COMPUTATION AND MEASUREMENTS OF MASS

TRANSFER AND DISPERSION COEFFICIENTS IN

FLUIDIZED BEDS

Dimitri Gidaspow1

Mayank Kashyap1, Benjapon Chalermsinsuwan2, Veeraya

Jiradilok1

(1) Chemical and Biological Engineering, Illinois Institute of

Technology, 10W 33rd St., Perlstein Hall, Chicago, IL 60616, (2)

Chemical Technology, Chulalongkorn University, Phayathai Road,

Patumwan, Bangkok, 10330, Thailand

DE-FG26-06NT42736

Thursday, April 23, 2009

NETL 2009 Workshop on Multiphase Flow

Science

PROJECT PUBLICATIONS

DISPERSION COEFFICIENTS

• Jiradilok, V., D. Gidaspow, and R.W. Breault, “Computation of gas of solids dispersion

coefficients in turbulent risers and bubbling beds,” Chemical Engineering Science 62 (2007)

3397-3409

• Jiradilok, V., D. Gidaspow, R.W. Breault, L.J. Shadle, C. Gunther, and S. Shi, “Computation of

turbulence and dispersion of cork in the NETL riser”, Chemical Engineering Science 63 (2008)

2135-2148

MASS TRANSFER COEFFICIENTS

• Chalermsinsuwan, B., P. Piumsomboon, and D. Gidaspow, “Kinetic theory based computation

of PSRI riser- Part I: Estimate of mass transfer coefficient”, Chemical Engineering Science, 64

(2009a) 1195-1211

• Chalermsinsuwan, B., P. Piumsomboon, and D. Gidaspow, “Kinetic theory based computation

of PSRI riser- Part II: Computation of mass transfer coefficient with chemical reaction”, Chemical

Engineering Science, 64 (2009b) 1212-1222

• Kashyap, M. and Gidaspow, D, “Measurement of mass transfer coefficients in a bubbling bed

with ozone decomposition”, Paper in preparation

IMPROVED FUTUREGEN CONCEPT

• Gidaspow, D. and V. Jiradilok, “Nanoparticle gasifier fuel cell for sustainable energy future,”

Journal of Power Sources 166 (2007a) 400-410

• Gidaspow, D. and V. Jiradilok, “Efficient Coal Gasifier-Fuel Cell with CO2 Sequestration,” The

Clearwater Coal Conference, The 32nd International Technical Conference on Coal Utilization &

Fuel Systems, Clearwater, Florida, U.S.A. June 13, 2007b

kmkvkkt

kk&=⋅∇+

∂

∂)(

)(ερ

ερ

[ ] kk

N

l

klkkkkkkkkkk vmvvgvv

t

v ~)(~)()(

&+−+⋅∇+=⋅∇+∂

∂∑βτρεερ

ερ

[ ] [ ][ ] [ ]

[ ] [ ] [ ]IvvvS

SIvP

k

T

kkk

kkkkkk

⋅∇−∇+∇=

+∇+−=

3

1)(

2

1

2µξτ

• Continuity Equation for Phase k

• Momentum Equation for Phase k

acceleration of phase ‘k’ = buoyancy + stress + drag force + phase change

• Constitutive Equation for Stress (Above Min. Fluidization)

Kinetic Theory ModelKinetic Theory Model

[ ]sosss geP εθερ )1(21 ++=kinetic collision

- Solid-phase Pressure

• Solid Phase Stress

- Solid-phase Bulk Viscosity

πθ

ρελ )1(3

4 2 egd ossss +=

- Solid-phase Shear Viscosity

( ) πθ

ρεεµ

µ )1(5

4)1(

5

41

1

22

0

egdgege

osssso

s

sdil ++

+++

=

- Radial distribution function - Solid-phase dilute viscosity

[Bagnold(1954)]

13/1

max,

1

−

−=

s

sog ε

ε2

1

96

5θρ

πµ pps d

dil=

)3

1( 2 ><= Cθ

θββγτθρεθρε ApgAssssssss CCqvvt

3:)()(2

3−>⋅<+−−∇=

⋅∇+∂∂

• Fluctuating Energy Equation

- Collisional Energy Dissipation

( )

