Ministry of Higher Education &
Scientific Research
University of Technology
Chemical Engineering Department
Hydrodynamic Characteristics of a Gas- Liquid –
Solid Fluidized Bed Containing a Binary Mixture
of Particles
A Thesis
Submitted To The
Department of Chemical Engineering of the
University of Technology in Partial Fulfillment of
the Requirements for the Degree of Master of
Science in Chemical Engineering/Unit Operation
By
Adiba Ali Mahmmod
(B.Sc. in Chemical Engineering)
November 2008
Dedication to………..
My Parents
Who supported & encouraged me from the
beginning of my life up to date
My Husband
Who granted me the needed strength to
continue
Supervisor’s Certification
We certify that this thesis entitled “Hydrodynamic
Characteristics of a Gas- Liquid –Solid Fluidized Bed
Containing a Binary Mixture of Particles” was prepared by
“Adiba Ali Mahmmod AL- Nuaimy” under our supervision at the
Chemical Engineering Department, The University of Technology
Baghdad-Iraq, as a partial fulfillment of the requirements for the
award of the degree of Master of Science in Chemical Engineering.
Signature:
Name: Amer A.
(Supervisor)
Date: / / 2008
Signature:
Name: Dr. Mohammed F. Abed
(Supervisor)
Date: / / 2008
In view of the available recommendations I forward
this thesis for debate by the examination committee.
Signature:
Name: Dr. Khalid A. Sukker
Head of Post Graduate Committee
Department of Chemical
Engineering
Date: / / 2008
Linguistic
I certify that this thesis entitled “Hydrodynamic
Characteristics of a Gas- Liquid –Solid Fluidized Bed
Contaning a Binary Mixture of Particles”” was prepared by
“Adiba Ali Mahmmod AL- Nuaimy” under my linguistic
supervision. It was amended to meet the style of English
language.
Signature:
Name: Eyad G. Shamslden
Title: Assistant Professor
Date: / /2008
Acknowledgments
I wish to express my deep gratitude to my
supervisors Dr.Mohammed Fadhel and Dr. Amer Aziz for
their invaluable help, advice and encouragement during
the project.
Special thanks go to the Head and staff of the
chemical Engineering Department for their support and
advice.
Finally, I would like to thank all staff of the working
shop in University of Technology for their help.
Adiba
I
Abstract
Fluidization-bed bubble columns (FBCs) are widely used as absorbers
and chemical reactors in industrial practice. Knowledge of the effect of the
solid properties on the hydrodynamic parameters(i.e., gas holdup, bubble rise
velocity and back mixing) of the (FBCs) is an important issue in the design
field.
The present work is an experimental study on the effect of solid loading
and solid properties of both single and binary mixtures on the hydrodynamic
parameters (gas holdup and bubble dynamics) of a fluidized –bed bubble
column.
All experimental were performed in a QVF glass made column of 15 cm
diameter and a constant clear liquid (i.e, tap water0 of 95cm height. Wide
range of solid particle diameters (0.5 to 3mm) with two different densities
(i.e., 1025 and 1150 kg/m3 ) were investigated for the bubble effect on gas
holdup and bubble dynamics using air with different gas superficial velocities
( 3 to 9 cm/s).
A binary mixture consisting of different compositions of solid particles
was prepared to be utilized in the study.
It was observed that for specified operating conditions used in the experiments
there is a proportional relationship between gas holdup and both superficial
gas velocity and particle diameter while an inverse relationship exists between
gas holdup and both solid concentration and particles density.
Bubble dynamics (i.e., bubble diameter and bubble rise velocity) is looked at
from a different view point, it increases with increasing solid concentration
and with decreasing particles diameter.
For binary mixture of solid particles, it was proved experimentally that the
effect of each species on the hydrodynamic parameters is proportional to its
II
weight fraction in the mixture, the gas holdup of a binary mixture may be well
presented by the following equation
εg =
x 1 ε g1 + x 2 ε g2
A statistical analysis was performed to get general correlation for the
overall gas holdup in a single and in binary mixtures of solid particles in a
fluidized bed column as a function of the parameters studied:
-single state:
ε g = 0.17808(
(
dp
dc
) 0.201744 (
u g2
gd c
)
ρs
ρ s − ρl
−0.333189
ρ l u g2 d c 1.086486 ρ l d c u g −0.569585 −0.245182
(
)
(
)
cs
σl
µl
) 0.332514
R = 0.96811
error = 0.0049345
-binary mixture state:
ε g = 0.057009(
(
d p1
dc
) 0.075001 (
d p2
dc
u g d c ρl
µl
)1.515572 cs
) 2.443881
R = 0.995641008
error = 0.000521
III
− 0.389035
0.568996
x1
x2
− 0.703610
List of Contents
page
Acknowledgment
Abstract
List of Contents
Nomenclature
I
II
IV
VII
Chapter One : Introduction
1.1
1.2
1.3
1.4
Definition of Bubble column Reactor (BCR)
Fluidized Bed Application
Solid-Suspended Bubble Columns
The Aim of the Present Research
1
1
2
4
Chapter Two: Literature Review
2.1
2.2
Scope
Review of Fluidization Basics
5
2.3
Flow Regimes in Bubble Columns
7
2. 4
Fluidization Regimes
11
2.5
Gas Holdup in Bubble Columns
12
2.6
Phase Holdup
14
2.7
Bubble Size
18
2.8
Bubble Rise Velocity
20
2.9
Solid-Mixing & Solid-Replacement
22
2.10
Settling Velocity of Solid Particles
22
2.11
Effect of Solid Concentration
23
2.12
The Flow Transition in the Bubble Column
25
IV
6
page
Chapter Three: Experimental Work
3.1
3.2
3.2.1
3.2.2
3.2.3
3.2.4
3.3
3.4
3.4.1
3.4.2
3.4.3
Introduction
Measuring-Devices
Air-Supply System
Gas Distributor
Digital Camera
Solid Phase
Computerized Conductivity Probe System (CCPS)
Experiments Procedure
Studying the Effect of Superficial Gas Velocity & Probe
Position.
Studying the Effect of Solid Concentration
Measuring the Bubble Diameter
28
30
30
31
32
32
33
35
35
35
36
Chapter Four: Results and Discussion
4.1
4.1.1
Determination of Transition point
Effect of solid concentration and particle diameter on
37
37
transition point
4.1.2
Effect of particles density on transition point
4.1.3
4.2
Effect of solid composition (binary mixture) on transition
point
Gas holdup
4.2.1
Effect of superficial gas velocity on gas holdup
47
4.2.2
Effect of solid concentration on gas holdup
54
4.2.3
Effect of solid properties on gas holdup
55
42
44
47
4.2.3.1
Effect of particles diameter
55
4.2.3.2
Effect of solid density
57
4.2.3.3
4.3
Effect of solid composition ( binary mixture)
Bubble Dynamics
58
V
63
4.3.1
Effect of superficial gas velocity on bubble dynamics
63
4.3.2
Effect of solid concentration on gas bubble dynamics
71
(bubbles rise velocity and bubble diameter)
4.3.3
Effect solid properties on bubble dynamics
72
4.3.3.1
Effect of solid diameter
72
4.3.3.2
Effect of solid Density
73
4.3.3.3
Effect of solid composition (binary mixture)
74
4.4
75
Effect of superficial gas velocity on solid holdup
4.5
Empirical Correlations
77
4.5.1
Gas Holdup Correlation for Single State
78
4.5.2
Gas Holdup Correlation for Binary State
79
5.1
Conclusions
5.2
Recommendations for future work
References
Appendix-A
Appendix-B
Appendix-C
Appendix-D
Appendix-E
Appendix-F
Appendix-G
Appendix-H
VI
80
81
Nomenclature
Greek Letters
Symbols
Definition
Definition
Unit
Unit
Ac
Cross sectional area of column
(m2)
A
Cross sectional area of vessel
(m2)
db
Bubble diameter
(m)
Ms
Total solid mass in bed
kg
HL
Static slurry height
(m)
g
Gravitational acceleration=9.81
Hf
Level of liquid phase + solid
(m)
Hf ′
Level of aerated slurry
(m)
L
Clear liquid height
(m)
N
Number of holes in the gas distributor
(-)
∆p
Presser drop along the bed
P
P
P
P
(m/s2)
P
P
(N/ m2)
P
U g ,U sg
Superficial gas velocity
(m/s)
U br ,V br
Bubble rise velocity
(m/s)
Ub
Individual bubble velocity
(m/s)
U mf
Minimum fluidization velocity
(m/s)
U trans.
Transition gas velocity
(m/s)
U t ,V s
Setting velocity of particles
(m/s)
Superficial dispersed phase velocity
(m/s)
Superficial continuous (water) phase
(m/s)
R
R
R
R
R
R
R
R
R
R
R
R
Ud
R
U L ,U c
R
R
R
VII
P
do
Hole diameter in gas distributor
(mm)
εg
Gas Hold up
(-)
εL
Liquid hold up
(-)
εs
Solid hold up
(-)
εc
Hold up of continuous water
(-)
εd
Hold up of dispersed
(-)
ε dr
Droplet relative hold up
(-)
γ
Interfacial tension
(N/M)
µL ,µ
Liquid viscosity
(Pa.s)
π
Constant=(22/7)
(-)
ρ, ρ L
Liquid density
(kg/m3)
ρ p , ρs
Particle density
(kg/m3)
ρg
Gas density
(kg/m3)
σ
Liquid surface tension
(N/m)
τ
Shear stress of liquid (Viscous Force)
( N/m2)
ρc
Channel plus continuous density
(kg/m3)
τ1
The width of the pulse from the
(s)
upper channel
The delay between the trailing edge
τ2
of the upper channel and the trailing
VIII
(s)
edge of the lower channel
τ3
Time between
channel pulses
Greek Letters
consecutive
upper
Definition
(s)
Unit
do
Hole diameter in gas distributor
εg
Gas Hold up
(-)
εL
Liquid hold up
(-)
εs
Solid hold up
(-)
εc
Hold up of continuous water
(-)
εd
Hold up of dispersed
(-)
ε dr
Droplet relative hold up
(-)
γ
Interfacial tension
(N/M)
µL ,µ
Liquid viscosity
(Pa.s)
π
Constant=(22/7)
(-)
R
R
R
R
R
(mm)
ρ, ρ L
Liquid density
(kg/m3)
ρ p , ρs
Particle density
(kg/m3)
ρg
Gas density
(kg/m3)
σ
Liquid surface tension
P
P
P
P
P
IX
P
(N/m)
τ
ρc
τ1
Shear stress of liquid (Viscous Force)
Channel plus continuous density
( N/m2)
(kg/m3)
The width of the pulse from the
(s)
upper channel
The delay between the trailing edge of
τ2
the upper channel
IX and the trailing
(s)
edge of the lower channel
τ3
Abbreviations◌ِ
BCR
SBCR
FBCs
Time between
channel pulses
consecutive
Definition
Bubble Column Reactor
Slurry Bubble Column Reactor
Fluidized bed bubble columns
X
upper
(s)
Chapter One
Introduction
Chapter One
Introduction
1.1 Definition of Bubble Column Reactor (BCR)
A bubble column reactor (BCR) is basically a cylindrical vessel with a
gas distributor at the bottom. The gas is sparged in the form of bubbles into
either a liquid phase or a liquid solid suspension.
BCRs are intensively utilized as multiphase contactors and reactors in
chemical, petrochemical, biochemical and metallurgical industries [1]. BCR is
used especially in chemical processes involving reactions such as oxidation,
chlorination, alkylation, polymerization and hydrogenation in the manufacture
of synthetic fuels by gas conversion processes and in biochemical processes
such as fermentation and biological wastewater treatment[2,3].
1.2 Fluidized Bed Application
In three-phase fluidization, the particles are fluidized by the co-current
flow of liquid and gas. The three phase fluidized beds can be classified into
the expanded bed and transport regimes, the solid can be introduced either
continuously or batch wise [4].
Fluidization has been utilized in many different processes, including the
production of silicon for semiconductors and the cultivation of micro
organisms in what has come to be called “ biofluidization” some of these
application are listed in Table(1.1).
1
Chapter One
Introduction
Table (1.1): Applications of Fuidized Beds, [5].
Application
Transportation of solids
Heat exchange
Drying
Examples
Slurry pipeline for coal, air slide
conveyor for fly ash, flour, etc.
Energy recovery from hot ceramic
powders.
Hot air drying of dolomite, coal ,grains
Combustion
Catalytic Reactions
Atmospheric pressure combustion
Fischer-tropsch synthesis, waste
incineration, catalytic cracking of
hydrocarbons
1.3 Solid-Suspended Bubble Columns
Fluidized bed reactors (FBR s ) can be classified according to the phases
where the reactants are present. Table (1-2) gives an overview .The most
important distinction is whether the solid phase is a reactant or a catalyst.
In principle, the solids could also be inert and only present to increase
mass transfer between phases as is often the case, e.g., in trickle flow reactor.
In FB reactors the introduction of solids for this purpose only is not
worthwhile, with the exception of solids like zeolites and activated carbon for
enhancement of mass transfer or improvement of selectivity [6,7]. The solidsuspended bubble column is widely used as a three-phase FB reactor in
industrial chemical processes and has drawn attention in relation to coal
liquefaction recently. In the column of a liquid-solid batch operation; the
liquid is a fluidizing medium and the solid particles are fluidized by the
bubble agitation.
To design a column of this type as a FB reactor, the behavior of the
suspended solid particles, that is, the values of the critical gas velocity are
2
Chapter One
Introduction
required for complete suspension of solid particles and the concentration
distribution of the solid particles, should be known.
However, only a few research works have been done on the critical gas
velocity (VGc) required for complete suspension of solid particles [8].
Table(1-2)An overview of slurry reactors classification according to the
phases where the reactants are present
System
Gas-liquid-solids
Typical examples
Remarks
Ref.
Thermal coal liquefaction
9
CO2 absorption in lime
10
all reactants.
suspension
Single cell protein
11
Gas and solids are
reactants.
Hydride formation and
decomposition in slurry.
Gas phase is reactant,
Fischer-Tropsch process
Liquid phase is used to
13
solid is a catalyst,
suspend catalyst and
Hydrogenation of
ethylene using a suspended Raney improve heat transport
nickel catalyst.
14
Hydrogenation of edible coal
15
liquid is inert
Gas phase and liquid
phase are reactants,
Liquid to improve heat
transport properties avoid
dust entrainment.
Active carbon may also
12
enhance oxygen transfer
solid is a catalyst
Hydro-desulphurization
16
Oxygen consuming reactions in
activated carbon slurries.
17
3
Chapter One
Introduction
1.4 The Aim of the Present Research
The purpose of the present research could be summarized as follows:1- Finding experimentally the effect of superficial gas velocity on gas holdup,
bubble dynamics i.e. (bubble rise velocity and bubble diameter) in three
phase fluidized bed column.
2- To study the influence of the solid particles concentration on the local
volume fraction of gas (local gas holdup) and bubble dynamics.
3- Studying the effect of probe position on the hydrodynamic parameters by
moving the probe axially through the column, the probe putting at the center
of the column (r/R =0).
4- To develop an empirical correlation to correlate the gas holdup with the
operating variables.
4
Chapter Two
Literature Survey
Chapter Two
Literature Survey
2.1 Scope
U
Three-phase fluidized beds have been widely used in the polymer,
chemical, petrochemical and biochemical industries.
The aim of this chapter is to give a comprehensive review of literature
to gain a fundamental understanding of the hydrodynamic characteristics of
three-phase in bubble columns. Therefore, the starting point is the
hydrodynamic mechanisms occurring in bubble columns, i.e. gas hold – up,
bubble rise and resulting phenomenon. Three-phase fluidized describes a
gas-liquid-solid flow system in which particles are in motion induced by
gas and / or liquid phases-fundamental studies of transport phenomena and
modeling
of
bubble
columns
to
understand
the
hydrodynamic
characteristics of these units are fairly established [18,19].
In three-phase fluidized bed the solid particles are fluidized by an
upward co-current flow of two-fluid phase. One of the fluids can be a
liquid and serves as the continuous phase while the other gas serves as the
dispersed phase and both of them can be immiscible liquids [20,21].
Figure (2.1) summarizes the bubble column under operation, also it
illustrates the factors which affect hydrodynamics of three phase Fluidized
Bed Columns (FBCs), such as: solid concentration, column diameter,
superficial gas velocity and probe position.
5
Chapter Two
Literature Survey
Distributor type and
column configuration
Liquid and
Gas Mixing
Flow regimes
Homogeneous
Heterogeneous
Liquid
Circulation
Uc
Heat
Transfer
in Bubble
Column
Superficial gas
Velocity Ug
Bubble Size
at the
Distributor
Bubble
size in the
column
Gas
Holdup
Mass
Transfer
in
Bubble
Column
Bubble Rise
Velocity
Medium Properties
Viscosity, Density
Coalescence Prop.
Liquid Side
Mass
Transfer
Gas Phase
Separation
Figure (2.1): Interrelated parameters in a bubble column [22]
2.2 Review of Fluidization Basics
U
The fluidized bed is one of the best known contacting methods used in
processing industry. Among its chief advantages are that the particles are
well mixed leading to low temperature gradients, they are suitable for both
small and large scale operations and they allow continuous processing.
There are many well established operations that utilize this technology,
including cracking and reforming of hydrocarbons, coal carbonization and
gasification, ore roasting, Fisher-Tropsch synthesis, coking, aluminum
production, melamine production, and coating preparations . Fluidization is
6
Chapter Two
Literature Survey
a process in which solids are caused to behave like a fluid by blowing gas
or liquid upwards trough the solid-filled reactor [23 ].
Fluidization is widely used in commercial operations; the applications
can be roughly divided into two categories, i.e., Physical operations, such
as transportation, heating, absorption, mixing of fine powder, etc. and
chemical operations, such as reactions of gases on solid catalysts and
reactions of solids with gases etc., the application of fluidization is also
well recognized in nuclear engineering as a unit operation for example, in
uranium extraction, nuclear fuel fabrication, reprocessing of fuel and waste
disposal[24].
“The arrival time of a space probe traveling to Saturn can be predicted
more accurately than the behavior of a fluidized bed chemical reactor”. The
difficulties in prediction stem in part from the complexity and ambiguity in
defining the fundamental parameters such as size, shape and density of the
particles. These parameters play an important role the calculation and
prediction of dynamic behavior in fluidized beds [25].
2.3 Flow Regimes in Bubble Columns
U
Generally, when a column filled with a liquid is sparged with a gas the
bed of liquid begins to expand as soon as the gas is introduced. Three
different flow regimes have been identified to occur in bubble columns or
(BCRs), which are mainly determined by the gas superficial velocity.
These three regimes are described as follows [26]:
Homogeneous bubbly flow regime, which occurs generally for
superficial gas with velocity less than 0.05 m/s. This regime is
characterized by small uniformly sized bubbles with a rise in velocity in the
range of 0.18 to 0.3 m/s.
7
Chapter Two
Literature Survey
Heterogeneous or churn – turbulent regime, which is characterized by
the simultaneous presence of large and small bubbles. The large bubbles
can be of sizes of about 0.08 to 0.15 m with a rise in velocities greater than
0.8 m/s.
Slug flow regimes, where large bubbles (called slugs) occupy the
entire column cross – section.
As the gas velocity is increased the
bed height increases almost
linearly with the superficial gas velocity U sg , provided the value of U sg
R
R
R
R
stays below a certain value U trans . This regime of operation of a bubble
R
R
column is called the homogeneous bubbly flow regime. When the
superficial gas velocity U sg reaches the value U trans , coalescence of bubbles
R
R
R
R
takes place to produce the first fast-rising “large” bubble. The appearance
of the first large bubble changes the hydrodynamic picture dramatically.
The hydrodynamic picture in a gas – liquid system for velocities exceeding
U trans is commonly referred to as the heterogeneous or churm-turbulent
R
R
flow regime [27].
Numerous investigators have studied the regime transition in bubble
column [28,29,30]. All these authors pointed to the importance of the effect
of column dimensions and liquid physical properties on the homogeneous –
heterogeneous regime transition in bubble column. Figure (2.2) best
illustrates the difference between the possible regimes discussed.
8
Chapter Two
Literature Survey
Figure (2.2): Schematic of possible flow regimes in bubble
columns [1].
Several flow regimes charts have been presented in literature to identify
the boundaries of possible flow regimes [31].
In Figure (2.3), one such flow regime map presented by Deckwer et al
[32] is shown below. The map describes quantitavely the dependence of
flow regimes on (D c ) and (U g ) and is valid for both bubble and slurry bubble
R
R
R
R
column reactors with a batch (stationary) liquid phase operated with a low
viscosity liquid phase.
9
Chapter Two
Literature Survey
Ug
(m/s)
Dc (m)
Figure (2.3): Flow regime map for (BCRs) [1].
Near the maximum gas holdup, gross liquid circulation current sweeps
the entire volume indicating the beginning of liquid circulation regimes
[33].
In Figure(2.4) the depletion of increase in (ε g ) at lower (U g ) is mainly
R
R
R
R
due to the gross in the coalescence and break-up of bubbles and thus raises
bubble velocity.
The decrease in (ε g ) at higher (U g ), however, is attributed to the
R
R
R
R
development of regular circulation of liquid, which is firmly established in
the liquid circulation regime [34].
10
Chapter Two
Literature Survey
Superficial gas velocity Ug (m/s)
Figure (2-4): Qualitative sketches of observed flow pattern and gas
hold-up as a function of superficial gas velocity [35].
2.4 Fluidization Regimes
U
The fluidized bed behaves differently as velocity, gas and solid
properties are varied, when the solid particles are fluidized. It has become
evident that there are a number of regimes of fluidization, as shown in
Figure (2.5). When the flow of a gas passed through a bed of particles is
increased continually, a few vibrate, but still within the same height as the
bed at rest. This is called a fixed bed (Figure 2.5 A).
With increasing gas velocity, a point is reached where the drag force
imported by the upward moving gas equals the weight of the particles, and
the voidage of the bed increases slightly: this is the onset of fluidization
and is called minimum fluidization (Figure 2.5 B) with a corresponding
minimum fluidization velocity, U mf . Increasing the gas flow further, the
R
R
11
Chapter Two
Literature Survey
formation of fluidization bubbles sets in, at this point, a bubbling fluidized
bed occurs as shown in Figure (2.5 c). If the ratio of the height to the
diameter of the bed is high enough, the size of bubbles may become almost
the same as diameter of the bed. This is called slugging (Figure 2.5 D). If
the particles are fluidized at a high enough gas flow rate, the velocity
exceeds the terminal velocity of the particles. The upper surface of the bed
disappears and, instead of bubbles, one observes a turbulent motion of solid
clusters and voids of gas of various sizes and shapes. With further increases
of gas velocity, eventually the fluidized bed becomes an entrained bed in
which, we have disperse, dilute or lean phase fluidized bed, which amounts
to Pneumatic transport of solids [36].
Figure (2.5): Schematic representation of fluidized beds in different
regimes [36]
2.5 Gas Holdup in Bubble Columns
U
The gas holdup (ε g or gas void fraction) in the gas–liquid– solid
R
R
fluidized bed varies strongly with bubble flow properties, depending on the
gas flow rate, liquid flow rate, and physical properties of the particles.
Bubble flow in a gas–liquid–solid fluidized bed can be classified into three
distinct regimes, namely, dispersed bubble flow regime, coalesced bubble
flow regime, and slug flow regime [37].
12
Chapter Two
Literature Survey
In the transition regime the increase in the gas flow rate increases the
bubble coalescence.
Gas holdup (ε g ) can be defined as the ratio of the volume of gas to the total
R
R
volume of gas and liquid mixture in a finite length of the column. In order
to predict gas holdup values it is necessary to know the relationship
between gas– liquid slip velocity and gas holdup [38].
There are many other techniques used for gas holdup measurements,
such as, optical probe, hot–film anemometer, particle image velocimetry,
ultrasonic techniques, electrical capacitance and resistance tomography
[39].
The effect of surface tension on gas holdup can be qualitatively
described in that a lower surface tension gives a lower bubble rise velocity
and therefore a higher holdup [40]. Such a variation in surface tension can
be achieved in several ways:
1. by the addition of surface – tension – lowering compounds to a
spure liquid.
2. or by changing to a liquid with a lower surface tension. The
hydrodynamics of a binary system was studied in bubble columns of
diameter > 0.1 m, the superficial gas velocity was varied in the range 0.004
to 0.45 m/s [41].
correlation for gas holdup.
εg =1/(2+ 0.35/Usg(ρL σ /72)1/3)
……………. (2.1)
For liquids of low viscosity and for water eqn. (2.1) becomes.
εg= 1/(2+0.35/Usg)
……………
(2.2)
The following simple correlation was proposed by [42]:
(εG)s = εG(ρL / ρs )0.4
L
13
…….. ..... (2.3)
Chapter Two
Literature Survey
where:
(ε G ) s and ε G are the values of fractional gas holdup in two and three phases
, respectively.
R
R
R
R
R
R
ρ sL is the slurry density, given by the following equation:
R
R
ρ sL = ε s ρ s +(1- εs) ρ L
R
R
R
R
R
R
R
…………….. (2.4)
R
2.6 Phase Holdup
U
The phase holdup is the fraction of individual phase occupied in three
phase contacting thereby it is one of the most important parameters to
determine the hydrodynamic properties of liquid – liquid – solid fluidized
beds.
The following equations have typically been used to determine the volume
fraction (holdup of each phase in a three – phase fluidized beds ):
εc+ εs+ εd = 1
R
R
R
R
R
................ (2.5)
R
where
ε c = holdup of continuous (water)
R
R
ε d = holdup of dispersed (air)
R
R
∆P =gH f (ρ c ε c +ρ s ε s +ρ d ε d )
…………. (2.6)
εs =
…. ............. (2.7)
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
R
Ms / ρsAcHf
R
R
R
R
R
R
R
R
The beds height in equations (2.6) and (2.7) can be obtained either
visually or from the measured pressure gradient [43,44].
There are several experimental methods to measure the holdup [45].
1. The use of quick-closing valves.
2. Measurement of pressure drop.
14
Chapter Two
Literature Survey
3. Dynamic analysis of radioactive tracers; and
4. The use of electroconductivity or electrosensitivity probs.
Figure (2.6) Effect of dispersed phase velocity on the average εd and local
droplet holdups at the center in the beds of 3.0 mm glass beads [21].
The effect of dispersed phase velocity (U d ) on dispersed phase holdup
R
R
(ε d ) in the beds of 3 mm glass beads is shown in Figure (2.6), in which the
R
R
solid lines represent (ε dr ) values obtained to a local point from the probe
R
R
method and the dotted lines represent the values obtained from the pressure
method, that is, the mean value of (ε d ) in the beds. As can be seen (ε d )
R
R
R
R
values from the two different methods are in a good agreement so that the
local and mean values of (ε d ) are nearly the same since variation in droplet
R
R
size is marginal throughout the beds. The dispersed droplet phase holdup
(ε d ) increases with an increase in (U d ) but it decreases with increasing (U c ),
R
R
R
R
R
R
because a higher (U c ) provides a higher droplet rising velocity [21,46]. In
R
R
the beds of smaller particles droplet coalescence increases and the rate of
increase in (ε dr ) decreases with increasing (U d ). The effect of (U c ) on (ε d )
R
R
R
15
R
R
R
R
R
Chapter Two
Literature Survey
in the beds of 1.7 and 3.0 mm glass beads is shown in Figure (2.7), where
(ε dr ) decreases almost linearly with increasing (U c ) due to the reduction in
R
R
R
R
viscosity and increase in the droplet rise velocity that may result in a
reduction of the residence time of the droplets in the beds. [21]
Figure (2.7): Effect of continuous phase velocity on εdr in the
beds of 1.7 and 3.0 mm glass beads [21]
As can be seen, (ε d ) in the beds of 3 mm glass beads is greater than
R
R
that for the case of 1.7 mm glass beads because droplets may break down in
the former beds, but droplets may coalesce in the latter beds so that the
drag force acting on the larger droplets may be larger and the residence
time of larger droplets may be shorter in the beds of larger particles
[46,47].The obtained data of (ε d ) [21,46,47] have been correlated with
R
R
16
Chapter Two
Literature Survey
Froude number and the ratio of dispersed to the total fluid velocities. In the
