Bioenergetic Modeling of the Relationship Between Voltage and Electroactive Microbial Biomass Yield for Bioelectrochemical Carbon Dioxide Reduction to Methane

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The study is based on thermodynamic modeling and hypotheses, but does not include experimental data to validate the theoretical results.

 

Suggestion: Adding experimental results or a discussion of how to test the models would increase the credibility and applicability of the research.

Although the article mentions the effects of temperature and concentration, their analysis is limited.

 

Suggestion: Extending the study to include more non-standard working scenarios such as pressure variation, electrode types or more complex media would make the model more robust.

Although two methods for modeling (empirical and theoretical) are discussed, their comparison is not sufficiently thorough.

 

Suggestion: It would be useful to explore the advantages and limitations of each method in more detail, perhaps even through a concrete practical application of both approaches.

The article does not sufficiently detail the type of electrode materials or other components of the BES system.

 

Suggestion: Adding some information on the materials used (conductivity, stability, costs) would make the research more applicable.

mandatory for publication, the part of references, although the previous ones are correctly identified and used, from my point of view, at least 7-8 more bibliographic references should be added...

Author Response

Reviewer Response file Reviewer 1

1. Summary

We would like to thank the reviewer for providing such valuable feedback, which helped to improve the quality of the manuscript. As suggested by the reviewer, the manuscript has been significantly revised. All of the reviewers' concerns have been addressed comprehensively, as detailed below.

2. Questions for General Evaluation

The reviewer suggested that the introduction, research design, and method can be improved. Therefore, those sections were significantly revised, and as listed below, the reviewer response section

3. Point-by-point response to Comments and Suggestions for Authors

Comment 1: The study is based on thermodynamic modeling and hypotheses but does not include experimental data to validate the theoretical results

• Reviewer 1

Comment 1: The study is based on thermodynamic modeling and hypotheses but does not include experimental data to validate the theoretical results.

 Suggestion: Adding experimental results or a discussion of how to test the models would increase the credibility and applicability of the research.

• Response 1: To address this comment, we added a validation section to describe how the model is validated and used to evaluate the biomass yield, methane yield, and ohmic losses in a real system based on the obtained stoichiometric microbial growth reactions based on different substrates. The text is marked in blue in section 2.5 line 292-329 as follows:

“Implementing the model in a complex BES system

To evaluate and implement the model in a more complex system the model was used to estimate the yield of ARB and methanogens in a laboratory scale reactor to assess the model in a more complex system with heat-treated stainless-steel grade 314 as the anode and grade 316 as cathode material. The microbial media consisted of a complex media including acetic acid, soluble CO₂ (added as NaHCO₃), and soluble chemical oxygen demand (SCOD). The single chamber BES reactor had an already developed anodic and cathodic biofilm. Additionally, the bioanode and biocathode potential in open circuit voltage (OCV) condition was reported to be average -0.43 V vs SHE for biocathode and -0.4 V vs SHE for bioanode. The experimental study had sets of different operations. The data used in this paper is taken from the last week of CCV1 (applied -0.6 V vs SHE) and CCV3 (applied -0.7 V vs SHE) operation. The average daily results from the experimental study are given in table 1 [31].

Table 1. The extracted data from an experimental study to calculate the bioenergetic bioanode and biocathode in a single chamber BES reactor.

Applied voltage at cathode (v vs SHE)	-0.6	-0.7
Anodic potential response (v vs SHE)	-0.34	-0.24
Relative anodic voltage considering to OCP (v vs SHE)	+0.06	+0.16
Average daily CH4 production (ml/L/d)	215	130
Average SCOD consumption (mg/L/d)	264	136
Average acetic acid consumption (mg/L/d)	80	No acetic acid content
Average CO2 consumption (g/L)	0.41	0.41
*Acetic acid value equal to 1.32 mmol/L/d, the molar CO2 value is 4.8 mmol/L/d, and the molar CH4 values are respectively 8.8 mmol/L/d and 5.3 mmol/L/d. The molar value of protein assumed as the SCOD is 0.8 mmol/L/d and 0.386 mmol/L/d.

The data in Table 1 was used to establish the yield of methanogens and ARB. In a complex microbial media especially in single chamber designs, calculating the yield of biofilm requires opening the reactor and take samples directly from the electrode, which may disturb the biofilms due to air exposure. This model helps to estimate the daily biofilm yield in different steps of the operation. In this work, the yield was calculated for 1 week in order to compare the effect of the applied voltage on biomass and CH₄ yield.

