micro- and nanoparticle technology fixed and fluidized beds · fixed and fluidized beds micro- and...

21. April 2020

Fixed and Fluidized BedsMicro- and Nanoparticle Technology

Dr. K. Wegner - Lecture 21.04.2020

Micro- and Nanoparticle Technology - FS2020 2

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

Micro- and Nanoparticle Technology - FS2020

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


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


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


1


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:


( )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):


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.


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


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


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.


Applications of packed beds in industry

13

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


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.


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.


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


Examples of fluidized bed reactors

17

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


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/


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


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.


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


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.


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


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).


Source: A. Rhodes, “Introduction to Powder Technology”; 2nd ed. 2008, J. Wiley

Umf: minimum fluidization velocity


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.


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:


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


: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.


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


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

= >−


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:


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


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


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= = =


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

micro- and nanoparticle technology fixed and fluidized beds · fixed and fluidized beds micro- and...

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