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LIBRARY
Michigan State
University

 

 

 

This is to certify that the

thesis entitled

COMBUSTION AND MASS TRANSFER CHARACTERISTICS OF
LARGE CARBON PARTICLES IN THE GRID REGION
OF A FLUIDIZED BED COMBUSTOR

presented by

Alexander Seung Choi

has been accepted towards fulfillment
of the requirements for

Ph.D. Jag-ecu. Chemical Engineering

 

 

Date ApriT 14L1988

0—7 539

 

 

 

 

PVTESI_J RETURNING MATERIALS:
Place in book drop to
“saunas remove this checkout from

Ali-zSIIIL. your record. FINES will
be charged if book is

 

 

returned after the date
stamped below.

 

 

 

 

 

COMBUSTION AND MASS TRANSFER CHARACTERISTICS
OF LARGE CARBON PARTICLES IN THE GRID REGION

OF A FLUIDIZED BED COMBUSTOR

By

Alexander Seung Choi

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemical Engineering

1988

ABSTRACT

COMBUSTION AND MASS TRANSFER CHARACTERISTICS
OF LARGE CARBON PARTICLES IN THE GRID REGION

OF A FLUIDIZED BED COMBUSTOR

By

Alexander Seung Choi

A fluidized bed coal combustor is a diluted system in which each
burning coal particle is surrounded by many inert bed particles due to
its low concentration in the bed. These inert particles present a
major resistance to oxygen transfer. Most studies on mass transfer
have been for the bubbling region; this study characterizes combustion
and mass transfer phenomena in the grid region near the multi-orifice
gas distrubutor where the gas and solids contacting is more efficient.

Single particle experiments measure the combustion rates of large
electrode graphite spheres fixed at various positions within the grid
region. The results show that the relative importance between mass
transfer and chemical kinetics in the overall combustion depend
strongly on all operating variables considered such as inert particle
size, superficial gas velocity and, most importantly, particle

position. Inert particle size is found to determine the rate of gas

leakage into the dense phase as well as the voidage distribution in the
dilute phase.

Based on the new definition of the grid region height determined
from the reaction point of view, the experimental results are analyzed
in light of theories for spouted beds and two-phase flows, and mass
transfer correlations are proposed for oxygen transfer in the grid
region. The results of theoretical analyses further suggest that
a different description of the overall combustion phenomena is needed
in the grid region. This description could be combined with some of
the bubbling bed models for better prediction of the overall bed

performance.

Copyright

by

Alexander Seung Choi

1988

To my parents

Howard C. and.Hye Ran Choi

ACKNOWLEDGEMENTS

I would like to express my deep gratitude to my academic advisor,
Professor Martin C. Hawley, for his insight, encouragement, and
financial support. I would also like to thank Dr. Anderson for his
continued support throughout my stay at Michigan State. Many thanks
are due to Dr. Petty, Dr. Jayaraman, Dr. Miller and Dr. Yen for their
helpful suggestions. I greatly appreciate the dedicated effort and
patience of Dr. Hye Kyung Kim for typing this manuscript. Finally,

I am greatly indebted to my family: without their help and support,

I would not have been able to finish my education.

vi

TABLE OF CONTENTS

List of Tables
List of Figures

Symbols

CHAPTER 1:

1-3.

CHAPTER 2:

MN
I
NH

nae
I I
kw»

MN
I
0“.”

CHAPTER 3:

3-3.

GRID REGION PHENOMENA IN A FLUIDIZED BED AND
OBJECTIVES OF THE RESEARCH.

Introduction

Review of Grid Region Phenomena

1-2-1. Experimental observations of gas and solids
flows in the grid region

. 1-2-2. Development of grid region models

Objectives of the Reserch

SINGLE PARTICLE COMBUSTION OF ELECTRODE GRAPHITE

SPHERES IN THE GRID REGION OF A FLUIDIZED BED

COMBUSTOR

Introduction

Combustion Characteristics of Carbon in a Fluidized

Bed Combustor

Definition of the Grid Region

Single Particle Experiments

2-4-1. Experimental equipments

2-4-2. Experimental procedures

Estimation of Minimum Fluidization Velocities

Experimental Results and Discussion

2-6-1. Mode of combustion

2-6-2. Estimation of the grid region height

2-6-3. Mass transfer characteristics of fixed carbon
samples

2-6-4. Effects of superficial air velocity on RCA

and Sh
2-6-5. Effects of inert particle size on RCA and Sh

2-6-6. Vertical profiles of mass transfer resistance

THEORETICAL ANALYSIS OF MASS TRANSFER CHARACTERISTICS
IN THE GRID REGION OF A FLUIDIZED BED COMBUSTOR

Introduction

Review of Studies in Multiparticle-Fluid Systems

3-2-1. Background

3-2-2. Studies on the mechanism of mass transfer in
a fluidized bed combustor

3-2-3. Studies on the mechanism of mass transfer in
other multi-particle fluid systems

Development of Mass Transfer Correlations in the Grid

vii

ix

xiii

12
17

18

83
89

94

95

95

96

100

3-3-1. Formulation of the problem of mass transfer

in a diluted system 103
3-3-2. Analogy between the grid region and a spouted
bed 106
3-3-3. Axial voidage distributions in the grid region 108
3-3-4. Axial velocity distributions in the grid
region 118
3-3-5. Development of mass transfer correlations 123
3-3-6. Discussion 131
3-4. Estimation of the Dead Zone Height 134
CHAPTER 4: SUMMARY OF CONCLUSIONS AND SUGGESTIONS FOR FUTURE
RESEARCH 138
4-1. Summary of Conclusions 139
4-1-1. Conclusions on single particle experiments 140
4-1-2. Conclusions on the theoretical analyses 142
4-2. Suggestions for Future Research 144
Appendix
A-l. Design of Gas Distributors 147
A-2. Sample Calculations
A-2-1. Particle terminal velocity 149
A-2-2. Calculation of e and u 150
A-2-3. Calculation of Re’ d and Sh 153
A-3. Experimental Data 156
References 171

viii

Table
Table

Table
Table

Table
Table

Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table

MN
HU‘

”RRP’RRE”?3”???????????????????PP

NH

\DQNGUI-PUJNHUN

List of Tables

Physical properties of bed materials 30
Experimental conditions for single particle combustion

of electrode graphite spheres in air at 1163 K and

1 atm 36

Kinetic and physical data for mass transfer calculations 40
Comparisons of grid region height with jet penetration

length (ds - 460 pm, TB - 1163 K) 50
Experimental grid region height at 1163 K 51
Values of the parameters used in the calculation of IO

pp - 2,700 kg/m3, pf - 0.3892 kg/ma, no - 6.35 mm 113
Mean bed voidage calculated from Eq. (3.20) and (3.21) 115
Estimated values of the dead zone height 136
Experimental results (Run # 1) 156
Experimental results (Run # 2) 156
Experimental results (Run # 3) 157
Experimental results (Run # 4) 157
Experimental results (Run # 5) 158
Experimental results (Run # 6) 158
Experimental results (Run # 7) 159
Experimental results (Run # 8) 159
Experimental results (Run # 9) 160
Experimental results (Run # 10) 160
Experimental results (Run # 11) 161
Experimental results (Run # 12) 161
Experimetnal results (Run # 13) 162
Experimental results (Run # 14) 162
Experimental results (Run # 15) 163
Experimental results (Run # 16) 163
Experimental results (Run # 17) 164
Experimental results (Run # 18) 164
Experimental results (Run # 19) 165
Experimental results (Run # 20) 165
Experimental results (Run # 21) 166
Experimental results (Run # 22) 166
Experimental results (Run # 23) 167
Experimental results (Run # 24) 167
Experimental results (Run # 25) 168
Experimental results (Run # 26) 168
Experimental results (Run # 27) 169
Experimental results (Run # 28) 169
Experimental results (Run # 29) 170

ix

Fig.
Fig.

Fig.

Fig.
Fig.
Fig.

Fig.

Fig.

Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.
Fig.

Fig.

NNN

.10

.11

.12

.13

.14

.15

.16

.17

.18

.19

List of Figures

Behavior of particles above an orifice: (a),(b) radial
profile, (c) vertical profile, from Oki et a1. (15).

A coal particle burning in the particulate phase of the
bubbling region, from La Nauze (34).

A schematic sketch of the grid region: (A) dead zone,
(B) quasi-dead zone, (C) zone of sluggish particle
motion.

Experimental fluidized bed unit.

Multi-orifice gas distributor used in the study.
Fraction of initial diameter and the ratio of densities
versus fractional burn-off (Uo- 16.6 m/s, ds- 460 pm).

Apparent carbon densitiy versus carbon diameter during
burn-off (Uo - 16.6 m/s, ds - 460 pm).

Variations in the Sherwood number and degree of mass
transfer control,¢, with particle diameter during
burn-off (Uo - 16.6 m/s, ds - 460 pm).

Overall combustion rate versus particle diameter for a
freely moving graphite sphere(Uo- 16.6 m/s, ds- 460pm).

Overall combustion rate versus particle diameter
(Uo - 22.6 m/s, ds - 620 pm, 2 - 1 inch, U - 2 Um

Overall combustion rate versus particle diameter
(Uo - 22.6 m/s, ds - 620 pm, 2 - 2 inch, U - 2 Um

Overall combustion rate versus particle diameter
(Uo - 22.6 m/s, dS - 620 pm, 2 - 3.5 inch, U - 2 Umf).

Effect of particle position on overall combustion rate
(Uo- 22.6 m/s, ds- 620 pm, z-l, 2, 3.5 inch, U - 2Umf).

Overall combustion rate versus particle diameter
(Uo - 33.8 m/s, ds - 620 pm, U - 3 Umf)'

Overall combustion rate versus particle diameter

(Uo - 45.2 m/s, ds - 620 pm, U - 4 Umf)’

Overall combustion rate versus particle diameter
(Uo - 9.4 m/s, ds - 460 pm, U - 1.5 Umf)'

Overall combustion rate versus particle diameter
(UO- 12.5 m/s, ds- 460 pm, 2 - l, 3 inch U - 1.5 Um
Overall combustion rate versus particle diameter
(Uo- 25.0 m/s, ds- 460 pm, 2 - 1, 2.25 inch U - 4 Um

Overall combustion rate versus particle diameter

(Uo - 4.7 m/s, ds - 230 pm, 2 - 1, 3 inch U - 3 Umf).

f)‘

f)'

f)'

f)‘

Overall combustion rate versus particle diameter

- - - 0 ' -
(Uo 9.4 m/s, ds 230 pm, 2 1, 2.25 inch U 6 Umf).

20

27
31
32

43

44

45

46

52

53

54

55

56

57

58

59

60

61

62

Fig.

Fig.

Fig.

Fig.

Fig.
Fig.
Fig.
Fig.

Fig.

Fig.
Fig.
Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

.20

.21

.22

.23

.24

.25

.26

.27

.28

.29

.30

.31

.32

.33

.34

.35

.36

.37

Ratio of grid region height to pitch size versus U/U
ds - 230 pm.

Ratio of grid region height to pitch size versus U/U
ds - 460 um.

Ratio of grid region height to pitch size versus U/Umf’
ds - 620 pm.

Effect of particle position on overall combustion rate
in the bubbling region (Uo - 25.0 m/s, ds - 460 pm,

U - 4 Umf)'

Variations in Sherwood number with particle diameter
(Uo - 22.6 m/s, ds - 620 pm, 2 - 1 inch, U - 2 Umf)‘

Variations in Sherwood number with particle diameter
(Uo - 22.6 m/s, ds - 620 pm, 2 - 2 inch, U - 2 Umf)'

Variations in Sherwood number with particle diameter
(Uo - 22.6 m/s, dS - 620 pm, 2 - 3.5 inch, U - 2 Umf).

Effect of particle position on Sherwood number
(Uo - 25.0 m/s, ds - 460 pm, u - 4 Umf).

Effect of particle position on Sherwood number above
grid region height (Uo - 25.0 m/s, ds - 460 pm,

z-2.25, 3, 4 inch, u-4U ).
mf

Effect of U on overall combustion rate
(ds - 620 pm, 2 - 1 inch u - 2, 3, 4 Umf)'

Effect of U on the Sherwood number in the dilute phase
((18 - 620 pm, 2 - 1 inch, U - 2, 3, 4 Umf)'

Temperature rise above bed temperature (ds - 620 pm,
2 - 1 inch, U - 2, 3, 4 Umf)’

Effect of U on the Sherwood number in the dense phase
(ds - 620 pm, 2 - 1 inch, U - 2, 3, 4 Umf).

Effect of U on the Sherwood number (ds - 230 pm,
2 - 1 inch, U - 3, 4, 6 Umf)'

Effect of U on the Sherwood number in the dilute phase
(ds - 460 pm, 2 - 1.5 inch, U - 1, 2, 4 Umf).

Effect of U on the Sherwood number in the dense phase
(dS - 460 pm, 2 - 1 inch, U - 1.5, 2, 4 Umf).

Effect of inert particle size on overall combustion
rate ((18 - 230, 460 pm, 2 - 1 inch, UO - 11 cm/s).

Effect of inert particle size on the Sherwood number

mf’

mf’

xi

63

64

65

66

69

7O

71

72

76

77

78

79

80

81

82

(dS - 230, 460 pm, 2 - 1 inch, Uo - 11 cm/s). 86

Fig. 2.38 Effect of inert particle size on the Sherwood number in
the dilute phase (ds - 230, 460, 620 pm, 2 - 1 inch,

U - 4 Umf). 87
Fig. 2.39 Effect of inert particle size on the Sherwood number in

the dense phase ((18 - 230, 460, 620 pm, 2 - 1 inch,

U - 4 Umf)' 88
Fig. 2.40 Variations in the Sherwood number along the vertical

distance in the dilute phase (ds - 620 pm, 2 - 1, 2 inch,

U - 4 Umf). 91
Fig. 2.41 Variations in the Sherwood number along the vertical

distance in the dilute phase ((18 - 230 pm,

2 - 1, 2, 2.25 inch, U - 6 Umf)' 92
Fig. 2.42 Variations in the Sherwood number along the vertical

distance in the dense phase (ds - 620 pm,

2 - 1, 2, 3.5 inch, U - 2 Umf)' 93
Fig. 3.1 Spouted bed model as applied to the grid region

( , solids flow; é, gas flow). 107
Fig. 3.2 Axial voidage distribution in the dilute phase

calculated from Eqs. (3.13) and (3.19). 117
Fig. 3.3 Axial velocity distribution in the dilute phase

at U - 4 U . 122

mf

Fig. 3.4 Plot of 1n[(Sh - 26)/Sc1/3] versus 1n Re in the dilute

phase for 0 s z < he. 127
Fig. 3.5 Plot of 1n[(Sh - 26)/Sc1/3] versus In Re in the dilute

phase for he 5 z 5 H. 128
Fig. 3.6 Plot of 1n[(Sh - 25)/Sc1/3] versus In Re in the dense

phase for 0 < z s H. 129
Fig. 3.7 Plot of 1n[(Sh - 26)/Sc1/3] versus 1n Re (dilute phase

(open symbol), dense phase (closed symbol)). 130
Fig. 3.8 Mass transfer factor versus Reynolds number in a diluted

system. 133
Fig. 3.9 Axial velocity distribution in the dense phase at

U - 4 Umf' 137

Fig. 4.1 Research plan for the overall combustion modeling. 146

xii

0
'0

U0
Om

D'OQFIO-O-UO-UU
(DQWE 90311039“!!!

HEEED‘D‘E
0:

Symbols

external surface area of a carbon particle

preexponential factor, kgC/m2 3 atom

Archimedes number, defined as d: pf (pS -pf)g /p§
concentration of reactant A at the exit of the grid region,

moles/liter ,
concentration of reactant A entering the bed moles/liter

drag coefficient defined in Eq. (A.7)
orifice discharge coefficient

oxygen concentration entering the bed, kg/m3

oxygen concentration in the partuculate phase, kg/m3

oxygen concentration at the surface of carbon, kg/m3

equivalent diameter of a spouted bed, m

diffusivity of oxygen in air, mz/s

jet diameter, m

particle moving zone diameter, m

orifice diameter, m

diameter of a carbon or active particle, m
mean diameter of inert particles, m
activation energy of reaction, kcal/mole
gravitational accleration - 9.8 m/s2
jet height, m

heat of reaction, kJ/kgC
Bed height, m

dead zone height, m
height of entrance effects, m

grid region height, m
maximum spoutable bed depth, m

constants used in Eqs. (3.12)-(3.16)

mass transfer factor, defined as kmSc2/3

/U

fraction of gas visible as bubbles

apparent chemical rate coefficient, kg C/m2 5 atm

xiii

G rd n’n to 01m
5 7f thaF 'u o 5‘ o

(1'

<
U

external mass transfer coefficient, m/s

-1
first-order rate constant, 5
mass transfer coefficient per unit volume of reactor in the

bubbling region, kg/m3s
mass transfer coefficient per unit volume of reactor in the

jet region, kg/m3s
jet penetration length, m
catalyst loading in the particulate phase, m3/m3 particulate

phase
distributor thickness

exponent in Eq. (3.20)
apparent reaction order

bubble frequency, 5-1

Peclet number, defined as dp U/Dg
mass flow through bubbles, kg/s
mass flow through the particulate phase, kg/s

gas constants - 1.987 cal/g mole K
reaction rate per unit weight of catalyst in the particulate

phase, kg/s kg
reaction rate per unit external surface area of carbon, kg/mzs
Reynolds number, defined as pf u d/pf

pitch size, m
Schmidt number, defined as pf/pf Dg

Sherwood number, defined as km dp/Dg

time, s
time taken for a bubble to form compeletly, 5

particle temperature, K

superficial gas velocity, m/s
interstitial gas velocity in the dilute phase, m/s

superficial velocity of gas leakage, m/s
relative velocity between gas and soids, m/s
particle terminal velocity, m/s

bubble volume, m3

xiv

Vd volume of the particulate phase, m3
particle velocity in the dilute phase, m/s

J

AW weight loss, kg

yb,yco mass fraction of reactant in the bubble and particulate phase,
respectively.

2 axial coordinate,m

zb distance travelled by bubbles prior to coalescence, m

Greek letters

6 _, stoichiometric coefficient
6 gas-solids interphase drag coefficient, defined in Eqs. (3.7)
and (3.8)

e voidage

6b mean bed voidage

C dimensionless axial coordinate, z/H
9r angle of repose

A constant in Eq. (3.12)

pf gas viscosity

5 ratio of average channeling length to particulate diameter
p density

¢ degree of mass transfer control

$8 particle shape factor

Subscripts

b bubble

B bed

d dense phase

D distributor

exp experimental

f gas or fluid

j dilute phase
‘mf minimum fluidization

ms minimum spouting

o orifice

p active particle

s inert particle

XV

CHAPTERI

GRID REGION PHENOHENA B1 A FLUIDIZED BED

AND OBJECTIVES OF THE RESEARCH

1-1. Int odu on

Fluidized bed coal combustion provides one option for utilizing
coal for purpose of energy generation. A major contributing factor to
the success of fluidized bed coal combustion technology is the ability
of fluidized beds to handle coals of widely varying composition,
including low grade coals with high ash content, compared with other
contacting devices such as stoker and pulverized coal firing.

Fluidized bed combustion also provides a capability of in-bed sulfur
capture, which is an important factor from the standpoint of stringent
environmental pollution standards imposed by government legislation and
regulation. Another important advantage of fluidized bed combustion is
its excellent heat and mass transfer rates due to vigorous gas and
solids mixing to increase the efficiency of combustion considerably.
Especially, gas and solids contacting is known to be more efficient in
the grid region near the distributor than higher up in gas fluidized
beds so that for fast reactions much of the conversion may take place
in this narrow region. As a result, the temperature gradient in the
grid region can be quite high, and the presence of stagnant zones near
the distributor can cause hot spots resulting in solids agglomeration,
gas entry point blockage, and eventual reactor failure in such
applications as fluidized bed coal gasification, coal combustion, and
exothermic catalytic reactions (1).

For example, industrial pilot plant experiments performed by Cooke
et a1. (2) in a 1.2 m diameter bed have shown that up to 90 % of the

conversion in coal carbonization can take place in the first half meter

of bed height. Cole and Essenhigh (3) also observed that the gas

temperature increased from 150°F to 1900°F within 1 inch from the
bottom in a fluidized bed coal combustor.

It is also this region that determines the distinct size, shape
and frequency of bubbles which in turn affect the overall
hydrodynamics, uniformity, and stability of the bed. Therefore, not
only from the standpoint of design and scale-up of gas distributor
systems but from the important effects of the grid region on the
physical and chemical performance of the bed, it is of considerable
practical interest to understand correctly how the gas flow through the
orifice enters the bed and how it induces such high rates of heat and
mass transfer before it is fully established as bubbles and
interstitial gas flow (4).

Unlike many other fluidized bed applications of commercial
interest, one distinct feature of fluidized bed coal combustion is that
not all particles in the bed are active; each burning coal particle in
a fluidized bed coal combustor is virtually surrounded by many inert
bed particles due to its low concentration in the bed. The shielding
effect by these inerts represents a major resistance to the mass
transfer of oxygen to the burning carbon particles, which has been the
focus of many intensive studies in the past decade. Despite the
importance of the grid region on the overall performance of the bed as
described above, most studies on mass transfer and reactor modeling,
however, have been made exclusively in the bubbling region

(5,6,7,8,9,10,ll) and there appears to be little work reported in the

literature which focuses its attention on the investigation of high
mass transfer rates in the grid region of a fluidized bed combustor.

Considering the fact that many existing bubbling bed models
available in the literature may not be used to accurately predict the
overall performance of the entire bed without taking into consideration
the combustion characteristics in the grid region, it is believed that
there is a need for better understanding the grid region whose
hydrodynamic as well as thermal features are markedly different from
those in the bubbling region.

