s g r a d u a l ; the s l o p e a l s o changes g r a d u a l l y , from a low v a l u e a t t h e bottom t o a h i g h v a l u e a t t h e t o p . At the bottom of t h e i n s e r t , t he p r e s s u r e i s n e a r l y e q u a l t o the p r e s s u r e a t t h e same l e v e l i n t h e a n n u l a r r e g i o n , and a t t h e t o p of t h e i n s e r t i t i s h i g h e r - a s i t u a t i o n w h i c h r e f l e c t s t h e c i r c u l a t i o n p a t t e r n i n t h e system. Everywhere a l o n g t h e i n s e r t , t h e r a d i a l p r e s s u r e d i s t r i b u t i o n was found t o be u n i f o r m . 63 1.6 1.2 .2> 0.8 0.4 i O Column m outer o Inner 1 2 3 Pressure, kPa F i g u r e 6.2 T y p i c a l p r e s s u r e p r o f i l e f o r PVC, medium i n v e n t o r y , Ui=1.7 m/s, U o=0.046 m/s, v e r t i c a l i n l e t . 6 4 6 . 3 . 2 E F F E C T O F I N N E R A I R V E L O C I T Y F i g u r e 6 . 3 e x e m p l i f i e s w h a t h a p p e n s w h e n t h e i n n e r a i r v e l o c i t y ( U \ ) i s c h a n g e d . F i g u r e 6 . 3 g i v e s t h e p r e s s u r e p r o f i l e s f o r t h e s a m e s y s t e m a s i n f i g u r e 6 . 2 , f o r f i v e d i f f e r e n t i n n e r v e l o c i t i e s . A s i s i n c r e a s e d , t h e p r e s s u r e p r o f i l e i n t h e o u t e r c o l u m n d o e s n o t c h a n g e , a l t h o u g h t h e c u r v e o f f i g u r e 6 . 2 i s s h i f t e d t o t h e r i g h t . W h i l e t h e g u a g e p r e s s u r e i n c r e a s e s i n t h e s y s t e m , t h e o u t e r b e d h e i g h t a n d b e d d e n s i t y d o n o t c h a n g e s i g n i f i c a n t l y . T h a t i s , t h e p r e s s u r e a t t h e b o t t o m o f t h e o u t e r c o l u m n ( p ^ Q / p o s i t i o n 11 i n f i g u r e 5 . 2 ) a n d a t t h e t o p ( p t 0 ' p o s i t i o n 1 4 ) b o t h i n c r e a s e b u t t h e p r e s s u r e d r o p a c r o s s t h e o u t e r c o l u m n ( A P Q = ^ b o ~ P t o ^ ^ o e s n o t v a r y v e r y m u c h . I n t h e i n n e r c o l u m n h o w e v e r , t h e p r o f i l e b e c o m e s f l a t t e r . T h e p r e s s u r e a t t h e t o p o f t h e i n s e r t ( p t i ' p o s i t i o n 1 0 ) i n c r e a s e s w i t h i n c r e a s i n g 0 \ , w h i l e t h e p r e s s u r e a t t h e b o t t o m o f t h e i n s e r t ( p D i . ' p o s i t i o n 1) v a r i e s v e r y l i t t l e . T h e o v e r a l l r e s u l t i s t h a t t h e t o t a l p r e s s u r e d r o p a c r o s s t h e i n s e r t ( A P . = P , . - P . . ) d e c r e a s e s w i t h i n c r e a s i n g 0 . . S i n c e A P . I b i t i 3 I I d e c r e a s e s a n d A P Q d o e s n o t c h a n g e s i g n i f i c a n t l y a s i s i n c r e a s e d , t h e p r e s s u r e d i f f e r e n c e b e t w e e n t h e t o p o f t h e i n s e r t a n d t h e t o p o f t h e o u t e r c o l u m n m u s t n e c e s s a r i l y i n c r e a s e . T h i s p r e s s u r e d i f f e r e n c e m a y b e t a k e n t o b e t h e p r e s s u r e d r o p a c r o s s t h e b a f f l e ( A P f a = P t i ~ P o ^ ' F i g u r e 6 . 4 r e p o r t s t h e c h a n g e s i n g a u g e p r e s s u r e a n d p r e s s u r e d r o p w i t h , f o r a m e d i u m i n v e n t o r y o f P V C w i t h a v e r t i c a l i n l e t a n d a n o u t e r v e l o c i t y o f 0 . 0 4 6 m / s . I t c a n b e 65 1.6 1.2 .5? 0.8 T l I I I 1 A O D O O bed level 0.4 air inlet nser t 0 1 2 3 Pressure, kPa F i g u r e 6.3 E f f e c t of i n n e r gas v e l o c i t y on i n s e r t a x i a l p r e s s u r e p r o f i l e f o r PVC, medium i n v e n t o r y , U o=0.046 m/s, v e r t i c a l i n l e t . 66 1.5 2 2.5 Inner gas velocity, m/s F i g u r e 6.4 E f f e c t of i n n e r gas v e l o c i t y on gauge p r e s s u r e and p r e s s u r e d r o p f o r PVC, medium i n v e n t o r y , U o=0.046 m/s, v e r t i c a l i n l e t . 67 seen from f i g u r e 6.4 t h a t P. . , P, , P. , and AP, i n c r e a s e t1 bo t o b w i t h w h i l e AP^ d e c r e a s e s . A P Q and P^^ do not change v e r y much. 6.3.3 EFFECT OF OUTER AIR VELOCITY The e f f e c t of t h e o u t e r a i r v e l o c i t y (U ) on t h e o p r e s s u r e p r o f i l e i s not e a s i l y d i s c e r n i b l e . When U Q i s i n c r e a s e d , the i m m e d i a t e l y a p p a r e n t conseguences a r e t h e r i s e of the o u t e r bed l e v e l and t h e i n c r e a s e of b u b b l i n g a c t i v i t y . T h i s means t h a t the break p o i n t of the o u t e r bed p r e s s u r e p r o f i l e of f i g u r e 6.2 moves h i g h e r up. The s l o p e of the l i n e below the bed s u r f a c e may or may not change, 'depending on the r e s p o n s e of t h e p r e s s u r e d r o p a c r o s s t h e bed t o a change i n U^. T h i s r e sponse i s not s y s t e m a t i c , however. Changes i n gauge p r e s s u r e and p r e s s u r e drop w i t h a change i n o u t e r v e l o c i t y a r e i l l u s t r a t e d f o r two d i f f e r e n t systems i n f i g u r e s 6.5 and 6.6. F i g u r e 6.5 i s f o r a medium i n v e n t o r y of c r a c k i n g c a t a l y s t w i t h a v e r t i c a l i n l e t and U^=1.7 m/s, w h i l e f i g u r e 6.6 i s f o r a low i n v e n t o r y of PVC w i t h a v e r t i c a l i n l e t and U^-1.7 m/s. When the o u t e r v e l o c i t y i s f i r s t i n c r e a s e d , t h e i m m e d i a t e l y r e c o g n i z a b l e p a t t e r n i n b o t h f i g u r e s i s the sudden i n c r e a s e of Pjj0» p D i ' AP. and AP . W i t h f u r t h e r i n c r e a s e i n U , t h e response of 1 0 o r t h e two systems i s d i f f e r e n t . I n f i g u r e 6.5, P j ^ and A P Q d e c r e a s e and P ^ and AP^ a r e r e l a t i v e l y c o n s t a n t , w h i l e i n f i g u r e 6.6 P^^, p D O r A p 0 and AP^ a l l i n c r e a s e . I t i s t h e r e f o r e d i f f i c u l t t o g e n e r a l i z e the e f f e c t of o u t e r 68 D CL C L O 0 3 C/) V) C L O CD 3 CO CD _^ Q_ o -Q < 4 .v—v--O—o- - O -—^  ^ 3 ^ " P b o A P o "A A — - A — P bi " 0 — - O — A P P t i P t o A P b 3 6 9 Outer velocity, cm/s 12 E f f e c t of o u t e r gas v e l o c i t y on gauge p r e s s u r e and p r e s s u r e d r o p f o r c r a c k i n g c a t a l y s t , medium i n v e n t o r y , U j - l . 7 m/s, v e r t i c a l i n l e t . 69 F i g u r e 6.6 E f f e c t of o u t e r gas v e l o c i t y on gauge p r e s s u r e and p r e s s u r e d r o p f o r PVC, low- i n v e n t o r y , 0"i = 1.7 m/s, v e r t i c a l i n l e t . 70 v e l o c i t y on the p r e s s u r e p r o f i l e . However, the e f f e c t i s g e n e r a l l y s m a l l , p r o v i d i n g t h a t U Q i s h i g h enough t h a t the o u t e r bed i s a t or above the minimum f l u i d i z a t i o n p o i n t . When the o u t e r bed i s not f l u i d i z e d , t h e gauge p r e s s u r e and the p r e s s u r e drop a r e much lower than when i t i s f l u i d i z e d . 6.3.4 EFFECT OF INVENTORY Changing the i n v e n t o r y has a p r e d i c t a b l e and d e f i n i t e e f f e c t on the p r e s s u r e p r o f i l e , as f i g u r e 6.7 d e m o n s t r a t e s . F i g u r e 6.7 g i v e s the p r e s s u r e p r o f i l e of a system s u b j e c t e d t o the same c o n d i t i o n s as i n f i g u r e 6.2, f o r t h r e e d i f f e r e n t bed i n v e n t o r y l e v e l s . In t h e a n n u l a r r e g i o n the p r e s s u r e a t t h e bottom i n c r e a s e s w i t h the amount of s o l i d s i n the system, w h i l e the p r e s s u r e a t the t o p v a r i e s l i t t l e w i t h a change i n i n v e n t o r y . The o b v i o u s consequence of i n c r e a s i n g the i n v e n t o r y i s t h a t t h e break p o i n t i n t h e p r e s s u r e p r o f i l e moves up s i n c e t h e bed l e v e l i s h i g h e r . In t h e i n s e r t , a s i m i l a r phenomenon i s o b s e r v e d . F i g u r e 6.7 shows how, as t h e i n v e n t o r y i s i n c r e a s e d , t h e l e n g t h of t h e r e g i o n c o r r e s p o n d i n g t o t h e upper p o r t i o n of t h e p r o f i l e where the s l o p e i s v e r y s t e e p d e c r e a s e s . Here a g a i n , t h e p r e s s u r e a t the bottom i n c r e a s e s s i g n i f i c a n t l y w i t h i n v e n t o r y w h i l e the p r e s s u r e a t the t o p does not change v e r y much. F i g u r e 6.8 i l l u s t r a t e s f u r t h e r t h e p r e s s u r e r e s p o n s e of t h e system t o a change i n i n v e n t o r y . The o v e r a l l e f f e c t of i n c r e a s i n g t h e i n v e n t o r y i s t o i n c r e a s e t h e p r e s s u r e d r o p 71 Bed Inventory A Small o Medium o 1 2 3 4 Pressure, kPa F i g u r e 6 . 7 E f f e c t o f b e d i n v e n t o r y o n i n s e r t a x i a l p r e s s u r e p r o f i l e f o r P V C , U " i = 1 . 7 m / s , U o = 0 . 0 4 6 m / s , v e r t i c a l i n l e t . 72 D Q _ CL 2 4 " O CO CD 3 Q . o CD \5 2 CO CO CD CL £ 1 J 3 O to _ Q < P b O / D APO /V P t i - o -P t o - o A P b - ^ -• o o o -10 14 Bed inventory, kg 18 F i g u r e 6.8 E f f e c t of bed i n v e n t o r y on gauge p r e s s u r e and p r e s s u r e drop f o r PVC, Ui=1.7 m/s, U o=0.046 m/s, v e r t i c a l i n l e t . 73 a c r o s s t h e i n s e r t and a c r o s s t h e o u t e r bed. The p r e s s u r e d r o p a c r o s s t h e b a f f l e does not v a r y i n a monotonic f a s h i o n . 6.3.5 EFFECT OF SOLIDS PROPERTIES R e p l a c i n g the PVC by t h e s m a l l e r , d e n s e r , and more f r e e - f l o w i n g c r a c k i n g c a t a l y s t a f f e c t s t h e p r e s s u r e p r o f i l e i n b o t h t h e i n s e r t and the o u t e r column. The e f f e c t i s shown i n f i g u r e 6.9 and t a b l e 6.2. T a b l e 6.2 shows t h a t f o r a g i v e n i n v e n t o r y ( i . e . o u t e r bed l e v e l ) , i n l e t t y p e , i n n e r and o u t e r v e l o c i t i e s , P, . , P.., P, , AP. , AP , and AP, a r e b i t i bo l o b a l l h i g h e r when c r a c k i n g c a t a l y s t i s used. F i g u r e 6.9 compares t h e p r e s s u r e d i s t r i b u t i o n s f o r c r a c k i n g c a t a l y s t and PVC. The c o n d i t i o n s a r e the same as i n f i g u r e 6.2. Both the gauge p r e s s u r e and the o v e r a l l p r e s s u r e d r o p a r e g r e a t e r when c r a c k i n g c a t a l y s t i s used, as one would e x p e c t i n view of t h e g r e a t e r d e n s i t y of t h e c a t a l y s t p a r t i c l e s . 6.3.6 EFFECT OF AIR INLET CONFIGURATION Two a s p e c t s of the a i r i n l e t a r e c o n s i d e r e d : the h e i g h t of t h e i n l e t above t h e d i s t r i b u t o r p l a t e and t h e c o n f i g u r a t i o n of the i n l e t a i r j e t ( t a n g e n t i a l or v e r t i c a l ) . F i g u r e 6.10 shows t h a t t h e lower t h e i n l e t , t he h i g h e r t h e p r e s s u r e a t e v e r y p o i n t a l o n g t h e i n s e r t . The impact of the a i r i n l e t c o n f i g u r a t i o n was found t o depend t o a c e r t a i n e x t e n t on t h e t y p e of s o l i d s used. When a t a n g e n t i a l i n l e t i s used and t h e bed m a t e r i a l i s PVC, t h e 74 1.6 Solid A cracking catalyst o pvc 1.2 . ! ? 0.8 0.4 h 0 0 1 2 Pressure, kPa Figure 6.9 Effect of solid type on insert axial pressure profile for medium inventory, Ui=1.7 m/s, Uo=0.046 m/s, vertical inlet. 75 T a b l e 6.2 E f f e c t of s o l i d s t y p e on gauge p r e s s u r e and p r e s s u r e drop f o r medium i n v e n t o r y , Uj_ = 1.7 m/s, v e r t i c a l i n l e t . u0 P b i P t i Pbo Pto A P i APo A P b m/s kPa kPa kPa kPa kPa kPa kPa C r a c k i n g c a t a l y s t 0.023 2.92 0.60 4.,63 0.35 2.32 4.28 0.25 0.034 2.83 0.61 4.67 0.36 2.22 4.31 0.25 0.046 2.83 0.62 4.55 0.36 2.21 4.19 0.26 0.056 2.83 0.64 4.50 0.37 2.20 4.12 0.26 PVC 0.023 1 .97 0.45 2.99 0.32 1 .52 2.67 0.13 0.034 2.24 0.45 3.43 0.29 1 .79 3.14 0.16 0.046 2.67 0.55 3.73 0.35 2.12 3.37 0.20 0.056 I 2.66 0.55 3.63 0.32 2.1 1 3.31 0.23 76 1.6 1.2 O ) o.8 CD 0.4 -O A Height above distributor A Q . | 8 m O 0 - 2 8 m • 0-3 4 m C L O A 1 2 3 Pressure, kPa F i g u r e 6.10 E f f e c t of h e i g h t of i n l e t above t h e d i s t r i b u t o r p l a t e on i n s e r t a x i a l p r e s s u r e p r o f i l e f o r PVC, h i g h i n v e n t o r y , Ui=2.2 m/s, U o=0.034 m/s, v e r t i c a l i n l e t . 77 a i r s e n t t o t h e o u t e r bed seems t o be e n t r a i n e d i n t o the i n s e r t s i n c e a h i g h e r a i r f l o w must be sent t o t h e a n n u l a r r e g i o n t o f l u i d i z e i t . When c r a c k i n g c a t a l y s t i s use d , the bed behaves s l i g h t l y d i f f e r e n t l y . There does not appear t o be any e n t r a i n m e n t of the o u t e r a i r i n t o the i n s e r t ( i . e . f o r a g i v e n a i r f l o w t o the a n n u l a r r e g i o n , t h e o u t e r bed s t r u c t u r e remains v i s u a l l y the same) when a t a n g e n t i a l i n l e t i s used. T a b l e 6.3 shows the e f f e c t of i n l e t c o n f i g u r a t i o n on p r e s s u r e d i s t r i b u t i o n f o r PVC. The gauge p r e s s u r e (pbi» P t i ' P b o ' P t o ^ a n d P r e s s u r e d r o p ( A P j , A P Q , AP f a) t e n d t o be s l i g h t l y l o w e r when a t a n g e n t i a l i n l e t i s used. F i g u r e 6.11 and t a b l e 6.4 i l l u s t r a t e t h e e f f e c t of a i r i n l e t geometry f o r c r a c k i n g c a t a l y s t . A l t h o u g f i g u r e 6.11 seems t o i n d i c a t e t h a t P ^ and AP^ a r e h i g h e r when a t a n g e n t i a l i n l e t i s used, i t a p pears from t a b l e 6.4 t h a t P^<0» p b i ' A P o ' a n d ^ P i a r e g e n e r a l l y l o w e r f o r the t a n g e n t i a l i n l e t . 6.3.7 PRESSURE FLUCTUATIONS P r e s s u r e f l u c t u a t i o n s r e l a t i v e t o the average p r e s s u r e , r e c o r d e d f o r a medium i n v e n t o r y of c r a c k i n g c a t a l y s t , U Q=0.034 m/s, and U^ v a r i e d from 0.6 t o 2.6 m/s, a r e shown i n f i g u r e 6.12. The magnitude of t h e f l u c t u a t i o n s measured 0.3 m above t h e i n l e t i s much g r e a t e r than a t 0.3 m below the b a f f l e , but t h e t r e n d s appear t o be the same. The p r e s s u r e f l u c t u a t i o n p a t t e r n changes v e r y g r a d u a l l y as the i n n e r v e l o c i t y i s i n c r e a s e d . At U^=0.6 m/s, no s o l i d s a re c i r c u l a t i n g . The f r e q u e n c y of t h e f l u c t u a t i o n s , w h i c h can be 9 78 T a b l e 6.3 E f f e c t of a i r i n l e t c o n f i g u r a t i o n on gauge p r e s s u r e and p r e s s u r e drop f o r PVC, Ui=2.2 m/s, low i n v e n t o r y . m/s P b i kPa P t i kPa Pbo kPa P t o kPa A P i kPa APo kPa A P b kPa V e r t i c a l i n l e t 0.056 2.01 0.75 2.89 0.55 1.26 2.34 0.20 0.073 1.93 0.82 2.94 0.59 1.11 2.35 0.23 0.108 2.31 0.89 3.14 0.69 1.42 2.45 0.20 T a n g e n t i a l i n l e t 0.056 1.80 0.74 2.33 0.073 1.81 0.78 2.86 0.108 2.15 0.86 2.89 0.56 1.06 1.74 0 .18 0.55 1.03 2.31 0.23 0.64 1.29 2.25 0.22 79 1.6 1.2 ,g> o.8 CD 0 .4 inlet A vertical o tangential o 1 2 3 Pressure, kPa F i g u r e 6.11 E f f e c t of a i r i n l e t c o n f i g u r a t i o n on i n s e r t a x i a l p ressure p r o f i l e f o r c r a c k i n g c a t a l y s t , medium i n v e n t o r y , Ui=1.7 m/s, U o=0.046 m/s. 80 T a b l e 6.4 E f f e c t of a i r i n l e t c o n f i g u r a t i o n on gauge p r e s s u r e and p r e s s u r e d r o p f o r c r a c k i n g c a t a l y s t , h i g h i n v e n t o r y , Ui=1.7 m/s. V e r t i c a l i n l e t 0.013 2.83 0.023 4.29 0.034 4.46 0.046 4.55 0.056 4.64 0.52 5.15 0.69 6.13 0.69 6.26 0.69 6.21 0.71 6.18 0.29 2.31 0.34 3.60 0.36 3.77 0.37 3.86 0.36 3.93 4.86 0.23 5.79 0.35 5.90 0.33 5.84 0.32 5.82 0.35 T a n g e n t i a l i n l e t 0.013 3.09 0.60 • 4.63 0.32 2.49 4.31 0.28 0.023 3.95 0,67 5.66 0.34 3.28 ' 5.32 0.33 0.034 4.20 0.72 5.92 0.35 3.48 5.57 0.37 0.046 4.29 0.72 5.97 0.37 3.57 5.60 0.35 0.056 4.20 0.72 5.92 0.39 3.48 5.53 0.33 81 (sec) (sec) U; i' i 1 1 1 1 1 1 r — — i i 1 1 1 1 m / S 0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 0-6 0-7 o-8 HAT Wv^\bhN\fW\nJiMAWlrWi^ukn **** - 4 A f % j H ^ ^ ^ K ^ k "? ^ ^ ^ ^ /iHm>^^ (a) (b) F i g u r e 6.12 P r e s s u r e f l u c t u a t i o n s f o r c r a c k i n g c a t a l y s t , medium i n v e n t o r y , U o=0.034 m/s. (a) 0.3 m above the a i r i n l e t , (b) 0.3 m below t h e b a f f l e . 82 a s s o c i a t e d w i t h b u b b l i n g a c t i v i t y , i s a p p r o x i m a t e l y 2.0 Hz. As the i n n e r a i r v e l o c i t y i s i n c r e a s e d from 0.6 t o 1.2 m/s, both the a m p l i t u d e and t h e f r e q u e n c y i n c r e a s e . At U\=1.2 m/s, the p a t t e r n i s s t r i k i n g l y r e g u l a r , w i t h a fr e q u e n c y of 3.3 Hz. At IK=1.9 m/s, t h e r e seem t o be two superimposed p a t t e r n s : more r a p i d , s m a l l a m p l i t u d e f l u c t u a t i o n s w i t h a f r e q u e n c y of 3.0 Hz, and a l a r g e r a m p l i t u d e w a v e l i k e m o t i o n w i t h a f r e q u e n c y of about 0.25 Hz. The p a t t e r n i s s i m i l a r a t U^=2.6 m/s, which i s j u s t below the f l o o d i n g p o i n t . Over the range i n v e s t i g a t e d t h e r e i s no e v i d e n c e of a sudden d e c r e a s e i n the a m p l i t u d e of f l u c t u a t i o n s w i t h an i n c r e a s e i n of the t y p e r e p o r t e d by Y e r u s h a l m i and C a n k u r t ( 1 9 7 9 ) . 