Analysing and optimizing the electrolysis efficiency of a lithium cell based on the electrochemical and multiphase model

Based on an electrochemical multiphysical simulation, a method for analysing electrolysis efficiency has been presented that considers the energy consumption required to produce a single kilogram of lithium and for the production of lithium, rather than the voltage in various parts. By adopting them as the criteria for analysing electrolysis efficiency in the lithium cell, several structural parameters have been optimized, such as the anode radius and anode–cathode distance. These parameters strongly affect the cell voltage and the velocity field distribution, which has a significant impact on the concentration distribution. By integrating the concentration distribution, the lithium production and energy consumption per kilogram, lithium is computed. By appointing the minimum of the chlorine and lithium concentration as the secondary reaction intensity, it is clear where the secondary reaction intensity is strong in the cell. The structure of a lithium electrolysis cell has been optimized by applying an orthogonal design approach, with the energy consumption notably decreasing from 35.0 to 28.3 kWh (kg Li)−1 and the lithium production successfully increasing by 0.17 mol.

The editor assigned to your manuscript has now received comments from reviewers. We would like you to revise your paper in accordance with the referee and Subject Editor suggestions which can be found below (not including confidential reports to the Editor). Please note this decision does not guarantee eventual acceptance.
Please submit your revised paper before 09-Oct-2019. Please note that the revision deadline will expire at 00.00am on this date. If we do not hear from you within this time then it will be assumed that the paper has been withdrawn. In exceptional circumstances, extensions may be possible if agreed with the Editorial Office in advance. We do not allow multiple rounds of revision so we urge you to make every effort to fully address all of the comments at this stage. If deemed necessary by the Editors, your manuscript will be sent back to one or more of the original reviewers for assessment. If the original reviewers are not available we may invite new reviewers.
To revise your manuscript, log into http://mc.manuscriptcentral.com/rsos and enter your Author Centre, where you will find your manuscript title listed under "Manuscripts with Decisions." Under "Actions," click on "Create a Revision." Your manuscript number has been appended to denote a revision. Revise your manuscript and upload a new version through your Author Centre.
When submitting your revised manuscript, you must respond to the comments made by the referees and upload a file "Response to Referees" in "Section 6 -File Upload". Please use this to document how you have responded to the comments, and the adjustments you have made. In order to expedite the processing of the revised manuscript, please be as specific as possible in your response. ********************************************** RSC Associate Editor: Comments to the Author: (There are no comments.) RSC Scientific Editor: Comments to the Author: (There are no comments.) ********************************************** Reviewers' Comments to Author: Reviewer: 1 Comments to the Author(s) In this manuscript, authors reported a modeling study of lithium cell by coupling electric field, flow field and concentration distribution together. They developed a 'multiphase model' using COMSOL software package and conducted optimization calculation to study the lithium and chlorine bubble production. Overall, this is an interesting work, but there are still many places that might need to be further improved and clarified: 1. Since 'lithium electrolysis process' was considered in the model, it is not clear what electrochemical reactions and how they were applied on the electrolyte and electrodes interface in their model. 2. In the '3.2.1 electric field' section, what kind boundary conditions were applied on two electrode surface? and How to couple them with the given equation-5? Besides, it might be not appropriate to use 'equation-5' for both solid electrode and liquid electrolyte since the physical meaning of 'sigma' in them will be different. 3. In section '3.2.2velocity field', parameters including subscripts in given equations should be well explained (e.g. eq-6,8,9,10,11), otherwise, it is very difficult for readers to understand their meanings.
4. In section '3.2.3', 'Ri is equal to the electrolysis reaction generation rate when on the electrodes…', Question is what electrolysis reaction generation rate was used on the electrode surface? 5. In figure 2, it is very confusing which part is electrode, and which part stands for electrolyte, can authors clarify and mark them on the figure? 6. In their Table 3, it is not clear how 'electrochemical reactions' were applied as boundary conditions in the 'Concentration field'. 7. In addition, there are a few typos and grammar mistakes that need to be removed.

Reviewer: 2
Comments to the Author(s) This paper studies the electrolysis efficiency of lithium cell based on electro-chemical and multiphase model. The authors analyzed a series of energy features of the as-studied system. This is an interesting study, which well-suits for the journal. The results are of good novelty and significance. The manuscript is well-prepared. Before it is acceptable, I have several concerns that should be carefully addressed by the authors. Therefore, I recommend that this nice piece of work is acceptable for Royal Society Open Science after a minor revision. Details of my comments are shown as follows. 1. In the introduction the authors may refer to the aluminum reduction cell. 2. The structure of the model was shown before the structured mesh in Figures 2 may be clearer for this article. 3. Line 127, the "starting conditions" is "initial conditions". 4. There are several typos in this manuscript. Please double-check the paper. 5. The author should edit formula alignment and make them more beautiful, such equation 1-5, and 23-24.

Author's Response to Decision Letter for (RSOS-191124.R0)
See Appendix A.

