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21. April 2020
Fixed and Fluidized BedsMicro- and Nanoparticle Technology
Dr. K. Wegner - Lecture 21.04.2020
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Flow through a packed bed of particles
Applications, e.g. - Flow of liquid or gas through a
filter cake - Flow of reactants through a bed
of catalyst particles- Fixed bed separators for
adsorption of substances- Fixed bed dryer
crossA
HDpipedP
FV
ϕ fraction volume Particle
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Simple cubicpacking
0.526ϕ =0.741ϕ =
Random packing0.6ϕ ≈
Bed structures for monodisperse spheres
Face-centeredcubic packing
εϕ −== 1volume Total
particles of Volume :fraction volume Particle
porosity, void fractionor “voidage”
3
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For simplicity, the dimensionless numbers (e.g. Reynolds-#) are formed with the velocity of the approaching flow uA.
Fluid velocity for fixed beds:
reltionseccross
F0A vA
Vuu ===−
uA: velocity of the approaching flowu0: superficial velocity (“Leerrohrgeschwindigkeit”)vrel: relative velocity
Attention! The real velocity inside pores is:ε
0uvlocal =
!Def.
For a fixed bed with random packing: 02.5localv u≈ ⋅
Particles are stationary: c = 0
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Pressure drop across a packed bedFrench engineer Henry Darcy observed 1856 that the flow of water through a packed bed of sand is governed by:
0p u H∆ ⋅
A few years before, Poiseuille and Hagen investigated laminar flow through capillaries:
1
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1
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The hydraulic diameter DH is defined as:
area surface wettedtube in volume fluid4
perimeter wettedareaflow 4Dh
⋅=
⋅=
Hydraulic diameter for a packed bed:
00
44A
VAVD Fh
⋅⋅=
⋅=
ε
with A0: surface area of pores ≈ surface area of particles
Using the volume-specific surface area: PV VAA ⋅=0
( ) VAVD
Vh ⋅−⋅
⋅⋅=
εε
14
The cross-section is not circular. Use an equivalent diameter:
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( )2201 1 2 02 3
14ebed V
h
u Hp C C C H u AD
εη η
ε ε−
∆ = ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
( )223 0 3
1bed Vp C H u A
εη
ε−
∆ = ⋅ ⋅ ⋅ ⋅ ⋅
C3 typically has values of 3.5 – 5.5 for porosities of 0.32 – 0.45.
Carman-Kozeny equation for laminar flow through randomly packed particles
( )202 3
1180bed
P
H upd
εηε−⋅ ⋅
∆ = ⋅ ⋅( )2 20
3
1180Re
bedF
P P
p uH d
ερ
ε−∆
=or
Hagen-Poiseuille law modified for laminar flow through a packed bed:
ReP < 1
For monosized spheres with AV=6/dP and C3=5 (Rep < 1):
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Empirical correlation covering laminar and turbulent flow:
Applicable to fluids with constant ρF, ηF and to homogeneous beds containing a large number of particles.
empty,Fbed ppp ∆−∆=∆
( )F
P
bed
du
Hp ρ
εεψ ⋅−⋅=∆
20
31 ( )1150 1.75
ReP
εψ
−= +with
Note:
Ergun equation for 1 < ReP < 4000
S. Ergun (1952), Chem. Eng. Prog. 48, 89-94.
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Derive an average specific force for the packed bed by comparing the flow forces (drag force) acting on the bed with its apparent weight:
( )( ) ( )( )1 1bed cross bedD
G B cross P F P F
p A pFnF F A H g H gε ρ ρ ε ρ ρ
∆ ⋅ ∆= = =
− ⋅ ⋅ − − ⋅ ⋅ − − ⋅
( )20
3D F
G B P P F
uFnF F g d
ρψε ρ ρ
= =− ⋅ −
with Ergun-eq.:
( )FPF
PFrn ρ−ρρ
⋅ψε⋅
= 23 43
34
For flow opposing the gravitational force: 1n <
n
forces nalgravitatio
forces inertial
pp dg
uFr⋅
=20
( ) ( )FPF2
Pp Fr43Ren
ρ−ρρ
⋅α=Compare single sphere:
with :
(Re , )pξ ϕ
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Applications of packed beds in industrySeparation processes: Absorption
Packed bed absorption columns used in a natural gas dehydration.Image: Bertsch GmbH; Austria
Laboratory gas purification column with zeolitesImage: W.A. Hammond Drierite Co Ltd, USA
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Applications of packed beds in industrySeparation processes and off-gas treatment: Scrubbing
Scrubbers are used to wash out undesired pollutants from gas streams, esp. acidic gases.In wet scrubbing, pollutants are absorbed in a solution where a packed bed is often used to increase the liquid surface area. In dry scrubbing, pollutants are absorbed on particles (e.g. in a packed bed).
Image: Benitez (2009), Principles and modern applications of mass transfer operations, J. Wiley.
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Applications of packed beds in industry
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Distillation columns in an oil refinery Examples of packing materialPacking in distillationcolumn (B/R Instr. Corp.)
Increase of interface area between liquids and gasses to improve mass transfer and separation efficiency.
Separation processes in manufacturing of chemicals:Distillation, extraction
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Chemical reactions over a fixed bed of catalyst particles Applications of packed beds in industry
Typical particle diameters: 2 mm (high pressure drop) – 10 mm (low specific surface area)Challenge: Heat management, esp. for exothermic reactions
A) Adiabatic and B) multi-tube fixed bed reactor with heat removal.Ertl, Knözinger, Weitkamp, “Handbook of heterogeneous catalysis” Vol 3, Wiley-VCH, 1997
Example: Fischer-Tropsch Synthesis
e.g. nCO + (2n+1) H2 → CnH2n+2 + nH2O
Type B reactor with iron catalyst (200 m3)200 – 250°C, 25 bar. Removal of reaction heat by pressurized(boiling) water.
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Fluidizing a bed of (catalyst) particles can yield to the following advantages over fixed bed reactors:
Fluidized bed reactors
• Smaller particles can be used, increasing the solid-fluid exchange area.
• Uniform temperature distribution due to intensive solids mixing (no hot spots).
• High heat transfer coefficients between bed and immersed heating or cooling surfaces.
• Uniform product in batch-wise process because of intensive solids mixing
• Easy handling and transport of particles due to fluid-like behavior.
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Cycloneseparator
Fluidizationgas, in
Distributorplate
Gas, out
Gas bubbles
Solidsrecirculation
Circulating Fluidized BedFluidizedBed
Ertl, Knözinger, Weitkamp, “Handbook of heterogeneous catalysis” Vol 3, Wiley-VCH, 1997
Examples of fluidized bed reactors
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Examples of fluidized bed reactors
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Example: Fischer-TropschSynthesis with the “Synthol” reactor, a type of circulating fluidized bed reactor
(a) Hopper with Fe-catalyst particles(b) Standpipe with catalyst(c) Riser(d) Heat exchanger tube bundles(e) Reactor
Mean porosity in riser: 85%3 – 12 m/s gas velocity; 350°C
Ertl, Knözinger, Weitkamp, “Handbook of heterogeneous catalysis” Vol 3, Wiley-VCH, 1997
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Synthol Reactor at SasolSasol: South African Synthetic Oil Ltd.(originally) Suid-Afrikaanse Steenkool en Olie
Images: www.sasol.com (right) and UMichigan (top);
http://www.sasol.com/
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Applications of fluidized beds
Physical ProcessesDrying, coating, granulation, absorption, mixing
Chemical ProcessesReaction (on catalyst particles), combustion (e.g. coal),absorption
Example:Fluidized bed coating(“Wurster coater”)
Fluidization air
Distributor plate
Spray nozzle
Coating solution spray
Particle recirculation
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Fluidized bed reactors generally have the following drawbacks:
Disadvantages of fluidized bed reactors
• Expensive solid separation and gas purification because of solids entrained in fluidizing gas.
• Erosion of internals and attrition of solids resulting from high particle velocities.
• Possibility of de-fluidization due to agglomeration of solids “inhomogeneous fluidized bed”
• Backflow of (product) gas because of high solids mixing rate resulting in lower conversion.
• Undesired reaction gas bypass or broadening of the residence time distribution in case of inhomogeneous bed fluidization.
• Scale-up can be difficult.
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States of mobility in fluid-solids systems
Liquid-solidssystems
Dispersion(dense)
Dispersion(dilute)
Fixed bed
increasing fluid velocity
Gas-solidssystems
Fixed bed Bubbles Chokingslugging
Strands Dispersion
Homogeneousfluidized bedIdeal state
Fixed bed → Fluidized bed → Particle transport / conveying
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Powder fluidization according to GeldartGeldart (1973) classified powders according to their fluidization properties in air at ambient T and p:
Group A: Initially non-bubbling fluidization, followed by bubbling fluidization and bed expansion with increasing fluid velocity. Stable bubble size is reached; good mixing and homogeneity. Small particle size and/or low density
Group B: Only bubbling fluidization; coalescence of bubbles. Some bed expansion; good mixing (< Group A), homogeneity.Most powders
Geldart, D. (1973), Powder Technol. 7, 285-292.
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Group C:Very fine cohesive powders, which are incapable of fluidization. Strong interparticleforces. Formation of channels and discrete plugs but no bubbles.
