Exploring the Function of Ion-Exchange Membrane in Membrane Capacitive Deionization via a Fully Coupled Two-Dimensional Process Model

Round 1

Reviewer 1 Report

The reviewed manuscript presents studies on the MCDI process described by means of two dimensional model. The authors created their model that covered ‘regular’ variables of CDI process and typical properties of ion exchange membranes. They verified it with experimental data from literature and concluded that it could be used for evaluation of the capacitive deionization process. The created model allowed them to show some effects that MCDI components introduced to the process of desalination: membrane and electrode properties. What is more, the model allows to follow how some operation parameters, voltage, cell geometry, thickness of spacers, affect desalination efficiency what could be interesting for the potential readers. Hence, according my opinion the manuscript can be accepted and shifted to the next steps of editorial process.

Author Response

Reviewer 1

The reviewed manuscript presents studies on the MCDI process described by means of two dimensional model. The authors created their model that covered ‘regular’ variables of CDI process and typical properties of ion exchange membranes. They verified it with experimental data from literature and concluded that it could be used for evaluation of the capacitive deionization process. The created model allowed them to show some effects that MCDI components introduced to the process of desalination: membrane and electrode properties. What is more, the model allows to follow how some operation parameters, voltage, cell geometry, thickness of spacers, affect desalination efficiency what could be interesting for the potential readers. Hence, according my opinion the manuscript can be accepted and shifted to the next steps of editorial process.

Author response: Thank you so much for your approval of our manuscript!

Reviewer 2 Report

The paper ‘Exploring the function of ion-exchange membrane (IEM) in membrane capacitive deionization (MCDI) via a fully coupled two-dimensional process model’ by Xin Zhang and Danny Reible is an interesting study on how to model desalination performance and how it is affected by cell design and operation parameter. Hereby, the influence of the ion exchange membrane properties including water uptake volume fraction, membrane thickness, cell length, electrode thickness, channel thickness, dispersion and fixed charge density were examined. This paper presents a new two dimensional process model which can be used to predict the salt removal efficiency and the cycle time. Therefore, this process model makes a great contribution to understand the mechanisms and the key influences on cell performance. The results can be used to improve the cell design for future efficient MCDI modules.

The strength of this paper lies in:

• The good description of the theory and the results. Also people who usually do not model a lot can understand the method
• The clear identification on which data and literature this study is based on
• New results about the influence of dispersivity in relation with other parameter effects
• Good and short introduction
• Good and matching references used
• Good figure quality

The weakness of this paper:

• Results are too little discussed with results of the literature. Some effects of parameters were already discussed in the present literature as the channel thickness, increase of voltage, reduction of flow rate (results of this paper should be compared to this results e.g. by Biesheuvel group (Zhao,…)
• Does the results of the presented model differs to other existing models?
• Outlook is missing: what about the influence about the resistance of IEMs, fluid, the influence of single salt selectivity, temperature,… how can the results can be used in the future? What needs to be done to make the model better? Relation to energy consumption is totally missing ! The results need to be discussed in wider extent.
• Bad quality of equations
• Sometimes references are missing to strengthen states of the author
• Definition of discussed parameters (e.g. water uptake volume fraction, fixed charge density) is partly missing

Specific comments:

• Program code of model should be published as well à many people can easily use and extend the model
• L 22: it sounds like, there is a special cycle time between the adsorption and the regeneration: ‘cycle time between adsorption and regeneration’. I think you mean adsorption duration (duration from beginning to end of adsorption time)
• Water uptake volume fraction need to be defined more: what is it and what is it good for?
• L32: I would not call fresh water as an ingredient
• Sometimes the text should be more specific in the introduction. Brackets are used to often. Sometimes singular should be changed to plural
• L 42: why only for low volume? Reference needed, why not for drinking water?
• L 51: to slow
• L 57: this figure equals Porada et al. 2013 a lot, maybe he should be mentioned here?
• L 97: what does non ideal IEMs mean?
• L 114: where does the other parameters come from?
• Maybe mmol/L should be used instead of mol/m³. You can find both in the literature
• L118: water uptake volume fraction and fixed charge density of IEMs needs to be defined (what is it exactly and how does it influence the desalination performance)?
• L 122: µm?
• L123 equals L 143 (reference only in 143 given)
• L150: personification of Re
• L 173: I don’t know what a sink term is
• L194: verb is missing
• L122: which kind of equilibrium? Why is it better, when it is short (electric current is not that high and therefore lower energy demand?) Use references here.
• L 213: does the fitting of the 2 parameters does not influence the fitting of each other? How can these parameters be measured? Is the fitting results equal to values from the literature?
• Sometimes space in front of references used, sometimes not
• Sometimes IEM, sometimes IEMs
• L 221: Add the mass of electrode this figure is made for, then it can be easier compared to values in the literature with other electrode masses. I think also the specification, which kind of electrode material was used is missing (activated carbon?)
• Figures should not be in front of new headline. Better: surrounded by text
• Units often on the next line
• L 248: describe single –pass mode or give reference
• L 253: Why is the blue line going down again in the figure?
• Sometimes mmol/g sometimes mg/kg is used (fig. 3 & 6)
• L 265: first line is bold?
• L265: how was the percentage in table 2 calculated? Explanation is missing, why the flow rate had more or less no influence-> just en influence on time, but not on adsorption place?
• Why constant current more is used and not constant current mode?
• L 271: abbreviation CV is introduced already before
• Definition of limits in equation 17 missing (which time?). Here the difference between c,out,average and c,out is not clear. Is it used in other references as well?
• Capital L whould be used for ml (https://www.mdpi.com/authors/english-editing)
• L 296: strange expression: cycle faster
• L 300: explain electromigration to reader
• L 302: feed, effluent, ... concentration?
• Why is salt removal efficiency decreasing in 8a?
• L 321: “more” on wrong place in the sentence?
• L 320: How can the dispersion increase/decrease? Dependence on ions, fluid characteristic, spacer, concentration gradient, tortuosity, structure of pores in electrodes…? Only longitudinal effect is discussed here, can the lateral effects (in direction of pores be neglected)?
• Table 3: (non) effect of dispersivity on cycle time needs to be discussed
• L 328: properties of IEMs (as thickness) play a major role for resistance (e.g. Folaranmi et al. 2020)
• Table 4&5: formatting

Author Response

View the response in the attached file.

Author Response File: Author Response.pdf

Reviewer 3 Report

This manuscript utilises a two-dimensional process model to explore the key performance indicators between CDI and MCDI. This paper does show trends that have been shown and discussed experimentally in the field, but the novelties of this paper need to be emphasized better. Revisions are required before this manuscript can accepted for publication in PROCESSES. Specific comments are listed as follows:

1. Line 95-96. It says here that the Hemmatifar’s model was modified to introduce a dispersion term to account for the hydrodynamic effect. Where about is the modification of this model shown in Section 2.2? In Line 123-130, a ratio of 1:10 was selected between the transverse dispersivity and the axial dispersivity. This is not really something advanced/modified from the original Hemmatifar model in Reference [35].
2. Following from the previous comment, while well-developed mathematical models are put together in this manuscript to examine the different process variables and membrane properties in (M)CDI, the authors need to revise the introduction and better demonstrate the novelties of this study.
3. Table 1. Please specify in the table what is the range of values before the comma? And the values after the comma are referenced to REF [1] and how they were used in the models needs to be stated here (maybe as footnotes). In line 135 it refers to the use of asterisks in Table 1. But there are no asterisks found in Table 1.
4. Lines 117-121. It is claimed that data for IEMs are incomplete. This may be true for the particular membranes used in Biesheuvel’s studies. It should be acknowledged here that the key membrane properties such as water uptake, fixed charge density and thickness can still be quite different between CEMs and AEMs, although the modelling later does suggest that the variation in these parameters of IEMs has little impact on salt removal efficiency.
5. Where is the term tortuosity in Equation (3)?
6. Figure 5. Is t=50 s the point in Figure 4 at which the transient effluent concentration is the lowest? If so please indicate this in the text between Figure 4 and Figure 5; and please justify why this particular time point was selected.
7. Figure 6. Y-axis: Is the adsorption amount refer to total mass of NaCl in both anode and cathode? Or is this only Na in Cathode? Cl in anode?
8. Table 2. Similar to the comment above, please specify the accumulation of what ions? Do you also assume that the adsorption behaviour in carbon electrodes is the same between Na and Cl ions?
9. Lines 326-335. The IEM properties are not sensitive to the salt removal efficiency and the cycle time. Can the authors cite any papers in the literature which show similar experimental trends? If not, this is a very important new finding from this study.