droplet coalescing flow regime is
(1.0 < dp <2.3 mm ):
ε d = 0.577 (U d /gd p )0.11 [( U d / (U c + U d
R
R
R
R
R
R
P
P
R
R
R
R
R
))]0.616
R
P
……….(2.8)
In the droplet disintegrating flow regime(2.3<dp<6.0 mm) is:
ε d = 1.200 (U d /gd p )0.188 [( U d / (U c + U d
R
R
R
R
R
R
P
P
R
R
R
R
R
R
))]1.050
P
……….(2.9)
Liquid holdups in three-phase fluidized beds with glass beads and
cylindrical γ-alumina particles were determined experimentally by [48], it
was found that liquid holdup in the three-phase fluidized beds is equal to
that in corresponding liquid – solid fluidized beds.
A method of measurement of solid holdup in a three-phase-reactor by
analyzing the shape and the phase lag or lead has been proposed by [49].
The solid dilute three-phase fluidized beds could be measured without
being affected by the presence of gas bubbles.
A light transmittance technique using a dual optical probe was
proposed by [50,51] to measure the local solid holdup in three – phase
fluidized beds. Bubble frequency and local gas holdup in different radial
and axial
positions was measured by [52],
using a dual electro-
conductivity probe in air-water-glass beads fluidization systems. It has
been found that the bubble characteristics differ significantly in various
flow regimes, depending on the operating conditions and the radial
distribution of bubble parameters and also changes from one flow regime to
another. Thus it is necessary to employ local bubble behavior in the
modeling of three-phase fluidized beds. Characteristics of gas-liquid–solid
flow behavior in a riser were investigated by [53] in a three – phase
circulating fluidized beds (0.102 m I.D x 3.5 m in height). Local gas
17
Chapter Two
Literature Survey
holdup, solid holdup distribution have been measured and utilized to
describe the gas-liquid-solid flow behavior more conveniently.
2.7 Bubble Size
U
Many researchers have attempted to predict the size of bubbles, not
only the variation in mean size, but also the distributions of the diameters
and volumes. The mean size of the bubble population in fluidized beds
increases with height above the distributor plate due to coalescence of
bubbles. A new correlation for estimation of mean bubble size of bubble
swarms under dispersed and fluidized operation of bubble columns
employing single and multi-orifice distributors was obtained by [54]. The
following equations fit the mean bubble size data above and below the
critical Re of 2100 for orifice diameters between 0.0419 and 0.6 cm and for
1<Re<10:
d b = 1.56Re 0.058 (d 0 2σ / g∆ρ) 1/4
R
R
P
P
R
RP
P
P
……….(2.10)
P
with an average deviation of 0.54% for
10< Re < 2100:
d b = 0.32Re 0.425 (d 0 2σ / g∆ρ) 1/4
R
R
P
P
R
RP
P
P
……….(2.11)
P
with an average deviation of 12.63 % for
4000 < Re< 70000:
d b = 100Re -0.4 (d 0 2σ / g∆ρ)1/4
R
R
P
P
R
RP
P
P
……….(2.12)
P
With an average deviation of + 9.4%,where (d 0) is the nozzle diameter.
R
R
The bubble size was studied at sparger by [55]. They obtained at low
gas rate a simple force balance:
Buoyancy force is equal to surface tension force. The bubble grows
until its buoyancy force exceeds the surface tension. The correlation found
is as follows:
18
Chapter Two
Literature Survey
d b =[ 6 d 0 σ/g(ρ L -ρ g )]1/3
R
R
R
R
R
R
R
R
P
………… (2.13)
P
d b /d 0 =3.23 Re 0 -0.1 Fr 0.21
R
R
R
R
R
R
P
P
P
..……. (2.14)
P
Bubble size for beds of 2, 4 and 6mm diameter glass particles was
measured using both water and octanol solution with surface tension about
half that of water [56].
Large bubbles were observed with 2mm diameter particles, decreasing
with increasing particle sizes. The octanol solution was found to stabilize
much smaller bubbles than water.
The bubble size was studied at a distance from the sparger using air–
water system and the following correlation was obtained experimentally
[57]:
d b = 4.15 σ L 0.6/(g U sg )0.4 ρ L 0.6
R
R
R
R
P
P
R
R
P
P
R
R
P
………..(2.15)
P
The expression of bubble diameter was proposed in cylindrical bubble
column (Height = 0.9 m and diameter = 0.254 m) as a function of Bond,
Galileo and Froud numbers as well as the ratio of orifice diameter to the
column diameter [58].
d b / D = f ( Bo , Ga, Fr, d o / D)
R
R
R
………….(2.16)
R
A cylindrical Perspex tank was used as a bubble column of diameter
(50 cm) filled with de–ionized water to adepth of 40 cm [59]. The bubbles
were produced by blowing air through a porous plug of diameter 6 cm,
which was positioned centrally at the base of the tank .The bubble plume
rise to the surface entraining liquid from the pool and generating a large
scale circulation. Measurements were taken at elevation of 50, 100, 200,
300, and 380 mm above the plug. A double contact, electro – resistivity
probe mounted on a movable carriage was used to obtain bubble axial
19
Chapter Two
Literature Survey
diameter in the plume, at which a well defined bubble swarm was
observed. There was negligible coalescence or break – up and a uniform
bubble size distribution with height was observed. Several investigations
have reported the results of studies that involve the measurement of bubble
diameter as a function of different parameters. Collectively, these studies
employ most of the commonly used spargers (porous plates, perforated
plates, single orifice and perforated pipe) [60].
The bubble size is governed by the ratio of forces stabilizing the
bubble and the forces acting to break up the bubble . The bubble is
stabilized by the surface tension forces and the viscous stresses inside the
bubble and de – stabilized by the deformation due to the shear stresses [61].
2.8
Bubble Rise Velocity
U
The bubble rise velocity was measured in gas –liquid- solid fluidized
beds using an electro– resistivity probe, the probes were analyzed with a
hybrid computer. It is reported as a function of fluidization level, particle
size and position within the bed. [62]
The bubble rise velocity was measured by means of movie photography
in two and three phase fluidized beds [63] . Three solids (1 – 6mm), a
variety of liquids and air were employed as the three phases. The bubble
rise velocity was found to increase with gas velocity but is relatively
insensitive to the liquid velocity, viscosity and surface tensions. The
correlation presented for calculating bubble rising velocity is:
U br = 83.1U L -0.133 U sg 0.341 µ L 0.026
R
R
R
RP
P
R
RP
P
R
R
P
…(2.17)
P
The following correlation for the bubble rise velocity in three phase
fluidized beds was proposed by [64]:
….(2.18)
where:
20
Chapter Two
Literature Survey
K = 16.062 dp 0.228
P
The under limited conditions was indicated in three phase systems, the
rise velocities of single bubbles were found to be similar to those in highly
viscous [65].
As in the case of gas – liquid – solid
fluidized beds, the increase in
U c results in an increase in drag force acting on the droplet upward,
R
R
therefore V d increases with increasing U c .
R
R
R
R
The obtained droplet rising velocity has been correlated with the
experimental variables as [21]
………(2.19)
The relative droplet rising velocity
In the beds of 1.0, 2.3 and 3.0 mm glass beads with variation in U d is
R
R
shown in Figure (2.8). As can be expected, V dr decreases in the droplet –
R
R
disintegrating beds (dp=3.0 mm), whereas V dr increases in the droplet –
R
R
coalescing beds (dp=1.0 mm) with an increase in U d , on the other hand, V dr
R
R
R
remains almost constant in the beds of 2.3 mm glass beads with increasing
R
Ud.
R
R
21
Chapter Two
Literature Survey
Figure (2.8): Effect of dispersed phase velocity on the relative
droplet rising (V dr ) in beds of 1.0, 2.3 and 3.0mm glass beads [21]
2.9 Solid-Mixing & Solid-Replacement
U
Solid-mixing and solid-replacement are important factors in cases
where they have a short life-time. This can be the case if the solid phase is
to be converted or if the catalyst is rapidly deactivating [66].
Solid-mixing in a gas-liquid-solid system was studied by [67]. She
reported three-states which are solid mixing, intermixing and complete
intermixing.
2.10 Settling Velocity of Solid Particles
U
The optimal operation of a slurry bubble column reactor requires that
the solid phase be fluidized in the liquid phase over the entire height of the
column. The solid phase is fluidized by upward forces caused by rising gas
bubbles and acting against the downward gravitational forces. The ability
to fluidize the particles arises from mixing induced by the gas bubbles and
therefore, at the expense of some back mixing of the particles. Plug-Flow
behavior can still be achieved , however , because for gas mixing the
22
Chapter Two
Literature Survey
importance of the dispersion must be compared to the gas velocity
(U g ), rather than to the particle settling velocity (U s ). Low particles settling
R
R
R
R
velocities increase the window of acceptable operating parameters but are
not themselves a necessary condition for good performance. The settling
velocity increases with increasing the particle size, therefore, higher liquid
circulation and turbulence is required to suspend the solid particles .The
tendency of particles to settle can be overcome, however, by maximizing
the dispersion effects resulting from the rising gas bubbles and enhanced
by increasing either the effective reactor diameter or the flow rate of gas
through the reactor [68].
2.11 Effect of Solid Concentration
U
The solid concentration is defined as the volume fraction, (ε s ), of solids
R
R
in the gas-free slurry. The effect of solid concentration and particle size on
gas holdup has been investigated by a number of researchers. Several of
researchers concluded that an increase in solids concentrations generally
reduces the gas holdup [69]. There is a strong dependence of gas holdup
on solids concentration at low solid concentration [70].
The effect of solid concentration on gas holdup becomes significant at
high gas velocities (> 10-20 cm/s) [71],
the influence of particle size has
been found to depend on a number of factors including flow regime, gas
velocity, liquid properties and slurry concentration. It is now generally
reported that addition of solids to a two-phase system decreases the holdup
[72]. For a fixed gas velocity and solid concentration, increasing the solid
diameter also decreases the holdup and this effect of particle size is more
pronounced for low concentration slurry system [73].
Decreases a holdup with increasing solid concentration up to 25% by
volume concentration. Afterwards, the gas holdup shows a slight increase .
23
Chapter Two
Literature Survey
This unusual behavior was attributed to the accumulation of fine
bubbles at high slurry concentration and decrease in the rise velocity of
small bubbles. Also the presence of solids and solid concentration has an
impact on bubble properties. It was reported that the presence of solids
leads to larger bubble size. This is attributed to an increase in the apparent
slurry concentration [72].
[3] utilized yeast cell in their column and reported that, as the yeast
concentration increases, the rise velocity of small bubbles decreases. [73]
indicated that for particles less than 1mm in size, the gas holdup is
significantly reduced by the presence of solid particles. This is attributed to
the fact that small particles promote bubble coalescence which results in
higher rising velocities, while the effect of larger particles was found to be
less significant, since these particles instead tend to cause break-up of
bubbles .
Some investigators have found that when relatively small particles or
low density particles are used, the addition of solids may cause the gas
holdup increase. In general, it was claimed that the increase in gas holdup
is due to poor wettability of the solids. The researchers of the eighties
explained that there exists an optimum ratio between the particle diameter
and micro scale of turbulence which depends on density, particle shape and
structure of liquid turbulence. Upon reaching the optimum ratio, the
turbulence associated with the three-phase systems is greater than that with
the two-phase system, and as a result, smaller bubbles are produced and
this gives rise for higher gas holdup. This increase in turbulence is only
possible to certain values of gas holdups and solids concentration because
the distance between the bubbles and particles becomes very small in
turbulence subsides, resulting in larger bubbles and consequently lower
holds up [74].
24
Chapter Two
Literature Survey
2.12 The Flow Transition in the Bubble Column:
U
The detection of regime transition from homogeneous to churnturbulent flow and the investigation of the transition regime are quite
important [75].
Based on experimental data of [76], flow regime map was constructed
as shown in Figure (2-3) for air-water system. Transition between flow
regimes is strongly influenced by other factors such as change in physical
properties of the liquid, presence of solids, increase in system pressure and
temperature, superficial gas velocity, column diameter, and distributor
design, which are characteristics of industrial reactors. Due to such effects
the boundaries in Figure(2-3) are only approximate. The influence of these
parameters on flow regime transition have been extensively studied by [77,
78, 79].
The approach used by these researchers in studying flow regime is
based on interpretation of Dynamic Gas Disengagement (DGD)
experiments. The DGD technique was originally developed by [80], to
study the structure of the gas holdup in bubble columns. They present a
theoretical basis for the technique and show that the static and dynamic
holdup are detected by the size of distributions and rise velocities of the
bubbles.
Using DGD experiments [80,81,82,83], have measured the transition
gas velocity and the contributions of small and large bubbles to the overall
holdup. A typical DGD curve, i.e. dispersion height versus time, is shown
in Figure (2.10) for the air-water system in the 0.15 m column.
25
Chapter Two
Literature Survey
Figure (2.10): Typical gas disengagement experiment
showing dispersion height H d vs time [81].
R
R
When the gas distribution is very good, the regime transition region is
often characterized by a maximum in the gas holdup [84]. The transition
between homogeneous and churn-turbulent regimes is often difficult to
characterize [85].
Knowledge of the existing flow regime and identification of the
transition between bubbly flow and churn-turbulent flow is necessary to
provide a clear picture upon which modeling and design efforts for a
particular process can be based. One approach that has been commonly
used in identifying the prevailing regime is based on the concept of the drift
flux, as introduced by [86]. The drift flux, jGL represents the volumetric
flux of gas through a surface moving at the volumetric average velocity of
the dispersion ,(U g ±U L /2), and is given by [87].
R
R
R
R
j GL = U g ( 1- ε g )
R
R
R
R
R
……….(2.20)
R
26
Chapter Two
Literature Survey
where U g is the superficial gas velocity of the flow regime between
R
R
the gas and liquid. A plot of j GL vs ε g reveals the gas velocity at which
R
R
R
R
transition occurs, by the indication of the change in the slope in the curve
Figure (2.11). In the bubbly flow regime, which is characterized by a
uniform bubble size, the drift flux remains approximately constant with
increase in gas velocity and holdup. Upon transition to the turbulent flow
regime, the drift increases sharply with gas holdup.
Figure (2.11): Identification of flow regime from behavior of
drift flux with representation of gas holdup [86].
27
ChapterThree
Experimental Work
Chapter Three
Experimental work
3.1 Introduction
The experimental study was carried out to investigate the effect of
the following parameters on the gas hold-up and bubble dynamics in
solid-suspended bubble column:
 Superficial gas velocity
 Solid- particles concentration (single solid phase and binary
mixture of solid phase).
 Probe position
The experiments were performed in one column with inner
diameter of (0.15) m.
The bottom of the column consists of an inverted cone section
with cone angle of 45, the cone section of the column with diameter
of 0.15cm it was made of QVF.
The conical bottom geometry was used in order to minimize the
occurrence of dead spaces at the bottom of the column.
the column was made of QVF glass, and operated in the semibatch mode, in which the liquid is stationary and the gas flows
upward.
The experimental apparatus is shown schematically and
photographically in Figures (3.1 and 3.2) respectively.
28
ChapterThree
Experimental Work
10
9
8
5
11
12
7
4
6
3
13
1
2
1 Air-compressor
2 Check valve
3 Air-filter
4 Needle valve
5 Air-flow meter
6 on-off valve
7 Discharge valve
8 Gas distributor
9 QVF column
10 Electroresistivity Probe
11 Interface
12 Pc (PIII)
13 Digital Camera
Figure (3.1): Schematic diagram
of the experimental apparatus.
29
ChapterThree
Experimental Work
Figure (3.2 ): Photographic picture of the
Experimental apparatus
3.2 Measuring-Devices
3.2.1 Air-Supply System
Figure (3-2): Photographic picture of the Experimental apparatus
3.2 Measuring-Devices
3.2.1 Air-Supply System
Air was used as the gas phase. The compressed air was passed
through a stabilizer then was fed to the column.
The gas flow rate was adjusted with the aid of needle valves and a
calibrated rotameter.
30
ChapterThree
Experimental Work
Calibrated rotameter of capacity (280) lit/min was used in this work in
order to cover the operating range of the air flow rate, the calibration curve
of the rotameter is illustrated in Appendix (A). The range of superficial gas
velocity which is used in these experiments was varied from (0.03-0.09)
m/s, for Dc= (0.15) m.
3.2.2 Gas Distributor
Air was introduced into the system through a perforated plexiglass of
thickness 3 mm. The holes of the distributor having a circular arrangement.
The shape and dimension of the distributor are shown in Figure (3-3) and
listed in Table (3-1). The design of the air distributor is illustrated in
Appendix (B).
Figure(3.3): Shape of the gas distribution ,for Dc=15 cm.
Table (3-1): Specifications of Air Sparger.
Column
Diameter Dc
(cm)
15
No. of Holes
Hole
Diameter
(mm)
2
47
31
% Free area
0. 836
ChapterThree
Experimental Work
Digital Camera
Digital camera type (OLYMPUS, C-400/ZOOM) with high resolution
(4 pixels) was used in the experimental work to measure the bubble
diameter; the camera was connected to the computer.
3.2.4 Solid Phase
The solid phase which was used in the experiment shown in. Tables
(3-2) and (3-3).
Table (3-2) Physical Properties of Particles used in this study.
Particle
Notation
Type of
Particles
Dp
( mm )
ρs
( Kg / m3 )
Ut
( cm / s )
A
B
C
D
E
PVC
PVC
PVC
Plastic
Plastic
3
1.5
0.65
3
0.5
1025
1025
1025
1150
1150
2.37
0.529
0.09
2.772
0.057
R
Table (3-3) Description of Binary Mixture of Particles
Mixture
Notation
0B
Ma
Mb
Mc
Na
Nb
Nc
Ia
Ib
Ic
Va
Vb
Vc
Descriptio
n
1B
A&B
A&C
A&D
A&E
Weight
Ratio
1/2
Diameter
Ratio
(large /
small)
Density
Ratio
(heavy /
light)
2
1
4.48
4.6
1
26.33
1
1.122
0.855
6
1.122
41.57
1:1
1:3
3:1
1:1
1:3
3:1
1:1
1:3
3:1
1:1
1:3
3:1
32
Ut Ratio
(large /
small)
2B
ChapterThree
Experimental Work
Three concentrations of these particles (0, 5 and 10)%
kgsolid/kg(water + solid) were used in the experiments of this work.
3.3 Computerized Conductivity Probe System (CCPS)
Elecetroresistivity probe is used in this work to measure the
hydrodynamic parameters which affect the design and performance
of the bubble column, these parameters are: (Local gas hold up,
bubble frequency, bubble rise velocity, number of bubbles and
average bubble diameter).
The basic principle in the working of this system is that, it utilizes
the difference in the electrical conductivity between the gas and liquid
phases, generating a pulse of voltage when the probe senser a bubble
in the liquid. Therefore, as the bubble intercepts the tips, the interface
system will convert these signals to a series of pulses denoting the
arrival of front and rear of a bubble.
This unit of measurement is programmed by a computer (PIII)
connected on-line to the bubble column throughout an interface
system which is run with the help of appropriate software (Visual
Basic Program). The two tips of the probe were made of stainless
steel because this material resists corrosion, the two tips were
aligned vertically 0.3 cm apart. The electrodes were insulated except
for a distance approximately 0.25 mm from the tips where insulation
was carefully removed. The electrodes were contained in a glass tube
of 1 cm diameter and 150 cm height.
The probe was mounted at the top of the column so that the tips
could be moved axially and radially to the desired measuring point
within the column. Figures (3.4 and 3.5) show a schematic diagram
for the electroresistivity probe and the output signals from it
respectively. Details of interface unit and mathematical presentation
of computer output are sited in Appendix (C and D).
33
ChapterThree
Experimental Work
0.5 mm diameter
Alumel Electrode
0.5 mm diameter
Chromel Electrode
10 mm diameter
Glass tube
3 cm Lower sensor
3 mm Upper sensor
Figure (3-4): The electroresistivity probe.
Lower Ti
τ3
0
`
τ1
τ2
1
Upper Ti
0
1
Figure (3-5): Signals from resistivity probe.
34
ChapterThree
Experimental Work
3.4 Experimental Procedure
In all experiments which applied in this work, the level of clear
liquid was kept at 90 cm.
The electroresistivity probe was moved in axial positions, to
measure the local gas hold up in three different positions.
3.4.1 Studying the Effect of Superficial Gas Velocity and Probe Position
1. The column was filled with distilled water at the desired height.
A little amount (5gm) of salt was added to the liquid to make it a
conductive media.
2. The probe was maintained at the 1st axial position.
3. A needle valve was used to adjust the flow rate of the air at the
desired range of Ug.
4. The experiment was given enough time=10minutes to make a
scanning on the bubble hydrodynamics, and when the experiment
time was completed, the data was analyzed with aid of Visual
Basic program.
5. The axial distance was changed and steps 3, 4 were repeated.
6. Single solid phase was supplied according to Table (3-2) and steps
1 to 5 were repeated for solid loading 5 % w/w and 10 % w/w
respectively for each solid specification.
7. Binary mixture solid phase was supplied according to Table (3-3)
and steps 1 to 5 were applied for solid loading 5 % w/w and 10 %
w/w respectively for each solid specification.
35
ChapterThree
Experimental Work
3.4.2 Studying the Effect of Solid Concentration
The same sequence of the above procedure was repeated from
step 1 to step 6 with adding three different concentrations of the
solid particles which are: (0, 5%, and10%) w/w.
The solid hold up (ε s ) was measured by using the following equation:
ε s = W s / AH′ f ρ s
………..(3.1)
for single solid phase. And the equation
εs =( (W1 / ρs1) + (W2 / ρs2)) / AH′f
………….(3.2)
Is used for binary mixture of solid phase.
3.4.3 Measuring the Bubble Diameter
The
bubble
diameter
was
measured
by
using
the
electororesistivity probe and was compared with the photographing
method and these two methods were applied to the same column and
the experimental results are cited in Appendix (F).
36
Chapter Four
Results and Discussion
Chapter Four
Results and Discussion
4.1 Determination of Transition Point
A common procedure to locate the transition point between the
homogeneous and heterogeneous regimes is to apply the drift flux analysis
[83].
The basic quantity is the drift flux, j GL , which represents the gas flux
through a surface moving at the average velocity of the mixture and is
given by:
……………….. 4.1
j GL = U sg (1-ε g )
If the drift flux is plotted versus the gas holdup, the change in slope of the
curve indicates the transition from the homogeneous to the heterogeneous
regime [2].
4.1.1 Effect of Solid Concentration and Particle Diameter on Transition
Point
Figure (4.1) to Figure (4.4) show the drift flux versus the
corresponding gas holdup for the experimental data of the solid
concentrations tested with different particle diameters. The points where
the change of the slope occurs are determinated and the corresponding
superficial velocities (U sg ) are calculated. Table (4-1) represents the trend
of a (0.5mm) and (1.5mm) particles, other experimental data are cited in
Appendix (H). A general comment is that an increase in solid
concentration shifts the transition to slightly lower velocities so decrease
the stability of the homogeneous regime. This behavior can be attributed
to the effect of solid particles which accelerate the rate of bubble
coalescence resulting in higher bubble velocity. The only exception is the
solid particles of (3mm) diameter tend to increase bubbles breakage. Table
37
Chapter Four
Results and Discussion
(4-1) shows the transition between homogeneous and heterogeneous
regime (dp=0.5mm and dp=1.5mm). This behavior is in agreement with
the findings of [86].
Table (4-1) Transition between homogeneous and heterogeneous
regime (dp=0.5mm and dp=1.5mm)
Solid
concentration%(w/w)
dp,mm ε trans U trans ,cm/s
0
5
10
38
0.5
0.333
7.2
1.5
0.333
7.2
0.5
0.126
6.38
1.5
0.17
6.92
0.5
0.078
5
1.5
0.14
5.69
Drift flux
cm/s
Chapter Four
Results and Discussion
Cs = 10%
10
9
8
7
6
5
4
3
2
1
0
Cs = 5%
Cs = 0%
0
0.1
0.2
0.3
0.4
Overall gas holdup
Drift flux
cm/s
Figure (4.1,a)
cs=10%
9
8
7
6
5
4
3
2
1
0
Cs=5%
Cs=0%
0
0.1
0.2
0.3
0.4
Overall gas holdup
Drift flux
cm/s
Figure (4.1,b)
Cs=10%
9
8
7
6
5
4
3
2
1
0
Cs=5%
Cs=0%
0
0.1
0.2
0.3
0.4
overall gas holdup
Figure (4.1,c)
Figure (4.1): Drift Flux vs. Overall gas holdup for ρs=1025 kg/m3, different values of
solid concentration (Cs) and (dp) at: (a) dp=3mm (b) dp=1.5mm (c) dp=0.65 mm
39
drift flux
Chapter Four
Results and Discussion
Cs=10%
10
9
8
7
6
5
4
3
2
1
0
Cs=5%
Cs=0%
0
0.1
0.2
0.3
0.4
Overall gas holdup
drift flux
Figure (4.2,a)
Cs=10%
10
9
8
7
6
5
4
3
2
1
0
Cs=5%
Cs=0%
0
0.1
0.2
0.3
0.4
Overall gas holdup
Figure (4.2,b)
Figure (4.2): Drift flux vs. overall gas holdup for ρs =1150 kg/m3 ,different
values of solid concentration (cs ) and (dp) at :( a) dp=3mm (b)= 0.5 mm
40
drift flux
Chapter Four
Results and Discussion
dp=0.65mm
9
8
7
6
5
dp=1.5mm
dp=3mm
4
3
2
1
0
0
0.1
0.2
0.3
0.4
Overall gas holdup
drift flux
Figure (4.3): Drift Flux vs. Overall gas holdup for different particles diameter (Cs
= 5%), and(ρs=1025) kg/m3 ) (dp)
dp = 0.5mm
9
8
7
6
5
dp = 3mm
4
3
2
1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Overall gas holdup
Figure (4.4): Drift Flux vs. Overall gas holdup for different particles diameter (Cs
= 5%), and (ρs=1150) kg/m3 )
41
Chapter Four
Results and Discussion
4.1.2 Effect of Particles Density on Transition Point
Figure (4.5) shows the effect of particles density on transition point.
The plot shows an opposition relationship between transition holdup (ε trans.
) and particles density for all operating conditions applied. This can be
attributed to that as particles density increases, with a simultaneous
increase in particle terminal velocity resulting in decrease of overall gas
holdup at specified gas superficial velocity and this lowers the transition
conditions.
Table
(4-2)
shows
the
terminal
velocity
measured
experimentally in water for different types of solid particles in agreement
with [87,88].
Table (4-2) Terminal velocity (V t ) of solid particles
Dp Average
diam.(mm)
ρ p Density
g/cm3
Terminal Velocity
(cm/s)
pvc
3
1.025
2.37
pvc
1.5
1.025
0.529
pvc
0.65
1.025
0.09
plastic
3
1.150
2.772
plastic
0.5
1.150
0.057
Particles
Type
42
Drift flux
Chapter Four
Results and Discussion
8
7
6
5
4
3
2
1
0
ρs = 1150 kg/m3
ρs = 1025 kg/m3
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Overall gas holdup
Figure (4.5,a)
8
ρs = 1150 kg/m3
7
ρs = 1025 kg/m3
Drift flux
6
5
4
3
2
1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Overall gas holdup
Figure (4.5,b)
Figure (4.5): Drift flux vs. overall gas holdup for different densities of
particles, dp=3mm at: (a) Cs=5% (b) Cs=10%
43
Chapter Four
Results and Discussion
4.1.3 Effect of Solid Composition (Binary Mixture) on Transition Point
Figures (4.6) and (4.7) show the effect of varying composition of
