Introduction to Gas-solid Fluidized Bed Reactors

1
Introduction to Gas-solid Fluidized Bed Reactors
Professor M. H. Al-Dahhan
2
Outline/Contents

• 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.

3
INTRODUCTION
4
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
5
Advantages 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.

• 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.

6
Industrial Applications of Fluidized Bed Reactor

• Acrylonitrile by the Sohio Process.
• 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).

Yang 2003
7
Fluidization Flow Regimes
8
Geldart's Classic Classification of Powders

• Group A (Aeratable) - (e.g., Ammoxidation of
  propylene) small mean particle size and/or low
  particle density (lt1.4 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).
• Group C (Cohesive) - very fine particle,
  particle size lt 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.

Kunii and Levenspiel (1991)
Diagram of the Geldart classification of
particles, Geldart (1973 ).
9
Flow Regimes in Fluidized Beds
J. Ruud van Ommen, 2003
10
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.
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
is plotted against U on log-log
coordinates.
Kunii and Levenspiel (1991)
11
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.

12
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
13
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
14
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).

15
Transition between Fluidization Regimes.

• 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).
• 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
16
Fluidization diagram
Solid hold-up
Yerushalmi and Cankurt, 1970
17
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-
• 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
18
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) gt 2. On the other hand, for a shallow fluidized bed of (Hmf/Dt) lt 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 gt 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.
19
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 gt 0.2 m.
• Similar trends were observed by Zhao and Yang
  (1991) in columns with internals.

20
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.

21
OVERALL GAS (VOIDAGE) AND SOLID HOLDUP
22
Overall gas holdupIt 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
23
Effect of operating and design parameters on gas holdup or bed density 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.
24
Effect of column diameter
Hilal et al. 2002

• 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
25
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 !!!!!!!!!
26
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.

27
Radial and Axial Solids Hold-Up Profiles
28
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.
• 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).

Mabrouk et al. 2005
U0.53 m/s, sand particle (250 microns, 2.5
g/cm3)Bubbling regime, Fiber optical needle
probe
29
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
30
Measurement techniques of Radial and Axial Solids
Hold-Up Profile
CARPT

• Mabrouk et al. 2005

31
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.

32
Gas and Solid Mixing
33
(a) Axial Solid Mixing
Lee and Kim 1990
Du et al. 2002
34
(b) Radial Solid Mixing
Du et al. 2002
35
(a) Axial Gas Mixing
Gas Mixing
Foka et al. 1996
36
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 pseudo-homogeneous 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.
37
(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).

Du et al. 2002
Lee and Kim 1989
38
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
39
Radioactive particle tracking selected results
Mostoufi and Chaouki, 2001
40
Solids diffusivities
Mostoufi and Chaouki, 2001
41
Velocity field, velocity gradient and axial solid
diffusivity
Mostoufi and Chaouki, 2001
42
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.

43
Fluidized Bed Scale-up
44
Scale-up criteria
Sanderson and Rhodes, 2005
Glicksman et al, 1993, 1998
Horio et al., 1986
van den Bleek and Schouten, 1996
45
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.
46
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 AB pair.
Comparison of the dimensionless average cycle
frequency for the pressure fluctuation data for
all preliminary experiments.
Sanderson and Rhodes, 2005
47
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 ensemble-averaged
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
48
Sanderson and Rhodes, 2005
Comparison of the dimensionless average absolute
deviation of pressure measured from pressure
probes located at h/Hs0.77 and r/R0 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.
Comparison of the dimensionless average cycle
frequency of pressure measured from pressure
probes located at h/Hs0.46 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.
49
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).
50
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/R0 and
h/H0.2.
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/R0 and h/H0.77.
51
Additional evaluation for scale-up criteria,
Glicksman et al., 1993
52
Low velocity
High velocity
Solid fraction profiles, plastic particles
Solid fraction profiles, glass particles
53
Selected References

1. Sanderson, John, and Rhodes, Martin, Bubbling
   Fluidized Bed Scaling Laws Evaluation at Large
   Scales, AIChE Journal, 200551 (10) 2686-2694.
2. Glicksman LR, Hyre M, Woloshun K. Simplified
   scaling relationships for fluidized beds. Powder
   Technol. 199377177-199.
3. Horio M, Nonaka A, Sawa Y, Muchi I. A new
   similarity rule for fluidized bed scale-up. AIChE
   J. 1986321466-1482.
4. Glicksman LR. Scaling relationships for fluidized
   beds. Chem Eng Sci. 1988431419-1421.
5. van den Bleek CM, Schouten JC. Deterministic
   chaos A new tool in fluidized bed design and
   operation. Chem Eng J. 19935375-87.
6. Schouten JC, van der Stappen MLM, van den Bleek
   CM. Scale-up of chaotic fluidized bed
   hydrodynamics. Chem Eng Sci. 1996511991- 2000.
7. Glicksman LR, Hyre MR, Farrell PA. Dynamic
   similarity in fluidization. Int J Multiphase Flow
   Suppl. 199420331-386.
8. Glicksman LR. Fluidized bed scale-up. In Yang
   W-C, ed. Fluidization Solids Handling and
   ProcessingIndustrial Applications. Park Ridge,
   NJ Noyes 1999.

54
Reactor Modeling
55
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.

56
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).

57
Generalization of Models
(Mahecha and Grace et al. 2006).

• The set of generalizations for the model is as
  follows
• 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).
• The model equations can be written in any
  coordinate system.
• The development is for a system of NC
  components and NR reactions, depending on the
  feedstock/reactions.
• 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.
• Both mass and heat dispersion are included along
  all coordinate axes (Bird, Stewart et al., 2002).
• The model deals with anisotropic mass diffusion
  and heat conduction.
• The model takes into consideration
  three-dimensional convective velocities (Bird,
  Stewart et al., 2002).
• 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.

58
Generalization of Models (cont.)
(Mahecha and Grace et al. 2006).

1. The model accounts for catalyst chemisorption
   (Elnashaie, Elshishini, 1993) and solid capture
   of any species.
2. Hydrodynamic parameters are obtained from
   appropriate correlations and equations relevant
   to the different flow regimes (Grace, Abba et
   al., 1999).
3. The model accounts for deactivation of catalyst
   (Chen, Yan et al., 2004).
4. 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).
5. The catalyst effectiveness factor may differ from
   1 (Elnashaie, Elshishini, 1993).
6. 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).
7. 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.

59
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).
60
Mole and Energy Fundamental balances
Mahecha and Grace et al. 2006).
61
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-

62
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-

63
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
64
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).
65
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.
66
CASE STUDY APPLICATION OF MODEL TO AN
OXYCHLORINATION FLUIDIZED-BED REACTOR (Contd)
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
67
Results
(Mahecha and Grace et al. 2006).
Predicted steady-state ETY molar flows in the
high- and low-density pseudo-phases vs height in
the reactor.
Predicted steady-state HCl molar flows in the
high- and low-density pseudo-phases vs height.
Predicted steady-state oxygen 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).
68
Results (Contd)
(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 COx molar flows in the
high- and low-density pseudo-phases vs height.
Predicted steady-state impurity molar flows in
the high- and low-density pseudo-phases vs height.
Pressure vs reactor height.
Predicted axial profile of steady-state overall
ETY conversion.
69
Remarks
(Mahecha and Grace et al. 2006).

• The generalized dynamic model provides a new
  approach for simulating complex fluidizedbed
  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.