SCOD can be the source of CO₂ and H⁺ in the system. The analysis in the experimental study shows that proteins (amino acids, proteins, nitrogenous organics) can be a strong candidate as the SCOD, corresponding to degradation reaction shown in Eq. 25 [15]

32.22 kJ/e- eq  = +0.33 V SHE

(25)

SCOD oxidizers were enriched on anode as one type of ARB. The acetate consuming bacteria were also found on anode. Nonetheless as stated in the experimental study, a part of CH₄ production has taken place in the suspended media by taking electrons directly from anode, in addition to the cathodic methanogens. For simplicity, in this work, it is assumed that the whole CH₄ production occurs on cathode. Moreover, in this real complex system, the source of H+ was not only from COD and acetate oxidation. According to the mass balance, water reduction mechanisms were most probably active in the system to provide extra H⁺ for CO₂ reduction to CH₄.

It should be noted that in a real BES reactor, extra potential due to ohmic resistances and the intrinsic potential of the electrode material leads to applying higher voltage on the working electrodes. Measurements anode and cathode potential in in stable mode is important to calculate the relative positive potential of anode for microbial growth. For cathodic microbial growth, the exact applied voltage on cathode should be considered to include the losses in the model.”

 

And in the results section 3.4 line 484-503 as follows:

“According to the data from the experimental study described in section 2.5, the SCOD and acetic acid could be the most possible feed for the anodic microbes. The stoichiometry of bioelectrochemical protein and acetate oxidation was established as follows:

Table 8. Bioenergetic coefficients calculated for at two different applied voltages.

Applied cathodic voltage	Microbes
-0.6 V vs SHE	SCOD oxidizers	0.947	0.053
	Acetate oxidizers	0.9532	0.0468
	Autotrophic Methanogens	0.89	0.11
-0.7 V vs SHE	SCOD oxidizers	0.87	0.13
	Acetate oxidizers	0.884	0.116
	Autotrophic Methanogens	0.877	0.123

At -0.6 and -0.7 V vs SHE, the stoichiometry of anodic ARB for COD and acetate oxidizers and the calculated yield is given by Eq. 41-44 in table 9, and the methanogenic growth stoichiometry with molar biomass and CH4 production yield is given by Eq. 45 and 46 in table 10. 

Table 9. The stoichiometric reactions of the ARB in real system with calculated biomass yield.

Applied cathodic voltage	Microbes	Reaction	Biomass yield (molar)
-0.6 V vs SHE	SCOD oxidizers		0.84	(41)
	Acetate oxidizers		0.088	(42)
-0.7 V vs SHE	SCOD oxidizers		2.06	(43)
	Acetate oxidizers		0.221	(44)

 

Table 10. The stoichiometric reaction of methanogens and CH4 production in a real BES system.

Applied cathodic voltage	Microbes	Reaction	Biomass yield (molar)	CH4 yield
-0.6 V vs SHE	Autotrophic Methanogens		0.19	0.81	(45)
-0.7 V vs SHE	Autotrophic Methanogens		0.205	0.77	(46)

 

The model in the complex system with experimental data shows that the molar biomass yield increases when higher electric potential is applied to cathode, while molar CH₄ yield decreases at higher voltage. This model thermodynamically proves that -0.6 V vs SHE is the optimum voltage for CH₄ production, which aligns with the results of the experimental study. The model is valid for implementation in real systems with multiple substrates, considering ohmic losses due to many factors such as non-STD conditions, electrode material intrinsic potential and mixed microbial environment.” 

 

Additionally, the results of the model is compared with the overall production results from other experimental work in the discussion section 3.3.2 line 452-464 as follows:

“Although the model is developed for STD conditions, the results align with CH₄ yield obtained from experimental studies. In a study conducted in long term operation of heat-treated steel electrodes, lower applied voltage on cathode (-0.6 V vs SHE) resulted in higher CH₄ production compared to higher voltage (-0.7 V vs SHE). It is stated that higher voltage disturbed the methanogens and was not favorable for increasing CH₄ production [31]. Another research on a single chamber BES reactor with graphite felt cathode showed that -0.65 V vs SHE was in favor of enhancing CH₄ evolution while increasing the voltage to -0.8 V vs SHE shifted the system toward acetic acid production [16]. Another experimental study with amended iron graphite cathode also showed that between -0.65, -0.7, -0.75 and -0.8 V vs SHE, the optimum voltage for the highest CH₄ production was -0.75 V vs SHE [33]. The different optimum voltage in different reactors is due to factors such as different electrode material, various substrate, microbial community, and conductivity in different systems which impacts ionic gradients in the BES reactors [34]. “

 

Comment 2: Although the article mentions the effects of temperature and concentration, their analysis is limited.

