Introduction to
Gas-solid Fluidized Bed Reactors
Professor M. H. Al-Dahhan
CHEMICAL REACTION ENGINEERING LABORATORY
Outline/Contents
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Introduction.
Fluidization Flow Regimes.
Overall Gas (Voidage) and solids Hold-up.
Radial and Axial Solids Hold-Up Profiles.
Radial and Axial voidage distribution.
Gas and Solid Mixing.
Scale-Up.
Reactor Modeling.
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INTRODUCTION
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Fluidized Bed Reactor Components
Inlet to cyclone
The material fluidized is a solid (catalyst).
The fluidizing medium is either
a gas or a liquid.
Gas distributor
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Advantages
 It has the ability to
process large volumes
of fluid.
 Excellent gas-solid
contacting.
 Heat and mass transfer
rates between gas and
particles are high when
compared with other
modes of contacting.
 No hot spot even with
highly
exothermal
reaction.
 Ease of solids handling.
Disadvantages
 Broad residence time
distribution of the gas
due to dispersion and
bypass in the form of
bubbles.
 Broad residence time
distribution of solids due
to intense solids mixing.
 Erosion of internals.
 Attrition
of
catalyst
particles.
 Difficult Scale-up due to
complex hydrodynamics.
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Industrial Applications of Fluidized Bed Reactor
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Acrylonitrile by the Sohio Process.
Yang 2003
Fischer-Tropsch Synthesis.
Phthalic anhydride synthesis.
Methanol to gasoline and olefin processes.
Cracking of Hydrocarbons (Fluid Catalytic Cracking, etc).
Coal combustion.
Coal gasification
Cement clinker production.
Titanium dioxide production.
Calcination of AL(OH)3.
Granulation drying of yeast.
Heat exchange
Absorption
Nuclear energy (Uranium processing, nuclear fuel fabrication,
reprocessing of fuel and waste disposal).
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Fluidization Flow Regimes
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Geldart's Classic Classification of Powders
 Group A (Aeratable)
:- (e.g.,
Ammoxidation of propylene) small
mean particle size and/or low particle
density (<~1.4 g/cm3), gas bubbles
appear at minimum bubbling velocity
(Umb).
 Group B (Sand-Like) :- (e.g.,Starch)
particle size 40 μm to 500 μm and
density 1.4 to 4 g/cm3, gas bubbles
appear at the minimum fluidization
velocity (Umb).
Kunii and Levenspiel (1991)
kg^3
 Group C (Cohesive)
:- very fine
particle, particle size < 30 μm, difficult
to fluidize because inter-particle
forces are relatively large, compared
to those resulting from the action of
gas.
 Group D (Spoutable) :- (e.g., Roasting
coffee beans) large particle, stable
spouted beds can be easily formed in
this group of powders.
Diagram of the Geldart classification of
particles, Geldart (1973 ).
Flow Regimes in Fluidized Beds
J. Ruud van Ommen, 2003
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Minimum Fluidization Velocity
This equation can be used to calculate the minimum fluidization velocity
U if the void fraction emf at incipient fluidization is known.
mf
2
 f umf
 p   f g 
3
 s D p mf
1501   mf 

 1.75

  s D p u mf  f

Experimentally, the most common method of measurement requires that pressure drop
across the bed be recorded as the superficial velocity is increased stepwise through Umf
and beyond, Umf is then taken at the intersection of the straight lines corresponding to
the fixed bed and fluidized bed portions of the graph obtained when Pbed is plotted
against U on log-log coordinates.
Kunii and Levenspiel (1991)
Bubbling Fluidization
 This type of fluidization has
been called ‘aggregative
fluidization’, and under
these conditions, the bed
appears to be divided into
two phases, the bubble
phase and the emulsion
phase.
 The bubbles appear to
be very similar to gas
bubbles formed in a
liquid and they behave
in a similar manner. The
bubbles coalesce as
they rise through the
bed.
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Turbulent Fluidization
Turbulent regime has the following features: High solid hold-ups (typically 25-35 %
by volume).
 Limited axial mixing of gas.
 Suitable for exothermic and fast
reactions.
 Good gas-solid contact and hence,
favors reactant conversion.
 high gas flow-rates operation and good
for isothermal operation.
 Favorable bed to surface heat transfer.
Canada et al. 1978
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Some commercial processes in turbulent
fluidization
Process
Particle classification
Typical gas velocity
(m/s)
FCC regenerators
Group A
0.5-1.5
Acrylonitrile
Group A
~0.5
Maleic anhydride
Group A
~0.5
Phthalic anhydride
Group A
~0.5
Ethylene dichloride
Group A
~0.5
Roasting of zinc sulfide
Group A
~1.5
Bi et al. 2000
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Fast Fluidized Bed
 The fast fluidization occurs as a result of
continuing increasing in operating velocity
beyond that required at turbulent
fluidization, a critical velocity, commonly
called the transport velocity (Utr), will be
reached where a significant particle
entrainment occurs.
 The CFB has significant industrial
applications because of its efficiency,
operational
flexibility,
and
overall
profitability (Berruti et al., 1995).
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Transition between Fluidization Regimes.
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Grace (1986a) summarized the effects of particles properties and operating conditions
on fluidization behavior and prepared a flow regime diagram. The flow regime diagram
was further modified by Kunii and Levenspiel (1997).
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For given particles and operating velocity, the gas-solid contact pattern can be
determined using this diagram. Likewise, for a given flow regime, this diagram could
provide available combinations of particle properties and gas velocity.
Yang 2003
Fluidization diagram
Us 
U


Gs
Solid hold-up
 av
Yerushalmi and Cankurt, 1970
Methods for Regime Transition Identification
Several measurement methods have been utilized to
determine the transition from bubbling or slugging to
turbulent fluidization which can be classified into three
groups:
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Visual Observation,.
Pressure Drop-versus Velocity diagram.
local and overall bed expansion.
Based on signals from pressure transducers, capacitance
probes, optical fiber probes, X-ray facilities.
Bi et al. 2000
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Generalized effect of operating and design parameters on
flow regime transition
Parameter
Effect on flow regime transition
Pressure
In general, pressure accelerates the flow regime transition, thereby decrease
transition velocity (Lanneau , 1960, Cai et al. 1989, Yates 1996).
Temperature
Transition velocity increases as the temperature is increased, (Peeler et al.,
1999, Cai et al., 1989 and Foka et al., 1996).
Static Bed Height
The transition velocity was almost independent of the static bed height, which
varied from 0.4 to 1.0 m (Grace and Sun 1990). Similar results were reported by
Cai (1989) and Satija and Fan (1985) with (Hmf/Dt) > 2. On the other hand, for
a shallow fluidized bed of (Hmf/Dt) < 2 with Group B and D particles, Canada et
al. (1978) and Dunham et al. (1993) found that Uc increased with static bed
height. This could be related to the undeveloped bubble flow in shallow beds
before transition to turbulent fluidization can occur (Bi et al. 2000).
Particle Size and
Density
Uc increases with increasing mean particle size and density (Cai et al. 1989, Bi
et al. 2000).
Column Diameter
Transition velocity decreases with increasing column diameter for small column,
becoming insensitive to column diameter for Dt > 0.2 m, (Cai, 1989). Similar
trends were observed by (Zhao and Yang, 1991) with internals.
Internals
Transition to turbulent fluidization tends to occur at lower gas velocities in the
presence of internals which usually restrict bubble growth and promote bubble
breakup.
Effect of column diameter
Cai (1989)
 Uc decreases with increasing column diameter for small columns
(less than 2 m), becoming insensitive to column diameter for Dt >
0.2 m.
 Similar trends were observed by Zhao and Yang (1991) in
columns with internals.
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Some Selected References
 Cai et al., 1989, “Effect of operating temperature and pressure on
the transition from bubbling to turbulent fluidization”, AICHE
Symposium series, 85, 37-43.
 Chehbouni et al., (1994), “Characterization of the flow transition
between bubbling and turbulent fluidization”, Ind. Eng. Chem. Res.,
33, 1889-1896.
 Bi et al., (2000), “A state-of-art review of gas-solid turbulent
fluidization”, Chemical engineering science, 55, 4789-4825.
 Andreux et al. (2005), “New description of fluidization regimes”,
AICHE Journal, 51, No.4, 1125-1130.