6.4 SOLIDS CIRCULATION FLUX 6.4.1 INTRODUCTION The c i r c u l a t i o n f l u x e s r e p o r t e d i n t h i s c h a p t e r a r e g i v e n o n l y f o r t h e i n t e r n a l l y r e c i r c u l a t e d p a r t i c l e s , i . e . f o r t h e s o l i d s f a l l i n g back i n t h e a n n u l a r r e g i o n a f t e r s e p a r a t i o n by t h e b a f f l e . The amount of s o l i d s e s c a p i n g t o the c y c l o n e was measured f o r a few c a s e s and was found t o be i n s i g n i f i c a n t ( l e s s than 2% of the amount i n t e r n a l l y c i r c u l a t i n g ) when t h e bed i s o p e r a t e d below t h e f l o o d i n g v e l o c i t y . 83 6.4.2 EFFECT OF INNER VELOCITY F i g u r e 6.13 g i v e s a t y p i c a l s e t of c i r c u l a t i o n f l u x measurements. As e x p e c t e d , t h e c i r c u l a t i o n of the s o l i d s i n c r e a s e s w i t h i n c r e a s i n g i n n e r gas v e l o c i t y . I n a l l the c a s e s , t h e c i r c u l a t i o n f l u x was found t o i n c r e a s e with' i n n e r v e l o c i t y . However, the shape and s l o p e of t h e c i r c u l a t i o n f l u x v e r s u s i n n e r gas v e l o c i t y c u r v e s depend on p a r t i c l e t y p e , o u t e r gas v e l o c i t y , and bed i n v e n t o r y l e v e l . When the bed m a t e r i a l i s PVC, t h e i n c r e a s e i n c i r c u l a t i o n f l u x w i t h i n n e r v e l o c i t y i s g e n e r a l l y l i n e a r . T h i s can be seen i n f i g u r e 6.14. Moreover, t h e o u t e r v e l o c i t y a f f e c t s t he s l o p e of t h e c u r v e s : t h e h i g h e r t h e o u t e r v e l o c i t y , t he s t e e p e r t h e i n c r e a s e i n f l u x . As shown i n f i g u r e 6.15, the bed i n v e n t o r y a f f e c t s t h e i n c r e a s e i n the same way: t h e l a r g e r t h e i n v e n t o r y , t h e s t e e p e r the i n c r e a s e . When c r a c k i n g c a t a l y s t i s used as bed m a t e r i a l , t h e system responds i n a s l i g h t l y d i f f e r e n t way t o an i n c r e a s e i n i n n e r v e l o c i t y . F i r s t , t h e f l o o d i n g v e l o c i t y i s l o w e r . T h i s has t h e u n f o r t u n a t e consequence of r e d u c i n g t h e range over w h i c h measurements can be o b t a i n e d . I n some i n s t a n c e s , t h e c i r c u l a t i o n r a t e s f o r o n l y t h r e e i n n e r v e l o c i t i e s c o u l d be measured. Second, t h e i n c r e a s e of t h e c i r c u l a t i o n w i t h i n n e r v e l o c i t y i s no l o n g e r l i n e a r . T h i r d , t h e bed i n v e n t o r y and t h e o u t e r v e l o c i t y i n f l u e n c e t h e shape of t h e c i r c u l a t i o n f l u x v e r s u s i n n e r gas v e l o c i t y c u r v e v e r y s t r o n g l y . F i g u r e s 6.16 and 6.17 i l l u s t r a t e t h e s e t r e n d s . 84 1 1.5 2 2 . 5 3 Inner gas velocity, m/s Figure 6.13 T y p i c a l s o l i d s c i r c u l a t i o n fluxes for PVC, medium inventory, Uj=1.7 m/s, Uo=0.046 m/s. 8 5 30 C N 20 \-X 00 ~o 00 10 0 1.5 2 2.5 Inner gas velocity, m / s F i g u r e 6.14 E f f e c t of inner and outer gas v e l o c i t y on the c i r c u l a t i o n of PVC, medium i n v e n t o r y , v e r t i c a l i n l e t . 8 6 30 cs 20 h X ~ o 1 0 10 f-0 Bed Inventory A low o medium • high 1.5 2 2.5 Inner gas velocity, m / s Figure 6.15 Effect of inner gas velocity and bed inventory on the circulation of PVC, Uo=0.046 m/s, vertical inlet. 87 U o r cm/s A 1 - 3 O 2-3 1 1.5 2 2.5 3 Inner gas velocity, m / s 16 E f f e c t of i n n e r and o u t e r gas v e l o c i t y on t h e c i r c u l a t i o n of c r a c k i n g c a t a l y s t , medium i n v e n t o r y , v e r t i c a l i n l e t . 88 60 CN 4 5 5 30 ~o 00 15 Bed inventory A low o medium • high • 1.5 2 2.5 Inner gas velocity, m /s F i g u r e 6.17 E f f e c t of i n n e r gas v e l o c i t y and bed i n v e n t o r y on the c i r c u l a t i o n of c r a c k i n g c a t a l y s t / U o=0.023 m/s, v e r t i c a l i n l e t . 89 F i g u r e 6.16 shows the combined e f f e c t of i n n e r and o u t e r v e l o c i t y . Each c u r v e t e n d s t o l e v e l o f f , e s p e c i a l l y a t l o w e r o u t e r v e l o c i t i e s . As i n the case of PVC, t h e h i g h e r t h e o u t e r v e l o c i t y , the h i g h e r the c i r c u l a t i o n f l u x f o r a g i v e n i n n e r v e l o c i t y , and the s t e e p e r the i n c r e a s e . F i g u r e 6.17 shows t h e e f f e c t of bed i n v e n t o r y , and he r e a g a i n , t h e h i g h e r the i n v e n t o r y , t h e h i g h e r the c i r c u l a t i o n f l u x f o r a g i v e n i n n e r v e l o c i t y and the s t e e p e r the i n c r e a s e . The t y p e of a i r i n l e t c o n f i g u r a t i o n does not appear t o have a s i g n i f i c a n t e f f e c t on t h e c i r c u l a t i o n r a t e v e r s u s i n n e r v e l o c i t y c u r v e . 6.4.3 EFFECT OF SOLIDS INVENTORY The s o l i d s i n v e n t o r y l e v e l e x e r t s a c r u c i a l impact on the c i r c u l a t i o n of s o l i d s . F i g u r e 6.18, w h i c h i s a c r o s s - p l o t of f i g u r e 6.15, shows t h a t the c i r c u l a t i o n f l u x i s a u s u a l l y a m o n o t i c a l l y i n c r e a s i n g f u n c t i o n of t h e amount of s o l i d s i n the bed. The s l o p e of each l i n e depends on t h e i n n e r gas v e l o c i t y : t h e h i g h e r t h e i n n e r v e l o c i t y , t h e s t e e p e r t h e s l o p e . The o u t e r v e l o c i t y a l s o i n f l u e n c e s t h e impact of i n v e n t o r y on s o l i d s c i r c u l a t i o n . As shown i n f i g u r e 6.19, the i n c r e a s e i n c i r c u l a t i o n due t o an i n c r e a s e i n i n v e n t o r y i s more s i g n i f i c a n t f o r h i g h e r o u t e r v e l o c i t i e s . F i g u r e s 6.18 and 6.19 show t r e n d s t y p i c a l of a bed f i l l e d w i t h PVC. When th e bed m a t e r i a l i s c r a c k i n g c a t a l y s t , the e f f e c t of i n v e n t o r y on c i r c u l a t i o n f l u x i s s i m i l a r . The e f f e c t s of 90 U •,, m/s A 1-4 O 1-7 6 10 14 18 Bed inventory, kg F i g u r e 6 . 1 8 E f f e c t of bed i n v e n t o r y and i n n e r gas v e l o c i t y on the c i r c u l a t i o n of PVC ( C r o s s - p l o t of f i g . 6 . 1 5 ) . 91 Bed Inventory 0 2 4 6 Outer gas velocity, c m / s Figure 6.19 Effect of outer gas velocity and bed inventory on the circulation of PVC, U"i = 2.4 m/s, vertical i n l e t . 92 c h a n g i n g .the i n v e n t o r y and t h e i n n e r v e l o c i t y a r e g i v e n i n f i g u r e 6.20, w h i l e f i g u r e 6.21 shows the i n f l u e n c e of c h a n g i n g the i n v e n t o r y and o u t e r v e l o c i t y f o r c r a c k i n g c a t a l y s t p a r t i c l e s . 6.4.4 EFFECT OF OUTER VELOCITY The f a c t t h a t the c i r c u l a t i o n f l u x of s o l i d s i n c r e a s e s w i t h o u t e r v e l o c i t y has a l r e a d y been d e m o n s t r a t e d ( e . g . f i g u r e s 6.19 and 6.21). Moreover, f i g u r e s 6.14, 6.16, 6.19, and 6.21 show t h a t t h e impact of t h e o u t e r v e l o c i t y on t h e c i r c u l a t i o n f l u x i s s t r o n g e r f o r h i g h i n n e r v e l o c i t i e s and l a r g e r i n v e n t o r i e s . For t h e l o w e s t i n n e r v e l o c i t y (U^=1.4 m/s), t h e i n c r e a s e i n o u t e r v e l o c i t y may or may not cause an i n c r e a s e i n c i r c u l a t i o n . F i g u r e 6.22, a c r o s s - p l o t of f i g u r e 6.14, shows t h a t t h e c i r c u l a t i o n r a t e of PVC i n c r e a s e s l i n e a r l y w i t h o u t e r v e l o c i t y . F i g u r e 6.23, a c r o s s - p l o t of f i g u r e 6.16, i l l u s t r a t e s t h e same t r e n d f o r c r a c k i n g c a t a l y s t . 6.4.5 EFFECT OF SOLIDS PROPERTIES The main e f f e c t of r e p l a c i n g PVC w i t h c r a c k i n g c a t a l y s t as bed m a t e r i a l i s t o i n c r e a s e t h e s o l i d s mass c i r c u l a t i o n . T h i s can be r e a d i l y d e m o n s t r a t e d by comparing f i g u r e s 6.19 and 6.21. R a t i o s of the c i r c u l a t i o n f l u x of c r a c k i n g c a t a l y s t t o t h a t of PVC appear i n t a b l e 6.5. The r a t i o s r ange from a minimum of 2.1 t o a maximum of 8.4. They d e c r e a s e w i t h i n n e r v e l o c i t y ; t h e y a l s o d e c r e a s e w i t h o u t e r 9 3 F i g u r e 6.20 E f f e c t of bed i n v e n t o r y and i n n e r gas v e l o c i t y on the c i r c u l a t i o n of c r a c k i n g c a t a l y s t ( C r o s s - p l o t of f i g . 6.17). 9 4 0 2 4 6 Outer gas velocity, c m / s F i g u r e 6.21 E f f e c t of outer gas v e l o c i t y and bed i n v e n t o r y on the c i r c u l a t i o n of c r a c k i n g c a t a l y s t , Ui = 1.7 m/s, v e r t i c a l i n l e t . 9 5 30 20 I-10 h 0 0 2 4 Outer gas velocity, c m / s F i g u r e 6.22 E f f e c t of o u t e r and i n n e r gas v e l o c i t y on the c i r c u l a t i o n of PVC ( C r o s s - p l o t of f i g . 6 . 1 4 ) . 9 6 0 2 4 6 Outer gas velocity, c m / s F i g u r e 6 . 2 3 E f f e c t o f o u t e r a n d i n n e r g a s v e l o c i t y o n t h e c i r c u l a t i o n o f c r a c k i n g c a t a l y s t ( C r o s s - p l o t o f f i g . 6 . 1 6 ) . 97 T a b l e 6.5 R a t i o s of the c i r c u l a t i o n f l u x f o r c r a c k i n g c a t a l y s t t o t h a t f o r PVC. U i U D, cm/s m/s 2.3 3.4 4. 6 5. 6 Low i n v e n t o r y , v e r t i c a l i n l e t 1.4 5.0 4. 3 5. 3 1.7 3.8 3. 5 3. 0 1.9 2.7 3. 0 2. 5 2.2 2.2 2. 6 2. 5 2.4 2.1 2. 0 Medium i n v e n t o r y , v e r t i c a l i n l e t 1.4 8.4 5.3 3. 7 4. 0 1.7 5.7 5.2 4. 4 3. 4 1.9 4.5 3.4 3. 5 3. 0 2.2 4.2 3.2 3. 0 H i g h i n v e n t o r y , v e r t i c a l i n l e t 1.4 5.3 6.2 7. 1 5. 0 1.7 6.0 5.7 5. 7 4. 8 1.9 4.6 4.5 4. 5 3. 3 2.2 3.7 3.7 Low i n v e n t o r y , t a n g e n t i a l i n l e t 1 .4 5. 7 1.7 4. 2 1.9 2. 6 2.2 2. 1 Medium i n v e n t o r y , t a n g e n t i a l i n l e t 1 .4 5. 6 1 .7 7. 7 1.9 6. 7 2.2 6. 0 98 velocity in most of the cases. The inventory level does not seem to affect the ratio. The ratios are higher than the particle density ratio of 1.4. 6.4.6 EFFECT OF AIR INLET CONFIGURATION The height of the inlet above the distributor plate has a definite influence on the circulation rate of solids. As figure 6.24 shows, the lower the inlet, the higher the circulation rate. It should be remembered that the inlet is always above the bottom of the insert. The inlet configuration also influences the circulation rate of solids. The vertical inlet always produces circulation rates higher than the tangential i n l e t . Table 6.6 l i s t s ratios of the circulation flux for a vertical inlet to that for a tangential inlet. These ratios range from 1.0 to 2.2. 9 9 O / 1 1.5 2 2 . 5 3 Inner gas velocity, m / s F i g u r e 6.24 E f f e c t of h e i g h t of i n l e t above the d i s t r i b u t o r p l a t e on the c i r c u l a t i o n of PVC, h i g h i n v e n t o r y , U o=0.034 m/s, v e r t i c a l i n l e t . 100 T a b l e 6.6 R a t i o s of the c i r c u l a t i o n f l u x f o r a v e r t i c a l i n l e t t o t h a t f o r a t a n g e n t i a l i n l e t . U i U 0, cm/s m/s 1.3 2.3 3.4 4.6 5.6 7 .3 10 .8 PVC, low i n v e n t o r y 1 .4 1 .6 1 .2 3 .0 1 .7 1 .9 1 .5 1 .9 1 .9 1 .3 1 .2 1 .4 2.2 1,3 1 .2 1 .4 2.4 1 .3 1 .2 1 .4 2.6 1 . 1 1 .5 2.7 1.3 PVC, medium i n v e n t o r y 1 .4 1 .6 1.7 2.5 1 .9 2.6 2.2 2.7 2.4 2.8 C r a c k i n g c a t a l y s t , low i n v e n t o r y 1 .4 2.2 2.2 1.9 1.8 1 .5 1 .7 1.8 1.8 1.9 1.5 1.3 1.9 1.9 1.8 1.7 1.7 1.6 2:2 1.7 1.6 1.7 1.7 1.5 2.4 1.6 1.5 2.6 1.5 1.6 2.7 1.5 1.6 C r a c k i n g c a t a l y s t , medium i n v e n t o r y 1 .4 1.5 1.3 1.3 1.0 1 . 1 1.7 1.7 1.3 1.1 1.3 1 . 1 1,9 1.8 1.3 1.1 1.1 1 .1 2.2 2.1 1.2 1.3 1.1 C r a c k i n g c a t a l y s t , h i g h i n v e n t o r y 1.4 1.0 1.2 1.0 1.3 1 .3 1.7 1.0 1.2 1.3 1.3 1 .3 1 .9 1.2 1.2 1.2 1.3 1 .2 2.2 1.3 1.2 1.2 7. DISCUSSION 7.1 INTRODUCTION A s i m p l e q u a l i t a t i v e d e s c r i p t i o n of t h e r e s u l t s was g i v e n i n the p r e v i o u s c h a p t e r . In t h e f i r s t p a r t of t h i s c h a p t e r , i n f e r e n c e s about the n a t u r e o f t h e system a r e made u s i n g t h o s e r e s u l t s : (1) The c o n c e p t of p r e s s u r e drop b a l a n c e i s d e s c r i b e d and d e n s i t y p r o f i l e s a r e d e r i v e d . (2) The c i r c u l a t i o n f l u x measurements a r e a n a l y z e d w i t h t h e a i d of a s i m p l e s t a t i s t i c a l model. (3) The p r e s s u r e d r o p and c i r c u l a t i o n f l u x measurements a r e combined t o y i e l d i n f o r m a t i o n on the p a r t i c l e and s l i p v e l o c i t i e s . I n t h e second p a r t of t h e c h a p t e r the r e s u l t s a r e compared t o the s c a n t i n f o r m a t i o n r e p o r t e d i n t h e l i t e r a t u r e . F i n a l l y , some comments a r e made on t h e t a n g e n t i a l i n l e t and the b a f f l e . The i n f o r m a t i o n g i v e n i n g r a p h i c a l form t h r o u g h o u t the c h a p t e r i s t a b u l a t e d i n appendix D. 7.2 PRESSURE DROP 7.2.1 THE CONCEPT OF PRESSURE DROP BALANCE F i g u r e 7.1 draws an a n a l o g y between t h e n o v e l c i r c u l a t i n g f l u i d i z e d bed and an e l e c t r i c a l c i r c u i t . The a n a l o g y i s s u g g e s t e d by the geometry of the system and the p r e s s u r e d r o p b a l a n c e r e q u i r e m e n t . W h i l e the system forms a c l o s e d l o o p w i t h r e s p e c t t o t h e s o l i d s , t h e gas may escape the u n i t t h r o u g h t h r e e d i f f e r e n t r o u t e s . One a l t e r n a t i v e i s 101 102 F i g u r e 7.1 P r e s s u r e d r o p " c i r c u i t " . 1 03 to bypass through the c y c l o n e (path AED on f i g u r e 7.1), a second one to t r a v e l through the a n n u l a r r e g i o n to the c y c l o n e (path AFCD), and a t h i r d one to go up the ' i n s e r t , through the b a f f l e , and i n t o the c y c l o n e (path ABCD). Depending on the i n v e n t o r y , the gas flow, and the type of s o l i d s , the g a s - s o l i d m i x t u r e d i s t r i b u t e s i t s e l f so as to create- an e q u a l p r e s s u r e drop a c r o s s the t h r e e branches. T h i s s e l f - b a l a n c i n g mechanism d i c t a t e s how the system responds to a change in o p e r a t i n g v a r i a b l e s . The p r e s s u r e drop depends on any of the f a c t o r s l i s t e d below: 1. Weight of s o l i d s . 2. D e n s i t y of the gas. 3. F r i c t i o n l o s s e s between the gas and the w a l l . 4. F r i c t i o n l o s s e s between the. s o l i d s and the w a l l . 5. F r i c t i o n l o s s e s between the s o l i d s and the gas. 6. Entrance l o s s e s i n the i n s e r t . . 7. Losses i n the b a f f l e . In the a n a l y s i s which f o l l o w s , only the paths through, the annular r e g i o n (AFC) and the i n s e r t (ABC) are c o n s i d e r e d s i n c e , i f o p e r a t i n g p r o p e r l y , a plug of s o l i d s in moving packed bed should b u i l d up i n the lower p a r t of the e x t e r n a l r e t u r n l i n e , e f f e c t i v e l y a c t i n g as a s e a l l i m i t i n g flow v i a the AED r o u t e . At steady s t a t e , i t i s p o s s i b l e to w r i t e a p r e s s u r e drop e q u a t i o n : which the system must s a t i s f y : ( P b i - p t i ) + ( P t i - p t o } = ( P b o * - p t o } ( 1 ) * P j 3 0 r e f e r s to the p r e s s u r e taken at the same datum l e v e l as P D i , u n l i k e P^Q used in c h a p t e r 6. 1 04 7.2.2 CONTRIBUTIONS TO PRESSURE DROP One i m p o r t a n t reason f o r measuring the p r e s s u r e i s t o e s t i m a t e t h e v o i d a g e d i s t r i b u t i o n o r d e n s i t y p r o f i l e a l o n g the i n s e r t . I t i s t h e r e f o r e i m p o r t a n t t o know what p o r t i o n of t h e measured p r e s s u r e d r o p can be a c c o u n t e d f o r by s o l i d s h o l d - u p . I n f a s t f l u i d i z e d s y s t e m s , f r i c t i o n l o s s e s a r e i n s i g n i f i c a n t and t h e bed d e n s i t y can be o b t a i n e d d i r e c t l y from t h e p r e s s u r e g r a d i e n t ( Y e r u s h a l m i , 1978; B i e r l e t a l . , 1980). I n pneumatic c o n v e y i n g , however, f r i c t i o n l o s s e s may ac c o u n t f o r a s i g n i f i c a n t f r a c t i o n of t h e t o t a l p r e s s u r e d r o p . The t o t a l p r e s s u r e d r o p i s commonly w r i t t e n a s : <AP/L> t o t = ( A P / L ) g r a v • < 4 P / L ) f r i c • ( A P / U a c c (2) where ( A P / L ) g r a v = [ p p ( 1 - e ) + p g e ] g (3) ( A P / L ) f r . c = 2f gp gV g 2<=/D + 2f g ( 1 - e ) p ^ 2/D (4) ( A P / L ) a c c = G gdV g/dz + G sdV g/dz (5) A l t h o u g h t h e r e a r e many p u b l i s h e d c o r r e l a t i o n s t o e s t i m a t e f r i c t i o n l o s s e s , none i s v e r y s a t i s f a c t o r y ( K n o w l t o n , 1979; Teo and Leung, 1984). The c o r r e l a t i o n of Konno and S a i t o (1969) i s chosen here because i t i s s i m p l e and has been shown t o work r e a s o n a b l y w e l l (Modi e t a l . , 1978). I t g i v e s : U - V = U. (6) g s t f s = 0.02B5/(V s//(gD)) (7) 105 The f r i c t i o n f a c t o r f can be a p p r o x i m a t e d by t h e F a n n i n g f r i c t i o n f a c t o r , and Vg by Ug s i n c e t h e v o i d a g e i s v e r y h i g h , t y p i c a l l y 0.977-0.996. F i g u r e 7.2 r e p r o d u c e s a t y p i c a l measured p r e s s u r e p r o f i l e . The c o n t r i b u t i o n s of g r a v i t y and f r i c t i o n t o t h e p r e s s u r e d r o p i n the upper r e g i o n of t h e i n s e r t have been c a l c u l a t e d f o r the system shown i n f i g u r e 7.2 (see a p p e n d i x E) assuming t h a t the f l o w i s f u l l y d e v e l o p e d . T a b l e 7.1 shows the r e s p e c t i v e c o n t r i b u t i o n of g r a v i t y and f r i c t i o n . F o r t h a t p a r t i c u l a r c a s e , t h e v o i d a g e o b t a i n e d when f r i c t i o n l o s s e s a r e c o n s i d e r e d i s 0.979 , and 0.977 when t h e y a r e n e g l e c t e d . The d i f f e r e n c e i s q u i t e s m a l l . The a c c e l e r a t i o n l o s s e s a t the bottom of t h e i n s e r t a r e d i s c u s s e d l a t e r . I t s h o u l d be n o t e d t h a t the s o l i d s f r i c t i o n l o s s e s may even be n e g a t i v e because of movement of. s o l i d s p a r t i c l e s downward a l o n g the w a l l . T h i s i s d i s c u s s e d i n d e t a i l by Van S w a a i j e t a l . (1970) and Nakamura and Capes (1 9 7 3 ) . 7.2.3 DENSITY PROFILES D e n s i t y p r o f i l e s p r o v i d e v a l u a b l e i n f o r m a t i o n on t h e n a t u r e of a g a s - s o l i d system. In f i g u r e 7.3, t h e a x i a l v o i d a g e d i s t r i b u t i o n i s shown f o r t h r e e d i f f e r e n t r e g i m e s : b u b b l i n g f l u i d i z a t i o n , f a s t f l u i d i z a t i o n , and pneumatic t r a n s p o r t ( W e i n s t e i n e t a l . , 1981; L i and Kwauk, 1982). T y p i c a l n u m e r i c a l v a l u e s f o r the v o i d a g e a r e g i v e n but do n o t by any means c o n s t i t u t e a b s o l u t e d e m a r c a t i o n s f o r each r e g i m e . F i g u r e 7.2 T y p i c a l measured i n s e r t p r e s s u r e p r o f i l e f o r c r a c k i n g c a t a l y s t , h i g h i n v e n t o r y , Uj_ = 1 .9 m/s, U o=0.046 m/s, t a n g e n t i a l i n l e t . 107 T a b l e 7.1 C o n t r i b u t i o n s t o p r e s s u r e d r o p f o r c r a c k i n g c a t a l y s t , 0"i = 1.9 m/s, U 0= 0.046. m/s, h i g h i n v e n t o r y , t a n g e n t i a l i n l e t . C o n t r i b u t i o n (kPa) (%) g r a v i t y , gas 0.011 2.4 g r a v i t y , s o l i d s 0.404 87.8 f r i c t i o n , gas 0.000 » 0*0 f r i c t i o n , s o l i d s 0.045 9.8 t o t a l 0.460 100.0 1 08 B U B B L I N G F L U I D I Z A T I O N (£ ui X F A S T F L U I D I Z A T I O N P N E U M A T I C T R A N S P O R T ~\ i r 0-+ 0-6 0-8 1-0 T 1 r — i — • r 0-7 0-8 0-9 1-0 0-9 V O I D A G E Figure 7.3 Density p r o f i l e and f l u i d i z a t i o n regimes. 1 09 For a b u b b l i n g bed, t h e time-mean v o i d a g e below the bed s u r f a c e i s r e l a t i v e l y low ( g e n e r a l l y l e s s than 0.7) and n e a r l y i ndependent of h e i g h t . Above t h e bed s u r f a c e t h e f r e e b o a r d i s v i r t u a l l y empty of s o l i d s e x c e p t f o r some e n t r a i n e d p a r t i c l e s . I n t h e f r e e b o a r d , t h e c o n c e n t r a t i o n of p a r t i c l e s decays e x p o n e n t i a l l y w i t h h e i g h t u n t i l t h e t r a n s p o r t disengagement h e i g h t (TDH) i s r e a c h e d . Above t h e TDH t h e c o n c e n t r a t i o n i s c o n s t a n t and may c o r r e s p o n d t o t h e 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 of t h e gas. I n a f a s t f l u i d i z e d column, t h e v o i d a g e p r o f i l e t y p i c a l l y c o n s i s t s of two asymptotes l i n k e d t o g e t h e r t h r o u g h an i n f l e c t i o n p o i n t . The g a s - s o l i d m i x t u r e i s d e n s e r a t t h e bottom and more d i l u t e a t the t o p . The magnitude of t h e a s y m p t o t i c v a l u e s depends on 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 w h i l e the p o s i t i o n of t h e i n f l e c t i o n p o i n t i s g o v e r n e d by t h e e x t e r n a l p r e s s u r e d r o p imposed on t h e bed ( i . e . by t h e i n v e n t o r y of s o l i d s i n t h e accompanying slow b e d ) . Pneumatic t r a n s p o r t i s c h a r a c t e r i z e d by a h i g h and r e l a t i v e l y u n i f o r m v o i d a g e t h r o u g h o u t t h e column. V o i d a g e d i s t r i b u t i o n s were o b t a i n e d f o r a l l the runs i n which p r e s s u r e p r o f i l e s were r e c o r d e d . They a r e t a b u l a t e d i n Appendix F. F r i c t i o n l o s s e s , a c c e l e r a t i o n l o s s e s and t h e mass of gas were i g n o r e d and t h e v o i d a g e was e s t i m a t e d u s i n g : AP/L = (1 - e)gp (8) The v o i d a g e s r e p o r t e d i n the work a r e a t b e s t r e a s o n a b l e e s t i m a t e s . The v a l u e s a r e not e x t r e m e l y a c c u r a t e because of 1 10 e x p e r i m e n t a l e r r o r and the a p p r o x i m a t i o n t h a t the p r e s s u r e i s e n t i r e l y due t o t h e h oldup of s o l i d s . F i g u r e s 7.4 and 7.5 show t y p i c a l d e n s i t y p r o f i l e s f o r c r a c k i n g c a t a l y s t and PVC r e s p e c t i v e l y . The parameter i n f i g u r e s 7.4 and 7.5 i s i n v e n t o r y l e v e l . I t i s i m m e d i a t e l y a p p a r e n t t h a t t h e v o i d a g e d i s t r i b u t i o n i s s t r o n g l y i n f l u e n c e d b o t h by the t ype of s o l i d s and by t h e bed i n v e n t o r y l e v e l . For c r a c k i n g c a t a l y s t ( f i g . 7.4) s t r i k i n g d i f f e r e n c e s i n the shape of t h e t h r e e c u r v e s e x i s t . T h i s i s h a r d l y s u r p r i s i n g s i n c e t h e i n v e n t o r y c o n t r o l s the s o l i d s c i r c u l a t i o n r a t e . A l l t h r e e c u r v e s show e n t r a n c e e f f e c t s . Two of the c u r v e s a r e s i m i l a r t o the g e n e r a l p a t t e r n d e s c r i b e d i n f i g u r e 7.3. For t h e l o w e s t i n v e n t o r y , the c i r c u l a t i o n r a t e i s low and the system i s i n t h e pneumatic t r a n s p o r t regime: u n i f o r m , h i g h v o i d a g e (e = 0.988, p„ =24 kg/ms 3), e x c e p t a t the bottom. At the h i g h e s t susp 3 i n v e n t o r y two zones a r e c l e a r l y i d e n t i f i a b l e : above the -i n f l e c t i o n p o i n t t h e v o i d a g e i s 0.977 ( P S U S p = 4 6 kg/m 3), and 0.825 (p„ =350 kg/m 3) below. The c u r v e f o r the medium susp i n v e n t o r y may be l o o k e d on as p a r t of a t r a n s i t i o n r e g i o n . Leung (1980) r e f e r s t o a " f u z z y " t r a n s i t i o n between d i l u t e phase f l o w and n o n - s l u g g i n g dense f l o w or f a s t f l u i d i z a t i o n . The d e n s i t y p r o f i l e f o r PVC ( f i g . 7.5) shows the same dependence of v o i d a g e on s o l i d s i n v e n t o r y : a t any p o i n t i n t h e i n s e r t , t h e v o i d a g e i n c r e a s e s w i t h d e c r e a s i n g i n v e n t o r y . However, none of t h e t h r e e c u r v e s e x h i b i t s t h e " t y p i c a l " 111 Suspension density, k g / m ' 1000 800 600 400 200 1.6 1.2 ,2> 0.8 CD 0.4 Bed inventory A low o medium • high h i g h m e d i u m h low air in le t i n s e r t 0.5 0.6 0.7 • I i • i i • o' i i • o i A o • r O A' 0.8 Voidage D2M I OAI Al / / A'' i 0.9 F i g u r e 7.4 Voidage p r o f i l e f o r c r a c k i n g c a t a l y s t , D*i=1.7 m/s, U o=0.046 m/s, v e r t i c a l i n l e t . 1 1 2 Suspension density, k g / m 3 700 560 420 280 140 0 1.6 1.2 .2> o.8 CD 0.4 i — — I — - Bed inventory 1 i T /! • i A lOW (~ o medium • J • high / / • Q — 7 / r / /! • OA 7 / i / / i / • O A •> i / / i — • / O y x A" / / / / / / / / y / y A ' ' / y^y / — 1 1 A t i i 0.5 0.6 0.7 0.8 Voidage 0.9 F i g u r e 7.5 Voidage p r o f i l e f o r PVC, Uj=1.7 m/s, U o=0.046 m/s, v e r t i c a l i n l e t . 113 f a s t f l u i d i z e d p r o f i l e . Even the h i g h e s t i n v e n t o r y of s o l i d s does not seem s u f f i c i e n t t o g e n e r a t e a h i g h enough s u s p e n s i o n d e n s i t y i n the i n s e r t . U n f o r t u n a t e l y , the equipment cannot accommodate a l a r g e r i n v e n t o r y because of the p o s i t i o n of t h e s l i d e v a l v e used t o measure the c i r c u l a t i o n r a t e s . Moreover, u s i n g a h i g h e r i n v e n t o r y would f u r t h e r d e c r e a s e t h e range of i n n e r a i r v e l o c i t y a l l o w a b l e because the upper l i m i t f o r i n n e r V e l o c i t y ( t h e f l o o d i n g v e l o c i t y ) d e c r e a s e s w i t h i n c r e a s i n g i n v e n t o r y . The re s p o n s e s of t h e v o i d a g e d i s t r i b u t i o n t o a change i n i n n e r a i r v e l o c i t y , o u t e r a i r v e l o c i t y , and i n l e t c o n f i g u r a t i o n a r e shown i n f i g u r e s 7.6 t o 7.8. Because of t h e s c a t t e r and ap p a r e n t c r o s s i n g of t h e c u r v e s , i t i s i m p o s s i b l e t o e x t r a c t from t h e s e f i g u r e s the e f f e c t of the t h r e e p a r a m e t e r s on the d e n s i t y p r o f i l e . 7.2.4 ENTRANCE EFFECT The d e n s i t y p r o f i l e s shown i n f i g u r e s 7.4 t o 7.8 have i n common an e l o n g a t e d t a i l a t t h e bottom. T h i s t a i l l i k e l y r e f l e c t s t h e p r e s s u r e l o s s e s a s s o c i a t e d w i t h e n t r a n c e e f f e c t s . The e n t r a n c e e f f e c t s c o m p r i s e j e t energy d i s s i p a t i o n , a c c e l e r a t i o n of t h e s o l i d s from r e s t t o t h e i r f i n a l v e l o c i t y , i n t e r n a l r e c i r c u l a t i o n , and h i g h e r bed d e n s i t y . I n pneumatic t r a n s p o r t s t u d i e s , many a t t e m p t s have been made t o e x p r e s s t h e p r e s s u r e d r o p due t o a c c e l e r a t i o n l o s s e s and t h e a c c e l e r a t i o n l e n g t h as a f u n c t i o n of l i n e d i a m e t e r , p a r t i c l e d i a m e t e r , and gas and s o l i d f l o w r a t e s 1 1 4 Suspension density, k g / m 1000 800 600 400 200 0 0.5 0.6 0.7 0.8 0.9 1 Voidage F i g u r e 7.6 / E f f e c t of inner gas v e l o c i t y on voidage p r o f i l e f o r c r a c k i n g c a t a l y s t , high i n v e n t o r y , Uo=0.046 m/s, t a n g e n t i a l i n l e t . 1 1 5 Suspension density, k g / m ' 1000 800 600 400 200 o 1.6 h 1.2 .cp o.8 CD 0.4 0 U o , c m / s A 1-3 O 2-3 • 3-4 O 4-6 O 5-6 0.5 0.6 0.7 0.8 0.9 Voidage F i g u r e 7 . 7 E f f e c t of outer gas v e l o c i t y on voidage p r o f i l e f o r c r a c k i n g c a t a l y s t , h i g h i n v e n t o r y , = 1 . 7 m/s, t a n g e n t i a l i n l e t . 1 1 6 Suspension density, k g / m ' 1000 800 600 400 200 1.6 h 1.2 h .2* 0.8 CD ZE 0.4 Inlet A vertical o tangential o ir i A O A 0.5 0.6 0.7 0.8 0.9 1 Voidage Figure 7.8 Effect of air inlet configuration on voidage profile for cracking catalyst, high inventory, Ui=1.9 m/s, Uo=0.023 m/s. 117 and properties. Apart from the fact that the correlations published tend to give disparate r e s u l t s , the p a r t i c u l a r geometry and hydrodynamics of the novel c i r c u l a t i n g f l u i d i z e d bed make i t somewhat f u t i l e to apply expressions derived for a t o t a l l y d i f f e r e n t system. In fast f l u i d i z a t i o n studies, there has only been one unsatisfying attempt to q u a l i t a t i v e l y account for acceleration losses (Weinstein, 1981). Inspection of figures 7.4, and 7.6 to 7.8 reveals that for a high inventory of cracking catalyst the acceleration length i s limited to the f i r s t 0.15 m above the inner a i r i n l e t . If the difference between the pressure drop across the bottom 0.15 m and and the pressure drop across the 0.15 m immediately above i s assumed to be due to entrance losses, the pressure drop due to acceleration losses ( A P ) can be acc estimated by difference. Some results estimated in t h i s manner are shown in table 7.2. Neither the inner v e l o c i t y , the outer v e l o c i t y , nor the s o l i d c i r c u l a t i o n flux seems to have an e f f e c t on A P „ „ . However, AP i s consistently acc acc higher when the tangential i n l e t i s used, which suggests that i n t e r n a l r e c i r c u l a t i o n and jet energy d i s s i p a t i o n are the main contributors to entrance losses. For lower inventories of cracking c a t a l y s t and for PVC, the acceleration zone i s harder to delineate. T a b l e 7.2 Approximate a c c e l e r a t i o n l o s s e s f o r c r a c k i n g c a t a l y s t , h i g h i n v e n t o r y . . I n l e t U i , m/s U 0, cm/s A P a C c k P a V e r t i c a l 1 .4 3.4 0.26 1 .4 4.6 ~ 0.00 1 .4 5.6 0.34 1 .7 1 .3 0.00 1 .7 2.3 0.43 1 .7 3.4 0.34 1.7 4.6 0.43 1 .7 5.6 0.43 1 .9 2.3 0.26 2.2 1 .3 0.17 T a n g e n t i a l 1.4 4.6 0.69 1 .7 2.3 0.60 1.7 3.4 0.69 1 .7 4.6 0.60 - 1.7 5.6 0.69 1 .9 2.3 0.69 1 .9 3.4 0.52 1 .9 4.6 0.60 1.9 5.6 0.60 2.2 4.6 0.69 119 7.2.5 PRESSURE FLUCTUATIONS The s t u d y of p r e s s u r e f l u c t u a t i o n s i n f a s t f l u i d i z e d beds i s of c o n s i d e r a b l e i n t e r e s t because each f l u i d i z a t i o n regime and the t r a n s i t i o n between them can be c h a r a c t e r i z e d by p r e s s u r e f l u c t u a t i o n s . In p a r t i c u l a r , Y e r u s h a l m i and C a n k u r t (1979) have shown t h a t t h e t r a n s i t i o n between the b u b b l i n g and the t u r b u l e n t regimes c o r r e s p o n d s t o a peak i n f l u c t u a t i o n s f o l l o w e d by a sudden decay. There does not appear t o be such a t r a n s i t i o n i n t h e f l u c t u a t i o n s r e p o r t e d i n t h i s s t u d y , even i f d i f f e r e n t f l u c t u a t i o n p a t t e r n s can be i d e n t i f i e d , as d e s c r i b e d i n c h a p t e r 6. T h i s may be because the v e l o c i t i e s were not h i g h enough t o r e a c h t h e t r a n s i t i o n o r because th e geometry of the system i n v e s t i g a t e d i s such t h a t t h e n a t u r e of t h e f l o w regimes i s a l t e r e d . C e r t a i n l y , v i s x t a l o b s e r v a t i o n and c i r c u l a t i o n f l u x e s i n d i c a t e d t h a t t h e c o n d i t i o n s c h a r a c t e r i z e d as " f a s t f l u i d i z a t i o n " p r e v a i l e d i n the i n n e r column. 7.3 SOLIDS CIRCULATION RATE The r e sponse of the s o l i d s c i r c u l a t i o n r a t e t o v a r i o u s changes i n the system was d e s c r i b e d i n the p r e v i o u s c h a p t e r . In what f o l l o w s , a s i m p l i s t i c e m p i r i c a l s t a t i s t i c a l model i s sought of t h e form: G = C U. a v j I 7 (9) The s o l i d s c i r c u l a t i o n r a t e d a t a were d i v i d e d i n t o f o u r s e t s : (1) PVC p a r t i c l e s w i t h a v e r t i c a l a i r i n l e t , (2) PVC p a r t i c l e s w i t h a t a n g e n t i a l i n l e t , (3) CC p a r t i c l e s w i t h a 120 v e r t i c a l i n l e t , and (4) CC p a r t i c l e s w i t h a t a n g e n t i a l i n l e t . T a b l e 7.3 g i v e s t h e e m p i r i c a l c o n s t a n t s o b t a i n e d w i t h a m u l t i p l e r e g r e s s i o n a n a l y s i s . D e t a i l s on the s t a t i s t i c a l p r o c e d u r e a r e g i v e n i n Appendix G. F i g u r e s 7.9 to7.12 i l l u s t r a t e t h e f i t . I n s p e c t i o n of t a b l e 7.3 r e v e a l s t h a t t h e c o e f f i c i e n t and exponents depend s t r o n g l y on t h e t y p e of s o l i d s . W h i l e i n n e r v e l o c i t y seems t o p l a y a more i m p o r t a n t r o l e f o r PVC, i n v e n t o r y has a h i g h e r exponent f o r c r a c k i n g c a t a l y s t . A l s o , t h e c o e f f i c i e n t C i s much h i g h e r f o r c r a c k i n g c a t a l y s t than f o r PVC. A number of f a c t o r s , i n c l u d i n g s o l i d d e n s i t y , p a r t i c l e d i a m e t e r , i n t e r - p a r t i c l e p r o p e r t i e s and e l e c t r o s t a t i c e f f e c t s may c o n t r i b u t e t o t h e s e d i f f e r e n c e s . T h i s g r o s s s t a t i s t i c a l model does have a major f l a w s i n c e i t does not r e f l e c t t h e tendency f o r the c i r c u l a t i o n r a t e t o l e v e l o f f as i n n e r v e l o c i t y i s i n c r e a s e d . The d e f e c t i s more s e v e r e f o r c r a c k i n g c a t a l y s t , f o r which th e model o y e r p r e d i c t s t h e h i g h e s t c i r c u l a t i o n r a t e s . The r e s u l t s were a l s o c o r r e l a t e d w i t h o u t t a k i n g t h e i n l e t t y p e i n t o a c c o u n t . The r e s p e c t i v e c o n s t a n t s f o r PVC and CC appear i n t a b l e 7.3. F i g u r e s 7.13 and 7.14 show t h a t t h e f i t i s not so good. F i n a l l y , the d a t a were combined i n one unique s e t and a model of t h e form : G e = C U. a I 7 A r 5 (10) s 1 o where Ar i s t h e Archimedes number, was a p p l i e d . The u n s a t i s f a c t o r y f i t r e p o r t e d i n f i g u r e 7.15 s u g g e s t s t h a t p r o p e r t i e s o t h e r than Ar a r e r e q u i r e d t o c o r r e l a t e t h e f l u i d 121 T a b l e 7.3 E m p i r i c a l c o n s t a n t s f o r s t a t i s t i c a l model. Data s e t C a 0 7 5 PVC, v e r t 1 .77 2.28 0.71 1 .45 N.A. PVC, tang 0.51 2.63 0.94 1 .28 N.A. CC, v e r t 25.52 1 .03 0.51 1 .82 N.A. CC, tang 21 .31 1.12 0.60 2.31 N.A. PVC 2.04 2.37 0.50 1 .44 N.A. CC 22.54 1.12 0.55 2.04 N.A. A l l 43.28 1 .88 0.59 1 .84 -0.89 Figure 7 . 9 F i t of the s t a t i s t i c a l model for i n l e t . PVC, vert i c a l 1 23 Figure 7.10 F i t of the s t a t i s t i c a l model for PVC, t a n g e n t i a l i n l e t . 0 20 4 0 60 80 Measured flux, k g / m 2 s Figure 7.11 F i t of the s t a t i s t i c a l model f o r c r a c k i n g c a t a l y s t , v e r t i c a l i n l e t . Figure 7.12 F i t of the s t a t i s t i c a l model for c r a c k i n g c a t a l y s t , t a n g e n t i a l i n l e t . Figure 7.13 F i t of the s t a t i s t i c a l model for PVC. Figure 7.14 F i t of the s t a t i s t i c a l model for cracking c a t a l y s t . 1 28 Figure 7.15 F i t of the s t a t i s t i c a l s e t . model for the e n t i r e data 129 m e c h a n i c a l b e h a v i o u r of t h e system. The use of a p p r o p r i a t e d i m e n s i o n l e s s numbers t o c o r r e l a t e the r e s u l t s i s p r o b a b l y more i n f o r m a t i v e and adequate than the use of the model p r e v i o u s l y d e s c r i b e d . One p o s s i b i l i t y i s : G D ( U. 2(p -p) )a However, t h e d i a m e t e r of the i n s e r t was not v a r i e d , and, more i m p o r t a n t l y , o n l y two t y p e s of p a r t i c l e s were t r i e d . T h i s g e n e r a t e s o n l y 8 t o 10 d i s t i n c t v a l u e s f o r t h e m o d i f i e d Froude number i n Eq. ( 1 1 ) . The range of v a r i a b l e s i s t h u s t o o s m a l l t o t e s t such an e q u a t i o n . 7.4 RELATIONSHIP BETWEEN SOLIDS HOLD-UP AND FLUX 7.4.1 PARTICLE AND SLIP VELOCITIES The p r e s s u r e and c i r c u l a t i o n f l u x d a t a may be combined t h r o u g h t h e e x p r e s s i o n : G s * V p ( 1 " e ) p p ( 1 2 where V p i s t h e p a r t i c l e v e l o c i t y , t o p r o v i d e some i n s i g h t t o t he b e h a v i o u r of the system. The s l i p v e l o c i t y r e l a t e s t h e p a r t i c l e v e l o c i t y t o t h e gas v e l o c i t y : U_, = U /e - V^ (13 s i g p The r e l a t i o n s h i p between s l i p v e l o c i t y and v o i d a g e i s commonly used t o i d e n t i f y and demarcate d i f f e r e n t g a s - s o l i d regimes (Matsen, 1982). 130 The p a r t i c l e and s l i p v e l o c i t i e s can be e s t i m a t e d d i r e c t l y from the v o i d a g e d i s t r i b u t i o n and the s o l i d s c i r c u l a t i o n f l u x . T a b l e 7.4 c o n t a i n s v a l u e s of p a r t i c l e and s l i p v e l o c i t i e s f o r a number of c a s e s . The v a l u e of t h e numbers i s d u b i o u s , however, because of the g r e a t u n c e r t a i n t i e s a s s o c i a t e d w i t h v o i d a g e d e t e r m i n a t i o n , and because th e s o l i d v e l o c i t y i s v e r y s e n s i t i v e t o v o l u m e t r i c c o n c e n t r a t i o n . For i n s t a n c e , i f p =2000 kg/m 3, G =10 kg/m 2s, p s and e = 0.994, V i s 0.83 m/s. However i f the v o i d a g e i s tr s l i g h t l y lower (e = 0.988), V i s h a l v e d because th e v o l u m e t r i c c o n c e n t r a t i o n i s d o u b l e d . On a manometer, t h i s v o i d a g e d i f f e r e n c e c o r r e s p o n d s t o a d i f f e r e n c e i n p r e s s u r e d r o p of b a r e l y 0.002 m of w a t e r . Thus an e x p e r i m e n t a l e r r o r of the o r d e r of 5% i n t a k i n g the measurement may r e s u l t i n an e r r o r of t h e o r d e r of 100% i n d e t e r m i n i n g t h e p a r t i c l e v e l o c i t y . A c c o r d i n g t o t h e - f i g u r e s i n t a b l e 7.4, t h e p a r t i c l e v e l o c i t y and t h e s l i p v e l o c i t y do not behave c o n s i s t e n t l y w i t h changes i n o p e r a t i n g v a r i a b l e s . N e v e r t h e l e s s , t h e c o n c e p t of p a r t i c l e and s l i p v e l o c i t i e s i s u s e f u l t o u n d e r s t a n d t h e c h a r a c t e r i s t i c b e h a v i o r of t h e system, and w i l l be used t o a n a l y z e c o u p l i n g e f f e c t s and l e v e l l i n g o f f of s o l i d s c i r c u l a t i o n r a t e s . 7.4.2 COUPLING EFFECT Among o t h e r o b s e r v a t i o n s , i t was r e p o r t e d i n the p r e v i o u s c h a p t e r t h a t t h e e f f e c t of i n n e r v e l o c i t y on c i r c u l a t i o n r a t e i s more i m p o r t a n t f o r c r a c k i n g c a t a l y s t and 131 T a b l e 7.4 P a r t i c l e and s l i p v e l o c i t i e s . I n l e t I n v . D 9 Gs e V P U S1 m/s cm/s kg/m 2s CI m/s m/s PVC v e r t low 1 .4 4.6 4.6 0.995 0.7 0.7 v e r t medium 1 .7 3.4 6.3 0.990 0.5 1 .2 v e r t medium 1 .7 4.6 9.1 0.990 0.7 1 .0 v e r t medium 2.2 4.6 16.1 0.990 1 .2 1 .0 v e r t h i g h 1 .7 4.6 10.8 0.995 1 .5 0.2 tang medium 1.7 4.6 4.7 0.995 0.7 1.0 C r a c k i n g c a t a l y s t v e r t low 1 .9 4.6 21 .3 0.988 0.9 1.0 ta n g low 1 .9 4.6 12.7 0.994 1 . 1 0.8 v e r t medium 1 .9 4.6 ' 44. 1 0.982 1.2 0.7 tang medium 1.9 4.6 39.4 0.982 1.1 0.8 v e r t h i g h 1 .4 4.6 41 .0 0.982 1 .1 0.3 v e r t h i g h 1.7 2.3 48.8 0.982 1 .4 0.3 v e r t h i g h 1.7 3.4 54.5 0.982 1 .5 0.2 v e r t h i g h 1.7 4.6 61 .3 0.971 1 . 1 0.6 ta n g h i g h 1 .4 4.6 32.6 0.982 0.9 0.5 ta n g h i g h 1 .7 2.3 40.9 0.988 •1.7 0.0 ta n g h i g h 1 .7 3.4 42.7 0.982 1 .2 - 0.5 ta n g h i g h 1 .7 4.6 48.0 0.975 1.0 0.7 ta n g h i g h 1 .9 4.6 55.5 0.982 1.5 0.4 1 32 f o r h i g h e r s o l i d s i n v e n t o r i e s , and t h a t t h e e f f e c t of i n v e n t o r y i s more i m p o r t a n t f o r c r a c k i n g c a t a l y s t . A s i m p l e a n a l y s i s based on t h e r e l a t i o n s h i p s e x p r e s s e d i n (12) and (13) and a few a s s u m p t i o n s may h e l p t o r a t i o n a l i z e t h e s e c o u p l i n g e f f e c t s between independent v a r i a b l e s . C o n s i d e r : G S = y i - e ) p P ( 1 2 ) U s l = V e * V P ( 1 3 ) In pneumatic t r a n s p o r t , the s l i p v e l o c i t y i s o f t e n c o n s i d e r e d t o be e q u a l t o t h e p a r t i c l e t e r m i n a l s e t t l i n g v e l o c i t y . I n view of the. h i g h v o i d a g e s o b s e r v e d i n t h e i n s e r t , t h i s a s s u m p t i o n i s ad o p t e d , and we may w r i t e : VP = V e " u t ( 1 4 ) As t h e - i n v e n t o r y i n c r e a s e s , e d e c r e a s e s and (1 - e) i n c r e a s e s . T h e r e f o r e f o r a g i v e n i n c r e a s e i n i n n e r v e l o c i t y ( i . e . U g ), the r e s u l t i n g i n c r e a s e i n s o l i d s f l u x w i l l be h i g h e r f o r t h e l a r g e r i n v e n t o r y . F o l l o w i n g the same r e a s o n i n g , the i n c r e a s e i n c i r c u l a t i o n f o r a g i v e n i n c r e a s e i n a i r v e l o c i t y w i l l be g r e a t e r f o r t h e denser p a r t i c l e s ( i n t h i s c a s e c r a c k i n g c a t a l y s t ) p r o v i d e d t h a t t h e v o i d a g e does not i n c r e a s e w i t h p a r t i c l e d e n s i t y . S i m i l a r l y , a t a g i v e n a i r v e l o c i t y , t h e term (1 - e ) P p w i l l i n c r e a s e more r a p i d l y w i t h i n v e n t o r y f o r g r e a t e r p a r t i c l e d e n s i t i e s . 7.4.3 LEVELLING OFF AND DROPPING OF SOLIDS RATE F i g u r e 7.16 g i v e s a t y p i c a l r e s ponse of s o l i d c i r c u l a t i o n f l u x t o a change i n i n n e r v e l o c i t y . The f l u x 1 33 X 3 < O or o o co FLOODING POINT SUPERFICIAL INNER VELOCITY Figure 7.16 Typical response of solid circulation flux to a change in inner a i r velocity. 134 f i r s t i n c r e a s e s l i n e a r l y w i t h v e l o c i t y , l e v e l s o f f f o r a s h o r t i n t e r v a l , and f i n a l l y d e c r e a s e s p a s t t h e f l o o d i n g p o i n t . One way t o e x p l a i n t h i s b e h a v i o r i s t o use the p r e s s u r e d r o p b a l a n c e r e q u i r e m e n t i n c o n j u n c t i o n w i t h the concept of c l u s t e r f o r m a t i o n . F i g u r e 7.17, which i s analogo u s t o f i g u r e 7.1, g i v e s t h e p o s i t i o n of f o u r c r i t i c a l p r e s s u r e p o i n t s i n t h e equipment. The f o r m a t i o n of c l u s t e r s of p a r t i c l e s i s commonly b e l i e v e d t o govern the c h a r a c t e r i s t i c b e h a v i o r of f a s t f l u i d i z e d beds. Y e r u s h a l m i e t a l . (1978) argued t h a t t h e c l u s t e r d i a m e t e r i n c r e a s e s w i t h d e c r e a s i n g v o i d a g e . As t h e i n n e r v e l o c i t y i s i n c r e a s e d , G i n c r e a s e s l i n e a r l y . But s i n c e t h e p r e s s u r e d r o p on t h e o u t s i d e ( A P A B ) does not change w i t h i n n e r v e l o c i t y and t h e p r e s s u r e d r o p a c r o s s the b a f f l e (~APDfi) i n c r e a s e s , t h e p r e s s u r e d r o p , a c r o s s the i n s e r t ( A P C D ) must d e c r e a s e . A P C D i s e s s e n t i a l l y used t o s u p p o r t t h e s o l i d s h o l d - u p . S i n c e t h e s o l i d s c i r c u l a t i o n f l u x i n c r e a s e s and the h o l d - u p d e c r e a s e s , the p a r t i c l e v e l o c i t y must be i n c r e a s i n g . A c c o r d i n g t o Y e r u s h a l m i e t a l . , t h e s l i p v e l o c i t y may be th o u g h t of b e i n g of the o r d e r of the c l u s t e r - not t h 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 . As the v e l o c i t y i s i n c r e a s e d , the c o n c e n t r a t i o n d e c r e a s e s and t h u s t h e c l u s t e r d i a m e t e r d e c r e a s e s . T h i s means t h a t t h e t e r m i n a l v e l o c i t y of the c l u s t e r d e c r e a s e s t o e v e n t u a l l y r e a c h the 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 . To r e c a p i t u l a t e , as i n n e r v e l o c i t y i s i n c r e a s e d , the amount of s o l i d s c i r c u l a t i n g b e g i n s e v e n t u a l l y t o d e c r e a s e , t h e s i z e of t h e c l u s t e r d e c r e a s e s , t h e a b s o l u t e v e l o c i t y of t h e gure 7.17 C r i t i c a l pressure points in the bed. 1 36 c l u s t e r i n c r e a s e s , and t h e s l i p v e l o c i t y d e c r e a s e s . The p r e s s u r e d r o p a c r o s s the b a f f l e e v e n t u a l l y becomes so l a r g e t h a t t h e d e c r e a s e i n h o l d - u p cannot be compensated f o r by t h e i n c r e a s e i n p a r t i c l e v e l o c i t y : the c i r c u l a t i o n f l u x then l e v e l s o f f , and e v e n t u a l l y d e c r e a s e s . T h i s b e h a v i o r i s f u r t h e r i l l u s t r a t e d by f i g u r e 7.18 w h i c h shows how the s o l i d s mass l o a d i n g r a t i o (G /U p ) changes w i t h i n n e r s g g v e l o c i t y . The l o a d i n g r a t i o f i r s t i n c r e a s e s w i t h i n n e r v e l o c i t y , then l e v e l s o f f and f i n a l l y d e c r e a s e s . 7.5 COMPARISON WITH LITERATURE DATA The c o l l e c t i o n of p u b l i s h e d f a s t f l u i d i z a t i o n s t u d i e s i s meagre, and major d i f f e r e n c e s i n equipment d e s i g n mean t h a t i t i s p o s s i b l e o n l y t o make q u a l i t a t i v e ' c o m p a r i s o n s . The importance of the e x t e r n a l p r e s s u r e d r o p imposed upon the f a s t f l u i d i z e d bed has been s t r e s s e d h e r e ; t h i s p r e s s u r e d r o p i s i n f l u e n c e d by the s o l i d s i n v e n t o r y , the c y c l o n e s , the s o l i d s r e t u r n l i n e s , the a i r i n l e t s , e t c . Thus the r e s u l t s t e n d t o be v e r y s p e c i f i c t o the equipment used. In a d d i t i o n t o the b a f f l e , t h e n o v e l f a s t f l u i d i z e d bed used i n t h i s s t u d y d i f f e r s from o t h e r f a s t f l u i d i z e d e x p e r i m e n t a l s e t - u p s on two main p o i n t s . F i r s t , t h e f a s t f l u i d i z e d bed i s r e l a t i v e l y s h o r t . Other e x p e r i m e n t e r s have used columns up t o 8 m t a l l ( e . g . Y e r u s h a l m i e t a l . , 1978; L i and Kwauk, 1980). Second, t h e r e i s no independent way of c o n t r o l l i n g t h e s o l i d s f l o w r a t e . The s o l i d s c i r c u l a t i o n r a t e i s a u t o m a t i c a l l y d e t e r m i n e d by the i n v e n t o r y l e v e l and 1 37 1 1.5 2 2.5 3 Inner gas velocity, m / s F i g u r e 7.18 Mass s o l i d s l o a d i n g r a t i o as a f u n c t i o n of inner and outer gas v e l o c i t y f o r c r a c k i n g c a t a l y s t , h i g h i n v e n t o r y , v e r t i c a l i n l e t . I 30 the air flow rate. Other set-ups are f i t t e d with a valve (pneumatic or mechanical) which can reduce the solids flow rate to a value below the maximum capacity of the unit. For the sake of comparison, figure 7.19 reproduces density profiles obtained by other researchers (Weinstein et a l . , 1984; L i and Kwauk, 1980). The data exhibit the characteristic double-asymptotic density p r o f i l e . The circulation fluxes obtained by Weinstein et a l . are much higher than those obtained with the novel unit. However, they used a much higher solids inventory and a larger column. In contrast, Li and Kwauk's results for a catalyst with similar properties to the one used in this study show a much lower circulation rate. They do not report the inventory l e v e l . L i and Kwauk (1982) have developed a model to predict the asymptotic voidage- values and the position of the inflection point. However, their correlation does not predict voidage distributions which agree with those estimated in the present study. Density profiles in a fast fluidized bed have also been studied by Strdmberg (1981). The pressure distributions obtained in cold and hot models were described by : P = ah b (15) The height, h, must be greater than the entrance length. The pressure profiles measured in the present work cannot be adequately represented by an equation of the form of equation (15). The main d i f f i c u l t y l i e s in determining the end of the acceleration zone. 10 08 X 06H V) UJ _J O 0 4 02 0 10 1 08 09 10 VOIDAGE Gs: 16 kg/1n26 A o i8 • 15 o 2 0 0 8 X o UJ I 06 w in uj I 0 4 z UJ a 02 0 / 0 d 1 / I / 7 o V © A 41 0-6 08 TO VOIDAGE 'q I 2 9 Gs i k g / h i s A 75 o 108 v 118 (a) From L i and Kwauk, 1980. (b) From W e i n s t e i n et a l . , 1984 F i g u r e 7.19 D e n s i t y p r o f i l e s from p u b l i s h e d s t u d i e s . 140 F i n a l l y , l e a v i n g the domain of f a s t f l u i d i z a t i o n , t h e d e n s i t y p r o f i l e s appear t o be s i m i l a r t o the d e n s i t y p r o f i l e s o b s e r v e d i n e n t r a i n m e n t s t u d i e s . I s m a i l and Chen (1984) r e p o r t e x p e r i m e n t a l measurements of s o l i d volume f r a c t i o n s i n the f r e e b o a r d r e g i o n of f l u i d i z e d beds. T h e i r r e s u l t s show t h a t a t any g i v e n gas v e l o c i t y , t h e s o l i d c o n c e n t r a t i o n d e c r e a s e s m o n o t i c a l l y but not l i n e a r l y w i t h h e i g h t , and t h a t t h e e f f e c t of a i r v e l o c i t y on s o l i d s c o n c e n t r a t i o n depends on h e i g h t . A t low f r e e b o a r d e l e v a t i o n t h e s o l i d s c o n c e n t r a t i o n was found t o d e c r e a s e w i t h i n c r e a s i n g gas v e l o c i t y , w h i l e a t h i g h e l e v a t i o n t h e c o n c e n t r a t i o n i n c r e a s e d w i t h i n c r e a s i n g v e l o c i t y . 7.6 COMPARISON WITH OTHER CIRCULATING BED DESIGNS Two t y p e s of c o m m e r c i a l c i r c u l a t i n g f l u i d i z e d beds, t h e L u r g i bed (Reh e t a l . , 1980) and t h e S t u d s v i k bed (Stro m b e r g , 1982) a r e shown i n f i g u r e 7.20. The two d e s i g n s t a k e a d i f f e r e n t a p p r o a c h t o c o n t r o l t h e d e n s i t y i n t h e f a s t bed ( i . e . , u l t i m a t e l y , t o c o n t r o l t h e heat t r a n s f e r ) . In t h e L u r g i c o n c e p t , t h e amount of s o l i d s i n t h e f a s t bed i s f i x e d and the a x i a l d e n s i t y p r o f i l e can be a l t e r e d by v a r y i n g t h e a i r f l o w . The s o l i d s c i r c u l a t i o n r a t e changes a c c o r d i n g l y . I n t h e S t u d s v i k c o n c e p t , the amount of s o l i d s i n t h e f a s t bed can be v a r i e d by c o n t r o l l i n g t he non-m e c h a n i c a l v a l v e ( L - v a l v e ) w h i c h c o n n e c t s the f a s t bed t o t h e p a r t i c l e s t o r a g e / r e c y c l e v e s s e l . The v a l v e shown i n f i g u r e 7.20 (b) i s a m e c h a n i c a l v a l v e , which was used p r i o r t o the t e s t i n g F i g u r e 7.20 Two commercial c i r c u l a t i n g S E C O N D A R Y C Y C L O N E P R I M A R Y P A R T I C L E S E P A R A T O R R E A C T O R V E S S E L P A R T I C L E S T O R A G E R E C I R C U L A T I O N V A L V E S E C O N D A R Y A I R P R I M A R Y A I R ( b ) bed systems: (a) L u r g i ; (b) S t u d s v i k . 142 of t h e L - v a l v e . Thus, e x c e p t f o r t h e s m a l l amount of a i r r e q u i r e d t o c o n t r o l t h e L - v a l v e , t h e s o l i d s c i r c u l a t i o n r a t e can be a d j u s t e d i n d e p e n d e n t l y of t h e a i r f l o w . The n o v e l c i r c u l a t i n g bed i s , i n some ways, a h y b r i d of t h e two c o n c e p t s . The o u t e r bed a c t s as a s t o r a g e / r e c y c l e v e s s e l , and w h i l e t h e r e i s no a c t u a l n o n - m e c h a n i c a l (or m e c h a n i c a l ) v a l v e t o c o n t r o l t h e amount of s o l i d s f e d t o the f a s t bed, t h e d e n s i t y i n t h e bed can be a d j u s t e d by v a r y i n g the i n n e r and o u t e r a i r f l o w s . I f the i n n e r a i r f l o w i s i n c r e a s e d , t h e h o l d - u p of s o l i d s i n the i n s e r t d e c r e a s e s ( i . e . t h e d e n s i t y d e c r e a s e s ) and t h e s o l i d s c i r c u l a t i o n r a t e i n c r e a s e s . Changing t h e o u t e r a i r f l o w , however, i s s i m i l a r t o c o n t r o l l i n g t h e a i r f l o w i n an L - v a l v e . T h e r e f o r e , i f the o u t e r a i r f l o w i s i n c r e a s e d , t h e h old-up of s o l i d s i n the i n s e r t i n c r e a s e s and the c i r c u l a t i o n r a t e a l s o i n c r e a s e s . M oreover, th e t o t a l i n v e n t o r y i n the system can e a s i l y be changed t o m o d i f y the s o l i d c i r c u l a t i o n r a t e and t h e d e n s i t y p r o f i l e . 