Linear Optimization Model with Nonlinear Constraints to Maximize Biogas Production from Organic Waste: A Practical Approach
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors## General comments
This article presents the development of a linear programming model with non-linear constraints aimed at maximizing biogas production from organic waste. The proposal considers critical factors such as the carbon/nitrogen (C/N) ratio, pH, moisture, organic matter, and volatile solids. Below are the detailed comments and recommendations for improvement.
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## Title and abstract
### 1. Title:
- The title is clear and reflects the article's content.
- **Commnett**: Consider making it more specific by explicitly mentioning the use of linear programming with non-linear constraints, which is the main innovation of the work.
### 2. Abstract:
- The abstract appropriately presents the problem, objective, methodology, results, and conclusions.
- **Suggestion**: Include key result values (e.g., efficiency or improvement achieved) to make it more informative.
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## Introduction
### 1. Contextualization:
- The introduction effectively situates the global problem of fossil fuel usage and solid waste, emphasizing the relevance of biogas as a solution.
- **Strengths**:
- Focus on sustainability and the need for energy transition.
- Clear justification for developing the model.
- **Areas for Improvement**:
- A deeper review of recent studies integrating optimization with artificial intelligence, IoT, or hybrid models is missing.
- The introduction could better explore research gaps to justify the proposed model.
### 2. Objective:
- The objective is well-defined and aligned with the rest of the text.
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## Methodology
### 1. Clarity and Detail:
- The methodology is clear and provides all necessary steps for replication, which is a strong point.
- **Observation**: There is considerable reliance on empirical coefficients, such as the potential biogas production (PP), which can vary significantly depending on waste origin.
### 2. Mathematical Model:
- Using linear programming with non-linear constraints is a valid and innovative approach.
- **Critiques**:
- While the choice of constraints and the objective function seems appropriate, there is no explicit justification for certain limits (e.g., the animal waste proportion between 20-40% of total volume).
- The computational tools used to solve the model are not discussed, which affects replicability.
### 3. Experimental Data or Simulations:
- The methodology appears to focus on theoretical or pre-existing empirical data.
- **Recommendation**: Experimental tests should be conducted to validate the predicted results.
### 4. Reproducibility:
- The article provides detailed formulas, coefficient tables, and practical examples.
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## Results
### 1. Presentation:
- Results are presented in an organized manner with detailed tables and descriptions.
- **Strengths**:
- Tables summarizing critical factors (C/N, pH, volatile solids) are useful for readers.
- Sensitivity analyses and different scenarios strengthen the conclusions.
- **Weaknesses**:
- Results could be enhanced with graphs to visualize trends better.
- It is unclear whether the values used in the tables reflect real data or are entirely hypothetical.
### 2. Interpretation:
- Discussions about the results are coherent and well-founded.
- **Observation**: The analysis lacks direct comparison with other models in the literature (if possible).
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## Discussion
### 1. Connection to Literature:
- While the text cites relevant works, its integration with the literature is superficial.
- **Suggestion**: Include a comparative table or graph showing the performance of similar models.
### 2. Limitations:
- The article does not explicitly address the limitations of the proposed model, which is a significant gap.
- **Examples of Possible Limitations**:
- Heavy reliance on empirical values that may vary.
- Practical implementation challenges, such as costs or computational complexity.
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## Conclusions
### 1. Clarity and Relevance:
- The conclusions effectively summarize the article's findings and highlight their practical relevance.
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Author Response
The observations have been addressed in the manuscript, and both the updated version of the article and the responses to the evaluators for each point are attached.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsManuscript with the title: " BIO-OPT: Non-linear optimization model for maximizing biogas production from organic waste" written by Juan Carlos Vesga Ferreira, Alexander Florez Martinez, Jhon Erickson Barbosa Jaimes, corresponds to the scope of Journal Applied Sciences, and I suggest the editorial board accept this manuscript after minor revision.