Author Response

Reviewer 3

This manuscript utilises a two-dimensional process model to explore the key performance indicators between CDI and MCDI. This paper does show trends that have been shown and discussed experimentally in the field, but the novelties of this paper need to be emphasized better. Revisions are required before this manuscript can accepted for publication in PROCESSES. Specific comments are listed as follows:

1. Line 95-96. It says here that the Hemmatifar’s model was modified to introduce a dispersion term to account for the hydrodynamic effect. Where about is the modification of this model shown in Section 2.2? In Line 123-130, a ratio of 1:10 was selected between the transverse dispersivity and the axial dispersivity. This is not really something advanced/modified from the original Hemmatifar model in Reference [35].

Author response: We included a dispersion term D_disp in equation (2) to capture the hydraulic dispersion caused by fluid flowing in the porous spacer-filled channel. Hydraulic dispersion is different from diffusion. It is a combination of molecular diffusion and mechanical dispersion. Mechanical dispersion comes from non-uniform flow through porous media, specifically, the uneven interstitial velocity caused by the hinder of pore walls. The correlation between dispersion coefficient and diffusion coefficient, dispersivity, Darcy velocity and porosity of the porous spacer is displayed in equation (4). Also, we model MCDI instead of CDI in Hemmatifar’s model by including co-ions’ transport in non-ideal IEM to explore the role of IEM. We also propose a cycle time with maximal salt removal efficiency and analyze the effects of dispersivity, IEM properties and cell configuration on MCDI performance.

2. Following from the previous comment, while well-developed mathematical models are put together in this manuscript to examine the different process variables and membrane properties in (M)CDI, the authors need to revise the introduction and better demonstrate the novelties of this study.

Author response: Yes, we have revised the introduction part, especially the last paragraph, to link the goals with the state-of-the-art research, and make the novelties and contributions of this work clearer (L122-141).

3. Table 1. Please specify in the table what is the range of values before the comma? And the values after the comma are referenced to REF [1] and how they were used in the models needs to be stated here (maybe as footnotes). In line 135 it refers to the use of asterisks in Table 1. But there are no asterisks found in Table 1.

Author response: We have made some changes in Table 1. The values after comma marked by superscript * are from ref [25] and are only used as inputs for model validation. The range of values before comma are used for the subsequent simulation efforts. Detailed statements can be found in footnotes (L154-155).

4. Lines 117-121. It is claimed that data for IEMs are incomplete. This may be true for the particular membranes used in Biesheuvel’s studies. It should be acknowledged here that the key membrane properties such as water uptake, fixed charge density and thickness can still be quite different between CEMs and AEMs, although the modelling later does suggest that the variation in these parameters of IEMs has little impact on salt removal efficiency.

Author response: We have cited a reference to acknowledge the differences between CEM and AEM properties in reality (L166-167).

5. Where is the term tortuosity in Equation (3)?

Author response: We have switched the position of equation (3) and (4). Tortuosity equals porosity^-1/3. We have added a formula in-between in equation (4) to make it clearer (L211).

6. Figure 5. Is t=50 s the point in Figure 4 at which the transient effluent concentration is the lowest? If so please indicate this in the text between Figure 4 and Figure 5; and please justify why this particular time point was selected.

Author response: Since it costs different time for CDI and MCDI to reach the lowest effluent concentration, ‘t=50 s’ is not the exact time to reach the lowest effluent concentration of either, but is in between to make sure the ion flux is large enough to clearly show the deviations between CDI and MCDI (L295-298).

7. Figure 6. Y-axis: Is the adsorption amount refer to total mass of NaCl in both anode and cathode? Or is this only Na in Cathode? Cl in anode?

Author response: This adsorption amount refers to total mass of adsorbed NaCl divided by total mass of cathode and anode (L316-317).

8. Table 2. Similar to the comment above, please specify the accumulation of what ions? Do you also assume that the adsorption behaviour in carbon electrodes is the same between Na and Cl ions?

Author response: Here the adsorption amount also refers to the adsorbed NaCl (L330-333). Considering the assumption of a symmetric MCDI (L241), the adsorption behavior in electrode micropores is the same between Na and Cl.

9. Lines 326-335. The IEM properties are not sensitive to the salt removal efficiency and the cycle time. Can the authors cite any papers in the literature which show similar experimental trends? If not, this is a very important new finding from this study.