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OVERALL GAS (VOIDAGE)
AND SOLID HOLDUP
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Overall gas holdup
It is an important hydrodynamic parameter which is defined as the fraction
of reactor dynamic volume occupied by the gas. Typical relationship
between overall gas (voidage) holdup and superficial gas velocity in where
is shown in following schematic
Avidan and Yerushalmi, 1970
Effect of operating and design parameters on gas holdup or bed
density
Inertial bed
height
It is independent on initial bed height (Hilal et al., 2002).
Particle size
The dimensionless density (/mf) decreases as the particle
size is reduced. The bed expansion is larger for a wide than
a narrow distribution of particles. (Grace and Sun, 1991).
Particle
density
/mf decreases as the particle density decreases.
Column
diameter
The bed expansion increases with increasing bed diameter.
Temperature
The voidage increases with increasing temperature.
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Hilal et al. 2002
Effect of column diameter
 The
bed
expansion
increases with increasing
bed diameter (Volk et al.
1962, Xavier et al., 1978).
 The
bed
expansion
decreases with increasing
beds, a condition he
attributed
to
the
development of bubble
channeling in the larger
beds (De-Groot 1967).
 The bed density is greatest
for the smaller diameter
bed at the same excess
velocity (Hilal et al., 2002).
Matsen 1996
Effect of pressure
 Higher operating pressures reduced the bed expansion (H/Hmf)
(Miller et al., 1981) .
 The increase of bed expansion with pressure (Chiba et al., 1986,
and Chitester et al., 1984) .
 The physical properties of the fluidizing gas, density and viscosity
did not have any significant effect on bed expansion (Denloye, 1982),
and Knowlton,1977).
 Bed expansion increased significantly with pressure but this
influence, very strong at low pressures, seemed to reach a
maximum at approximately 800kPa and decreased thereafter up to
1200kPa (Llop et al., 1995; 2000, and Olowson and Almstedt, 1990) .
Some conflict !!!!!!!!!
Some Selected References
 Avida and Yerushalmi (1982), “Bed expansion in high velocity
fluidization”, Powder technology, 32, 223-232.
 Meller et al., (1984), “The effect of particle density on the hold-up in
a fast fluid bed”, AICHE Symposium series, No.234, 80, 52-59.
 Lee and Kim (1990), “Bed expansion characteristics and transition
velocity in turbulent fluidized beds”, 62, 207-215.
 Hilal et al., (2002), “Solid hold-up in gas fluidized beds”, Chemical
engineering and processing, 41, 373-379.
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Radial and Axial Solids Hold-Up Profiles
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Radial Profile
 Although, overall gas holdup
has been traditionally used
for
characterization
of
hydrodynamics of fluidized
bed columns, it is a single
lumped parameter. Hence,
for detailed characterization,
one need to look at the way
solid is distributed across the
reactor.
Mabrouk et al. 2005
U=0.53 m/s,
sand particle (250 microns, 2.5 g/cm^3)
Bubbling regime, Fiber optical needle probe
 The local solid holdup was
greater
near
the
wall
compared to that near the
centerline and that the radial
particle velocity was nearly
parabolic (Van Zoonen, 1962;
Mabrouk et al. 2005).
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Axial Profile
The axial solid hold-up obtained by fiber optical needle probe and CARPT
shows a quasi linear profile (Mabrouk et al. 2005).
Mabrouk et al. 2005
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Measurement techniques of Radial and Axial Solids Hold-Up Profile
CARPT
Mabrouk et al. 2005
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Some Selected References
 Bi et al., (2000), “A state-of-art review of gas-solid turbulent
fluidization”, Chemical engineering science, 55, 4789-4825.
 Mabrouk et al., “Scale effects on fluidized bed hydrodynamics”
Inter. J. of Chemical Reactor Eng, 2005.
 Schweitzer et al., (2001), “Local gas hold-up measurement in
fluidized bed and slurry bubble column.
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Gas and Solid Mixing
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(a) Axial Solid Mixing
Lee and Kim 1990
Du et al. 2002
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(b) Radial Solid Mixing
Du et al. 2002
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Gas Mixing
(a) Axial Gas Mixing
Foka et al. 1996
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Selected gas mixing studies
Investigators
Model
Tracer
injection
dp (µm)
D(m)
U (m/s)
Uc (m/s)
Dzg (m2/s)
Lee and Kim (1989b)
(Air-CO2)
Diffusion process with
axial and radial
dispersion coefficients
Steady state
362
0.1
0.8
0.88
1.00
1.08
1.20
0.85
0.22
0.235
0.230
0.245
0.215
Li and Weinstein (1989)
(Air-He)
One dimensional
dispersion
Steady state
59
0.152
0.1
0.5
1.3
0.43
0.1
0.55
0.60
Li and Wu (1991)
(Air-H2)
1D pseudohomogeneous
diffusion
Non-ideal pulse
58
0.09
1.0
1.0
1.0
0.44
0.45
0.51
0.56
Foka et al. (1994)
(Air-Ar)
One dimensional
dispersion
Pulse
75
0.1
0.417
0.516
0.614
0.691
0.792
0.892
0.977
1.051
1.142
0.47
0.080
0.102
0.11
0.195
0.130
0.167
0.097
0.060
0.075
Foka et al. (1996)
(Air-Ar)
Two-phase model of
van
Deemter (1980)
Pulse (less than
0.5 s)
75
0.1
0.21
0.4
0.5
0.6
0.7
0.8
0.94
0.55
0.09
0.16
0.19
0.175
0.14
0.13
0.14
Zhang et al. (1996)
(Air-O2)
Pseudo-homogeneous
model with axial and
radial dispersion
Steady state
77.6
0.19
0.392
0.588
0.784
1.078
0.5
0.374
0.514
0.619
0.783
Wei et al. (1993)
(Air-flue gas)
One dimensional
dispersion
Steady state
58
5.76
1.26
1.41
0.41
3.05
3.4
Warsito et al. (2002)
(helium and phosphor)
2-D Dispersion model
Unsteady state
60
0.203
0.21-1.5
0.5
Plotted in Fig.
(b) Radial Gas Mixing
For turbulent fluidized beds, almost all gas mixing studies have been
concentrated on the axial mixing, very limited information is available regarding
the radial gas mixing (Du et al. 2002).
Lee and Kim 1989
Du et al. 2002
Solids flow pattern and mixing
Radioactive particle tracking technique for solids mixing investigations
Mostoufi and Chaouki,
2001
152 mm ID, 1500
mm in height
Experimental setup and the used detectors configuration
Radioactive particle tracking
selected results
Mostoufi and Chaouki,
2001
Solids diffusivities
Mostoufi and Chaouki, 2001
Velocity field, velocity gradient
and axial solid diffusivity
Mostoufi and Chaouki,
2001
Some Selected References
 Lee and Kim (1989), “Gas mixing in slugging and turbulent fluidized
beds”, Chem. Eng. Comm., 86, 91-111.
 Foka et al., (1996), “Gas phase hydrodynamics of a gas-solid
turbulent fluidized bed reactor”, Chemical engineering science,
No.5, 51, 713-723.
 Du, B., Fan, L.-S., Wei, Fan, Warsito, W., “Gas and solids mixing in
a turbulent fluidized bed”, AIChE Journal, 48, No.9, 1896-1909.
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Fluidized Bed Scale-up
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Scale-up criteria
Sanderson and Rhodes,
Glicksman et al, 1993, 1998
2005
Horio et al., 1986
van den Bleek and Schouten, 1996
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Sanderson and Rhodes, 2005
Properties of the Silica Sand Bed Materials Used in the Similarity Experiments
Vertical distance from top surface of distributor plate to each pressure
tapping point.
The tapping point heights correspond to the same dimensionless probe height
(h/Hs) at each scale.
Scale-up criteria evaluation in small scale fluidized beds
Results for the average absolute deviation
of dimensionless pressure for correct and
misscaled beds.
Materials A and B in the 146- and 300-mm
beds, respectively, are correctly scaled.
Materials A* and B* in the 146- and 300-mm
beds, respectively, are also correctly scaled,
but different from the A–B pair.
Comparison of the dimensionless
average cycle frequency for the pressure
fluctuation data for all preliminary
experiments.