7.7 THE TANGENTIAL INLET G i v e n t h a t one of t h e f o r e s e e n a p p l i c a t i o n s of t h e n o v e l system i s c o m b u s t i o n and t h a t c y c l o n e c ombustion o f f e r s many advantages ( S y r e d and B e er, 1974), i t i s of i n t e r e s t t o t e s t the e f f e c t of s w i r l i n g f l o w on t h e b e h a v i o r of t h e system. The f e a s i b i l i t y of a p r o c e s s c o m b i n i n g f l u i d i z a t i o n and s w i r l f o r c o m b u s t i o n has a l r e a d y been t e s t e d and e n c o u r a g i n g r e s u l t s ( i . e . h i g h s p e c i f i c heat r e l e a s e ) o b t a i n e d 143 ( K o r e n b e r g , 1984). A c c o r d i n g t o t h e d a t a c o l l e c t e d , the c i r c u l a t i o n r a t e when a t a n g e n t i a l i n l e t i s used i s always l o w e r than when a v e r t i c a l i n l e t i s used, f o r a g i v e n i n v e n t o r y and a i r f l o w . The l o w e r c i r c u l a t i o n r a t e may be due t o a number of r e a s o n s . F i r s t , t h e r e s i d e n c e t i m e may be i n c r e a s e d because the s w i r l i n g p a r t i c l e has t o t r a v e l a l o n g e r p a t h . S e c o n d l y , some of t h e p a r t i c l e s may s e p a r a t e from t h e g a s - s o l i d m i x t u r e b e f o r e i t r e a c h e s the b a f f l e and f a l l down the i n n e r w a l l o f t h e i n s e r t . F i n a l l y , t h e h o l d - u p of s o l i d s i n t h e i n s e r t may be l o w e r . However, i t i s not p o s s i b l e t o a s c e r t a i n from t h e e x p e r i m e n t a l d a t a what e f f e c t t h e s w i r l i n g motion has on t h e d e n s i t y p r o f i l e . When the bed m a t e r i a l i s PVC a much h i g h e r a i r f l o w t o t h e a n n u l a r r e g i o n i s r e q u i r e d t o f l u i d i z e d t h e o u t e r bed. The o u t e r a i r a p p e a r s t o be e n t r a i n e d i n the i n s e r t . I t i s not c l e a r why t h e PVC and c r a c k i n g c a t a l y s t powders behave so d i f f e r e n t l y . A l t h o u g h the use of a t a n g e n t i a l i n l e t i s p r o m i s i n g , t h e c u r r e n t d e s i g n s u f f e r s from many drawbacks. C y c l o n e combustors a r e e x t r e m e l y s e n s i t i v e t o s m a l l changes i n t h e d e s i g n ( p o s i t i o n , s i z e , c o n f i g u r a t i o n ) of t h e i n l e t s i n c e i t a f f e c t s r e c i r c u l a t i o n and m i x i n g p a t t e r n s ( S y r e d and B e e r , 1974). S y r e d and Beer recommend the use of s y m m e t r i c a l l y a r r a n g e d i n l e t s . The use of a s i n g l e i n l e t i n t r o d u c e s asymmetry and may cause uneven b u r n i n g , e s p e c i a l l y i n l o n g chambers. In a d d i t i o n , c a r e f u l a t t e n t i o n must be p a i d t o t h e i n t e r a c t i o n between the t h r e e d i f f e r e n t s w i r l i n g m o t ions 1 4 4 generated by the t a n g e n t i a l i n l e t , the s e p a r a t i n g b a f f l e , and the secondary c y c l o n e . 7 . 8 THE BAFFLE The d e s i g n of the b a f f l e i s c r i t i c a l both from s e p a r a t i o n e f f i c i e n c y and p r e s s u r e drop c o n s i d e r a t i o n s . The p r e s s u r e drop across the b a f f l e p a r t l y governs the s o l i d s hold-up i n the i n s e r t and the s o l i d s c i r c u l a t i o n r a t e . The p a r t i c u l a r d e s i g n used i n the study was chosen because of i t s s i m p l i c i t y , but c l e a r l y there a r e an i n f i n i'te' number of p o s s i b i l i t i e s . The pressure drop a c r o s s the b a f f l e i s of the order of 0.15 to 0.30 kPa. I t i n c r e a s e s with s o l i d s c i r c u l a t i o n r a t e although the f r a c t i o n a l i n c rease in p r e s s u r e drop i s small compared to the f r a c t i o n a l increase in c i r c u l a t i o n r a t e as t a b l e 7.5 shows. 145 T a b l e 7.5 E f f e c t of s o l i d c i r c u l a t i o n f l u x on the p r e s s u r e drop a c r o s s the b a f f l e f o r c r a c k i n g c a t a l y s t , t a n g e n t i a l i n l e t . Gs A P b l o w e s t h i g h e s t r a t i o 6.8 kg/m 2s 59.3 kg/m 2s 8.7 1.75 kPa 2.23 kPa 1 .3 CONCLUSION The work done w i t h the n o v e l c i r c u l a t i n g f l u i d i z e d bed p r o v e s the f e a s i b i l i t y of t h e c o n c e p t . W h i l e the absence of any moving p a r t s and the s e l f - a d j u s t i n g n a t u r e of t h e system c o n f e r s i m p l i c i t y , f l e x i b i l i t y of o p e r a t i o n i s r e t a i n e d . By s e l e c t i n g a p p r o p r i a t e a i r f l o w s , i n v e n t o r y l e v e l s , and i n l e t and o u t l e t c o n f i g u r a t i o n s , a s e r i e s of g a s - s o l i d c o n t a c t i n g p a t t e r n s can be g e n e r a t e d . C l e a r l y , more fundamental r e s e a r c h on f a s t f l u i d i z a t i o n and equipment o p t i m i z a t i o n i s r e q u i r e d . At t h e p r e s e n t t i m e , t h e r e i s l i t t l e known about the d e n s i t y p r o f i l e s , t h e n a t u r e of c l u s t e r s , t h e p a r t i c l e t r a j e c t o r i e s , and the r o l e of p a r t i c l e p r o p e r t i e s i n a f a s t f l u i d i z e d u n i t . The s i m p l e i n t e r a c t i v e n a t u r e of the equipment has been d e m o n s t r a t e d . However, i n i t s p r e s e n t form, the equipment r e s t r i c t s t h e p o s s i b i l i t i e s of the n o v e l f a s t f l u i d i z e d bed c o n c e p t . The a l l o w a b l e range of a i r f l o w and i n v e n t o r y i s l i m i t e d , and t h e s h o r t n e s s of t h e u n i t a c c e n t u a t e s the dominant e n t r a n c e and e x i t e f f e c t s . C a r e f u l l y d e s i g n e d , the n o v e l system i s h y d r o d y n a m i c a l l y i n t e r e s t i n g . U l t i m a t e l y , however, the v i a b i l i t y of t h e geometry must be e s t a b l i s h e d by h eat t r a n s f e r and r e a c t i o n k i n e t i c s s t u d i e s . 146 RECOMMENDATIONS FOR FURTHER STUDIES The f e a s i b i l i t y of t h e system has been dem o n s t r a t e d . However, many a r e a s r e q u i r e f u r t h e r i n v e s t i g a t i o n : 1. The need f o r b a f f l e o p t i m i z a t i o n has been s t r e s s e d a l r e a d y . As i n a l l g a s - s o l i d s e p a r a t i n g d e v i c e s , the aim i s t o i n c r e a s e e f f i c i e n c y and t o m i n i m i z e p r e s s u r e drop. Some m o d i f i c a t i o n s t h a t c o u l d be made t o improve t h e b a f f l e a r e : t a l l e r b l a d e s l a r g e r gap between t h e column and the b a f f l e b l a d e s w i t h e l l i p t i c a l c u r v a t u r e . i n c r e a s e d number of b l a d e s . The t r a d e - o f f between p r e s s u r e d r o p and e f f i c i e n c y i s v e r y i m p o r t a n t because of t h e i n t e r a c t i v e n a t u r e of the system. The p r e s s u r e d r o p a c r o s s t h e b a f f l e d i c t a t e s the amount of s o l i d s h e l d up i n t h e i n s e r t : t h e h i g h e r the p r e s s u r e d r o p , t h e lo w e r t h e h o l d - u p - an u n d e s i r a b l e s i t u a t i o n . A l s o , i n l a r g e r equipment, a number of i n t e r n a l c y c l o n e s c o u l d r e p l a c e the b a f f l e . 2. Among t h e o t h e r d e s i g n p a r a m e t e r s t h a t s h o u l d be s t u d i e d a r e t h e e f f e c t of the o u t e r c o l u m n / i n s e r t d i a m e t e r r a t i o and the d i s t a n c e above and below t h e i n s e r t . 3. To e n s u r e s t a b l e and s t e a d y s t a t e o p e r a t i o n of t h e u n i t , a smooth r e t u r n of t h e s o l i d s from t h e c y c l o n e t o the o u t e r bed i s e s s e n t i a l . To m i n i m i z e chances of p l u g g i n g and 147 148 s t i c k - s l i p t y p e f l o w , t h e i n s t a l l m e n t of a f l a p p e r v a l v e a t the bottom of t h e r e t u r n l i n e and of a e r a t i o n p o r t s p l a c e d a l o n g the l i n e a t a j u d i c i o u s a n g l e i s recommended. 4. In o r d e r t o b e t t e r v i s u a l i z e the a c c e l e r a t i o n zone and t h e d e n s i t y g r a d i e n t a l o n g the i n s e r t , i t would be p r o f i t a b l e t o complement the p r e s s u r e measurements w i t h s o l i d s volume f r a c t i o n measurements made w i t h a c a p a c i t a n c e p r o b e . 5. The e f f e c t of p a r t i c l e t y p e ( d i a m e t e r , d e n s i t y , s i z e d i s t r i b u t i o n ) s h o u l d be f u r t h e r i n v e s t i g a t e d . 6. In o r d e r t o b e t t e r u n d e r s t a n d t h e o p e r a t i o n c h a r a c t e r i s t i c s of the b a f f l e , i t would be advantageous t o use t r a c e r p a r t i c l e s and f o l l o w t h e i r p a t h from the b a f f l e back t o t h e a n n u l a r r e g i o n o r t o the c y c l o n e . 7. In o r d e r t o o b t a i n h i g h e r s o l i d s c i r c u l a t i o n r a t e s , and/or bed d e n s i t i e s than t h o s e r e p o r t e d , the i n v e n t o r y must be i n c r e a s e d . However, th e e n t r a n c e and e x i t e f f e c t s become more s i g n i f i c a n t as t h e i n v e n t o r y i s i n c r e a s e d and t h e column i s t o o s h o r t t o p e r m i t a f u l l y d e v e l o p e d f a s t f l u i d i z e d f l o w w i t h i t s 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 . F u r t h e r hydrodynamic s t u d i e s s h o u l d be done w i t h a t a l l e r column and a l a r g e r i n v e n t o r y of s o l i d s . NOMENCLATURE a e m p i r i c a l c o e f f i c i e n t , e q u a t i o n (15) A r A r c h i m e d e s n u m b e r , P g ( P s ~ P g ) g d 3 / M 2 b . e m p i r i c a l e x p o n e n t , e q u a t i o n (15) C e m p i r i c a l c o n s t a n t , e q u a t i o n s (9) a n d (10) D i n s e r t d i a m e t e r L d p p a r t i c l e d i a m e t e r L f j f l u i d f r i c t i o n f a c t o r f g F a n n i n g f r i c t i o n f a c t o r f s o l i d f r i c t i o n f a c t o r s g a c c e l e r a t i o n d u e t o g r a v i t y L / T 2 Gg g a s mass f l u x M / L 2 T G„ s o l i d m a s s c i r c u l a t i o n f l u x M / L 2 T s h h e i g h t L I a v e r a g e i n v e n t o r y h e i g h t L P p r e s s u r e M / L T 2 P j ^ p r e s s u r e a t t h e b o t t o m o f t h e i n s e r t M / L T 2 p r e s s u r e a t t h e b o t t o m o f t h e o u t e r b e d M / L T 2 P t ^ p r e s s u r e a t t h e t o p o f t h e i n s e r t M / L T 2 P f c Q p r e s s u r e a t t h e t o p o f t h e o u t e r b e d M / L T 2 AP p r e s s u r e d r o p M / L T 2 A P ^ p r e s s u r e d r o p a c r o s s t h e b a f f l e M / L T 2 A P . p r e s s u r e d r o p a c r o s s t h e i n s e r t M / L T 2 149 1 50 APQ p r e s s u r e d r o p a c r o s s the o u t e r bed M/LT2 U gas v e l o c i t y L/T Ug a i r s u p e r f i c i a l v e l o c i t y L/T a i r s u p e r f i c i a l v e l o c i t y i n the i n s e r t L/T U Q a i r s u p e r f i c i a l v e l o c i t y i n the o u t e r bed L/T minimum f l u i d i z a t i o n v e l o c i t y L/T U g l s l i p v e l o c i t y L/T Ufc t e r m i n a l v e l o c i t y L/T Vg a c t u a l gas v e l o c i t y L/T Vp a c t u a l p a r t i c l e v e l o c i t y L/T (1,0,7,5 e m p i r i c a l c o n s t a n t s , e q u a t i o n s (9) and (10) e v o i d a g e M a i r v i s c o s i t y M/LT p^ b u l k d e n s i t y M/L3 Pg a i r d e n s i t y M/L3 p p a r t i c l e d e n s i t y M/L3 p s u s p e n s i o n d e n s i t y M/L3 REFERENCES B i e r l , T.W., G a j d o s , C.J., M c l v e r , A.E., and McGovern, J . 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K u n i i and R. T o e i , E n g i n e e r i n g F o u n d a t i o n , New York, 299-306. W e i n s t e i n , H., Shao, M. and Wasserzug, L. (1984) R a d i a l s o l i d d e n s i t y v a r i a t o n i n a f a s t f l u i d i z e d bed, AIChE Symp. S e r i e s , 80, no. 241, 117-121. APPENDIX A CALIBRATION OF AIR FLOW METERS 155 156 1. R o t a m e t e r s c a l i b r a t i o n A d r y gas meter was used t o c a l i b r a t e t h e r o t a m e t e r s . T a b l e A1 C a l i b r a t i o n f o r model Ch.E 2228 S c a l e r e a d i n g Flow r a t e , m 3/s A i r v e l o c i t y , m/s 50 0.00036 0.013 100 0.00066 0.023 150 0.00097 0.034 200 0.00132 0.046 240 0.00159 0.056 T a b l e A2 C a l i b r a t i o n f o r model Ch.E 32888 S c a l e r e a d i n g Flow r a t e , m 3/s A i r v e l o c i t y , m/s 1.0 0.00209 0.073 1.5 0.00308 0.108 Based on o u t e r column c r o s s - s e c t i o n a l a r e a (0.0285 m 2) 157 2. O r i f i c e meter c a l i b r a t i o n T a b l e A3 g i v e s the c a l i b r a t i o n r e l a t i o n s h i p f o r t h e o r i f i c e meter. The r e l a t i o n s h i p was computed f o l l o w i n g t h e method d e s c r i b e d i n the ASME R e s e a r c h R e p o r t : F l u i d m e t e r s , t h e i r t h e o r y and a p p l i c a t i o n s , 5 t h ed., The American S o c i e t y of M e c h a n i c a l E n g i n e e r s , New Y o r k , 1959. T a b l e A3 C a l i b r a t i o n f o r o r i f i c e meter (1 i n d i a m e t e r , f l a n g e t a p s , squared edges) AP, cm H-0 Flow r a t e , m 3/s A i r v e l o c i t y , m/s 2 0.00869 1-4 3 0.01055 1 .7 4 0.01179 1 .9 5 0.01366 2.2 6 0.01490 2.4 7 0.01614 2.6 8 0.01676 2.7 9 0.01800 2.9 10 0.01924 3.1 1 1 0.01986 3.2 12 0.02048 3.3 * Based on i n s e r t c r o s s - s e c t i o n a l a r e a (0.00621 m 2) A P P E N D I X B M I N I M U M F L U I D I Z A T I O N V E L O C I T Y 158 A . C a l c u l a t e d 1 . PVC p g = 1 . 1 6 4 k g / m 3 Mg = 1 . 8 2 4 x 1 0 " 5 k g / m s p p = 1400 k g / m 3 d * = 75 x 1 0 " 6 m P A r = p g ( p s - p g ) g d 3 / M 2 = 2 0 . 2 S i n c e A r < 1 0 3 , ° m f = 0 . 0 0 0 7 5 ( p p - p g ) g d p = 0 . 0 0 3 2 m / s 2 . C r a c k i n g c a t a l y s t Pg = 1 . 1 6 4 k g / m 3 Mg = 1 . 8 2 4 x 1 0 " 5 k g / m s p = 2000 k g / m 3 tr * d p = 40. x 1 0 " 6 m A r = 4 . 4 A r < 1 0 3 a n d U - = 0 . 0 0 1 3 m / s * d „ „ s h o u l d be u s e d . 160 B) D e t e r m i n e d e x p e r i m e n t a l l y The minimum f l u i d i z a t i o n v e l o c i t y of b o t h powders was d e t e r m i n e d e x p e r i m e n t a l l y i n a 15 cm c y l i n d r i c a l column. F i g u r e B1 and B2 g i v e the r e l a t i o n s h i p between the p r e s s u r e d r o p a c r o s s the bed and a i r s u p e r f i c i a l v e l o c i t y . The minimum f l u i d i z a t i o n v e l o c i t y i s 0.0087 m/s f o r PVC and 0.0052 m/s f o r c r a c k i n g c a t a l y s t . 161 0 0.2 0.4 0.6 0.8 1 Superficial velocity, cm /s F i g u r e B1 Minimum c r a c k i n g f l u i d i z a t i o n c a t a l y s t . v e l o c i t y d e t e r m i n a t i o n f o r 1 62 25 20 h O CL CL O ~o CD L_ 3 (/) CO <D 15 h 10 h 5 h 0.5 1 Superficial velocity, cm /s 1.5 F i g u r e B2 Minimum f l u i d i z a t i o n v e l o c i t y d e t e r m i n a t i o n f o r tr V w * APPENDIX C RAW DATA 163 T a b l e C l P r e s s u r e p r o f i l e fo r PVC, low i n v e n t o r y , v e r t i c a l i n l e t . ( P r e s s u r e in kPa) P o s . U j . m/s 1 . 7 1 . 7 1 . 7 1 . 7 1 .7 1 . ,9 1 . 9 2 . 2 2 . 2 2 2 2 . 2 U 0 . cm/s 3 .4 4 , 6 5 6 7 . 3 10.8 4 . 6 7 . 3 4 .6 5 .6 7 3 10 . 8 1 1 03 1 . 59 1 . 55 2 05 1 .93 1 72 2 . 14 2 10 2 01 1 93 2.31 2 O .69 1 17 1 12 1 . 29 1 .47 1 20 1 . 47 1 33 1 . 33 1 42 1 . 63 3 0. .53 O. 78 0. 75 0. 86 1 .04 0. 88 1 . 1 1 1 03 0. 99 1 20 1 . 29 4 0. 52 O 62 0. 64 0. 62 0.82 O 78 O. 82 0 .92 0 87 0 . 96 1.13 5 o 50 O 59 0. 62 0 60 0.7 1 0. 75 0. 78 0 , 89 O 84 0 . 92 0. 98 6 0. 48 0. 57 0. 60 0. 58 0.67 0 72 0. 77 0 86 0 8 1 O . 90 0 . 96 7 0 46 0. 55 0. 58 O. 56 0.65 o. 69 0. 75 O . 83 0 79 0 87 0. 94 8 0 : 45 0 53 0 56 0, 54 0.63 0. 67 0 73 0 .81 0 7B 0 . 85 0.92 9 o 44 O. 52 0 54 0. 53 0.61 o. 65 0. 7 1 0 . 79 0 76 0 83 0.91 10 o 43 o 51 0. 53 0 52 0 .60 0. 64 0. 69 0. 78 0 75 0 82 0 . 89 1 1 2 35 2 . 84 2 . 84 2 . 84 3. 14 2 . 84 2 . 94 2 . 94 2 . 89 2 94 3.14 12 1 .55 2 06 2 . 10 2 . 15 2 . 49 2 . 06 2 . 24 2 . 15 2 . 13 2 3 1 2 . 49 13 0 33 0. 34 0. 37 0. 39 0. 42 0. 42 0. 51 0 53 0 56 0 6 1 0. 70 14 0 33 0. 34 0. 37 0. 39 0. 42 0. 4 1 0. 51 0 52 0. 55 0 59 0 . 69 T a b l e C2 P r e s s u r e p r o f i l e f o r PVC, medium Inventory , v e r t i c a l i n l e t . ( P r e s s u r e in kPa) Pos . U i - on/s 1 . 4 1 . 7 1 . . 7 1 7 1 . 7 1 . .9 2 . 2 2 .2 2 2 2 . 2 2 . 4 2 . 6 %• cin/s 4 . 6 2 3 3 . 4 4 6 5 .6 4 6 2 3 3 4 4 6 5 6 4 . 6 5 . 6 1 2 58 1 . 97 2 . 24 2 .67 2 66 2 66 1 80 2 . 24 2 . 7 1 2 . 75 2 7 1 2 . 83 2 1 . 97 1 29 1 55 1 . .97 1 98 2 02 1 25 1 61 1 98 2 . 10 1 . 93 2 .07 3 1 38 0. 77 1 12 1 .38 1 59 1 50 0. 95 1 . 21 1 50 1 72 1 64 1 64 4 1 . 04 0 62 0 72 1 04 1 25 1 08 O. 83 O. 95 1 16 1 38 1 . 29 1 . 36 5 0. 73 0 55 0. 57 0 . 78 0 81 0 95 0. 78 0. 82 O 95 1 02 1 . 12 1 19 6 0. 