⋅∇−−= s

s

osss vd

geπθ

θρεγ4

13 22

- Conductivity of Fluctuating Energy

( ) πθ

ρεκεκ )1(2)1(5

61

1

2 2

2

0

egdgege

osssdilso ++

+++

=

21

384

75θπρκ ssdil d=

-Dilute Phase (Eddy Type) Granular Conductivity

)( θκ∇−=q

4

3

8.0for drag, sphere singleon Based -

75.1)(

150

8.0for equation,Ergun on Based -

65.2

2

2

−−

=

>

−+=

<

g

sp

sggsg

d

g

sp

sgsg

spg

gs

g

d

vvC

d

vv

d

εφ

εερβ

ε

φ

ερ

φε

µεβ

ε

[ ]

g

sgpgg

p

pd

pp

p

d

vvd

C

C

µ

ρε −=

>=

<+=

Re

1000 Refor 44.0

1000 Refor Re15.01Re

24 687.0

where,

• Gas-Solid Drag Coefficients

A BRIEF REVIEW

0

1

2

3

4

5

6

7

8

0.70 0.80 0.90 1.00

Bed Void

Heig

ht,

m

Simulation

Experiment

Jiradilok et al. (2006), Chem. Eng. Sci. 61, 5544-5559

Wei et al. (1998) FCC riser

TURBULENT FLOW REGIME

COMPUTED ENERGY SPECTRUM COMPARED COMPUTED ENERGY SPECTRUM COMPARED

TO SINGLE PHASE TURBULENT FLOWTO SINGLE PHASE TURBULENT FLOW

( )fyy

yy

vv

nEv

Λ′′

0.0001

0.001

0.01

0.1

1

10

0.001 0.01 0.1 1 10 100

Wall Region

Central Region

Single Phase Flow

y

f

v

nΛ

Jiradilok et al. (2006), Chem. Eng. Sci. 61, 5544-5559

NETL AND PSRI RISERS

Computation of turbulence and dispersion of cork in the NETL rise,

Jiradilok, V., Gidaspow, D., Breault, R.W., Shadle, L.J., Guenther, C.,

Shi, Shaoping, Chem. Eng. Sci. 63 (2008), 2135-2148

185 CFM

115 PSIG

First Floor

3.6 m

4.1 m

Second Floor

Solids

Exhaust Air Splash Plate

CCD Video Camera

Rotating Table

Detector

γ –Ray

Source

Fiber Optic

Light

Source

Rotating

Transparency

PC Pentium

IIT riser with splash plate and

fluidized downcomer to obtain high

flux

Up flow

Rotating

Transparency

Electric

Motor

Fiber Optic Light

Source

CCD Video

Camera

Probe

0.5 cm ID

Up

flow

7.75 cm

Particle image velocity measurement

system with probe and typical streak

images captured by the CCD camera.

(Gidaspow et al. (2004))

IIT RISER

DISPERSION COEFFICIENTSDISPERSION COEFFICIENTS

Due to particle oscillations, “laminar”

( ) ( )td

v

ttvtvTL ′

′

′+′′= ∫

∞

02

( ) ( ) LTurbulent TavavaD )(′′=

where,

Lagrangian integral time scale

( ) )(avav ′′ Reynolds normal stress in x or y direction

Due to cluster or bubble, “turbulent”

= Turbulent

Kinetic energy

Characteristic

Time×

EL TT ≈ Eulerian integral time scale approximately

equals Lagrangian integral time scaleHinze, H. O., 1965. Turbulence. McGraw-Hill, New York.

tsCoefficienFriction

eTemperaturGranularD nsoscillatioParticles =

For Brownian motion:tCoefficienFrictionnumberAvagadro

RTD

1⋅=

Axial Gas Dispersion CoefficientsAxial Gas Dispersion Coefficients

Radial Gas Dispersion CoefficientsRadial Gas Dispersion Coefficients

0.001

0.01

0.1

1

10

100

0.01 0.1 1 10

Gas Velocity (m/sec)

Ax

ial

So

lid

s D

isp

ersi

on

(m2/s

ec)

Du et al. (2002)

Thiel and Potter (1978)Aviden and Yerushalmi (1985)

Wei et al. (1998)Wei et al. (1995)

Gidaspow et al . (2004), IIT RiserNETL unit, 850µm Cork particles

Jiradilok et al . (2006), FCC particles

2 m.

4 m.

6 m.

This study (Bubbling Bed, 500µm)

Experiment

Computation

Bubble

Computation, 1 atm

Single particle

oscillation

Cluster

Computation

NETL ,

Cork particles

Axial Solids Dispersion CoefficientsAxial Solids Dispersion Coefficients

0.001

0.01

0.1

1

0.1 1 10

Gas Velocity (m/sec)

Rad

ial S

olid

s D

isp

ersi

on

(m2/s

ec)

Du et al.(2002)

Koenigdorff and Werther (1995)

Wei et al. (1998)Wei et al. (1995)

Jiradilok et al. (2006), FCC particles

2 m.