Sanderson and Rhodes, 2005
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Scale-up criteria evaluation in large scale fluidized beds
Ranges of Superficial and Dimensionless
Superficial Gas Velocities and Particle
Reynolds Number for the Hydrodynamic
Similarity Experiments*
Comparison of the normalized ensembleaveraged amplitude spectra for the
dimensionless pressure fluctuations
from the 146-mm bed with material A and
the 300-mm bed with mismatched bed
material B* at low gas velocity.
Sanderson and Rhodes, 2005
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Sanderson and Rhodes, 2005
Comparison of the dimensionless average
absolute deviation of pressure measured
from pressure probes located at h/Hs=0.77
and r/R=0 in all five fluidized beds for a
range of dimensionless gas velocities.
Comparison of the dimensionless average
cycle frequency of pressure measured
from pressure probes located at h/Hs=0.46
and r/R = 0 in all five fluidized beds for a
range of dimensionless gas velocities.
All beds, with the exception of the 600-mm
bed with material D, have been scaled using
the simplified scaling criteria.
All beds, with the exception of the 600-mm
bed with material D, have been scaled using
the simplified scaling criteria.
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Sanderson and Rhodes, 2005
Agreement map showing qualitatively how well the pressure fluctuations
from the various probe locations and superficial gas velocities from 1.25
to 3.5Umf match for the scaled fluidized beds.
Black dots indicate the location of the probe tips in the actual measurement
runs; the results have been extended across the bed width assuming the
behavior to be axisymmetric (excellent agreement trends are
indistinguishable; good agreement trends are similar with some scatter; poor
agreement trends are only marginally better than for the misscaled scenario).
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Sanderson and Rhodes, 2005
Comparison of the normalized probability
distributions for the correctly scaled beds
(300 mm, material B; 1560 mm, material D)
with the mismatched bed (600 mm, material
D) at low gas velocity for the probe located
at r/R=0 and h/H=0.2.
Comparison of the normalized probability
distributions for the correctly scaled beds
(146 mm, material A; 300 mm, material B;
1560 mm, material D) at high gas velocity
for the probe located at r/R=0 and
h/H=0.77.
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Additional evaluation for scale-up criteria, Glicksman et al., 1993
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Low velocity
High velocity
Solid fraction profiles, glass particles
Solid fraction profiles, plastic particles
Selected References
1. Sanderson, John, and Rhodes, Martin, Bubbling Fluidized Bed Scaling Laws:
Evaluation at Large Scales, AIChE Journal, 2005;51 (10): 2686-2694.
2. Glicksman LR, Hyre M, Woloshun K. Simplified scaling relationships for
fluidized beds. Powder Technol. 1993;77:177-199.
3. Horio M, Nonaka A, Sawa Y, Muchi I. A new similarity rule for fluidized bed
scale-up. AIChE J. 1986;32:1466-1482.
4. Glicksman LR. Scaling relationships for fluidized beds. Chem Eng Sci.
1988;43:1419-1421.
5. van den Bleek CM, Schouten JC. Deterministic chaos: A new tool in fluidized
bed design and operation. Chem Eng J. 1993;53:75-87.
6. Schouten JC, van der Stappen MLM, van den Bleek CM. Scale-up of chaotic
fluidized bed hydrodynamics. Chem Eng Sci. 1996;51:1991- 2000.
7. Glicksman LR, Hyre MR, Farrell PA. Dynamic similarity in fluidization. Int J
Multiphase Flow Suppl. 1994;20:331-386.
8. Glicksman LR. Fluidized bed scale-up. In: Yang W-C, ed. Fluidization Solids
Handling and Processing—Industrial Applications. Park Ridge, NJ: Noyes;
1999.
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Reactor Modeling
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Review of Fluidized bed reactor modeling
(Mahecha and Grace et al. 2006).
Predicting the behavior of a gas-solid fluidized-bed reactor requires information on the
stoichiometry, thermodynamics, heat and mass transfer, reaction rates and flow pattern of
the different phases in the reactor (Kunii, Levenspiel, 1990).
Many reactor models have been proposed for fluidized bed reactors.
 In addition to those reviewed by Yates (1983), Crace (1986) and Ho (2003), more recent
ones include (Thompson, Bi et al. 1999), (Abba, Grace et al. 2003) and (Chen, Yang et al.
2004).
 Each of these incorporate a different set of assumptions leading to a different set of
mathematical expression to simulate the reactor.
