Modelling of membrane and comparison to the experiment

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Modelling of membrane and comparison to the

experiment

J. Duhamet, J. Theisen, Helmuth Moehwald, Maximilian Pleines, C. Penisson,

J.-Ch. Gabriel, T. Zemb

To cite this version:

J. Duhamet, J. Theisen, Helmuth Moehwald, Maximilian Pleines, C. Penisson, et al.. Modelling of membrane and comparison to the experiment. ICMAT 2019 - International Conference on Materials for Advanced Technologies, Jun 2019, Singapour, Singapore. �cea-02394061�

FROM RESEARCH TO INDUSTRY

Modelling of membrane and

comparison in the case of

pertraction experiments

10

_{International Conference on Materials for Advanced Technologies – Symposium W June 24}

_{, 2019}

J. DUHAMET

1

_{, J. THEISEN}

1

_{, H. MOEHWALD}

2

_,

M. PLEINES

1

_{, Ch. PENISSON}

1

_,

_{J.-Ch. GABRIEL}

1

_{, T. ZEMB}

1

1

_{CEA, France}

Pertraction principle

Liquid-liquid extraction across hollow fibers (membrane)

Interfacial area determined by the geometry of the device

No emulsion is generated

organic

phase

aqueous

phase

fiber

wall

Transfert

at the

interphase

Hollow

fibers

module

Aqueous phase

input

Organic phase

output

Organic phase

input

Aqueous phase

output

Diffusion transport

within the

membrane

Liquid-liquid extraction across membrane



_Advantages

-

No need for density difference between phases

-

No problem of phase emulsification

-

Well defined geometry: easy scale-up

-

Co or counter-current configuration



_Drawbacks

-

Generally lower mass transfer flux compared to classical

extraction devices (mixers-settlers, agitated columns,

centrifuge extractors)

-

Pressure in each phase must be well control to avoid phase

entrainments

-

Risk of clogging

∆𝑃 <

2𝛾𝑐𝑜𝑠𝜃

𝑟

6.3 cm

20 cm

Liqui-Cel® contactor

10,000 fibers

Ext diam 0.3 mm

Thickness 30 µm

Porosity 30%

Exchange area 0,56 m²

Pertraction experimental setup

λ = 584 nm

HDEHP 0.5 M

in Isane IP 175

28 mL

Nd 1g/L

HNO

0.05 M

Spectrophotometric cuvette

10 cm optical path

Q

=100 mL/h

Q

=10 mL/h

Extraction of Nd in co-current closed loop on solvent with HDEHP 0.5M

Online measurement of neodymium

concentration in the output organic

phase by spectrophotometry at

λ = 584 nm

0,9 mm

1,3 mm

2 mm

Characteristics of the membrane:

Material: Polypropylene

Pores size: 200 µm

Porosity: 72%

Tortuosity: ~ 2

Thickness: 400 µm

Manufacturer: Microdyn-Nadir

Evolution of Nd concentration in the outlet solvent

Slope increase from

low

concentrations

till saturation

shell side lumen side

Modelling of extraction through a cylindrical hollow fiber (1/2)

Laminar flow (Re<1) axisymmetric Hagen-Poiseuille flow

e

_m

Q

_org

Q

_aq

r

z

r

_int

r

_cal

r

_ext

Membrane: porosity ε tortuosity τ

Organic channel inside the fiber

Aqueous channel outside the fiber

L

𝑢 𝑟 =

2𝑄

𝑎𝑞

𝜋

𝑟

_𝑐𝑎𝑙

2

− 𝑟

2

+ 𝑟

_𝑐𝑎𝑙

2

− 𝑟

_𝑒𝑥𝑡

2

𝐿𝑛

_𝑟

𝑟

𝑐𝑎𝑙

𝐿𝑛

_𝑟

𝑟

𝑐𝑎𝑙

𝑒𝑥𝑡

𝑟

_𝑐𝑎𝑙

4

− 𝑟

_𝑒𝑥𝑡

4

−

𝑟

𝑐𝑎𝑙

2

_{− 𝑟}

𝑒𝑥𝑡

2

2

𝐿𝑛

𝑟

_𝑟

𝑐𝑎𝑙

𝑒𝑥𝑡

outside the fiber

𝑢 𝑟 =

2𝑄

𝑜𝑟𝑔

𝜋𝑟

_𝑖𝑛𝑡

2

1 −

𝑟

𝑟

_𝑖𝑛𝑡

2

Modelling of extraction through a cylindrical hollow fiber (2/2)

-

General transport equation of a solute in each phase

𝜕𝐶 𝑟, 𝑧, 𝑡

𝜕𝑡

= −𝑢 𝑟, 𝑧

𝜕𝐶 𝑟, 𝑧, 𝑡

𝜕𝑧

+ 𝐷

𝜕

𝜕𝑧

𝜕𝐶 𝑟, 𝑧, 𝑡

𝜕𝑧

+

𝜕

𝜕𝑟

𝜕𝐶 𝑟, 𝑧, 𝑡

𝜕𝑟

+

1

𝑟

𝜕𝐶 𝑟, 𝑧, 𝑡

𝜕𝑟

-

Kinetics of transfer at the interphase between the aqueous phase and the organic phase

mass transfer flux at the interphase

-

Constant or variable distribution coefficient

-

Discretization of equations with finite differences scheme and resolution of the matrix system with a

time implicit scheme using Scilab software

𝐷 = 𝐷

_𝑎𝑞

in the aqueous channel

𝐷 = 𝐷

_𝑜𝑟𝑔

in the organic channel

in the hydrophobic membrane (i.e. filled with organic phase)