Fluidization problems might be overcome by mechanical action (vibration / stirring)
Source: A. Rhodes, “Introduction to Powder Technology”; 2nd ed. 2008, J. Wiley
Geldart powder classification
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Source: H. Schubert “Handbuch der mechanischen Verfahrenstechnik”, 2003; Wiley-VCH
Geldart powder classification
Sauter diameter
(ρP
–ρ F
) in
kg/m
3
Group D: Large particles. Formation of slowly rising large bubbles that can lead to spouting. Little mixing and bed homogeneity.
A spouting bed (right) is a fluid bed in which the air forms a single opening through which some particles flow and fall to the outside.Image: Rhodes (2008).
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Source: A. Rhodes, “Introduction to Powder Technology”; 2nd ed. 2008, J. Wiley
Umf: minimum fluidization velocity
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Forces in different fluidization states Bulk solids Fluidized bed Solids transport Compressive forces (buoyancy) Viscous forces Gravity Inertial forces Friction forces betw. particles Friction forces particles - wall Impact betw. particles Impact particles - wall Clustering of particles due to shape Adheasive / repulsive forces
x x x x
x x x x x
(x) x
(x) x x
x x x x x x x x
(x) x
Higher particle mobility leads to a larger number of forces. To be considered as well:Spatiotemporal distribution of particles.Velocity, momentum, mass, concentration, temperature,...Even today, the mathematical description of such systems is hardly possible.
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Similarity of fluid-solids flows A general similarity description of fluid-solids flows is not possible.
Further:
( )
1) Geometric similarity of systems
2) Re
3)
4)
A PP
F
AP
P
F
P F
u d const
uFr constg d
const
ν
ρρ ρ
⋅= =
= =⋅
=−
• No forces due to friction, impact or adhesion• Flow direction opposing gravity• Monodisperse spheres• Homogeneous bed: no demixing/segregation
Circulating fluidized beds, solids transport:
0A relu v u c= = −u0: superficial velocity; c: particle velocity
Fixed beds, stationary fluidized beds:
0 ; 0A relu u v c= = =
Simplify:
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Δp in fluidized beds and upright particle transport
Acceleration of particles along dh;differential momentum balance:
dh
u0
u0
p
p-dp c+dc
c
1) Pressure drop keeping particles floating (stationary fluidized bed with height H, Across):
( ) ( ) gHApA FPcrossfloatzcross ⋅−⋅⋅⋅=∆⋅ ρρϕ( )( )
zp n 1floatP FH gϕ ρ ρ
∆⇒ = =
⋅ ⋅ − ⋅
2) Pressure drop due to acceleration of particles (transport)
( ) dcmdpA Pacccross ⋅=⋅
( ) ∫∫ =H
P
H
acccross dcmdpA00
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:nnacc factor load the to onaccelerati particle the of onContributi
( )( )
( )cross z accDacc
G B cross P F
dcA pF dtnF F A H g gφ ρ ρ
⋅ ∆= = ≈
− ⋅ ⋅ ⋅ − ⋅
Total pressure drop: ( ) ( )z z zfloat accp p p∆ = ∆ + ∆
Load factor: ( ) accFPz n
gHpn +=
⋅−⋅⋅∆
= 1ρρϕ
( ) ( )0 0 cross acc cross z z H P z H z PA p A p p m c c m c= = = =⋅ ∆ = ⋅ − = ⋅ − = ⋅ ∆
After the acceleration phase, particle transport can be considered a uniformly moving fluidized bed.
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Pressure drop vs. fluid velocity for fixed and fluidized beds
( )ε ϕ0 01= −
Fluidized bed Expandingfluidized bed
Fluidized bed
Particle transport
Fixed bed
0, L constϕ ϕ = 0 0ϕ ϕ> >
minimum fluidization velocity umf
log
Δp
log u
0 0ϕ ϕ> >
( ) 01 εϕε >−= LL
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Assume monodisperse spheres and homogeneous flow against gravity.
Flow through particle bedsDescription of the states of motion
( ) ( )23Re 1
4F
P PP F
n Fr ραρ ρ
= ≥−
( ) ( )23, Re 1
4F
P PP F
n Fr ρξ ϕρ ρ
= <−Packed bed:
Floating and transportof single particles:
Fluidized bed, floating: ( ) ( )23, Re 1
4F
P PP F
n Fr ρξ ϕρ ρ
= =−
Particle transport: ( ) ( )23, Re 1
4F
P PP F
n Fr ρξ ϕρ ρ
= >−
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Drag coefficient for homogeneous fluidized beds Based on experiments, Lewis, Gilliland and Bauer developed a correlation describing drag in homogeneous fluidized beds by comparison with a individual sphere (α) settling with its terminal velocity:
( ) ( ) ( )( ) 654654 1
.P
.P
PReReRe,ϕ
αε
αϕξ−
==
The correlation can be applied for the range φ ≈ 0.6 (beginning fluidization) to φ → 0 (floating single particles).
sphere, terminal
nAuu
ε= withRe < 1: n = 4.65 (typical)1 ≤ Re ≤ 500: n = 4.45 Re-0.1Re > 500: n = 2.4
Re < 1
W.K. Lewis, E.R. Gilliland, W.C. Bauer (1949), Ind. Eng. Chem. 41, 1104.J.F. Richardson, W.F. Zaki (1954), Trans. Inst. Chem. Eng. 32, 35.