solid binary mixture on stability of homogeneous regime. It is clear from
plots that the effect depends mainly on the percentage of the individual
species. Table (4-3) summarizes this trend in a agreement with [88,89].
Table (4-3) Effect of binary mixture composition on stability of
homogeneous regime
Binary code
ε trans .
U trans .
MA
0.22
6.85
MB
0.19
5.38
MC
0.2437
6.95
IA
0.23
6.94
IB
0.226
6.42
IC
0.245
7
44
Drift flux
Chapter Four
Results and Discussion
9
Mb
8
Ma
7
Mc
6
5
4
3
2
1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
Overall gas holdup
drift flux
Figure (4.6,a)
9
Mb
8
Ma
7
Mc
6
5
4
3
2
1
0
0
0.05
0.1
0.15
0.2
Overall gas holdup
0.25
0.3
Figure (4.6,b)
Figure (4.6): Drift flux vs. overall gas holdup for binary mixture of
particles, at: (a) Cs=5% (b) Cs=10%
45
Drift flux
Chapter Four
Results and Discussion
Ib
9
8
7
6
5
4
3
2
1
0
Ia
Ic
0
0.05
0.1
0.15
0.2
0.25
0.3
Overall gas holdup
Drift flux
Figure (4.7,a)
9
Ib
8
Ia
7
Ic
6
5
4
3
2
1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
overall gas holdup
Figure (4.7,b)
Figure (4.7): Drift flux vs. overall gas holdup for binary mixture of
particles, at: (a) Cs=5% (b) Cs=10%
46
Chapter Four
Results and Discussion
4.2 Gas Holdup
4.2.1 Effect of Superficial Gas Velocity on Gas Holdup
Figures (4.8) to (4.14) show the effect of superficial gas velocity on
the measured local gas holdup and overall gas holdup. All figures indicate
that gas holdup increases with an increase in the superficial gas velocity,
although this increase shows different characteristics in the homogeneous
and heterogeneous regimes. The average gas holdup increases almost
linearly with increasing superficial gas velocity in the homogeneous
regime, while this increase is less pronounced in the heterogeneous
regime, because large bubbles are formed due to bubble coalescence and
these large bubbles have a notable bubble-wake attraction effect. This
behavior is in agreement with the findings of [90] .
47
Chapter Four
Results and Discussion
30 cm axial
local gas holdup
50 cm axial
0.5
70 cm axial
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
superficial gas velocity(cm/s)
8
9
10
Figure (4.8,a)
30 cm axial
50 cm axial
Local gas holdup
0.5
70 cm axial
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity (cm /s)
Figure (4.8,b)
30 cm axial
local gas holdup
50 cm axial
70 cm axial
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s
Figure (4.8,c)
Figure (4.8): Local gas holdup vs. superficial gas velocity for different
axial position for ρs =1025 kg/m3,dp=3mm at: (a) Cs=0% ,(b) Cs=5%, (c)
Cs=10%
48
Chapter Four
Results and Discussion
30 cm axial
50 cm axial
70 cm axial
local gas holdup
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm/s)
Figure (4.9,a)
30 cm axial
50 cm axial
Local gas holdup
0.5
70 cm axial
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity (cm /s)
Figure (4.9,b)
local gas holdup
0.5
30 cm axial
50 cm axial
0.4
70 cm axial
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s
Figure (4.9,c)
Figure (4.9): Local gas holdup vs. superficial gas velocity for different axial
position for ρs =1025 kg/m3,dp=1.5 mm at: (a) Cs=0% ,(b) Cs=5%, (c)
Cs=10%
49
Chapter Four
Results and Discussion
30 cm axial
local gas holdup
50 cm axial
70 cm axial
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm/s)
Figure (4.10,a)
Local gas holdup
30 cm axial
0.5
50 cm axial
0.4
70 cm axial
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity (cm /s)
Figure (4.10,b)
30 cm axial
local gas holdup
0.5
50 cm axial
0.4
70 cm axial
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s
Figure (4.10,c)
Figure (4.10):Local gas holdup vs. superficial gas velocity for different
axial position for ρs =1025 kg/m3,dp=0.65 mm at: (a)Cs=0% ,(b)
Cs=5%, (c) Cs=10%
50
Chapter Four
Results and Discussion
30 cm axial
50 cm axial
local gas holdup
0.5
70 cm axial
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
superficial gas velocity(cm/s)
8
9
10
Figure (4.11,a)
30 cm axial
Local gas holdup
0.5
50 cm axial
0.4
70 cm axial
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity (cm /s)
local gas holdup
Figure (4.11,b)
0.5
30 cm axial
0.4
50 cm axial
70 cm axial
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s
Figure (4.11,c)
Figure (4.11): Local gas holdup vs. superficial gas velocity for different
axial position for ρs =1150 kg/m3,dp=3 mm at: (a) Cs=0% ,(b) Cs=5%, (c)
Cs=10%
51
Chapter Four
Results and Discussion
30 cm axial
50 cm axial
local gas holdup
0.5
70 cm axial
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm/s)
Local gas holdup
Figure (4.12,a)
0.5
30 cm axial
0.4
50 cm axial
70 cm axial
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity (cm /s)
local gas holdup
Figure (4.12,b)
0.5
30 cm axial
0.4
50 cm axial
0.3
70 cm axial
0.2
0.1
0
0
2
4
6
8
10
superficial gas velocity(cm /s
Figure (4.12,c)
Figure (4.12):Local gas holdup vs. superficial gas velocity for different
axial position for ρs =1150 kg/m3,dp=0.5 mm at: (a) Cs=0% ,(b) Cs=5%,
(c) Cs=10%
52
Chapter Four
Results and Discussion
Cs=10%
Cs=5%
Cs=0
Overall holdup
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.13,a)
Cs=10%
Cs=5%
Overall holdup
0.4
Cs=0%
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity (cm /s)
Figure (4.13,b)
Cs=10%
Cs=5%
Overall holdup
0.4
Cs=0%
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.13,c)
Figure (4.13): Overall gas holdup vs. superficial gas velocity for
different Cs for ρs =1025 kg/m3 at: (a) dp=3mm, (b) dp=1.5mm, (c)
dp=0.65
53
Chapter Four
Results and Discussion
Cs=10%
Overall holdup
Cs=5%
Cs=0
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
superficial gas velocity(cm/s)
8
9
10
Figure (4.14,a)
Cs=10%
Cs=5%
Cs=0%
Overall holdup
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity (cm /s)
Figure (4.14,b)
Figure (4.14):Overalll gas holdup vs. superficial gas velocity for different
Cs for ρs =1150 kg/m3 at: (a) dp=3mm ,(b) dp=1.5mm
4.2.2 Effect of Solid Concentration on Gas Holdup
Figure (4.15) shows the measured local gas holdup as function of
solid concentration. All Figures show an increasing solid concentration
generally decreases the gas holdup. This was verified by equ.[ε L+ ε g+ ε s =1]
, and this can be attributed to that increasing solid concentration was
accompanied by significant increase of average bubble size which results
in an increase in bubble rise velocity and a decreases in the gas holdup
[91].
54
Local gas holdup
Chapter Four
Results and Discussion
0.4
ug=3cm/s
0.35
ug=4cm/s
0.3
ug=5cm/s
0.25
ug=7cm/s
0.2
ug=9cm/s
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10
11
Cs% W/W
Figure (4.15,a)
ug=3cm/s
Local gas holdup
ug=4cm/s
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
ug=5cm/s
ug=7cm/s
ug=9cm/s
0
1
2
3
4
5
6
7
8
9
10
11
Cs% W/W
Figure (4.15,b)
Figure (4.15): Overall gas holdup vs. solid concentration for different
Ug and ρs =1150 kg/m3 at: (a) dp=0.5 mm ,(b) dp=3mm
4.2.3 Effect of Solid Properties on Gas Holdup
4.2.3.1 Effect of Particles Diameter
A wide range of particles diameter has been investigated to study this
behavior. Figures (4.16) and (4.17) show the measured overall gas holdup
for various particle diameters, the plots indicate a proportional relationship
between particles diameter and measured gas holdup. This can be
attributed to the fact that rate of bubble coalescence is increased as the
particles diameter decreases. This results in large bubble size which has
55
Chapter Four
Results and Discussion
larger bubble rise velocity than small bubbles. Gas holdup decreases as a
result of bubble coalescence. This behavior is in agreement with the
findings of [92].
dp=0.65
Overall holdup
dp=1.5mm
0.4
dp=3mm
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.16,a)
dp=0.5mm
0.4
Overall holdup
dp=3mm
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity (cm /s)
Figure (4.16,b)
Figure (4.16):Overalll gas holdup vs. superficial gas velocity for
different Particles diameter and Cs=5% at: (a) ρs =1025 kg/m3,(b)
ρs =1150 kg/m3
56
Chapter Four
Results and Discussion
dp=0.65
Overall holdup
dp=1.5mm
dp=3mm
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.17,a)
dp=0.5mm
Overall holdup
0.25
dp=3mm
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity (cm /s)
Figure (4.17,b)
Figure (4.17): Overall gas holdup vs. superficial gas velocity for
different Particles diameter and Cs=10% at: (a) ρs =1025 kg/m3,(b)
(a) ρs =1150 kg/m3
4.2.3.2 Effect of Solid Density
Figure (4.18) shows the relationship between the particle density and
overall gas holdup. The Figure indicates an inverse relationship between
particles density and overall gas holdup for the specified operating
conditions. This trend can be attributed to particle density increases, the
particles terminal velocity increases resulting in a decrease in overall gas
holdup[93,94].
57
Chapter Four
Results and Discussion
ρs=1025 kg/m3
Overall gas holdup
0.35
ρs=1150 kg/m3
0.3
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity(cm /s)
Overall gas holdup
Figure (4.18,a)
0.35
ρs=1025 kg/m3
0.3
ρs=1025 kg/m3
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity(cm /s)
Figure (4.18,b)
Figure (4.18): Overall gas holdup vs. superficial gas velocity for different
densities to the same diameter (dp=3mm) at: (a) Cs=5% (b) Cs=10%
4.2.3.3 Effect of Solid Composition ( Binary Mixture)
Figures (4.19) to (4.22) show the measured overall gas holds up
versus superficial gas velocity for different compositions of binary
mixture of particles diameter. Analysis the plots behavior indicates that
the effect of each species on the overall gas holdup depends on its
percentage in the binary mixture. This analysis is of a valuable
hydrodynamic aspect to the industrial reactors where different sizes of a
catalyst particle an utilized. An approximate correlation can be developed
to describe this behavior:
58
Chapter Four
Results and Discussion
εg = x1 εg + x2 εg
……………(4.2)
where x 1 and x 2 are the weight fraction of particles 1 and 2 respectively.
Cs=10%
Cs=5%
Cs=0
Overall gas holdup
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity( cm /s)
Figure (4.19,a)
Cs=10%
Overall gas holdup
0.4
Cs=5%
Cs=0%
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity (cm /s)
Figure (4.19,b)
Cs=10%
Overall gas holdup
Cs=5%
Cs=0%
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.19,c)
Figure (4.19): Overall gas holdup vs. superficial gas velocity for
different Cs and binary mixture of particles at: (a) Ma,(b) Mb,(c) Mc
59
Chapter Four
Results and Discussion
Cs=10%
Overall gas holdup
Cs=5%
0.4
Cs=0
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm/s)
Figure (4.20,a)
Cs=10%
Cs=5%
Cs=0%
Overall gas holdup
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity (cm /s)
Figure (4.20,b)
Overall gas holdup
Cs=10%
Cs=5%
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Cs=0%
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.20,c)
Figure (4.20): Overall gas holdup vs. superficial gas velocity for
different Cs and binary mixture of particles at: (a) Na,(b) Nb,(c) Nc
60
Chapter Four
Results and Discussion
Cs=10%
Cs=5%
Overall gas holdup
Cs=0
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.21,a)
Cs=10%
Overall gas holdup
Cs=5%
Cs=0%
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity (cm /s)
Figure (4.21,b)
Cs=10%
Overall gas holdup
Cs=5%
0.4
Cs=0%
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.21,c)
Figure (4.21):Overall gas holdup vs. superficial gas velocity for
different Cs and binary mixture of particles at: (a) Ia,(b) Ib,(c) Ic
61
Chapter Four
Results and Discussion
Cs=10%
Cs=5%
Overall gas holdup
Cs=0
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm/s)
Figure (4.22,a)
Cs=10%
Overall gas holdup
Cs=5%
0.4
Cs=0%
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity (cm /s)
Figure (4.22,b)
Cs=10%
Overall gas holdup
Cs=5%
0.4
Cs=0%
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.22,c)
Figure (4.22): Overall gas holdup vs. superficial gas velocity for different
Cs and binary mixture of particles at: (a) Va,(b) Vb,(c) Vc
62
Chapter Four
Results and Discussion
4.3 Bubble Dynamics
4.3.1 Effect of Superficial Gas Velocity on Bubble Dynamics
Figures (4.23) to (4.29) show the effect of superficial gas velocity on
bubble rise velocity size for all tested solids. From these Figures one can
notice that there is a slight increase in the bubble behavior with increasing
superficial gas velocity. This increase is attributed to the fact that the
increase in superficial gas velocity increases the probability of bubbles
collision and coalescence resulting in greater bubble size. This in
agreement with [95,96]
63
Chapter Four
Results and Discussion
Cs=0%
Bubble rise velocity(cm/s)
Cs=5%
Cs=10%
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
superficial gas velocity(cm /s)
8
9
10
Figure (4.23,a)
Cs=0%
Bubble rise velocity (cm/s)
Cs=5%
Cs=10%
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity (cm /s)
Bubble rise velocity (cm/s)
Figure (4.23,b)
Cs=0%
Cs=5%
60
Cs=10%
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm/s)
Figure (4.23,c)
Figure (4.23):Bubble rise velocity vs. superficial gas velocity for
ρs=1025 kg/m3 ,dp=3mm at different values of Cs and axial position
at:(a) 30cm, (b)50cm, (c)70cm
64
Chapter Four
Results and Discussion
Cs=0%
Bubble rise velocity(cm/s)
Cs=5%
Cs=10%
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.24,a)
Bubble rise velocity (cm/s)
Cs=0%
Cs=5%
Cs=10%
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity (cm /s)
Bubble rise velocity (cm/s)
Figure (4.24,b)
Cs=0%
60
Cs=5%
50
Cs=10%
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm/s)
Figure (4.24,c)
Figure (4.24):Bubble rise velocity vs. superficial gas velocity for
ρs=1025 kg/m3 ,dp=1.5mm at different values of Cs and axial position
at:(a) 30cm, (b)50cm, (c)70cm
65
Chapter Four
Results and Discussion
Cs=0%
Bubble rise velocity(cm/s)
Cs=5%
Cs=10%
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
superficial gas velocity(cm /s)
9
10
Figure (4.25,a)
Bubble risevelocity (cm/s)
Cs=0%
Cs=5%
Cs=10%
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity (cm /s)
Figure (4.25,b)
Bubble rise velocity
(cm/s)
Cs=0%
Cs=5%
60
Cs=10%
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm/s)
Figure (4.25,c)
Figure (4.25):Bubble rise velocity vs. superficial gas velocity for
ρs=1025 kg/m3 ,dp=0.65mm at different values of Cs and axial position
at:(a) 30cm, (b)50cm, (c)70cm
66
Chapter Four
Results and Discussion
Cs=0%
Cs=5%
Cs=10%
Bubble rise velocity(cm/s)
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
superficial gas velocity(cm /s)
9
10
Figure (4.26,a)
Bubble risevelocity (cm/s)
Cs=0%
Cs=5%
Cs=10%
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity (cm /s)
Figure (4.26,b)
Cs=0%
Bubble rise velocity (cm/s)
Cs=5%
Cs=10%
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.26,c)
Figure (4.26):Bubble rise velocity vs. superficial gas velocity for
ρs=1150 kg/m3 ,dp=3mm at different values of Cs and axial position
at:(a) 30cm, (b)50cm, (c)70cm
67
Chapter Four
Results and Discussion
Cs=0%
Bubble rise velocity(cm/s)
Cs=5%
Cs=10%
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.27,a)
Cs=0%
Bubble risevelocity (cm/s)
Cs=5%
Cs=10%
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity (cm /s)
Figure (4.27,b)
Bubble rise velocity (cm/s)
Cs=0%
Cs=5%
Cs=10%
70
50
30
10
-10 0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.27,a)
Figure (4.27):Bubble rise velocity vs. superficial gas velocity for
ρs=1150 kg/m3 ,dp=0.5mm at different values of Cs and axial position
at:(a) 30cm, (b)50cm, (c)70cm
68
Chapter Four
Results and Discussion
Bubble diameter (mm)
Cs=0
18
Cs=0
16
Cs=5
14
Cs=5
12
Cs=10
10
Cs=10
8
6
photo
4
probe
2
0
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity (cm /s)
Figure (4.28,a)
Cs=0%
Cs=0
Bubble diameter (mm)
Cs=5
18
16
14
12
10
8
6
4
2
Cs=5
Cs=10
Cs=10
photo
probe
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity (cm /s)
Figure (4.28,b)
Bubble diameter (mm)
Cs=0
Cs=0
18
16
14
Cs=5
Cs=5
Cs=10
12
10
8
6
Cs=10
photo
4
2
0
probe
0
1
2
3
4
5
6
7
8
9
10
superficialgas velocity (cm/s)
Figure (4.28,c)
Figure (4.28): measurements of bubble diameter using photographic
method and electroresistivity probe method for ρs=1025 kg/m3 and different
values of Cs and dp at: (a) dp=3mm (b)dp=1.5mm (c) dp=0.65
69
Chapter Four
Results and Discussion
Bubble diameter (mm)
Cs=0
18
16
14
Cs=0
12
10
8
6
Cs=10
Cs=5
Cs=5
Cs=10
photo
4
2
0
probe
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity (cm /s)
Figure (4.29,a)
Bubble diameter (mm)
Cs=0
18
Cs=0
16
14
Cs=5%
Cs=5%
12
Cs=10%
10
8
Cs=10%
6
photo
4
2
probe
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity (cm/s)
Figure (4.29,b)
Figure (4.29): measurements of bubble diameter using photographic
method and electroresistivity probe method for ρs=1150 kg/m3 and
different values of Cs and dp at: (a) dp=3mm (b)dp=0.5mm
70
Chapter Four
Results and Discussion
4.3.2 Effect of Solid Concentration on Gas Bubble Dynamics (Bubble
Rise Velocity and Bubble Diameter)
Figure (4.30) shows the effect of solid concentration on bubble
diameter. All plots indicate a proportional relationship between solid
concentration and bubble rise velocity. This can be attributed to increasing
solid concentration which results in an increase in the rate of bubble
coalescence which leads to increase in bubble size and then an increase in
Bubble diameter(mm)
bubble rise velocity. This is in a agreement with [97,98]
14
Ug=9 cm/s
12
Ug=7 cm/s
10
Ug=5 cm/s
Ug=4cm/s
8
Ug=3 cm/s
6
4
2
0
0
1
2
3
4
5
6
7
8
9
10
11
12
Cs%w /w
Figure (4.30,a)
Ug=9 cm/s
14
Ug=7 cm/s
Ug=5 cm/s
10
Ug=4cm/s
8
Ug=3 cm/s
Bubble diameter(mm)
12
6
4
2
0
0
1
2
3
4
5
6
7
8
9
10
11
12
Cs%w /w
Figure (4.30,b)
Figure (4.30): Bubble diameter vs. solid concentration for different values of
superficial gas velocity for the same (dp=3mm ) at: (a)ρs=1025 kg/m3 (b)
ρs=1150 kg/m3
71
Chapter Four
Results and Discussion
4.3.3 Effect Solid Properties on Bubble Dynamics
4.3.3.1 Effect of Solid Diameter
Figure (4.31) shows the measured bubble diameter vs. superficial gas
velocity with solid diameter for different values of (U g ) at (Cs = 10%).
This Figure shows increase in the bubble rise velocity or bubble diameter
with decreasing the particles diameter. The reason for this increase is that
small particular sizes will increase or enhance the rate of bubble
coalescence, leading to a decrease in gas holdup. This is in agreement with
Bubble diameter(mm)
the work of [99,101].
dp=0.65mm
18
16
14
12
10
8
6
4
2
0
dp=1.5mm
dp=3mm
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity(cm /s)
Bubble diameter(mm)
Figure (4.31,a)
18
dp=0.5mm
16
dp=3mm
14
12
10
8
6
4
2
0
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity(cm /s)
Figure (4.31,b)
Figure (4.31): Bubble diameter vs. superficial gas velocity for different
values of particles diameter and Cs=10% at: (a)ρs=1025 kg/m3 (b)
ρs=1150 kg/m3
72
Chapter Four
Results and Discussion
4.3.3.2 Effect of Solid Density
Figure (4.32) shows the measured bubble diameter vs. superficial gas
velocity for different values of solid density. From the figure we can see
that the bubble dynamics increase with increasing particle density. This in
a agreement with the results of [102,103].
ρs=1150 kg/m3
ρs=1025 kg/m3
Bubble diameter(mm)
12
10
8
6
4
2
0
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity(cm /s)
Figure (4.32,a)
ρs=1150 kg/m3
Bubble diameter(mm)
14
ρs=1025 kg/m3
12
10
8
6
4
2
0
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity(cm /s)
Figure (4.32,b)
Figure (4.32): Bubble diameter vs. superficial gas velocity for
different densities of (dp=3mm) at: (a)Cs=5%(b) Cs=10%
73
Chapter Four
Results and Discussion
4.3.3.3 Effect of Solid Composition (Binary Mixture)
Figure(4.33) shows the measured bubble diameter vs. superficial gas
velocity at different values of binary mixture of particles, the bubble
dynamics will be increased when the solid particles are mixed with the
ratio of large percentage of high density with the low percentage of low
Bubble diameter(mm)
density. This is in agreement with the results[104,95].
12
11.5
11
10.5
10
9.5
9
8.5
8
7.5
7
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Ib
Ia
Ic
0
1
2
3
4
5
6
7
Superficial gas velocity(cm /s)
8
9
10
Bubble diameter(mm)
Figure (4.33,a)
12
11.5
11
10.5
10
9.5
9
8.5
8
7.5
7
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Ib
Ia
Ic
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity(cm /s)
Figure (4.33,b)
Figure (4.33): Bubble diameter vs. superficial gas velocity for binary
mixture of particles for the same diameter (dp=3mm)at: (a)Cs=5%(b)
Cs=10%
74
Chapter Four
Results and Discussion
4.4 Effect of Superficial Gas Velocity on Solid Holdup
Figures (4.34) and (4.35) represent the solid holdup with superficial
gas velocity, from this figure the solid holdup decreases with increase in
superficial gas velocity and increases with increase in solid concentration.
This is attributed to the fact that the dispersion height (H′ f ) is proportional
to the superficial gas velocity according to eqn. ε s =W s /A c H′ f ρ s ), so for a
certain solid loading any increase in dispersion height leads to a decrease
in solid holdup.
75
solid holdup
Chapter Four
Results and Discussion
0.12
Cs=10%
0.1
Cs=5%
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm/s)
solid holdup
Figure (4.34,a)
0.12
Cs=10%
0.1
Cs=5%
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.34,b)
0.12
Cs=10%
Cs=5%
solid holdup
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.34,c)
Figure (4.34): Solid holdup vs. superficial gas velocity for ρs =1025
kg/m3, different values of Cs and dp at: (a)dp=3mm (b) dp=1.5mm (c)
dp=0.65mm
76
Chapter Four
Results and Discussion
Cs=10%
solid holdup
0.12
Cs=5%
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.35,a)
Cs=10%
solid holdup
0.12
Cs=5%
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.35,b)
Figure (4.35): Solid holdup vs. superficial gas velocity for ρs =1150
kg/m3, different values of Cs and dp at: (a) dp=3mm (b) dp=0.5mm
4.5 Empirical Correlations
An attempt was made to formulate a correlation that would permit the
prediction of gas holdup, a variable that greatly affects the bubble column
operation. From the present work and the careful inspection of the
experimental results (from various investigators) it can be concluded that
the gas holdup value is the result of the interaction of several parameters as
follows:
• The superficial gas velocity.
• The physical properties of liquid phase (i.e., viscosity, density,
surface tension).
77
Chapter Four
•
Results and Discussion
The column cross section.
• Particles diameters.
• Particles densities .
In order to formulate a generalized correlation that would incorporate
the relative effect of all the above parameters, dimensional analysis using
Buckingham's π-theorem was performed. The resulting expression then has
two forms:
4.5.1 Gas Holdup Correlation for Single State
ε g = 0.17808(
(
dp
dc
) 0.201744 (
u g2
gd c
)
ρs
ρ s − ρl
−0.333189
ρ l u g2 d c 1.086486 ρ l d c u g −0.569585 −0.245182
(
)
(
)
cs
σl
µl
) o.332514 ..........................(4 − 3)
R = 0.96811
error = 0.0049345
Table (4.4 ) : Estimated values of the constant and
the powers of equation (4.3)
C0
C1
0.178087
-0.333189
C2
1.086486
C3
-0.569585
C4
-0.245182
C5
C6
0.201744
0.332514
The constants (Co) and the powers (C1, C2, C3, C4, C5 and C6) were
estimated by using the simplex method with the aid of a computer program.
The values of the constants and the powers of the above equation were
illustrated in table (4.4) above.
78
Chapter Four
Results and Discussion
4.5.2 Gas Holdup Correlation for Binary State
U
ε g = 0.057009(
(
d p1
dc
) 0.075001 (
d p2
dc
u g d c ρl
µl
)1.515572 cs
− 0.389035
0.568996
x1
x2
− 0.703610
) 2.443881..........................( 4 − 4)
R = 0.995641008
error = 0.000521
Table (4.5 ) : Estimated values of the constant and the
powers of equation (4.4 )
C0
C1
0.057009
1.515572
C2
-0.389035
C3
0.568996
C4
-0.703610
C5
C6
0.075001
2.443881
The constants (Co) and the powers (C1, C2, C3, C4, C5 and C6) were
estimated by using the simplex method with the aid of a computer program.
The values of the constants and the powers of the above equation were
illustrated in table (4.5) above.
79
Chapter Five
Conclusions & Recommendations
Chapter Five
Conclusions and Recommendations
5.1 Conclusions
U
The following major conclusions are drawn from the present study:
1.Experiments show that increasing the solid concentration tends to decrease
the gas holdup.
2.The visual observations and experimental results show that the superficial gas
velocity looks to be the most effective parameter on the gas holdup, where the
(ε g ) increases greatly with increasing the gas velocity .
R
R
3. The results show that there is a proportional relationship between gas holdup
and particles diameter for the specified operating conditions used in the
experiments.
4. It was concluded that the bubble rise velocity is increased with increasing the
solid concentration.
5. From experimental results of bubble diameter which was measured in the
electroresistivity probe method and also in the photographic method, a rational
agreement is obtained between the measured values from the two methods.
6. The bubble rise velocity and bubble diameter increased with decreasing
particles diameter.
7. For binary mixture, it was proved experimentally that the effect of each
species on the hydrodynamic parameters is proportional to its weight fraction
and other corresponding properties in the mixture.
80
Chapter Five
Conclusions & Recommendations
5.2 Recommendations for the Future Work
1. Other measuring technique such as Gamma Densitometry Tomography
(GDT) should be employed to measure the solid hold-up. This method is also
used to measure the radial variations in gas hold-up for slurry bubble column
reactor [89].
2. Using computational fluid dynamic (CFD) technique for simulation of the
hydrodynamics of slurry reactor.
3. It is recommended to operate a FBR with low density solid particles.
4. It is recommended to study mass transfer and kinetics in a fluidized bed
reactor.
5. Studying the effect of a variable temperature correlation on the
hydrodynamic of a FBC.
81
References
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Appendix (A)………………………………………Calibration Curve
Reading Scale (Lit/min)
300
250
200
150
100
50
0
0
40
80
120
160
200
240
280
Flom eter Reading (Lit/m in)
Figure (A◌-1)
ِ
Figure (A-1): Calibration curve for flowmeter of air
A-1
Appendix B
Design of Distributor
Appendix B: Design of Distributors
This appendix contains the design of the multi-orifice gas distributor.
The following procedure was given by Ruff and Pilhofer 1978 [106], to
design and operate the perforated plates in such a way that flow occurs
through all the perforations. If all the perforations of a perforated plate for
dispersing a gas or liquid in a liquid phase are not equipped by the dispersed
phase, weeping, back-flow etc. can occur, which are usually undesirable. In
bubble column reactors plates are frequently used with perforation of
diameters 0.5 to 5 mm. Mersmann 1962 [107], considered the problem of
complete gassing and the weeping point and found that, at small perforation
diameters, a constant Weber number must be maintained, while, at large
perforation diameters, a Froude number must be maintained in order to ensure
flow through all perforations or prevent weeping. We = 2 and Fr = 0.37 give
the minimum velocity of the disperse phase required in the perforations of a
perforated plate when flow is to occur through all the openings in the case of
small perforations, and significant weeping is to be prevented in the case of
large perforations.
Distilled water is to be aerated with a maximum superficial gas velocity of
0.09 m/s. array with 2 mm diameter round perforations is used for the
gassing.
The following steps are used to find the number of holes required to ensure
flow through all the perforations and to prevent weeping of the continuous
phase. The calculations are based on the following physical properties:
ρ =1000 kg / m 3 , ρ =1.206 kg / m 3 , σ = 0.0728 N / m
l
g
l
B-1
Appendix B
Design of Distributor
Step I:
Calculation of the diameter d o according to equation (b-1):
12
 σ   ρg
d ° = 2.32  l  
 ρ g g   ρ l − ρ g
d°
 0.0728 
= 2.32 