53 o . 52 0. 52 O. 66 0 64 0 78 0. 76 0. 80 0 89 O 90 1 .02 1 .07 7 0. 48 o 50 0 50 o. 61 0 60 0 74 0. 74 0. 79 0 86 0. 86 0 . 98 1 .05 a 0. 46 0. 48 0 48 ,0. 59 0 59 O 73 0. 73 0 78 0. 84 0 84 0 96 1 03 g 0. 45 0. 46 0 46 0 57 0 57 0. 7 1 0. 7 1 0. 76 0 82 0. 8 1 0 93 1 .01 10 0. 43 0. 45 0. 45 0 55 0 55 0. 69 0. 69 0 74 0 80 0 79 0 91 1 .00 11 3 . 73 2 . 99 3 43 3 73 3 63 3 82 2 89 3 38 3 . 92 3 82 4 .02 3 82 12 2 . 89 2 . 24 2 58 2 89 2 83 2 99 2 20 2 . 58 3 .07 3 02 3 . 15 3 . OO 13 ' 0. 29 O. 32 0 29 0 35 0 32 0. 47 0. 49 O 52 O 59 0 56 0 .67 0 73 14 0 29 0. 32 O 29 O 35 0 . 32 0 46 0 49 O 51 O 57 0 54 O . 65 0 . 7 1 T a b l e C3 P r e s s u r e p r o f i l e f o r PVC, h i g h i n v e n t o r y , v e r t i c a l i n l e t . ( P r e s s u r e In kPa) 1ow i n l e t Pos . U j . m/s 2 . 2 2 . 2 2 . 2 1 U 0 , cm/s 3 . 4 4 6 5 6 4 1 3 . 22 3 . 31 3 .44 3 2 2 . 66 2 . 75 2 . 83 2 3 2 . 23 2 32 2 49 1 4 1 .80 1 . . 98 2 . 06 1 5 1 . .42 1 . 54 1 . 68 0 6 1 20 1 20 1 33 0 7 0 .99 1 . 00 1 1 1 0 8 0 93 0. 93 O. 94 0 9 0 89 0. 89 0 9 1 0 10 0 86 0. 86 0 89 0 1 1 4 . 1 1 4 . 07 4 14 4 12 ' 3 . 33 3 34 3 43 3 13 0 97 1 . 25 1 31 1 14 0 55 0 55 0 57 0 middle i n l e t h i g h i n l e t 7 2 . 2 2 . , 2 2 . 7 2 2 2 2 6 3 . 4 4 .6 4 . 6 2 3 3 4 00 3.09 3 .09 3 . 86 2 .36' 2 75 3 1 2 . 35 2 . 40 3 . 27 1 72 2 06 72 1 .89 1 89 2 . 83 1 2 1 1 63 28 1 . 39 1 . 46 2 . 49 0 . 96 1 25 94 1 . 12 1 12 2 . 24 O .83 1 04 78 0.95 O 94 1 . 97 0 8 1 0. 90 63 0. 79 0. 86 1 . 89 0 79 0 85 54 O. 76 O 79 1 86 O 76 o 80 53 0. 73 0. 78 1 . 83 0 74 0 76 52 0.71 0. 78 1 .80 0. 73 0. 76 17 3 . 94 4 . 14 4 .89 3 . 80 3 . 94 43 3 . 18 3 43 4 . 22 3 .04 3 . 18 47 1 . 42 1 . 54 2 43 1 28 1 . 42 39 0.51 O. 55 1 .72 0 54 O 50 * measurement p o i n t between p o s . 1 and 2 T a b l e C4 P r e s s u r e p r o f i l e fo r PVC, low i n v e n t o r y , t a n g e n t i a l i n l e t . ( P r e s s u r e in kPa) Pos . U f m/s 1 7 1 7 1 7 1 9 2 2 2 2 2 . 2 2 4 2 7 U o - cm/s 5 6 7 3 10.8 7 3 5 6 7 3 10. a 7 3 7 3 1 1 72 1 97 2 15 1 97 1 80 1 81 2.15 1 98 2 1 1 2 1 1 1 1 29 1 63 1 46 1 12 1 46 1 .72 1 54 1 67 3 0 66 O 72 0 99 1 12 O 86 1 20 1 . 29 1 16 1 37 4 0 53 ; 0 59 0 82 0 82 0 82 0 95 1 .03 1 00 1 2 1 5 0 52 0 55 0 73 0 74 O 79 0 86 0.94 O 96 1 t7 6 0 50 0 53 O 69 0 7 1 O 78 0 82 0.91, O 94 1 15 7 0 50 0 52 0 66 0 69 O 77 0 80 0.89 o 9 1 1 15 8 0 48 0 52 0 66 0 69 O 75 0 79 0.87 o 89 1 14 9 0 46 0 50 0 64 0 69 0 76 0 78 0.87 0 87 1 12 to 0 46 0 48 0 64 0 67 O 74 0 78 0. 86 o 86 1 10 1 1 2 30 2 70 2 94 2 82 2 30 2 80 2 .89 2 70 2 89 12 1 63 1 99 2 24 2 10 1 63 2 15 2.15 2 06 2 15 13 ' 0 36 0 37 0 46 0 50 O 57 0 57 0.6b 0 66 0 82 14 0 36 0 37 0 46 0 49 o 56 0 55 0.64 0 64 0 80 T a b l e C5 P r e s s u r e p r o f i l e f o r PVC, medium i n v e n t o r y , t a n g e n t i a l i n l e t . ( P r e s s u r e in kPa) Pos . U i ' m/s 1 4 1 7 1 7 1 . 7 1 9 2 2 2 2 2 . 2 2 4 U o ^ cm/s 7 3 5 6 7 3 - IO. 8 7 3 5 6 7 3 10. 8 7 3 1 2 40 2 58 2 58 3.02 2 66 2 15 2 92 3 . 09 3 01 2 1 72 1 89 1 89 2 . 14 2 15 1 63 2 15 2 . 58 2 15 3 1 20 1 29 1 38 1 .68 1 72 1 29 1 55 2 . 15 1 67 4 0 78 1 03 0 99 1 . 25 1 29 1 03 1 35 1 . 80 1 46 5 0 57 0 69 0 80 0.95 O 99 0 96 1 20 1 . 46 1 25 6 0 55 O 57 0 69 0.8 1 0 92 0 94 1 07 1 . 19 1 19 7 0 54 0 55 0 67 0. 74 0 90 0 91 1 01 1 . 10 1 15 8 0 52 o 54 0 66 0.73 0 86 O 89 1 00 1 .07 1 14 9 O 50 o 53 0 66 0.7 1 0 84 0 89 1 00 1 .05 1 14 10 0 48 0 52 0 64 0.69 0 82 0 87 0 98 1 .03 1 12 1 1 3 38 3 38 3 04 3 .73 3 43 2 84 3 43 3 . 87 3 33 12 2 75 2 75 2 40 2 .92 2 83 2 24 2 92 3 . 18 2 66 13 0 34 0 39 0 46 0.52 0 60 O 70 0 76 0. 79 0 88 14 0 34 0 39 0 46 0 .5 1 0 59 0 69 0 74 0. 78 0 86 T a b l e C6 P r e s s u r e p r o f i l e for c r a c k i n g c a t a l y s t , low i n v e n t o r y , v e r t i c a l i n l e t . ( P r e s s u r e in kPa) Pos . U ( , m/s 1 4 U Q , 4.6 cm/s 1 1 2 9 2 0.82 3 0.69 4 0.62 5 0. 55 6 0. 52 7 0.48 8 0 45 9 0.4 1 10 0.38 11 3.00 12 1.72 13 0.28 14 0.28 1 . 4 1 7 .7 5 6 1 3 2 . 3 29 0. 94 1 54 0 82 O. 79 0 88 O. 69 0. 72 0 81 0 62 0. 69 0. 74 0 55 0 65 0. 69 0. 52 0 .60 o 65 0. 48 O. .58 0. 60 0. 45 0 57 0. 57 0. 43 0 55 0. 55 o. 40 0. 53 0. 53 3 . 00 2. 83 3. 09 1 . 72 1 72 1 . 89 0. 28 0. 32 0. 35 0. 28 0. 32 0. 34 1 . 7 1 . 7 1 . . 7 3 4 4 6 5 6 1 .63 1 42 1 60 0 94 0 99 1 . 00 0 82 0. 88 0. 88 0 74 O 77 0. 82 0. 69 0. 74 0. 77 0. 65 0 70 0. 72 0. 62 0 .67 0. 70 o 60 o. .64 0. .69 0. 58 o 58 O. 67 0. 57 0. 55 0. .65 3 . 09 3 . 09 3. 02 1 89 1 . 89 1 . 84 0. 35 0. 38 0. 40 0. 35 0. 37 0. 39 1 . 9 1 .9 2 2 4 . 6 5 . 6 4 6 1 . 54 , .46 1 54 1 lO 1 . 12 1 . 20 O. 96 1 .03 1 12 O. 91 O .96 1 03 0. 88 0 .91 0 98 0. 84 0 . 86 0, 94 0. 81 0 .84 0. . 93 0. 77 0 .81 o. 9 1 0. 74 0 .77 0 88 0. 70 o 74 0. 84 3. 18 3 . 18 3 . 31 1 . 97 1 . 99 2 06 0. 47 O . 48 O. 56 0. 47 O .47 0 56 2 4 2 4 2 . 4 1 3 2 3 3 4 1 20 1 46 1 54 1 01 1 17 1 . 20 0 94 1 08 1 12 0 9 1 1 .03 1 03 0. 88 O 98 1 . 00 0. 86 0 94 0 . 96 0. 84 0 89 0 . 94 0. 82 0 . 88 o . 93 0 8 1 0. 86 o 9 1 0. 79 0 82 o 89 2 . 92 3. 35 3 . 35 1 . 89 2 . 15 o 15 O. 57 0 57 o. 62 0. 55 0 57 0. 60 T a b l e C7 P r e s s u r e p r o f i l e fo r c r a c k i n g c a t a l y s t , medium i n v e n t o r y , v e r t i c a l i n l e t . ( P r e s s u r e in kPa) Pos . U 1 - m/s 1 . 4 1 4 1 . 7 1 7 ' 1 7 < • . 7 1 . 7 1 . 9 1 .9 2 . 2 2 . 4 . U o . cm/s 4 . 6 5 6 1 . 3 2 3 3 .4 4 . 6 5 6 3 . 4 4 6 2 3 1 3 1 2 . 75 2 83 2 . 13 2 . 92 2 .83 2 . 83 2 83 2 . 92 2 . 87 2 87 2 .06 2 1 . 89 1 80 1 50 2 06 2 .06 2 . 22 2 15 2 23 2 15 2 . 15 1 54 3 1 . 3G 1 03 1 03 1 . 54 1 .54 1 63 1 54 1 72 1 67 1 . 72 1 29 4 0. 86 0. 82 0 86 1 . 12 1 12 1 . 39 1 . 12 1 .46 1 29 1 37 1 17 5 O. 70 0 76 O .77 O. 94 0 .94 0. 96 0 94 1 . 29 1 12 1 . 17 1 10 6 0. 62 0 62 0 69 0. .82 0 .84 0. 86 0 86 1 . 15 1 00 1 10 1 03 7 O. 55 0. 57 0 . 64 O 76 0 77 0. 77 O. . 77 1. .08 O . 9 1 1 03 0 . 98 8 O. 50 O. 52 0 . 58 0. 69 0 . 70 0. 72 O. . 70 1 :03 O . 86 O 98 O 94 9 0. 46 0. 48 0. 55 0. 65 0. 65 0. 67 0 .67 1 .00 0. .81 0. 93" 0 91 10 0. 43 0. 45 0. .52 0. 60 0 .61 0. 62 0. 64 0 96 0 77 0 88 0. 86 1 1 4. 38 4 . 38 4 . 29 4 . 63 4 . 67 4 . 55 4 .50 4 .74 4- 63 4 . 72 4 . 03 12 3. 18 3 . 18 3 09 3. 43 3 38 3 . 35 3 30 3 .43 3. 43 3 52 2 83 13 0. 26 0 28 0. .31 0. 35 0 . 37 0. 36 0. 38 0 . 63 0. .47 0 54 O. 55 14 0. 24 0. 28 0. .31 0. 35 0. .36 0. 36 0. 37 0 . 59 0. 45 0. 52 o. 55 -4 O T a b l e C8 P r e s s u r e p r o f i l e fo r c r a c k i n g c a t a l y s t , h i g h i n v e n t o r y , v e r t i c a l i n l e t . ( P r e s s u r e in kPa) Pos . U i ' m/s 1 . 4 1 . 4 1 . 4 1 . 7 1 . 7 1 . 7 1 . 7 1 . 7 1 . 9 2 2 U o ^ cm/s 3 . 4 4 . 6 5 . 6 1 . 3 2 . 3 3 . 4 4 .6 5 . 6 2 . 3 1 . 3 1 4 . 29 4 . 46 4 . 55 2 .83 4 . 29 4 .46 4 . 55 4 . 64 4 . 20 2 75 2 3 . 35 3 .60 3 .52 2 .23 3 . 55 3 . 52 3 .61 3 61 3 .43 2 15 3 2 66 2 . 75 2 . 83 1 . 63 2 . 88 2 .92 3 .09 3 . 00 2 .92 1 .72 4 1 .97 1 97 2 . 23 1 . 24 2 . 23 2 .40 2 .58 2 . 49 2 .40 1 29 5 1 . 37 1 46 1 . 63 0 99 1 .63 1 89 2 .06 1 . 97 1 .89 1 .07 6 O . 86 1 07 1 . 20 0 .77 1 . 20 1 . 37 1 . 55 1 . 46 1 .42 0 98 7 0 .60 0 69 0 .77 O 69 0 86 0. 94 1 .03 1 03 1 .01 0 9 1 8 0 . 52 0 . 58 O 60 O .60 0. 77 O. 81 0 . 86 0. 86 O 94 0 88 g O . 46 O . 52 O 55 0 57 0. 72 0. 74 0 .77 0. . 77 O 88 0. . 84 10 0 . 43 0 46 0 .50 0 52 0. 69 0. 69 6 .69 0. 7 1 0 84 0 8 1 11 6 .01 6 .01 6 01 5 15 6 13 6. 26 6 2 1 6 . 18 6 18 4 . 8 1 12 4 . 72 4 81 4 8 1 3 95 4 . 89 5 . 01 4 . 98 4 . 98 4 98 3 . 60 13 1 03 1 05 1 . . 1 1 1 . 03 1 . 18 1 . 25 1 . 25 1 23 1 29 1 . 18 14 0. . 24 0. 26 O. 28 O. 29 O. 34 0. 36 0. . 37 0. 36 O. 40 0 . 4 7 T a b l e C9 P r e s s u r e p r o f i l e f o r c r a c k i n g c a t a l y s t , low i n v e n t o r y , t a n g e n t i a l i n l e t . ( P r e s s u r e in kPa) Pos . U , . m/s 1 . 7 1 . 7 1 . 7 1 . 7 1 . 7 1 9 2 2 2 . 2 2 . 2 2 2 2 . 2 U 0 , cin/s 1 . 3 2 . 3 3 4 4 . 6 5 . 6 4 . 6 1 3 2 . 3 3 4 4 . 6 5 6 1 1 . 08 1 . 24 1 37 1 . 37 1 . 46 ,. 49 1 . 03 1 46 1 59 1 .51 1 63 2 0. 48 0. 64 0 72 0. 77 0,88 0. 91 0. 72 0. 94 1 03 1 03 1 10 3 0. 45 0. 55 0 60 0. 67 0. 77 O. 81 0. 67 O. 8 1 0 . 93 O 94 0. 94 4 0. 43 0. 52 O 57 0. 58 0. 69 0. 76 0. 65 0. 76 0 86 0 .89 0. 9 1 5 O. 4 1 0. 50 0 53 0. 55 0. 65 0. .70 O. .64 0. 74 0 . 82 0 . 86 0. 88 6 O. 40 O. 48 0. 52 0. 53 0. 62 0. 67 0. .62 0. 72 0 79 o 84 0 84 7 0. 40 0. 46 0. 50 0 52 0. 60 o . 64 0. 62 0. 70 0 77 o 82 0 8 1 8 0. 40 O. 45 0. 48 0. 50 0. 58 0 62 0. 60 o . 69 0 . 76 0 8 1 0 77 9 0. 38 0. 43 0. 46 0. 48 0. 57 o . 60 0 60 o . 67 0 74 0 79 0 74 10 0. 36 0. 4 1 0. 45 0. 46 O. 55 0. 58 0. 60 0. 67 O 72 0 77 0 .72 1 1 2 . 70 2 . 88 3 . 00 3 . 00 3 . 06 3 02 2 . 68 3. 02 3 18 3 09 3 18 12 1 . 56 1 . 67 1 . 77 1 . 7 2 1 . 80 1 77 1 63 1 . 89 1 97 1 . 89 1 97 13 ' O. 29 0. 3 1 0. 32 0. 34 O. 37 0. 42 0. 47 0. 47 0. 49 0. 53 O 5 1 14 O. 29 0. 3 1 0. 32 0. 34 0. 37 0. 42 0 47 0. 47 0. .49 0. .52 0 5 1 f O T a b l e CIO P r e s s u r e p r o f i l e for c r a c k i n g c a t a l y s t , med P o s . U ( . m/s 1 . 4 1 . 7 1 . 7 1 . 7 1 7 u o - cm/s 4 . 6 1 . 3 2 . 3 3 . 4 4 . 6 1 3 . 09 2 . 06 2. 40 3 09 3 35 2 1 . 97 1 . 12 1 . 80 1 . 97 2 06 3 1 46 0. 93 1 . 29 1 . 46 1 . 63 4 0 94 0. 77 0. 93 0 89 1 . 20 5 0 74 0 72 0. 79 0 86 0 . 98 6 0. 64 0. 67 0. 74 0 76 0 . 86 7 0 55 0. 62 0. 69 0 70 0 76 B 0. 52 0. 58 O. 64 0 65 0 72 9 0. 48 0. 55 0. 58 0 62 0 69 10 0 45 0. 53 0. 55 0. 58 0 65 1 1 4 . 89 3 95 4 . 72 4 . 8 1 4 98 12 3 .69 2 83 3 . 43 3. 52 3 . 74 13 0 26 0. 34 0. 34 0 34 0 34 14 0 26* 0 34 0. 33 0 33 0 34 ium i n v e n t o r y , t a n g e n t i a l i n l e t . ( P r e s s u r e in kPa ) 1. 7 1 . 9 1 . 9 2 . 2 2 2 2 . 2 2 2 5 . 6 4 . 6 5. 6 1 . 3 2 . 3 3 . 4 4 . 6 3 . 18 3 . 35 3 09 2 . 06 2 . 92 3 . 35 3 . 35 2 . 06 2 .23 2 . 23 1 29 1 .97 2 40 2 . 32 1 . 59 1 . 79 1 72 1 . 17 1 . 55 1 . 89 1 94 1 12 1 . 36 1 32 1 . 03 1 . 37 1 . 46 1 46 0 . 9 1 1 . 20 1 17 0. 98 1 . 20 1 24 1 32 0 82 1 .05 1 .05 0. 93 1 . 13 1 . 13 1 . 25 0 . 76 0 96 0 . 98 0. 89 1 .06 1 08 1 . 19 0. 70 O . 88 0 . 93 0. 88 1 OI 1 03 1 . 13 0 65 O . 83 0 . 88 0 86 0 98 0 98 1 OS 0 60 0. 77 0 82 0. 84 0 .94 0 94 1 03 4 . 8 1 4 ,98 4 . 67 3 69 4 72 4 . 84 5 . 06 3 . 97 3 .69 3 69 2 . 66 3 . 60 3 60 3 . 78 0 36 O . 5 1 0 47 0. 54 0 .55 0 58 0. . 64 0 . 34 0 . 47 0 46 0. 54 0 . 54 0 57 0 59 T a b l e d 1 P r e s s u r e p r o f i l e f o r c r a c k i n g c a t a l y s t , h i g h i n v e n t o r y , t a n g e n t i a l i n l e t . ( P r e s s u r e in kPa) Pos . 1 2 3 4 5 6 7 B 9 10 1 1 12 13 14 1 . 4 1 . 7 1 .7 1 . 7 1 . 7 1 . 7 1 .9 1 .9 1 . 9 1 . 9 1 . 9 2 2 4 6 1 . 3 2 . 3 3 . 4 4 . 6 5 .6 1 . 3 2 . 3 3 . 4 4 .6 5 .6 4 .6 4 . 12 3 09 3 .95 4 . 20 4 . 29 4 . 20 2 .83 3 .95 4 . 12 4 . 29 4 . 29 4 63 2 . 75 2 .06 2 . 75 3 .00 3 .09 3 .00 1 .63 2 . 7B 3 .00 3 . 18 3 .09 3 . 4 3 2 . ,06 1 , 46 2 . 15 2 .49 2 . 49 2 . , 49 1 ,29 2 , 23 2 , . 40 2 .66 2 . 49 2 92 1 .54 1 . 12 1 . 54 1 . 97 1 .97 1 . 97 1 .05 1 . 72 1 . 97 2 . 15 2 OI 2 . 49 1 . ,03 0 . 94 1 , 20 1 . 46 1 .51 1 .46 0 .96 1 , ,42 1 . 54 1 . 63 1 , 58 2 . 15 0 86 O 77 0 94 1 .05 1 08 1 . 12 0 . 88 1 16 1 , 20 1 29 1 24 1 . 89 0 ,69 0 70 0 .82 0 . 87 0 . 94 1 00 0 .82 1 . ,03 1 .08 1 . 12 1 10 1 . 80 0 .60 0 . 67 O . 74 0 . 82 0 .86 O. . 86 0 . 77 O 9 1 0 , 98 1 03 1 OI 1 . 72 0 ,55 0 .64 0 , 70 0 , 77 0 . 79 0. , 77 0 , 72 O ,86 0 91 O 94 0 96 1 . 72 0 ,50 0 .60 0 .67 0 .72 0 .72 0. . 72 0 .69 0 .81 0 .86 0 ,89 0 .9 1 1 .72 5 . 75 4 ,63 5 66 5 .92 5 .97 5. ,92 4 , 46 5 .80 5 .87 6 01 6 .01 6 . 69 4 ,83 3 ,60 4 55 4 .72 4 .72 4 . 72 3 . 26 4 .55 4 67 4 .81 4 77 5 . 23 0 , 88 0 63 0 78 1 .00 1 .04 1 . ,08 O . 69 1 . . 46 0 98 1 .08 1 1 1 1 54 0 , 25 O 32 0, , 34 0. , 35 0 , 37 O 39 0 4 1 O. , 43 O. 47 0 82 0 4 9 1 37 175 T a b l e C12 S o l i d s c i r c u l a t i o n r a t e f o r PVC, low i n v e n t o r y , v e r t i c a l i n l e t . ( R a t e s i n kg/m 2s) U Q, cm/s U i , m/s 3.4 4.6 5.6 7.3 10.8 1 .4 0.8 2.8 2.3 2.7 6.4 1.7 3.4 4.7 5.7 5.1 8.4 1 .9 5.6 7.0 6.8 8.5 1 1.2 2.2 6.8 8.7 8.6 10.3 13.4 2.4 7.6 9.5 10.4 11.0 17.9 2.7 9.0 11.8 12.0 12.1 T a b l e C13 S o l i d s c i r c u l a t i o n r a t e f o r PVC, medium i n v e n t o r y , v e r t i c a l i n l e t . ( Rates i n kg/m 2s) U i , m/s U 0' cm/s 2.3 3.4 4.6 5.6 1 .4 2.3 4.2 6.6 6.8 1 .7 5.5 6.3 9.1 11.9 1.9 8.0 11.2 12.6 15.3 2.2 9.2 13.4 16. 1 19.1 2.4 11.7 16.3 19.1 21 .8 2.6 12.8 17.2 21.5 24.0 2.7 14.2 19.3 24.0 26.0 2.9 16.8 20.5 3.1 19.7 22.8 3.2 20.3 176 T a b l e C14 S o l i d s c i r c u l a t i o n r a t e f o r PVC, h i g h i n v e n t o r y , low v e r t i c a l i n l e t . (Rates, i n kg/m 2s) U i , m/s Uo. cm/s 2.3 3.4 4.6 5.6 1 .4 - 6.6 11.6 10.1 1.7 11.1 14.9 19.2 19.3 1.9 12.8 18.9 22.1 26.5 2.2 16.0 23.5 27.0 33.0 2.4 20.0 27.0 34.4 34.9 2.6 22.0 29.3 33.9 36.7 2.7 24.0 31 .6 2.9 24.3 3.1 25.0 T a b l e C15 S o l i d s c i r c u l a t i o n r a t e f o r PVC, h i g h i n v e n t o r y , m i d d l e v e r t i c a l i n l e t . ( Rates i n kg/m 2s) U i , m/s cm/s 2.3 3.4 4.6 5.6 1 .4 5.5 4.6 5.8 9.0 1.7 8.1 9.5 10.8 13.1 1.9 12.1 13.9 15.5 17.4 2.2 15.4 17.3 19.9 21 .6 2.4 18.8 20.2 23.8 25.1 2.6 20.3 25. 1 27.0 31.1 2.7 23. 1 27.7 30.0 28.9 2.9 23.8 25.5 3.1 24.4 177 T a b l e C16 S o l i d s c i r c u l a t i o n r a t e f o r PVC, h i g h i n v e n t o r y , h i g h v e r t i c a l i n l e t . ( R a t e s i n kg/m 2s) u 0 , cm/s U i , m/s 2.3 3.4 4.6 5.6 1 .7 8.0 9.5 10.6 13.1 1 .9 11.4 13.5 15.2 17.0 2.2 1 1.9 17.0 19.2 21 .0 2.4 14.8 20.0 20.9 24.0 2.6 - 23.9 26.5 30.3 2.7 15.8 26.7 24.5 2.9 15.9 25.7 3.1 16.9 21 .9 178 T a b l e C17 S o l i d s c i r c u l a t i o n r a t e f o r PVC, low i n v e n t o r y , t a n g e n t i a l i n l e t . ( R a t e s i n kg/m 2s) U i , m/s U 0 , cm/s 5.6 7.3 10.8 1 .4 1 .4 2.3 2.1 1.7 3.0 3.5 4.5 1.9 5.3 6.9 8.1 2.2 6.6 8.4 9.6 2.4 7.9 9.3 1 1.9 2.6 8.7 10.8 15.1 2.7 9.5 12.5 17.4 T a b l e C18 S o l i d s c i r c u l a t i o n r a t e f o r PVC;, . medium i n v e n t o r y , t a n g e n t i a l i n l e t . ( R a t e s i n kg/m 2s) U Q, cm/s U i , m/s 5.6 7.3 10.8 1 .4- 4.2 4.2 5.2 1.7 4.7 8.1 9.4 1.9 6.0 12.6 17.2 2.2 7.0 14.7 23.9 2.4 7.7 16.9 28.2 4 1 79 T a b l e C19 S o l i d s c i r c u l a t i o n r a t e f o r c r a c k i n g c a t a l y s t , low i n v e n t o r y , v e r t i c a l i n l e t . ( R a t e s i n kg/m 2s) U 1 ' m/s 1 .3 2.3 U o / c m / s 3.4 4.6 5.6 1 1 1 2 2 2.6 2.7 7.2 7.2 8.1 8.4 8.4 8.6 8.0 9.6 12.5 15.3 14.8 14.2 15.8 14.1 18.0 18.7 19.4 20.2 1 1 16 21 22 21 9 5 3 3 1 12 17 21 21 21 T a b l e C20 S o l i d s c i r c u l a t i o n r a t e f o r c r a c k i n g c a t a l y s t , medium i n v e n t o r y , v e r t i c a l i n l e t . ( R a t e s i n kg/m 2s) cm/s D"i , m/s 1 .3 2.3 3.4 4.6 5.6 1 .4 20.2 19.4 22.4 24.5 27.0 1 .7 24.1 31.1 32.8 40.4 40.9 1 .9 25.7 35.8 38.0 44. 1 45.9 2.2 25. 1 39.0 42.2 48.2 2.4 26.5 T a b l e C21 S o l i d s c i r c u l a t i o n r a t e f o r c r a c k i n g c a t a l y s t , h i g h i n v e n t o r y , v e r t i c a l i n l e t . ( R a t e s i n kg/m 2s) U j , m/s 1 .4 1 .7 1.9 2.2 U 1.3 25.0 29.2 35.7 38.2 2.3 29.2 48.8 55.1 57.2 or cm/s 3.4 28.4 54.5 63.1 63.4 4.6 41 .0 61.3 70.1 5.6 45.2 63.4 71 .7 180 T a b l e C22 S o l i d s c i r c u l a t i o n r a t e f o r c r a c k i n g c a t a l y s t , low i n v e n t o r y , t a n g e n t i a l i n l e t . ( R a t e s i n kg/m 2s) U 1 ' m/s 1 .3 2.3 U Q , cm/s 3.4 4.6 5.6 4 7 9 2 4 6 7 3, 3, 4, 5, 5, 5, 5, 4.4 6.8 8.4 9.4 9.6 7.1 9.6 11.1 11.2 6.6 10.8 12.7 12.8 7.9 12.6 13.5 13.9 T a b l e C23 S o l i d s c i r c u l a t i o n r a t e f o r c r a c k i n g c a t a l y s t , medium i n v e n t o r y , t a n g e n t i a l i n l e t . ( R a t e s i n kg/m 2s) U i , m/s 1.3 2.3 U Q , cm/s 3.4 4.6 5.6 1 .4 1 .7 1 .9 2.2 13, 14, 13, 12, 15.2 23.5 27.7 31 .3 17.2 28.8 34.9 33. 1 23.4 32.3 39.4 42. 1 23.5 36.2 40.0 42.0 T a b l e C24 S o l i d s c i r c u l a t i o n r a t e f o r c r a c k i n g c a t a l y s t , h i g h i n v e n t o r y , t a n g e n t i a l i n l e t . ( R a t e s i n kg/m 2s) U i , m/s 1.3 2.3 U O' cm/s 3.4 4.6 5.6 1 .4 1 .7 1 .9 2.2 24.8 29.9 31.0 28.7 25.3 40.9 46.7 49.4 27.9 42.7 53.6 54.6 32.6 48.0 55.5 56.3 33.6 48.2 59.3 63.2 181 C o n v e r s i o n 1. P r e s s u r e measurements To c o n v e r t from p r e s s u r e i n cm H 20 t o p r e s s u r e i n kPa, m u l t i p l y by 0.09806. To c o n v e r t from p r e s s u r e i n cm o i l ( s p . g r . 1.75) t o p r e s s u r e i n kPa, m u l t i p l y by 0.17161. 2. D e n s i t y d e t e r m i n a t i o n To c o n v e r t from p r e s s u r e g r a d i e n t i n (cm H 20/6 i n ) t o d e n s i t y i n kg/m 3, m u l t i p l y by 65.66. 3. S o l i d s c i r c u l a t i o n f l u x measurement. To c o n v e r t from r a t e of r i s e of a c c u m u l a t i o n of s o l i d s i n i n / s e c t o - f l u x i n kg/m 2s, m u l t i p l y by: ( d e n s i t y of a c c u m u l a t i o n ) ( 0 . 