 Suggestion: Extending the study to include more non-standard working scenarios such as pressure variation, electrode types or more complex media would make the model more robust.

• Response 2: The authors would appreciate your comments and suggestions to improve the quality and robustness of the study.

The study was extended to address effect of electrodes and more complex media with different microbes and substrate, we implemented the model with data from a real BES system as described in “Answer 1”.  The text is marked in blue in section 2.5 line 292-329, and in the results section 3.4 line 484-503. The relevant text is added in response 1.

Also, for more clarification the sentence was added to the assumptions in section 2.4, line 240:

“Atmospheric pressure is assumed for the entire model.”

The reactions used to develop this model do not directly include pressure. We totally agree that pressure variation has an impact on microbial growth and CH4 production. However, it has more effect when gaseous substrates are considered which is out of scope of this study. In this model, H⁺ and CO₂ are provided from acetate oxidation in atmospheric pressure. We appreciate your suggestion and will consider it in further studies.

 

Comment 3: Although two methods for modeling (empirical and theoretical) are discussed, their comparison is not sufficiently thorough.

Suggestion: It would be useful to explore the advantages and limitations of each method in more detail, perhaps even through a concrete practical application of both approaches.

• Response 3: The authors would appreciate the reviewer’s comment and suggestion. The comparison of the practical approach and empirical approach is thoroughly discussed in the methodology part to explain how each method can be used to establish the stoichiometry of different microbial growth reactions using various substrates. Since the comparison of these approaches was a part of this study to select which method can be used to relate the applied voltage to the Gibbs free energy and bioenergetic coefficients of bioanodic and biocathodic reactions. To increase the clarity about this point, we added a brief comparison in introduction, the steps of the study which is addressed in the following text:

Introduction section 1 was refined to add comparison and clearity, line 94-104:

“Two approaches are conventionally used to establish the stoichiometry of biological CH₄ production: the empirical approach, based on molar empirical biomass yield, and the theoretical approach, corresponding to thermodynamic biomass formation and electron equivalent reactions. The empirical approach is simpler to apply when calculating biomass growth stoichiometry, whereas the theoretical approach is more detailed and relates Gibbs free energy to the biomass growth stoichiometry based on electron equivalent reactions [19, 20]. However, there is a lack of clarity regarding which method is more straightforward and how it should be implemented in bioelectrochemical growth modeling to relate biomass yield to applied voltage. Understanding these relationships is essential for developing growth yield models for both anodic and cathodic biofilms.”

And line 122-125:

“To obtain this objective, the stoichiometry of autotrophic CH₄ production should be understood. Then, the stoichiometric growth of electroactive biofilm must be developed by a proper method to obtain the biomass yield on the biofilm at different voltages with respect to bioenergetics.”

Additionally, in section 2 line 129-135 we refined the text to increase the clarity as follows:

“Empirical and theoretical approaches were applied to obtain the stoichiometry of autotrophic microbial growth reaction for H₂ as electron donor and CO₂ as the inorganic carbon source as electron acceptor. Then, the stoichiometric growth reactions for 1 mol biomass via the two approaches was compared and the method which could be applicable in bioelectrochemistry was selected. The selected approach was used to establish the stoichiometry of growth for anodic biofilm growth, and the stoichiometric metabolism of cathodic biofilm where methane is produced.”

Comment 4: The article does not sufficiently detail the type of electrode materials or other components of the BES system.

 Suggestion: Adding some information on the materials used (conductivity, stability, costs) would make the research more applicable.

• Response 4: We would thank the reviewer’s comment. To address this, we refined the introduction to add the effect of electrode, conductivity and stability and impact of modeling on reducing the operation and construction costs, which is in the scope of the study.

Additionally, the new section implementing the model in a real complex system covers the impact of electrode, voltage, substrate, biomass complexity, and indirectly covers the conductivity of electrode by considering the anodic voltage response and stability of both cathode and anode in a real system and we described thoroughly how the model can be implemented and validated by data obtained from a real system.