 1.206 × 9.81 
d ° = 2.73 × 10
− 3
12



58
…………………………………. (b-1)


1.206
 1000 − 1.206 


58
m = 2.73 mm
The perforation diameter selected lays below this value of d o , and so
criterion We = constant must be used.
Step II:
We have:
ρ g d Vg2
We =
=2
σ
Vg2 =
……………………………………………………. (b-2)
2 × 0.0728
1.206 × 2 × 10−3
∴Vg = 7.7695 m / s
Applying a safety factor of 40 % gives:
Vg =10.8773 m / s
B-2
Appendix B
Design of Distributor
Step III: Calculate the number of holes (N)
Since:
overall volumetric flowrate of air = volumetric flowrate of air pass thhrough holes
Q=
π 2
d N Vg
°
4
Q =U × A
g
c
…………………………………………………… (A)
…………………………………………………… (B)
Equating equations (A) and (B)
π
U × A = d 2 N Vg
g
c 4 °
π
π
U × D 2 = d 2 N Vg
g 4 C 4 °
N=
DC2 U
g
2
d° Vg
…………………………………………………….(b-3)
• For 15 cm column diameter
N=
(0.15)2 × (0.09) = 47 hole
(0.002)2 × (10.8773)
B-3
Appendix B
Design of Distributor
Step IV:
Free area is calculated from equation (b-4)
free area =
area of holes
area of distributor
π
= 4
……………………………………….. (b-4)
d2 N
π
4
DC2
• For 15 cm column diameter:
free area = 0.00836 = 0.836%
B-4
Appendix (C)…………………………….Computer Out-Put
Computer Out-Put:
The following information was printed out; the program adapted was written
by Visual Basic.
a) The width of the pulse from the upper is τ1 (mili-seconds or seconds).
b) The transition time of the air bubble between the two tips τ2 (mili-second or
seconds).
c) The number of bubbles Nb.
d) The bubble frequency Fb (1/s):
Fb =
Nb
∑ τ3
..........(C.1)
e) Local gas hold-up (εg) can be calculated:
τ
εg = ∑ 1
∑ τ3
..........(C.2)
f) The bubble rise velocity Vbr (cm/s) can be obtained as:
Vb r = ∆L∗
∑ τ2
..........(C.3)
∑τ
∑ τ ∗2 = N 2
b
..........(C.4)
g) The average bubble diameter db (cm) can be calculated as follows:
d b = Vb r ∑ τ1∗
..........(C.5)
∑τ
∑ τ1∗ = N 1
b
..........(C.6)
C-1
Appendix (D)……………………………Program of Interface Unit
Program of Interface Unit:
Version 5.00
Begin VB.Form Form 1
= '' Form 1''
Caption
Client Height = 3195
Client Left
= 60
Client Top
= 345
Client Width = 4680
Link Topic = '' Form 1 ''
Scale Height = 3195
Scale Width = 4680
Startup Position = 3 Windows Default
Begin VB. Text Box Text2
Height
Left
= 285
= 2160
TabIndex = 2
Text
= '' Text2 ''
Top
= 960
Width
= 1455
End
Begin VB. Command Button Command 2
Caption
= '' Command 2 ''
Height
= 615
Left
= 2880
TabIndex = 1
Top
= 2040
Width
= 1215
End
D-1
Appendix (D)……………………………Program of Interface Unit
Begin VB. Timer 1
Left
= 1320
Top
= 2400
End
Begin VB. Text Box Text 1
Height
= 285
Left
= 2160
TabIndex = 0
Text
= ''1''
Top
= 480
Width
= 1455
End
End
Attribute VB_Name = '' Form ''
Attribute VB_GlobalNameSpace =False
Attribute VB_Creatable = False
Attribute VB_PredeclaredId = True
Attribute VB_Exposed = False
Option Explicit ' All variables must be declared
Private Declare Function Out8255 Lib ''8255.dll''_
(By Val PortAddress As Integer, _
By Val PortData As Integer) As Integer
Private Declare Function In8255 Lib ''8255.dll''_
(By Val PortAddress As Integer) As Integer .
' Define Mdule-level port variables
Dim base_adress, pstatuse_data As Long
' Define Mdule-level ports addresses
Dim data_port, control_port, status_port As Long
Dim ADCResolution As Single
' Define Module-level dummy variables
Dim dummy As Integer
D-2
Appendix (D)……………………………Program of Interface Unit
Private Sub Command2_Click()
Dim i
Dim x
Dim st, et, t, z, o
st = Timer
et = Timer
Open ''c: o.txt'' For Output As 1
Do While (et - st) < 1
et = Timer
x = rstatus() And 3
t = et – st
'If x = 1 Then
' o = o+1
' Else
' z = z+1
'End If
Print # 1, x
Loop
'Text 1.Text = z
'Text 1.Refresh
'Text 2.Text = o
'Text 2.Refresh
Close # 1
Beep
End Sub
Private Sub Form_Load()
base_address = &H378 ' Here is the LPT1: Address
data_Port = base_address 'Data port address
status_port = base_address+1'Status port address
contrl_port = base_address +2 'Control port address
D-3
Appendix (D)……………………………Program of Interface Unit
dummy = Out8255(data_port, 0) 'Clear data port
dummy = Out8255(control_port, 4) 'Clear control port
Call wport(''Control", 147)'Port 146 A & B are inputs, Port C as output
End Sub
Public Sub wcontrol(pdata As long)
If (pdata And 1) = 1Then pdata = pdata And 254 Else pdata = pdata Or 1
If (pdata And 2) = 2Then pdata = pdata And 253 Else pdata = pdata Or 2
If (pdata And 8) = 8Then pdata = pdata And 247 Else pdata = pdata Or 8
dummy = Out8255(control_port, pdata)
End Sub
Public Function rstatus()
rstatus = (In8255(status_port) And 120) / 8
End Function
Public Sub Delay(dvalue As Double)
start_time = Timer
end_time = Timer
Do While(end_time – start_time)<dvalue / 1000
end_time = Tmer
Loop
End Sub
Public Sub wport(pname As String, pdata As Long)
Select Case pname
Case ''A"
wcontrol (15)
wdata (pdata)
wcontrol (3)
wcontrol (1)
wcontrol (3)
Case ''B"
wcontrol (15)
D-4
Appendix (D)……………………………Program of Interface Unit
wdata (pdata)
wcontrol (7)
wcontrol (5)
wcontrol (7)
Case "C":
wcontrol (15)
wdata (pdata)
wcontrol (11)
wcontrol (9)
wcontrol (11)
Case "Control":
wcontrol (15)
wdata (pdata)
wcontrol (15)
wcontrol (13)
wcontrol (15)
End Select
End Sub
Public Function rport(pname As String)
Dim 1o, hi As Integer
Select Case pname
Case "A":
wcontrol (15)
wdata (0)
wcontrol (3)
wcontrol (2)
1o = rstatus()
wdata (1)
hi = rstatus()
wcontrol (3)
D-5
Appendix (D)……………………………Program of Interface Unit
Case "B":
wcontrol (15)
wdata (0)
wcontrol (7)
wcontrol (6)
1o = rstatus()
wdata (1)
hi = rstatus()
wcontrol
Case "C":
wcontrol (15)
wdata (0)
wcontrol (11)
wcontrol (10)
1o = rstatus()
wdata (1)
hi = rstatus()
wcontrol (11)
End Select
rport = 1o + hi * 16
End Function
Private Sub Timer_Timer()
Text 1.Text = rconverter(1)
Text 1.Refresh
End Sub
D-6
Appendix (E)……………………………………Experimental results
Table ( E – 1 ) :
Particles : PVC , ρp = 1025 Kg / m3 , d p = 3mm
εs =
M / ρs
εg =
HH’
, A = ╥ / 4 ( 0.15 )²
f f= _90Hcm
f
AH’f
Cs %
(w/w)
0
5
10
H’f
Hf
( cm )
H’f
( cm )
εg
1
2
3
4
5
1
2
3
4
5
Ug
Superficia
l
Velocity
( cm / s )
3
4
5
7
9
3
4
5
7
9
90
90
90
90
90
92.5
92.5
92.5
92.5
92.5
97.30
107.143
117.80
135.14
137.614
99.47
107.56
117.10
128.5
130.3
0.075
0.16
0.236
0.334
0.346
0.07
0.14
0.21
0.28
0.29
0.047
0.043
0.04
0.036
0.035
1
2
3
4
5
3
4
5
7
9
93.8
93.8
93.8
93.8
93.8
100.13
106.6
113
117
118.74
0.063
0.12
0.17
0.2
0.21
0.098
0.092
0.087
0.084
0.0827
Run
no .
E-1
εs
Appendix (E)……………………………………Experimental results
Table ( E- 2 ) :
Particles : PVC , ρp = 1025 Kg / m3 , d p = 1.5 mm
Cs %
(w/w)
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
Superficial
( cm )
( cm )
gas
Velocity
( cm / s )
3
90
97.30
4
90
107.143
5
90
117.80
7
90
135.14
9
90
137.614
3
91.3
96.93
4
91.3
99.58
5
91.3
103.76
7
91.3
110
9
91.3
111.09
3
92.2
97.15
4
92.2
100
5
92.2
102.23
7
92.2
107.33
9
92.2
108.09
E-2
εg
0.075
0.16
0.236
0.334
0.346
0.058
0.083
0.12
0.17
0.178
0.051
0.078
0.097
0.14
0.146
εs
0.048
0.047
0.045
0.0423
0.041
0.101
0.098
0.096
0.091
0.09
Appendix (E)……………………………………Experimental results
Table ( E- 3 ) :
Particles : PVC , ρp = 1025 Kg / m3 , d p = 0.65 mm
Cs %
(w/w)
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
Superficial
( cm )
( cm )
gas
Velocity
( cm / s )
3
90
97.30
4
90
107.143
5
90
117.80
7
90
135.14
9
90
137.614
3
90.9
95.58
4
90.9
98.5
5
90.9
100.78
7
90.9
105.7
9
90.9
106.45
3
4
5
7
9
E-3
91.3
91.3
91.3
91.3
91.3
95.5
98.1
99.9
101.22
101.45
εg
εs
0.075
0.16
0.236
0.334
0.346
0..049
0.077
0.098
0.14
0.146
0.048
0.047
0.046
0.044
0.043
0.044
0.069
0.086
0.098
0.1
0.103
0.1
0.098
0.097
0.096
Appendix (E)……………………………………Experimental results
Table ( E- 4 ) :
Particles : Plastics , ρp =1150 Kg / m3 , d p = 3 mm
Cs %
(w/w)
0
5
10
Table ( E- 5 ) :
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
Superficial
( cm )
( cm )
gas
Velocity
( cm / s )
3
90
97.30
4
90
107.143
5
90
117.80
7
90
135.14
9
90
137.614
3
92.5
99.15
4
92.5
102.78
5
92.5
112.4
7
92.5
121.72
9
92.5
123.33
3
93.8
98.95
4
93.8
103.99
5
93.8
106.11
7
93.8
110.35
9
93.8
111.67
E-4
εg
0.075
0.16
0.236
0.334
0.346
0.067
0.10
0.177
0.24
0.25
0.052
0.098
0.116
0.15
0.16
εs
0.047
0.045
0.041
0.038
0.037
0.099
0.094
0.092
0.09
0.088
Appendix (E)……………………………………Experimental results
Particles : Plastics , ρp =1150 Kg / m3 , d p = 0.5 mm
Cs %
(w/w)
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
Superficia
( cm )
( cm )
l
gas
Velocity
( cm / s )
3
90
97.30
4
90
107.143
5
90
117.80
7
90
135.14
9
90
137.614
3
90.7
94.3
4
90.7
97.22
5
90.7
99.7
7
90.7
103.77
9
90.7
104.26
3
91
94.11
4
91
96.81
5
91
98.7
7
91
99.58
9
91
100
E-5
εg
0.075
0.16
0.236
0.334
0.346
0.038
0.067
0.09
0.126
0.13
0.033
0.06
0.078
0.086
0.09
εs
0.049
0.048
0.047
0.045
0.044
0.104
0.101
0.1
0.099
0.0983
Appendix (E)……………………………………Experimental results
Binary Mixture of Particles
Physical Properties of Particles used in this study
Ut
( cm / s )
2.37
ρs
( Kg / m3 )
1025
Dp
( mm )
3
Type of
Particles
PVC
Particle
Notation
A
0.529
1025
1.5
PVC
B
0.09
1025
0.65
PVC
C
2.772
1150
3
Plastic
D
0.057
1150
0.5
Plastic
E
Description of Binary Mixture of Particles
Ut Ratio
(large /
small)
4.48
Density
Ratio
(heavy /
light)
1
Diameter
Ratio
(large /
small)
2
26.33
1.169
1
4.6
1.122
1
41.578
1.122
6
E-6
Weight
Ratio
1/2
Mixture
Notation
1:1
1:3
3:1
1:1
1:3
3:1
1:1
1:3
3:1
1:1
1:3
3:1
Ma
Mb
Mc
Na
Nb
Nc
Ia
Ib
Ic
Va
Vb
Vc
Description
A&B
A&C
A&D
A&E
Appendix (E)……………………………………Experimental results
Table ( E- 6 ) :
Ma ( Binary Mixture ) , Weight ratio ( 1 : 1 )
Cs %
(w/w)
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
Superficia
( cm )
( cm )
l
gas
Velocity
( cm / s )
90
97.30
3
90
107.143
4
90
117.80
5
90
135.14
7
90
137.614
9
93
98.1
3
93
104.5
4
93
110.716
5
93
119.3
7
93
120.78
9
3
4
5
7
9
E-7
94.5
94.5
94.5
94.5
94.5
97.82
101.29
105
111.176
112.56
εg
εs
0.075
0.16
0.236
0.334
0.346
0.052
0.11
0.16
0.22
0.23
0.047
0.0445
0.042
0.039
0.038
0.034
0.067
0.1
0.15
0.16
0.1004
0.097
0.0936
0.088
0.087
Appendix (E)……………………………………Experimental results
Table ( E- 7 ) :
Mb ( Binary Mixture ) , Weight ratio ( 1 : 3 )
Cs %
(w/w)
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
Superficia
( cm )
( cm )
l
gas
Velocity
( cm / s )
90
97.30
3
90
107.143
4
90
117.80
5
90
135.14
7
90
137.614
9
93.5
98.43
3
93.5
103.89
4
93.5
110
5
93.5
116.875
7
93.5
118.36
9
3
4
5
7
9
Table ( E- 8 ) :
E-8
95
95
95
95
95
98.14
101.71
105.24
109.2
110.73
εg
εs
0.075
0.16
0.236
0.334
0.346
0.05
0.1
0.15
0.2
0.21
0.0473
0.045
0.0423
0.04
0.039
0.032
0.066
0.097
0.13
0.141
0.1002
0.096
0.093
0.09
0.089
Appendix (E)……………………………………Experimental results
Mc ( Binary Mixture ) , Weight ratio ( 3 : 1 )
Cs %
(w/w)
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
εg
Superficia
( cm )
( cm )
l
gas
Velocity
( cm / s )
90
97.30
0.075
3
90
107.143
0.16
4
90
117.80
0.236
5
90
135.14
0.334
7
90
137.614
0.346
9
92
97.46
0.056
3
92
103.6
0.112
4
92
112.2
0.18
5
92
121.64
0.2437
7
92
122.67
0.25.
9
93
96.4
0.035
3
93
99.79
0.068
4
93
104.5
0.11
5
93
111.64
0.167
7
93
112.05
0.17
9
Table ( E- 9 ) :
Na ( Binary E-9
Mixture ) , Weight ratio ( 1 : 1 )
εs
0.0477
0.0449
0.0414
0.038
0.0379
0.1019
0.098
0.094
0.088
0.087
Appendix (E)……………………………………Experimental results
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
Superficia
( cm )
( cm )
l
gas
Velocity
( cm / s )
90
97.30
3
90
107.143
4
90
117.80
5
90
135.14
7
90
137.614
9
εg
εs
Cs %
(w/w)
Run
No .
0
1
2
3
4
5
5
1
2
3
4
5
3
4
5
7
9
91.8
91.8
91.8
91.8
91.8
95.92
100.88
106.75
111.95
117.69
0.043
0.09
0.14
0.18
0.22
0.0485
0.0461
0.0436
0.0416
0.039
10
1
2
3
4
5
3
4
5
7
9
92.9
92.9
92.9
92.9
92.9
95.77
98.83
102.1
106.8
108.02
0.03
0.06
0.09
0.13
0.14
0.103
0.099
0.0963
0.0917
0.0907
Table ( E- 9 ) :
Nb ( Binary Mixture ) , Weight ratio ( 1 : 3 )
E-10
0.075
0.16
0.236
0.334
0.346
Appendix (E)……………………………………Experimental results
Cs %
(w/w)
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
Superficia
( cm )
( cm )
l
gas
Velocity
( cm / s )
90
97.30
3
90
107.143
4
90
117.80
5
90
135.14
7
90
137.614
9
92.7
96.28
3
92.7
99.68
4
92.7
105.34
5
92.7
109.45
7
92.7
111.02
9
3
4
5
7
9
94
94
94
94
94
96.61
98.95
101.3
106
107.5
Table ( E- 10 ) :
E-11
Nc ( Binary Mixture ) , Weight ratio ( 3 : 1 )
εg
εs
0.075
0.16
0.236
0.334
0.346
0.037
0.07
0.12
0.153
0.165
0.0483
0.0466
0.044
0.0425
0.0419
0.027
0.05
0.072
0.113
0.126
0.101
0.099
0.097
0.0924
0.0912
Appendix (E)……………………………………Experimental results
Cs %
(w/w)
Run
No .
0
1
2
3
4
5
5
10
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
Superficia
( cm )
( cm )
l
gas
Velocity
( cm / s )
90
97.30
3
90
107.143
4
90
117.80
5
90
135.14
7
90
137.614
9
92
92
92
92
92
93.6
93.6
93.6
93.6
93.6
3
4
5
7
9
3
4
5
7
9
96.84
102.91
109.52
117.95
119.5
97.30
107.143
117.80
135.14
137.614
Table ( E- 11 ) :
Ia ( Binary Mixture ) , Weight ratio ( 1 : 1 )
E-12
εg
εs
0.075
0.16
0.236
0.334
0.346
0.05
0.106
0.16
0.22
0.23
0.037
0.07
0.1
0.15
0.165
0.048
0.045
0.042
0.039
0.038
0.1011
0.0976
0.0945
0.0892
0.0876
Appendix (E)……………………………………Experimental results
Cs %
(w/w)
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
Superficia
( cm )
( cm )
l
gas
Velocity
( cm / s )
90
97.30
3
90
107.143
4
90
117.80
5
90
135.14
7
90
137.614
9
92.5
97.78
3
92.5
105.12
4
92.5
114.2
5
92.5
121.71
7
92.5
9
3
4
5
7
9
93.8
93.8
93.8
93.8
93.8
97.3
101.19
106.6
113.01
114.11
Table ( E- 12 ) :
Ib ( Binary Mixture )E-13
, Weight ratio ( 1 : 3 )
εg
εs
0.075
0.16
0.236
0.334
0.346
0.054
0.12
0.19
0.24
0.249
0.0449
0.0418
0.0385
0.0361
0.0355
0.036
0.073
0.12
0.17
0.178
0.0955
0.0918
0.085
0.08
0.079
Appendix (E)……………………………………Experimental results
Cs %
(w/w)
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
εg
Superficia
( cm )
( cm )
l
gas
Velocity
( cm / s )
90
97.30
0.075
3
90
107.143
0.16
4
90
117.80
0.236
5
90
135.14
0.334
7
90
137.614
0.346
9
92.5
97.47
0.051
3
92.5
104.17
0.112
4
92.5
110.12
0.16
5
92.5
119.51
0.226
7
92.5
120.13
0.230
9
93.8
97
0.033
3
93.8
100.75
0.069
4
93.8
104.23
0.1
5
93.8
110.615
0.152
7
93.8
112
0.1625
9
Table ( E- 13 ) :
E-14
εs
0.044
0.041
0.039
0.036
0.0355
0.0931
0.09
0.087
0.082
0.081
Appendix (E)……………………………………Experimental results
Ic ( Binary Mixture ) , Weight ratio ( 3 : 1 )
Cs %
(w/w)
0
5
10
Table ( E- 14 ) :
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
εg
Superficia
( cm )
( cm )
l
gas
Velocity
( cm / s )
90
97.30
0.075
3
90
107.143
0.16
4
90
117.80
0.236
5
90
135.14
0.334
7
90
137.614
0.346
9
92.5
98.6
0.06
3
92.5
105.96
0.127
4
92.5
115.63
0.2
5
92.5
123.33
0.25
7
92.5
124.16
0.255
9
93.8
97.57
0.0386
3
93.8
101.63
0.077
4
93.8
108.6
0.136
5
93.8
114.4
0.18
7
93.8
115.8
0.19
9
E-15
Va ( Binary Mixture ) , Weight ratio ( 1 : 1 )
εs
0.046
0.0426
0.039
0.0366
0.0362
0.097
0.0934
0.0874
0.081
0.08
Appendix (E)……………………………………Experimental results
Cs %
(w/w)
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
Superficial
( cm )
( cm )
gas
Velocity
( cm / s )
90
97.30
3
90
107.143
4
90
117.80
5
90
135.14
7
90
137.614
9
91.8
95.83
3
91.8
100.66
4
91.8
105.52
5
91.8
113.2
7
91.8
114.75
9
0.075
0.16
0.236
0.334
0.346
0.042
0.088
0.13
0.189
0.20
0.0458
0.0436
0.0416
0.0388
0.0383
92.7
92.7
92.7
92.7
92.7
0.03
0.058
0.083
0.12
0.13
0.097
0.094
0.091
0.088
0.087
3
4
5
7
9
95.57
98.41
101.1
105.34
106.55
E-16
Table ( E- 15 ) :
Vb ( Binary Mixture ) , Weight ratio ( 1 : 3 )
εg
εs
Appendix (E)……………………………………Experimental results
Cs %
(w/w)