This research is, therefore, directed toward investigating
combustion and mass transfer characteristics of large carbon particles
in the grid region of a fluidized bed combustor, which is of crucial

importance in combustion modeling studies.

 

For the purpose of modeling a fluidized bed reactor, one can
conveniently divide the bed into two hydrodynamically distinct regions,
the bubbling and the grid region. Except for shallow beds, the
bubbling region usually occupies much of the reactor volume, and the
overall bed uniformity is maintained by vigorous gas and solids mixing
induced by fast rising bubbles. However, the increase in bubble size
due to coalescence leads to significant gas by-passing and considerable
lowering of the reactor performance, particularly with deep beds. 0n
the other hand, hydrodynamics and transport processes in the grid

region are far from compeletely understood due to their complexity, and

this section discusses some of the important features of gas and solids
flows and the modeling studies in the grid region near the multiorifice

gas distributor.

1-2-1.

 

The mode of gas entry through the discrete grid holes into gas
fluidized beds has been considered by many to be always in the form of
discrete gas jets or spouts with bubbles detaching from the ends of
these jets or spouts (12,13,14), as shown in Figure 2.2. Recently,
Rowe et al. (4) found from their x-ray study in a three-dimensional bed
that gas issuing from the orifice entered the bed in the form of
bubbles, instead of a permanent flame-like jet, at sufficiently high
gas flow rates. They also found that it was possible to establish a
jet when the particles were not fluidized locally and when there were
surfaces present to hinder the flow of particles toward the orifice.
These findings were later confirmed by others (15,16). Besides the
degree of bed fluidization and the presence of surfaces, particle size
and particle density are also known to affect the development of gas
jets. For a given inlet gas velocity at the orifice, the mode of gas
discharge gradually changes from the chain of bubbles to the jet type,
as bed particle size increases from fine powders (Geldart Group A) to
coarse beads (Geldart Group D) (17).

Regardless of whether a jet or bubbles are formed at the orifice,
depending on the presence of the dead zone, recent experimental results

further showed that a considerable amount of gas leaks from the void to

the dense phase at the entry point. Yates et al. (18) observed that
only about one third of the gas flow entering the bed was visible as
bubbles, leading to significant deviations from the classical two-phase
theory of fluidization (19) in the lower region of the bed. They
concluded that such high rates of gas leakage from a bubble during
formation caused the dense phase voidage to increase above its minimum
fluidization value, which resulted in good contacting between gas and
solid particles and, therefore, high rates of heat and mass transfer.
Wen et al. (16) further proposed a mechanism for the formation of jets
and bubbles; gas entering a fluidized bed through orifices disperses
partially through the bubble or jet boundary to fluidize the entire
bed, and bubbles form only at a height where the cumulative leakage is
compelete and the bed is compeletely fluidized. In the case of large
pitches and small orifice diameters, this condition occurs only above a
certain height, and consequently a spout of gas is formed from which
bubbles take off (16).

A common way of experimentally measuring the amount of gas leakage
is to plot the observed bubble volumes against the ratio of inlet gas
flow rate to the frequency of bubble formation which gives rise to a

reasonably linear relationship as:

I
7‘:
D
O

(1.1)

 

Z
0"

K is a proportionality constant which represents the fraction of

entering gas visible as bubbles. The value of K depends on the

operating conditions, and reported values at the orifice are usually
less than 0.5. One significant outcome of this experimental technique
is that it can give an estimate of the grid region height by
experimentally observing the distance from the distributor where the
value of K satisfies the distribution of gas flow between bubbles and
interstitial flow according to the two-phase theory (19).

Oki et al. (15) measured the averaged local upward particle
velocities at various heights above the center orifice of three
different types of multi-orifice distributors by using a fiber optic
probe. They showed that particles initially accelerated to their
maximum velocities beyond which the velocities decreased to the
limiting values, which might be related to the velocities of ascending
bubbles, as shown in Figure 1.1 (c). It seems to be reasonable to
assume that the height of constant upward particle velocity corresponds
to the grid region height measured from the hydrodynamic point of view,
and it will be interesting to compare with the height where the value
of K satisfies the two-phase theory. It can also be seen from Figure
1.1 (c) that for the same air velocity, the maximum particle velocity
as well as the vertical velocity profile for the distributor which has
a larger pitch size are considerably different from those with smaller
pitch sizes.

In view of current interest in combustion and gasification of coal
in fluidized beds, Ghadiri and Clift (20) measured jet penetration

length by noting the erosion marks on the wall of an air-fluidized bed

of sand at 800°C, and found that all correlations at ambient conditions

 

 

 

 

 

 

 

 

 

Distrib or
P 6 .3 8+ 8% “1F
3 .4 .3 30 A
L 6 . B
.l . as
.. “I C
54* 4 ’ a; \‘L
v e. 1 .0. ~g
N 2 p T‘ p
b b
2 2 6- 1 (3"
0:22: ° .=_-_-_:0 H
l 3 5
Distributor A Distributor B Vs (m/s)
(a) (b) (C)

Fig. 1.1 Behavior of particles above an orifice: (a),(b) radial
profile, (c) vertical profile, from Oki et al. (15).

except that of Merry (l4) grossly overpredicted jet penetration length
under their experimental conditions. They further argued that since
the particle motion is very rapid in the vicinity of a developing
bubble chain at the tip of a jet, wall erosion may occur beyond the
point at which the jet degenerates into bubbles. Since a distribution
orifice should be located close to the wall in order to have distinct
erosion marks, it seems that the experimental technique employed by
Ghadiri and Clift (20) might have overpredicted jet penetration length
due to wall effects. However, one significant outcome of their
experiment is that correlations for jet penetration length at ambient
conditions cannot reliably be extended for use at much higher
temperatures, and this is particularly true when there is a reaction
involved in the grid region. An extensive survey of jet penetration

length studies and correlations is made by Massimila (17), and some of

the widely used correlations for jet penetration length are given

 

below.
Merry (14):
0.3 2 0.2
p D U
L_ - 5.2 f g 1.3 _g - l (1.2)
Do psds gDo
Yang and Keairns (21):
p 02 0 187
L_ - 15.0 f o ' (1.3)
Do ps ' pf gDo

Wen et a1. (22)

2 0.47
L. _ 814.2 p d -O.585 pED U -0.654 32 (1 4)
Do pro ”f gDo
Zenz (55):
L 2
0.0144 _m§3 + 1.3 - 0.5 log (pf U0) (1.5)

D
o

10

where L is jet penetration length, Do orifice diameter, Uo mean gas

velocity at the orifice, ”f gas viscosity, dS particle diameter, and
pf and ps are gas and solids densities, respectively.

The experimental measurement of the grid region height is also
possible with the use of a highly sensitive temperature measuring
device. Fan et al. (23) measured the transient axial particle and gas
temperature profiles near the distributor in a three-dimensional gas
fluidized bed by means of suction and bare thermocouples. They found

from the analysis of experimental results at temperatures not higher

than 100°C that the height required for the temperature of gas and
particles to be equalized is approximately the height of jet
penetration defined as the length of jet before breaking up into
bubbles. They also found that the particle temperature rose rapidly
near the distributor to a maximum, due to the existance of the dead
zone, while the grid region height decreased as the gas flow rate
increased. The key assumptions made in their analysis were that the
region between the adjacent grid holes was so packed with particles
that a bare thermocouple would come into close and direct contact with
relatively immobile particles at all times and that the jetting region
was free of solids.

It is, however, known that particles are indeed entrained into the
voids formed above the orifice (24), which in turn results in the
modification of the streamlines for the fluidizing fluid. Considering
the statistical nature of jetting phenomena, Oki et a1. (15) obtained

the time averages of jet lengths in terms of void fractions with the

ll

use of an optical-fiber array probe. They found that the jet boundary
was diffusive in nature; the change in solids concentration was gradual
over the whole radial dimensions of the jet, as shown in Figure 1.1 (a)
and (b). Their results clearly show that a significant amount of
solids are present even in the core of the jet and that solids occupy
almost 90 % of the jet volume at the boundary if the jet boundary is
defined as where solids change their upward motion to downward one.

The rate of solids entrainment immediately above the orifice is
probably enhanced by the low resistance to the radial flow of the dense
phase and by the concurrent flow of entrained gas (25).

Hirato et al. (26) measured the particle velocities in a large
three-dimensional fluidized bed using a spring plate detector with
strain gauge. Their results showed that due to the presence of many
small bubbles above the distributor, both upward and downward
velocities of particles near the distributor were small enough to
assume that particles moved in a radial direction rather than in an
axial direction.

Ishida et al. (27) made interesting observations on the behavior
of particles in the jet using a linearly-arrayed multi-fiber optical
probe. Their detailed analysis of the experimental results showed that
the concentration of particles in the jet was not uniform; particles
tended to form swarms, and dense and dilute swarms of particles passed
alternatively through the jet. This periodic appearance of particle
swarms may indicate that the solids entrainment into the jet does not

take place uniformly in time and it will be useful to measure the times

12

between two successive dense swarms to see if they are related to the
frequency of bubble formation.

In a bed with auxiliary gas flow, fluidizing gas is also known to
be entrained into the jet from the dense phase up to a certain distance
from the orifice, jet gas eventually re-entering the dense phase from
there on. Depending on particle size and density, the inversion in the
direction of gas flow between the jet and the dense phase occurs at

difference distances from the orifice (25).

1-2-2. v f 0

As pointed out earlier, many models which have been proposed in
the literature for the bubbling region of gas fluidized beds cannot
properly describe the high rates of heat and mass transfer and high
conversion rates near the distributor, especially for fast reactions.
In order to compelete the modeling of fluidized bed reactors, it is,
therefore, necessary to have a separate description of gas and solids
behavior in the grid region which can then be combined with many
existing bubbling bed models for better prediction of the overall
performance of the bed.

Behie and Kehoe (13) proposed a simple two-phase model by assuming
that gas enters the bed as well-mixed grid jets with plug flow in the
axial direction and that the jets break up into bubbles and
interstitial gas flow at a certain distance h above the distributor
with a dense phase perfectly mixed throughout the bed. The equations

describing their model are

l3

jet region (0 5 z 5 h):

dy _ _
Qo 321 + kj aj A (yj ya) 0 (1.6)

bubble phase (h < z 5 HB):

ngth+kbabA(yb-ym)-o (1.7)

dense phase (0 5 z 5 HB):

h
Qd (yd - y”) + kj aJ A I0 (yj - ya) dz
0

H
+ kb ab A [11303, - ya) dz - La vc1 p5 Rom) (1.8)

and Q0 - Qb + Qd (1.9)

where y's and Q's are mass fractions and flow rates of reacting gas

respectively, kjaj and kbab are mass transfer coefficients per unit

volume of reactor for the jet and bubbling regions, respectively, and

LdVdpsR(ym) represents the total reaction rate in the dense phase.

They showed experimentally that kjaj is much greater than kbab (28),

l4

and they assumed a first-order gas-solids reaction with no diffusional
limitations in the dense phase. With a bed 0.6 m deep, their
calculations showed that their model predicted a conversion of 84 %,
while the bubble model with h - 0 predicted a conversion of only 11 %
for fast reactions. For slow reactions, the difference in conversion
rate was much less significant since mass transfer resistance did not
limit the rate as severely (13). One key assumption made in the Behie
and Kehoe model was that there was no entrainment of solid particles
into the jet. However, as shown experimentally by others
(15,24,26,27), particles are indeed entrained into the voids formed
above an orifice, and it is known that even very low concentrations of
solids in dilute phase regions of the bed can have a considerable
effect on overall conversion for highly exothermic reactions such as
fluidized bed coal combustion (29).

Grace and De Lasa (30) set out to test the sensitivity of the jet
model by Behie and Kehoe (13) to the mode of gas mixing in the dense
phase by considering two extreme cases of gas mixing. In the first
case, the entire dense phase was assumed to be a stagnant region with
no vertical gas flow within it, while mass transfer of gas between the
dense phase and the jet and bubbles was allowed by assuming different
interphase mass transfer coefficients. In the other case, they
considered the dense phase to consist of two regions, a stagnant region
from the distributor to the top of the jet and the remaining dense
phase in the bed with perfect mixing. Qualitatively, both cases
predicted much higher conversion for a fast reaction as in the jet

model by Behie and Kehoe (13) than pure bubble models.

15

Yates et al. (18) developed a simple model of gas entry into the
bed in which a large part of gas that ultimately forms a bubble with
restricted mass transfer to the particles first enters the dense phase
for a brief period during which appreciable chemical reactions can
occur if it is a fast reaction. For a pseudohomogeneous first-order
.reaction between gas and soids, the fraction of reactant A remaining

unconverted in the bubble at the exit of the grid region was given as:

259 - K + (1-x) exp [-0 s (l-ed) ks te] (1.10)

CAo

where K - fraction of gas flow visible as bubbles at the orifice
ed - dense phase voidage in the grid region
ks - first-order rate constant

te - time taken for the bubble to form compeletely

Yang et al. (31) later refined this model by Yates et al. (18) by
introducing the residence time distribution function of the gas in the
dense phase prior to entering the bubble, instead of just assuming it

to be 0.5 te. Further tests of the model using the oxidative catalytic

dehydrogenation in air of butene-l to butadiene showed a qualitative
correspondence between experimental observations and model predictions
in the trend of decreasing conversion with increasing orifice flow rate
(31). They seemed to exclude the gas-solids reaction in the bubble

wake which was estimated to occupy approximately one-fourth of the

16

volume of the sphere centered on the bubble, and the parameters used in
their model, especially the relationship between the expanded dense
phase voidage and orifice flow rate, needed to be estimated accurately
from careful experiments in order to improve model predictions.

Patrose and Caram (32) studied two-dimensional modeling of the
carbon oxidation reactions in the grid jet in a fluidized bed coal
combustor for the purpose of assessing the extent of reactions that can
occur due to solids entrainment into the jet. Their overall picture of
the grid region was similar to that of Behie and Kehoe (13); the main
difference was that the reactions took place only in the jet phase in
the former model, while the fluidized dense phase surrounding the jet
was the reaction zone in the latter. The effect of the inert bed
particles on the diffusion of oxygen to burning particles in the jet
was ignored just by using the well-known correlation by Ranz and
Marshall (33) for a single sphere in an infinite medium. Although no
comparison was made with experimental data, their simulation results
showed that the solids entrainment rates were high enough to consume
all the oxygen in the entering air and absorb the heat released from
the combustion.

Recognition of the importance of the grid region on the overall
performance of fluidized bed reactors did not appear in the literature
until 70’s and only a handful of works on the grid region modeling have
been reported since then. As briefly summarized here, the modeling is
still at an early stage of development, and more fundamental
experimental works on the complicated behavior of gas and solids flows

and their effects on the transport properties and the chemical

17

reactions in the grid region are needed for any further improvement of

existing models.

1-3. Ob ect ve esearch

This study examines combustion and mass transfer characteristics
of large carbon particles in the grid region of a fluidized bed

combustor. Briefly, the research is directed toward:

(1) single particle experiments of measuring combustion rates of
electrode graphite spheres fixed at various locations in the
grid region for each set of operating variables such as inert
bed particle size and superficial air velocity.

(2) estimation of the grid region height, the dead zone height
and external mass transfer coefficient local to a carbon
particle from the results of single particle experiments.

(3) development of mass transfer correlations for oxygen
transfer to a burning carbon particle in the dilute and dense

phases of the grid region.

It is the ultimate aim of this study that results of both
experimental and theoretical works described above can contribute

significantly to the combustion modeling of the grid region.

CHAPTERZ

SINGLE PARTICLE COMBUSTION 0F ELECTRODE GRAPHITE SPHERES

IN THE GRID REGION OF A FLUIDI- B- COMBUSTOR

18

19

2-1. I t od c n

The rate of combustion of single carbon particles in a fluidized
bed of inert particles is an overall result of physical processes such
as transport of heat and mass and chemical reactions taking place in
and around the carbon particles. Figure 2.1 shows a carbon particle
burning in the bubbling region of a fluidized bed. According to the
two-phase theory of fluidization (19), there are two sources of oxygen
for the combustion of a carbon particle which spends most of its time
in the particulate phase; mass transfer of oxygen from gas flowing

through the particulate phase at a velocity of Umf/emf and from bubbles
rising at a velocity of Ub' Oxygen flowing with bubbles must diffuse

out of the bubble and through the particulate phase to reach the active
surface of burning carbon particles. As outlined by La Nauze (34), the
advantage of single particle experiments is the elimination of the
bubble-particulate phase interchange resistance which allows the oxygen
concentration in the particulate phase to be taken as that of the inlet
gas. In the grid region, this advantage is equally well preserved,
since the resistance to oxygen transfer from the jet forming right
above the orifice to the dense phase between two adjacent jets can also
be ignored due to low oxygen consumption involved in single particle
experiments. If the chemical reactivity of a specific type of carbon
is carefully measured or known, the external mass transfer resistance
by the inert particles around the burning carbon particle can be
estimated once the overall rate of combustion is measured from suitable

experiment.

20

Unlike in the bubbling region, the combustion rates of carbon
particles fixed in the grid region are expected to depend strongly upon
the particle position due to the presence of gas jets and the dense
phase consisting of relatively immobile inert particles. This chapter
discusses the single particle experiments of measuring the combustion
rates of electrode graphite spheres fixed at various locations within
the grid region near the multi-orifice gas distributor. The
experimental results will be analyzed in light of the experimental
observations of gas and solids flows in the grid region, as discussed
in Chapter 1, and the external mass transfer coefficients local to a

carbon particle will also be calculated from the combustion data.

0 O vol-adage . 6 02 diffusion

Q 00 .
O D 0%0 O
0 m. 00 0000

O
0 Bubble OOof gas

exchange 00 0 surface reaction
Ofl 000 000%)0 00 60 heat and mass

Q particulate 00060 transfer
4670 II p ase

C0, C02 diffusion

Fig. 2.1 A coal particle burning in the particulate phase of the
bubbling region, from La Nauze (34).

21

2-2. C b o c e 0 ho n a l dized ed

£22m

Despite many intensive studies, the mechanism of the C-02 reaction

is probably the least understood among carbon gasification reactions of
commercial interest. An excellent review has been given by Laurendeau
(35).

As shown in Figure 2.1, oxygen diffuses through the gaseous
boundary layer around the burning carbon particle to the active surface

where it reacts with carbon to form CO and CO with the CO/CO2 ratio

2.
increasing substantially at higher temperatures and lower pressures.
Under the typical conditions for atmospheric combustion, it appears as
a concensus that solid carbon reacts with oxygen to form CO only

according to Eq.(2.l), with subsequent CO oxidation taking place in the

gaseous boundary layer according to Eq.(2.2):

C (s) + 1/2 02 (g) a CO (g) (2.1)

CO (g) + l/2 02 (8) 4 002 (8) (2.2)

The homogeneous reaction by Eq.(2.2) contributes approximately two

third of the heat produced by the overall heterogeneous reaction:

0 (s) + 02 (g) - 602 (g) (2.3)

22

AH - -33,000 kJ/kgC

rxn, 1163K
Hence, it is of considerable importance in heat and mass balance of
combustion to know just how much of the heat produced by CO oxidation
is used to heat the carbon particle. This is still the subject of
intense controversy due to the lack of adequate experimental techniques
of measuring the precise location of CO oxidation. Using the kinetic
expression by Howard et a1. (36) for CO oxidation in postflame gases,
Ross and Davidson (6) calculated the approximate radius of CO oxidation
zone and concluded that CO burns close to the carbon particles with
diameters ranging from 0.5 to 2 mm. The theoretical analysis by Caram
and Amundsen (37) also shows that the escape of CO does not occur until
the particle diameter decreases below 0.1 mm. Although some degree of
CO escape into the surrounding particulate phase takes place depending
on the velocity and temperature of the gas phase (38), it is generally
assumed in many studies (7,8,39) that for large carbon particles of

diameter greater than 3 mm the conversion of solid carbon to 002 occurs

essentially at the surface of carbon particles according to Eq.(2.3).
Consequently, large carbon particles burn at much higher temperatures
than the bed up to 250 K above, and the combustion has been shown to be
controlled mainly by diffusion of oxygen through the particulate phase
due to high reaction rates (6,7,8,38,39,45).

The combustion rate, expressed as the weight of carbon consumed

per unit external surface area of the particle, is given by:

n 2
Rc - kc CS - 8 km ( Cp - CS ), kgC/m s (2.4)

23

where kc is the apparent chemical rate coefficient including any

intraparticle diffusional effects, n is the apparent reaction order of

combustion, C8 is the oxygen concentration at the surface of the carbon
particle, km is the external mass transfer coefficient in the dense or
particulate phase including the boundary layer diffusion, Cp is the

oxygen concentration in the dense phase, and fl is the stoichiometric
coefficient which takes the value of 3/4 if the overall reaction is

C + 1/2 02 4 CO and 3/8 if the overall reaction is C + 02 4 C02.

Eq.(2.4) merely states that during steady-state combustion the amount
of carbon consumed at the surface must be balanced by that of oxygen
transferred to the surface through the stoichiometric coefficient 6.

By eliminating the unknown 03, Eq.(2.4) can be writtn as:

n
RC - kc I (1 - ¢) Co] (2 5)

where ¢ is the degree of mass transfer control, defined as Rc / Rcm

Rcm is the maximum possible combustion rate when the combustion is

controlled only by mass transfer of oxygen local to the carbon, i.e. CS

- 0, and Cp has been replaced by Co’ the oxygen concentration of

incoming air for single particle experiments.