Richardson and Zaki:
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Substitute
( ) ( )3
22
3 Re Re4
p fpp p
f f
g dAr
ρ ρξ
ν ρ
−⋅= ⋅ =
Substitute
( ) ( )3 Re4
3 Reprel f
f p f p
vg v
ρρ ρ ξ
Ω = =⋅ −
p
fprel d
Rev
ν⋅=
rel
fpp v
Red
ν⋅=
depends only on fluid and particle properties!
( )2 2
3
Re3Re 14
p f fp
p p f
ng d
ν ρξρ ρ
= ⋅ ⋅ ⋅ =⋅ −
Archimedes-#
Omega-# or Lijatschenko-#
Proceed similar to the definition of Ar and Ω numbers for single sphere at steady state but now ξ(φ,ReP) instead of α(ReP).
Ar-Ω diagram for fluidized bed
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Ar-Ω diagram forhomogeneous fluidized bedsof monodisperse spheres
Ar =g dP3 (ρP - ρF )νF2 ρF
= 34 ξ (ϕ, ReP) ReP2
Ω =vrel3 ρFνF g (ρP - ρF )
=43
RePξ (ϕ, ReP)
10 4
10 3
10 2
10 1
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
102
103
104
105
106
Ω
ReP = 10 0
n 1
ϕ=0.6
, n=1
10 -2
ϕ=0,
n=1
Schüttgut
Förderung
homoge
ne Wi
rbelsc
hicht
n = 1
Schw
eben
Einz
elpart
ikel
Lock
erung
Sch
üttun
gEr
höhu
ng R
elat
ivge
schw
indi
gkei
t
10-2 10-1 100 101 102 103 104 105 106 107 108 109
Ar
particle transportn>1
bulk solids1
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General Ar-Ω diagram for a fluidized bed taking also inhomogeneous fluidization into account“Red” region:homogeneous fluidized bed(e.g. for liquid-solids systems)“Pink” region:inhomogeneous fluidized bed(often observed for gas-solids systems)
Circulating fluidized beds, particle transp.
0A relu v u c= = −u0: superficial velocity; c: particle velocity
Remember:Fixed beds, stationary fluidized beds:
0 ; 0A relu u v c= = =
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Fluid-solids reactors - Overview
SolidsGas
Bulk solids / Fixed bed Fluidized bed Solids transport
Type of reactor
overflow
throughflow
Fluidized bed
Circulating Fluidized bed
Typical reactors • Muffle kiln • Multi-decker passage kiln • Rotary kiln • Belt-dryer
• Toploader kiln • Grate stoker furnace / kiln • Furnaces for pellets
heating
• Fluidized bed • Fluidized bed roaster • Multi-decker fluidized bed
• Circulating fluidized bed • Venturi fluidized bed
• Flash dryer • Cyclone-preheater • Smelting cyclone • Burner
Particle movement by: Mechanics Gravity Mechanics Gravity
Fluid flow Gravity
Fluid flow
Gas/solids flow counter-flow co-flow
cross-flow
co-flow counter-flow (in steps) cross-flow (in steps)
Co-flow Single stream reflux counterflow (steps)
Particle size small to very large medium to very large medium very small - small very small
Particle residence time hours - days hours minutes seconds or less
Gas residence time seconds seconds seconds or less
Heat & mass transfer very low low - medium high very high very high
Temperature control medium - good bad - medium good very good medium - good
Space-time yield very low - medium medium medium - high high very high
Gas
Solids
Fixed and Fluidized BedsFlow through a packed bed of particles Slide Number 3Slide Number 4Pressure drop across a packed bedSlide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Applications of packed beds in industryApplications of packed beds in industryApplications of packed beds in industryApplications of packed beds in industryFluidized bed reactorsExamples of fluidized bed reactorsExamples of fluidized bed reactorsSlide Number 18Applications of fluidized bedsDisadvantages of fluidized bed reactorsStates of mobility in fluid-solids systemsPowder fluidization according to GeldartGeldart powder classificationGeldart powder classificationSlide Number 25Forces in different fluidization statesSimilarity of fluid-solids flows Δp in fluidized beds and upright particle transportSlide Number 29Slide Number 30Flow through particle beds�Description of the states of motionDrag coefficient for homogeneous fluidized beds Slide Number 33Slide Number 34Slide Number 35Fluid-solids reactors - Overview