This information is covered in the introduction section 1, line 39-55:

“These advancements have facilitated the optimization of BES configurations and operational strategies, such as reactor flow modes and electrode arrangements, ultimately reducing construction and operation costs as well as extensive expenses related to testing various parameters separately [2].

Early models often assumed constant biomass density, whereas more recent studies incorporate variable biofilm growth, substrate diffusion, and dynamic electrochemical interactions. Effective mixing enhances substrate diffusion and improves nutrient distribution in the biofilm, consequently improving microbial metabolism and electron transfer. However, excessive mixing can generate shear stress, leading to biofilm detachment and reduced electrochemical performance [3, 4]. Therefore, modeling efforts often include mixing intensity or biofilm detachment velocity as a key parameter to balance nutrient availability and biofilm integrity [5, 6]. Electrode properties such as conductivity, surface area, and porosity also influence electron transfer efficiency and biofilm formation and must be incorporated in BES modeling. Another critical aspect of BES modeling is the correlation between applied voltage and microbial yield. In microbial electrochemical cells, the applied voltage directly impacts the electron transfer driving force, influencing both production efficiency and microbial growth rates [1, 7].”

 

In addition, section 2.5 and 3.4 in which we have implemented validation with experimental data, includes the effect of electrode, conductivity, substrate, biomass, mixing, and many other experimental parameters within the scope of this study, which finally affect organic oxidation, biomass growth stoichiometry and methane production, both directly and indirectly.

 

Comment 5: Mandatory for publication, the part of references, although the previous ones are correctly identified and used, from my point of view, at least 7-8 more bibliographic references should be added.

Response 5: We appreciate this suggestion, which will improve the quality of the manuscript. The following reference lists were added in relevant parts as suggested by reviewer:

“[1]    Z. Li et al., “Model development of bioelectrochemical systems: A critical review from the perspective of physiochemical principles and mathematical methods,” Water Res, vol. 226, p. 119311, 2022.

[2]      G. S. Jadhav, Y. D. Jagtap, G. D. Bhowmick, and M. M. Ghangrekar, “Modelling of Bioelectrochemical Systems: Biophysicochemical Processes and Mathematical Methods,” Microbial Electrochemical Technologies: Fundamentals and Applications, vol. 2, pp. 529–554, 2023.

[3]      P. Mullai et al., “Energy generation from bioelectrochemical techniques: Concepts, reactor configurations and modeling approaches,” Chemosphere, vol. 342, p. 139950, 2023.

[4]      S. Luo, Z.-W. Wang, and Z. He, “Mathematical modeling of the dynamic behavior of an integrated photo-bioelectrochemical system for simultaneous wastewater treatment and bioenergy recovery,” Energy, vol. 124, pp. 227–237, 2017.

[5]      L. Mais, J. Rodriguez, N. Melis, A. Vacca, and M. Mascia, “Computational modelling as a design tool for bioelectrochemical systems,” Curr Opin Electrochem, p. 101460, 2024.

[7]      A. G. Capodaglio, D. Cecconet, and D. Molognoni, “An integrated mathematical model of microbial fuel cell processes: bioelectrochemical and microbiologic aspects,” Processes, vol. 5, no. 4, p. 73, 2017.

[8]      D. Deb, R. Patel, and V. E. Balas, “A review of control-oriented bioelectrochemical mathematical models of microbial fuel cells,” Processes, vol. 8, no. 5, p. 583, 2020.

[18]    A. Ware and N. Power, “Modelling methane production kinetics of complex poultry slaughterhouse wastes using sigmoidal growth functions,” Renew Energy, vol. 104, pp. 50–59, 2017, doi: https://doi.org/10.1016/j.renene.2016.11.045.

[21]    B. Korth, L. F. M. Rosa, F. Harnisch, and C. Picioreanu, “A framework for modeling electroactive microbial biofilms performing direct electron transfer,” Bioelectrochemistry, vol. 106, pp. 194–206, 2015.

[22]    E. Desmond-Le Quéméner, R. Moscoviz, N. Bernet, and A. Marcus, “Modeling of interspecies electron transfer in anaerobic microbial communities,” Curr Opin Biotechnol, vol. 67, pp. 49–57, 2021, doi: https://doi.org/10.1016/j.copbio.2020.12.019.