The combustion rate, RC, is calculated directly from the weight

and diameter data during burn-off. For one interval of t second

burning:

24

2
Rc - AW / t n dp (2.6)

where AW is the weight loss, and dp is the average particle diameter

during a combustion interval of t seconds.

The apparent chemical rate coefficient, kc, is usually given in

Arrhenius form as:

kc - Ao exp [ -Ea / RTP] (2.7)

where Tp is the average particle temperature during burn-off. The
preexponential factor, A0, the apparent activation energy, Ea' and the

apparent order, n, are determined from separate kinetic experiments for
a specific type of carbon. At the present time, there are numerous
kinetic data reported in the literature for various types of coal chars
and purified carbons, and excellent reviews have been given by Smith
(41,42).

Assuming that the heterogenous reaction in Eq.(2.3) has the
apparent order of one, as is done in many studies for temperatures

greater than 1,000 K, Eq.(2.5) can be rewritten as:

RC - co / (1/kc + dp / p Sh Dg) (2.8)

where Sh is the Sherwood number, defined as kmdp/Dg, and Dg is the

diffusivity of oxygen in air. The reciprocal of the terms in the

25

bracket in Eq.(2.8) can be regarded as the overall rate coefficient,
which clearly shows the effects of both chemical kinetics and local
mass transfer on combustion of carbon particles.

As noted earlier, the degree of mass transfer control, ¢. is
expected to decrease from unity as the particle size decreases during
burn-off, and can be calculated from Eq.(2.5) once the combustion rates
and the kinetic data are obtained from experiments. The dimensionless

mass transfer coefficient, Sh, is then calculated from:

Sh k d R d (2.9)
‘ _m__2 '.__J£_JL_.

2-3. Wen

As shown in Figure 2.2, the gas flow in the grid region near the
multi-orifice gas distributor is mainly in the form of gas jets forming
right at the orifice and small bubbles detaching from these jets, and
we call this region of relatively low solids concentration the dilute
phase. Gas also leaks throughout the jet boundary to fluidize the
region between two adjacent vertical jets, and the mobility of bed
particles in this dense phase is expected to increase from that in the
packed bed at the distributor to that in the bubbling region at some
distance above.

Here we define the grid region height, H, to be the vertical
distance from the distributor to a height where bubbles first begin to

deviate from their vertical path due to the bed momentum. It is worth

26

noting that this definition of the grid region height is similar in
concept to that of the jet penetration length by Knowlton and Hirsan
(43). Hence, above H, the time averaged bed voidage is uniform

everywhere at Eb the mean bed voidage including bubbles. Furthermore,

combustion and mass transfer characteristics should be the same
regardless of particle position above the grid region height due to the

overall uniformity of the bubbling region.

27

  

bubbling
region

 

 

grid
region

 

 

 

 

 

 

 

 

(0), sample
location

orifice

Figure 2.2 A schematic sketch of the grid region
( (A), dead zone; (B), quasi-dead zone;
(C), zone of sluggish particle motion ).

28

2-4. e a e t

This section discusses the experimental equipment and procedures
of measuring combustion rates of single electrode graphite spheres

fixed at various locations within the grid region.

244. W

A schematic sketch of the experimental fluidized bed unit is shown
in Figure 2.3. The bed is 15.5 cm I.D. and 43.5 cm high, and is made
of 6.4 mm thick stainless steel. The gas distributor consists of two
identical plates, each having seven 6.4 mm diameter holes in a
triangular pitch with pitch size 5.56 cm, as shown in Figure 2.4. In
order to ensure a uniform gas distribution, the thickness of each
distributor plate was estimated to be about 4.5 mm for a bed of silica
sand, 20 cm high at minimum fluidization and mean particle diameter of
0.2 mm or greater. See Appendix A.1 for the calculational method of
determining the thickness. A layer of stainless steel mesh wire of
0.15 mm aperature is inserted between the two distributor plates to
retain the sand during shut-downs.

The bed is heated externally by four quarter-circular 40.64 cm
high nickel-chrome heating units of 1625 W each at 230 V with Lindberg
control console of the proportional-integral type. The spacing between
the bed and the cylindrical heating unit is kept at 2.5 cm, and the
whole bed assembly is insulated by a one-inch thick blanket of High
Alumina Ceramic Fiber. In order to prevent any significant heat loss

through the gas distributor, the inlet gas stream is first heated by

29

the heating tape and then by the main heating unit in the plenum
chamber, before it enters the bed.

Laboratory air saturated at 90 psig and ultra pure nitrogen are
used as fluidizing gases. The flow rate of each gas is monitored by a
high resolution variable area flowmeter for low flow rates and by a
variable area bypass flowmeter for high flow rates, each with a needle
valve. The instantaneous switch from one gas to the other is made by a
highly sensitive three-way valve, and the dynamic pressure of each gas
stream is measured by a pressure gauge.

Silica sand of three different mean particle sizes is used as
inert bed particles, and electrode graphite spheres of 1 cm initial
diameter are used as carbon samples.. Table 2.1 summarizes the physical
properties of silica sand and electrode graphite spheres used in this
study. A thin chromel-alumel thermocouple of 63.5 cm long and Inconel
600 sheath of 1.02 mm O.D. is dipped into an alumina base adhesive and
inserted into a 1.07 mm hole drilled straight halfway to the center of
each graphite sphere for the measurement of particle temperatures. The
long thermocouple-carbon sphere assembly is then supported rigidly by
passing it through a stainless steel tube of 1.27 mm I.D. which is in
turn held tightly by a precision clamp for an exact positioning of the
graphite spheres within the grid region. A seperate chromel-alumel
thermocouple monitors the bed temperature continuously, and all
temperatures are recorded by highly sensitive digital readout meters.
The weight and particle diameter of each graphite sphere are measured

with the use of an analytical balance and a micrometer, respectively.

30

Table 2.1 Physical properties of bed materials

 

 

 

Silica sand : ps - 2700 Kg/m3
a 0* 1163 K * t 1163K
3 (pm) mf (cm/s) at emf a
230 1.85 0.4
460 7.35 0.4
620 13.25 0.4

 

Electrode graphite spheres**: Initial diameter z 1 cm
pp - 1600 Kg / m3

porosity - 20 % by volume
Impurity level z 1,000 ppm

 

* See Section 2-5 for the calculations.
** Manufactured by Bay Carbon, Bay City, Michigan.

3l

 

To Digital Temp.

 

 

Readout Meters '4?—
<e~

.5

u.

4

Fan 3. L To Exhaust
\___ 5i -——e>
.4

_. Fluidized
‘-Bed

 

0

Insulation \ \
-5::::m\—§
9 , §
\

 

 

Heating
Unit

 

-Sample

00000000000

Distributor

 

 

 

 

 

LgcabCioc>oc>o<531

 

 

Plenum
Chamber

 

IOOOOOea‘

 

Air

Heating Tape

Figure 2.3 Experimental fluidized bed unit.

32

 

Figure 2.4 Multiorifice gas distributor.

33

2-4-2. W

The mode of combustion of electrode graphite spheres has to be
determined first. An electrode graphite sphere attached to a thin,

flexible nichrome wire is dropped into a hot bed of sand fluidized by
N2 at 1163 K. The wire is long enough to ensure the freedom of

particle movement in all directions, including the grid region. After
the carbon particle reaches the bed temperature, usually within one
minute, the fluidizing gas is quickly switched to air using a three-way
valve. After a predetermined time, depending on the particle

reactivity, the gas is switched back to N2 to stop further combustion.

The carbon sample is then quickly removed from the bed and transferred
into a liquid nitrogen container for cooling. After the weight and
diameter of the graphite sphere are measured, the carbon sample is put

back into the hot bed and heated in N2 up to the bed temperature, after

which the gas is switched again to air to continue the combustion. The
same sequence of procedures is repeated, until the carbon sample burns
down to a size too small to be held by the wire.

The ratio of the particle diameter to its initial value, d/do’ is

plotted against the fractional burn-off, f, to see if the combustion
follows the shrinking sphere mode. The apparent density of the carbon
sample during each interval of combustion is also calculated from the
weight and diameter data. The relationship between apparent density
and particle diameter is used later in the analysis of the experimental

results involving fixed carbon samples. Since the particle moves

34

freely within the entire bed, the combustion rates measured are the
overall ones which reflect the combustion characteristics both in the
bubbling and in the grid region. It should be noted here that many
studies (7,8,44,45) imposed some restrictions on the particle movement
so that the combustion rates were measured exclusively in the bubbling
region.

After the combustion mode of electrode graphite spheres has been
examined, the next step is to measure the burning rates at various
locations in the grid region. As shown in Figure 2.2, a graphite sphere
is fixed at a location along the axis of the jet, while another
graphite sphere is fixed at the same vertical distance from the
distributor along the axis of the dense phase. The method of holding
each carbon sample rigidly at its position has been described in the

previous section. While the bed is fluidized with N2, both carbon

samples are heated until the temperature of each carbon measured with a
thermocouple cease to change. Unlike in the bubbling region, the bed
temperature may not be uniform in the grid region due to entrance
effects, especiallly very near the distributor. The fluidizing gas is
then quickly switched to air, and the particle temperatures are
continuously recorded on a digital readout meter during combustion.
After a predetermined time, again depending on the particle reactivity,

the gas is switched back to N2 to stop further combustion, and the

carbon samples are quickly removed from the bed simply by lifting the
clamp. After cooling in the liquid nitrgen container, three
perpendicular dimensions of each of the carbon samples are carefully

measured, after which they are returned to their specified positions in

35

the bed fluidized with N2. The same sequence of procedures is repeated

until both carbon samples burn down to a size too small to be held by
thermocouples.

Due to a slight distortion in the spherical shape during
combustion, the diameter of each carbon sphere is calculated as the
average of three perpendicular dimensions, and the weight loss due to
combustion is estimated from the apparent density-particle diameter
relationship obtained earlier. The bed temperature in the bubbling
region is also monitored with the use of a separate thermocouple so
that the temperature differences between each of the carbon samples and
the bed as well as the temperature gradient within the entire bed can
be obtained experimentally. As shown in Figure 2.2, the vertical
distance of fixed carbon samples can be varied from very near the
distributor to the grid region height, H, where the two burning rates
are expected to become approximately equal. The effects of superficial
air velocity and inert particle size on the combustion rates are also
to be examined, and Table 2.2 summarizes the experimental conditions

considered in this study.

36

Table 2.2 .Experimental conditions for single particle combustion

of electrode graphite spheres in air at 1163 K and 1 atmx

 

 

Run dp(pm) U(cm/s) U/Umf Uo(m/s) fixed sample
number position (cm)**

1 460 11.0 1.5 9.4 2.54
2 460 11.0 1.5 9.4 6.35
3 460 11.0 1.5 9.4 7.62
4 460 11.0 1.5 9.4 8.26
5 460 14.7 2.0 12.5 2.54
6 460 14.7 2.0 12.5 7.62
7 460 29.4 4.0 25.0 2.54
8 460 29.4 4.0 25.0 5.72
9 460 29.4 4.0 25.0 7.62
10 460 29.4 4.0 25.0 10.16
11 230 5.5 3.0 4.7 2.54
12 230 5.5 3.0 4.7 5.08
13 230 5.5 3.0 4.7 7.62
14 230 7.3 4.0 6.2 2.54
15 230 7.3 4.0 6.2 5.08
16 230 7.3 4.0 6.2 7.00
17 230 11.0 6.0 9.4 2.54
18 230 11.0 6.0 9.4 5.08
19 230 11.0 6.0 9.4 5.72
20 620 26.5 2.0 22.6 2.54
21 620 26.5 2.0 22.6 5.08
22 620 26.5 2.0 22.6 8.90
23 620 39.7 3.0 33.8 2.54
24 620 39.7 3.0 33.8 5.08
25 620 39.7 3.0 33.8 7.62
26 620 53.0 4.0 45.1 2.54
27 620 53.0 4.0 45.1 5.08
28 620 29.0 2.2 25.0 2.54
29 620 29.0 2.2 25.0 5.08

 

37

* Static bed height - 20 cm.
** Denotes the vertical distance of two carbon samples from the
distributor, one fixed in the dilute phase and the other fixed

in the dense phase.

2-5. Estimation of the Minimum Fluidization Velocity, Um:

The experimental fluidized bed unit described in the prvious
section is not equipped with a pressure-measuring device for the

estimation of Umf at high temperatures. Unlike in the bubbling region

where a burning particle spend most of its time in the particulate
phase, the minimum fluidization velocity is not expected to play an
important role in the grid region, since there is no significant
quantity of bubbles present to affect the bed hydrodynamics as severely

as in the bubbling region. However, reasonable values of Umf for

silica sand are needed in the theoretical analyses given in Chapter 3,
and we resort to use the available correlations for its estimation.
At the moment, there are numerous empirical correlations available

in the literature for an order-of-magnitude estimation of UInf for

various bed materials at ambient conditions. For example, Wen and Yu

(46) suggested the following formula:

3 1/2
ds Umf Pg - 33.72 + 0.0408 Es Pf (Pg ‘”£) 3 - 33.7 (2.10)

#f #f2

38

Eq. (2.10) can be used as a first approximation if the particulate

phase voidage, emf’ and the particle sphericity, ¢s’ are unknown, and

similar correlations have been suggested by many investigators
(47,48,49).
As for the prediction of the minimum fluidization velocity at the

conditions of practical importance such as high temperatures and

pressures, Bin (50) concluded recently that the Ergun (51) equation can

be applied successfully to predict the values of Umf at different

conditions provided that experimentally determined values of UInf and

emf at ambient conditions from experiments with air or nitrogen are

used. Note here that Bin (50) assumed that emf and ¢s calculated as

fitting parameters remain essentially constant over the entire range of
operating variables. On the other hand, Stubington et al. (52)

suggested measuring Umf directly at different conditions, since ¢s's
are difficult to determine for a coal-derived char and emf may vary
with temperature. The variation of emf with temperature and pressure

was verified experimentally and explained in terms of variation in the
interparticle forces due to changing fluid-flow conditions around the
particle by Mathur et al. (53).

Due to the difficulties associated with accurately measuring emf

and ¢s at high temperatures, the values for Um in Table 2.1 have been

f
calculated using Eq. (2.10) with its parameters evaluated at 1163 K and

1 atm. Noting the fact that free bubbling occurs at or a little above

39

Umf for Geldart Group B particles such as silica sands used in this

study, the accuracy of Umf's in Table 2.1 has been checked by visual
observations, and the discrepancy between the calculated Umf's and the

observed ones is within 10 %. The particulate phase voidages at
minimum fluidization in Table 2.1 have been assumed to be constant at

0.4 for sand as in the study by La Nauze et a1. (8).

2-6. R su n Ex e me ts a d D' us io s

The experimental results of single particle combustion described

in Section 2-4 are presented and discussed in this section.

2-6-1. Wan
Many combustion studies (7,40) have concluded that carbon
particles burn primarily in a shrinking sphere mode. It can be seen in

Figure 2.5 that the data of fractional diameter, d/do’ lie considerably

above the curve for the shrinking sphere combustion at high fractional
burn-off, which indicates a significant internal burning as evidenced
by large reduction in the apparent density. Due to its less reactive
nature than coal chars and petroleum cokes, the reaction rate of
electrode graphite spheres appears to be low enough for oxygen to
penetrate a little farther into the inner pore surfaces before it
reacts with carbon. The apparent densities are plotted against the

particle diameter in Figure 2.6, and Eq. (2.11) is shown to predict the

40

apparent density within :5 % accuracy for the range of particle

sizes considered:

pp - 500 83'“ , kg/m3 (2.11)

where dp is in mm. It should be noted here that Eq. (2.11) is used to

calculate the overall combustion rates of fixed carbon samples from the
diameter data obtained during burn-off.
The calculation of Sherwood number in Eq. (2.9) requires the

overall kinetic data of graphite combustion along with the values of Dg
and Co’ Field et al. (54) re-examined the previous data using large

carbons such as electrode carbon samples of 10 - 15 mm diameter, and
suggested the apparent kinetic parameters tabulated in Table 2.3. Due
to the similarities in the size, porosity and type of carbon, we have
assumed that the combustion kinetics of electrode graphite spheres used

in this study is well represented by those in Table 2.3.

Table 2.3 Kinetic and physical data for mass transfer calculations

 

Overall reaction : C + O 4 CO

2 2 (2.3)

Kinetic data : n - 1
A0 - 87,000 kg/m2 s atmn
Ea - 36 kcal/mole

950 S T 5 1,600 K, 0.01 S P S 0.21 atm
P 02

 

41

Physical data : 0g - 0.0002542 m2/s

co - 0.0707 kg/m3

at 1163 K and 1 atm

 

The Sherwood numbers thus calculated for a freely moving graphite

sphere are shown in Figure 2.7 to be fitted quite well by Eq. (2.12):

-1.05
. m
emf (JD)mf Remf - 0.105 + 1.505 [ ] , (2.12)

an- Inn.

for 0.1 < Re < 20 and l S d /d < 200,
m p s

f

where m - 0.35 + 0.29 (dp/ds)-O.50'

mass transfer factor (jD)mf - km Sc2/3/ Umf’

Re - Umf d

p pf / pf (1 - emf), and (1p and (18 are the carbon and bed

mf

inert particle size, respectively. Eq. (2.12) is an empirical

correlation derived by Prins et al. (9) near ambient conditions, and
has been shown to correlate well other combustion data at extreme
conditions (9). The good agreement between Eq (2.12) and our data in
Figure 2.7 thus seems to validate the assumption of using the kinetic
data by Field et al. (54) for our electrode graphite samples.

As expected, the degree of mass transfer control for a freely

moving graphite sphere is shown in Figure 2.7 to decrease with

42

decreasing particle size with their values being substantially less
than unity. This is another indication of the chemical kinetics having
a more pronounced effect on the combustion of electrode graphite
samples than more reactive petroleum cokes (7). Throughout the
calculations of Sh and d, the particle temperature was assumed to be
constant at 1233 K during burn-off, i.e. 70 K above the bed
temperature, which was verified to be reasonably valid in a separate
experiment using a flexible thermocouple.

The overall combustion rate in Eq. (2.8) can be rewritten as:

 

2
do N
R A - c d , (2-13)
c1 dp/Sh + c2 3 p

where c's are constants. If the Sherwood number is large, i.e. the
combustion rate is controlled purely by the chemical kinetics, N takes
the values of 2. On the other hand, if the Sherwood number number is
small or the rate is controlled by mass transfer, N becomes unity. As
shown in Figure 2.8, the combustion of electrode graphite samples is
controlled solely by the chemical kinetics at 1073 K due to its low
reactivity, and the influence of mass transfer becomes significant at
1163 K. The analysis given above is based on the assumption of the
Sherwood number remaining constant during burn-off. As will be shown
later in Section 2-6, the Sherwood number indeed decreases with
increasing burn-off %, and the accuracy of Eq. (2.13) is, therefore,
questionable in determining the relative influence of the chemical

kinetics and mass transfer in the combustion of carbons.

43

 

 

d/do=- (l—f)l/3

.3 .. \

 

 

 

 

~4>
.2—
.1—

l I L I ll 11 1_
0 1 2 3.4 5 6 7 8 91.

Figure 2.5 Fraction of initial diameter and the ratio
of densities versus fractional burn-off, f
( TB: 1163 K, U0: 16.6 m/s, d8: 460 pm ).

O

Apparent carbon density of graphite,[3(Kg/m3)

Figure

H
O\

1..»
\n

i-’
r:

i-‘
M.)

1.1
N

1.1
[—1

1...;
O

44

 

 

     

 

 

 

x10-3
7 _ .4 3
p 600 CID , Kg/m
_T where dp is in mm.
1 1 1 1 1 1 1
1 2 3 4 5 6 7 8 9 10 ll
dp (M)
2.6 Apparent carbon density versus carbon

diameter during burn-off ( TB-ll63 K,
Uo- 16.6 m/s, dsa 460 pm ).

45

 

 

 

 

 

 

10 1.0
9 - - -9
8 "' A AAAAA‘ 8

A AAAAAA M
.__,, ..
7 ' A 7
A i
6 " "‘ .6
5 - - -5
sn <15
14, s - .4
Prins et a1. (9) o 3

3 .
2 .2
1 .1
O l J l J l l l l - 0.0

1 2 3 4 5 6 7 8 9 10
dp (mm

Figure 2.? Variations in Sherwood number and degree
of mass transfer control,¢, with particle
diameter during burn-off ( TB=1163 K,
Uo=-16.6 m/s, ds- 460 pm ).

46

 

 

 

 

 

x107

1; 10

\m9t

x 8 L

< 7 _

mo 6 _

85L-

“'{5

a 4 '

$2

.3

pp 3 ‘

U)

s

,0

8

o 2 —

H

H

m

m

d.)

>

<3

1 1 1 l 1 1 1 11
2 3 4 5678910 20
dp(mm)

Figure 2.8 Overall combustion rate versus particle
diameter for a freely moving graphite
sphere ( Uo- 16.6 m/s, ds= 460 pm ).

47

2-6-2. Est at n f t e id re 10 ei ht

Figures 2.9 - 2.11 are log-log plots of overall combustion rate
versus carbon particle diameter in a bed of silica sand of mean
diameter 620 pm with superficial air velocity being twice that at
minimum fluidization. At 1 inch above the distributor (Figure 2.9),
the combustion rates of a graphite sphere fixed in the dilute phase are
shown to be at least twice as high as those in the dense phase. While
the difference between the two combustion rates is still significantly
large at 2 inches above (Figure 2.10), they become approximately equal
at 3.5 inches above the distributor (Figure 2.11).