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
Superficial
( cm )
( cm )
gas
Velocity
( cm / s )
90
97.30
3
90
107.143
4
90
117.80
5
90
135.14
7
90
137.614
9
91.3
94.51
3
91.3
97.96
4
91.3
103.75
5
91.3
108.32
7
91.3
109.34
9
92.2
94.46
3
92.2
96.04
4
92.2
98.19
5
92.2
101.32
7
92.2
103.6
9
Table ( E- 16 ) :
E-17 ) , Weight ratio ( 3 : 1 )
Vc ( Binary Mixture
εg
0.075
0.16
0.236
0.334
0.346
0.034
0.068
0.12
0.157
0.165
0.024
0.04
0.061
0.09
0.11
εs
0.0452
0.044
0.0412
0.04
0.0391
0.0955
0.094
0.09196
0.0891
0.087
Appendix (E)……………………………………Experimental results
Cs %
(w/w)
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
H’f _ Hf
εg = ___________ , Hf = 90 cm
H’f
Ug
Hf
H’f
Superficial
( cm )
( cm )
gas
Velocity
( cm / s )
90
97.30
3
90
107.143
4
90
117.80
5
90
135.14
7
90
137.614
9
92
96.74
3
92
101.88
4
92
108.5
5
92
113.6
7
92
116.46
9
92.9
96.27
3
92.9
98.83
4
92.9
102.99
5
92.9
108.05
7
92.9
109.55
9
E-18
εg
0.075
0.16
0.236
0.334
0.346
0.049
0.097
0.152
0.19
0.21
0.035
0.06
0.098
0.14
0.152
εs
0.046
0.044
0.0418
0.039
0.038
0.098
0.096
0.092
0.087
0.086
Appendix (F)…………………………… Bubble diameter results
Table F- 1
Bubble diameter results
Dp = 3 mm ,
Cs
%
0
5
10
ρp = 1025 , axial position = 50 cm
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Ug
Superficial
( cm / s )
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-1
Bubble Diameter ( mm )
Electroresistivity
Photographic
Method
Method
5.431
5.19
6.123
5.93
7.525
7.24
8.634
8.44
9.773
9.62
5.872
5.84
6.334
6.21
7.862
7.63
8.974
8.96
10.563
10.17
6.282
6.14
6.823
6.75
7.882
7.84
9.44
9.337
11.763
11.6
0B
Appendix (F)…………………………… Bubble diameter results
Table F- 2
ρp = 1025 , axial position = 50 cm
Dp = 1.5 mm ,
Cs
%
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Ug
Superficial
( cm / s )
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-2
Bubble Diameter ( mm )
Electroresistivity
Photographic
Method
Method
5.431
5.19
6.123
5.93
7.525
7.24
8.634
8.44
9.773
9.62
6.747
6.24
7.821
7.63
8.923
8.44
10.211
9.73
11.46
11.21
6.813
6.55
7.882
7.85
9.211
8.93
10.623
10.41
12.281
12.02
1B
Appendix (F)…………………………… Bubble diameter results
Table F- 3
Dp = 0.65 mm ,
Cs
%
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
ρp = 1025 , axial position = 50 cm
Ug
Superficial
( cm / s )
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-3
Bubble Diameter ( mm )
Electroresistivity
Photographic
Method
Method
5.431
5.19
6.123
5.93
7.525
7.24
8.634
8.44
9.773
9.62
7.1
6.821
8.3
7.934
9.45
8.832
10.62
9.862
12.2
11.664
7.63
7.45
8.93
8.86
11.22
11.17
13.763
13.34
16.675
16.2
2B
Appendix (F)…………………………… Bubble diameter results
Table F- 4
Dp = 3 mm ,
Cs
%
0
5
10
ρp = 1150 , axial position = 50 cm
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Ug
Superficial
( cm / s )
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-4
Bubble Diameter ( mm )
Electroresistivity
Photographic
Method
Method
5.431
5.19
6.123
5.93
7.525
7.24
8.634
8.44
9.773
9.62
6.223
6.10
6.71
6.681
8.114
7.95
9.421
8.93
10.672
10.42
7.214
6.51
7.512
6.85
8.33
7.95
9.885
9.86
11.852
11.72
3B
Appendix (F)…………………………… Bubble diameter results
Table F- 5
ρp = 1150 , axial position = 50 cm
Dp = 0.5 mm ,
Cs
%
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Ug
Superficial
( cm / s )
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-5
Bubble Diameter ( mm )
Electroresistivity
Photographic
Method
Method
5.431
5.19
6.123
5.93
7.525
7.24
8.634
8.44
9.773
9.62
7.313
7.22
8.831
8.52
10.883
10.85
11.732
11.63
13.754
13.51
9.814
9.52
10.885
10.86
13.63
13.453
15.814
15.132
17.85
17.212
4B
Appendix (F)…………………………… Bubble diameter results
Type : Vb ( Binary Mixture ) , Weight Ratio ( 1 : 3 )
Cs
%
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Ug
Superficial
( cm / s )
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-6
Bubble Diameter ( mm )
Electroresistivity
Photographic
Method
Method
5.431
5.19
6.123
5.93
7.525
7.24
8.634
8.44
9.773
9.62
6.837
6.76
8.019
7.76
9.886
9.78
10.822
10.75
11.921
11.73
8.648
8.40
9.546
9.50
11.378
11.72
13.219
13.43
15.061
15.78
5B
Appendix (F)…………………………… Bubble diameter results
Type : Va ( Binary Mixture ) , Weight Ratio ( 1 : 1 )
Cs
%
0
5
10
Run
No .
Superficial
Velocity
Ug (cm/ s)
Bubble Diameter ( mm )
1
3
Electroresistivity
Prope Method
5.431
2
3
4
5
1
2
3
4
5
1
2
4
5
7
9
3
4
5
7
9
3
4
6.123
7.525
8.634
9.773
6.592
7.585
9.372
10.353
12.158
8.048
8.854
5.93
7.24
8.44
9.62
6.50
7.36
9.24
10.30
11.84
7.83
8.80
3
5
10.667
10.74
4
7
12.234
12.63
5
9
14.487
14.72
F-7
Photographic
Method
5.19
6B
Appendix (F)…………………………… Bubble diameter results
Type : Ic ( Binary Mixture ) , Weight Ratio ( 3 : 1 ),axial position=50cm
Cs
%
0
5
10
Run
No .
Superficial
Velocity
Ug (cm/ s)
Bubble Diameter ( mm )
1
3
Electroresistivity
Prope Method
5.431
2
3
4
5
1
2
3
4
5
1
2
4
5
7
9
3
4
5
7
9
3
4
6.123
7.525
8.634
9.773
6.02
6.448
7.945
9.122
10.597
6.589
7.051
5.93
7.24
8.44
9.62
6.0
6.37
7.74
8.95
10.25
6.26
6.78
3
5
8.030
7.89
4
7
9.58
9.518
5
9
11.792
11.64
F-88
Photographic
Method
5.19
7B
Appendix (F)…………………………… Bubble diameter results
Type : Ib ( Binary Mixture ) , Weight Ratio ( 1 : 3 ),axial position=50cm
Cs
%
0
5
10
Run
No .
Superficial
Velocity
Ug (cm/ s)
Bubble Diameter ( mm )
1
3
Electroresistivity
Prope Method
5.431
2
3
4
5
1
2
3
4
5
1
2
4
5
7
9
3
4
5
7
9
3
4
6.123
7.525
8.634
9.773
6.107
6.566
8.031
9.203
10.636
6.906
7.284
5.93
7.24
8.44
9.62
6.0
6.54
7.93
8.98
10.34
6.39
6.82
3
5
8.182
7.93
4
7
9.715
9.71
5
9
11.823
11.68
F-9
Photographic
Method
5.19
8B
Appendix (F)…………………………… Bubble diameter results
Type : Ia ( Binary Mixture ) , Weight Ratio ( 1 : 1 )
Cs
%
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Superficial
Velocity
Ug (cm/ s)
Bubble Diameter ( mm )
Electroresistivity
Prope Method
5.431
6.123
7.525
8.634
9.773
6.047
6.507
8.988
9.197
10.617
6.748
7.167
8.106
9.611
11.807
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-10
Photographic
Method
5.19
5.93
7.24
8.44
9.62
5.97
6.46
7.79
8.94
10.29
6.32
6.8
7.9
9.65
11.66
9B
Appendix (F)…………………………… Bubble diameter results
Type : Nc ( Binary Mixture ) , Weight Ratio ( 3 : 1 ),axial position=50cm
Cs
%
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Superficial
Velocity
Ug (cm/ s)
Bubble Diameter ( mm )
Electroresistivity
Prope Method
5.431
6.123
7.525
8.634
9.773
6.25
6.9
8.230
9.50
10.926
6.667
7.552
8.98
10.797
13.384
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-11
Photographic
Method
5.19
5.93
7.24
8.44
9.62
6.185
6.862
8.182
9.274
10.84
6.63
7.47
8.97
10.73
13.12
10B
Appendix (F)…………………………… Bubble diameter results
Type : Ma ( Binary Mixture ) , Weight Ratio ( 1 : 1 ),axial position=50cm
Cs
%
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Superficial
Velocity
Ug (cm/ s)
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
Bubble Diameter ( mm )
Electroresistivity
Prope Method
5.431
6.123
7.525
8.634
9.773
6.315
7.175
8.425
9.592
11.115
6.547
7.352
8.546
10.0
12.122
Photographic
Method
5.19
5.93
7.24
8.44
9.62
6.0
6.9
8.04
9.3
10.7
6.32
7.31
8.40
9.983
11.81
1B
Appendix (F)…………………………… Bubble diameter results
Type : Nb ( Binary Mixture ) , Weight Ratio ( 1 : 3 ),axial position=50cm
Bubble Diameter ( mm )
Photographic
Electroresistivity
F-12
Method
Prope Method
5.19
5.431
3
1
5.93
6.123
4
2
7.24
7.525
5
3
8.44
8.634
7
4
9.62
9.773
9
5
6.68
6.68
3
1
7.61
7.61
4
2
8.85
8.85
5
3
10.1
10.1
7
4
11.53
11.53
9
5
7.064
7.14
3
1
8.192
8.211
4
2
10.085
10.11
5
3
12.05
12.302
7
4
14.68
15.054
9
5
Appendix (F)…………………………… Bubble diameter results
F-13
Type : Na ( Binary Mixture ) , Weight Ratio ( 1 : 1 ),axial position=50cm
Bubble Diameter ( mm )
Photographic
Electroresistivity
Method
Prope Method
5.19
5.431
3
1
5.93
6.123
4
2
7.24
7.525
5
3
8.44
8.634
7
4
9.62
9.773
9
5
6.346
6.47
3
1
7.134
7.25
4
2
8.347
8.54
5
3
9.418
9.79
7
4
11.11
11.18
9
5
6.866
6.885
3
1
7.84
7.845
4
2
9.526
9.54
5
3
11.39
11.55
7
4
13.9
14.219
9
5
F-14
Appendix (F)…………………………… Bubble diameter results
Type : Mc ( Binary Mixture ) , Weight Ratio ( 3 : 1 )
Bubble Diameter ( mm )
Photographic
Electroresistivity
Method
Prope Method
5.19
5.431
3
1
5.93
6.123
4
2
7.24
7.525
5
3
8.44
8.634
7
4
9.62
9.773
9
5
6.0
6.160
3
1
6.68
6.824
4
2
7.9
8.212
5
3
9.21
9.382
7
4
10.51
10.860
9
5
6.27
6.464
3
1
7.11
7.173
4
2
8.21
8.324
5
3
9.76
9.77
7
4
11.74
11.934
9
5
Appendix (F)…………………………… Bubble diameter results
F-15 Ratio ( 1 : 3 ),at axial position=50 cm.
Type : Mb ( Binary Mixture ) , Weight
Bubble Diameter ( mm )
Photographic
Electroresistivity
Method
Prope Method
5.19
5.431
3
1
5.93
6.123
4
2
7.24
7.525
5
3
8.44
8.634
7
4
9.62
9.773
9
5
6.11
6.458
3
1
7.16
7.330
4
2
8.17
8.573
5
3
9.47
9.803
7
4
10.86
11.163
9
5
6.27
6.450
3
1
7.11
7.123
4
2
8.21
8.313
5
3
9.76
9.831
7
4
11.74
11.825
9
5
F-16
Appendix (F)…………………………… Bubble diameter results
Type : Vc ( Binary Mixture ) , Weight Ratio ( 3 : 1 ),axial position=50cm
Bubble Diameter ( mm )
Photographic
Electroresistivity
Method
Prope Method
5.19
5.431
3
1
5.93
6.123
4
2
7.24
7.525
5
3
8.44
8.634
7
4
9.62
9.773
9
5
6.30
6.347
3
1
6.97
7.158
4
2
8.69
8.859
5
3
9.84
9.844
7
4
11.27
11.616
9
5
7.25
7.447
3
1
8.11
8.163
4
2
9.721
9.76
5
3
11.249
11.54
7
4
13.561
13.66
9
5
F-17
Appendix (F)…………………………… Bubble diameter results
Appendix (F)…………………………… Bubble diameter results
Table F- 1
Bubble diameter results
Dp = 3 mm ,
Cs
%
0
5
10
ρp = 1025 , axial position = 50 cm
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Ug
Superficial
( cm / s )
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-1
Bubble Diameter ( mm )
Electroresistivity
Photographic
Method
Method
5.431
5.19
6.123
5.93
7.525
7.24
8.634
8.44
9.773
9.62
5.872
5.84
6.334
6.21
7.862
7.63
8.974
8.96
10.563
10.17
6.282
6.14
6.823
6.75
7.882
7.84
9.44
9.337
11.763
11.6
0B
Appendix (F)…………………………… Bubble diameter results
Table F- 2
ρp = 1025 , axial position = 50 cm
Dp = 1.5 mm ,
Cs
%
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Ug
Superficial
( cm / s )
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-2
Bubble Diameter ( mm )
Electroresistivity
Photographic
Method
Method
5.431
5.19
6.123
5.93
7.525
7.24
8.634
8.44
9.773
9.62
6.747
6.24
7.821
7.63
8.923
8.44
10.211
9.73
11.46
11.21
6.813
6.55
7.882
7.85
9.211
8.93
10.623
10.41
12.281
12.02
1B
Appendix (F)…………………………… Bubble diameter results
Table F- 3
Dp = 0.65 mm ,
Cs
%
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
ρp = 1025 , axial position = 50 cm
Ug
Superficial
( cm / s )
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-3
Bubble Diameter ( mm )
Electroresistivity
Photographic
Method
Method
5.431
5.19
6.123
5.93
7.525
7.24
8.634
8.44
9.773
9.62
7.1
6.821
8.3
7.934
9.45
8.832
10.62
9.862
12.2
11.664
7.63
7.45
8.93
8.86
11.22
11.17
13.763
13.34
16.675
16.2
2B
Appendix (F)…………………………… Bubble diameter results
Table F- 4
Dp = 3 mm ,
Cs
%
0
5
10
ρp = 1150 , axial position = 50 cm
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Ug
Superficial
( cm / s )
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-4
Bubble Diameter ( mm )
Electroresistivity
Photographic
Method
Method
5.431
5.19
6.123
5.93
7.525
7.24
8.634
8.44
9.773
9.62
6.223
6.10
6.71
6.681
8.114
7.95
9.421
8.93
10.672
10.42
7.214
6.51
7.512
6.85
8.33
7.95
9.885
9.86
11.852
11.72
3B
Appendix (F)…………………………… Bubble diameter results
Table F- 5
ρp = 1150 , axial position = 50 cm
Dp = 0.5 mm ,
Cs
%
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Ug
Superficial
( cm / s )
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-5
Bubble Diameter ( mm )
Electroresistivity
Photographic
Method
Method
5.431
5.19
6.123
5.93
7.525
7.24
8.634
8.44
9.773
9.62
7.313
7.22
8.831
8.52
10.883
10.85
11.732
11.63
13.754
13.51
9.814
9.52
10.885
10.86
13.63
13.453
15.814
15.132
17.85
17.212
4B
Appendix (F)…………………………… Bubble diameter results
Type : Ma ( Binary Mixture ) , Weight Ratio ( 1 : 1 ),axial position=50cm
Cs
%
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Superficial
Velocity
Ug (cm/ s)
Bubble Diameter ( mm )
Electroresistivity
Prope Method
5.431
6.123
7.525
8.634
9.773
6.315
7.175
8.425
9.592
11.115
6.547
7.352
8.546
10.0
12.122
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-6
Photographic
Method
5.19
5.93
7.24
8.44
9.62
6.0
6.9
8.04
9.3
10.7
6.32
7.31
8.40
9.983
11.81
5B
Appendix (F)…………………………… Bubble diameter results
Type : Mb ( Binary Mixture ) , Weight Ratio ( 1 : 3 ),at axial position=50 cm.
Bubble Diameter ( mm )
Photographic
Electroresistivity
Method
Prope Method
5.19
5.431
3
1
5.93
6.123
4
2
7.24
7.525
5
3
8.44
8.634
7
4
9.62
9.773
9
5
6.11
6.458
3
1
7.16
7.330
4
2
8.17
8.573
5
3
9.47
9.803
7
4
10.86
11.163
9
5
6.27
6.450
3
1
7.11
7.123
4
2
8.21
8.313
5
3
9.76
9.831
7
4
11.74
11.825
9
5
F-7
0
5
10
Appendix (F)…………………………… Bubble diameter results
Type : Mc ( Binary Mixture ) , Weight Ratio ( 3 : 1 )
Bubble Diameter ( mm )
Photographic
Electroresistivity
Method
Prope Method
5.19
5.431
3
1
5.93
6.123
4
2
7.24
7.525
5
3
8.44
8.634
7
4
9.62
9.773
9
5
6.0
6.160
3
1
6.68
6.824
4
2
7.9
8.212
5
3
9.21
9.382
7
4
10.51
10.860
9
5
6.27
6.464
3
1
7.11
7.173
4
2
8.21
8.324
5
3
9.76
9.77
7
4
11.74
11.934
9
5
F-8
0
5
10
Appendix (F)…………………………… Bubble diameter results
Type : Na ( Binary Mixture ) , Weight Ratio ( 1 : 1 ),axial position=50cm
Bubble Diameter ( mm )
Photographic
Electroresistivity
Method
Prope Method
5.19
5.431
3
1
5.93
6.123
4
2
7.24
7.525
5
3
8.44
8.634
7
4
9.62
9.773
9
5
6.346
6.47
3
1
7.134
7.25
4
2
8.347
8.54
5
3
9.418
9.79
7
4
11.11
11.18
9
5
6.866
6.885
3
1
7.84
7.845
4
2
9.526
9.54
5
3
11.39
11.55
7
4
13.9
14.219
9
5
F-9
0
5
10
Appendix (F)…………………………… Bubble diameter results
Type : Nb ( Binary Mixture ) , Weight Ratio ( 1 : 3 ),axial position=50cm
Bubble Diameter ( mm )
Photographic
Electroresistivity
Method
Prope Method
5.19
5.431
3
1
5.93
6.123
4
2
7.24
7.525
5
3
8.44
8.634
7
4
9.62
9.773
9
5
6.68
6.68
3
1
7.61
7.61
4
2
8.85
8.85
5
3
10.1
10.1
7
4
11.53
11.53
9
5
7.064
7.14
3
1
8.192
8.211
4
2
10.085
10.11
5
3
12.05
12.302
7
4
14.68
15.054
9
5
F-10
0
5
10
Appendix (F)…………………………… Bubble diameter results
Type : Nc ( Binary Mixture ) , Weight Ratio ( 3 : 1 ),axial position=50cm
Cs
%
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Superficial
Velocity
Ug (cm/ s)
Bubble Diameter ( mm )
Electroresistivity
Prope Method
5.431
6.123
7.525
8.634
9.773
6.25
6.9
8.230
9.50
10.926
6.667
7.552
8.98
10.797
13.384
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-11
Photographic
Method
5.19
5.93
7.24
8.44
9.62
6.185
6.862
8.182
9.274
10.84
6.63
7.47
8.97
10.73
13.12
10B
Appendix (F)…………………………… Bubble diameter results
Type : Ia ( Binary Mixture ) , Weight Ratio ( 1 : 1 )
Cs
%
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Superficial
Velocity
Ug (cm/ s)
Bubble Diameter ( mm )
Electroresistivity
Prope Method
5.431
6.123
7.525
8.634
9.773
6.047
6.507
8.988
9.197
10.617
6.748
7.167
8.106
9.611
11.807
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
F-12
Photographic
Method
5.19
5.93
7.24
8.44
9.62
5.97
6.46
7.79
8.94
10.29
6.32
6.8
7.9
9.65
11.66
1B
Appendix (F)…………………………… Bubble diameter results
Type : Ib ( Binary Mixture ) , Weight Ratio ( 1 : 3 ),axial position=50cm
Cs
%
0
5
10
Run
No .
Superficial
Velocity
Ug (cm/ s)
Bubble Diameter ( mm )
1
3
Electroresistivity
Prope Method
5.431
2
3
4
5
1
2
3
4
5
1
2
4
5
7
9
3
4
5
7
9
3
4
6.123
7.525
8.634