4 m.

6 m.

This study (Bubbling Bed, 500µm)

Experiment

Computation

Bubble

Computation, 1

atm

Cluster

Computation

Radial Solids Dispersion CoefficientsRadial Solids Dispersion Coefficients

IIT 2-D FLUIDIZED BED

INSTANTANEOUS VELOCITES

H = 69.85 cm

Ug = 46.67 cm/s

t = 1/250 s

0

500

1000

1500

2000

2500

-30 -20 -10 0 10 20 30 40 50 60 70 80

Axial velocity (cm/s)

Nu

mb

er

of

part

icle

s

0

500

1000

1500

2000

2500

-25 -20 -15 -10 -5 0 5 10 15 20 25 30

Radial velocity (cm/s)

Nu

mb

er

of p

art

icle

s

GRANULAR TEMPERATURE

Comparison of laminar and turbulent granular temperatures

in IIT 2- D circulating fluidized bed and IIT riser

2.54 x 10-36.67 x 10-3Right Wall2-D CFB, 75 µm

FCC particles

2.61 x 10-29.48 x 10-2WallIIT Riser, 1093 µm

2-D CFB, 75 µm

FCC particles

System

Granular Temperature, m2/s2

Center

Radial Position

6.73 x 10-31.27 x 10-2

Turbulent due to

cluster

oscillations

Laminar due to

individual

particle

oscillations

2.54 x 10-36.67 x 10-3Right Wall2-D CFB, 75 µm

FCC particles

2.61 x 10-29.48 x 10-2WallIIT Riser, 1093 µm

2-D CFB, 75 µm

FCC particles

System

Granular Temperature, m2/s2

Center

Radial Position

6.73 x 10-31.27 x 10-2

Turbulent due to

cluster

oscillations

Laminar due to

individual

particle

oscillations

Mixing is on the level of particles

GRANULAR TEMPERATURES

1

10

100

1000

10000

100000

1 10 100 1000 10000

Gas Velocity (cm/sec)

Gran

ula

r T

em

peratu

re (

cm2

/sec

2)

Gidaspow and Huilin(1996) 75µm FCC Polasenski and Chen(1999) 94µm FCC

Cody et al(1996) 70µm FCC Polasenski and Chen(1997) 94µm FCC

Jung(2003) 42µm Cody et al(1996) 63µm

Tartan and Gidaspow(2004) 530µm Campbell and Wang(1991) 500µm

Cody et al(1996) 420µm Polasenski and Chen(1997) 283µm

Cody et al(1996) 297µm Jung(2003) 530µm

Jiradilok et al(2005) 75µm FCC Bubbling beds, 530µm

Bubbling beds with a jet, 42µm This study, Simulation, IIT riser, Wall (1093 µm particles)

This study, Experiment, IIT riser, Wall (1093 µm particles) This study, Experiment, 2-D CFB, Center (75 µm FCC)

This study, Experiment, 2-D CFB, Right Wall (75 µm FCC) Driscoll et al .- (Riser) 10 nm (2006)

Driscoll e t al .- Rect. Bed 10 nm (2006) Kashyap et al . (2008)- 10 nm, 0 kV/cm

Kashyap et al . (2008)- 10 nm, 0.70 kV/cm Kashyap et al . (2008)- 10 nm, 1.05 kV/cm

Kashyap et al . (2008)- 10 nm, 1.40 kV/cm

10 nm silica

particles

•No bubbles

•No core-

annular flow in

IIT 2 story riserIIT riser (1093

µm particles)

Simulations

Experiments

IIT 2-D

bubbling bed

(75 µm FCC)

AXIAL SOLID DISPERSION COEFFICIENTS

0.0001

0.001

0.01

0.1

1

10

100

1000

0.01 0.1 1 10 100

Gas Velocity (m/sec)

Ax

ial

Soli

ds

Dis

persi

on

(m2

/sec)

Fan et al . (2002)

Thiel and Potter (1978)

Aviden and Yerushalmi (1985)

Wei et al. (1998)

Wei et al. (1995)

This study (Simulation, wall); 4.5 m; 14 m/s

This study, IIT riser, 1093 µm

This study, 2-D Bed, Center, 75 µm FCC

This study, 2-D Bed, Right Wall , 75 µm FCC

Experiment (laminar)

Simulations (laminar)

Experiment (turbulent)

Simulations (turbulent)