As the vertical distance from the distributor or the axial
distance increases, the cumulative amount of solids entrained into the
jet increases, while the amount of gas remaining in the jet decreases
due to the gas leakage into the dense phase throughout the jet height.
Hence, the overall effect is to increase the mass transfer resistance
local to a burning carbon particle and to decrease the convective
transport of oxygen by the bulk gas, which results in lowering the
overall combustion rates in the dilute phase, as shown in Figure 2.12.

Particles between two adjacent vertical jets near the distributor
are relatively immobile, and the combustion in this dead zone is
expected to closely resemble that in a packed bed. Above the dead
zone, there is a region of sluggish particle motion, called the quasi-
dead zone above which the so-called intermittenly mixed region exists
(23). It is, therefore, expected that the combustion rate of a carbon

particle fixed in the dense phase increases with increasing vertical

48

distance, until it eventually becomes equal to the combustion rate of a
carbon particle fixed in the dilute phase at the same vertical
distance, as shown in Figure 2.12. This vertical distance of two equal
combustion rates can be regarded as the grid region height measured
from the reaction point of view. The accurate measurement of the grid
region height is of great practical importance in the modeling study of
the entire bed.

As the superficial air velocity increases, the grid region height
is shown in Figures 2.13 and 2.14 to decrease from 3.5 inches at
U - 2 Um

to 3 inches at U - 3 U and 2 inches at U - 4 U . The same
mf mf

f
trend is also observed in beds of sand of mean diameters 460 pm
(Figures 2.15 - 2.17) and 230 pm (Figures 2.18 and 2.19). The
experimental grid region heights are further tabulated in Table 2.5,
and compared in Table 2.4 with the jet penetration length calculated
from Eqs. (1.2)-(1.5). As shown in Table 2.4, all correlations predict
the trend opposite to our results, since they do not take into account
the fact that the dense phase becomes completely fluidized at lower
heights with increasing gas flow rate.

Based on the theory of spouted beds by Lefroy and Davidson (56),
Fakhimi et a1 (57) derived the following expression for the height of

entrance effect, he:

3

0.3 .-1
he - 0.51 s (S/ds) Sin (Umf/U), (2.14)

49

where S is the orifice spacing or the pitch size. It should be noted

here that he was defined as the vertical distance from the distributor

at which the dense phase becomes fluidized (57). Hence, according to

Wen et al. (16), bubbles should form at z - he’ as shown in Figure 2.2.
Furthermore, the values of he should always be smaller than those of

the grid region height, except at minimum fluidization, as shown in

Figures 2.20 - 2.22 for U somewhat greater than 2 Umf' For U less than
2 Umf’ Eq. (2.14) significantly overpredicted the experimental results

of Fakhimi et al. (57) in a three dimensional bed of sand of 350 pm
mean diameter, and its limited application near minimum fluidization is
indicated by the dashed portion of the curve in each of Figures 2.20 -

2.22. This is unfortunate because H and he should become equal at

minimum fluidization due to the absence of bubbles in the bed and Eq.
(2.14) could otherwise be used to determine the grid region height at

minimum fluidization, Hmf' As will be shown in Chapter 3, HInf is an

important parameter in the grid region study and is difficult to
measure due to factors explained in Section 2-5. As shown in Figures

2.20 -2.22, Hmf's have been estimated by extrapolating the data to U -
Umf’ and tabulated in Table 2.5. However, Eq. (2.14) still seems to be

the only one of its kind which correctly predicts the trend of
decreasing grid region height with increasing gas flow rate. Eq. (2.14)
may also be used to estimate the portion of the grid region occupied by

the bubbles or the distance travelled by bubbles prior to coalescence.

50

This is denoted by z in Figures 2.20 - 2.22, and is shown to increase

b

with increasing U except for ds - 620 pm.

The grid region height for 460 pm sand is given in Table 2.5 as

5.7 cm or 2.25 inch at U - 4 Umf' As shown in Figure 2.23, the overall

combustion rates are the same, regardless of fixed particle position
above the grid region height, which indeed verifies the uniformity of
the bubbling region. Figure 2.23 further indicates that the grid
region height, as defined in Section 2-3, is the correct measure of
dividing the bed for the modeling purpose. The values of H in Table
2.5 also show that the grid region occupies up to 40 % of the entire
volume of the bed, which suggests that the grid region cannot be

ignored in the overall modeling study.

Table 2.4 Comparison of grid region height with jet penetration

 

 

length (dg- 460 pm, TB -1163 K)
correlations U/Umf -2.0 U/Umf - 4.0
Merry (14) 2.7 cm 3.7 cm
Yang and Keairns (21) 7.9 cm 10.2 cm
Wen et al. (22) 7.5 cm 9.3 cm
Zenz (55) 7.6 cm 17.3 cm
Fakhimi (57) 7.3 cm 3.5 cm
Present work 7.6 cm 5.7 cm

 

51

Table 2.5 Experimental grid region heights at 1163 K

 

 

 

 

Inert particle U/U H(cm) h**(cm)

size mf e

1.0 8.8* 27.2

230 3.0 7.6 5.9

4.0 7.0 4.4

6.0 5.7 2.9

1.0 9.0* 21.7

460 1.5 8.3 10.1

2.0 7.6 .3

4.0 5.7 .5

1.0 11.2* 19.6

620 2.0 8.9 6.5

3.0 .5 .3

4.0 .1 3.2

 

* Extrapolated values.
** Calculated from Eq. (2.14).

52

 

 

 

 

30
ds=620 pm
20 r- .
z-l inch
U=2 Umf
10—
m 5"
\
00
M ....
. e
o-
2 —- e
x
<:
O
a:
l l l l l l L Ll I ,
l 5 10 20
d
p (m)

Figure 2.9 Overall combustion rate versus particle
diameter ( TB: 1163 K, an 22.6 m/s;
dilute phase (0), dense phase (e) ).

53

 

 

 

 

 

20
dS=620pm
z = 2 inch
10 U = 2 Umf
Q L.
00
5d ._.
s- 5-
<3
r1
x _
q;
0
a: _
1 l
1 5 10 15
d mm
I)()

Figure 2.10 Overall combustion rate versus particle
diameter ( TB 8 1163 K, Uo = 22.6 m/s;
dilute phase (0), dense phase (e) ).

54

 

 

 

 

20
dS = 620 pm
Z = 3.5 inCh
U = 2 U
10___ mf
0) hi
\bD
as 5..
N. P-
C)
r1
N
‘< _
o
a:
o
1-—- e
8 I l 1 l I 1 1 ill
1 5 10 15
d
p (m)

Figure 2.11 Overall combustion rate versus particle
diameter ( TB = 1163 K, UO = 22.6 m/s;
dilute phase (0), dense phase (e) ).

30

20

10

RCA x107, Kg/S
kn

Figure 2.

55

 

    
   

 

 

 

d s 620 pm 1"
S 3 5"
I" U = 2 U .
Inf 2"
Z = l inCh (A 9‘)
= 2 inch (0,!) l
= 3.5 inch (0.0)
1..
- l l l I 1 1 14 1
l 5 10 20
d
p (mm
12 Effect of particle position on overall

combustion rate ( TB = 1163 K, UO - 22.6 m/s;
dilute phase (open symbols), dense phase
(closed symbols) ).

56

 

Kg/s

RCA x107,

 

 

 

 

dp (mm)

Figure 2.13 Overall combustion rate versus particle
diameter ( TB = 1163 K, Uo = 33.8 m/s;
dilute phase (open symbols), dense
phase (closed symbols) ).

57

 

 

 

 

3O
20 —
lO ———
(I) _
\
m _
k:
to.
H 5 _
N
< _.
O
a:
l
l

 

dp (mm

Figure 2.14 Overall combustion rate versus particle
diameter ( TB = 1163 K, Uo = 45.2 m/s;
dilute phase (open symbols), dense phase
(closed symbols) ).

10

58

 

 

 

 

 

1- d3 = “'60 pm
" U : 1.5 Umf
"' 3.25"
L
_ l"
<+——-//
I
2 5 10 20
dp (mm)

Figure 2.15 Overall combustion rate versus particle

diameter ( TB s 1163 K, Uo s 9.4 m/s;
dilute phase (open symbols), dense phase
(closed symbols) ).

59

 

  
   
   

 

 

 

20
ds=460plm
= 3 inch (o,e)
10L_U=2Umf
m ._
\\ _.
110
x:
to 5-
H
x _
<
O
m
l...
.8 I lJlllll
2 5 10 20
dp(mn0

Figure 2.16 Overall combustion rate versus particle
diameter ( TB = 1163 K, Uo - 12.5 m/s;
dilute phase (open symbols), dense
phase (closed symbols) ).

60

 

 
 
  

 

 

20
(1S = 460 pm
2 = 1 inch (A,A)
= 2.25 inch (0,0)
- o
m _
\
w _
:24
so 5—
H
x —
<
o
a:
l I 4 I I 1 II I
2 5 10 20

dp (mm)

Figure 2.17 Overall combustion rate versus particle
diameter ( TB s 1163 K, Uo = 25.0 m/s;
dilute phase (open symbols), dense
phase (closed symbols) ).

 

61

 

5 _
dS : 230 pm
.. z s 1 inch (0.0) °
= 3 111.011 (Ap‘) O
o

*- U=3Umf

7
RCA x10 , Kg/s

i-'

 

 

 

 

dp (mm)

Figure 2.18 Overall combustion rate versus particle
diameter ( TB = 1163 K, UO = 4.7 m/s;
dilute phase (open symbols), dense
phase ( closed symbols) ).

62

 

 

 

 

 

lO
_ dS s 230 pm 0
_ z = 1 inch (o,e)
— = 2.25 inch (4,4)
5._ U = 6 Umf
a) .-
\
no
a:
B. .—
O
H
x
<:
o
a:
1
1h-
.5'—
3 J l
1 15
d mm
p ( )

Figure 2.19 Overall combustion rate versus particle
diameter ( TB = 1163 K, Uo = 9.4 m/s;
dilute phase ( open symbols), dense
phase (closed symbols) ).

63

 

22.2 \

H/S

Eq.

 

(2.14)

GB

Data

s 230 pm

 

 

U/U

mf

Figure 2.20 Ratio of grid region height to pitch
size versus U/Umf , TB s 1163 K.

 

64

 

\ d =Li'60’lm

H/S

 

 

 

 

Figure 2.21 Ratio of grid region height to pitch

Size versus U/Umf , TB 3 1163 K.

65

 

d = 620 pm

H/S

 

 

Eq. (2.14)

 

 

 

U/Umf

Figure 2.22 Ratio of grid region height to pitch
size versus U/Umf , TB - 1163 K.

66

 

 

 

 

 

2 5 10 20

dp (mm)

Figure 2.23 Effect of particle position on overall
combustion rate in the bubbling region

( TB = 1163 K. Uo = 25-0 m/S: 2.25 inch
(0). 3 inch (0). 4 inch (4) )-

67

2-6-3. Ma ran r chara terist cs f f'xed carbon sam les

As discussed in Section 2-6-2, the mass transfer resistance in the
dilute phase is expected to increase with increasing vertical distance
from the distributor due to solids entrainment and gas leakage
throughout the jet height. On the other hand, the reverse trend should
hold in the dense phase. These trends have been verified experimentally
and the typical results are shown in Figures 2.24 - 2.27.

It is further indicated by Figures 2.26 and 2.27 that at the grid
region height, as determined in Section 2-6-2, not only the overall
combustion rate but the mass transfer resistance of the dilute phase
are the same as those of the dense phase. Hence, it can be concluded
that the mass transfer resistance as well as the overall combustion
rate of fixed carbon samples should be independent of the sample
position above the grid region height, due to the uniformity of the
bubbling region. Figure 2.28 indeed shows that to be the case, thus
substantiating the validity of H, as defined in Section 2-3, in the
modeling study. It should be noted here that for a carbon sample
moving freely in the bubbling region, the actual values of both overall
combustion rate and mass transfer coefficient are lower than those
depicted in Figures 2.23 and 2.28 under the same operating conditions.
This is because fixed carbon samples are under the constant influence
of bubbles, which increases both rates. Using the first principles and
the theories of spouted beds, mass transfer correlations are developed

from experimental Sherwood numbers in Chapter 3.

68

 

 

 

 

20
d3 = 620 pm
Z 2: 1 inch
B U : 2 Umf
O
O
h— 0
10- ° °
0
Sh
O O
0
o ° .. . e
0
e ’ .
— 0
O I l l l l l l l
2 5 10
d
p (mm

Figure 2.24. Variations in Sherwood number with
particle diameter ( TB = 1163 K,

Uo s 22.6 m/s; dilute phase (0).

dense phase (0) ).

69

 

 

 

 

20
d8 : 620 pm
— Z = 2 inch
__ U = 2 Umf
O O
'_ o
o
10 " ° ..
Sh ° . e
- .o o
e e
e
_ o e ‘9
0 e
O . . .

— e
0 l I l J l l l l

2 5 10

d (mm)

P

Figure 2.25 Variations in Sherwood number with
particle diameter ( TB = 1163 K,
U = 22.6 m/s; dilute phase (0),

o
dense phase (e) )-

7O

 

 

 

 

20
_ dS = 620 pm
2 = 3.5 111011
_ U = 2 Umf
e
_ o
o 8 8
10 — e
Sh o
o e
' e
6
e
o
‘ e
d) o
_ o
e
o I I I I I I I
2 5 10
d
p (m)

Figure 2.26 Variations in Sherwood number with particle
diameter ( TB s 1163 K, Uo s 22.6 m/s;
dilute phase (0), dense phase (e) ).

lO

Sh

71

 

 

d = 460 pm

U s 4 Umf

 

2.25 inch

 

 

dp (mm)

Figure 2.27 .Effect of particle position on Sherwood

number ( TB = 1163 K, UO - 25.0 m/s;
dilute phase (open symbols), dense phase
(closed symbols) ).

72

 

 

 

 

lO

'- d3 = “60 pm

Z = 2.25 111311 (0)
= 3 inch (A) 02
" s 4 inch (0) A
U s 4 Umf ° 0°
_ A0
00
o o
__ A
0 <3
0 0
U A0
5 o 8
Sh 8°
.. 99
o O
A

o I .J I I I I I I

l 5 10

d (mm)

P

Figure 2.28 Effect of particle position on Sherwood
number above grid region height
( TB s 1163 K, UO s 25.0 m/s ).

73

2-6-4. Effects of superficial air velocity on RcA and Sh

 

For all inert particle sizes considered in this study, the overall
combustion rate has been found to increase with increasing U both in
the dilute and in the dense phase, as shown in Figure 2.29 for 620 pm
sand. Figure 2.30 also shows that for the same inert particle size of
620 pm, the increase in U has no effect on the mass transfer resistance

in the dilute phase. Hence, according to Eq.(2.9), the increase in RC

must be compensated by the corresponding increase in the degree of mass
transfer control, d, in order for the Sherwood number to remain the
same. In other words, the chemical rate must increase with increasing

U, and this is shown in Figure 2.31 by the significant increase in Tp

in the dilute phase. It is further shown in Figure 2.31 that the

increase in Tp with increasing U is much less significant in the dense

phase. Hence, the increase in the overall combustion rate of the dense
phase must be reflected upon the decrease in the mass transfer
resistance with increasing U, and this is shown in Figure 2.32 by the
significant increase in the Sherwood number with increasing U.

For 230 pm sand, the mass transfer resistance is shown in Figure
2.33 to decrease considerably with increasing U in the dilute phase,
while the effect of U on the mass transfer resistance is small in the
dense phase. It should be noted that this trend is generally opposite
to what has been observed for 620 um sand. For 460 pm sand, the mass

transfer resistance is shown in Figures 2.34 and 2.35 to decrease

74

considerably with increasing U both in the dilute and in the dense
phase.

Therefore, in the dilute phase of large inert particles, the
overall combustion rate is affected by U due to the change in the
chemical rate. As the inert particle size decreases, the influence of
the chemical kinetics diminishes, and the overall combustion rate is
affected by U mainly due to the change in the mass transfer resistance
in a bed of small inert particles. In the dense phase, the
corresponding trend is opposite to what has been stated for the dilute
phase above.

Prins et al. (9) observed that for all inert patricle sizes, the
mass transfer resistance is independent of U in the bubbling region in
which a burning carbon particle spend most of its time in the
particulate phase. This finding is consistent with the two—phase
theory of fluidization (19) which states that the gas flow in excess of
that required for minimum fluidization passes through the bed in the
form of bubbles. As shown in Eq. (2.10), the minimum fluidization
velocity strongly depends upon the particle size and, to a less extent.
the particle density. As the inert particle size increases, it thus
becomes more difficult to fluidize the dense phase, and a larger
portion of the gas flow entering the bed must leak into the dense
phase. Therefore, it seems that for 620 pm sand, the increase in U up

to 4 Umf has no significant effect on the mass transfer resistance of

the dilute phase due to a significant gas leakage, as shown in Figure
2.30. This result further suggests that the amount of gas leakage is

considerably more than what is required to fluidize the dense phase,

75

which is in essence consistent with the conclusion by Yates et a1.
(18); the dense phase voidage increases beyond its minimum value
briefly during the bubble formation.

By the same analogy, it is relatively easy to fluidize the dense
phase of small inert particles, and much of the gas flow entering the
bed remains in the jet to decrease the mass transfer resistance of the
dilute phase, while the dense phase is little affected by U, as shown
in Figure 2.23 for 230 pm sand. For 460 pm sand, the gas leakage is
relatively moderate, and the influence of U is significant in both
regions, as shown in figures 2.34 and 2.35. The relative difficulty of
fluidizing the dense phase can also be seen in Table 2.5 by noting that

the value of HInf increases with increasing inert particle size.

Furthermore, the minimum fluidization velocity appears to play a rather
important role in an implicit manner also in the grid region, since the
process of fluidizing the dense phase influences significantly the

distribution of the gas flow between the dilute and the dense phase and

possibly the solids entrainment rate as well.

76

 

 

 

 

30
20"
10 ___
to _.
\ _
b0
2 —
“o 5—
t—l
>4 _
<3
0
a: _.
l
l

 

dp (mm

Figure 2.29 Effects of U on overall combustion rate
( TB = 1163 K, dilute (open symbols),
dense phase (closed symbols) ).

77

 

 

 

 

20
r' d8 = 620 pm
2 = 1 inCh U
,_ U s 2 Umf :0;
s 3 Um. a 40
_ =4Umf (a) 8
_ 8&8
A ”b
10 r 80°
%A
Sh _ A g
o
A c?
.. o
O I I I I I I I I
2 5 10
d1) (mm)

Figure 2.30 Effects of U on the Sherwood number
in the dilute phase ( TB = 1163 K ),

78

 

 

 

 

200- a
o
_. U o o
x A o
c A o
H _ o o o
(n 65 0A A A D I: ‘3 o
B _ 0 00AA
I 0 %%AA
99‘ __ o
J
U]
a 100—
e e e . .
G) . . .
g ._ 44 A. A 1L .I IN"= TI“."‘
1; ‘ A AA
a
0)
C81. P-
; dS=620pm
U - 2 Umf (o)
__ =30,111.05)
- 4 Umf (a)
O I I I I I I I I
2 5 10
d (mm)

P

Figure 2.31 Temperature rise above bed temperature
( TB = 1163 K, dilute phase (open
symbols), dense phase (closed symbols) ).

20

10

Sh

79

 

 

 

ds=620pm
Z=linCh
U=2Umf(.)
=3Umf(A)
_ I
- 4 Umf ( )
I
I a ' A
A
I A
A
I ‘ .
1 A
n .e'
I‘ .0
0
e 0 '
e
I I I I I I I
5 10
d
p (mm)

Figure 2.32 Effects of U on the Sherwood number

in the dense phase ( TB = 1163 K ).

 

8O

 

 

 

 

10
d8 = 230 pm
— Z = 1 111.011
U = 3 Umf (01.)
= 6 Umf (09.)
U
D
U
5 - ° 0 °
0
D
Sh D
A A
A
._ A O
A A A A O O 0
"' O
O
o o 0° 0 z
_ I .5
. A 4. {:etefiiz'..
O I I I I .11 I I I
2 5 10
d
p (m)

Figure 2.33 Effects of U on the Sherwood number
( TB = 1163 K, dilute phase (open
symbols), dense phase (closed symbols) ).

81

 

 

 

 

lO
_ o
F o
o
A
F
A
_ o
o
A
5F 0 AA 0
D 0
Sh _ AA 00
0
A0
_ A
o o
F- ds=l+60pm
U=lo5Umf(0)
_ =2Umf(A)
= 4 Umf (n)
0 I I I I I I I I
2 5 10
d (mm)

P

Figure 2.3h Effects of U on the Sherwood number
in the dilute phase ( TB = 1163 K ).

82

 

 

 

 

10
— ds=1+60pm
Z=linCh
_ U:1.5Umf(.)
= 2 Umf (A)
L = 4 Umf (U)
I
I
5F"
Sh ' I
_ I I
I
._ I A
II
_. A.‘
A ‘ '
_ .I ...I,
O I I I I I I I I
2 5 10
d
p(mm)

Figure 2.35 Effects of U on the Sherwood number

in the dense phase ( TB : 1163 K ).

83

2-6-5. Effects of inert particle size on RCA and Sh

 

As shown in Table 2.1, the range of minimum fluidization
velocities for the three different sized sand particles is rather
large; the bed of 230 pm sand was found experimentally to be easily
slugging with considerable elutriation even at U equal to or a little
above that for 620 pm sand at minimum fluidization. It was, therefore,
possible only to compare two different inert particle sizes at a time
for the same superficial air velocity.