[23]    A. Kato Marcus, C. I. Torres, and B. E. Rittmann, “Conduction‐based modeling of the biofilm anode of a microbial fuel cell,” Biotechnol Bioeng, vol. 98, no. 6, pp. 1171–1182, 2007.

[24]    C. I. Torres, A. K. Marcus, P. Parameswaran, and B. E. Rittmann, “Kinetic Experiments for Evaluating the Nernst−Monod Model for Anode-Respiring Bacteria (ARB) in a Biofilm Anode,” Environ Sci Technol, vol. 42, no. 17, pp. 6593–6597, Sep. 2008, doi: 10.1021/es800970w.

[26]    P.-L. Tremblay, N. Faraghiparapari, and T. Zhang, “Accelerated H2 evolution during microbial electrosynthesis with Sporomusa ovata,” Catalysts, vol. 9, no. 2, p. 166, 2019.

[31]    V. Ahmadi, C. Dinamarca, and N. Aryal, “Durability and mass loss effect of heat-treated stainless-steel cathode for methane production from organic and inorganic carbon in a bioelectrochemical system,” Journal of Hazardous Materials Advances, vol. 17, p. 100573, 2025, doi: https://doi.org/10.1016/j.hazadv.2024.100573.

[32]    M. T. D and M. W. W, “Energy Conservation and Hydrogenase Function in Methanogenic Archaea, in Particular the Genus Methanosarcina,” Microbiology and Molecular Biology Reviews, vol. 83, no. 4, pp. 10.1128/mmbr.00020-19, Sep. 2019, doi: 10.1128/mmbr.00020-19.

[33]    C. M. Dykstra and S. G. Pavlostathis, “Zero-valent iron enhances biocathodic carbon dioxide reduction to methane,” Environ Sci Technol, vol. 51, no. 21, pp. 12956–12964, 2017.

[34]    N. Aryal, L. Feng, S. Wang, and X. Chen, “Surface-modified activated carbon for anaerobic digestion to optimize the microbe-material interaction,” Science of The Total Environment, vol. 886, p. 163985, 2023, doi: https://doi.org/10.1016/j.scitotenv.2023.163985.”

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

I have thoroughly reviewed this interesting research aimed at evaluating the external voltage impacts on the biomass yield of anode-respiring bacteria and methanogens to optimize methane production. This is a well-written manuscript with interesting results and discussion that support the overall conclusion of this study. I am in favor of accepting it in Fermentation with minor revisions as follows:

1.     Lines 46-79, is it imperative to describe reactions at the introduction section? I do not recommend it; they may be better fitted for the following section.

2.     In the introduction, include more up to date peer studies focusing on the same topic, which should be discussed to highlight the significance of this study.

3.     Overall, the introduction is well-written. However, at the end of the introduction, add a little summary of all the key steps followed in this study.

4.     Check format of all the equations as some of them have a larger font size than others.

5.     Figure 1, increase resolution and font size.

6.     Overall, the results were very well discussed in section 3.

7.     Elaborate more on the conclusions. Consider elaborating on the future research that can be conducted to enhance the results of this study.

Author Response

Reviewer Response file Reviewer 2

1. Summary

We would like to thank the reviewer for providing such valuable feedback, which helped to improve the quality of the manuscript. As suggested by the reviewer, the manuscript has been significantly revised. All of the reviewers' concerns have been addressed comprehensively, as detailed below.

2. Questions for General Evaluation

The reviewer suggested that the introduction background and method can be improved. Therefore, those sections were significantly revised, and as listed below, the reviewer response section

3. Point-by-point response to Comments and Suggestions for Authors

Comments and Suggestions for Authors:

I have thoroughly reviewed this interesting research aimed at evaluating the external voltage impacts on the biomass yield of anode-respiring bacteria and methanogens to optimize methane production. This is a well-written manuscript with interesting results and discussion that support the overall conclusion of this study. I am in favor of accepting it in Fermentation with minor revisions as follows:

We would like to thank the reviewer for providing such valuable feedback, which helped to improve the quality of the manuscript.

Comment 1:    Lines 46-79, is it imperative to describe reactions at the introduction section? I do not recommend it; they may be better fitted for the following section.

• Response 1: Thank you for suggesting comment. All the equations and reaction were transferred from the introduction into section 2, in the method part: line 213-217 and line 228-232. The transferred text is marked in blue.

Comment 2:     In the introduction, include more up to date peer studies focusing on the same topic, which should be discussed to highlight the significance of this study.

• Response 2: The authors would appreciate this suggestion. The following text was added in the introduction to include the advancements in modeling and the gaps in Line 33-65:

“Modeling and simulation of bioelectrochemical systems (BES) have gained significant attention recently, integrating microbiology, electrochemistry, and reactor engineering. Several mathematical models have been developed to describe substrate degradation, microbial growth, and electron transfer in BES. Key parameters of BES models include substrate and biomass concentrations, biofilm thickness, current generation, and bioelectrochemical reaction kinetics, typically described using Nernst-Monod or Butler-Volmer equations [1]. These advancements have facilitated the optimization of BES configurations and operational strategies, such as reactor flow modes and electrode arrangements, ultimately reducing construction and operation costs as well as extensive expenses related to testing various parameters separately [2].

Early models often assumed constant biomass density, whereas more recent studies incorporate variable biofilm growth, substrate diffusion, and dynamic electrochemical interactions. Effective mixing enhances substrate diffusion and improves nutrient distribution in the biofilm, consequently improving microbial metabolism and electron transfer. However, excessive mixing can generate shear stress, leading to biofilm detachment and reduced electrochemical performance [3, 4]. Therefore, modeling efforts often include mixing intensity or biofilm detachment velocity as a key parameter to balance nutrient availability and biofilm integrity [5, 6]. Electrode properties such as conductivity, surface area, and porosity also influence electron transfer efficiency and biofilm formation and must be incorporated in BES modeling. Another critical aspect of BES modeling is the correlation between applied voltage and microbial yield. In microbial electrochemical cells, the applied voltage directly impacts the electron transfer driving force, influencing both production efficiency and microbial growth rates [1, 7].

While some studies have modeled microbial yield using coulombic efficiency and biofilm density [8], accurately quantifying microbial biomass yield in response to varying applied voltages remains a challenge. This highlights the need for more comprehensive models capable of predicting yield coefficients under diverse operating conditions [4].

BES modeling has progressed from simplified kinetic descriptions to integrated, multi-physics frameworks, such as computational fluid dynamics and machine learning, to optimize system performance. However, gaps remain in accurately predicting microbial yield under different applied voltages, necessitating further research into parameter-specific models that account for reactor configurations, electrode materials, and biofilm behavior.”

 

Comment 3:     Overall, the introduction is well-written. However, at the end of the introduction, add a little summary of all the key steps followed in this study.

• Response 3: The summary of the steps in this study is added in the last paragraph in the introduction in line 122-125. Also, the first paragraph in section 2 was refined as follows:

“To obtain this objective, the stoichiometry of autotrophic CH₄ production should be understood. Then, the stoichiometric growth of electroactive biofilm must be developed by a proper method to obtain the biomass yield on the biofilm at different voltages with respect to bioenergetics.”

Line 129-140:

“Empirical and theoretical approaches were applied to obtain the stoichiometry of autotrophic microbial growth reaction for H₂ as electron donor and CO₂ as the inorganic carbon source as electron acceptor. Then, the stoichiometric growth reactions for 1 mol biomass via the two approaches was compared and the method which could be applicable in bioelectrochemistry was selected. The selected approach was used to establish the stoichiometry of growth for anodic biofilm growth, and the stoichiometric metabolism of cathodic biofilm where methane is produced. The thermodynamic model was established in Microsoft Excel solver spreadsheet-based program to relate the stoichiometry of biofilm growth to the voltage applied on the cathode and electroactive methanogen growth reaction. In addition, the effect of non-STD conditions on the applied voltage, biomass yield and CH₄ production was assessed. Then the model was validated with experimental data from a BES reactor. “

 

Comment 4:     Check format of all the equations as some of them have a larger font size than others.

• Response 4: All the equations were corrected to have a similar front size 9.

Comment 5:     Figure 1, increase resolution and font size.

• Response 5: The figure was enhanced both in resolution and font size.

Comment 6:     Elaborate more on the conclusions. Consider elaborating on the future research that can be conducted to enhance the results of this study.

• Response 6: The conclusion was refined according to the sections added to the manuscript, such as research gaps, and validation of the model with experimental data in line 520-526 as follows:

“Implementing the thermodynamic model using real data, aligned with experimental results, which proves that the model can be used as an accurate tool for biomass and CH₄ yield prediction, enabling more effective system design and operation. By enhancing predictions of biofilm growth dynamics, this approach supports enhancement of dynamic microbial growth models, and development of more energy-efficient BES configurations for sustainable CH₄ recovery.”

