An Electrical Equivalent Model of an Electromembrane Stack with Fouling Under Pulsed Operation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Major Revision

1. Abstract: Chemistry involved in the present study is completely missing. Additionally, some of the prominent results must be incorporated in the revised abstract.
2. Introduction: Problem statement must be limited to only one paragraph.
3. Introduction: Include a schematic diagram representing the concept of the present study.
4. Figure 1 is too generic. Kindly improvise in terms of scientific insights. Additionally caption of Figure 1 is way too lengthy.
5. Equations: Mathematical expressions must be accompanied by valid references.
6. Before conclusion, a state-of-art table must be provided discussing about various case studies based on electromembrane studies, fouling analysis, performance metrics and references in table format to exhibit the potential of this present research topic.
7. Evaluate the long-term stability as membrane surfaces often face issues such as fouling, wetting, and degradation over extended operation.
8. Conclusion is in premature stage. It needs major revision. Kindly highlight the major findings which is completely missing from the manuscript.

Author Response

We sincerely appreciate your valuable corrections. Please find all the corresponding changes and detailed responses in the attached PDF file.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript presented a hybrid electrical equivalent model for electromembrane stacks under pulsed operation by combining an equivalent circuit with an empirical fouling representation. The work addressed a relevant modeling issue by extending single membrane models to full stacks and by incorporating fouling induced resistance growth during pulsed electrodialysis reversal. The main strengths were the clear physical meaning, simple model structure, and systematic calibration and validation with laboratory data, which showed acceptable agreement between simulations and experiments. The model appeared practical for engineering analysis and process optimization. However, the approach relied strongly on empirical calibration, and the fouling description remained phenomenological, which limited its predictive capability beyond the tested conditions. In addition, the applicability of the model to different feed compositions, fouling mechanisms, and long term operation was not sufficiently discussed. Therefore, I suggest the manuscript has to be reviewed after a Major Revision. The specific comments are as follows:

 

Major Concerns:

• The introduction covered a wide range of electromembrane technologies, while the manuscript focused on electrical modeling of electrodialysis stacks under pulsed operation. The transition from the general background to the specific modeling objective was not sufficiently focused, and the motivation for selecting pulsed electrodialysis reversal was not clearly articulated.
• Line 68–76. The assumption that a stack could be represented by serially connecting identical single membrane circuits was stated without sufficient critical discussion.
• Line 88–89. Fouling was included through additional resistance and capacitance terms, but the physical meaning of these parameters was not clearly explained. The relation between these electrical terms and fouling phenomena was not explicitly clarified.
• Line 149–166. Organic fouling and inorganic scaling were treated as electrically equivalent processes. This simplification was asserted without sufficient theoretical or literature based justification.
• Line 189–197. Model calibration relied mainly on peak and steady state current values. The choice of these metrics was not fully explained, and other relevant electrical features of pulsed operation were not discussed.
• Line 233–267. Calibration factors were constrained by membrane number, but the physical interpretation of these bounds was only briefly mentioned. Parameter sensitivity and robustness were not clearly examined.
• Line 271–282. Model validation focused on short term pulsed experiments. The behavior of the model under long term operation or progressive fouling conditions was not discussed.
• Line 283–294. The conclusions emphasized practical applicability without clearly defining the operational range and conditions under which the model assumptions remained valid.
• The description of solution chemistry and fouling composition was limited. The link between experimental fouling conditions and empirical model parameters was not clearly established.
• The literature review listed several modeling approaches but did not clearly position the proposed model relative to existing studies in terms of novelty.

Author Response

Thank you for your insightful feedback. We have addressed all the points raised, and the corresponding corrections are included in the attached PDF.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have addressed all my queries. The revised manuscript can be accepted in the present format. 

Reviewer 2 Report

Comments and Suggestions for Authors

The comments have been well addressed, and the manuscript has been revised accordingly. It is suggested to be accepted for publication.