0 8 3 4 7 ) . APPENDIX D PLOTS OF CHAPTERS 6 AND 7 182 183 F i g u r e 6.2 T y p i c a l p r e s s u r e p r o f i l e f o r PVC, medium i n v e n t o r y , U^=1.7 m/s, U o=0.046 m/s, v e r t i c a l i n l e t . ( P r e s s u r e i n kPa) Column H e i g h t (m) P r e s s u r e Outer • 1.58 0.35 0.51 0.35 0.20 2.89 0.05 , 3.73 In n e r 0.25 2.67 0.41 1.97 0.56 1.38 0.71 1.04 0.86 0.78 1.02 0.66 1.17 0.61 1.32 0.59 1,47 0.57 1.63 0.55 F i g u r e 6.3 E f f e c t o f i n n e r gas v e l o c i t y on i n s e r t a x i a l p r e s s u r e p r o f i l e f o r PVC, medium i n v e n t o r y , U o=0.046 m/s, v e r t i c a l i n l e t . ( P r e s s u r e i n kPa) H e i g h t (m) 0.25 0.41 0.56 0.71 0.86 1 .02 1.17 1 .32 1 .47 1 .63 1 .4 2.58 1 .97 1 .38 1 .04 0.73 0.53 0.48 0.46 0.45 0.43 1 ,7 2.67 1 .97 1 .38 1 .04 0.78 0.66 0.61 0.59 0.57 0.55 U i , m/s 1 .9 2.66 2.02 1 .50 1 .08 0.95 0.78 0.74 0.73 0.71 0.69 2.2 2.71 1 .98 1 .50 1.16 0.95 0.89 0.86 0.84 0.82 0.80 2.4 2.71 1 .93 1 .64 1 .29 1.12 1 .02 0.98 0.96 0.93 0.91 184 F i g u r e 6.4 E f f e c t of i n n e r gas v e l o c i t y on a b s o l u t e p r e s s u r e and p r e s s u r e drop f o r PVC, medium i n v e n t o r y , U o=0.046 m/s. ( P r e s s u r e i n kPa) 1 .4 1.7 P b i . kPa 2.58 2.67 P t i . kPa 0.43 0.55 p b o . kPa 3.73 3.73 P t o . kPa 0.29 0.35 A P i , kPa 2.15 2.12 A P 0 , kPa 3.44 3.38 APb. kPa 0.14 0.20 U i , m/s 1.9 2.2 2.4 2.66 2.71 2.71 0.69 0.80 0.91 3.82 3.92 4.02 0.46 0.57 0.65 1 .97 1 .91 1 .80 3.36 3.35 3.37 0.23 0.23 0.26 F i g u r e 6.5 E f f e c t of o u t e r gas v e l o c i t y on a b s o l u t e p r e s s u r e and p r e s s u r e drop f o r c r a c k i n g c a t a l y s t , medium i n v e n t o r y , Uj=1.7 m/s, v e r t i c a l i n l e t . ( P r e s s u r e i n k P a ) . U Q , cm/s 1 .3 2.3 3.4 4.6 5.6 P b i . kPa 2.13 2.92 2.83 2.83 2.83 P t i . kPa 0.52 0.60 0.61 0.62 0.64 Pbo. kPa 4.29 4.63 4.67 4.55 4.50 P t O ' kPa 0.31 0.35 0.36 0.36 0.37 A P i , kPa 1 .61 2.32 2.22 2.21 2.19 A P 0 , kPa 3.98 4.28 4.31 4.1 9 4.13 A P b , kPa 0.21 0.25 0.25 0.26 0.27 185 F i g u r e 6.6 E f f e c t of o u t e r gas v e l o c i t y on a b s o l u t e p r e s s u r e and p r e s s u r e d r o p f o r PVC, low i n v e n t o r y , Ui=1.7 m/s, v e r t i c a l i n l e t . ( P r e s s u r e i n kPa) 3.4 4.6 P b i - kPa 1 .03 1 .59 P t i ' kPa 0.43 0.51 PbO' kPa 2.35 2.84 Pto- kPa 0.33 0.34 A P i , kPa 0.60 1 .08 kPa 2.02 2.50 A F b , kPa 0.10 0.17 U 0 , cm/s 5.6 7.3 10.8 1 .55 2.05 1 .93 0.53 0.52 0.60 2.84 2.84 3.14 0.37 0.39 0.42 1 .02 1 .53 1 .33 2.47 2.45 2.72 0.16 0.13 0.18 F i g u r e 6.7 E f f e c t of i n v e n t o r y l e v e l on i n s e r t a x i a l p r e s s u r e p r o f i l e f o r PVC, Ui=1.7 m/s, U o=0.046 m/s, v e r t i c a l i n l e t . ( P r e s s u r e i n kPa) Bed i n v e n t o r y H e i g h t (m) low medium h i g h 0.25 1 .59 2.67 3.00 0.41 .1.17 1 .97 2.31 0.56 0.78 1 .38 1 .72 0.71 0.62 1 .04 1 .28 0.86 0.59 0.78 0.94 1 .02 0.57 0.66 0.78 1.17 0.55 0.61 0.63 1 .32 0.53 0.59 0.54 1 .47 0.52 0.57 0.53 1 .63 0.51 0.55 0.52 186 F i g u r e 6.8 E f f e c t of bed i n v e n t o r y on a b s o l u t e p r e s s u r e and p r e s s u r e d r o p f o r PVC, Uj=1.7 m/s, U o=0.046 m/s, v e r t i c a l i n l e t . ( P r e s s u r e i n kPa) Bed i n v e n t o r y • low medium h i g h P b i . kPa 1 .59 2.67 3.00 P t i . kPa 0.51 0.55 0.52 Pbo. kPa 2.84 3.73 4.17 P t o . kPa 0.34 0.35 0.39 A P i , kPa 1 .08 2.12 2.48 A P 0 , kPa 2.50 3.38 3.78 A P b , kPa 0.17 0.20 0.13 F i g u r e 6.9 E f f e c t of s o l i d t y p e on i n s e r t a x i a l p r e s s u r e p r o f i l e f o r medium i n v e n t o r y , Uj=1.7 m/s, U o=0.046 m/s, v e r t i c a l i n l e t . ( P r e s s u r e i n kPa) H e i g h t (m) S o l i d PVC C r a c k i n g c a t a l y s t 0.25 0.41 0.56 0.71 0.86 1 .02 1.17 1 .32 1 .47 1 .63 2.67 1 .97 1 .38 1 .04 0.78 0.66 0.61 0.59 0.57 0.55 2.83 2.22 1 .63 1 .39 0.96 0.86 0.77 0.72 0.67 0.62 187 F i g u r e 6.10 E f f e c t of h e i g h t of a i r i n l e t above t h e d i s t r i b u t o r on i n s e r t a x i a l p r e s s u r e p r o f i l e f o r PVC, h i g h i n v e n t o r y , Ui=2.2 m/s, U o=0.034 m/s, v e r t i c a l i n l e t . ( P r e s s u r e i n kPa) H e i g h t (m) .18m 0.25 3.22 0.41 2.66 0.56 2.23 0.71 1 .80 0.86 1 .42 1 .02 1 .20 1.17 0.99 1 .32 0.93 1 .47 0.89 1 .63 0.86 I n l e t l e v e l .28 m .34 m 3.09 2.75 2.35 2.06 1 .89 1 .63 1 .39 1 .25 1.12 1 .04 0.95 0.90 0.79 0.85 0.76 0.80 0.73 0.76 0.71 0.76 F i g u r e 6.11 E f f e c t of a i r i n l e t c o n f i g u r a t i o n on i n s e r t a x i a l p r e s s u r e p r o f i l e f o r c r a c k i n g c a t a l y s t , medium i n v e n t o r y , Ui=1.7 m/s, U o=0.046 m/s. ('Pressure .in kPa) I n l e t H e i g h t (m) v e r t . t a n g . 0.25 2.83 3.35 0.41 2.22 2.06 0.56 1 .63 1 .63 0.71 1 .39 1 .20 0.86 0.96 0.98 1 .02 0.86 0.86 1.17 0.77 0.76 1 .32 0.72 0.72 1 .47 0.67 0.69 1 .63 0.62 0.65 188 F i g u r e 6.13 T y p i c a l s o l i d s c i r c u l a t i o n f l u x e s f o r PVC, medium i n v e n t o r y , U o=0.046 m/s, v e r t i c a l i n l e t . D 1 ' m/s F l u x , kg/m 2s 1 .4 1 .7 1 .9 2.2 2.4 2.6 2.7 6.6 9. 1 12.6 16.1 19.1 21 .5 24.0 F i g u r e 6.14 E f f e c t of i n n e r and o u t e r gas v e l o c i t y on t h e c i r c u l a t i o n of PVC, medium i n v e n t o r y . ( F l u x i n kg/m 2s) cm/s U i , m/s 2.3 3.4 4.6 5.6 1 .4 2.3 4.2 6.6 6.8 1.7 5.5 6.3 9.1 11.9 1 .9 8.0 1 1 .2 12.6 15.3 2.2 9.2 13.4 16.1 19.1 2.4 1 1 .7 16.3 19.1 21 .8 2.6 12.8 17.2 21 .5 24.0 2.7 14.2 19.3 24.0 26.0 2.9 16.8 20.5 3.1 19.7 22.8 189 F i g u r e 6.15 E f f e c t of i n n e r gas v e l o c i t y and bed i n v e n t o r y on the c i r c u l a t i o n of PVC, U o=0.046 m/s, v e r t i c a l i n l e t . . ( F l u x i n kg/m 2s) Bed i n v e n t o r y U i , m/s low medium h i g h 1 .4 2.8 6.6 5.8 1 .7 4.7 9.1 10.8 1 .9 7.0 12.6 15.5 2.2 8.7 19.1 19.9 2.4 9.5 21 .5 23.8 2.6 24.0 23.8 2.7 11.8 30.0 F i g u r e 6.16 E f f e c t of i n n e r and o u t e r gas v e l o c i t y on the c i r c u l a t i o n of c r a c k i n g c a t a l y s t , medium i n v e n t o r y , v e r t i c a l i n l e t . ( F l u x i n kg/m 2s) U Q, cm/s U i , m/s 1 .3 2.3 3.4 4.6 5.6 1 .4 20.2 19.4 22.4 24.5 27.0 1.7 24.1 31.1 32.8 40.4 40.9 1 .9 25.7 35.8 38.0 44. 1 45.9 2.2 25. 1 39.0 42.2 48.2 2.4 26.5 190 F i g u r e 6.17 E f f e c t of i n n e r gas v e l o c i t y and bed i n v e n t o r y on the c i r c u l a t i o n of c r a c k i n g c a t a l y s t , U o=0.023 m/s, v e r t i c a l i n l e t . ( F l u x i n kg/m 2s) Bed i n v e n t o r y U i , m/s low med i um h i g h 1 .4 9.6 19.4 29.2 1.7 12.5 31.1 48.8 1.9 15.3 35.8 55. 1 2.2 14.8 39.0 57.2 2.4 14.2 2.6 15.8 F i g u r e 6.18 E f f e c t of bed i n v e n t o r y and i n n e r gas v e l o c i t y on t h e c i r c u l a t i o n of PVC ( C r o s s - p l o t of f i g . 6.15). F i g u r e 6.19 E f f e c t of o u t e r gas v e l o c i t y and bed i n v e n t o r y on t h e c i r c u l a t i o n of PVC, Ui= 2.4-m/s, v e r t i c a l i n l e t . ( F l u x i n kg/m 2s) Bed i n v e n t o r y U Q , cm/s low medium h i g h 2.3 11.7 18.8 3.4 7.6 16.3 20.2 4.6 9.5 19.1 23.8 5.6 10.4 21 .8 .25.1 191 F i g u r e 6.20 E f f e c t of bed i n v e n t o r y and i n n e r gas v e l o c i t y on the c i r c u l a t i o n of c r a c k i n g c a t a l y s t ( C r o s s - p l o t of f i g . 6.17) F i g u r e 6.21 E f f e c t of o u t e r v e l o c i t y and bed i n v e n t o r y on c i r c u l a t i o n of c r a c k i n g c a t a l y s t , Ui=1.7 m/s, v e r t i c a l i n l e t . ( F l u x i n kg/m 2s) Bed i n v e n t o r y U 0, cm/s low medium h i g h 1 .3 7.2 24. 1 29.2 2.3 12.5 31.1 48.8 3.4 18.0. 32.8 54.5 4.6 16.5 40.4 61 .3 5.6 17.0 40.9 63.4 F i g u r e 6.22 E f e c t -of o u t e r and i n n e r gas v e l o c i t y on t h e c i r c u l a t i o n of PVC ( C r o s s - p l o t of f i g . 6.14). F i g u r e 6.23 E f f e c t of o u t e r and i n n e r gas v e l o c i t y on t h e c i r c u l a t i o n of c r a c k i n g c a t a l y s t ( C r o s s - p l o t of f i g . 6.16) 192 F i g u r e 6.24 E f f e c t of h e i g h t of i n l e t above t h e d i s t r i b u t o r p l a t e on t h e c i r c u l a t i o n of PVC, h i g h i n v e n t o r y , U o=0.034 m/s, v e r t i c a l i n l e t . ( F l u x i n kg/m 2s) I n l e t l e v e l U i , m/s low m i d d l e h i g h 1 .4 11.6 5.8 1.7 19.2 10.8 10.6 1.9 22.1 15.5 15.2 2.2 27.0 19.9 1 9 .2 2.4 34.4 23.8 20.9 2.6 33.9 27.0 26.5 2.7 30.0 24.5 193 F i g u r e 7.2 T y p i c a l measured i n s e r t p r e s s u r e p r o f i l e f o r c r a c k i n g c a t a l y s t , h i g h i n v e n t o r y , U~i = 1.9 m/s, U o=0.046 m/s, t a n g e n t i a l i n l e t . H e i g h t P r e s s u r e (m) (kPa) 0.25 4.29 0.41 3.18 0.56 2.66 0.71 2.15 0.86 1 .63 1 .02 1 .29 1.17 1.12 1 .32 1 .03 1 .47 0.94 1 .63 0.89 F i g u r e 7.4 Voidage p r o f i l e f o r c r a c k i n g c a t a l y s t , Ui-1.7 m/s, U o=0.046 m/s, v e r t i c a l i n l e t . H e i g h t (m) Bed i n v e n t o r y low medium h i g h 0.33 .843 .791 .679 0.49 .963 .800 .825 0.64 .965 .854 .825 0.79 .965 .854 .825 0.94 .988 .933 .825 1.10 .988 .971 .825 1 .25 .988 .983 .941 1 .40 .982 .982 .971 1 .55 .988 .983 .971 1 94 F i g u r e 7.5 Voidage p r o f i l e f o r PVC, Uj=1.7 m/s, U o=0.046 m/s, v e r t i c a l i n l e t . H e i g h t (m) Bed i n v e n t o r y . low medium h i g h 0.33 .798 .662 .666 0.49 .807 .714 .709 0.64 .924 .833 .790 0.79 .985 .872 .833 0.94 .990 .943 .919 1.10 .990 .976 .929 1 .25 .991 .990 .957 1 .40 .995 .991 .995 1 .55 .995 .990 .995 F i g u r e 7.6 E f f e c t of i n n e r gas v e l o c i t y on v o i d a g e p r o f i l e f o r c r a c k i n g c a t a l y s t , h i g h i n v e n t o r y , U o=0.046 m/s, t a n g e n t i a l i n l e t . H e i g h t (m) U i , m/s 1 .4 1.7 1 .9 2.2 0.33 .533 .591 .621 .591 0.49 .766 .796 .825 .825 0.64 .825 .825 ..825 .854 0.79 .825 .843 .825 .883 0.94 .941 .854 .883 .913 1.10 .941 .960 .941 .914 1 .25 .971 .971 .971 .971 1 .40 .982 .971 .971 .995 1 .55 .983 .977 .982 .995 195 F i g u r e 7.7 E f f e c t of o u t e r gas v e l o c i t y on v o i d a g e p r o f i l e f o r c r a c k i n g c a t a l y s t , Ui=1.7 m/s, t a n g e n t i a l i n l e t . H e i g h t (m) 1.3 2.3 U Q , l l l / b 3.4 4.6 5.6 0.33 .650 .591 .591 .591 .591 0.49 .796 .796 .825 .796 .825 0.64 .883 .796 .825 .825 .825 0.79 .941 .883 .825 .843 .825 0.94 .942 .913 .861 .854 .883 1.10 .977 .959 .940 .960 .930 1 .25 .988 .971 .983 .971 .971 1 .40 .988 .988 .983 .971 .982 1 .55 .988 .988 .983 .977 .983 F i g u r e 7.8 E f f e c t of i n l e t c o n f i g u r a t i o n on v o i d a g e p r o f i l e f o r c r a c k i n g c a t a l y s t , h i g h i n v e n t o r y U*i = 1.9 m/s, U o=0.023 m/s. I n l e t H e i g h t (m) v e r t . t a n g . 0.33 .737 .591 0.49 .825 .825 0.64 .825 .825 0.79 .825 .898 0.94 .839 .913 1.10 .863 .956 ' 1 .25 .977 .959 1 .40 .977 .982 1 .55 .988 .983 196 F i g u r e 7.9 F i t of t h e s t a t i s t i c a l model f o r PVC, v e r t i c a l i n l e t . ( F l u x i n kg/m 2s) Obt. P r e d . Obt. P r e d . , Obt. P r e d . .8 2.2 11.2 8.7 19.9 21 .3 3.4 3.4 13.4 12.2 23.8 26.0 5.6 4.3 16.3 14.9 27.0 31 .2 6.8 6.0 1.7.2 17.8 30.0 34.0 7.6 7.4 19.3 19.4 9.0 8.7 9.0 9.6 20.5 22.9 13.1 13.5 2.8 2.7 22.8 26.6 17.4 17.4 4.7 4.2 6.6 5.4 21 .6 24.3 7.0 5.4 9.1 8.4 25. 1 29.7 8.7 7.5 12.6 10.8 31.1 35.6 9.5 9. 1 16.1 15.1 11.8 1 1.9 19.1 18.4 2.3 3.1 21 .5 22. 1 5.7 4.8 24.0 24.1 6.8 6.1 6.8 6.2 8.6 8.5 1 1 .9 9.6 10.4 10.4 15.3 12.4 12.0 13.6 19.1 17.3 2.7 3.7 21 .8 21 .0 5.1 5.8 24.0 25.2 8.5 7.5 26.0 27.5 10.3 10.4 5.5 4.7 11.0 12.7 8.1 7.3 12.1 15.2 12.1 9.4 6.4 4.9 15.4 13.1 8.4 7.6 18.8 16.0 11.2 9.8 20.3 19.2 13.4 13.7 23. 1 20.9 17.9 16.7 23.8 24.6 2.3 3.3 24.4 28.6 5.5 5.2 4.6 6.1 8.0 6.7 9.5 9.5 9.2 9.3 13.9 12.3 1 1 .7 11.3 17.3 17.2 12.8 13.6 20.2 20.9 14.2 14.8 25. 1 25. 1 16.8 17.4 27.7 27.4 19.7 20.3 5.8 7.6 4.2 4.4 10.8 1 1 .9 6.3 6.8 15.5 15.3 197 F i g u r e 7.10 F i t of t h e s t a t i s t i c a l model f o r PVC, t a n g e n t i a l i n l e t . ( F l u x i n kg/m 2s) Obt. P r e d . 1 .4 1 .7 3.0 2.9 5.3 3.8 6.6 5.6 7.9 7.1 8.7 8.7 9.5 9.6 2.3 2.2 3.5 3.7 6.9 5.0 8.4 7-3 9.3 9.2 10.8 11.3 12.5 12.5 14.2 15.1 2.1 3.2 4.5 5.4 8.1 7.2 9.6 10.5 11.9 13.2 15.1 16.3 17.4 18.0 4.2 3.2 4.7 5.3 6.0 7.1 7.0 10.5 7.7 13.2 4.2 4.1 8.1 6.9 12.6 9.2 14.7 13.6 16.9 17.1 5.2 6.0 9.4 9.9 17.2 13.3 23.9 19.6 28.2 24.6 198 F i g u r e 7.11 F i t of t h e s t a t i s t i c a l model f o r c r a c k i n g c a t a l y s t , v e r t i c a l , i n l e t . ( F l u x i n kg/m 2s) Obt. P r e d . Obt. P r e d . 7.2 6.7 40.4 38.1 7.2 8.2 44. 1 42.7 8.1 9.2 48.2 49.7 8.4 10.6 27.0 34.3 8.4 11.6 40.9 41.9 8.6 12.6 45.9 46.9 9.6 9.1 25.0 24.7 12.5 1 1.2 29.2 30. 1 15.3 12.5 35.7 33.8 14.8 14.6 38.2 39.3 14.2 15.9 29.2 33.8 15.8 17.3 48 .8 41.2 14.1 1 1 .1 55.1 46.3 18.0 13.6 57.2 53.8 18.7 15.2 28.4 41 .0 19.4 17.7 54.4 50.1 20.2 19.3 63. 1 56.2 1 1.9 13.0 63.4 65.3 16.5 15.8 41 .0 47.9 21 .3 17.8 61 .3 58.5 22.3 20.7 70. 1 65.5 21 .2 22.6 45.2 52.7 12.2 14.3 63.4 64.3 17.0 17.4 71.7 72. 1 21 .5 19.5 21.5 22.7 20.2 16.1 24.0 19.6 25.7 22.0 25. 1 25.6 26.5 28.0 19.4 22.0 31.1 26.9 35.8 30.1 39.0 35.0 22.4 26.7 32.8 32.6 38.0 36.6 42.2 42.5 24.5 31 .2 9 199 F i g u r e 7.12 F i t of t h e s t a t i s t i c a l model f o r c r a c k i n g c a t a l y s t , t a n g e n t i a l i n l e t . ( F l u x i n kg/m 2s) Obt. P r e d . Obt. P r e d . 3.3 3.6 36.2 33.1 3.9 4.5 40.0 37.5 4.3 5.1 42.0 44.2 5.0 6.0 24.8 18.9 5.3 6.6 29.9 23.5 5.6 7.2 31 .0 26.7 4.4 5.2 28.7 31.4 6.8 6.4 25.3 27.3 8.4 7.3 40.9 34.0 9.4 8.6 46.7 38.5 9.6 9.5 49.4 45.4 7.1 6.5 27.9 34.3 9.6 8.1 31.0 42.7 11.1 9.2 28.7 48.3 11.2 10.8 25.3 57.0 6.6 7.8 42.7 42.7 10.8 9.7 53.6 48.3 12.7 11.0 54.6 57.0 12.8 12.9 32.6 41.1 7.9 8.7 48.0 51.1 12.6 10.8 55.5 5.7.9 13..5 12.3 56.3 68.3 13.9 14.5 33.6 45.9 13.1 11.0 48.2 57. 1 14.0 13.6 59.3 64.7 13.9 15.4 63.2 76.3 12.1 18.2 15.2 15.8 23.5 19.7 27.7 22.3 31 .3 26.3 17.2 19.9 28.8 24.7 34.9 28.0 33.1 33.0 23.4 23.8 32.3 29.6 39.4 33.6 42. 1 39.6 23.5 26.6 200 F i g u r e 7.13 F i t . of t h e s t a t i s t i c a l model f o r PVC. ( F l u x i n kg/m 2s) Obt. P r e d . Obt. P r e d . Obt. P r e d . Obt. P r e d . .8 2.0 11.2 8.3 19.9 19.3 14.7 17.3 3.4 3.2 13.4 11.8 23.8 23.7 16.9 21 .2 5.6 4.1 16.3 14.4 27.0 28.6 5.2 7.2 6.8 5.9 17.2 17.5 30.0 31 .3 9.4 11.4 7.6 7.2 19.3 19.1 9.0 7.2 17.2 1 4.8 9.0 9.5 20.5 22.6 13.1 11.5 23.9 21 .0 2.8 2.3 22.8 26.5 17.4 14.9 28.2 25.8 4.7 3.7 6.6 4.7 21 .6 21.1 7.0 4.8 9.1 7.4 25. 1 26.0 8.7 6.8 12.6 9.7 31.1 31.4 9.5 8.4 16.1 13.7 1 .4 2.6 11.8 11.1 19.1 16.8 3.0 4.1 2.3 2.6 21 .5 20.3 5.3 5.3 5.7 4.1 24.0 22.3 6.6 7.5 6.8 5.3 6.8 5.2 7.9 9.2 8.6 7.5 1 1 .9 8.2 8.7 11.1 10.4 9.2 15.3 10.6 9.5 12.2 12.0 12.2 19.1 15.0 2.3 2.9 2.7 3.0 21.8 18.5 3.5 4.7 5.1 4.7 24.0 22.3 6.9 6.1 8.5 6.1 26.0 24.4 8.4 8.6 10.3 8.6 5.5 4.7 9.3 10.6 11.0 10.6 8.1 7.4 " 10.8 12.8 12.1 12.8 12.1 9.6 12.5 14.0 6.4 3.6 15.4 13.6 14.2 16.6 8.4 5.7 18.8 16.8 2.1 3.6 11.2 7.4 20.3 20.3 4.5 5.7 13.4 10.5 23. 1 22.2 8.1 7.4 17.9 12.9 23.8 26.2 9.6 10.5 2.3 3.3 24.4 30.7 1 1.9 12.9 5.5 5.3 4.6 5.7 15.1 15.6 8.0 6.9 9.5 9.0 17.4 17.0 9.2 9.7 13.9 1 1.7 4.2 5.2 1 1.7 1 1 .9 17.3 16.5 4.7 8.2 12.8 14.4 20.2 20.3 6.0 10.6 14.2 15.8 25. 1 24.5 7.0 15.0 16.8 18.7 27.7 26.8 7.7 18.5 19.7 21 .9 5.8 6.6 4.2 5.9 4.2 4.0 10.8 10.5 8.1 9.4 6.3 6.4 15.5 13.6 12.6 12.2 201 F i g u r e 7.14 F i t of t h e s t a t i s t i c a l model f o r c r a c k i n g c a t a l y s t . ( F l u x i n kg/m 2s) Obt. P r e d . Obt. P r e d . Obt. P r e d . Obt. P r e d . 7.2 4.9 40.4 33.6 10.8 12.5 48.0 54.4 7.2 6.1 44.1 38.0 12.7 14.2 55.5 61 .6 8.1 6.9 48.2 44.8 12.8 ' 16.7 56.3 72.7 8.4 8.2 27.0 29.9 7.9 11.1 33.6 48.4 8.4 9.0 40.9 37.2 12.6 13.8 48.2 60.2 8.6 9.8 45.9 42. 1 13.5 15.7 59.3 68.3 9.6 6.9 25.0 21.3 13.9 18.5 63.2 80.5 12.5 8.6 29.2 26.6 13.1 13.2 15.3 9.7 35.7 30. 1 14.0 16.4 14.8 1 1 .4 38.2 35.5 13.9 18.6 14.2 12.6 29.2 30.0 12.1 21 .9 15.8 13.8 48.8 37.3 15.2 18.5 14.1 8.5 55. 1 42.2 23.5 23.0 18.0 10.6 57.2 49.8 27.7 26. 1 18.7 12.0 28.4 37.0 31 .3 30.7 19.4 14.1 54.5 46.0 17.2 22.8 20.2 15.6 63. 1 52. 1 28.8 28.4 1 1 .9 10.0 63.4 61.5 34.9 32.2 16.5 12.5 41 .0 43.7 33. 1 37.9 21 .3 14.2 61 .3 54.4 23.4 27.0 22.3 16.7 70. 1 61 .6 32.3 33.6 21 .2 18.4 45.2 48.4 39.4 38.0 12.2 11.1 63.4 60.2 42. 1 44.8 17.0 13.8 71 .7 68.3 23.5 29.9 21 .5 15.7 3.3 4.9 36.2 37.2 21 .5 18.5 3.9 6. 1 40.0 42. 1 20.2 13.2 4.3 6.9 42.0 49.7 24.0 16.4 5.0 8.2 24.8 21 .3 25.7 18.6 5.3 9.0 29.9 26.6 25. 1 21 .9 5.6 9.8 31 .0 30. 1 26.5 24. 1 4.4 6.9 28.7 35.5 19.4 18.5 6.8 8.6 25.3 30.0 31 . 1 23.0 8.4 9.7 40.9 37.3 35.8 26.1 9.4 11.4 46.7 42.2 39.0 30.7 9.6 12.6 49.4 49.8 22.4 22.8 7.1 8.5 27.9 37.0 32.8 28.4 9.6 10.6 42.7 46.0 38.0 32.2 11.1 12.0 53.6 52. 1 42.2 37.9 11.2 14. 1 54.6 61 .5 24.5 27.0 6.6 10.0 32.6 43.7 202 F i g u r e 7.15 F i t of the s t a t i s t i c a l model f o r t h e e n t i r e d a t a s e t . ( F l u x i n kg/m 2s) PVC Obt. P r e d . Obt. P r e d . Obt. P r e d . Obt. P r e d . .8 2.1 11.2 8.85 19.9 21 .5 14.7 18.3 3.4 3.0 13.4 1 1.7 23.8 25.4 16.9 21 .6 5.6 3.6 16.3 13.7 27.0 29.5 5.2 9.9 6.8 4.8 17.2 16.0 30.0 31 .6 9.4 14.2 7.6 5.7 19.3 17.1 9.0 10.3 17.2 17.5 9.0 7.1 20.5 19.6 13.1 14.8 23.9 23.0 2.8 2.5 22.8 22.2 17.4 18.2 28.2 27. 1 4.7 3.5 6.6 6.0 21.6 24.0 7.0 4.4 9.1 8.6 25.1 28.3 8.7 5.7 12.6 10.6 31.1 32.9 9.5 6.8 16.1 13.9 1 .4 2.7 1 1 .8 8.4 19.1 16.4 3.0 3.9 2.3 2.7 21 .5 19.1 5.3 4.9 5.7 3.9 24.0 20.5 6.6 6.4 6.8 4,9 6.8 6.7 7.9 7.5 8.6 6.4 1 1 .9 9.6 8.7 8.8 10.4 7.5 15.3 11.8 9.5 9.4 12.0 9.4 19.1 15.6 2.3 3.2 2.7 3.2 21 .8 18.3 3.5 4.6 5.1 4.7 24.0 21 .3 16,9 5.7 8.5 5.7 26.0 22.9 8.4 7.5 10.3 7.5 5.5 6.1 9.3 8.9 11.0 8.9 8.1 8.9 10.8 10.3 12.1 10.3 12.1 10.9 12.5 11.1 6.4 4.1 15.4 1 4.4 14.2 12.7 8.4 5.8 18.8 16.9 2.1 4. 1 11.2 7.2 20.3 19.7 4.5 5.8 13.4 9.5 23.1 21.1 8.1 7.2 17.9 11.2 23.8 24. 1 9.6 9.5 2.3 4.0 24.4 27.4 1 1.9 1 1 .2 5.5 5.7 4.6 7.7 15.1 13.0 8.0 7. 1 9.5 11.1 17.4 13.9 9.2 9.3 13.9 13.7 4.2 6.7 11.7 11.0 17.3 18.0 4.7 9.6 12.8 12.7 20.2 21 .2 6.0 11.8 14.2 13.7 25. 1 24.6 7.0 15.6 16.8 15.6 27.7 26.4 7.7 18.3 19.7 17.7 5.8 . 9.2 4.2 7.8 4.2 5.0 10.8 13.3 8.1 11.3 6.3 7.2 15.5 16.3 12.6 13.9 203 C r a c k i n g c a t a l y s t Obt. P r e d . Obt. P r e d . 