9.773
6.107
6.566
8.031
9.203
10.636
6.906
7.284
5.93
7.24
8.44
9.62
6.0
6.54
7.93
8.98
10.34
6.39
6.82
3
5
8.182
7.93
4
7
9.715
9.71
5
9
11.823
11.68
F-13
Photographic
Method
5.19
12B
Appendix (F)…………………………… Bubble diameter results
Type : Ic ( Binary Mixture ) , Weight Ratio ( 3 : 1 ),axial position=50cm
Cs
%
0
5
10
Run
No .
Superficial
Velocity
Ug (cm/ s)
Bubble Diameter ( mm )
1
3
Electroresistivity
Prope Method
5.431
2
3
4
5
1
2
3
4
5
1
2
4
5
7
9
3
4
5
7
9
3
4
6.123
7.525
8.634
9.773
6.02
6.448
7.945
9.122
10.597
6.589
7.051
5.93
7.24
8.44
9.62
6.0
6.37
7.74
8.95
10.25
6.26
6.78
3
5
8.030
7.89
4
7
9.58
9.518
5
9
11.792
11.64
F-14
Photographic
Method
5.19
13B
Appendix (F)…………………………… Bubble diameter results
Type : Va ( Binary Mixture ) , Weight Ratio ( 1 : 1 )
Cs
%
0
5
10
Run
No .
Superficial
Velocity
Ug (cm/ s)
Bubble Diameter ( mm )
1
3
Electroresistivity
Prope Method
5.431
2
3
4
5
1
2
3
4
5
1
2
4
5
7
9
3
4
5
7
9
3
4
6.123
7.525
8.634
9.773
6.592
7.585
9.372
10.353
12.158
8.048
8.854
5.93
7.24
8.44
9.62
6.50
7.36
9.24
10.30
11.84
7.83
8.80
3
5
10.667
10.74
4
7
12.234
12.63
5
9
14.487
14.72
F15
Photographic
Method
5.19
14B
Appendix (F)…………………………… Bubble diameter results
Type : Vb ( Binary Mixture ) , Weight Ratio ( 1 : 3 )
Cs
%
0
5
10
Run
No .
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Ug
Superficial
( cm / s )
3
4
5
7
9
3
4
5
7
9
3
4
5
7
9
Bubble Diameter ( mm )
Electroresistivity
Photographic
Method
Method
5.431
5.19
6.123
5.93
7.525
7.24
8.634
8.44
9.773
9.62
6.837
6.76
8.019
7.76
9.886
9.78
10.822
10.75
11.921
11.73
8.648
8.40
9.546
9.50
11.378
11.72
13.219
13.43
15.061
15.78
15B
F-16
Appendix (F)…………………………… Bubble diameter results
Type : Vc ( Binary Mixture ) , Weight Ratio ( 3 : 1 ),axial position=50cm
Bubble Diameter ( mm )
Photographic
Electroresistivity
Method
Prope Method
5.19
5.431
3
1
5.93
6.123
4
2
7.24
7.525
5
3
8.44
8.634
7
4
9.62
9.773
9
5
6.30
6.347
3
1
6.97
7.158
4
2
8.69
8.859
5
3
9.84
9.844
7
4
11.27
11.616
9
5
7.25
7.447
3
1
8.11
8.163
4
2
9.721
9.76
5
3
11.249
11.54
7
4
13.561
13.66
9
5
F-17
0
5
10
Appendix (G)……………… Results of experiments
Table G-1
Colum Hl ( cm )
diameter
Dc ( cm )
15
90
Axial position (
cm )
70 , 50 , 30
Particles : PVC , ρp = 1025 Kg / m3 , d p = 3mm , Cs = 0 % w/w
Axial position
0B
Run
No.
1
2
3
4
5
Superficial gas
Velocity
Ug ( cm/s )
3
4
5
7
9
Local gas
holdup
(r/R =0)
0.06
0.12
0.2
0.304
0.34
Bubble rise
Velocity
( cm / s )
21.76
25.21
32.64
36.17
38.98
1
2
3
4
5
3
4
5
7
9
0.076
0.18
0.24
0.34
0.38
18.15
20.65
24.73
27.81
32.45
1
2
3
4
5
3
4
5
7
9
0.09
0.19
0.27
0.36
0.41
16.40
20.57
24.13
26.70
29.48
( cm )
30
50
70
G-1
1B
Appendix (G)……………… Results of experiments
Table G-2
Colum Hl ( cm )
diameter
Dc ( cm )
15
90
Axial position (
cm )
70 , 50 , 30
Particles : PVC : ρp = 1025 Kg / m3 , d p = 3mm , Cs = 5 % w/w
Axial position
( cm )
1B
30
50
70
Run
No.
1
2
3
4
5
Superficial gas
Velocity
Ug ( cm/s )
3
4
5
7
9
Local gas
holdup
(r/R =0)
0.05
0.1
0.17
0.24
0.29
Bubble rise
Velocity
( cm / s )
23.24
26.81
34.21
37.68
39.27
1
2
3
4
5
3
4
5
7
9
0.06
0.16
0.22
0.29
0.34
19.72
21.98
26.34
29.26
34.18
1
2
3
4
5
3
4
5
7
9
0.08
0.18
0.25
0.33
0.38
17.84
18.31
23.42
26.70
31.62
G-2
12B
Appendix (G)……………… Results of experiments
Table G-3
Colum Hl ( cm )
diameter
Dc ( cm )
15
90
Axial position (
cm )
70 , 50 , 30
Particles : PVC , ρp = 1025 Kg / m3 , d p = 3mm , Cs = 10 % w/w
Axial position
2B
Run
No.
1
2
3
4
5
Superficial gas
Velocity
Ug ( cm/s )
3
4
5
7
9
Local gas
holdup
(r/R =0)
0.04
0.08
0.12
0.17
0.2
Bubble rise
Velocity
( cm / s )
28.34
32.10
37.8
43.3
49.76
1
2
3
4
5
3
4
5
7
9
0.048
0.084
0.15
0.2
0.23
25.41
29.61
32.92
36.45
46.71
1
2
3
4
5
3
4
5
7
9
0.06
0.12
0.16
0.24
0.27
21.91
26.82
28.78
33.11
36.38
( cm )
30
50
70
G-3
13B
Appendix (G)……………… Results of experiments
Table G-4
Colum Hl ( cm )
diameter
Dc ( cm )
15
90
Axial position (
cm )
70 , 50 , 30
Particles : PVC , ρp = 1025 Kg / m3 , d p = 1.5 mm , Cs = 5 % w/w
Axial position
3B
Run
No.
Local gas
holdup
(r/R =0)
Bubble rise
Velocity
( cm / s )
1
2
3
4
5
Superficial
gas
Velocity
Ug ( cm/s )
3
4
5
7
9
0.033
0.07
0.093
0.14
0.18
29.2
33.3
35.1
40.4
50.0
1
2
3
4
5
3
4
5
7
9
0.04
0.08
0.12
0.18
0.21
26.14
30.5
34.07
38.2
46.72
1
2
3
4
5
3
4
5
7
9
0.05
0.1
0.14
0.2
0.22
23.3
30.2
33.7
35.52
38.94
( cm )
30
50
70
G-4
14B
Appendix (G)……………… Results of experiments
Table G-5
Colum Hl ( cm )
diameter
Dc ( cm )
15
90
Axial position (
cm )
70 , 50 , 30
Particles : PVC , ρp = 1025 Kg / m3 , d p = 1.5 mm , Cs = 10 % w/w
Axial position
( cm )
4B
30
50
70
Run
No.
1
2
3
4
5
Superficial gas
Velocity
Ug ( cm/s )
3
4
5
7
9
Local gas
holdup
(r/R =0)
0.022
0.043
0.061
0.084
0.1
Bubble rise
Velocity
( cm / s )
31.2
34.1
35.4
45.3
55.3
1
2
3
4
5
3
4
5
7
9
0.03
0.06
0.08
0.095
0.12
28.5
32.1
35.4
38.38
47.36
1
2
3
4
5
3
4
5
7
9
0.04
0.08
0.1
0.13
0.15
26.4
30.7
34.1
36.2
39.31
G-5
15B
Appendix (G)……………… Results of experiments
Table G-6
Colum Hl ( cm )
diameter
Dc ( cm )
15
90
Axial position (
cm )
70 , 50 , 30
Particles : PVC , ρp = 1025 Kg / m3 , d p = 0.65 mm , Cs = 5 % w/w
Axial position
( cm )
5B
30
50
70
Run
No.
1
2
3
4
5
Superficial gas
Velocity
Ug ( cm/s )
3
4
5
7
9
Local gas
holdup
(r/R =0)
0.014
0.022
0.036
0.065
0.087
Bubble rise
Velocity
( cm / s )
36.7
37.9
40.2
47.4
56.3
1
2
3
4
5
3
4
5
7
9
0.021
0.034
0.058
0.093
0.1
32.4
34.6
37.6
39.4
41.2
1
2
3
4
5
3
4
5
7
9
0.036
0.057
0.092
0.11
0.13
27.4
29.9
33.5
36.22
39.3
G-6
16B
Appendix (G)……………… Results of experiments
Table G-7
Colum Hl ( cm )
diameter
Dc ( cm )
15
90
Axial position (
cm )
70 , 50 , 30
Particles : PVC , ρp = 1025 Kg / m3 , d p = 0.65 mm , Cs = 10 % w/w
Axial position
6B
Run
No.
Local gas
holdup
(r/R=0)
Bubble rise
Velocity
( cm / s )
1
2
3
4
5
Superficial
gas
Velocity
Ug ( cm/s )
3
4
5
7
9
0.01
0.016
0.02
0.041
0.062
39.3
41.2
44.2
50.1
58.3
1
2
3
4
5
3
4
5
7
9
0.017
0.024
0.033
0.052
0.071
34.4
36.7
38.5
42.6
50.1
1
2
3
4
5
3
4
5
7
9
0.023
0.044
0.062
0.083
0.094
33.6
35.7
36.8
40.1
45.5
( cm )
30
50
70
Table G-8
G-7
17B
Appendix (G)……………… Results of experiments
Colum Hl ( cm )
diameter
Dc ( cm )
15
90
Axial position (
cm )
70 , 50 , 30
Particles : Plastics , ρp = 1150 Kg / m3 , d p = 3 mm , Cs = 5 % w/w
Axial position
( cm )
7B
30
50
70
Run
No.
1
2
3
4
5
Superficial gas
Velocity
Ug ( cm/s )
3
4
5
7
9
Local gas
holdup
(r/R =0)
0.043
0.09
0.13
0.2
0.24
Bubble rise
Velocity
( cm / s )
25.3
28.41
35.8
40.22
45.62
1
2
3
4
5
3
4
5
7
9
0.05
0.1
0.19
0.25
0.28
22.3
23.43
28.62
33.71
40.24
1
2
3
4
5
3
4
5
7
9
0.08
0.14
0.21
0.27
0.3
19.72
21.53
26.33
30.27
34.12
Table G-9
G-7
18B
Appendix (G)……………… Results of experiments
Colum Hl ( cm )
diameter
Dc ( cm )
15
90
Axial position (
cm )
70 , 50 , 30
Particles : Plastics , ρp = 1150 Kg / m3 , d p = 3 mm , Cs = 10 % w/w
Axial position
8B
Run
No.
Local gas
holdup
(r/R =0)
Bubble rise
Velocity
( cm / s )
1
2
3
4
5
Superficial
gas
Velocity
Ug ( cm/s )
3
4
5
7
9
0.02
0.05
0.08
0.12
0.15
30.1
33.5
39.7
46.4
52.23
1
2
3
4
5
3
4
5
7
9
0.03
0.06
0.1
0.15
0.19
27.44
31.7
36.63
41.83
49.77
1
2
3
4
5
3
4
5
7
9
0.04
0.08
0.13
0.18
0.22
24.97
27.12
32.21
45.3
53.3
( cm )
30
50
70
Table G-10
Colum Hl ( cm )
Axial position
(
G-8
19B
Appendix (G)……………… Results of experiments
diameter
Dc ( cm )
15
cm )
90
70 , 50 , 30
Particles : Plastics , ρp = 1150 Kg / m3 , d p = 0.5 mm , Cs = 5 % w/w
Axial position
9B
Run
No.
1
2
3
4
5
Superficial gas
Velocity
Ug ( cm/s )
3
4
5
7
9
Local gas
holdup
(r/R =0)
0.011
0.018
0.028
0.05
0.07
Bubble rise
Velocity
( cm / s )
37.2
39.4
42.1
49.2
57.3
1
2
3
4
5
3
4
5
7
9
0.019
0.029
0.04
0.07
0.083
31.6
33.1
36.7
41.4
53.2
1
2
3
4
5
3
4
5
7
9
0.028
0.049
0.076
0.091
0.1
25.9
28.1
31.4
40.8
47.7
( cm )
30
50
70
Table G-11
G-9
Colum Hl ( cm )
diameter
Axial position (
cm )
20B
Appendix (G)……………… Results of experiments
Dc ( cm )
15
90
70 , 50 , 30
Particles : Plastics , ρp = 1150 Kg / m3 , d p = 0.5 mm , Cs = 10 % w/w
Axial position
10B
Run
No.
1
2
3
4
5
Superficial gas
Velocity
Ug ( cm/s )
3
4
5
7
9
Local gas
holdup
(r/R =0)
0.008
0.01
0.015
0.029
0.041
Bubble rise
Velocity
( cm / s )
43.7
45.2
49.3
53.4
60.7
1
2
3
4
5
3
4
5
7
9
0.011
0.016
0.02
0.038
0.053
35.8
40.3
44.2
47.4
54.1
1
2
3
4
5
3
4
5
7
9
0.017
0.022
0.03
0.04
0.076
30.4
34.3
38.2
43.3
47.9
( cm )
30
50
70
G-10
21B
Appendix (G)……………… Results of experiments
G-12
Appendix (H)……………… Results of experiments
Table H-1
Solid Concentration
Cs%
0
ε Trans.
Dp,mm
5
10
R
U trans. ,cm/s
R
R
R
0.5
0.65
0.5
0.65
0.5
0.333
0.333
0.126
0.14
0.078
7.2
7.2
6.38
6.52
5
0.65
0.086
5.37
Table H-2
Solid Concentration
Cs%
0
5
10
Dp, average
diameter (mm)
Mc=2
Ic=1
Mc=2
Ic=1
Mc=2
ε Trans.
R
Ic=1
Solid Concentration
Cs%
0
5
10
U trans. ,cm/s
R
R
0.333
0.333
0.2437
0.245
0.1672
7.2
7.2
6.98
7
6.54
0.17
6.71
ε Trans.
Dp,mm
R
R
U trans. ,cm/s
R
R
R
3
3
3
3
3
0.333
0.333
0.28
0.239
0.17
7.2
7.2
6.9
6.1
6
3
0.14
5.62
H-1
‫ﺍﻝ ّﺥﻻﺹﺓ‬
‫ﺃﻋﻤﺪﺓ ﺍﻟﺘﻤﻴﻊ ﺍﻟﻔﻘﺎﻋﻴﺔ ﻣﺴﺘﺨﺪﻣﺔ ﺑﺼﻮﺭﺓ ﻭﺍﺳﻌﺔ ﻓﻲ ﻣﺠﺎ ﻝ ﺍﻟﺼﻨﺎﻋﺔ ﻭﺧﺼﻮﺻﺂ‬
‫ﻓﻲ ﺍﻟﻤﻔﺎﻋﻼﺕ ﺍﻟﻜﻴﻤﻴﺎﺋﻴﺔ ﻭﺍﻋﻤﺪﺓ ﺍﻵﻣﺘﺼﺎﺹ ‪.‬‬
‫ﺗﻢ ﻓﻲ ﻫﺬﺍ ﺍﻟﺒﺤﺚ ﺩﺭﺍﺳﺔ ﺍﻟﺨﻮﺍﺹ ﺍﻟﻬﻴﺪﺭﻭﺩﻳﻨﺎﻣﻴﻜﻴﺔ ﺑﺄﺳﺘﺨﺪﺍﻡ ﺟﺴﻴﻤﺎﺕ ﺻﻠﺒﺔ‬
‫ﻣﺨﺘﻠﻔﺔ ﺍﻷﻗﻄﺎﺭﻭﺍﻟﻜﺜﺎﻓﺔ ﻓﻲ ﻧﻈﺎﻡ ﺛﻼﺛﻲ ﺍﻟﻄﻮﺭ )ﻏﺎﺭ ‪ -‬ﺳﺎﺋﻞ – ﺻﻠﺐ(ﻭﻣﻌﺮﻓﺔ ﺗﺄﺛﻴﺮﻫﺎﻋﻠﻰ‬
‫)ﺍﻟﻐﺎﺯﺍﻟﻤﺤﺘﺒﺲ ‪,‬ﺱﺭﻋﺔ ﺃﺭﺗﻔﺎﻉ ﺍﻟﻔﻘﺎﻋﺔ ﻭﺍﻟﻤﺰﺝ ﺍﻟﺮﺟﻌﻲ‬
‫‪(back mixing‬ﺣﻴﺚ ﺃﻥ‬
‫ﻣﻌﺮﻓﺔﻫﺬﺍ ﺍﻟﺘﺄﺛﻴﺮﻳﻌﺘﺒﺮﺃﺣﺪ ﺍﻟﻌﻮﺍﻣﻞ ﺍﻻﺳﺎﺳﻴﺔ ﻓﻲ ﺗﺤﺪﻳﺪ ﻛﻔﺎءﺓ ﺍﻷﺩﺍء‪.‬‬
‫ﻛﺎﻥ ﺩﺭﺍﺳﺔ ﺗﺠﺮﻳﺒﻴﺔ ﻋﻠﻰ ﺗﺄﺛﻴﺮﺗﺮﻛﻲﺯﺍﻟﻤﺎﺩﺓ ﺍﻟﺼﻠﺒﺔ‬
‫ﺗﻀ ّﻤ ُﻦ ﺍﻟﻌﻤ ُﻞ ﺟﺰءﺍﻥ‪ ،‬ﺍﻷﻭﻝ‬
‫ِ‬
‫ﺍﻟﺨﻠﻴﻂ ﺍﻟﻤﻔﺮﺩ ﻭﺍﻟﺜﻨﺎﺋﻲ ﻭﻋﻠﻰ ﺍﻟﻤﺘﻐﻴﺮﺍﺕ ﺍﻟﻬﻴﺪﺭﻭﺩﻳﻨﺎﻣﻴﻜﻴﺔ‬
‫ﻭﺧﺼﺎﺋﺺﻫﺎ ﻟﻜﻞ ﻣﻦ‬
‫)ﺍﻟﻐﺎﺯﺍﻟﻤﺤﺘﺒﺲ ‪ ،‬ﺩﻳﻨﺎﻣﻴﻜﻴﺔ ﺍﻟﻔﻘﺎﻋﺎﺕ( ﻓﻲ ﻋﻤﻮﺩﺍﻟﻄﺒﻘﺔ ﺍﻟﻤﺘﻤﻴﻌﺔ ‪.‬‬
‫ﻛﻞ ﺍﻟﺘﺠﺎﺭﺏ‬
‫ﺗﻢ ﺃﺟﺮﺍءﻫﺎ ﺑﺄﺳﺘﺨﺪﺍﻡ ﻋﻤﻮﺩ ﺯﺟﺎﺟﻲ ﻣﺼﻨﻮﻉ ﻣﻦ ﻣﺎﺩﺓ‬
‫)‪(QVF‬‬
‫ﻭﺑﻘﻄﺮ)‪ (15cm‬ﻟﺪﺭﺍﺳﺔ ﺟﺮﻳﺎﻥ ﻓﻘﺎﻋﺎﺕ ﺍﻟﻐﺎﺯ ﻓﻲ ﺳﺎﺋﻞ )ﻣﺎء( ﺛﺎﺑﺖ ﻭﺑﺄﺭﺗﻔﺎﻉ )‪(95cm‬‬
‫ﻛﻤﺎ ﺗﻢ ﺃﺳﺘﺨﺪﺍﻡ ﻧﻮﻉ ﻭﺍﺣﺪ ﻣﻦ ﻣﻮﺯﻉ ﺍﻟﻔﻘﺎﻋﺔ ﺫﻭﺛﻘﻮﺏ ﻗﻄﺮﻫﺎ )‪ ، (2mm‬ﻛﻤﺎ ﺷﻤﻞ ﺍﻟﺒﺤﺚ‬
‫ﺩﺭﺍﺳﺔ ﺗﺄﺛﻴﺮ ﺃﻗﻄﺎﺭ ﻭﻛﺜﺎﻓﺎﺕ ﺍﻟﺠﺴﻴﻤﺎﺕ ﺍﻟﺼﻠﺒﺔ ﻋﻠﻰ ﺍﻟﻤﺘﻐﻴﺮﺍﺕ ﺃﻋﻼﻩ ‪.‬‬
‫ﺍﻥ ﺍﻟﺠﺴﻴﻤﺎﺕ ﺍﻟﺼﻠﺒﺔ ﺍﻟﻤﺴﺘﺨﺪﻣﺔ ﻣﺼﻨﻮﻋﺔ ﻣﻦ ﻣﺎﺩﺓ ﺍﻟﺒﻮﻟﻲ ﻓﻨﻴﻞ ﻛﻠﻮﺭﺍﻳﺪ‬
‫ﺫﺍﺕ‬
‫ﻛﺜﺎﻓﺔ )‪ (1025kg/m3‬ﻭﺑﺄﻗﻄﺎﺭ) ‪ ،1.5 ،3‬ﻭ‪ ( mm 0.65‬ﻭﺍﻟﻨﻮﻉ ﺍﻟﺜﺎﻧﻲ ﻣﻦ ﺍﻟﻤﻮﺍﺩ‬
‫‪P‬‬
‫‪P‬‬
‫ﺍﻟﺒﻼﺳﺘﻴﻜﻴﺔ ﺫﺍﺕ ﻛﺜﺎﻓﺔ )‪ (1150 kg/m3‬ﻭﺑﺄﻗﻄﺎﺭ) ‪ ( mm 0.5 ،3‬ﻛﻤﺎ ﺗﻢ ﺃﺳﺘﺨﺪﺍﻡ ﺍﻟﻬﻮﺍء‬
‫‪P‬‬
‫‪P‬‬
‫ﺑﺴﺮﻉ ﻣﺨﺘﻠﻔﺔ ﻭﺑﻤﺪﻯ ) ‪، (cm / sec 9-3‬ﻭﻗﺪ ﺗﻢ ﻣﻼﺣﻈﺔ ﺷﺮﻭﻁ ﺍﻟﺘﺸﻐﻴﻞ ﺍﻟﻨﻮﻋﻲ‬
‫ﺍﻟﻤﺴﺘﺨﺪﻣﺔ ﻓﻲ ﺍﻟﺘﺠﺎﺭﺏ‪.‬ﻭﻗﺪ ﻟﻮﺣﻆ ﺃﻥ ﻫﻨﺎﻙ ﻋﻼﻗﺔ ﻁﺮﺩﻳﺔ ﺑﻴﻦ ﺍﻟﻐﺎﺯﺍﻟﻤﺤﺘﺒﺲ ﻭﻛﻶ ﻣﻦ‬
‫ﺳﺮﻋﺔﺍﻟﻐﺎﺯﻭﻗﻄﺮ ﺍﻟﺠﺴﻴﻤﺎﺕ ﺍﻟﺼﻠﺒﺔ ﺑﻴﻨﻤﺎ ﻫﻨﺎﻙ ﻋﻼﻗﺔ ﻋﻜﺴﻴﺔ ﻣﻮﺟﻮﺩﺓ ﺑﻴﻦ ﺍﻟﻐﺎﺯﺍﻟﻤﺤﺘﺒﺲ‬
‫ﻭﻛﻶﻣﻦ ﺗﺮﻛﻴﺰﺍﻟﻤﺎﺩﺓ ﺍﻟﺼﻠﺒﺔ ﻭﻛﺜﺎﻓﺘﻬﺎ ‪ .‬ﺍﻥ ﺩﻳﻨﺎﻣﻴﻜﻴﺎﺕ ﺍﻟﻔﻘﺎﻋﺔ )ﻗﻄﺮ‪ ،‬ﺳﺮﻋﺔ ﻭﺃﺭﺗﻔﺎﻉ‬
‫ﺍﻟﻔﻘﺎﻋﺔ ( ﺗﻤﻠﻚ ﻧﻘﻄﺔ ﺃﺧﺘﻼﻑ ﻣﻈﻬﺮﻳﺔ ﻭﺍﻟﺘﻲ ﺗﺰﺩﺍﺩ ﺑﺰﻳﺎﺩﺓ ﺗﺮﻛﻴﺰﺍﻟﻤﺎﺩﺓ ﺍﻟﺼﻠﺒﺔ ﻭﻣﻊ‬
‫ﻧﻘﺼﺎﻥ ﻗﻄﺮﺍﻟﻤﺎﺩﺓ ﺍﻟﺼﻠﺒﺔ‪.‬‬
‫ﺃﻥ ﺍﻟﻐﺎﺯ ﺍﻟﻤﺤﺘﺒﺲ ﻓﻲ ﺍﻟﺨﻠﻴﻂ ﺍﻟﺜﻨﺎﺋﻲ ﻳﺘﻢ ﺣﺴﻠﺒﻪ ﻣﻦ ﺍﻟﻤﻌﺎﺩﻟﺔ ﺍﻟﺘﺎﻟﻴﺔ ‪-:‬‬
‫‪ε g = x1ε g1 + x 2 ε g 2‬‬
‫ﻧﻒ ﻟﻠﺤﺼﻮﻝ ﻋﻠﻰ ﻋﻼﻗﺔ ﻋﺎﻣﺔ ﻟﻠﻐﺎﺯﺍﻟﻤﺤﺘﺒﺲ ﻓﻲ ﺣﺎﻟﺘﻲ‬
‫ﺃﻥ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻹﺣﺼﺎﺋﻲ ﺫ‬
‫ﺍﻟﺨﻠﻴﻂ ﺍﻟﻤﻔﺮﺩ ﻭﺍﻟﺜﻨﺎﺋﻲ ﻣﻦ ﺍﻟﺠﺴﻴﻤﺎﺕ ﺍﻟﺼﻠﺒﺔ ﻓﻲ ﻋﻤﻮﺩﺍﻟﻄﺒﻘﺔ ﺍﻟﻤﺘﻤﻴﻌﺔ ﻭﻛﺪﺍﻟﺔ ﻟﻠﻤﺘﻎ ﻳﺮﺍﺕ‬
‫ﺍﻟﻤﺪﺭﻭﺳﺔ ﻭﻛﻤﺎ ﻳﻠﻲ ‪-:‬‬
‫ﻓﻲ ﺣﺎﻟﺔ ﺍﻟﺨﻠﻴﻂ ﺍﻟﻤﻔﺮﺩ ‪-:‬‬
‫‪ρ l u g2 d c 1.086486 ρ l d c u g −0.569585 −0.245182‬‬
‫(‬
‫)‬
‫(‬
‫)‬
‫‪cs‬‬
‫‪σl‬‬
‫‪µl‬‬
‫‪−0.333189‬‬
‫‪) o.332514‬‬
‫)‬
‫‪u g2‬‬
‫‪gd c‬‬
‫‪ρs‬‬
‫(‪ε g = 0.17808‬‬
‫‪ρ s − ρl‬‬
‫( ‪) 0.201744‬‬
‫‪dp‬‬
‫‪dc‬‬
‫(‬
‫‪R = 0.96811‬‬
‫‪error = 0.0049345‬‬
‫ﻓﻲ ﺣﺎﻟﺔ ﺍﻟﺨﻠﻴﻂ ﺍﻟﺜﻨﺎﺋﻲ‪-:‬‬
‫‪−0.703610‬‬
‫‪x2‬‬
‫‪0.568996‬‬
‫‪x1‬‬
‫‪−0.389035‬‬
‫‪)1.515572 cs‬‬
‫‪u g d c ρl‬‬
‫‪µl‬‬
‫‪) 2.443881‬‬
‫(‪ε g = 0.057009‬‬
‫‪d p2‬‬
‫‪dc‬‬
‫( ‪) 0.075001‬‬
‫‪d p1‬‬
‫‪dc‬‬
‫(‬
‫‪R = 0.995641008‬‬
‫ﺟﻤﻬﻮﺭﻳﺔ ﺍﻟﻌﺮﺍﻕ‬
‫ﻭﺯﺍﺭﺓ ﺍﻟﺘﻌﻠﻴﻢ ﺍﻟﻌﺎﻟﻲ ﻭﺍﻟﺒﺤﺚ ﺍﻟﻌﻠﻤﻲ‬
‫ﺍﻟﺠﺎﻣﻌﺔ ﺍﻟﺘﻜﻨﻮﻟﻮﺟﻴﺔ‬
‫ﻗﺴﻢ ﺍﻟﻬﻨﺪﺳﺔ ﺍﻝﻙﻳﻤﻴﺎﻭﻳﺔ‬
‫ﺩﺭﺍﺳﺔ ﺍﻟﺧﻭﺍﺹ ﺍﻟﻬﻳﺩﺭﻭﺩﻳﻧﺎﻣﻳﻛﻳﺔ ﻓﻲ ﺃﺑﺭﺍﺝ ﺍﻟﺗﻣﻳﻊ‬
‫ﺛﻼﺛﻳﺔ ﺍﻟﻁﻭﺭ )ﻏﺎﺭ‪ -‬ﺳﺎﺋﻝ ‪ -‬ﺻﻠﺏ(‬
‫ﺇﻁﺮﻭﺣﺔ ﻣﻘﺪﻣﺔ‬
‫ﺍﻟﻰ ﻗﺴﻢ ﺍﻝﻫﻨﺪﺳﺔ ﺍﻟﻜﻴﻤﻴﺎﻭﻳﺔ ﻑﻱ ﺍﻟﺠﺎﻣﻌﺔ ﺍﻟﺘﻜﻨﻮﻟﻮﺟﻴﺔ ﻭﻫﻲ ﺟﺰء ﻣﻦ ﻣﺘﻄﻠﺒﺎﺕ‬
‫ﻧﻴﻞ ﺷﻬﺎﺩﺓ ﺍﻟﻤﺎﺟﺴﺘﻴﺮ ﻓﻲ ﺍﻟﻬﻨﺪﺳﺔ ﺍﻟﻜﻴﻤﻴﺎﻭﻳﺔ‪.‬‬
‫ﻣﻦ ﻗﺒﻞ ﺍﻟﻤﻬﻨﺪﺱﺓ‬
‫ﺃﺩﻳﺒﺔ ﻋﻠﻲ ﻣﺤﻤﻮﺩ‬
‫ﺫﻱ ﺍﻟﺤﺠﺔ ‪ 1429‬ﻫﺠﺮﻳﺔ‬
‫ﺗﺸﺮﻳﻦ ﺍﻟﺜﺎﻧﻲ ‪ ۲۰۰۸‬ﻣﻴﻼﺩﻳﺔ‬
The present work is an experimental study
on the effect of solid
loading and solid properties of both single and binary mixtures on the
hydrodynamic parameters (gas holdup and bubble dynamics) of a
fluidized –bed bubble column.
All experimental were performed in a QVF glass made column of
15 cm diameter and a constant clear liquid (i.e, tap water0 of 95cm
height. Wide range of solid particle diameters (0.5 to 3mm) with two
different densities (i.e., 1025 and 1150 kg/m3 ) were investigated for the
bubble effect on gas holdup and bubble dynamics using air with different
gas superficial velocities ( 3 to 9 cm/s).
A binary mixture consisting of different compositions of solid
particles was prepared to be utilized in the study.
It was observed that for specified operating conditions used in the
experiments there is a proportional relationship between gas holdup and
both superficial gas velocity and particle diameter while an inverse
relationship exists between gas holdup and both solid concentration and
particles density.
Bubble dynamics (i.e., bubble diameter and bubble rise velocity) is
looked at from a different view point, it increases with increasing solid
concentration and with decreasing particles diameter.
For binary mixture of solid particles, it was proved experimentally that
the effect of each species on the hydrodynamic parameters is proportional
to its weight fraction in the mixture, the gas holdup of a binary mixture
may be well presented by the following equation
εg =
x 1 ε g1 + x 2 ε g2
A statistical analysis was performed to get general correlation for
the overall gas holdup in a single and in binary mixtures of solid particles
in a fluidized bed column as a function of the parameters studied.
Keywords : Fludized_ Bed bubble column , Hydrodynamics , gas
holdup.
Introduction:
U
BCRs are intensively utilized as multiphase contactors and reactors
in chemical, petrochemical, biochemical and metallurgical industries [1].
BCR is used especially in chemical processes involving reactions such as
oxidation, chlorination, alkylation, polymerization and hydrogenation in
the manufacture of synthetic fuels by gas conversion processes and in
biochemical processes such as fermentation and biological wastewater
treatment[2,3].
In three-phase fluidization, the particles are fluidized by the cocurrent flow of liquid and gas. The three phase fluidized beds can be
classified into the expanded bed and transport regimes, the solid can be
introduced either continuously or batch wise [4].
Gas hold-up is dimensionless key parameter for phenomena
purposes of bubble column systems [39]. All studies examine gas
hold up because it plays an important role in design and analysis of
bubble columns.
In slurry columns the presence of suspended solid particles
reduces the values of (εg) and their reduction by an addition of
solid particles to the column is high in the transition regime and
low in the heterogeneous flow regime.
Abdul-Rahman [44] studied the gas hold-up in three phase systems
and correlated the general empirical equations:
ε g = 1.32 U g µ L−0.028 C −v0.06
For U g < 0.07 m / s
..........(2.6)
ε g = 0.445 U 0g.6 µ L−0.028 C −v0.6 For U g > 0.07 m / s
..........(2.7)
Auroba-Nafaa [45] studied the effect of solid particles with
different liquid-phase (alcohols and electrolytes) on gas hold-up. The
dimensional analysis was used to correlate the gas hold-up with gas
velocity and liquid properties. The correlations which was used to
measure the gas hold-up is.
εg
=
(1 − ε g )4
C
1 + 1.25  s
ρ
 s
0.92
−0.22
4 