In Figure 2.36, the overall combustion rate is shown to decrease
in the dilute phase, as the inert particle size increases from 230 pm
to 460 pm at U - 11 cm/s. Figure 2.37 shows that the decrease in the
overall combustion rate is due to the increase in the mass transfer
resistance with increasing inert particle size. This is expected
because for larger inert particles, a smaller portion of the gas flow
entering the bed remains in the dilute phase due to a higher rate of
gas leakage in order to fluidize the dense phase. It will also be
difficult to aerate the larger particles with a lower gas flow rate,
thus decreasing the dilute phase voidage and increasing the resistance.
0n the other hand, the superficial gas flow rate increases with
increasing inert particle size in the dense phase, and the overall
combustion rate is higher for larger inert particles, as shown in
Figure 2.36. Figure 2.37 further indicates that this increase in the
overall combustion rate is mainly due to the increased chemical rate in

the dense phase. The small decrease in the mass transfer resistance is

84.

perhaps due to the difficulty of expanding the dense phase of larger
particles.
When the Sherwood numbers are plotted against the carbon particle

diameter at U - 4 Umf’ larger inert particles are clearly shown in

Figures 2.38 and 2.39 to give higher mass transfer coefficients in both
phases. It is worth noting here that similar results were obtained by
Prins et al. (9). for the bubbling region in which the transfer
coefficients are independent of the superficial gas velocity. On the
other hand, the transfer coefficients of the grid region were shown in
Section 2-6-4 to depend upon the superficial gas velocity in a rather
complicated manner, and the range of U covered in Figures 2.38 and 2.39
is so large that the effect of inert particle size alone cannot be
singled out as clearly as in Figures 2.36-2.37. However, one
interesting observation to be made in these figures is that all
experimental values of the Sherwood number, except those in the dense
phase of 230 pm sand, seem to approach a limiting value of a little
less than two, which is the theoretical minimum for a single sphere in
an infinite medium of stagnant fluid. Furthermore, small Sherwood
numbers exhibited by 230 pm sand seem to be related either to a
significant change in the mass transfer mechanism or to the dead zone
formation. These points are further examined in detail in the

theoretical analyses given in Chapter 3.

85

10

 

RCA x107, Kg/s

 

 

 

 

dp (mm)

Figure 2.36 Effects of inert particle size on
overall combustion rate ( TB = 1163 K.

dilute phase (open symbols), dense
phase (closed symbols) ).

86

 

 

 

 

lO
ZzlinCh
Uo = 11 cm/s
_ dS = 230 pm, (A,A)
2,460,111], (09.)
h-
A
_. O
A A
A A
5" A o
S A A o C)0
h
a. A o 0 O
O
L.
O
‘ 0001A
_. e O o
‘.A :Aa‘A
0 I I I I I I I J
2 5 10
dp (mm)

Figure 2.37 Effect of inert particle size on the
Sherwood number ( TB = 1163 K, dilute
phase (open symbols), dense phase

(closed symbols) ).

87

 

20
Z : 1 inch
F u U
U : mf
r ds = 230 um, (a)
= “'60 um, (A)
f- : 620 um. (O)

 

 
 
 
  

 

 

dp (mm)

Figure 2.38 Effect of inert particle size on the
Sherwood number in the dilute phase
( TB = 1163 K ).

lO

20

10

Sh

88

 

 

 

 

 

Z : 1 inch
U = 1+ Umf
L d8 = 230 um! (.)
t: “'60 um, (A)
I” I I I I l I " ' -
I I I I ' I" I I I I
O 5 10
dp (mm)

Figure 2.39 Effect of inert particle size on the

Sherwood number in the dense phase
( TB = 1163 K ).

89

2-6-6. Vertiggl prgfiles of mass transfer resistance

The experimental results have shown in Section 2-6-3 the general
trend that with increasing vertical distance, the mass transfer
resistance increases in the dilute phase and decreases in the dense
phase. Now, it will be useful to examine what the approximate profile
of the resistance look like in each phase.

Figure 2.40 shows that for 620 pm sand, the resistance at 1 inch
above in the dilute phase is practically as high as that at 2 inch
above, which seems to indicate that the resistance increases sharply
within a relatively short distance downstream the orifice and remains
constant thereafter. It is not possible to know with our experimental
data precisely how short the distance is, but it must be at most one
half of the grid region hight. As the inert particle size is decreased
to 230 pm, the resistance in the latter half of the grid region is
shown in Figure 2.41 to increase more significantly than 620 pm sand.
For all inert particle sizes, the resistance of the dilute phase must
increase abruptly at the orifice due to sudden gas leakage and solids
entrainment. Therefore, both mass transfer coefficient and voidage in
the dilute phase are expected to decrease with upward concavity along
the axial coordinate, and the concavity smooths out with decreasing
inert particle size.

The mass transfer resistance of the dense phase appears to
decrease more or less gradually over the entire grid region for all
inert particle sizes and superficial gas velocities, as shown in Figure

2.42 for 620 pm sand. The voidage of the dense phase can be regarded

90

as that in a packed bed, ep, at the distributor and increases to e at

b

the grid region hight. Noting that the difference between Eb and 6p is

on the order of 0.1, the profile of e is expected to be rather flat in
the dense phase along the vertical coordinate. Hence, the gradual
decrease in the resistance appears to be caused by the continuous

influx of gas from the dilute phase throughout the jet height.

91

 

20
_ dS = 620 pm
U = # Umf A
= 2 inch, (O)

10 -

Sh -

 

 

 

 

d mm

p()

Figure 2.40 Variations in the Sherwood number along
the vertical distance in the dilute phase
( TB = 1163 K ).

92

 

 

 

 

 

10
as u 230 um
U = 6 Umf
z = 1 inch, (A)
h.
A
A
A A A A
5 _ A
A
A
Sh r
O
O I I I I J I I I
2 5 10
d mm
10( )

Figure 2.41 Variations in the Sherwood number along
the vertical distance in the dilute phase
( TB = 1163 K ).

93

 

 

 

 

 

20
_ ds=620pm
U = 2 Umf
10 _
Sh _
r
O l l l I I l l l I
l 5 10
d mm
p()

Figure 2.42 Variations in the Sherwood number along
the vertical distance in the dense phase

( TB : 1163 K ).

CHAPTER3

THEORETICAL ANALYSIS OF BASS TRANSFER CHARACTERISTICS

IN THE GRID REGION OF A FLUIDIZED BED COHBUSTOR

94

95

3-1- W

Although there are many correlations proposed in the literature
concerning mass transfer in multiparticle-fluid systems, their
applicability in fluidized bed combustion is severely limited due to a
dilute situation and a significant difference in size between active
and inert particles. Furthermore, unlike in the bubbling region, the
experimental results in Chapter 2 have shown that the mass transfer
resistance in each phase of the grid region varies in a rather
complicated manner, depending on all operating variables considered
such as inert particle size, superficial gas velocity and particle
position. It appears that no effort has been made to study mass
transfer in the grid region of a fluidized bed combustor, and we now
attempt in this chapter to examine its theoretical aspects and to

derive mass transfer correlations from the experimental data.

3-2. v w Mass ans e tud es 1 Mu ti article-Fluid S stems

3-2-1. naskzreuns

Oxygen can be transported to a carbon particle burning in a dense
bed of inert particles by both molecular diffusion and convection. In
the single particle combustion of reactive carbons, the chemical rates
are so fast that the concentration gradient for the diffusive and
convective transport of oxygen can be assumed to exist only within the
gaseous boundary layer surrounding each carbon particle in which CO

oxidation takes place. For unreactive carbons such as electrode

96

graphite, it was shown in Figure 2.7 that the same assumption can be
made regarding the concentration gradient of oxygen, if the apparent
kinetic data based on the external surface area of the particle are
used for the calculation of mass transfer coefficients.

The effective area available for diffusion is reduced due to the
presence of inert particles and commonly taken as the local voidage
times the total area free of inert particles. On the other hand, the
characteristic velocity for convection in the boundary layer is
difficult to calculate even in a laminar fluid.

In this Section, we review some of the important works on mass
transfer in general multiparticle-fluid systems as well as fluidized
beds by focusing our attention particularly on how the local voidage

and the convective velocity were handled in each model.

3-2-2.

 

As mentioned earlier, despite the importance of the grid region on
the overall bed performance, all the studies on mass transfer reported
in the literature have been done exclusively in the bubbling region,
and the following is a brief summary of such studies.

Avedesian and Davidson (5) first developed a comprehensive
mathmatical model for the burn-out time of a batch of char particles.

They assumed in their model that neither CO2 nor 02 were present on the

particle surface at a bed temperature of 1173 K and that the transport

of O2 to the burning particle was primarily by molecular diffusion due

97

to small Reynolds number, based on Umf’ of order of l. The Sherwood

numbers were shown to be fairly constant at 1.42 during burn-off, which
suggested that forced and natural convection effects were indeed
negligible. They further proposed that the limiting value of 2 for the
Sherwood number in the absence of inert particles must be multiplied by
the particulate phase voidage.

Ross and Davidson (6) later extended the work by Avedesian and

Davidson (5) by noting that the rate of reduction of CO2 by carbon is

negligible at a bed temperature of 1173 K. They also included the
effects of the chemical kinetics in the model, and concluded that the
higher values of the Sherwood number on the order of 3.5 was indicative
of convection.

Tamarin (58) calculated the average tangential stress created by a
uniform flow around a sphere using the solution of the Prandtl boundary
layer equations and equated the stress to the bed weight divided by the

surface area of the sphere to obtain the following expression:
Sh - 0.243 (Sc Ar)1/3 (dp/ds)1/2 (3.1)
where Ar is the Archimedes number, defined as d: pf (pS - pf) g / p: ,

and Sc is the Schmidt number, defined as pf/prg. Eq. (3.1) states

that the mass transfer coefficient does not depend on the gas velocity
but is determined by the average tangential stress created at the

surface of the particle suspended in a gas flow (58). The term,

98

(dp/ds)1/2’ was inserted into Eq. (3.1) without any experimental

verification simply to account for the difference in size between
active and inert particles, and its inherent difficulties in predicting
the experimental observations have been discussed by Prins et a1. (9).

La Nauze and Jung (7) calculated the Sherwood numbers of petroleum
coke particles using their known kinetic data, along with the
assumptions of CO burning close to the particle and a constant particle
temperature of 1303 K, 130 K higher than the bed temperature. The
Sherwood numbers were shown to be well correlated by the Ranz and
Marshall equation (33) modified a little to account for the presence of
inert particles, viz:

1/2 1/3

Sh - 2 e + 0.69 (Re/ab)

b Sc

(3.2)

where the Reynolds number is based on the superficial gas velocity, U.
Although Eq. (3.2) well represented the experimental results by La
Nauze and Jung (7), the two-phase theory of fluidization (19) suggests

that the characteristic velocity and voidage should be Umf and Emf’

respectively, instead of U and ab, since the particles burn mostly in

the particulate phase. This point was later grasped by La Nauze et al.
(8) in their unsteady state model. In addition to the oxygen transport
from the gas flowing through the particulate phase, they assumed in
their model that packets of particles formed around the periphery of a
bubble transport fresh oxygen to the burning particles, while they are

circulating within the bed. They solved the unsteady state diffusion

99

equation in the same manner as Higbie's formulation of the penetration

theory, and suggested the following expression:

 

1/2
Sh - 2 emf + “emf dp(Umf/€mf + Ub ) , (3.2)
2
«D
8

which is now of the form consistent with the two-phase theory.
In deriving Eq. (3.2), La Nauze et a1. (8) represented the
resistance by inert particles to oxygen transfer by using the effective

diffusivity, D - emf

D8, in the diffusion equation. Carvalho and
Coelho (59) later argued that instead of D, the diffusivity of oxygen

in air, Dg’ should be used, since it is the area open to diffusion
which is only emf times the total area. Agreement between the

corrected version of Eq. (3.2) and the experimental Sherwood numbers
was shown to be not as good (59). It should be noted that Eq. (2.3)
further requires the accurate estimation of the size, frequency and
velocity of bubbles which are difficult to measure experimentally.
Using extensive mass transfer data of naphthalene spheres

vaporizing in air-fluidized beds of glass beads, alumina and silica

sand at 65°C, Prins et al. (9) proposed an empirical correlation, as
shown in Eq. (2.12), which explicitly shows the effects of both active
and inert particle sizes on the mass transfer coefficient. The
validity of correlating experimental data with the modified Reynolds

number, Remf - Umf dp pf / uf (l-emf), was questioned by Nishimura and

'IOO

Ishii (60). Where the voidage approaches unity, namely for a single
sphere in an infinitive medium, this modified Reynolds number becomes
infinity and physically meaningless, and such a Reynolds number cannot
be derived theoretically (60).

One interesting observation made by Prins et al. (9) was that
samples fixed right above the distributor exhibited higher mass
transfer coefficients by 20 -50 % than the rest of the bed even for
this low temperature vaporization with no considerable heat of
reaction. Even though they provided no explanation for these high
rates, their results indeed suggest a quite different mechanism for

mass transfer in the grid region.

3-2-3.

 

When all particles are actively involved in the mass transfer
process, the boundary conditions are not the same as in a diluted
system, and studies on such diluted systems are rather rare. Here, we
begin by reviewing two works which have been tested against the data in
diluted systems.

Kunii and Suzuki (61) developed a channeling model in which void
spaces in packed beds were assumed to be unevenly distributed so that
the selective flowing of fluid or channeling occured in the loose
section in a bed of fine particles. They divided the bed into many
blocks of particles which were seperated from one another by the void
channels, and further assumed that molecular diffusion took place in

the direction perpendicular to flow in each channel. They proposed the

101

following expression for mass transfer under the flow condition of low

I
Peclet number:

Sh - w: Pe , for Fe < 10 (3.3)
6 (1-.) s P P

where us is the particle shape factor, 6 is the ratio of average

channeling length to particle diameter, and Pep is the Peclet number
for mass transfer, defined as de/Dg' The drawback of this approach is

the accurate estimation of 6 which was incidently used as a fitting
parameter in correlating experimental data. It is interesting to note
that the data by Bar-Ilan and Resnick (62) in a diluted system was
fitted well by Eq. (3.3) with 6 - 1, that is, no channeling of flow,
which suggests that in diluted systems, the effect of flow channeling
is negligible.

Prins et al. (9) measured additional mass transfer coefficients in

the same bed as before but at U - 0.8 Umf’ and found that those packed

bed data could also be represented reasonably well by Eq. (2.12), if
the superficial gas velocities were used in 1D and Re, instead of Umf'
The important conclusion was that the rate of mass transfer in a
fluidized bed is the same as in a fixed bed of similar particles, the
same porosity and at the same gas velocity.

We now further review two other studies on all particles active

systems, because of their distinctive approach to the problem of

finding the local voidage and the characteristic velocity of

102

convection. The study of Nelson and Galloway (63) was initiated from
the difficulties of explaining extremely low mass transfer rates in the
low Reynolds number range with the theory for a single sphere in an
infinite medium. They formulated the problem according to the method
of the penetration theory using the concentric spheres free surface
cell model of Pfeffer and Happel (64) and a finite radius boundary
condition. They further introduced the boundary layer theory in their
model to estimate the surface renewal frequency, and this resulted in

1/2 1/3

the terms, Re and Sc , appearing in their final expression for the
Sherwood number at infinite dilution. It should be noted that the
Reynolds number was based on the bulk fluid velocity. The local
voidage was calculated simply by letting the voidage of the sphere and
its surroundings enclosed by the outer spherical shell match that of
the system. The significance of their results was that the dependence
of the Sherwood number on Re was linear at low enough flow rates, and
the Sherwood number became zero, instead of two, when there was no
flow.

For high Reynolds number situations, Nishimura and Ishii (65)
applied the same free surface cell model (64) in their numerical
calculation of the velocity profiles and the local voidage around a
sphere in a swarm which were subsequently used in their later work (60)
in solving the steady state diffusion equation. They further assumed
that the Sherwood number has two components, molecular diffusion and

convective, and suggested the following correlation from their

theoretical results:

103

1/2 1/3 6-1/2

Sh - ____2____ + 0.60 Re Sc

(l-e)1/3

(3.4)

where the Reynolds number is based on the relative velocity between a

solid and fluid , uR. It is interesting to note that Eq. (3.4) reduces

to the Ranz and Marshall equation (33) when 6 - 1.

Both of these studies clearly showed some promising features in
the direction of improving the model predictions in multiparticle-fluid
systems. However, it is unfortunate that they are applicable only to

the systems in which all particles are active.

3-3. v n o o e at s G id Re ion

3-3-1. e sf u tem

Regardless of the concentration of active particles in a
multiparticle-fluid system, most mass transfer correlations were shown
in Section 3-2 to have been developed around the steady state forced
convection equation by Ranz and Marshall (33):

1/2 1/3

Sh - 2 + a Re Sc , (3.5)
where a is usually taken as 0.6. Eq. (3.5) is applicable to single
spheres in a fluid for the Reynolds number, based on the bulk fluid
velocity, usually greater than 5. Any attempt to modify Eq. (3.5) for

the application in multiparticle-fluid systems was exclusively to

104

account for the effects of other particles on the local voidage and the
characteristic velocity around one particle of interest.

In all particles active systems, these attempts oftentimes have
been found to be unsuccessful especially at low Reynolds numbers, since
the infinite radius boundary condition of Eq. (3.5) cannot be met. On
the other hand, in diluted systems, this infinite radius boundary
condition can be tolerated, since the concentration of active particles
is so low that each active particle is virtually surrounded by many
inert particles at all times. Figures 2.38 and 2.39 indeed show that
the Sherwood numbers approach a value a little less than two as the
particle diameter approaches zero except those for 230 pm sand, which
suggests that the presence of inert particles is merely to decrease the
area available for molecular diffusion.

Furthermore, the bulk fluid velocity in the convective component
of Eq. (3.5) should also be replaced by a characteristic velocity in a
multiparticle-fluid system, and the most logical choice would be to use
the interstitial velocity among inert particles. However, the
distribution of local voidage near the active particle has been shown
by Basu (66) to be similar to a damped oscillatory function even for
uniformly sized particle systems; the voidage is maximum at the active
particle surface, and the fluctuating local voidage dies down to the
mean voidage of the system away from the active particle. Further
complications are expected to arise in the variation of local voidage,
if the active and inert particles are different sized and the active
particle size actually decreases during the transfer process. A full

mathematical treatment of this problem is extremely complicated and far

105

beyond the scope of this work. Hence, if we are to contend with the
interstitial velocity, u, based on the local mean voidage, the Sherwood

number dependence should be different from Rel/2.

The exponent 1/3 of the Schmidt number in Eq. (3.5) has been shown
in recent studies (67) to be inadequate for Re > 1. The value of l/3
was obtained from the case of developing boundary layer which probably
exists in the front half of the sphere near the stagnation point, and
would not apply to the wake region where its value may increase to l/2
for unsteady state flow. However, in a typical fluidized bed combustor,
the Schmidt number is on the order of unity, and the Sherwood number
dependence is not as significant as on the Reynolds number.

To sum up, we now propose the following expression for the

Sherwood number in the grid region:

Sh - 2 e + a Reb SCI/3 , (3.6)

where a and b are constants to be evaluated from the experimental data,

and the Reynolds number is defined as pf u dp/pf. In order to evaluate

the constants a and b, it is necessary to calculate e and u as a
function of the axial distance from the distributor in each phase of

the grid region.

106

3-3-2. A a o b twee he d e o d a s outed bed

A spouted bed is an efficient device of contacting coarse
particles with gas, and many of its hydrodynamic features are quite
analogous to those of the grid region. Both a spouted bed and the
section WXYZ in Figure 2.2 consist of a dilute phase of gas jet and
entrained particles and a dense phase of under-fluidized particles
surrounding the jet. As shown in Figure 3.1, there is a continuous
flow of solids from the dense phase into the jet throughout the jet
height, and gas leaks in the opposite direction. The main difference
is that the jet breaks up into small bubbles in the grid region for

U > Umf’ whereas it always penetrates to the bed surface in a spouted

bed. However, when a spouted bed is at the minimum spouting condition,
both the particles entrained in the dilute phase and those in the dense
phase are by definition just fluidized at the bed surface. As noted in
Section 2-6-2, the same degree of fluidization is also attained at the

grid region height at minimum fluidization, H without any bubble

mf'
formation.

Therefore, the general behavior of gas and solids flows of a
spouted bed at minimum spouting can be assumed to be identical to that
of the grid region at minimum fluidization, and consequently some of
the useful theories of spouted beds can be readily applied to the grid

region study.

107

Dilute phase

_JD. .__

 

 

 

 

jUdm-I-dz)

“’ULM)

u.(z+dz)
J _ z+dz

 

 

uj(z)-

Dense
phase

.-- Ud(z)

1

‘IOIOI‘I‘iE?[ I Jib
I ‘u‘

1

‘IfIAI
:1

r
l
I

1

 

 

 

 

W

2:30

 

 

O

é)-
TI

C
0

Figure 3.1 Spouted bed model as applied to
the grid region ( ‘r--, solids flow;
‘-> , gas flow ).

108

3-3-3. Axial voidage distributions in rhe grid regigg

Since the dense phase voidage remains relatively constant in the
axial direction at or even above minimum fluidization, we now
concentrate mainly on the axial voidage distribution in the dilute
phase. Currently, there are two different methods of calculating the

dilute phase voidage, ej, in a spouted bed: the variational method by

Morgan et al. (68) and the numerical method of solving the mass and
momentum balance equations, as done by Lefroy and Davidson (56) using
an additional empirical equation describing the axial pressure
distribution just outside the spout. Due to its simplicity and
applicability at the minimum spouting condition, we will directly

employ the variational method to calculate Ej at minimum spouting and
later use a similarity relationship to find the values of e. above

minimum fluidization.