The research topic is highly relevant and interesting. This manuscript is adequately written, and the following points should be considered:
1. Manuscript formatting (to be in accordance with Journals template) and a thorough review for any mistakes or typos (lines 151, 156, etc., the word Biogas; lines 147, 148, etc.; write formulas with subscript, etc.);
2. Section 2 is written too extensively and in too much detail, so my suggestion is to combine all analyzed parameters and all analyzed wastes into one table (e.g., Tables 1 and 2 should be merged into one table, without separating "animal waste" from "food and agricultural waste, and density, C/N ratio, moisture, and pH value, to be consolidated into a single table; additionally a single unit of measurement (e.g., kg/L or kg/m³) should be used).
3. Explain in more detail why the waste composition modeled in scenario 1 and scenario 2 was chosen;
4. Add/perform model validation. Explain the importance of model validation.
Author Response
The observations have been addressed in the manuscript, and both the updated version of the article and the responses to the evaluators for each point are attached.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThis study describes an optimization model for maximizing biogas production from organic waste. In order to solve the limitations of existing biogas production optimization model, a linear programming model is constructed. Simulation of two scenarios and Monte Carlo sensitivity analysis show that the model can effectively optimize biogas production. However, points below should be well addressed prior to being considerable for publication in this suitable journal:
1. Title: The abbreviation "BIO-OPT" used in the title is rather cryptic and fails to convey the essence of the research effectively. It is highly recommended that the authors replace this abbreviation with a descriptive and comprehensive title reflecting the key aspects of the optimization model and its biogas production application.
2. The introduction, while comprehensive, appears overly lengthy. It is strongly recommended to simplify its content to more concisely convey the need for this study.
3. The materials and methods section should be structured according to the outline of an overview of bio-gas production from organic waste, data collection, input parameter, regression analysis, model establishment, and Monte Carlo analysis. Descriptions like "What is biogas" should not be included. It is strongly recommended that the authors draw a schematic flowchart to present the methodology of this research and then write this section in separate items according to the outline. Please select the important parts to present in the main text, and place the unimportant ones in the appendix. There is no need to list all the tables in the main text, which can enhance the readability for readers. At most 1 to 2 tables can be used to list the most crucial parameters and their value ranges when researching biogas production from waste especially.
4. In the results section, the content of 3.1 and 3.2 should be placed in the materials and methods section.
5. The results of model training and testing under different scenarios should be presented and accompanied by appropriate analysis.
6. The model's performance in different scenarios is notable, yet a comparison with advanced existing models is lacking.
Comments for author File: Comments.pdf
Author Response
The observations have been addressed in the manuscript, and both the updated version of the article and the responses to the evaluators for each point are attached.
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsReviewer Comments to applsci-3326950
1. The manuscript lacks in-depth analysis.
Comment 1
The authors name the model as a non-linear optimization model while naming the model as a linear optimization model with nonlinear constraints. Hence, the tilt should be modified to “BIO-OPT: Non-linear constraint optimization model for maximizing biogas production from organic waste”.
Comment 2
The authors should clarify the density stands for stacking density in Tables 1 and 2.
Comment 3
All analysis and calculation should be rigorous, i.e., all equations must be carefully derived based on their physical meanings. For instance, the unit of buffering capacity should be m3/kg, and Eqs. 2 and 3 should be revised as follows.
(2)
(3)
Herein, ni(H+) represents the number of moles of buffering hydrogen protons capacity of the residue i.
Additionally, Eqs. 16~19 should also be modified as the revised Eq. 3.
The average pH values of residue i should be 7.0, 6.5, 4.8, 6.3, 7.5 and 5.3 from top to bottom in Table 8. The pHavg is equal to 6.03 according to the revised Eq. 3, while it is equal to 6.76 according to the original Eq. 3, indicating there is a significant difference in pHavg. Hence, all relevant data should be recalculated according to the revised equations.
