HEAT AND MASS TRANSFER TO PARTICLES IN FLUIDIZED BED

Bo LecknerAvdelningen för Energiteknik

Chalmers University of TechnologyGöteborg, Sweden

IEA Technical Meeting, Skive, Denmark, October 2017

1

2

CORRELATIONS: SINGLE‐PHASE FLOW

Relationships for single spherical particles in single‐phase flow have been determined by Frössling (1938), Ranz‐Marshall (1952) , Rowe (1965)

Nua=2+0.69Rea0.5Pr0.33   

Sha=2+0.69Rea0.5Sc0.33

Gas conduction and gas convection terms, related to the particle diameter da, are analogous for heat and mass transfer in this case.

Contribution from radiation has to be added in the heat transfer case. 

Heat transfer Nua=hda/k Pr=cp/kMass transfer Sha=da/D Sc=/D

3

HEAT AND MASS TRANSFER BETWEEN THE GAS AND ACTIVE PARTICLES IN THE BED

Two large active particles surrounded by smaller inert particles in a bed with fluidization velocity u.

Gas passes through the space between the particles with velocity umf/ε

di

da

APPLICATIONS Various chemical engineering processes in fluidized bed, e.g. in fuel conversion 

Drying and pyrolysis of fuel particles

Combustion of char

4

CORRELATIONS: FLUIDIZED BEDThere are many correlations giving different results having a similar structure (Shown for heat transfer (Nu) but analogous for mass transfer (Sh))

3 2where / and ( ) /

( / )

i c i g i g s g

n mi a i

Nu h d k Ar d g

Nu const Ar d d

or

0.33,

,where

(Re / ) Pr

/ Re /a c a g a mf m

na a mf mf

f a g

Nu const c

Nu h d k u d

onst

Transformations, ,

/Re /

i a i a

i mf a mf i a

Nu Nu d dRe d d

5

0.5,Re /(1400 5.22 )i mf Ar Ar

Baskakov‐Palchonok’s approach: HEAT AND MASS TRANSFER INTERPOLATED BETWEEN da=di and da>>di

The interpolation formulae:

100 102

104

106

10810

-2

10 -1

100

101

102

Archimedes number, Ar

Nus

selt

or S

herw

ood

num

ber,

Nu,

Sh

Nu, da=di

Nu, da>>di

Sh, da=di

Sh, da>>di

• Sh1 or Nu1  is the low limit da=di• Shi,∞ or Nui,∞  is the large limit da>>di• Shi or Nui are in between the limits

10 -2 100 102 104 10 6 10 810-3

10-2

10-1

100

101

102

10 3

Archimedes number Ar

Mas

s an

d he

at tr

ansf

er c

oeffi

cien

tsre

late

d to

bed

par

ticle

s S

hi o

r Nui

Thin lines da/di= 1 2 5 10 50 100Thick full lines --- ShThick dashed lines---Nu

6

,

1 ,

,

1 ,

( / )

( / )

i ni a

i

i mi a

i

i

i

Nu

S

Nud d

Nu NuSh

d dSh Shh

THE  di=da LIMIT

7

fit to data in the limit da=di (Palchonok et al., 1992)

Nu1 = 6 + 0.117Ari0.39 Pr0.33 Sh1 =2εmf + 0.117Ari0.39 Sc0.33

100

102

104

106

10810

-1

100

101

102

Ar

Sh1

----- da=di, Palchonok's correlation* Baskakov et al.+ Hsiung and Thodos Palchonok and Tamarin

100

102

104

106

10810

0

101

102

Ar

Nu 1

da=di ----Palchonok's correlation+ Turton and Levenspiel* Baskakov et al. (10-->6)o Palchonok and Tamarin Scott et al.(2-->6)

THE LARGE ACTIVE PARTICLE LIMIT  da>>di

8

Transfer to a large, fixed, and rounded object in a fluidized bed, Baskakov (1973),

0.19 0.5 0.33, 0.85 0.006 PriNu Ar Ar

0.5 0.33, 0.009iSh Ar Sc

The mass (and heat) transfer coefficient goes to asymptotic values as da∞

(data from Prins 1987)

0 0.5 1 1.5 2x 10

4

0

0.005

0.01

0.015

0.02

0.025

Ar

Lim

iting

mas

s tra

nsfe

r coe

ffici

ent m

/s

Large particle asymptoteaccording to Baskakov

0.5 tmes the above

Lines according to Baskakov.o asymptotic value: Prins diagramx limiting value of da-->infinity: Prins correlation

0 0.5 1 1.5 2 2.5x 10

4

250

300

350

400

450

500

550

600

650

Ar

h a a

sym

ptot

, W/m

2 K

o Prins heat transfer data, da--> infinity----Large-particle limit, Baskakov

AVAILABLE HEAT TRANSFER CORRELATIONS

9

Scott et al. 2004

Tsukada and Horio, 1992

Prins, 1987

Babosa 1985

Shah, 1983

Palchonok and Tamarin, 1983

102

104

106

10810

0

101

102

Ar

Nu i

Scott's data (modified)Lines for da/di=1, 2 and 2.75(thick--within range, thin--extrapolated)

0.6 0.26,2 1.0 Re ( )aa mf a

i

dNud

HT: Scott et al. 2004;

10

102

104

106

10810

0

101

102

Ar

Nu i

Barbosa et al. dataLines for da=0.002-0.010 (thick--within range, thin--extrapolated)o(upper) extapolated for da=dio(lower) extrapolated for da=0.08 m

0.09 0.25,max 5.33 ( )ii

a

dNu Ard

HT: Barbosa et al., 1995;

11

102

104

106

10810

0

101

102

Ar

Nu i

Tsukada and Horio's dataLines for da=0.002-0.020 (thick--within range, thin--extrapolated)o(upper) extrapolated for da=dio(lower) extrapolated for da=0.08 m

0.8 0.2,max ,max( / ) ; (7.5 0.1Pr Re )( / )a a i i mf i aNu d d Nu d d

HT: Tsukada and Horio, 1992:

12

102

104

106

10810

0

101

102

Ar

Nu i

Prins'dataLines for da=0.004-0.020 (thick--within range, thin--extrapolated)o(upper) extapolated for da=dio(lower) extrapolated for da=0.08 m

0.257 0.062,max 3.539 ( ) 0.105( )

n i ii

a a

d dNu Ar where nd d

HT: Prins, 1987;

13

102

104

106

10810

0

101

102

Ar

Nu i

Palchonok and Tamarin's dataLines for da=0.005-0.015, thick lines within range, thin--extrapolated

0.3 0.2 0.07 0.66,max 0.41 ( ) ( )i ii

a a

dNu Ard

HT:Palchonok and Tamarin, 1983;

14

102

104

106

10810

0

101

102

Ar

Nu i

Shah's dataLines for da=0.004-0.020 within rangeo (upper) da=dio (lower) da=0.08 m

0.158 0.195 0.18,max

0.695 0.195,max

7.6 Re ( ) ( ) 40000

0.463Re ( ) 40000

paii opt

a pi

ii opt

a

cdNu for Ard c

dNu for Ard

HT: Shah, 1983;

15

102

104

106

10810

0

101

102

Ar

Nu i

Scott's data (modified)Lines for da/di=1, 2 and 2.75(thick--within range, thin--extrapolated)

OVERVIEW OF THE PUBLISHED HEAT TRANSFER DATA 

16

Fit of heat transfer data0.66

, 1 ,( )( / )i i i i aNu Nu Nu Nu d d

17

SELECTED MASS TRANSFER CORRELATIONS

18

Scala 2007

Hayhurst and Parmar 2002

Prins 1987

102

104

106

10810

-2

10-1

100

101

102

Ar

Sh i

Prins' correlationLines for da=2, 4, 8, 10, 14, 20 mmT=273+65 K, eps=0.4

da=di0.5 Sh (da large)

1

, 0.33 1.05

0.5,

1 Re(0.105 1.505( / ) )

0.35 0.29( / ) Re /

m m

mf mf ii i a

mf mf

i a mf i mf i

Sh Sc d d

m d d and u d

MT: Prins 1987;

19

102

104

106

10810

-2

10-1

100

101

102

Ar

Shi

Scala's datared * measured da=4.6 mmgreen * measured di=0.55 mmo correlation da=0.2; 1; 4.6; 8.2 mm within range+ correlation da=20 mm, Ar>2 10

4 outside range da=di (extrapolated)

Data:T=450+273 Kdensity 2500 kg/m3

D=5.13 10 -6* (T/273) 1.75 m2/s (Sc=2.5)eps=0.44

0.5*Sh (large da)

2.0 0.7 ,.

.MT: Scala, 2007; 

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OVERVIEW OF THE MASS TRANSFER CORRELATIONS

21

COMPARISON PRINS‐SCALA

22

100

101

102

103

104

10510

-2

10-1

100

101

Ar

Sh i

- - - - Prins da=2; 4; 10 mm------- Scala da=2.5; 4; 10 mmScala's conditions

101

102

103

104

10510

-2

10-1

100

101

Ar

Sh i

- - - - Prins da=2; 4; 10 mm------- Scala da=2.5; 4; 10 mmPrins' conditions

Quantity Scala Prins

Temperature, K 723 338

Bed particle density, kg/m3 2500 2750

Voidage, - 0.44 0.40

Diffusivity, m2/s 9.4·10-10T1.75 2.8·10-10T1.75

Sc 0.7 2.6

Scala’s   conditions in bothcorrelations

Prins’ conditions in bothcorrelations

Fit of mass transfer data1.0

, 1 ,( )( / )i i i i aSh Sh Sh Sh d d

23

10-1

100

101

10210

-3

10-2

10-1

100

101

102

Active particle size da mm

Shi

Scala

Prins

Scala

Prins

a

f

cbe

d

T= 723 KDensity 2650 kg/m3

Diffusivity for oxygen in air

di=0.1 mm

di=1.0 mm

CONCLUSIONS

0.66, 1 ,

1.0, 1 ,

( )( / )

( )( / )i i i i a

i i i i a

Nu Nu Nu Nu d d

Sh Sh Sh Sh d d

The agreement between available correlations on heat and mass transfer to active particles in fluidized beds is not extremely high.

However, the data in the measured ranges are at least within the limits of the Baskakov‐Palchonok approach. 

Therefore, an estimate of coefficients is obtained by        

A seemingly more accurate estimation would be given by the  correlation of choice, applied within its measured range. 

It was shown that most correlations (exception Prins’ for mass transfer) give erroneous values when extrapolated to large active particles.

Also, despite the dimensionless representation, the correlations depend on the properties of the media, e.g. the Schmidt number in the case of mass transfer.

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Appendix: HEAT TRANSFER TO AN ACTIVE PARTICLE (a) IN A BED OF INERT PARTICLES (i): Model‐free correlations 

Some available correlations:

Tamarin et al. (1982) 

Tamarin et al. (1985)

Shah (1983) 

Cobbinah et al. (1984)

Prins (1985)

Barbosa et al. (1993) 

Scott et al. (2004), Collier et al. (2004)(Cambridge)                                   

0.207 0.655 ( )aii

dNu Ard

0.3 0.2 0.07 0.66,max 0.41 ( ) ( )a ai

i i

dNu Ard

0.158 0.18 0.805max

0.695 0.805max

7.6Re ( ) ( ) Re 170

0.463Re ( ) Re 170

pa aopt opt

pi i

aopt opt

i

c dNu forc d

dNu ford

0.104 0.464,max 3.254 ( )aa

i

dNu Ard

0.257 0.062,max 3.539 ( ) 0.105( )

n a ai

i i

d dNu Ar where nd d

.0.14 0.15 0.17max

,

0.61 ( ) ( )p i iai p g g

cdNu Ard c

0.6 0.26,2 1.0 Re ( )aa mf a

i

dNud

25

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References

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