 Most models are developed for a specific process, or else so simplified that they cannot
adequately describe all important features of reactors and processes of real practical
interest. Moreover, the available models are overwhelmingly restricted to steady state
operation.
 While progress has been made in adding some of the complexities encountered in practice,
e.g. allowance for gradual transitions between flow regimes (Thompson, Bi et al., 1999;
Abba, Grace et al., 2003), volume change due to reaction (Abba, Grace et al., 2002),
membranes to selectively introduce or remove one species (Chen, Prasad et al., 2003),
and use of a sorbent to selectively capture one product component (Prasad, Elnashaie,
2004).
 Until 2005 there are no models general enough to incorporate all of these features. Recent
work has been done to handle and include all these features (Mahecha and Grace et al.
2006), while also facilitating the analysis of dynamic behavior.
FUNDAMENTAL DIFFERENTIAL DYNAMIC MODEL FOR
CATALYTIC SYSTEMS
 “The model is initially developed in rectangular coordinates for simplicity, but can be
transformed to any other coordinate system (e.g. cylindrical curvilinear) using
elementary vector calculus theory of vector operators (Mahecha and Grace et al.
2006).
 This model includes most existing fluid bed reactor models as special cases, allowing
clear connections to be established among the models and showing the significance
and implications of each simplifying assumption. This will lead to a more systematic
approach to fluidized-bed reactor modeling, facilitating what has been called the
“optimum degree of sophistication” (Aris, 1961).
 Once the more general model has been developed and debugged, we will be in a
position to apply it to important and potentially viable industrial processes such as
partial oxidation reactions and hydrogen production processes (Mahecha and Grace
et al. 2006).”
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Generalization of Models
(Mahecha and Grace et al. 2006).
The set of generalizations for the model is as follows:
1)
“The dynamic equations take into consideration in a rigorous manner the heat and mass
capacities of the gases and solids in each pseudo-phase (Elnashaie, Elshishini, 1993).
2)
The model equations can be written in any coordinate system.
3)
The development is for a system of “NC” components and “NR” reactions, depending on the
feedstock/reactions.
4)
The model is not restricted to a single flow regime. Its hydrodynamic parameters can be
calculated as proposed by (Abba, Grace et al., 2003) for several adjacent flow regimes.
5)
Both mass and heat dispersion are included along all coordinate axes (Bird, Stewart et al.,
2002).
6)
The model deals with anisotropic mass diffusion and heat conduction.
7)
The model takes into consideration three-dimensional convective velocities (Bird, Stewart et
al., 2002).
8)
The convective velocities can be calculated using any function (e.g. accounting for changes in
the number of moles and gas volumetric flow (Abba, Grace et al., 2002)). Changes with time,
temperature, pressure and chemical reaction are also covered.”
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Generalization of Models (cont.)
(Mahecha and Grace et al. 2006).
9)
“The model accounts for catalyst chemisorption (Elnashaie, Elshishini, 1993) and
solid capture of any species.
10)
Hydrodynamic parameters are obtained from appropriate correlations and
equations relevant to the different flow regimes (Grace, Abba et al., 1999).
11)
The model accounts for deactivation of catalyst (Chen, Yan et al., 2004).
12)
The model considers the use of membranes to remove certain products (i.e. to
break the thermodynamic barrier) or to supply certain reactants (i.e. to improve the
system selectivity to a desired product). Membrane deactivation fuctions can also
be included (Raich & Foley, 1995).
13)
The catalyst effectiveness factor may differ from “1” (Elnashaie, Elshishini, 1993).
14)
In the energy balance, different expressions for calculating the internal energy
(Smith, Van Ness et al., 1996) can be used including, where appropriate, sensible
and latent heats (in case of change of phase).
15)
The reactor cross-sectional area can vary along the height of the reactor. The
model does not need to be modified when using different geometries.”
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Pseudo-phase approach
Control volumes for the conservation balances include both gas and solid
phases, without ignoring the effect of the solids on the system dynamics (Gas
carried inside the solids and the heat and mass capacitances of the solids are
included in the mole and energy balances).
Solid sorbent (seq)
Terms are included for any non-catalytic solid phase, which sorbs/captures any
of the species in the reactor (i.e. for carbon dioxide capture to enhance steam
reforming and separate CO2 for subsequent sequestration).
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Mole and Energy Fundamental balances
Mahecha and Grace et al. 2006).
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Mole Balance
The molar rate balance over a differential element for phase (p) is given by:
The number of mole balance equations is NC .N(P) where NC is the number of
chemical species and N(P) is the number of pseudo-phases. The generalized mole
balance of each compound in phase (p) is as follows:-
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Energy Balance
The differential energy balance for phase (p) is given by:
Energy dissipation due to viscous effects is neglected. The number of energy balance
equations is N(P) where N(P) is the number of pseudo-phases. The generalized energy
balance for phase (p) is as follows:-
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Pressure Balance
A simplified differential pressure balance in the z direction for phase (p) is given by:
The density of phase (p) can be calculated using the void fraction as:
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Boundary and Initial Conditions



The differential control volume of pseudo-phase (p) has no external exchange with the surroundings.
The interaction of the pseudo-phase with its surroundings should thus be included in the boundary
conditions.
The boundary conditions should be specified according to the geometric arrangement of the system,
and may vary from case to case.
The boundary conditions (i.e. for the simplest single-phase case) may assume axial symmetry, zero flux
at the walls and Danckwerts criteria when the diffusion in the fore and aft sections is negligible
(Danckwerts, 1953). A base set of boundary conditions is displayed in Table 1. Other details of the
model can be found elsewhere (Mahecha-Botero, Grace et al., 2005).
(Mahecha and Grace et al. 2006).
CASE STUDY: APPLICATION OF MODEL TO AN
OXYCHLORINATION FLUIDIZED-BED REACTOR
(Mahecha and Grace et al. 2006)
“Here, as an example of application of the comprehensive model, it
simulates an industrial scale fluidized bed reactor which is carried out with
special emphasis on the oxychlorination process as a means of producing
ethylene dichloride (EDC) from ethylene (ETY). While this represents a
simplified special case of the full model, it demonstrates many of the
features of the model, while also facilitating verification of the numerical
code (written in Matlab 7), since this case has already been solved
previously (Abba et al., 2002) using g-PROMS.
The ethylene oxychlorination process involves complex reactions with
non-linear temperature dependence (Abba, Grace et al., 2002). Despite
the great industrial impact of oxychlorination reactions, few studies are
available in the literature (Carrubba, Spencer, 1970) and detailed studies
(e.g. (Ellis, Abba et al., 2000) are proprietary.”
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CASE STUDY: APPLICATION OF MODEL TO AN
OXYCHLORINATION FLUIDIZED-BED REACTOR (Cont’d)
The reaction network was simplified as suggested by (Abba,
Grace et al., 2002). We assume that the main product is EDC.
Byproducts include a few percent of carbon oxides (COx) and less
than one percent chlorinated hydrocarbons (IMP) that exclude
EDC.
Reactor parameters
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Results
Predicted steady-state ETY molar flows in the
high- and low-density pseudo-phases vs height in
the reactor.
Predicted steady-state oxygen molar flows in
the high- and low-density pseudo-phases vs
height.
(Mahecha and Grace et al. 2006).
Predicted steady-state HCl molar flows in the
high- and low-density pseudo-phases vs height.
Predicted steady-state EDC molar flows in
the high- and low-density pseudo-phases vs
height.
Mahecha and Grace et al. 2006).
Results (Cont’d)
(Mahecha and Grace et al. 2006).
Predicted steady-state H2O molar flows in
the high- and low-density pseudo-phases
vs height.
Predicted steady-state impurity
molar flows in the high- and lowdensity pseudo-phases vs height.
Predicted steady-state COx molar flows in
the high- and low-density pseudo-phases vs
height.
Pressure vs reactor height.
Predicted axial profile of steadystate overall ETY conversion.
Remarks
(Mahecha and Grace et al. 2006).
•
The generalized dynamic model provides a new approach for simulating
complex fluidized–bed catalytic systems.
•
The model is able to describe fluidized bed reactor systems relying on fewer
assumptions than other models in the literature. When different combinations
of assumptions are incorporated in the model, it simplifies to a number of fluid
bed reactor models previously presented in the literature.
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