Assuming that the jet diameter, Dj’ is constant throughout its

height, the momentum equations for gas and solids in the dilute phase

are given as (56):

Gas:
2 dP 2
d . - - - 6 . - . 3.7
pf 712(63 uj) ‘3 71.; (uJ VJ) ( )
Solids:
p d 2 _ _ _ dP. _ 2
p ‘5; [ (1 - ej) Vj ] (l ej) dz] + 6 (uj v )

109

- (pp - pf) g (l - ej) (3.8)

where uj and v: are the radially averaged velocity of gas and solids,
respectively, Ej and PJ are also the radially averaged voidage and

pressure, respectively, and 6 is a gas-solids interphase drag

coefficient.

Combining Eqs. (3.7) and (3.8), the average momentum equation of

the mixture becomes

2 2

.1,

- (pp- pf) g (1 - ej) (3 9)

Integrating Eq. (3.9) over the jet height at minimum spouting,

Hms’ commonly called the maximum spoutable bed depth, we obtain

2 2 ' 2
pf 61(Hms) uj(Hms) - pf 63(0) uj(0) + pp [ 1 - ej(Hms)] vj(Hms)

H
2 ms
- pp [ l-ej(0)] Vj (0) - APms - (pp - pf) g JO (1 - ej)msdz (3.10)

where APms is the bed pressure drop at minimum spouting.

110

At minimum spouting, vj(Hms) - 0, ej(HmS) - emf and uj(Hms) -

Umf / emf. Furthermore, at z - 0, ej(0) - 0 and vj(0) - 0. Also

. 2 . .
noting that uj(0) = (Do/Dj,ms) Uo,mf from continuity, Eq. (3 10) can
be rewritten as
2 4 2
pf Umf - pf (Do/Dj,ms) Uo,mf

H
ms
- APms - (pp -pf) g Io (1 - ej)ms dz (3.11)

Dividing by the pressure drop across a fluidized bed of the same

depth, Ame - (l - emf) g (pp -pf) Hms’ Eq. (3.11) further reduces to

 

 

 

1
[1 " £1 (§)]Q§ d;- _ I0 _
l - e
0 mf
4 2 2 l
APms + pf [(Do/Djrms) Uo.1_r_1f - Umf/emf (3'12)
Ame (1 - emf) (p p - pf) g Hms

where g is the normalized axial coordinate, defined as z/Hms, and the

boundary conditions are 6(0) - l and 6(1) - emf’

111

The solution to this variational problem is given as (68)

1/2

 

1 ' ‘1 (5)1mg - 12 - l [ 1 - (A; + 11)2 (3.13)
l - e A
mf
where A - ( 1 - 1i )1/2 - 11 (3.14)
' 2 1/2 2 1/2
12 - ( 1 - 11 ) [( 1 - 11 ) - 11] (3.15)
2 2 1/2
10 - 12 - ( 1/21 ) [( 1 - 11 ) ([11] - 11)
+ sin‘1[( 1 - Ii )1/2] - sin'1 11 ] (3.16)

11, 12 and A are obtained by solving Eqs. (3.14) -(3.16)

simultaneously.

In order to find the value of IO for each sand particle size

considered this study, the jet diameter at minimum spouting, Dj ms' is

estimated from the corelation by Lefroy and Davidson (56):

0. - 1.06 D 2/3 d 1/3 (3.17)
j c s

112

where Dc is the equivalent diameter of a spouted bed. Equation (3.7)

indicates that the jet diameter is independent of the gas flow rate,
which is a rather surprising result.

Furthermore, the force balance analysis of Mamuro and Hattori
(69), based on the assumption that Darcy's law governs the gas flow in

the dense phase, suggests the ratio of APms/Ame to be 0.75 at minimum

spouting regardless of particle size and density. Epstein et al. (70)
later showed that the value of the pressure drop ratio was somewhat
greater than what was generally observed experimentally and attributed
this discrepancy mainly to the deficiency in the Mamuro-Hattori model
by neglecting the shear stresses at the jet boundary and bed wall that
partially support the particles. However, at least no solid wall is
present around the section WXYZ in Figure 2.2, and thus we have

exclusively assumed that APms/Ame - 0.75 at minimum spouting.

Table 3.1 further shows that the dimensionless pressure drop term

is so dominating in Eq. (3.12) that the values of IO remain essentially

constant at 0.75 for all sand particle sizes. The significance of this
result is that under the operating conditions considered in this study,
the axial voidage profile in the dilute phase is the same at minimum
spouting regardless of the particle size, when plotted against the

dimensionless axial distance, z/Hms, as shown in Figure 3.2. It should

be noted here that due to many hydrodynamic similarities discussed in

Section 3-3-2, Hms can be assumed to be the same as Hm and Figure 3.2

f

should also represent the axial voidage profile in the dilute phase of

113

the grid region at U - Umf' As predicted in Section 2-6-6, the dilute

phase voidage is indeed shown to decrease monotonically with upward

concavity.

Table 3.1 Values of the parameters used in the calculation of IO

pp - 2,700 kg/m3, pf - 0.3892 kg/m3, Do - 6.35 mm

 

 

*

(13 (pm) Uo,mf (m/s) Dj (cm) Hms (cm) APms / Ame I0
230 1.55 0.98 8.8 0.75 0.7501
460 6.25 1.23 9.0 0.75 0.7508
620 11.28 1.36 11.2 0.75 0.7513

 

* Values of Hm from Table 2.5.

f

Above minimum spouting or when H < Hms’ the variational method is

no longer applicable, since the term v (H) does not vanish. Hence, the

J

dilute phase voidage above minimum fluidization, ej(z), is calculated

using the following similarity relationship (68):

1 ‘ ‘j (z) - 1 ' [‘1 (2)] mf (3.18)
1 - ej (H) 1 - emf

where ej(H) is equal to the mean bed voidage, and the values of

6b,

[Ej (2)]Inf are obtained from Figure 3.2.

114

Upon rearranging, Eq. (3.18) becomes

 

e. (z) — 1 - [l - [c.(z)]mf ] [1 - 6b ] (3.19)
J J l - e
mf

where 6b is the mean bed voidage.
Since the bed surface is always violently fluctuating in gas
fluidized beds, it is extremely difficult to measure the height of an

expanded bed accurately, and there is no reliable correlation available
for its estimation. Therefore, we used the following equation

suggested for a suspension system to calculate 6b for different

particle size and gas velocity:

(3.20).

where ut is the terminal velocity of particles, and the exponent m is

estimated from (72):

_ log (Remf/Ret)
log 6

m , (3.21)

 

mf

where emf is assumed to be 0.4 for all ds, and the values of 6b thus

calculated are tabulated in Table 3.2. It is further shown in Figure

115

3.2 that the dilute phase voidage calculated from Eq. (3.19) increases

with increasing U for all 2, as expected.

Table 3.2 Mean bed voidage calculated from Eq. (3.20) and (3.21)

 

 

 

 

ds(pm) ut(m/s) m U/Umf 6b
3.0 .434

230 3.97 5.13 4.0 .459
6.0 .497

1.5 .438

460 4.08 4.38 2.0 .468
4. .540
2.0 .474

2.2 .485
620 5.49 4.06 3.0 .524
4.0 .562

 

It was stated earlier in this section that the axial variation of
the dense phase voidage, 6d, is negligible at minimum fluidization,
since, 6p z Emf‘ However, according to the definition of the grid
region height, the voidage should increase from emf to 6b near 2 - H,
for U > Umf' It was further shown by Fakhimi et al. (57) that the

dense phase becomes completely fluidized at z - he' For all U, the

difference of (6b - emf) is relatively small, and the dense phase

116

voidage can be assumed to remain constant at emf up to the dead zone

height, 2 - h and increase linearly thereafter to 6b at z - H:

 

d,
( emf , for 0 s z s hd
€d(Z) - (3.22)
1 (6 - 6 ) z + 6 H - 6 h
H - he b mf f b e ’

 

where hd is the dead zone height and will be discussed in detail in

Section 3-4.

117

 

 

 

 

 

 

- dS = 620 pm, UO = 45.1 m/s
ds = 460 pm, Uo = 25.0 m/s
0.8 - <1S = 230 pm, UO - 9.4 m/s
_ a»
0.6 -
éj _
0.4 -
Uo = Uo,mf
)-
O.2 _
0.0 I I I I I I I I I
0.2 0.4 0.6 0.8 1
z/H
Figure 3.2 Axial voidage distribution in the dilute

phase calculated from Eqs. (3.13) and

(3-19)-

.0

118

3-3-4. a ve t i t u 'on the r'd e ion

At minimum spouting, the superficial gas velocity in the dense

phase of a spouted bed is given as (69)

Ud (z) - Umf [1 - (1 - z/Hms)3] , (3.23)

which was derived from the following differential force balance

equation and boundary conditions:

dad + de + (pp - pf) g (1 - 6d) dz - 0 (3.24)
B. c. 1. Ud (0) - 0

2' Ud (Hms) - Umf

3. - de / dz Hms = (Pp - Pf)(l ‘ 6d) S

where ad is the average stress borne by the solids. Epstein and Levine

(71) showed that Eq. (3.23) still satisfies well even the case of non-
Darcy flow in the dense phase. Furthermore, Yokogawa et al. (73)
reworked the Mamuro-Hattori analysis by including in Eq. (3.24) the
shear stresses acting on both sides of the dense phase, and their

complicated final expression for U contained an adjustable parameter

d

that had to be determined from experimental Ud (H). Hence, we have

119

assumed that the axial velocity distribution in the dense phase of the

grid region at U - UInf is well represented by Eq. (3.23) with Hms being
experimental Hmf'

The extention of Eq. (3.23) for H < Hms was successfully done by

A v

Grbarcic (74), and we exclusively use the following expression for the
axial velocity distribution in the dense phase above minimum

fluidization:

)3
f , (3.25)
3

Ud<z> - Ud<H> 1 ' ‘1 ' z/“g

1 - (1 - H/Hmf)

where Ud(H) is equal to the superficial gas velocity of fluidization,

U, from the definition of the grid region height, H. It should be

noted that all Ud's are also radially averaged ones, and the

corresponding interstitial velocity, ud(z), is Simply Ud(Z)/€d(2).
The interstitial axial velocity in the dilute phase, uj(z), is

calculated from differential mass balance equations (56) between 2 - z
and z - z + dz, as shown in Figure 3.1:

Dilute phase:

2
Dj d (ej uj) = UL « Dj dz (3.26)

Pl}!

120

Dense phase:

2 2
% (Dc - Dj) dUd - UL n Dj dz (3.27)

where UL(z) is the superficial velocity of gas leakage into the dense

phase, and solids entrainment as well as gas leakage is assumed to
occur only in the radial direction at the jet boundary, as shown in
Figure 3.1.

Combining Eqs. (3.26) and (3.27) and integrating from 2 - 0 to z -

2, we obtain

ej (z) uJ (z) - 6j (0) uJ (0) - 1 - [

“U Inc:

2
] [Ud(z) - Ud(0)J (3.28)

substituting Eq. (3.25) into Eq. (3.28) and noting that at z-O,

6j - Ud - 0 and uj (0) - (Do/Dj)2Uo’ Eq. (3.28) further reduces to

 

 

2 2 3
uJ.(z) - 1 UO[I_)_Q] + u 1 - [39.] 1 ‘ (1 ' z/Hmf) (3.29)
. z D D. l - 1 - H H
.J < > j J < / mp3
which is valid for all U 2 U . At the grid region height, 2 = H, Eq.

mf

(3.29) becomes

121

D 2 D 2
6.(H) u.(H) - U _Q + U 1 - _g (3.30)
J 3 ° D. D
J 3
Furthermore, from continuity, we have
U 02 - U D 2 (3.31)
o o c

Hence, Eq. (3.30) reduces to 6j(H) uj(H) - U - Ud(H), as it should.

The axial gas velocities calculated from Eq. (3.29) are shown in Fig.
3.3 to decrease monotonically with upward concavity as the axial
distance increases.

It is further to be noted that the equivalent diameter of a
spouted bed calculated from Eq. (3.31) is 5.86 cm, which is about 5 %
greater than the actual pitch size of 5.56 cm. This discrepancy arises
from the fact that the gas flow through the interstitial space among
the imaginary columns in contact with one another is unaccounted for,
when the diameter of each column is assumed to be the pitch size

itself.

122

 

 

 

 

L.

10 — dS -.- 620 pm
d8 = [4'60 pm
as = 230 pm

L
u-(Z)
(In/S) L
5—
O l I I I I I I 4 I
0 2 0.1+ O 6 O 8

z/H

Figure 3.3 Axial velocity distribution in the dilute

phase at U = 4 Umf.

. 0

123

3-3-5. Development of mass rransfer correlations

The general procedures of estimating the constants a and b in Eq.

(3.6) from the experimental data can be summarized as follows:

Dilute phase:

(1)

(2)

(3)

(4)

(5)

(6)

Calculate 10 in Eq. (3.12) at minimum fluidization.
Solve for [6j(z)]Inf from Eqs. (3.13) - (3.16).

Find 6j(2) for U > Umf from Eq. (3.19).

Find uj(z) for U 2 Umf from Eq. (3.29).

Calculate 6j(Z) and uj(z) at each 2, and

plot log [(Shexp - 2 ej)/Sc1/3] against log Rej.

Estimate the slope and y-intercept.

Dense phase:

(1)

(2)

(3)

(4)

For U > U find €d(Z) from Eq. (3.22).
For U - U 6d(Z) - emf for all 2.

For U > U find ud(z) - Ud(Z)/€d(Z) from Eq. (3.25).
For U - U find ud(z) - Ud(z)/6d(z) from Eq. (3.23).

Calculate €d(Z) and ud(z) at each 2, and

1/3 .
plot log [(Shexp - 2 6d)/Sc ] against log Red.

Estimate the slope and y-intercept.

124

As shown in Figures 3.4 and 3.5, the lower zone of the dilute

phase from z - 0 to z - he exhibited mass transfer characteristics
quite different from the upper zone from 2 - he to z = H. This is

certainly expected, because the mode of gas flow changes from a jet to

bubbles at z - he, as discussed in Section 2-6-2. The proposed

correlations for mass transfer in the dilute phase are

Lower zone ( o s z < he)

Shj(z) - 26j(z) + 0.006 Re§'35(z) Sol/3 (3.32)
for 70 < Rej < 500 and 3 < Res j < 30
Upper zone ( he 5 z 5 H )
Shj(z) - 26j(z) + 0.115 Re}'15(z) Scl/3 (3.33)

for 10 < Rej S 70 and 0.3 < Res j < 5

where Rej(z) - pf uj(z) dp / ”f and ReS j(z) - pf uj(z) ds / pf.

125

Unlike in the dilute phase, no abrupt change was observed in the
axial variation of mass transfer characteristics in the dense phase.
However, as shown in Figure 3.6, the data are correlated quite
differently, depending on the Reynolds number based on the inert

particle size, Res. The proposed correlations for mass transfer in the

dense phase are

1.4 1/3

Shd(z) - 2€d(Z) + 0.047 Red (2) Sc (3.34)
for 10 < Re < 70 and 1 < Re < 4.5
d s,d
Shd(z) - 2€d(2) + 0.001 Rei'65(z) Sol/3 (3.35)

for 7 < Re < 20 and 0.45 < Re < l
d s,d

where Red(z) - pf ud(z) dp /pf and Res’d(z) - pf ud(z) ds / pf

Noting that the ranges of both Reynolds numbers for Eqs. (3 33)

and (3.34) are almost identical, the data for the upper zone of the
dilute phase and for the dense phase are plotted together in Figure 3.7

and shown to be well represented by a single correlation:

l

Sh - 26(2) + 0.094 Re '22(z) Sci/3

(3.36)

126

for 10 < Re < 70 and 0.3 < Res < 5

where both 6 and u are calculated differently in each phase, as

outlined earlier in this section. This result appears to be surprising

but is indeed consistent with our definition of the grid region height,
because all hydrodynamic parameters eventually become identical at
z - H so that mass transfer data in both phases should be correlated by

the same type of expression, as shown in Figure 3.7.

127

 

   
  

 

 

 

30
lO--
1
m
\ —
HO
S 5"
\U _
02
l
g _
£3
I-n 'o
o
5<Res<30
Shj(z) = 26:]+0.006Re25.”35(z)Scl/3
l J I I I 11 l l L l 1
.5 1 5

Re no“2

Figure 3.4 Plot of lnkSh - 26)/Sc1/3] versus in Re
in the dilute phase for O$z<he.

128

 

 

 

 

 

3O
20
10'
Q 5
H
0
:0
>
u)
N
I
.c:
i“,
0.34Re845
1....
8 _l I ll I I I I I I I I
6 1 5 10
Re x10

Figure 3.5 Plot of 1n [(Sh - 26)/801/3] versus ln Re
in the dilute phase for hes z $H.

129

 

 

 

 

30
20-
o
o 000
10— Eq. (3.3“) 0.00
- 1<Res<4.5
5- O %.’.O O
_ od’ 0
.. 0 oo°
Ooo.'o
I— 0 00
m I
S - 6°
0 ..°.
13 1
l :— .
’c -
‘3, I
.5-
- I
I
I EQ- (3-35)
.. OJ+5<ReS<1
.lF-l l l l l I Ill 1 l l 1 I I ll
.2 .5 1 5
Re x10.1

10

Figure 3.6 Plot of 1n[(Sh - 26)/501/3] versus ln Re

in the dense phase for O<z£H.

130

 

30

20 _

10 ~—

 

(Sh — 26)/Sc1/3
U1
1

  
  

O.3<Res<5

311(2) = 26(2) +0.094Rel'zzscl/3

llll I III]!

 

Figure 3.7

l 5
Re x10
Plot of 1n[(Sh — 26)/Scl/3] versus ln Re

( dilute phase (open symbol ), dense phase
(closed symbol) ).

 

131

3-4. Discgggiog

It should be noted that in our study, carbon particles were fixed

at various positions in order to characterize the effects of bed
hydrodynamics on the combustion and mass transfer rates as a function
of particle position in both phases of the grid region. In actual

practice, however, active particles are also entrained into the jet

along with inert particles, accelerated and carried to the top of the
jet where some particles are swept into the wake of each rising bubble,
while the remaining particles are returning to the dense phase.
Therefore, the interstitial gas velocity, u(z), in Eqs. (3.32)-(3.36)

shoud be replaced by the relative velocity between gas and solids, uR -

u(z) - v(z), which is essentially the same as u(z) in packed and
fluidized beds (60). Hence, Eqs. (3.34)-(3.36) can be directly applied
to actual situations.

On the other hand, the particle velocity in the dilute phase,

vj(z), is expected to be more pronounced perhaps due to high rates of

momentum transfer in the jet, and can be calculated numerically from
the mass and momentum balance equations (56). However,the calculations
showed that for bed materials similar to the ones typically encountered

in a fluidized bed combustor, the ratio of vj(z) / uj(z) is still at

most 10 % for all z (68), which is certainly well within the range of
experimental errors, as shown by the degree of data scattering in
Figures 3.4 and 3.5. This relatively small velocity ratio is mainly

due to the fact that unlike other two-phase jet flows, a significant

132

amount of gas flow entering the bed with high momentum quickly leaks
throughout the jet boundary to fluidize the dense phase, instead of
transferring momentum to the particles entrained in the jet. It is,
therefore, suggested that Eqs. (3.32) and (3.33) be used in actual
situations under the operating conditions considered in this study.
Bar-Ilan and Resnick (62) measured the rate of vaporization of
naphthalene particles in a packed bed of inert particles of similar
size and shape, and their data with 460 pm granules are shown in Figure
3.8 to be reasonably well fitted by Eq. (3.34). It should be noted
that the size reduction of active particles during the transfer process
was assumed to be negligible in their study, whereas the active
particle size is explicitly shown in each correlation proposed in this
study so that this important problem of particle size variation can
still be accomodated for a broader range of applications. They also
found that the mass transfer characteristics changed drastically at

Reynolds numbers (Res) around unity, which is basically consistent with

our results, as shown in Figure 3.6. Furthermore, the transition from
a laminar to a turbulent flow regime in a packed bed is known to occur

at Reynolds numbers (Res) around 5 (63). Therefore, it appears that

Eqs. (3.34) and (3.35) are generally applicable to diluted systems in

laminar flow for ReS > 0.3.
For Res < 0.3, the experimental Sherwood numbers are extremely

small, as shown in Figure 2.39 for 230pm sand, and it is no longer
possible to represent the data in the form of Eq. (3.6). Hence, the

mechanism of mass transfer is mainly molecular diffusion at these low

133

Reynolds numbers, and the Sherwood numbers can be assumed to be

effectively 26.

 

 

 

 

 

1.0L.

u Data by Bar-Ilan (62)

i
0.5-

~10 P 0
Eq- (3.34)

P

.1 L I l I I I I I I I I
1 5 10

Re

Fig. 3.8 Mass transfer factor versus Reynolds number in a diluted
system.

134

3~4. Estimation of the Dead Zone Height

The dead zone is commonly defined as a portion of the dense phase
in which the particles are stationary, as in a fixed bed. In the
absence of any appreciable convective effects, the particles are
certainly immobile and still maintain their overall tranquility with
increasing gas flow, until the superficial gas velocity reaches a

critical value of Umf‘ It was shown experimentally that the dense
phase becomes compeletly fluidized at z - he(52)’ whereas Figure 3.9
shows that the superficial gas velocities at z - he far exceed their

values at minimum fluidization for all sand particle sizes considered.
This discrepancy may appear to be somewhat unexpected but nevertheless
is consistent with the experimental observations of Yates et al. (18)
that the local dense phase voidage increases above its minimum
fluidization value during the bubble formation. It should be noted
here that the dense phase voidage was already assumed to increase

linearly from emf at z - hd to 6b at z - H in the analysis given in

Section 3-3-3. Consequently, the dense phase is eXpected to become
unstable due to this excessive local expansion, and it is these
instabilities that disturb the tranquility of stationary particles.