7.2 4.2 40.4 31 .8 7.22 6.1 44.1 39.2 8.1 7.5 48.2 51 .6 8.4 9.9 27.0 24.6 8.4 11.6 40.9 35.5 8.6 13.5 45.9 43.7 9.6 6.1 25.0 15.8 12.5 8.7 29.2 22.8 15.3 10.8 35.7 28.1 14.8 14.2 38.8 37.0 14.2 16.7 29.2 22.7 15.8 19.4 48.8 32.7 14.1 7.6 55.1 40.4 18.0 10.9 57.2 53. 1 18.7 13.5 28.4 28.5 19.4 17.8 54.5 41 . 0 20.2 20.9 63.1 50.5 1 1.9 9.1 63.4 66.6 16.5 13.1 41 .0 34. 1 21 .3 16.1 61 .3 49. 1 22.3 21 .2 70.1 60.5 21 .2 25.0 45.2 38.0 12.2 10.1 63.4 54.8 17.0 14.6 71.7 67.5 21 .5 18.0 3.3 4.2 21 .5 23.7 3.9 6.1 20.2 10.2 4.3 7.5 24.0 14.8 5.0 9.9 25.7 18.2 5.3 11.6 25. 1 23.9 5.6 13.5 26.5 28.2 4.4 6.1 19.4 14.7 6.8 8.7 31.1 21 .2 8.4 10.8 35.8 26. 1 9.4 14.2 39.0 34.4 9.6 16.7 22.4 18.5 7.1 7.6 32.8 26.6 9.6 10.9 38.0 32.7 11.1 13.5 42.2 43. 1 1 1 .2 17.8 24.5 22. 1 6.6 9.1 Obt. P r e d . Obt. P r e d . 10.8 13.1 48.0 49.1 12.7 16.1 55.5 60.5 12.8 21 .2 56.3 79.7 7.9 10.1 33.6 38.0 12.6 14.6 48.2 54.8 13.5 18.0 59.3 67.5 13.9 23.7 63.2 88.9 13.1 10.2 14.0 14.8 13.9 18.2 12.1 23.9 15.2 14.7 23.5 21 .2 27.7 26. 1 31.3 34.4 17.2 18.5 28.8 26.6 34.9 32.7 33.1 43.1 23.4 22.1 32.3 31 .8 39.4 39.2 42.1 51 .6 23.5 24.6 36.2 35.5 40.0 43.7 42.0 57.6 24.8 15.8 29.9 22.8 31.0 28. 1 28.7 36.9 25.3 22.7 40.9 32.7 46.7 40.4 49.4 53. 1 27.9 28.5 42.7 41 .0 53.6 50.5 54.6 66.6 32.6 34. 1 204 F i g u r e 7.18 Mass s o l i d s l o a d i n g r a t i o as a f u n c t i o n of i n n e r and o u t e r gas v e l o c i t y f o r c r a c k i n g c a t a l y s t , h i g h i n v e n t o r y , v e r t i c a l i n l e t . U i , m/s U 0, cm/s 1 .3 2.3 3.4 4.6 5.6 1 .4 15.3 17.9 17.5 25.2 27.7 1.7 14.7 24.7 27.6 31.0 32.0 1 .9 16.1 24.9 28.5 31 .7 32.4 2.2 14.9 22.3 24.7 APPENDIX E CONTRIBUTIONS TO PRESSURE DROP 2 0 5 206 C o n t r i b u t i o n s t o p r e s s u r e drop i n i n s e r t f o r c r a c k i n g c a t a l y s t , U\ = 1.9 m/s, U Q=0.046 m/s, h i g h i n v e n t o r y , t a n g e n t i a l i n l e t . D = 0 . 0 8 8 9 m U g = 1 .9 m/s p = 1 . 1 6 4 kg/m 3 M = 1 . 8 2 4 x 1 0 - 5 kg/ms d = 40 x 1 0 - 6 m P p = 2000 kg/m 3 Re = pDUg/M = 10779 U t = 9 " < P p - P g ) d p 2 / l 8 , i = 0 . 1 0 m/s V g = U g - U t = 1 .8 m/s f g = 0 . 0 9 7 1 / R e ' 2 5 = 0 . 0 0 9 5 f s = 0 . 0 2 8 5 / ( V s / ( g D ) * 5 ) = 0 . 0 1 4 8 ( A P / L ) , . = 2 f p V 2/D = f n c g g^g g ' 0 . 0 0 8 9 8 kPa/m ( A P / L ) g r a v g = 1 . l 6 4 e g = 1 1 . 4 2 0 7 e Pa/m ( A P / L ) f r i c s " 2 f s ° " e ) » s V s2 / D = 2 1 5 8 ( 1 - e) Pa/m ( A P / L ) g r a v s = 2 0 0 0 ( l - e ) g = 1 9 6 0 0 ( 1 - e) Pa/m ( A P / L ) t o t a l = 2 1 6 4 6 . 5 7 9 e + 2 1 7 5 8 . 0 0 9 Pa/m ( A P / L ) m e a s " ( 1 ' 0 3 0 " « 8 9 2 ) kPa / 0 . 3 0 m = 0 . 4 6 kPa/m e = (21758.009 - 460) / 21746.579 = 0.979 I f e i s o b t a i n e d n e g l e c t i n g f r i c t i o n l o s s e s : ( 1 - e ) p p g = 460 Pa/m ( 1 - e) = .023 e = 0.977 A P P E N D I X F V O I D A G E P R O F I L E S Table FI Voidage p r o f i l e f o r PVC, low Inventory, v e r t l c a Pos. m/s 1.7 U 0, cm/s 3.4 1 .7 4.6 1 .7 5.6 1 .7 7.3 1 .7 10.8 1- 2 2- 3 3- 4 4- 5 5- 6 6- 7 7- 8 8- 9 9- 10 .833 .924 .995 .990 .990 .990 .995 .995 .995 . 798 .807 .924 .985 .990 .990 .991 .995 .995 .791 .819 .948 .990 .990 .990 .990 .990 .995 .628 .790 .883 .990 .990 .990 .990 .995 .995 .774 .791 .895 .945 .981 .990 .990 .990 .990 l e t . 1.9 4.6 .747 .845 .948 .948 .985 .985 .990 .990 .995 1.9 7.3 .676 .826 .860 .981 .990 .990 .990 .990 .990 2.2 4.6 .624 .855 .945 .988 .985 .985 .990 .990 .995 2.2 5.6 .672 .831 .945 .985 .986 .990 .990 .990 .995 2 . 2 7.3 .750 .895 .883 .981 .990 .986 .990 .990 .995 2 . 2 10.8 .672 .833 .916 .933 .990 .990 .990 .995 .990 Table F2 Voidage p r o f i l e f o r PVC, medium Inventory, v e r t i c a l I n l e t . Pos. m/s 1 .4 1 .7 1 .7 1 .7 1 .7 1 .9 2.2 2.2 2.2 2.2 2.4 2.6 Uo- cm/s 4.6 2.3 3.4 4.6 5.6 4.6 2.3 3.4 4.6 5.6 4.6 5.6 1-2 . 705 .671 .666 .662 .669 .690 .728 . 709 .647 .688 . 623 . 628 2-3 .714 .743 .791 .714 .812 . 747 .857 .790 . 766 .812 .857 . 791 3-4 .833 .929 .805 .833 .833 .795 .943 .876 .833 .836 .833 .864 4-5 .848 .966 .929 .872 .791 .938 .971 .938 .900 .826 .914 .914 5-6 .905 .986 .976 .943 .916 .'914 .990 .990 .971 .943 .952 .943 6-7 .976 .990 .990 .976 .979 .981 .990 .990 .986 .981 .981 .990 7-8 .990 .990 .990 .990 .995 .995 .995 .990 .990 .990 .990 .990 8-9 .995 .990 .990 .991 .990 .990 .990 .990 .990 .986 .986 .990 9-10 .990 .995 .995 .990 .990 .990 .990 .990 .990 .990 .990 .995 Table F3 Voidage p r o f i l e f o r PVC, high Inventory, v e r t i c a l I n l e t . low Inlet middle Inlet Pos. U,, m/s 2.2 2.2 2.2 1.7 2.2 2.2 U Q, cm/s 3.4 4.6 5.6 4.6 3.4 4.6 1- 2 .731 .731 .707 .666 .639 .667 2- 3 .791 .790 .833 .709 .777 .752 3- 4 .793 .833 .790 .790 .757 .790 4- 5 .812 .790 .814 .833 .869 .833 5- 6 .895 .833 .833 .919 .916 .914 6- 7 .896 .902 .893 .929 .926 .962 7- 8 .974 .967 .916 .957 .981 .966 8- 9 .981 .981 .986 .995 .986 .995 9- 10 .986 .986 .990 .995 .990 .996 high I n l e t .7 2.2 2.2 .6 2.3 3.4 709 .688 .669 791 .752 .791 833 .881 .812 876 .936 .897 871 .993 .935 962 .990 .974 985 .981 .979 984 .993 .976 987 .993 1.00 Table F4 Voidage p r o f i l e f o r PVC, low Inventory, tangential Inlet Pos. U,, m/s U 0, cm/s 1.7 5.6 1.7 7.3 1 .7 10.8 1 .9 7.3 2 . 2 5.6 2 . 2 7 . 3 1- 2 2- 3 3- 4 4- 5 5- 6 6- 7 7- 8 8- 9 9- 10 .705 .781 .936 .995 .990 1 .00 .991 .990 .990 .672 .721 .938 .981 .991 .995 1 .00 .990 .991 .747 .688 .917 .955 .981 .986 1 .00 .990 1 .00 . 752 .855 .959 .986 .990 1 .00 1 .00 1 .00 .991 .667 .876 .981 .985 .991 .995 .990 1 .OO .995 .833 .874 .876 .960 .981 .990 .995 .991 1 .00 2.2 10.8 ,.790 . 793 .874 .957 .986 .990 .991 1 .00 .995 2.4 7 . 3 . 790 .812 .921 .919 .990 .986 .990 .991 .995 2.7 7.3 . 785 .855 .855 .981 .990 1 .00 .991 .990 .990 Table F5 Voidage p r o f i l e f o r PVC, medium inventory, tangential i n l e t . Pos. , m/s U 0, cm/s 1.4 7.3 1 . 7 5.6 1 .7 7.3 1 .7 10.8 1 .9 7.3 2.2 5.6 2.2 7.3 2.2 10.8 2.4 7.3 1- 2 2- 3 3- 4 4- 5 5- 6 6- 7 7- 8 8- 9 9- 10 .667 . 750 .793 .900 .990 .990 .991 .990 .990 .662 .709 .874 .833 .943 .995 .995 .995 .995 .662 .752 .811 .907 .945 .990 .995 1 .00 .990 .576 .774 . 790 .855 .933 .965 .995 .990 .990 .752 .792 .791 .852 .966 .990 .983 .990 .990 . 747 .833 .874 .966 .990 .986 .990 1 .00 .990 .624 .708 .904 .928 .936 .971 .995 1 .00 .991 . 752 . 792 .831 .831 .869 .904 .986 .990 .990 .581 .767 . 773 .895 .972 .981 .995 1 .00 .990 Table F6 Voidage p r o f i l e f o r cracking c a t a l y s t , low inventory, v e r t i c a l Inlet Pos. Uj, m/s 1 .4 1 .4 1 . 7 1 . 7 1 .7 u o . 4.6 5.6 1.3 2.3 3.4 cm/s 1-2 .843 .843 .947 .772 .767 2-3 .953 .953 .977 .977 .959 3-4 .977 .977 .988 .977 .971 4-5 .977 . 977 .988 .982 .982 5-6 .988 .988 .983 .988 .988 6-7 .988 .988 .994 .983 .988 7-8 .988 .988 .994 .988 .994 8-9 .988 .994 .994 .994 .994 9- 10 .988 .988 .994 .994 .994 . 7 1 . 7 1 .9 1 .9 2.2 2.4 2.4 2.4 .6 5.6 4.6 5.6 4.6 1 .3 2.3 3.4 843 . 796 .348 .381 .883 .936 . 901 . 883 963 .959 .953 .971 .971 .977 .971 .971 965 .983 .983 .977 .971 .982 .983 ..971 988 .982 .982 .983 .982 .982 .982 .988 988 .983 .988 .982 .988 .994 .982 .988 988 .994 .982 .994 .994 .994 .982 .994 988 .994 .982 .982 .994 .994 .994 .994 982 .994 .982 .982 .982 .994 .994 . 994 988 .994 .982 .982 .982 .994 .982 .994 Table F7 Voidage p r o f i l e for cracking c a t a l y s t , medium Inventory, v e r t i c a l I n l e t Pos . 1- 2 2- 3 3- 4 4- 5 5- 6 6- 7 7- 8 8- 9 9- 10 U 4. m/s 1.4 U 0, cm/s 4.6 .708 .819 .831 .948 .971 .977 .983 .988 .988 1 .4 5.6 .650 .737 .930 .977 .953 .982 .983 .988 .988 1 .7 1.3 . 787 .839 .941 .971 .971 .983 .982 .988 .988 1 . 7 2.3 .708 .825 .854 .942 .959 .977 .977 .988 .983 1 .7 3.4 . 737 .825 .913 .941' .953 .977 .977 .982 .982 1 .7 4.6 . 791 .800 .854 .933 .965 .971 .983 .982 .983 1 .7 5.6 .766 .796 .854 .942 .971 .971 .977 .988 .988 1 .9 3.4 . 767 .825 .913 .941 .953 .977 .983 .988 .988 1 .9 4.6 . 755 .837 .871 .942 .959 .969 .983 .983 .986 2 . 2 2.3 . 752 .854 .883 .930 .977 .977 .982 .983 .982 2.4 1 .3 .825 .913 .959 .977 .977 .982 .988 .988 .982 Table F8 Voidage p r o f i l e for cracking c a t a l y s t , high inventory, v e r t i c a l i n l e t . Pos. U j , m/s 1.4. U 0, cm/s 3.4 1- 2 .679 2- 3 .767 3- 4 .761 4- 5 .796 5- 6 .825 6- 7 .913 7- 8 .971 8- 9 .982 9- 10 .988 1.4 1.4 1.7 4.6 5.6 1.3 .708 .650 .796 .708 .767 .796 .736 .795 .869 .825 .796 .912 .869 .854 .927 .869 .854 .971 .965 .942 .971 .977 .982 .988 .982 .983 .983 1.7 1.7 1.7 2.3 3.4 4.6 .752 .679 .679 .767 7 9 6 8 2 5 .781 .825 .825 .796 .825 .825 .854 .825 .825 .883 .854 .825 .971 .953 .941 .983 .977 .971 .988 .982 .971 1.7 1.9 2.2 5.6 2.3 1.3 .650 .737 .796 .796 .825 .854 .825 .825 .854 .825 .825 .924 .825 .839 .971 .854 .863 .977 .941 .977 .988 .971 .977 .988 .977 .988 .988 to Table F9 Voidage prof 11e for cracking c a t a l y s t , , 1 ow i nventory, tangent i a l i n l e t . Pos. U,, m/s 1 . 7 1 .7 1 .7 1.7 1 .7 1 .9 2.2 2 . 2 2.2 2.2 2.2 cm/s 1 .3 2.3 3 4 4.6 5.6 4.6 1 . 3 2 . 3 3.4 4.6 5.6 1-2 .796 .796 .778 .796 .801 .802 .895 .825 .808 .837 .819 2-3 .873 .971 .959 .965 .965 .965 .982 .953 .965 .971 .947 3-4 .994 .988 .988 .971 .971 .982 .994 .982 .977 .982 .988 4-5 .994 .994 .988 .982 .988 .988 .994 .994 .988 .988 .988 5-6 .994 .994 .994 .994 .988 .988 .994 .994 .982 .994 .988 6-7 1 .00 .994 .994 .994 .994 .988 1 .00 .994 .994 .994 .988 7-8 1 .00 .994 .994 .994 .994 .994 .994 .994 .994 .994 .988 8-9 .994 .994 .994 .994 .994 .994 1 . O O .994 .994 .994 .988 9- 10 .994 .994 .994 .994 .994 .994 1 .00 1 .00 .994 .994 .994 t o Table F10 Voidage prof 1le fo r cracking cata1yst , medium Inventory, tangential I n l e t . Pos. U 4, m/s 1.4 1 .7 1 . 7 1.7 1 .7 1 .7 1 .9 1 .9 2.2 2.2 2.2 2 . 2 uo- cm/s 4.6 1 .3 2.3 3.4 4.6 5.6 4.6 5.6 1 .3 2.3 3.4 4.6 1-2 .621 .679 .796 .621 .562 .620 .62 1 . 708 . 737 .681 .681 .650 2-3 .825 .936 .825 .825 .854 .839 .848 .825 .870 .855 .825 .837 3-4 .825 .947 .878 .807 .854 .839 .854 .866 .953 .942 .855 .953 4-5 .930 .983 .959 .954 .924 .930 .947 .948 .982 .942 .924 .953 5-6 .965 .982 .977 .982 .959 .971 .971 .959 .983 .977 .965 .977 6-7 .971 .983 .982 .983 .965 .977 .972 .977 .988 .977 .982 .977 7-8 .988 .988 .983 .982 .988 .983 .983 .983 .994 .982 .983 .982 8-9 .988 .982 .982 .988 .988 .982 .982 .982 .994 .988 .982 .982 9-10 .988 .994 .988 .988 .988 .983 .982 .983 .994 .988 .988 .983 Table F11 Voidage prof 11e for cracking c a t a l y s t . high 1nventory, tangential Inlet Pos. U,, m/s 1.4 1 .7 1 .7 1.7 1 .7 1.7 1 .9 1 .9 1 .9 1 .9 1 .9 2.2 uo- cm/s 4.6 1 .3 2.3 3.4 4.6 5.6 1 .3 2.3 3.4 4.6 5.6 4.6 1-2 .533 .650 .591 .591 .591 .591 .591 . 591 .620 .621 . 591 . 591 2-3 .766 .796 .796 .825 .796 .825 .883 .825 .796 .825 .796 .825 3-4 .825 .883 .796 .825 .825 .825 .918 .825 .854 .825 .837 .854 4-5 .825 .941 .883 .825 .843 .825 .971 .898 .854 .825 .854 .883 5-6 .941 .942 .913 .861 .854 .883 .971 .913 .883 .883 .883 .913 6-7 .941 .977 .959 .940 .960 .930 .983 .956 .959 .941 .953 .914 7-8 .971 .988 .971 .983 .971 .971 .982 .959 .965 .971 .971 .971 8-9 .982 .988 .988 .983 .971 .982 .983 .982 .977 .971 . 982 1 .00 9- IO .983 .988 .988 .983 .977 .983 .988 .983 .983 .982 . 983 1 .00 APPENDIX G STATISTICAL PROCEDURE 219 1 220 S t a t i s t i c a l r e g r e s s i o n a n a l y s i s was performed to determine the impact of each v a r i a b l e on s o l i d s c i r c u l a t i o n and on each o t h e r . The a n a l y s i s was performed with the s t a t i s t i c a l package 'MIDAS', developped at the U n i v e r s i t y of Michigan, and a v a i l a b l e on the UBC computer system. M u l t i p l e l i n e a r r e g r e s s i o n a n a l y s i s i s used to estimate the c o n s t a n t s (by l e a s t squares method) i n a l i n e a r model. Si n c e the model sought: G c = C U, a U * I 7 A r 5 S 1 o i s " not l i n e a r with r e s p e c t to the c o n s t a n t s , i t must be transformed to a l i n e a r model by t a k i n g l o g a r i t h m s on both s i d e s : lnG„ = InC + alnU. + /31nU + -ylnl + S l n A r . s 1 o T a b l e s G1 to G7 show the a n a l y s i s of v a r i a n c e f o r the seven cases i n v e s t i g a t e d . The a b b r e v i a t i o n s used i n these t a b l e s are d e f i n e d i n t a b l e G8. 221 Table G1 A n a l y s i s of v a r i a n c e f o r PVC, v e r t i c a l i n l e t . Source DF SS MS S i g R e g r e s s i o n 3 E r r o r 86 T o t a l 89 38.509 2.622 41.131 12.836 0.031 421 .0 .000 R = 0.968 SE=.175 V a r i a b l e k Coef f SE S i g Constant InUi l n U G l n l .950 .827 .909 0.57 2.28 0.71 1 .45 099 080 052 072 5.77 28.33 13.64 20.20 .000 .000 .000 .000 Table G2 Source A n a l y s i s of v a r i a n c e f o r PVC, t a n g e n t i a l i n l e t , DF SS MS S i g R e g r e s s i o n 3 E r r o r 33 T o t a l 36 14.930 1 .422 16.352 4.977 0.043 115.5 .000 R = 0.956 SE=.208 V a r i a b l e k Coeff SE S i g Constant InUi l n U 0 l n l .944 .791 .833 -.68 2.63 0.94 1 .28 .297 .160 .127 .148 -2.31 16.45 7.42 8'. 63 .028 .000 .000 .000 222 Table G3 Analysis of variance for CC, v e r t i c a l i n l e t . Source DF SS MS F Sig Regression 3 Error 60 Total 63 22.636 1 .351 23.987 7.546 0.023 335. 1 .000 R = 0.971 SE=. 150 Variable k Coeff SE Sig Constant InUi l n U 0 l n l .782 .879 .966 3.24 1 .03 0.51 1 .82 .083 .106 .036 .063 38.89 9.73 14.29 28.82 .000 .000 .000 .000 Table G4 Analysis of variance for CC, tangential i n l e t . Source DF SS MS F Sig Regression 3 Error 59 Total 62 39.499 1 .484 40.983 13.166 0.025 523.4 000 R = 0.982 SE=.159 Variable k Coeff SE Sig Constant InUi l n U Q l n l .786 .901 .977 3.06 1.12 0.60 2.31 .092 .115 .037 .066 33.28 9.76 16.00 34.93 .000 .000 .000 .000 223 Table G5 A n a l y s i s of v a r i a n c e f o r PVC. Source DF SS MS F S i g Regr e s s i o n 3 53.487 17.829 287.3 .000 E r r o r 123 7.634 0.062 T o t a l 126 61.121 R = 0.935 SE=.249 V a r i a b l e k Coeff SE t S i g Constant .71 .117 6.11 .000 InUi .910 2.37 .097 24.36 .000 l n U 0 .630 0.50 .056 9.00 .000 l n l .832 1.44 .087 16.65 .000 Table G6 A n a l y s i s of v a r i a n c e f o r CC. Source DF SS MS F S i g Regr e s s i o n 3 60.044 20.015 334.9 .000 E r r o r 123 7.350 0.060 T o t a l 126 67.394 R = 0.944 SE=.244 V a r i a b l e k C o e f f SE t S i g Constant 3.11 .098 31.84 .000 InUi .636 1.12 .123 9.14 .000 l n U Q .773 0.55 .041 13.52 .000 l n l .931 2.04 .072 28.35 .000 224 Table G7 A n a l y s i s of v a r i a n c e f o r a l l . Source DF SS MS F S i g R e g r e s s i o n 4 146.14 36.536 430 .7 .000 E r r o r 249 21.123 0.085 T o t a l 253 167'. 27 R = 0.935 SE=.291 -V a r i a b l e k Coef f SE t S i g Constant 3.78 .081 46. 71 .000 InUi .799 1 .88 .090 20. 97 .000 l n U Q .704 .59 .038 15. 63 .000 l n l .882 1 .84 .062 29. 47 .000 InAr -.881 -.86 .029 -29. 45 .000 Table G8 A b b r e v i a t i o n s . DF Degrees of freedom SS Sum of squares MS Mean square value (SS/DF) F F - s t a t i s t i c (MSR/MSE) R M u l t i p l e c o r r e l a t i o n c o e f f i c i e n t (R 2=SSR/SST) coef C o e f f i c i e n t of v a r i a b l e i n l i n e a r model SE Standard e r r o r k P a r t i a l c o r r e l a t i o n c o e f f i c i e n t t t - s t a t i s t i c ( c o e f f i c i e n t / S E ) s i g S i g n i f i c a n c e l e v e l APPENDIX H ERROR ANALYSIS 225 1. S o l i d s c i r c u l a t i o n f l u x . T a b l e H1 r e p o r t s the ex p e r i m e n t a l data used to determine the c i r c u l a t i o n f l u x f o r a hig h i n v e n t o r y of c r a c k i n g c a t a l y s t , v e r t i c a l i n l e t , U^ = 1.7 m/s, D*0= 0.023 m/s. The average f l u x i s 48.8 kg/m 2s and the standard d e v i a t i o n i s 1.9. The outer bed d e n s i t y was measured to be 850 kg/m3 ( i . e . a p r e s s u r e drop of 7.4 cm of o i l between p o s i t i o n s 11 and 12, as shown on f i g u r e 5.2). The r e p r o d u c i b i l i t y of the r a t e of s o l i d s accumulation measurements i s ve r y good; however the a c c u r a c y of the c i r c u l a t i o n f l u x a l s o depends on t h e accurac y of the bed d e n s i t y v a l u e . 2. P r e s s u r e p r o f i l e . T a b l e H2 i l l u s t r a t e s the r e p r o d u c i b i l i t y of the p r e s s u r e measurements by r e p o r t i n g 3 e x p e r i m e n t a l l y determined p r e s s u r e p r o f i l e s and the c o r r e s p o n d i n g c a l c u l a t e d voidage p r o f i l e s f o r a h i g h i n v e n t o r y of c r a c k i n g c a t a l y s t , v e r t i c a l i n l e t , 0^=1.7 m/s, U Q=0.023 m/s. The main source of e r r o r i n measuring the p r e s s u r e l i e s i n de t e r m i n i n g the average p r e s s u r e when the p r e s s u r e f l u c t u a t e s ( p o s i t i o n s 1 to 5 ) . 227 Table H1 E x p e r i m e n t a l d e t e r m i n a t i o n of the c i r c u l a t i o n f l u x . Time f o r a h e i g h t of 0.15 m C i r c u l a t i o n f l u x , kg/m 2s of s o l i d s to accumulate on c l o s e d v a l v e , sec 8.30 51.289 9.13 46.626 8.50 50.082 8.87 47.990 8.86 48.047 Table H2 R e p r o d u c i b i l i t y of the pressure and voidage p r o f i l e s determination. 1 2 3 P o s t 2 3 Average P, cm o i l P, cm o i l P, cm o i l t t t t 1 24.0-26.0 24.0-26 20.0-22 .0 24 O-26-O 1-2 .755 .767 .755 .759 2 19.5-22.O O 19 .5-22.0 2-3 . 767 . 767 . 767 . 767 3 15.5-1B.0 16.0-18 .0 15 .6-18.0 3-4 .778 .767 .778 .774 4 12.5-13.5 12.5-13 .5 12 .5-13.5 4-5 . 796 .796 . 796 .796 5 9.3- 9 7 9.5 9.5 5-6 .854 .854 .854 .854 6 7.0 7.0 7.0 6-7 .883 .883 .877 .881 7 5.0 5.0 4.9 7-8 .971 .971 .971 .971 8 4.5 4.5 4.4 8-9 .983 .988 .988 .986 9 4.2 4.3 4.2 9- 10 .988 .988 .988 . 988 10 4.0 4.1 4.0 

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