Comment 4
Biogas is composed of methane (CH4), carbon dioxide (CO2), carbon monoxide (CO), nitrogen gas (N2), hydrogen sulfide (H2S), along with small amounts of hydrogen (H2) and ammonia gas (NH3), in which methane is the main combustible gas. Hence, the quality of biogas relies on the proportion of methane. Apart from the production amount of biogas, from the perspective of energy efficiency, the authors should also pay close attention to estimating the proportion of methane.
Comment 5
To increase the credibility of the data, the corresponding references should be added for all values in each Table except your experimental data.
Comment 6
To increase the credibility of the model, the corresponding references should be added for some constraints or boundary conditions.
Comment 7
The constraints or boundary conditions should be clear and easy to determine. Hence, Eqs. 10 and 11 should be modified as follows.
(10)
(11)
Comment 8
The C/N ratio of the mixture (��/��)�� should be recalculated according to the following equation, i.e., Eq. 12 should be modified as follows.
(12)
Herein, yi(N) stands for the mass fraction of N element in the residue i. It should be noted that the original Eq. 12 is applicable only when the N contents in all residues are the same.
Additionally, Eqs. 13~15 should also be modified as the revised Eq. 3.
Thus, all relevant data should be recalculated according to the revised equation.
Comment 9
The Python code should be further optimized according to the revised equations.
Comment 10
Two cases are challenging to prove the effectiveness and reliability of the model, while the authors demonstrate the invalidity of the model only in one case. Hence, the authors provide more empirical cases.
Comment 11
Although the authors used the Monte Carlo method to analyze the data, there was still a lack of experimental evidence to confirm the reliability of the model.
2. The author should seriously prepare the manuscript.
Comment 1
The number of keywords should be 3 to 5.
Comment 2
The authors should use subscripts in the molecular formulas, such as CH4 and CO2.
Comment 3
Two words or sentences should be separated by one space (â—‡). For instance,
l It corresponds to······water (100% - % moisture).â—‡Higher values such as······to facilitate anaerobic digestion.
l Corresponds to the fraction ofâ—‡organic matter······during anaerobic digestion.â—‡This is a determining factor······a greater potential for biogas production.
Comment 4
The author should carefully check the spelling of words. For instance,
l It's the proportion of water present in the residue.â—‡Moisture affects the fluidity of the waste and its ability to mix properly in the digester.
Comment 5
The dimension of physical parameters should be balanced, such as BP in [m3], VS in [kg] and PP in [m3/kg VS].
Comment 6
The markings should be consistent in Eqs.1 and 4 for the same physical parameters.
Comment 7
To ensure uniformity in form, “cushioning Capacity” should be replaced with “buffering capacity” in the tables and full text.
Comment 8
For the convenience of readers' understanding, the unit of each physical parameter must be indicated.
Comment 9
The composition of biogas should be detailed. Biogas is composed of methane (CH4), carbon dioxide (CO2), carbon monoxide (CO), nitrogen gas (N2), hydrogen sulfide (H2S), along with small amounts of hydrogen (H2) and ammonia gas (NH3)
Comment 10
The pH value is a range in Tables 6 and 7. Hence, the column name should be revised to “pH” from “Average pH”.
Comment 11
The average pH value should be used in Table 8. Thus, the average pH values of residue i should be 7.0, 6.5, 4.8, 6.3, 7.5 and 5.3 from top to bottom.
Comment 12
There is one table between Tables 7 and 8. The author should number the table or convert it into text
Comment 13
The symbol labeling of physical parameters is too confusing in this work. For instance, the mass of residue i has two forms: mi and xi, which is the same for mT and xT. The authors should remove duplicate symbol labels.
Comment 14
Eq. 20 is incorrect. The authors should delete it from the manuscript.
Comments for author File: Comments.pdf
Author Response
The observations have been addressed in the manuscript, and both the updated version of the article and the responses to the evaluators for each point are attached.
Author Response File: Author Response.pdf