Recommendation? Accept as is
Comments to the Author(s) Authors have addressed my concern adequately, and made necessary changes accordingly. I think this version can be considered for publication It is a pleasure to accept your manuscript in its current form for publication in Royal Society Open Science. The chemistry content of Royal Society Open Science is published in collaboration with the Royal Society of Chemistry.
The comments of the reviewer(s) who reviewed your manuscript are included at the end of this email.
Thank you for your fine contribution. On behalf of the Editors of Royal Society Open Science and the Royal Society of Chemistry, I look forward to your continued contributions to the Journal. Comments to the Author(s) Authors have addressed my concern adequately, and made necessary changes accordingly. I think this version can be considered for publication

Reply:
The reviewer's advice is very valuable for our paper. The authors modified the section of introduction and the boundary conditions in the revised MS.

Action Taken:
In the section of introduction, For the second method, metallic lithium is typically produced by the electrolysis of LiCl, while the raw material resuls from the ore or brine. The molten salt LiCl-KCl (42:58 in mass ratio) with a low eutectic point of 625.15 K has been adapted for electrolysis. These phenomena at each electrode are running according to the following electrochemical reactions: Cathode: + + -→ ( ) Total: 2 →2 ( ) + 2( ) In the section of the boundary conditions, be not appropriate to use 'equation-5' for both solid electrode and liquid electrolyte since the physical meaning of 'sigma' in them will be different.

Reply:
The reviewer's advice is correct and very helpful for the article. The 'sigma' in the electrode and electrolyte is different. However, in these model, the 'sigma' only apply in the electrolyte. The boundary conditions of electric field were applied on the two electrode surface where contact with the electrolyte. The amendment is shown in the Action Taken part.

Action Taken:
In the section of boundary conditions The starting conditions for the electrolysis cell are listed in Table 2. The boundary conditions used in this model are listed in Table 3.

Comment 3
In section '3.2.2velocity field', parameters including subscripts in given equations should be well explained (e.g. eq-6,8,9,10,11), otherwise, it is very difficult for readers to understand their meanings.

Reply:
Thanks very much for the reviewer's advice. The authors revised the manuscript again and modified the section of 3.2.2 in the revised manuscript as shown in the Action Taken part.

Action Taken:
In the 3.2.2, In this equation, u is the speed ( ), p represents the pressure (Pa), is the fluid m • -1 ρ density , g is the gravitational acceleration ( ), and is the effective viscosity.
In this equation, is the added force on the fluid ( , and is the

Comment 4
In section '3.2.3', 'Ri is equal to the electrolysis reaction generation rate when on the electrodes…', Question is what electrolysis reaction generation rate was used on the electrode surface?

Reply:
The reviewer's advice is very valuable for our paper. The description in the original article is wrong. Ri was set to zero in the mathematical model. The authors modified in the revised MS in the Action Taken.

Action Taken:
In the section of 2.2.3, where R i means the homogeneous reaction rate of species i in the electrolyte. In the cell, R i is equal to the electrolysis reaction generation rate when on the electrodes and equals zero.

Comment 5
In figure 2, it is very confusing which part is electrode, and which part stands for electrolyte, can authors clarify and mark them on the figure?

Reply:
The reviewer's advice is very valuable for our paper. The authors modified the Figure 2 in the revised MS in the Action Taken.

Comment 6
In their Table 3, it is not clear how 'electrochemical reactions' were applied as boundary conditions in the 'Concentration field'.

Reply:
The reviewer's advice is very valuable for our paper. The authors modified the Table 3 in the revised MS in the Action Taken.

Comment 7
In addition, there are a few typos and grammar mistakes that need to be removed.

Reply:
Thank you very much for the careful check of the article. The authors have checked the whole manuscript carefully and the typos are revised in the manuscript as shown in Action Taken.
Finally, we appreciate very much for your time in editing our manuscript and the referees for their valuable suggestions and comments. I am looking forward to hearing your final decision when it is made.

Reviewer 2 Comment 1
In the introduction the authors may refer to the aluminum reduction cell.

Reply:
Thank you very much for the comment. And the comment is crucial for achieving satisfying result.

Action Taken:
In the introduction section,

Comment 2
The structure of the model was shown before the structured mesh in Figures 2 may be clearer for this article.

Reply:
Thank you very much for the comment and the comment is crucial for improving our paper. The authors modified the Figure 2 with adding the structure of the physical model in the revised MS in the Action Taken.
Action Taken:

Reply:
Thank you for pointing out the problem.

Action Taken:
In section of 3.3, the title was modified as "Initial and Boundary Conditions". The table was modified as " Table 2. Initial condition in the model"

Comment 4
There are several typos in this manuscript. Please double-check the paper.

Reply:
Thank you very much for the careful check of the article. The authors have checked the whole manuscript carefully and the typos are revised in the manuscript as shown in Action Taken.

Comment 5
The author should edit formula alignment and make them more beautiful, such equation 1-5, and 23-24.

Reply:
Thank you for the comment.

Action Taken:
In page 3, In this instance, the electric field could be described by the Ohm's law, continuity law and the Gauss's law as below: (1) = σ (2) ∂q ∂t +∇ • = 0 (3) = -∇φ where (A•m -2 ) is the current density; (S•m -1 ) is the electric conductivity; (V•m -1 ) is the electric field; q (C•m -3 ) represents the charge density; and (V) is the electric potential.
Connecting the above equations, we obtain the following: The electric reaction relating to current on the electrode surface is as follows: