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Numerical analysis of the effect of structural and operational parameters on electric and concentration fields of a lithium electrolysis cell

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Abstract

A fully integrated mass transfer and electrochemical model of a lithium production cell solved using a finite element method is presented. The coupled effect of momentum and mass transfer, kinetics, and electric fields is taken all into account. The turbulent flow resulting from the bubbles generated at the anode is solved based on a k-\(\epsilon\) model. The ohmic overpotential and hyperpolarization due to the bubbles are considered through a resistive layer and bubble coverage at the surface of the anode. Furthermore, the effects of the anode–cathode distance (ACD) and current density on the electric and concentration fields of the cell are simulated. The results of the transient simulation reveal that the diaphragm separates the cell in two regions with different flow fields: a first region between the anode and the diaphragm and a second zone between the diaphragm and the cathode. The flow of bubbles generated at the anode has an important impact only in the first region, where the most important gradients are found. The concentration of ions is uniform in the second region. As expected, the current density plays an important role in the electrokinetic of the cell. The change in the geometry of the cell, studied by varying the ACD or by removing the diaphragm, has an important impact on the cell potential and on the concentration of electroactive species near the electrodes. The cell voltage is reduced by as much as 40% when the diaphragm is removed.

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Abbreviations

c:

Concentration (mol m−3)

D:

Diffusion coefficient (m2 s−1)

Deff :

Effective diffusion coefficient (m2 s−1)

d:

Diameter (m)

E o :

Eotvos number

F:

Faraday‘s constant (A s mol−1)

g:

Earth gravitational acceleration (m s−2)

i:

Current density (A m−2)

i0 :

Exchange current density (A m−2)

im :

Average current density (A m−2)

k:

Turbulent kinetic energy (m2 s−2)

k r :

Reaction rate constant (m s−1)

M:

Morton number

n:

Number of electrons

N:

Mole flux (mol m−2 s−1)

R:

Gas constant (J mol−1 K−1)

R′:

Production term (mol m−3 s−1)

Re:

Reynolds

T:

Time (s)

T:

Temperature (K)

um :

Ions mobility (m2 s−1 V−1)

u T :

Bubble terminal velocity (m s−1)

V:

Velocity vector (m s−1)

x:

Mole fraction

z:

Valence

α:

Transfer coefficient

\(\epsilon\) :

Rate of dissipation of kinetic energy (m2 s−3)

σ:

Conductivity (S m−1)

ρ:

Density (kg m−3)

μ:

Viscosity (kg s−1 m−1)

γ :

Surface tension (N m−1)

Φ:

Potential field (V)

\(\emptyset _{{\text{g}}}\) :

Bubble coverage

η:

Activation overpotential (V)

a, c:

Anode/cathode

b:

Bubble

l:

Electrolyte

i:

Species i

j:

Species j

m:

Average

mix:

Mixture

s:

Electrodes’ surface

T:

Turbulent

*:

Bulk

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Acknowledgements

The authors wish to thank Dr. Mohsen Ariana, Postdoctoral researcher at Université de Sherbrooke, for his useful suggestions. We also appreciate Hydro-Québec for their financial support, for providing us with the experimental results and giving us the opportunity to publish this work. The authors are also grateful to the Natural Sciences and Engineering Council of Canada and Canadian (NSERC) and Network for Research and Innovation in Machining Technology for its financial support.

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Authors and Affiliations

  1. Department of Chemical and Biotechnological Engineering, Université de Sherbrooke, Sherbrooke, QC, J1K 2R1, Canada

    Elaheh Oliaii & Martin Désilets

  2. Laboratoire des Technologies de l’Energie, Institut de recherche d’Hydro-Québec, Shawinigan, QC, G9N 7N5, Canada

    Gaétan Lantagne

Authors
  1. Elaheh Oliaii
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  2. Martin Désilets
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  3. Gaétan Lantagne
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Correspondence to Elaheh Oliaii.

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Oliaii, E., Désilets, M. & Lantagne, G. Numerical analysis of the effect of structural and operational parameters on electric and concentration fields of a lithium electrolysis cell. J Appl Electrochem 47, 711–726 (2017). https://doi.org/10.1007/s10800-017-1073-2

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