 g.µ L 


 ρ .σ 3 
 L L
0.73
0.885
 ρ −ρ 
 D .U .ρ
  s

 c g L
L
 


µL

  ρL 
 U .µ
A ∗  g L
 σ
L









− 0.08
.........(2.10)
Nasser Al-Hapoby [47] studied the effect of solid particles and
column dimensions on the gas hold-up and liquid phase mass transfer
coefficient in solid suspended bubble column with draught tube and
he found that the gas hold-up is not affected with column diameter
and the effect of (Cs) on (εg) becomes less pronounced. The gas holdup and the volumetric liquid phase mass transfer coefficient were
correlated by the two correlations below, they are respectively:
ε g = 2.05915 ∗ 10 −10 ∗ Fr0.429 ∗ B1o.9891 ∗ G a0.2978
..........(2.11)
As reported by Li and Prakash [66], in a three-phase (SBCRs), the
static height can be expressed as:
∆P = (ρ g ε g + ρ L ε L + ρs ε s )g∆H
..........(2.13)
By proper substitutions, starting with the equation (2.13), one can
factor out the εg as:
∆P 
1

 g(ρ 1 φ 1 + ρ s φ s ) ∆H 

ε g = 
............(2.14)
Equation (2.14) can be directly applied for estimation of gas hold
up in a (SBCRs).
The critical gas velocity for complete suspension of solid particles
is the most important parameters that affect both hydrodynamic
design and operation of three-phase sparged columns (slurry bubble
column).
Smith et al [76] indicated that (VGc) and minimum superficial gas
velocity at which all solids are fluidized can be determined by visual
observation and by pressure drop measurements. They presented a
new method of evaluating (VGc) from concentration of the sample
withdrawn at the same port of slurry bubble column (three-phase), for
complete suspended solids the following inequality must be satisfied:
Cs <
(0.155 ln d b + 0.178) ρ s (exp(A) − 1)
(1 − ε G )(1 − A)A
..........(2.26)
Koide
et al [43] proposed that (VGc) increases with increasing number (N)
and pitch (P) of the holes in the gas distributor. The (VGc) was
correlated with N, P, D, and physical properties by the following
equation:
  2
VGc .µ L
δ  D .g.ρ L
= 9.95  
ρL
 ρ  N.σ L





−0.521
4

 g.µ L

 ρ .σ 3
 L L





0.384
..........(2.28)
Abdel-Rahman [44] studied the (VGc) for the three-phase sparged
systems, the experimental results for water with L/D=1.5 and of the
four glycerin solutions were correlated with absolute average error of
9.5% as follows:
 ∆P 