Author response: Two papers talking about IEM properties effects on MCDI have been cited (L435-441). However, no work has been found in exploring a separate effect of each IEM property experimentally since IEM properties are highly correlative. Within the parameter range in this study, no significant effects are discovered by only tuning one IEM parameter. If a solution has a similar concentration as the fixed charge density on IEM, then Donnan exclusion becomes weakened, and causes a significant co-ion transport through the IEM, MCDI performance would be impaired. Or if an IEM is super thick, the enlarged transport path would slow down ion transport towards the electrodes. However, commercial IEM and ion-exchange polymers are thin enough and have high fixed charge density, so choosing different IEMs does not affect MCDI performance significantly, especially when treating low concentration brackish water. Resistance effects of IEM are discussed in Discussion section (L498-500).

Reviewer 4 Report

The manuscript presents several flaws that the authors need to address before this manuscript is acceptable for publication.

Please see the individual comments to each section below.

Detailed Comments

1. Title: Please remove the acronyms from the title.
2. Introduction: The description of the study should be improved at the last paragraph. The authors should link the state-of-the-art analysis to their study goals, identifying the knowledge gaps in literature. The authors are also advised to reason both the relevance and novelties introduced by their study. Please the use bullets to emphasize the main relevant innovations and contributions.
3. Citations/References: The citations throughout the manuscript and the references section must be carefully checked. In addition, multiple references and reference lumps should be eliminated for the sake of clarity. Each reference should be cited separately with the corresponding explanation.
4. Nomenclature: For the sake of clarity, a Nomenclature section should be included in the manuscript with the description of all symbols used throughout the text.
5. Conclusions: The conclusions section should be considerably improved. The authors should clearly summarize the actions taken and main results. Besides, the authors should include an explanation about the significance of their results using quantitative reasoning in comparison with suitable benchmarks. Also, the originality and innovations and main results should be summarized and highlighted (the use of bullets is highly advised). Lastly, the authors should include a clear and concise paragraph about their research limitations and future work.

Author Response

Reviewer 4

The manuscript presents several flaws that the authors need to address before this manuscript is acceptable for publication.

Please see the individual comments to each section below.

Detailed Comments

1. Title: Please remove the acronyms from the title.

Author response: We have removed the acronyms from the title (L3).

2. Introduction: The description of the study should be improved at the last paragraph. The authors should link the state-of-the-art analysis to their study goals, identifying the knowledge gaps in literature. The authors are also advised to reason both the relevance and novelties introduced by their study. Please the use bullets to emphasize the main relevant innovations and contributions.

Author response: We have revised the introduction part, especially the last paragraph, to link the goals with the state-of-the-art research, and make the novelties and contributions of this work clearer (L122-141).

3. Citations/References: The citations throughout the manuscript and the references section must be carefully checked. In addition, multiple references and reference lumps should be eliminated for the sake of clarity. Each reference should be cited separately with the corresponding explanation.

Author response: We have carefully checked the citations in our manuscript and have removed those reference lumps by categorizing and explaining the specific insights of each reference throughout the manuscript.

4. Nomenclature: For the sake of clarity, a Nomenclature section should be included in the manuscript with the description of all symbols used throughout the text.

Author response: We have generated a ‘0. Nomenclature’ section above the ‘1. Introduction’ section (L34).

5. Conclusions: The conclusions section should be considerably improved. The authors should clearly summarize the actions taken and main results. Besides, the authors should include an explanation about the significance of their results using quantitative reasoning in comparison with suitable benchmarks. Also, the originality and innovations and main results should be summarized and highlighted (the use of bullets is highly advised). Lastly, the authors should include a clear and concise paragraph about their research limitations and future work.

Author response: We have expanded Conclusion section into a Discussion section. We have summarized the main actions, quantitative results and model applications in first paragraph, and discussed about some factors not included in the main text, such as temperature effects, energy consumption, energy losses, and systematic resistance in the second paragraph, followed by the model extension directions (L476-502).

Round 2

Reviewer 3 Report

The authors have addressed adequately all reviewers' comments and this manuscript is now recommended for publication in Processes.

Reviewer 4 Report

The revised version of the manuscript has improved its content and the authors have adequately responded to all my comments on the first version.

In general, I am satisfied with the revision performed by the authors and I believe that the paper is now suitable for publication in Processes.