𝐷 = 𝐷

_𝑚𝑒𝑚

=

𝐷

𝑜𝑟𝑔

𝜀

𝜏

negligible

𝐾

_𝑑

=

𝐶

𝑜𝑟𝑔 ,𝑒𝑞

𝐶

_{𝑎𝑞 ,𝑒𝑞}

∅ = 𝜀𝑘

_𝑣

𝐶

_{𝑎𝑞 ,𝑖}

−

𝐶

𝑜𝑟𝑔 ,𝑖

𝐾

_𝑑

Resistance to mass transfer

Co

n

cen

tr

at

io

n

r

Aqueous

phase

Membrane

Organic

phase

C

C

C

C

C

e

e

e

Calculation of the mass transfer coefficients from concentration profiles

Determination of the influence of the different terms in the resistance to mass transfer

∅ = 𝐾

𝐶

−

𝐶

𝐾

= 𝑘

𝐶

− 𝐶

= 𝐷

𝜕𝐶

𝜕𝑟

∅ = 𝐾

𝐾

𝐶

− 𝐶

= 𝑘

𝐶

− 𝐶

= 𝐷

𝜕𝐶

𝜕𝑟

∅ = 𝜀𝑘

𝐶

−

𝐶

𝐾

=

𝜀𝐷

𝑒

𝜏

𝐶

− 𝐶

1

𝐾

_𝑜𝑟𝑔

=

1

𝑘

_𝑜𝑟𝑔

+

𝑒

_𝑚

𝜏

𝜀𝐷

_𝑜𝑟𝑔

+

𝐾

_𝑑

𝜀𝑘

_𝑣

+

𝐾

_𝑑

𝑘

_𝑎𝑞

resistance in

aqueous phase

interfacial

resistance

resistance in

organic phase

membrane

resistance

Variation of distribution coefficient of Neodymium Kd

Set of parameters

-

D

_aq

= 5.8 10

-10

_m².s

-1

_{(experimental value*)}



D

_org

= 10.6 10

-11

_m².s

-1

_{(derived from experimental value* for [HDEHP] = 1 M and corrected for [HDEHP] = 0.5 M}

according to the variation of the viscosity)

-

Porosity = 72% (Mercury porosimeter)

-

Tortuosity = 2.6 Value adjusted to fit all the data (manufacturer’s data ~ 2)

-

Third phase at [Nd]

= 13 g.L

-1

_{(experimental value) blocking of the diffusion in the third phase layer}

Parameters of the model

0 20 40 60 80 100 120 140 0 0.1 0.2 0.3 0.4 0.5 0.6 Kd = [ Nd ]org /[ Nd ]aq [Nd]aq(g.L-1)

Third phase

formation

SAXS spectra of the third phase

Evolution of Nd concentration in the pertraction device

A

O

A

0

1 g/L

[Nd]

= 1 g L

A = 100 mL h

_{O = 10 mL h}

Nd concentration in the output organic phase (simulations/experiment)

Blocking of the diffusion in the third phase layer must

be taken into account to fit with experimental data.

Zoom inside the membrane

concen

tr

ation

Organic phase

Hollow fiber filled with organic phase

Third

phase

Aqueous phase

Building of

the third

phase layer

dismantling of the

Comparison of experimental data versus simulation

Run n° 21 [Nd]

= 1.5 g L

A = 97 mL h

_{O = 10.9 mL h}

Run n° 11 [Nd]

= 1 g L

A = 100 mL h

_{O = 10 mL h}

Run n°18 [Nd]

= 0.5 g L

A = 98.3 mL h

_{O = 9.9 mL h}

Run n° 19 [Nd]

= 0.25 g L

A = 99.2 mL h

_{O = 10.1 mL h}

Run n° 22 [Nd]

= 0.1 g L

A = 101.7 mL h

_{O = 10.7 mL h}

Evolution of resistance to mass transfer

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Resistance

to

transf

er

(s/m

)

[Nd]

(g/L)

Res mem (s/m)

Res org (s/m)

Res aq (s/m)

Res interf (s/m)

Resistance to mass transfer increase in the membrane with Nd concentration because of the

Conclusion and outlooks



_{Good agreement between experiments and simulation of}

neodymium pertraction with HDEHP



No correlation needed for mass transfer coefficients



Modelling of the blocking of the diffusion in the membrane due to third phase

formation fit well with experiments



The model can be used to design and scale-up pertraction process



_{More investigations should be done about the third phase layer:}



Can it be used to increase separation efficiency with other ions?

Acknowledgements

In memory of Helmuth Moehwald

for his kind help and all his wise advice

Maximilian Pleines

Experiments and characterization of third phase

Johannes Theisen

Discussions on experiences and models

Christophe Pennisson

Discussions on experiences and models

Jean-Christophe Gabriel

Co-coordination of REE-CYCLE

Thomas Zemb

Coordination REE-CYCLE

To the European Commission for financial support

FP7/ERC advanced grant #320915

FROM RESEARCH TO INDUSTRY

French Alternative Energies and Atomic Energy Commission -

www.cea.fr