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Effect of the design parameters on mass transfer and energy consumption inside a lithium electrolysis cell

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Abstract

A 2D axisymmetric electrochemical model of a lithium experimental cell is solved using a finite element method. The model is considering the coupled effect of momentum, electric, kinetic and mass transfer phenomena. The dense diaphragm used in the setup, which is not hydraulically permeable, separates the cell into two regions: 1 (a) turbulent region, between the anode and the diaphragm, and 2 (a) laminar region between the diaphragm and the cathode. The k-epsilon model is used to solve the turbulent flow resulting from bubbles generation at the anode. A two-phase flow model is also developed to simulate the volume fractions of bubbles and electrolyte in the cell. The non-uniform bubbles distribution over the anode surface, derived from the non-uniform current distribution, has been added to the two-phase model. The effects of the diaphragm length, position and porosity on the electric and two-phase flow fields are simulated. In fact, the diaphragm position and length both influence the current distribution at the surface of electrodes and the velocity distribution in the cell, all of which influence ohmic and kinetic overpotentials. The results show that up to 40% of energy can be saved when running the lithium electrolysis cell with a shorter porous diaphragm located as far as possible from the anode. The maximum current density, found at the bottom corner of anode, is higher when the diaphragm is longer and when it is closer to the anode.

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Abbreviations

A:

Area (m2)

CD :

Drag coefficient

c:

Concentration (mol m−3)

Deff :

Effective diffusion coefficient (m2 s−1)

db :

Bubble diameter (m)

F:

Faraday’s constant (A s mol−1)

Fb :

Volume force (kg m s−2)

FD :

Drag force (kg m s−2)

g:

Gravity acceleration constant (m s−2)

i:

Local current density (A m−2)

i0 :

Exchange current density (A m−2)

k:

Turbulent kinetic energy (m2 s−2)

L:

Length (m)

M:

Molecular weight (kg mol−1)

N:

Ions flux (mol m−2 s−1)

N:

Normal vector

p:

Pressure (kg m−1 s−2)

R:

Gas constant (J K−1 mol−1)

Re:

Reynolds number

T:

Temperature (K)

\({\text{T}}_{{\text{k}}}^{{{\text{turb}}}}\) :

Stress tensor (kg m−1 s−2)

t:

Time (s)

u:

Velocity magnitude (m s−1)

um :

Mobility (m2 s−1 V−1)

ut :

Bubbles terminal velocity (m s−1)

V:

Velocity vector (m s−1)

x:

Mole fraction

z:

Charge number

α0 :

Transfer coefficient

σ:

Electrolyte conductivity (S m−1)

\(\epsilon\) :

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

ε:

Porosity

\({{{\upeta}}}\) :

Activation overpotential (V)

µ:

Viscosity (kg m−1 s−1)

\({{{\uprho}}}\) :

Density (kg m−3)

τ:

Tortuosity

φ:

Volume fraction

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

Bubble coverage

a:

Anode

c:

Continuous phase

d:

Disperse phase

dia:

Diaphragm

i:

Species i

in:

Inlet

h:

Hyperpolarization

mean:

Mean

mix:

Resistive layer

T:

Turbulent

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Acknowledgements

The authors wish to thank Dr. Kamyab Amouzegar 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 (NSERC) 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. IREQ (Hydro-Québec’s Research Institute), Varennes, QC, J3X 1S1, 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. Effect of the design parameters on mass transfer and energy consumption inside a lithium electrolysis cell. J Appl Electrochem 48, 725–737 (2018). https://doi.org/10.1007/s10800-018-1179-1

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  • DOI: https://doi.org/10.1007/s10800-018-1179-1

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