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Technically, the article is weak. Substantive comments to the text: 1) The subject of the article is very interesting for which I would like to thank the author. 2) The article lacks innovative aspects from the world in the context of mixing techniques, especially hydrodynamic mixing in the fermentation process - it must be completed in the Introduction 3) What is the novelty of articles? This should be demonstrated in Abstract and Introduction. Technical notes to the text 1) Chemical reactions should be written as Eq. numbering. 2) Explanations of Eq. Insert at the very end of the article. 3) Figure: 1-8 enlarged so that they are legible. 4) In the text line (155-163) there is no description of Fig. 3b and Fig. 3c. 5) In line 323 insert Figure 4 from lines 331-333. 6) In line 347 insert Figure 6 from lines 353-355. 7) In line 361 insert Table 6 from lines 371-373. 8) Reduce the number of citations of position [4] – it is currently cited 9 times. After following the above-mentioned tips, your article can be published.

Comments for author File: Comments.pdf

Author Response

Reviewer Response file Reviewer 3

1. Summary

We would like to thank the reviewer for providing such valuable feedback, which helped to improve the quality of the manuscript. As suggested by the reviewer, the manuscript has been significantly revised. All of the reviewers' concerns have been addressed comprehensively, as detailed below.

2. Questions for General Evaluation

The reviewer suggested that the introduction background, research design, method, result and conclusion can be improved. Therefore, those sections were significantly revised, and as listed below, the reviewer response section

3. Point-by-point response to Comments and Suggestions for Authors

Comments and Suggestions for Authors

Technically, the article is weak. Substantive comments to the text:

Comment 1: The subject of the article is very interesting for which I would like to thank the author.

We would like to thank the reviewer for providing such valuable feedback, which helped to improve the quality of the manuscript. The reviewer's comments were addressed as suggested.

Comment 2: The article lacks innovative aspects from the world in the context of mixing techniques, especially hydrodynamic mixing in the fermentation process - it must be completed in the Introduction

• Response 2: The authors would appreciate this valuable comment. To address the mentioned aspects which was lacking in the manuscript, we added the following text in the introduction in line 43-55 in the second paragraph (effect of mixing in BES) in the following text:

“Modeling and simulation of bioelectrochemical systems (BES) have gained significant attention recently, integrating microbiology, electrochemistry, and reactor engineering. Several mathematical models have been developed to describe substrate degradation, microbial growth, and electron transfer in BES. Key parameters of BES models include substrate and biomass concentrations, biofilm thickness, current generation, and bioelectrochemical reaction kinetics, typically described using Nernst-Monod or Butler-Volmer equations [1]. These advancements have facilitated the optimization of BES configurations and operational strategies, such as reactor flow modes and electrode arrangements, ultimately reducing construction and operation costs as well as extensive expenses related to testing various parameters separately [2].

Early models often assumed constant biomass density, whereas more recent studies incorporate variable biofilm growth, substrate diffusion, and dynamic electrochemical interactions. Effective mixing enhances substrate diffusion and improves nutrient distribution in the biofilm, consequently improving microbial metabolism and electron transfer. However, excessive mixing can generate shear stress, leading to biofilm detachment and reduced electrochemical performance [3, 4]. Therefore, modeling efforts often include mixing intensity or biofilm detachment velocity as a key parameter to balance nutrient availability and biofilm integrity [5, 6]. Electrode properties such as conductivity, surface area, and porosity also influence electron transfer efficiency and biofilm formation and must be incorporated in BES modeling. Another critical aspect of BES modeling is the correlation between applied voltage and microbial yield. In microbial electrochemical cells, the applied voltage directly impacts the electron transfer driving force, influencing both production efficiency and microbial growth rates [1, 7].

While some studies have modeled microbial yield using coulombic efficiency and biofilm density [8], accurately quantifying microbial biomass yield in response to varying applied voltages remains a challenge. This highlights the need for more comprehensive models capable of predicting yield coefficients under diverse operating conditions [4].

BES modeling has progressed from simplified kinetic descriptions to integrated, multi-physics frameworks, such as computational fluid dynamics and machine learning, to optimize system performance. However, gaps remain in accurately predicting microbial yield under different applied voltages, necessitating further research into parameter-specific models that account for reactor configurations, electrode materials, and biofilm behavior.”