Therefore, the dead zone height, hd, is likely to be at or a little

above where Ud(z) - Umf'
Horio et al. (75) directly measured the dead zone shape by the wax

quenching method in a three-dimensional bed and proposed the following

correlations for the dead zone height:

135

d /0 - 4.4 x 10'3 01°5 + 1.75 (3.37)
m 0 O

hd - 0.5 (S - dm) tan 6r (3.38)

where dm is called the particle moving zone diameter, and Or is the

angle of repose which is commonly taken as 370 for the sand particle
sizes considered in this study.

As expected, it can be seen from Table 3.3 that the values of hd

calculated from Eqs. (3.37) and (3.38) are generally higher than those

based on the assumption of Ud(hd) - Umf and still considerably lower
than those he. It is also to be noted that the calculated values of
hd are shown to be rather insensitive to UC which is the only variable

affecting the dead zone formation for a given distributor pitch size.
The critical gas velocity required for the elimination of the dead zone

can be calculated simply by letting dIn - S in Eq. (3.37) and solving
for U0. Its value for our case is estimated to be about 136 m/s which
is more than 12 Umf even for 620 pm sand. At these high gas flow

rates, the elutriation rate of bed materials is so high that the
elimination of the dead zone is possible only by reducing the pitch

size.

136

Table 3.3 Estimated values of the dead zone height

 

hd(cm)
ds(pm) Uo(m/s) hd(cm) calculated from he(cm)

from Ud(hd)-UInf Eqs.(3.37) and

 

(3.38)

1.24 1.67 5.9

230 6.2 .82 1.66 .
.50 1.65 2.9

9.4 .77 65 10

460 12.5 1.85 1.63 .
25.0 .78 1.54 3.5
22.6 2.32 1.56 6.3
620 33.8 1.37 1.47 4.3

45.1 .85 1.36 2.2

 

137

 

 

 

 

 

.6 , I
I
5 Q—‘Hé— Unstable —"*— Fluidized '—>1
Dead : bed expansion : zone
zone I '
5 - I I
' i
I
_ , 1
I
u r—Ud(Z) = Umf I
I I (is = 620 pm
' I
.. I I
I I
I I
.3 _ I I
l I
”am _. i I
(m/S) I I
I I (is = “'60 pm
.2 - I ‘
l I
I I
L. | I
I
.1 .. I, fi-Ud(Z) = Ud(he)
' I
_ I
[I as e 230 pm
0 I I I I I .I I L I
2 .4 .6 .8 l.

z/H

Figure 3.9 Axial velocity distribution in the dense

phase at U = 4 Umf'

O

CHAPTER4

SUMMARY OF CONCLUSIONS AND SUGGESTIONS

I-‘ORFUTURERESEARCH

138

139

4-1. G s o s

The grid region can account for a major component of gas and
solids contacting, compensating for poor contacting in the bubbling and
slugging zones. Consequently, understanding the hydrodynamics and
transfer processes in the grid region is crucial to successful modeling
of fluidized bed reactors (76). In this study, we were particularly
concerned with combustion and mass transfer characteristics in the

grid region of a flidized bed combustor. Specifically, we aimed at:

1. experimentally measuring the grid region height from a
reaction point of view, which is useful for the modeling
purpose,

2. characterizing the combustion and mass transfer phenomena in
the dilute and dense phases of the grid region,

3. and developing mass transfer correlations for the dilute and

dense phases of the grid region.

The experimental methods involved measuring combustion rates of
sample carbon particles fixed at various locations near a multiorifice
gas distributor. The operating variables considered in this study were
inert particle size, superficial gas velocity and particle position.
Noting that there are many hydrodynamic similarities between a spouted
bed at minimum spouting and the grid region at minimum fluidization,

the experimental results were further analyzed in light of theories for

140

spouted beds and two-phase flows. The following is a summary of

conclusions on the experimental and theoretical results.

4-1-1. Con i n a er s

1. For unreactive carbons such as electrode graphite, the
chemical kinetics plays an important role in fluidized bed
combustion, and combustion cannot be assumed to be in a
shrinking sphere mode at high fractional burn-off due to a

significant internal burning.

2. Due to solids entrainment and gas leakage , the external mass
transfer resistance of the dilute phase increases with
increasing distance from the distributor, thus lowering the
overall combustion rate, while the reverse trend is observed

in the dense phase.

3. The grid region height was defined as where the bubbles
deviate from their vertical path due to bed momentum, and its
values determined experimentally are all consistent with its
own definition in the sense that the mass transfer as well as
the combustion characteristics are the same regardless of the

sample position above the grid region height.

4. The grid region height decreases with increasing gas flow

rate for all sand particle sizes considered in this study,

141

and available correlations for jet penetration length cannot

be used in the reactor modeling study.

Under the operating conditions considered in this study, the
grid region occupies up to 40 % of the entire bed volume and

cannot be neglected in the overall rector modeling study.

In the dilute phase of large inert particles, the overall
combustion rate increases with increasing gas flow rate
mainly due to the increase in the chemical rate. As the
inert particle size decreases, the influence of the chemical
kinetics diminishes, and the overall combustion rate is
affected by the gas flow rate mainly due to the change in
mass transfer resistance in a bed of small inert particles.

In the dense phase, the corresponding trends are reversed.

At a constant gas velocity, the effect of increasing inert
particle size is to decrease the overall combustion rate in
the dilute phase due to the increase in the mass transfer
resistance, while the trend is again reversed in the dense

phase.

From Conclusions #6 and #7, it can be concluded that gas
leakage into the dense phase increases with increasing inert
particle size perhaps due to the difficulties associated with

fluidizing larger particles.

142

9. Both the mass transfer coefficient and voidage of the dilute
phase decrease with upward concavity with increasing distance
from the distributor, and the concavity smooths out with
decreasing inert particle size. In the dense phase, both
quantities increase gradually with increasing distance from

the distributor.

4-1-2. 0 theor t a is

l. The general behavior of gas and solids flows in the grid
region at minimum fluidization can be assumed to be identical

to that of a spouted bed at minimum spouting.

2. The dilute phase can be further divided into the upper and

lower zone around 2 - he’ with each zone exhibiting mass

transfer characteristics quite different from each other, and
this is found to be consistent with the hydrodynamic picture
of the dilute phase outlined in the definition of the grid

region height.

3. The experimental Sherwood numbers are represented by one of

the following generalized correlations:

1 35 1/3

Sh - 26 + 0.006 Re ' Sc (4.1)

143

for 70 < Rep < 500 and 5 < ReS < 30

1 22 1/3

Sh - 26 + 0.094 Re ' Sc (4.2)

for 10 < Rep < 70 and 0.3 < Res < 5

Sh - 26 (4.3)

for Rep < 10 and Res < 0.3

where Rep - pf u dp/pf and Res - pf u ds/pf. It should be noted that

both 6 and u are calculated differently in each phase, as outlined in
Section 3-3-5.

The significance of this study is that the experimental technique
of determining the grid region height can be readily employed in other
fluidized bed applications for its estimation. Furthermore, the
proposed mass transfer correlations can accomodate the size variation
of active particles during the transfer processes and are shown to be

also applicable to other diluted systems.

144

4-2. Su st ns 0 u e ese c

This study was initiated from the need of developing a combustion
model in the grid region which can later be combined with bubbling bed
models for better prediction of the overall bed performance. As shown
in Figure 4.1, both experimental and theoretical works presented in
this study are concerned with only a small portion of the overall scope
of research needed for the combustion modeling of the grid region.
Here, we describe briefly some of the research areas of immediate

concern.

1. More combustion experiments need be done in the grid region
involving reactive carbons of known chemical reactivity to
determine the relative importance of the chemical kinetics and

mass transfer on the overall combustion rate.

2. The grid region height is perhaps the most important of all
modeling parameters. Dedicated efforts need be put into
experimentally measuring the grid region height under a wider
range of operating conditions for possible development of a

correlation.

3. Accurate prediction of particle temperature requires further
research toward developing a model of simultaneous heat and

mass transfer and CO oxidation in the boundary layer.

145

Hydrodynamic experiments using the fiber optic probe will give
a detailed picture of the complicated gas and solids flows in
the grid region. The jet boundary, solids entrainment rate and
residence time distribution of solids in the dilute and dense
phases can be estimated by further statistical treatment of the
data, and a comprehensive hydrodynamic modeling study should

follow for the generalization of data.

In the grid region, the size reduction of carbon particles due
to fragmentation and attrition caused by the impact with inert
bed particles is likely to be significant due to vigorous gas
and solids mixing in the jet and high temperature gradient.

A pattern of the attrition activity as a function of burn-off %
can be obtained by careful experimentation of monitoring the
weight loss of carbon particles, already burnt to different
degrees of burn-off, during a short stay in a shallow bed

fluidized by N2. The type and external surface area of carbon

particles, inert particle size and gas velocity seem to be the

important variables in the modeling study.

146

 

 

 

Combustion Hydrodynamic Attrition

 

 

 

Experiments Experiments Experiments

 

 

 

 

‘ Heat and Mass Transfer

Studies

 

 

 

 

Development of Combustionl

 

 

 

 

I Model in the Grid Region_J

 

 

Combustion Experiments -

in a Spouted Bed

 

 

 

Incorporation of the Grid Region Model

into Bubbling Bed Models

 

 

Combustion Data available

in the Literature

 

 

 

Combustion Experiments using

a single or batch of particles

Figure 4.1 Research plan for the overall combustion modeling.

APPENDIX

147

A-l. De t ut 3

If the pressure drop across a gas distributor is too low, not all
orifices are in continuous operation, and the result is poor
fluidization. The pitch size and orifice diameter have already been
set by the experimental conditions, and we now determine the thickness
of the multi-orifice distributor which will give the pressure drop high
enough for uniform gas distribution.

The pressure drop across the bed for U 2 U is

mf
APB - (ps - pf)(1 - ‘mf)Hmf g (A 1)
- (2700 - 0.3892)(1 - 0.4)(O.20)(9.8)

- 3175.2 N/m2

where Hmf is set at 20 cm, the static bed height, for all ds's

considered.

Quereshi and Creasy (77) proposed the following expression for the

pressure drop ratio for stable operation:

APD / AFB 2 0.01 + 0.2 [1 - exp(-0.5 DB / Hmf)] (A 2)

Hence, APD 2 0.0717 APB = 240 N/m2

148

Furthermore, Geldart and Baeyens (78) derived the following

expression for APD:

4
APD - 662 §_ (A.3)
«2 C2 Do
D pf

where G is the mass flux of gas and C is the discharge coefficient at

D

the orifice. Hence, AP is minimum at the lowest mass flux, and

D

-3 2
Gmin - 7.3 x 10 kg/m 8 at U - 3 Umf for 230 pm sand.

Upon rearranging Eq. (A.3),

2 1/2
c - ___5_‘imin_ §_2 (8.4)
D 2 0
" ”f (APD)min °

-3 2 1/2 2
- 6 (7.2 x 10 ) ] [ 0,0556 ]

«2(0.3892)(240) 0'00635

 

- 0.0445

Quereshi and Creasy (77) further suggested

0D - 0.82 (LD / 00)°'13 (A.5)

149

for LD /Do > 0.09, where LD is the thickness of the gas distributor.
Solving Eq. (A.5) for LD, we have

LD - 9.27 x 10'3m

A-2. §am212_§elculati2a§

A-2-l. P cle e a e o t

The upper limit to gas flow rate through a fluidized bed is

approximated by the terminal velocity of particles (79):

1/2
u _ 4 8 3(P§ " Pf) (A6)

3 pf Cd

where the drag coefficient, C for spherical particles is given as:

d,

Cd - 10 for 0.4 < Re < 500 (A.7)
1/2 5
Res

Combining Eqs. (A.6) and (A.7), we obtain

1/3
( _ )2 2
u - 4 p5 pf g d (A 8)
”f “f

150

for 0.4 < ReS < 500

For 620 pm sand,

2 2 1/3
ut - _g_ (2299 - 0,3892) (9,8) (0.00062)
225 (0.3892)(0.000046)
- 5.49 m/s
And ReS - ”g “c dg - 28.8 Hence, 0.4 < Res < 500
“f
A'2'2- W

The experimental conditions of Run number 26 are given in Table

2.2 as ds - 0.00062 m, U - 0.53 m/s, Uo - 45.1 m/s and z - 2.54 cm.
Furthermore, from Table 2.5, HInf - 0.112 m and H - 0.051 m.

First calculate 6 and u in the dilute phase. The jet diameter for
620 pm sand is

2/3 1/3

D. - 1.06 D d (3.17)
j c s

- 1.06 (O.0586)2/3 (0.00062)1/3

- 0.0136 m

151

At minimum fluidization,

 

4 2 2
Io — APns + pf [(Do/Di) Uo.mf ' Unf /€mf| (3.12)
Ame (1 - emf) (ps - pf) 8 Hmf

- 0.75 + (0.3892)I(0.00635/0.0136)“ (45.1/4)2 - 0.532 / 0.4]

(1 - 0.4) (2700 - 0.3892) (9.8) (0.112)

- 0.7513 z 0.75

From Figure 3.2, at z - 2.54 cm or g - 2.54/11.2 - 0.23, Gj mf - 0.63

Hence, the dilute phase voidage at U - 4 Umf becomes

1 ‘ 6b ] (3.19)

ej (2.54 cm) - 1 - [1 - [61(2.54 cm)]mf] [ 1 _ e f
m

- 1 - (1 - 0 63) [ 1 0,562 ] - 0.73
1 0.4

From Eq. (3.29), the interstial gas velocity then becomes

u.(2.54 cm) - 1 (45.1) 0.00635 2
3 0.73 0 0136

 

+ (0 53) [1 -[0 586]2] [1 - (1 - 2.54/11.2)3]]
°°°136 1 - (1 - 5.1/11.2)3

a 5.28 m/s

152

Furthermore,

Res (2.54 cm) - (0,3892)(5,28)(0,00062) - 27.7
'3 (0.000046)

Since the dead zone height is lower than 2.54 cm, the sample is in
the unstable expansion zone, and the dense phase voidage becomes, from

Eq. (3.22),

ed(2.54 cm) - 1 [(0.562 - 0.4)(2.54) + (0.4)(5.1)
5.1 - 0.85

- (0.562)(0.85)]

- 0.464
Furthermore, from Eq. (3.25),

Ud(2.54 cm) - (0.53) 1 - (l - 2.54111,2)3

1 - (1 - 5.1/11.2)3

- 0.34 m/s

Hence, the interstitial gas velocity in the dense phase becomes

ud(2.54 cm) - 0.34 / 0.464 - 0.733 m/s

And Res,d(2'54 cm) - 3.85

153

A-2-3. Calculation of Rc’ ¢ and Sh

 

The quantities measured experimentally for fixed samples are the

initial and final diameters of a carbon sphere, dp i and dp f

respectively, and the particle temperature during one combustion
interval of t seconds. The combustion rate per unit external surface

area is given as:

2
RC - AW / t « dp (2.6)
3 3 2
' pp (dp.i ' dp.f) / 6 t dP

0 4
where d - d + d 2, and - 600 d ' .
P ( v.1 p.f) / pp 9

For example, in Run # 21, dp i - 9.864 x 10'3 m, dp f - 9.275 x 10.3 m,

Tp - 1258 K, and t - 90 seconds.

Hence,
RC - 600 ( 9.57 x 10'3 )0'“ [[(9.864 x 10'3 )3 - (9.275 x 10'3 )311
/ (6)(90)(9.57 x 10'3 )2
- 4.85 x 10'3 kgC / m2 s.

 

154

Furthermore,
kC - A exp(-Ea / R Tp) (2.7)
- 87000 exp(-36000 / (l.987)(1258))
«2 2
- 4.84 x 10 kgC / m 5 atm
For n - 1, Eq. (2.5) can be rewritten as:

¢ - 1 - RC / kc Co

- 1 - (4.85 x 10‘3) / (4.84 x 10'2)(0.21)
- 0.523

In order to calculate the Sherwood number from Eq. (2.9), the

oxygen concentration of incomning air must be in kg / m3, instead of in

atm. Assuming an ideal gas,

P0 (MW)0
c - z 2
° RT

- 110.21)(32) - 0.0704 kg / m3
(82.057)(1163)

Furthermore, the variation of Dg with temperature is calculated

using the following equation by Fujita (80):

155

Dg(T) - 0g(273 K) (T / 273)1°823

- [1.81 x 10'5 m2/ 5] (1163 / 273)

- 2.542 x 10-4 m2 / 3

Hence,
k d R d
Sh - n n - c n
D B d Dg Co

- (0.00485)(0.00957)
(0.375)(0.523)(0.0005242)(0.0704)

- 13.16

 

A-3. Experimental Data

 

156

 

 

 

 

 

 

 

Table A.1 Experimental results (Run # l)
2 4 2

dp x10 (m) Tp(K) ch10 (kg/m s) ¢ Sh
dilute .915 1218 23.0 .64 4.91
phase .868 1216 22.6 .64 4.57
.810 1216 22.7 .63 4.31
.749 1218 23.5 .63 4.15
.681 1221 25.9 .61 3.80
.607 1221 26.4 .60 3.45
.500 1223 27.0 .59 2.90
dense .948 1208 9.6 .83 1.64
phase .901 1213 9.2 .84 1.46
.867 1213 9.1 .85 1.38
.833 1223 8.6 .87 1.21
.788 1217 8.9 .86 1.22
.742 1218 8.4 .87 1.06
.696 1218 8.3 .87 .99
.648 1218 9.5 .85 1.07
.591 1215 9.7 .84 1.01
.529 1206 10.9 .80 1.07
.473 1206 10.5 .81 .91

Table A.2 Experimental results (Run # 2)

2 4 2

(1p x10 (m) TP(K) ch10 (kg/m 5) d Sh
dilute .971 1209 22.3 .61 5.32
phase .916 1209 23.0 .59 5.27
.860 1211 21.3 .63 4.29
.807 1211 20.4 .65 3.75
.750 1211 20.6 .65 3.55
.663 1214 22.1 .63 2.43
.568 1214 22.1 .63 2.93
.500 1215 22.2 .64 2.60
.425 1215 23.9 .61 2.47
dense .985 1206 16.6 .70 3.50
phase .926 1204 16.0 .70 3.15
.867 1206 15.0 .73 2.67
.829 1204 15.1 .72 2.60
.788 1207 16.4 .70 2.72
.721 1207 16.7 .70 2.56
.653 1207 15.5 .72 2.09
.656 1207 17.1 .69 2.23
.555 1207 17.2 .69 2.06
.499 1212 19.4 .67 2. 3

 

 

157

 

 

 

 

 

 

 

Table A.3 Experimental results (Run # 3)
2 4 2
(1p x10 (m) Tp(K) ch10 (kg/m 5) ¢ Sh
dilute .957 1203 21.4 .59 5.12
phase .905 1206 21.3 .61 4.69
.851 1206 21.2 .61 4.38
.797 1209 21.0 .63 3.95
.741 1209 20.8 .63 3.61
.684 1209 20.9 .63 3.35
.624 1215 21.5 .65 3.08
.560 1211 21.9 .62 2.93
.492 1213 22.1 .63 2.57
.419 1213 22.8 .62 2.30
dense .952 1205 19.9 .63 4.46
phase .880 1206 18.7 .66 3.71
.831 1211 19.4 .67 3.60
.756 1209 18.7 .67 3.14
.682 1209 17.6 .69 2.58
.603 1211 18.5 .68 2.43
.519 1211 19.3 .67 2.23
.452 1211 19.9 .66 2.05
Table A.4 Experimental results (Run # 4)
d 2 4 2
p x10 (m) Tp(K) ch10 (kg/m 5) ¢ Sh
dilute .938 1213 17.2 .71 3.35
phase .854 1212 16.7 .72 2.96
.788 1212 17.5 .70 2.92
.741 1220 18.2 .72 2.78
.693 1217 16.6 .73 2.33
.646 1215 17.2 .72 2.30
.595 1215 17.7 .71 2.20
.542 1220 17.7 .73 1.96
.484 1218 19.4 .69 2.01
dense .962 1207 18.5 .66 3.98
phase .917 1205 17.8 .67 3.61
.874 1206 16.7 .69 3.11
.832 1205 16.3 .70 2.89
.788 1206 17.9 .67 3.11
.740 1210 18.2 .68 2.92
.692 1207 17.0 .69 2.51
.645 1205 16.5 .69 2.28
.594 1206 18.7 .66 2.50
.538 1208 18.7 .67 2.23
.477 1208 20.0 .64 2.19

 

 

158

Table A.5 Experimental results (Run # 5)

 

 

 

 

 

 

 

dp x102(m) Tp(K) ch104(kg/m25) ¢ Sh
dilute .977 1238 31.0 .61 7.32
phase .900 1248 31.4 .65 6.40
.850 1243 28.2 .67 5.30
.776 1241 28.8 .65 5.08
.725 1243 29.0 .66 4.72
.673 1243 27.9 .67 4.14
.617 1248 30.1 .67 4.12
.560 1248 28.6 .68 3.48
dense .947 1198 14.3 .71 2.83
phase .904 1198 11.8 .76 2.09
.864 1198 12.0 .76 2.03
.827 1198 9.8 .80 1.51
.790 1198 11.6 .76 1.78
.649 1201 12.1 .76 1.53
.603 1202 11.9 .77 1.39
.556 1203 12.0 .77 1.28
.483, 1204 .13.9 .74 1.34

Table A.6 Experimental results (Run # 6)