VGc = 4.1C0v.33 G a0.045 
 ρ 
 L 
0.95
 dp

 D





0.47
..........(2.29)
Several of researchers concluded that an increase in solids
concentrations generally reduced the gas hold up [77]. Kara et al
[76] found a strong dependence of gas hold up on solids
concentration at low solid concentration.
Krishna et al [80] proposed a correlation for small bubble hold up
showing its dependence on solids concentration:

ε df = ε df ,0  1 −


0.7 
φs 
ε df ,0 
..........(2.30)
The dense phase gas hold up for the gas-liquid, (εdf,0), can be
estimated using the correction proposed by Reilly et al [81] :
ρG0.96 .σ 0.12
ε trans = ε df ,0 = 0.59 B
ρL
B = 3.85 For air − water system
1.5
..........(2.31)
The above equation is applied for the gas void age at the regime
transition point (εtrans) as suggested by Krishna et al [81].
the presence of solids and solid concentration has an impact on
bubble properties. It was reported that the presence of solids led to
larger bubble size [78]. This was attributed to an increase in the
apparent slurry concentration.
Prakash et al [3] utilized Yeast cell in their column and reported
that, as the yeast concentration increases, the rise velocity of small
bubbles decreases. Viswanathan et al [79], Ostergaard and Micelsen
[82], indicated that for particles less than 1mm in size, the gas hold up
was significantly reduced by the presence of solid particles. This was
attributed to the fact that small particles promote bubble coalescence
which results in higher rising velocities, while the effect of larger
particles was found to be less significant, since these particles instead
tend to cause break-up of bubbles [83].
Many researchers have attempted to predict the size of bubbles, not
only the variation in mean size, but also the distributions of the diameters
and volumes. The mean size of the bubble population in fluidized beds
increases with height above the distributor plate due to coalescence of
bubbles. A new correlation for estimation of mean bubble size of bubble
swarms under dispersed and fluidized operation of bubble columns
employing single and multi-orifice distributors was obtained by [54].
Bubble size for beds of 2, 4 and 6mm diameter glass particles was
measured using both water and octanol solution with surface tension
about half that of water [56].
Large bubbles were observed with 2mm diameter particles,
decreasing with increasing particle sizes. The octanol solution was found
to stabilize much smaller bubbles than water.
The expression of bubble diameter
was proposed in cylindrical
bubble column (Height = 0.9 m and diameter = 0.254 m) as a function of
Bond, Galileo and Froud numbers as well as the ratio of orifice diameter
to the column diameter [58].
………….(2.16)
d b / D = f ( Bo , Ga, Fr, d o / D)
The bubble size is governed by the ratio of forces stabilizing the
bubble and the forces acting to break up the bubble . The bubble is
stabilized by the surface tension forces and the viscous stresses inside the
bubble and de – stabilized by the deformation due to the shear stresses
[61].
The bubble rise velocity was measured in gas –liquid- solid fluidized
beds using an electro– resistivity probe, the probes were analyzed with a
hybrid computer. It is reported as a function of fluidization level, particle
size and position within the bed. [62]
The bubble rise velocity was measured by means of movie photography
in two and three phase fluidized beds [63] . Three solids (1 – 6mm), a
variety of liquids and air were employed as the three phases. The bubble
rise velocity was found to increase with gas velocity but is relatively
insensitive to the liquid velocity, viscosity and surface tensions. The
correlation presented for calculating bubble rising velocity is:
U br = 83.1U L -0.133 U sg 0.341 µ L 0.026
…(2.17)
In the beds of 1.0, 2.3 and 3.0 mm glass beads with variation in U d is
R
R
shown in Figure (2.8). As can be expected, V dr decreases in the droplet –
R
R
disintegrating beds (dp=3.0 mm), whereas V dr increases in the droplet –
R
R
coalescing beds (dp=1.0 mm) with an increase in U d , on the other hand,
R
R
V dr remains almost constant in the beds of 2.3 mm glass beads with
increasing U d .
Figure (2.8): Effect of dispersed phase velocity on the relative
droplet rising (V dr ) in beds of 1.0, 2.3 and 3.0mm glass beads [21]
The optimal operation of a slurry bubble column reactor requires that the
solid phase be fluidized in the liquid phase over the entire height of the
column. The solid phase is fluidized by upward forces caused by rising
gas bubbles and acting against the downward gravitational forces
The settling velocity increases with increasing the particle size,
therefore, higher liquid circulation and turbulence is required to suspend
the solid particles .The tendency of particles to settle can be overcome,
however, by maximizing the dispersion effects resulting from the rising
gas bubbles and enhanced by increasing either the effective reactor
diameter or the flow rate of gas through the reactor [68].
Knowledge of the existing flow regime and identification of the
transition between bubbly flow and churn-turbulent flow is necessary to
provide a clear picture upon which modeling and design efforts for a
particular process can be based. One approach that has been commonly
used in identifying the prevailing regime is based on the concept of the
drift flux, as introduced by [86]. The drift flux, jGL represents the
volumetric flux of gas through a surface moving at the volumetric
average velocity of the dispersion ,(U g ±U L /2), and is given by [87].
j GL = U g ( 1- ε g )
……….(2.20)
where U g is the superficial gas velocity of the flow regime between
the gas and liquid. A plot of j GL vs ε g reveals the gas velocity at which
transition occurs, by the indication of the change in the slope in the curve
Figure (2.11). In the bubbly flow regime, which is characterized by a
uniform bubble size, the drift flux remains approximately constant with
increase in gas velocity and holdup. Upon transition to the turbulent flow
regime, the drift increases sharply with gas holdup.
Figure (2.11): Identification of flow regime from behavior of
drift flux with representation of gas holdup [86].
The aim of the present research is to investigate the effect of the solid
particles on the hydrodynamic parameters (gas holdup and bubble dynamics)
and To develop an empirical correlation to correlate the gas holdup with the
operating variables of the fluidized bed bubble column.
Experimental work
The experiments were performed in one column with inner diameter
of (0.15) m.
The bottom of the column consists of an inverted cone section with
cone angle of 45, the cone section of the column with diameter of 0.15cm
it was made of QVF.
The conical bottom geometry was used in order to minimize the
occurrence of dead spaces at the bottom of the column.
the column was made of QVF glass, and operated in the semi-batch
mode, in which the liquid is stationary and the gas flows upward.
The experimental apparatu is shown schematically and photographically in
Figure () .
10
9
8
5
11
12
7
4
6
3
13
1
2
1 Air-compressor
2 Check valve
3 Air-filter
4 Needle valve
5 Air-flow meter
6 on-off valve
7 Discharge valve
8 Gas distributor
9 QVF column
10 Electroresistivity Probe
11 Interface
12 Pc (PIII)
13 Digital Camera
Air was used as the gas phase. The compressed air was passed through a
stabilizer then was fed to the column.
The gas flow rate was adjusted with the aid of needle valves and a calibrated
rotameter.
Calibrated rotameter of capacity (280) lit/min was used in this work in order
to cover the operating range of the air flow rate, the calibration curve of the
rotameter is illustrated in Appendix (A). The range of superficial gas velocity
which is used in these experiments was varied from (0.03-0.09) m/s, for Dc=
(0.15) m.
3.2.2 Gas Distributor
Air was introduced into the system through a perforated plexiglass of
thickness 3 mm. The holes of the distributor having a circular arrangement. The
shape and dimension of the distributor are shown in Figure (3-3) and listed in
Table (3-1). The design of the air distributor is illustrated in Appendix (B).
Figure(3.3): Shape of the gas distribution ,for Dc=15 cm.
Table (3-1): Specifications of Air Sparger.
Column
Diameter Dc
(cm)
15
No. of Holes
47
Hole
Diameter
(mm)
2
% Free area
0. 836
Digital Camera
Digital camera type (OLYMPUS, C-400/ZOOM) with high resolution (4
pixels) was used in the experimental work to measure the bubble diameter; the
camera was connected to the computer.
3.2.4 Solid Phase
The solid phase which was used in the experiment shown in. Tables (3-2)
and (3-3).
Table (3-2) Physical Properties of Particles used in this study.
Particle
Notation
Type of
Particles
Dp
( mm )
ρs
( Kg / m3 )
Ut
( cm / s )
A
B
C
D
E
PVC
PVC
PVC
Plastic
Plastic
3
1.5
0.65
3
0.5
1025
1025
1025
1150
1150
2.37
0.529
0.09
2.772
0.057
R
Table (3-3) Description of Binary Mixture of Particles
Mixture
Notation
0B
Ma
Mb
Mc
Na
Nb
Nc
Ia
Ib
Ic
Va
Vb
Descriptio
n
1B
A&B
A&C
A&D
A&E
Weight
Ratio
1/2
1:1
1:3
3:1
1:1
1:3
3:1
1:1
1:3
3:1
1:1
1:3
Diameter
Ratio
(large /
small)
Density
Ratio
(heavy /
light)
Ut Ratio
(large /
small)
2
1
4.48
4.6
1
26.33
1
1.122
0.855
6
1.122
41.57
2B
Vc
3:1
Three
concentrations
of
these
particles
(0,
5
and
10)%
kgsolid/kg(water + solid) were used in the experiments of this work.
Elecetroresistivity probe is used in this work to measure the
hydrodynamic parameters which affect the design and performance of
the bubble column, these parameters are: (Local gas hold up, bubble
frequency, bubble rise velocity, number of bubbles and average bubble
diameter).
In all experiments which applied in this work, the level of clear
liquid was kept at 90 cm.
The electroresistivity probe was moved in axial positions, to measure
the local gas hold up in three different positions.
The bubble diameter was measured by using the electororesistivity probe
and was compared with the photographing method and these two methods
were applied to the same column
Results and Discussion
1 Effect of Particle properties on Transition Point
A common procedure to locate the transition point between the
homogeneous and heterogeneous regimes is to apply the drift flux
analysis [83].
The basic quantity is the drift flux, j GL , which represents the gas
flux through a surface moving at the average velocity of the mixture and
is given by:
j GL = U sg (1-ε g )
……………….. 4.1
If the drift flux is plotted versus the gas holdup, the change in slope of the
curve indicates the transition from the homogeneous to the heterogeneous
regime [2].
Figure (4.1) to Figure (4.4) show the drift flux versus the
corresponding gas holdup for the experimental data of the solid
concentrations tested with different particle diameters. The points where
the change of the slope occurs are determinated and the corresponding
superficial velocities (U sg ) are calculated. Table (4-1) represents the
trend of a (0.5mm) and (1.5mm) particles, other experimental data are
cited in Appendix (H). A general comment is that an increase in solid
concentration shifts the transition to slightly lower velocities so decrease
the stability of the homogeneous regime. This behavior can be attributed
to the effect of solid particles which accelerate the rate of bubble
coalescence resulting in higher bubble velocity. The only exception is
the solid particles of (3mm) diameter tend to increase bubbles breakage.
Table
(4-1)
shows
the
transition
between
homogeneous
and
heterogeneous regime (dp=0.5mm and dp=1.5mm). This behavior is in
agreement with the findings of [86].
Table (4-1) Transition between homogeneous and heterogeneous
regime (dp=0.5mm and dp=1.5mm)
Solid
concentration%(w/w)
0
5
10
dp,mm ε trans U trans ,cm/s
0.5
0.333
7.2
1.5
0.333
7.2
0.5
0.126
6.38
1.5
0.17
6.92
0.5
0.078
5
Figure (4.5) shows the effect of particles density on transition
point. The plot shows an opposition relationship between transition
holdup (ε trans. ) and particles density for all operating conditions applied.
This can be attributed to that as particles density increases, with a
simultaneous increase in particle terminal velocity resulting in decrease
of overall gas holdup at specified gas superficial velocity and this lowers
the transition conditions. Table (4-2) shows the terminal velocity
measured experimentally in water for different types of solid particles in
agreement with [87,88].
Table (4-2) Terminal velocity (V t ) of solid particles
Dp Average
diam.(mm)
ρ p Density
g/cm3
Terminal Velocity
(cm/s)
pvc
3
1.025
2.37
pvc
1.5
1.025
0.529
pvc
0.65
1.025
0.09
plastic
3
1.150
2.772
plastic
0.5
1.150
0.057
Particles
Type
Drift flux
8
7
6
5
4
3
2
1
0
ρs = 1150 kg/m3
ρs = 1025 kg/m3
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Overall gas holdup
Figure (4.5,a)
8
ρs = 1150 kg/m3
7
ρs = 1025 kg/m3
Drift flux
6
5
4
3
2
1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Overall gas holdup
Figure (4.5,b)
Figure (4.5): Drift flux vs. overall gas holdup for different densities of
particles, dp=3mm at: (a) Cs=5% (b) Cs=10%
4.1.3 Effect of Solid Composition (Binary Mixture) on Transition Point
Figures (4.6) and (4.7) show the effect of varying composition of
solid binary mixture on stability of homogeneous regime. It is clear from
plots that the effect depends mainly on the percentage of the individual
species. Table (4-3) summarizes this trend in a agreement with [88,89].
Table (4-3) Effect of binary mixture composition on stability of
homogeneous regime
Binary code
ε trans .
U trans .
MA
0.22
6.85
MB
0.19
5.38
MC
0.2437
6.95
IA
0.23
6.94
IB
0.226
6.42
IC
0.245
7
Drift flux
9
Mb
8
Ma
7
Mc
6
5
4
3
2
1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
Overall gas holdup
drift flux
Figure (4.6,a)
9
Mb
8
Ma
7
Mc
6
5
4
3
2
1
0
0
0.05
0.1
0.15
0.2
Overall gas holdup
0.25
0.3
Figure (4.6,b)
Figure (4.6): Drift flux vs. overall gas holdup for binary mixture of
particles, at: (a) Cs=5% (b) Cs=10%
4.2.1 Effect of operating parameters on Gas Holdup
Figures (4.8) to (4.14) show the effect of superficial gas velocity on
the measured local gas holdup and overall gas holdup. All figures
indicate that gas holdup increases with an increase in the superficial gas
velocity, although this increase shows different characteristics in the
homogeneous and heterogeneous regimes. The average gas holdup
increases almost linearly with increasing superficial gas velocity in the
homogeneous regime, while this increase is less pronounced in the
heterogeneous regime, because large bubbles are formed due to bubble
coalescence and these large bubbles have a notable bubble-wake
attraction effect. This behavior is in agreement with the findings of [90]
.
30 cm axial
70 cm axial
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
superficial gas velocity(cm/s)
8
9
10
Figure (4.8,a)
30 cm axial
50 cm axial
0.5
Local gas holdup
local gas holdup
50 cm axial
0.5
70 cm axial
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
Superficial gas velocity (cm /s)
Figure (4.8,b)
8
9
10
30 cm axial
local gas holdup
50 cm axial
70 cm axial
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s
Figure (4.8,c)
Figure (4.8): Local gas holdup vs. superficial gas velocity for different
axial position for ρs =1025 kg/m3,dp=3mm at: (a) Cs=0% ,(b) Cs=5%, (c)
Cs=10%
30 cm axial
50 cm axial
local gas holdup
0.5
70 cm axial
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
superficial gas velocity(cm/s)
8
9
10
Figure (4.11,a)
30 cm axial
Local gas holdup
0.5
50 cm axial
0.4
70 cm axial
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
Superficial gas velocity (cm /s)
Figure (4.11,b)
8
9
10
local gas holdup
0.5
30 cm axial
0.4
50 cm axial
70 cm axial
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s
Figure (4.11,c)
Figure (4.11): Local gas holdup vs. superficial gas velocity for different
axial position for ρs =1150 kg/m3,dp=3 mm at: (a) Cs=0% ,(b) Cs=5%, (c)
Cs=10%
Cs=10%
Overall holdup
Cs=5%
Cs=0
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
superficial gas velocity(cm/s)
8
9
Figure (4.14,a)
Cs=10%
Cs=5%
Cs=0%
Overall holdup
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
superficial gas velocity (cm /s)
Figure (4.14,b)
8
9
10
10
Figure (4.14):Overalll gas holdup vs. superficial gas velocity for different
Cs for ρs =1150 kg/m3 at: (a) dp=3mm ,(b) dp=1.5mm
4.2.3 Effect of Solid Properties on Gas Holdup
A wide range of particles diameter has been investigated to study this
behavior. Figures (4.16) and
(4.17) show the measured overall gas
holdup for various particle diameters, the plots indicate a proportional
relationship between particles diameter and measured gas holdup. This
can be attributed to the fact that rate of bubble coalescence is increased
as the particles diameter decreases. This results in large bubble size
which has larger bubble rise velocity than small bubbles. Gas holdup
decreases as a result of bubble coalescence. This behavior is in
agreement with the findings of [92].
dp=0.65
Overall holdup
dp=1.5mm
dp=3mm
0.25
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.17,a)
dp=0.5mm
Overall holdup
0.25
dp=3mm
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
6
7
superficial gas velocity (cm /s)
8
9
10
Figure (4.17,b)
Figure (4.17): Overall gas holdup vs. superficial gas velocity for
different Particles diameter and Cs=10% at: (a) ρs =1025 kg/m3,(b)
(a) ρs =1150 kg/m3
Figures (4.19) to (4.22) show the measured overall gas holds up
versus superficial gas velocity for different compositions of binary
mixture of particles diameter. Analysis the plots behavior indicates that
the effect of each species on the overall gas holdup depends on its
percentage in the binary mixture. This analysis is of a valuable
hydrodynamic aspect to the industrial reactors where different sizes of a
catalyst particle an utilized. An approximate correlation can be
developed to describe this behavior:
εg = x1 εg + x2 εg
……………(4.2)
where x 1 and x 2 are the weight fraction of particles 1 and 2 respectively.
Cs=10%
Overall gas holdup
Cs=5%
Cs=0
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
superficial gas velocity( cm /s)
Figure (4.19,a)
8
9
10
Cs=10%
Overall gas holdup
0.4
Cs=5%
Cs=0%
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity (cm /s)
Figure (4.19,b)
Cs=10%
Overall gas holdup
Cs=5%
Cs=0%
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.19,c)
Figure (4.19): Overall gas holdup vs. superficial gas velocity for
different Cs and binary mixture of particles at: (a) Ma,(b) Mb,(c) Mc
4.3.1 Effect of operating parameters on Bubble Dynamics
Figures (4.23) to (4.29) show the effect of superficial gas velocity
on bubble rise velocity size for all tested solids. From these Figures one
can notice that there is a slight increase in the bubble behavior with
increasing superficial gas velocity. This increase is attributed to the fact
that the increase in superficial gas velocity increases the probability of
bubbles collision and coalescence resulting in greater bubble size. This
in agreement with [95,96]
Figure (4.31) shows the measured bubble diameter vs. superficial gas
velocity with solid diameter for different values of (U g ) at (Cs = 10%).
This Figure
shows
increase in the bubble rise velocity or bubble
diameter with decreasing the particles diameter. The reason for this
increase is that small particular sizes will increase or enhance the rate of
bubble coalescence, leading to a decrease in gas holdup. This is in
Bubble diameter(mm)
agreement with the work of [99,101].
dp=0.65mm
18
16
14
12
10
8
6
4
2
0
dp=1.5mm
dp=3mm
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity(cm /s)
Bubble diameter(mm)
Figure (4.31,a)
18
dp=0.5mm
16
dp=3mm
14
12
10
8
6
4
2
0
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity(cm /s)
Figure (4.31,b)
Figure (4.31): Bubble diameter vs. superficial gas velocity for different
values of particles diameter and Cs=10% at: (a)ρs=1025 kg/m3 (b)
ρs=1150 kg/m3
Figure(4.33) shows the measured bubble diameter vs. superficial gas
velocity at different values of binary mixture of particles, the bubble
dynamics will be increased when the solid particles are mixed with the
ratio of large percentage of high density with the low percentage of low
Bubble diameter(mm)
density. This is in agreement with the results[104,95].
12
11.5
11
10.5
10
9.5
9
8.5
8
7.5
7
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Ib
Ia
Ic
0
1
2
3
4
5
6
7
Superficial gas velocity(cm /s)
8
9
10
Bubble diameter(mm)
Figure (4.33,a)
12
11.5
11
10.5
10
9.5
9
8.5
8
7.5
7
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Ib
Ia
Ic
0
1
2
3
4
5
6
7
8
9
10
Superficial gas velocity(cm /s)
Figure (4.33,b)
Figure (4.33): Bubble diameter vs. superficial gas velocity for binary
mixture of particles for the same diameter (dp=3mm)at: (a)Cs=5%(b)
Cs=10%
Figures (4.34) and (4.35) represent the solid holdup with
superficial gas velocity, from this figure the solid holdup decreases with
increase in superficial gas velocity and increases with increase in solid
concentration. This is attributed to the fact that the dispersion height (H′ f )
is proportional to the superficial gas velocity according to eqn. ε s
=W s /A c H′ f ρ s ), so for a certain solid loading any increase in dispersion
solid holdup
height leads to a decrease in solid holdup.
0.12
Cs=10%
0.1
Cs=5%
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm/s)
solid holdup
Figure (4.34,a)
0.12
Cs=10%
0.1
Cs=5%
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
superficial gas velocity(cm /s)
Figure (4.34,b)
8
9
10
0.12
Cs=10%
Cs=5%
solid holdup
0.1
0.08
0.06
0.04
0.02
0
0
1
2
3
4
5
6
7
8
9
10
superficial gas velocity(cm /s)
Figure (4.34,c)
Figure (4.34): Solid holdup vs. superficial gas velocity for ρs =1025
kg/m3, different values of Cs and dp at: (a)dp=3mm (b) dp=1.5mm (c)
dp=0.65mm
4.correlations for gas holdup
An attempt was made to formulate a correlation that would permit
the prediction of gas holdup, a variable that greatly affects the bubble
column operation. From the present work and the careful inspection of
the experimental results (from various investigators) it can be concluded
that the gas holdup value is the result of the interaction of several
parameters as follows:
• The superficial gas velocity.
• The physical properties of liquid phase (i.e., viscosity, density,
surface tension).
•
The column cross section.
• Particles diameters.
• Particles densities .
In order to formulate a generalized correlation that would incorporate
the relative effect of all the above parameters, dimensional analysis using
Buckingham's π-theorem was performed. The resulting expression then
has two forms:
4.1 Gas Holdup Correlation for Single State
ε g = 0.17808(
dp
(
dc
) 0.201744 (
u g2
gd c
)
ρs
ρ s − ρl
−0.333189
ρ l u g2 d c 1.086486 ρ l d c u g −0.569585 −0.245182
(
)
(
)
cs
σl
µl
) o.332514 ..........................(4 − 3)
R = 0.96811
error = 0.0049345
4.2 Gas Holdup Correlation for Binary State
U
ε g = 0.057009(
(
d p1
dc
) 0.075001 (
d p2
dc
u g d c ρl
µl
)1.515572 cs
− 0.389035
0.568996
x1
x2
− 0.703610
) 2.443881..........................( 4 − 4)
R = 0.995641008
error = 0.000521
Conclusions
The following major conclusions are drawn from the present study:
1.Experiments show that increasing the solid concentration tends to decrease
the gas holdup.
2.The visual observations and experimental results show that the superficial gas
velocity looks to be the most effective parameter on the gas holdup, where the
(ε g ) increases greatly with increasing the gas velocity .
R
R
3. The results show that there is a proportional relationship between gas holdup
and particles diameter for the specified operating conditions used in the
experiments.
4. It was concluded that the bubble rise velocity is increased with increasing the
solid concentration.
5. From experimental results of bubble diameter which was measured in the
electroresistivity probe method and also in the photographic method, a rational
agreement is obtained between the measured values from the two methods.
6. The bubble rise velocity and bubble diameter increased with decreasing
particles diameter.
7. For binary mixture, it was proved experimentally that the effect of each
species on the hydrodynamic parameters is proportional to its weight fraction
and other corresponding properties in the mixture.