 

Also, in the assumptions of the model, a sentence was added in section 2.4 line 241.

“The anodic and cathodic media is well mixed.”

 

Comment 3: What is the novelty of articles? This should be demonstrated in Abstract and Introduction.

• Response 3: Thank you for pointing out this. We clarified the novelty of this article by explaining the research gaps in the field of BES modeling. Then we elaborated the novelty in the abstract and in the introduction as follows:

In the abstract, line 19-28

“Additionally, sensitivity analyses reveal that lower substrate concentrations require more negative voltages to sustain microbial growth, highlighting a critical relationship between applied potential and substrate availability. The model was validated using experimental data from a BES reactor, demonstrating reasonable predictions of biomass and CH₄ yield under different operating voltages in a multi substrate system. The results show that higher voltage inputs increase biomass yield while reducing CH₄ output due to non-optimal voltage. This validated model provides a tool for optimizing BES performance to enhance CH₄ recovery and biofilm stability. These insights contribute to finding optimum voltage for the highest CH₄ production for energy efficient carbon dioxide reduction for scaling up BES technology.”

 

And in the introduction, line 56-65:

“While some studies have modeled microbial yield using coulombic efficiency and biofilm density [8], accurately quantifying microbial biomass yield in response to varying applied voltages remains a challenge. This highlights the need for more comprehensive models capable of predicting yield coefficients under diverse operating conditions [4].

BES modeling has progressed from simplified kinetic descriptions to integrated, multi-physics frameworks, such as computational fluid dynamics and machine learning, to optimize system performance. However, gaps remain in accurately predicting microbial yield under different applied voltages, necessitating further research into parameter-specific models that account for reactor configurations, electrode materials, and biofilm behavior.”

 

Line: 100-104:

“However, there is a lack of clarity regarding which method is more straightforward and how it should be implemented in bioelectrochemical growth modeling to relate biomass yield to applied voltage. Understanding these relationships is essential for developing growth yield models for both anodic and cathodic biofilms.”

 

Line 112-127:

“In most of the dynamic simulation work, only bioanode or biocathode is simulated. To the knowledge of authors, no model attempted to connect bioanodic oxidation to the biocathodic reduction. The biomass yield on the biofilm in the BES system is taken from other literature, and the voltage which biofilm growth is maximum is also assumed in most papers [6, 21, 22, 23, 24]To make the validation applicable, a method should be presented to calculate the electroactive biomass yield based on thermodynamics.

This paper presents a novel investigation into the thermodynamic evaluation of how external voltage impacts biomass yield and CH₄ production in electro-reductive systems involving ARB and methanogens. Additionally, it establishes stoichiometric frameworks for CH₄ production by autotrophic methanogens and bioelectrochemical processes, emphasizing the application of Gibbs free energy for reaction modeling. To obtain this objective, the stoichiometry of autotrophic CH₄ production should be understood. Then, the stoichiometric growth of electroactive biofilm must be developed by a proper method to obtain the biomass yield on the biofilm at different voltages with respect to bioenergetics. This research advances the understanding of BES dynamics and offers a more precise approach to designing efficient CH₄ production in BES.”

 

Comment 4: Chemical reactions should be written as Eq. numbering.

• Response 4: The numbering for all reactions was changed to Eq. in the entire text.

 

Technical notes to the text

Comment 5: Figure: 1-8 enlarged so that they are legible.

• Response 5: The text of all figures was enlarged together with resolution and contrast.

 

Comment 6: In the text line (155-163) there is no description of Fig. 3b and Fig. 3c. In line 323 insert Figure 4 from lines 331-333. In line 347 insert Figure 6 from lines 353-355. In line 361 insert Table 6 from lines 371-373.

• Response 6: The placement of tables and figures next to the relevant text was fixed.

Comment 7: Reduce the number of citations of position [4] – it is currently cited 9 times. After following the above-mentioned tips, your article can be published.

• Response 7: We have fixed this issue by removing the redundancy of this reference and cite other references as well. Overall, the following references (in the revised manuscript) were added to the paper:

“Ref [1], [2], [3], [4], [5], [7], [8], [18], [21], [22], [23], [24], [26], [31], [32], [33], [34]”

Author Response File: Author Response.pdf