IIT 2-D

bubbling bed

(75 µm FCC)

IIT riser (1093

µm particles)

RADIAL SOLID DISPERSION COEFFICIENTS

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

0.1 1 10 100

Gas Velocity (m/sec)

Ra

dia

l S

oli

ds

Dis

per

sio

n (

m2/s

ec) Fan et al .(2002)

Koenigdorff and Werther (1995)

Wei et al. (1998)

Wei et al. (1995)

This study (Simulation, wall); 4.5 m; 14 m/s

This study, IIT riser, 1093 µm

This study, 2-D Bed, Center, 75 µm FCC

This study, 2-D Bed, Right Wall, 75 µm FCC

IIT 2-D bubbling bed –

Center (75 µm FCC)

IIT 2-D bubbling bed –

Right wall (75 µm FCC)

IIT riser (1093

µm particles)

Simulations

Experiments

OZONE DECOMPOSITION REACTION EXPERIMENTAL

SETUP

OZONE CONCENTRATION

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1 1.2

Height (m)

Ozo

ne

co

nc

en

tra

tio

n (

PP

M)

Ug = 28.9 cm/s; H0 =0.054 m

Ug = 33.74 cm/s; H0 = 0.054 m

Ug = 34.34 cm/s; H0 = 0.054 m

Ozone decomposition reaction Ozone decomposition reaction ��������

Conservation of species equation in the code:Conservation of species equation in the code:

A one dimensional approximation leads to:A one dimensional approximation leads to:

where, where, ““KK”” is the overall rate constant given by the additive is the overall rate constant given by the additive

resistance concept asresistance concept as

Sherwood number, Sherwood number,

COMPUTATION OF SHERWOOD NUMBERS AND MASS COMPUTATION OF SHERWOOD NUMBERS AND MASS

TRANSFER COEFFICIENTSTRANSFER COEFFICIENTS

)(2)(3 32 gg OO →

reactionvtransfermass kakK

111+=

D

dkSh

ptransfermass=

sO

O

gy KCdY

dCv εε

3

3 −=

isreactioniigig CkvCCt

εεε =∇+∂∂

).()(

PARTICLE CLUSTER DIAMETERPARTICLE CLUSTER DIAMETER

-40

-35

-30

-25

-20

-15

-10

-5

0

0 2 4 6 8 10 12 14

Riser height (m)

Natu

ral lo

gari

thm

of

tim

e-a

vera

ged

ozo

ne m

ola

r

co

ncen

trati

on

kReaction = 3.96 1/s

kReaction = 39.60 1/s

kReaction = 99.00 1/s

kReaction = 198.00 1/s

Particle cluster diameters (m) Method Height (m)

Minimum Maximum Averaged

This study 3.5 0.0064 0.0232 0.0101

7.0 0.0040 0.0238 0.0095

10.5 0.0027 0.0150 0.0087

Averaged 0.0027a 0.0238

b 0.0095

Harris's correlation 3.5 0.0033 0.0151 0.0092

7.0 0.0035 0.0149 0.0092

10.5 0.0034 0.0165 0.0099

Averaged 0.0033a 0.0165b 0.0095

Gu's correlation 3.5 0.0028 0.0154 0.0091

7.0 0.0030 0.0149 0.0089

10.5 0.0029 0.0175 0.0102

Averaged 0.0028a 0.0175

b 0.0094

For PSRI riser Challenge Problem 1, overall mass transfer coeffiFor PSRI riser Challenge Problem 1, overall mass transfer coefficient, cient, KK = 30.81 s= 30.81 s--11

((Chalermsinsuwan, B., P. Piumsomboon, and D. Gidaspow, “Kinetic theory based computation of PSRI riser- Part II:

Computation of mass transfer coefficient with chemical reaction”, Chemical Engineering Science, 64 (2009) 1212-

1222)

The mass transfer coefficient is calculated from equation:The mass transfer coefficient is calculated from equation:

WithWith ddpp = 76= 76××××××××1010--66 mm

aavv = (3= (3××××××××44ππππππππ((particleparticle radiusradius22)) / (4)) / (4ππππππππ((particleparticle radiusradius33)) ))

= 3/particle radius = 3/particle radius

= 3/(= 3/(ddpp/2)/2)

= 3/((76= 3/((76××××××××1010--66)/2) = 78947.37 m)/2) = 78947.37 m--11

kkreactionreaction = 39.60 s= 39.60 s--11

Note that the overall resistance, 1/Note that the overall resistance, 1/KK, and the reaction resistance, 1/, and the reaction resistance, 1/kkreactionreaction, are close , are close

to each other. This implies that the mass transfer resistance isto each other. This implies that the mass transfer resistance is small.small.