2 4 2 -

dp x10 (m) Tp(K) ch10 (kg/m 5) ¢ Sh
dilute .917 1217 24.3 .61 5.39
phase .879 1211 22.1 .62 4.64
.842 1211 21.7 .63 4.32
.804 1214 21.9 .64 4.09
.745 1215 22.4 .63 3.93
.662 1217 22.9 .63 3.56
.598 1211 21.5 .63 3.02
.553 1214 23.8 .61 3.23
.503 1217 25.3 .60 3.17
.447 1218 26.9 .58 3.09
dense .896 1217 21.6 .65 4.40
phase .860 1213 21.9 .63 4.41
.822 1216 22.6 .63 4.36
.784 1214 21.6 .65 3.77
.724 1213 22.9 .62 4.00
.660 1213 23.4 .61 3.78
.592 1213 23.5 .60 3.43
.520 1217 25.2 .60 3.25
.466 1218 25.9 .59 3.04
.407 1220 27.2 .58 2.83

 

159

 

 

 

 

 

 

 

Table A.7 Experimental results (Run # 7)
2 4 2

(1p x10 (m) TP(K) ch10 (kg/m 5) ¢ Sh
dilute .859 1285 45.5 .67 8.67
phase .817 1293 45.2 .70 7.84
.735 1298 48.3 .69 7.58
.649 1290 44.4 .69 6.16
.584 1303 47.6 .72 5.76
.513 1303 45.8 .73 4.80
.403 1305 50.8 .70 4.37
dense .933 1214 26.3 .56 6.44
phase .892 1214 23.4 .61 5.06
.855 1212 20.6 .65 4.03
.786 1212 23.3 .61 4.46
.715 1212 22.0 .62 3.75
.674 1211 23.1 .60 3.82
.608 1213 22.9 .62 3.36
.540 1215 23.1 .62 2.97
.458 1221 23.0 .65 2.40
.405 1221 25.0 .62 2.42

Table A.8 Experimental results (Run # 8)

2 4 2

(1p x10 (m) TP(K) ch10 (kg/m s) ¢ Sh
dilute .889 1228 33.5 .54 6.90
phase .777 1233 33.2 .56 6.79
.719 1231 31.4 .58 5.83
.660 1231 32.2 .57 5.58
.598 1238 32.8 .59 4.90
.531 1233 33.9 .55 4.83
.459 1238 34.6 .57 4.13
1371 1243 37.8 .56 3.80
dense .928 1228 30.8 .57 7.44
phase .876 1231 31.2 .58 7.02
.824 1228 30.3 .58 6.43
.769 1233 32.4 .57 6.44
.713 1231 30.9 .58 5.60
.654 1238 32.3 .60 5.23
.593 1233 31.6 .58 4.76
.527 1241 33.6 .60 4.40
.456 1243 33.8 .60 3.78

 

 

160

Table A.9 Experimental results (Run # 9)

 

 

dp x102(m) Tp(K) ch104(kg/mzs) ¢ Sh

bubbling .958 1238 33.7 .58 8.24
region .903 1241 33.2 .60 7.38
.848 1238 32.9 .59 6.98

.761 1240 33.2 60 6.22

.638 1244 33.9 .61 5.23

.539 1243 33.7 .61 4.45

.465 1248 36.5 .60 4.22

.382 1251 37.7 .60 3.58

 

Table A.10 Experimental results (Run # 10)

 

 

 

dp x102(m) TP(K) ch104(kg/m23) ¢ Sh

bubbling .958 1236 34.5 .57 8.59
region .874 1235 33.3 .57 7.56
.788 1235 33.1 .58 6.67

.645 1243 35.0 .59 5 89

.445 1248 37.5 .59 4:23

 

161

 

 

 

 

 

 

 

Table A.11 Experimental results (Run # 11)

d 2 4 2
p x10 (m) Tp(K) ch10 (kg/m 5) ¢ Sh
dilute .933 1211 15.7 .73 2.97
phase .822 1213 15.1 .75 2.46
.783 1213 14.8 .75 2.29
.710 1213 12.4 .79 1.65
.674 1213 13.6 .77 1.76
.593 1218 13.6 .79 1.52
.530 1218 14.9 .76 1.54
dense .972 1220 6.9 .89 1.11
phase .891 1223 5.2 .92 .74
.809 1233 5.3 .93 .68
.770 1233 4.5 .94 .55
.734 1233 4.6 .94 .53
.696 1233 4.6 .94 .50
.658 1233 4.6 .94 .48
.616 1243 5.1 .94 .49
.571 1243 5.1 .94 .46
.522 1248, 5.7 .94 .47

Table A.12 Experimental results (Run # 12)

2 4 2
dp x10 (m) Tp(K) ch10 (kg/m s) d Sh
dilute .976 1208 10.2 .82 1.80
phase .930 1208 8.7 .84 1.43
.886 1208 8.8 .84 1.37
.841 1208 9.0 .84 1.34
.794 1210 9.2 .84 1.28
.747 1210 8.6 .85 1.12
.672 1208 9.3 .83 1.11
.559 1212 10.2 .83 1.02
.434 1213 14.4 .76 1.22
.334 1216 15.4 .75 1.02
dense .983 1221 5.4 .92 .86
phase .910 1225 6.0 .91 .90
.863 1220 6.7 .90 .96
.830 1223 6.2 .91 .84
.760 1223 6.4 .91 .79
.645 1225 7.0 .90 .75
.572 1228 7.7 .89 .73
.526 1243 7.5 .91 .64
.475 1227 8.9 .87 .71
.331 1228 11.9 .83 .70

 

162

 

 

 

 

 

 

 

Table A.13 Experimental results (Run # 13)
2 4 2
dp x10 (m) Tp(K) ch10 (kg/m 5) ¢ Sh
dilute .976 1203 9.8 .87 1.14
phase .909 1205 7.3 .87 1.13
.834 1206 7.0 .87 1.00
.753 1206 8.2 .85 1.07
.710 1206 7.8 .86 .95
.665 1206 8.7 .84 1.02
.562 1209 9.1 .84 .91
.507 1211 9.2 .84 .82
.438 1211 11.4 .89 .91
-352 .1213 13.5 .77 .91
dense .986 1209 6.5 .89 1.06
phase .921 1213 7.1 .88 1.10
.850 1214 7.3 .88 1.04
.771 1212 7.9 .87 1.05
.727 1212 8.6 .85 1.08
.633 1216 8.4 .86 .91
.580 1213 9.9 .83 1.03
.519 1215 10.0 .84 .92
.450 1218 11.5 .82 .94
.377 1218 14.1, .78 1.01
Table A.14 Experimental results (Run # 14)
d 2 4 2
9 x10 (m) Tp(K) ch10 (kg/m 5) ¢ Sh
dilute .997 1213 18.4 .69 3.94
phase .929 1215 18.9 .69 3.78
.833 1213 19.1 .68 3.47
.758 1215 19.9 .67 3.31
.704 1213 20.0 .66 3.15
.649 1213 19.4 .68 2.76
.593 1211 19.0 .67 2.49
.534 1212 20.2 .66 2.44
.467 1208 22.3 .60 2.56
.386 1213 26.1 .56 2.66
dense .966 1220 7.4 .89 1.20
phase .873 1226 5.9 .91 .84
.776 1223 5.7 .92 .72
.730 1241 5.7 .93 .67
.684 1236 5.6 .93 .62
.581 1241 6.3 .92 .59
.458 1241 7.3 .91 .54
.376 1239 8.7 .89 .55

 

Table A.15

Experimental results (Run # 15)

 

 

 

 

 

 

 

dp x102(m) p(K) ch104(kg/mzs) ¢ Sh
dilute .977 1200 8.5 .83 1.48
phase .885 1205 9.4 .83 1.49
.798 1201 8.5 .83 1.21
.750 1198 9.4 .81 1.30
.644 1205 10.1 .81 1.19
.583 1204 10.9 .80 1.18
.518 1206 10.8 .80 1.03
.445 1208 11.9 .70 1.00
1358 1210 1343 .77 .92
dense .957 1215 6.5 .89 1.03
phase .878 1209 6.5 .89 .95
.790 1214 7.0 .88 .93
.733 1213 7.6 .87 .94
.693 1218 7.1 .89 .82
.651 1221 8.0 .88 .88
.553 1215 8.9 .85 .86
.500 1223 8.6 .87 .73
.439 1224 9.7 .86 .74
.366 1224 11.5 .83 .75

Table A.16 Experimental results (Run # 16)

2 4 2

(1p x10 (m) p(K) ch10 (kg/m 5) ¢ Sh
dilute .978 1200 7.7 .85 1.31
phase .904 1202 6.8 .87 1.06
.872 ' 1202 6.8 .87 1.02
.801 1203 7.0 .87 .96
.746 1203 6.7 .87 .85
.709 1203 7.1 .87 .86
.641 1204 8.5 .84 .96
.566 1205 8.8 .84 .89
.508 1205 10.1 .81 .93
.441 1208 10.6 .80 .86
.358 1208 13.4 .76 .94
dense .985 1209 6.2 .89 1.03
phase .899 1212 6.3 .89 .94
.835 1212 6.2 .89 .86
.770 1213 6.3 .89 .81
.702 1211 6.7 .88 .79
.625 1217 6.8 .89 .70
.537 1213 7.4 .88 .68
.488 1213 8.3 .86 .69
.432 1216 8.9 .86 .67

 

164

 

 

 

 

 

 

 

Table A.17 Experimental results (Run # l7)
2 4 2

(1p x10 (m) TP(K) ch10 (kg/m 3) ¢ Sh
dilute .955 1228 28.0 .61 6.50
phase .900 1222 25.4 .62 5.49
.858 1220 25.0 .62 5.17
.766 1216 26.8 .57 .5.31
.664 1211 27.8 .51 5.23
.610 1208 28.1 .50 5.11
.554 1215 28.8 .53 4.47
.492 1215 31.3 .49 4.68
.423 .1218, 32.6 .49 4.20
dense .957 1204 6.8 .87 1.17
phase .904 1200 7.0 .86 1.10
.860 1200 6.7 .87 .99
.811 1200 6.2 .88 .83
.760 1202 6.8 .87 .88
.647 1202 7.3 .86 .81
.583 1202 7.5 .86 .76
.508 1202 8.9 .83 .80
.421 1204 9.2 .83 .68

Table A.18 Experimental results (Run # 18)

2 4 2

dp x10 (m) TP(K) ch10 (kg/m 5) ¢ Sh
dilute .994 1188 15.0 .65 3.39
phase .890 1192 14.0 .69 2.66
.853 1193 14.6 .69 2.70
.764 1194 14.9 .68 2.38
.691 1194 13.8 .71 2.00
.654 1195 12.3 .74 1.61
.619 1195 12.2 .74 1.50
.584 1194 12.0 .75 1.39
.510 1194 11.6 .75 1.17
.472 1194 11.5 .73 1.19
dense .972 1186 13.3 .69 2.80
phase .924 1186 12.9 .70 2.54
.859 1189 13.0 .70 2.36
.810 1189 12.6 .71 2.13
.713 1189 11.6 .74 1.67
.665 1191 11.7 .74 1.56
.578 1191 12.0 .73 1.41
.521 1192 13.7 .70 1.50

 

165

 

 

 

 

 

 

 

Table A.19 Experimental results (Run # 19)
2 4 2
(1p x10 (m) Tp(K) ch10 (kg/m 5) ¢ Sh
dilute .959 1191 11,8 .74 2.27
phase .864 1192 12.4 .73 2.18
.772 1191 11.0 .76 1.66
.722 1192 11.4 .75 1.62
.624 1192 11.5 .75 1.43
.567 1194 11.8 .75 1.33
.503 1195 13.1 .72 1.35
.430 1198 13.9 .72 1.24
dense .949 1191 12.6 .72 2.46
phase .901 1193 10.8 .77 1.88
.856 1193 10.6 .77 1.74
.751 1193 10.6 .77 1.53
.700 1190 11.9 .73 1.68
.643 1191 12.4 .73 1.63
.580 1191 13.5 .70 1.66
.511 1194 13.7 .71 1.47
.435 1196 14.4 .70 1.33
Table A.20 Experimental results (Run # 20)
2 4 2
(1p x10 (m) Tp(K) ch10 (kg/m 5) ¢ Sh
dilute .971 1285 58.8 .57 14.82
phase .885 1293 59.8 .60 13.07
.796 1293 61.6 .59 12.33
.743 1298 57.7 .64 10.00
.631 1303 62.0 .63 9.22
.572 1305 57.8 .66 7.42
.510 1313 63.9 .66 7.38
.444 1318 60.6 .69 5.70
.373 1308 65.5 .63 5.76
.293 1318 63.2 .68 4.06
dense .937 1243 26.8 .69 5.42
phase .881 1243 27.3 .68 5.24
.834 1245 28.2 .68 5.20
.787 1245 26.3 .70 4.39
.740 1249 26.9 .71 4.18
.693 1253 24.3 .75 3.33
.636 1253 24.1 .75 3.04
.563 1256 25.6 .74 2.88
.481 1256 27.3 .73 2.69
.394 1256 25.4 .74 1.99

 

166

 

 

 

 

 

 

 

Table A.21 Experimental results (Run # 21)
2 4 2
(1p x10 (m) TP(K) ch10 (kg/m 5) ¢ Sh
dilute .957 1258 48.5 .52 13.16
phase .871 1256 45.6 .54 10.80
.783 1258 46.6 .54 9.98
.721 1260 46.4 .55 8.90
.657 1256 46.1 .56 7.95
.587 1266 50.2 .55 7.96
.514 1266 46.5 .58 6.09
.436 1268 50.5 .56 5.86
.348 1268 50.9 .55 4.75
dense .976 1234 35.5 .53 9.55
phase .890 1237 35.6 .55 8.49
.846 1239 34.6 .58 7.39
.705 1246 35.2 .58 6.37
.656 1241 35.9 .57 6.14
.604 1241 36.6 .57 5.74
.551 1241 34.3 .59 4.77
.486 1241 37.5 .55 4.91
.400 1241 39.8 .51 4.51
.313 1241 39.5 .53 3.50
Table A.22 Experimental results (Run # 22)
2 4 2
dp x10 (m) Tp(K) ch10 (kg/m 5) ¢ Sh
dilute .969 1246 43.6 .51 12.30
phase .908 1248 42.6 .53 10.84
.853 1253 44.6 .54 10.56
.733 1253 43.8 .54 8.76
.671 1261 46.6 .56 8.31
.604 1261 46.1 .56 7.36
.535 1268 47.0 .59 6.35
.464 1266 43.4 .61 4.88
.384 1273 51.4 .57 5.11
.293 1263 47.0 .56 3.63
dense .971 1238 42.3 .47 12.85
phase .852 1252 43.9 .50 11.10
.794 1255 46.2 .53 10.27
.734 1255 42.9 .56 8.32
.600 1260 46.8 .55 7.57
.528 1265 48.7 .56 6.84
.451 1261 47.6 .55 5.81
.369 1268 48.7 .57 4.66
.287 1268 40.0 .53 3.21

 

167

 

 

 

 

 

 

 

Table A.23 Experimental results (Run # 23)
2 4 2
(11) x10 (m) Tp(K) ch10 (kg/m 5) ¢ Sh
dilute .963 1283 58.6 .57 14.85
phase .915 1283 59.0 .56 14.27
.866 1288 57.8 .59 12.50
.815 1298 61.8 .61 12.26
.761 1293 61.5 .59 11.76
.645 1308 63.4 .64 9.47
.585 1305 60.9 .64 8.22
.520 1313 68.0 .63 8.27
.446 1328 69.5 .68 6.76
.365 1338 73.5 .69 5.72
dense .954 1228 35.3 .51 9.88
phase .896 1228 35.4 .51 9.19
.835 1233 36.6 .52 8.76
.773 1233 34.9 .54 7.40
.646 1233 35.9 .54 6.68
.610 1243 37.1 .57 5.95
.536 1238 36.9 .54 5.42
.454 1243 41.2 .52 5.37
.362 1238 39.5 .51 4.16
Table A.24 Experimental results (Run # 24)
2 4 2
dp x10 (m) Tp(K) ch10 (kg/m 5) d Sh
dilute .972 1273 50.8 .58 12.65
phase .907 1273 52.2 .57 12.40
.841 1273 52.0 .57 11.42
.771 1278 54.6 .57 10.96
.700 1278 51.7 .59 9.06
.626 1283 54.1 .60 8.46
.547 1283 53.0 .61 7.08
.459 1291 58.9 .60 6.68
.357 1298 59.6 .62 5.06
dense .953 1248 40.5 .55 10.35
phase .902 1248 41.2 .55 10.10
.851 1248 40.5 .55 9.26
.768 1255 42.2 .57 8.74
.741 1255 42.4 .57 8.20
.683 1255 43.5 .56 7.92
.619- 1260 46.7 .55 7.80
.548 1265 49.4 .55 7.27
.471 1265 49.6 .55 6.31
.379 1275 58.3 .53 6.22

 

168

 

 

 

 

 

 

 

Table A.25 Experimental results (Run # 25)
2 4 2
dp x10 (m) Tp(K) ch10 (kg/m 5) ¢ Sh
dilute .965 1262 48.6 .54 12.79
phase .906 1266 47.1 .58 10.98
.849 1266 43.8 .61 9.09
.792 1266 44.5 .67 8.71
.732 1269 46.6 .60 8.35
.666 1273 49.1 .59 8.20
.593 1273 '51.2 .58 7.83
.514 1276 54.3 .56 7.33
.426 1276 54.5 .56 6.12
.365 1276 55.2 .56 4.85
dense .956 1253 47.6 .50 13.37
phase .899 1258 45.7 .55 11.06
.841 1258 46.0 .55 10.50
.782 1258 44.3 .56 9.13
.722 1262 46.2 .57 8.76
.657 1264 47.8 .56 8.30
.587 1268 48.6 .57 7.36
.511 1268 51.9 .54 7.22
.426 1268 52.2 .54 6.20
.331 1268 55.6 .56 5.34
Table A.26 Experimental results (Run # 26)
2 4 2
dp x10 (m) TP(K) ch10 (kg/m 5) ¢ Sh
dilute .989 1308 70.4 .60 17.20
phase .932 1320 68.8 .66 14.50
.878 1313 63.1 .66 12.44
.823 1320 66.8 .67 12.25
.764 1326 68.4 .68 12.41
.703 1333 67.0 .71 9.88
.649 1338 66.0 .73 8.65
.574 1343 70.6 .72 8.34
.503 1346 69.6 .73 7.07
.428 1355 68.3 .76 5.71
.341 1363 79.8 .74 5.45
dense .972 1240 41.8 .49 12.22
phase .906 1240 39.1 .53 10 00
.839 1240 40.0 .52 9.68
.767 1240 42.5 .48 9.99
.681 1244 42.5 .51 8.46
.527 1248 42.2 .53 6.27
.407 1248 42.6 .53 5.20
.327 1270 50.9 .56 4.38

 

169

 

 

 

 

 

 

 

Table A.27 Experimental results (Run # 27)
2 4 2
dp x10 (m) TP(K) ch10 (kg/m 5) ¢ Sh
dilute .932 1273 54.3 .55 13.82
phase .874 1273 55.2 .54 13.20
.805 1278 52.0 .59 10.50
.735 1275 53.9 .56 10.50
.659 1280 55.8 .57 9.56
.579 1288 55.4 .61 7.79
.491 1288 59.3 .58 7.40
.391 1293 61.2 .59 6.00
dense .960 1262 53.0 .50 15.05
phase .878 1262 52.7 .50 13.61
.832 1262 50.4 .53 11.80
.765 1263 52.3 .51 11.68
.693 1268 53.3 .53 10.29
.617 1271 54.7 .54 9.26
.535 1274 54.7 .56 7.83
.448 1275 55.7 .55 6.70
.350 1280 57.9 .56 5.40
Table A.28 Experimental results (Run # 28)
2 4 2
(1p x10 (m) Tp(K) ch10 (kg/m 3) ¢ Sh
dilute .950 1313 53.7 .71 10.64
phase .906 1313 54.7 .71 10.42
.860 1313 55.1 .70 10 00
.813 1313 54.4 .71 9.27
.766 1316 53.5 .72 8.44
.720 1323 49.4 .76 6.95
.659 1336 54.6 .77 6.86
.581 1353 54.5 .80 5.84
.496 1353 55.7 .80 5.12
.399 1353 62.4 .78 4.76
dense .972 1230 26.3 .64 5.93
phase .932 1133 23.5 .69 4.72
.891 1239 20.7 .75 3.68
.838 1239 24.9 .69 4.31
.779 1239 20.0 .75 3.07
.723 1243 21.8 .75 3.14
.663 1243 21.4 .75 2.80
.600 1245 22.7 .74 2.73
.533 1247 22.6 .75 2.32
.455 1253 22.9 .72 2.52

 

170

 

 

 

Table A.29 Experimental results (Run # 29)
2 4 2
dp x10 (m) Tp(K) ch10 (kg/m 5) ¢ Sh
dilute .922 1276 40.9 .67 8.34
phase .853 1276 41.2 .67 7.80
.782 1278 41.0 .68 7.02
.708 1278 41.4 .67 6.67
.628 1283 43.1 .68 5.91
.542 1288 44.0 .69 5.12
.442 1293 50.1 .67 4.94
.321 1293 53.7 .64 3.57
dense .965 1246 31.3 .65 6.93
phase .915 1246 30.5 .66 6.32
.864 1248 30.8 .66 5.98
.811 1248 31.5 .65 5.82
.756 1256 31.2 .67 5.23
.696 1253 34.0 .65 5.45
.633 1253 34.1 .65 4.96
.566 1253 34.2 .64 4.47
.493 1255 36.9 .62 4.32
.406 1260 42.4 .59 4.31

 

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171

W

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