Drop-Based Modelling of Coalescence in Batch Settlers Including Polydispersity

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1

Drop-based modelling of

coalescence in batch settlers

including polydispersity

David Leleu, Andreas Pfennig

andreas.pfennig@uliege.be

Products, Environment, and Processes (PEPs)

Department of Chemical Engineering

Université de Liège

www.chemeng.uliege.be/Pfennig

8th International Berlin Workshop (IBW 8) on

Transport Phenomena with Moving Boundaries

25th - 26th October 2018, Berlin, Germany

agenda



settling experiment



ReDrop concept



coalescence model



results

2

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settling cell

3

Leleu, Pfennig (2017). Standardized settling cell to characterize liquid-liquid dispersion. Proceedings of ISEC2017.

continuous phase

time

h

e

ig

h

t

sedimentation

zone

coalesced

disperse phase

t

principles of settling

4

Henschke, Schlieper, Pfennig (2002). Determination of a coalescence parameter from batch-settling experiments. Chemical Engineering J., 85((2-3)), 369-378.

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continuous phase

time

h

e

ig

h

t

_{sedimentation}

zone

coalesced

disperse phase

principles of settling

5 mask of the experiment

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experiment evaluation

7 ReDrop = REpresentative DROPs

time loop

• initialization

• data input

• definition of height elements

for each drop:

drop loop

• sedimentation velocity

• update position

• coalescence between drops

• coalescence with interface

for each height element:

• new hold-up

• new average drop size

• update close-packed zone

• detect settling time

8

Leleu, Pfennig, Bruns (2017). Coalescence in Highly Viscous System. Proceedings of ISEC2017.

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0

2

4

6

0

40

80

120 S

e

d

im

e

n

ta

ti

o

n

v

e

lo

c

it

y

i

n

m

/s

drop diameter in mm

rigid sphere

circulating

drop

oscillating drop

deformed drop

single-drop sedimentation

Kalem, Altunok, Pfennig (2010). Sedimentation behavior of droplets for the reactive extraction of zinc with D2EHPA. AIChE Journal, 56(1), 160-167.

Waheed, Henschke, Pfennig (2004). Simulating sedimentation of liquid drops. International Journal for Numerical Methods in Engineering, 59(14), 1821-1837.

9 comparison of simulation and experiment

experiment

simulation

rigid interface

10

Gross-Hardt, Amar, Stapf, Blümich, Pfennig (2006). Flow dynamics measured and simulated inside a single levitated droplet.

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coalescence model

11

Kopriwa, Pfennig (2016). Characterization of Coalescence in Extraction Equipment Based on Lab-Scale Experiments.

Solvent Extraction & Ion Exchange, 34(7), 622-642.

collision frequency

rcollision =

A

collision

A

cell

tcollision

=

π d1+d2

2 vrel

4Acell h1−h2

12 A

cell

d

1 d

1 +d

2 d

2 h

2 , v

2 h

1 , v

1

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free volume after Boublik and Mansoori

contact probability of two drops in polydisperse dispersion

with

compare: dimensionless density after Carnahan & Starling













3





2 3 2 2 2 2 2 3 2 3

1

8

1

6

1

j i j i j i j i ij

r

g





















V

R

x

N

i m i i m

6

2 







 

_







V

R

N

6

2

3

13

Kopriwa, Pfennig (2016). Characterization of Coalescence in Extraction Equipment Based on Lab-Scale Experiments.

Solvent Extraction & Ion Exchange, 34(7), 622-642.

Coulaloglou & Tavlarides

14

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coalescence probability

15 pnon−coal,Δt

=

exp −

Δt

tcoalescence

pcoal

= 1− exp −

tcontact

tcoalescence

pnon−coal

= exp −

tcontact

tcoalescence

∆t

n=

tcontact

Δt

tcontact

pnon−coal,nΔt

=

_{pnon−coal,Δt}

n

pnon−coal,nΔt

=

exp −

nΔt

tcoalescence

coalescence model: contact time

16 

assumptions:



drops follow

contour during the

sedimentation



detachment angle =

opposite of the

collision angle

α

collision

α

collision

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coalescence time, asymmetric dimple

tcoalescence=

3π1.5μReq

2 4rs∗ σFdrivingh

_min

17

Henschke, Schlieper, Pfennig (2002). Determination of a coalescence parameter from batch-settling experiments. Chemical Engineering J., 85((2-3)), 369-378. Pfennig, Schwerin (1995). Analysis of the Electrostatic Potential Difference in Aqueous Polymer 2-Phase Systems. Fluid Phase Equilibria, 108((1-2)), 305-315.

dodecahedron deformation after Henschke

18

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0

20

40

60

80

100

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16 time in s

s

e

tt

lin

g

c

e

ll

h

e

ig

h

t

in

m

1E-05 1E-04 1E-03 1E-02 1E-01 1E+00

local hold up

ReDrop result

19 status of the model validation

0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.2 0.4 0.6 0.8 1.0

q

0

drop diameter in mm

0 20 40 60 80 100 120 20 40 60 80 100 120 140 160 180

time in s

c

e

ll

h

e

ig

h

t

in

m

0 0 . 2 0 . 4 0 . 6 0 . 8 1 local holdup

20

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0

20

40

60

80

100

120

140

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14 time in s

h

e

ig

h

t

in

m

0.0

0.2

0.4

0.6

0.8

1.0 holdup

ReDrop result

21 close-packed zone

densely packed zone

lag time & system-typical effective diameter

22 average starting drop diameter:

0.05 mm 0.15 mm 0.25 mm

c

o

a

le

s

c

e

n

c

e

p

a

ra

m

e

te

r

0 .1

0

0 .0

5

0

0 .0

2

5

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conclusions



drop-based model

 detailed results



high-holdup flow

 densely-packed zone



sedimentation coalescence

 lag time

 system-typical effective diameter



consistent modelling of coalescence

23

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