Therefore,Therefore, kkmassmass transfertransfer aavv = 138.71 s= 138.71 s--11 andand

kkmassmass transfertransfer = 0.0018 = 0.0018 m/sm/s

The Sherwood number is calculated from equation:The Sherwood number is calculated from equation:

With With DD = 2.88= 2.88××××××××1010--55 mm22/s/s

Therefore, Therefore, ShSh = 0.0046 = 0.0046

EXAMPLE OF SHERWOOD NUMBER AND EXAMPLE OF SHERWOOD NUMBER AND

MASS TRANSFER COEFFICIENTMASS TRANSFER COEFFICIENT

reactionvtransfermass kakK

111+=

D

dkSh

ptransfermass=

•• Example: Simulation of PSRI riser with Example: Simulation of PSRI riser with kkreactionreaction = 39.6 s= 39.6 s--11

COMPUTATION OF MASS TRANSFER COEFFICIENTS COMPUTATION OF MASS TRANSFER COEFFICIENTS

Apparent low mass transfer coefficients in PSRI riser with kreaction = 39.6 s-1

For Sh = 0.0111, Shcluster = 1.46

Shcluster = Shparticle x (dcluster/dparticle)

dcluster = 0.87 to 1.01 cm

dparticle = 76 microns

Shcluster = 131 x Sh

EFFECTIVE RATE CONSTANT

saveragegg KCdY

dCv εε −=

Differential reactor analysis

Cluster regimekreaction = 14.45 sec-1

K = 3.62 sec-1

kmass transfer = 0.0000611 m/s

Sh (bubbling) = 0.00016

2

)(

2

)(

)(

)( 2121

12

12 ssg

CCK

YY

CCU

εε ++−=

−−

0

2

4

6

8

10

12

14

16

18

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Height (m)

Eff

ec

tiv

e r

ate

co

ns

tan

t (s

ec

-1)

Ug = 33.74 cm/s-Measured

Ug = 34.34 cm/s-Measured

Ug = 33.74 cm/s-Estimated

Ug = 34.34 cm/s-Estimated

Bubbling bed

CONCLUSIONS

We have shown that the kinetic theory based CFD codes correctly

compute:

(1) Dispersion coefficients

(2) Mass transfer coefficients

Hence, the kinetic theory based CFD codes can be used for fluidized

bed reactor design without any such inputs

BACKUP SLIDES

FUTUREGEN: COAL GASIFIER FUEL CELL SYSTEM

WITH CO2 SEQUESTRATION

BOILERwith heat from fuel cell # 2

CONDENSER

Air at Ambient Temperature

Air 600 - 800oC

Air 600 - 800 oC

Ash, Sulfate etc.

2CO

Steam OH 2

200 Mesh coal

Liquid – Solid Separator

(Cleaning Unit)

Electrolyte+

Solid ImpuritiesClear

Electrolyte

Unreactedfuel

2H CO

SH 2Pollutants e.g.

OH 2

Fuel Cell # 2

22 COOH +

SH 2Pollutants e.g.

Scrubber

(Cleaning Unit)

Air 600 - 800

oC

ANODE

MOLTEN SALT ELECTROLYTE

600 - 800 oC

CATHODE

−− ++↔+ eCOOHCOH 222

2

32

−− +↔+ eCOCOCO 22 2

2

3

−− ↔++ 2

322 22/1 COCOeO

−2

3CO−2

3CO

Liquid

OH 2

2CO SH 2& Pollutants

e.g.

2CO Sequestration

Electricity

Gasifier - MCFC

Pump

2CO

Q

Advantages over Futuregen

• No Oxygen plant

•Water is reused

•70% electrical efficiency

FUTUREGEN: IDEAL GASIFIER FUEL CELL WITH

CARBON FEED

Gasifier - MCFC

Electricity

BOILER

ANODE

MOLTEN SALT ELECTROLYTE 600 - 800 oC

CATHODE

−− ++↔+ eCOOHCOH 222

2

32

−− +↔+ eCOCOCO 22 2

2

3

−− ↔++ 2

322 22/1 COCOeO

−2

3CO −2

3CO

22 COOH + CONDENSER

Air at Ambient Temperature

Air 600 - 800 oC

Air 600 - 800 oC

Liquid

2CO

OH 2

Sequestration

Steam OH2

Carbon

2CO