Determination of Equilibrium Loading by Empirical Models for the Modeling of Breakthrough Curves in a Fixed-Bed Column: From Experience to Practice
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsIn Figure 3, please add the axis.
Please revise all the figures more clearly.
Besides research significance, please add a section of the conclusion of your research.
Comments on the Quality of English Language
The English of the manuscript needs to be revised.
Author Response
- In Figure 3, please add the axis.
Reply: Thanks for your warm work. This figure was a schematic diagram. So, it did not need the axis with a scale. Moreover, we provided a line Ct/C0 = 1 in the revised manuscript.
- Please revise all the figures more clearly.
Reply: Thanks for your suggestion. We improved the resolution of all figures in this revision.
- Besides research significance, please add a section of the conclusion of your research.
Reply: Thanks for your suggestion. We added a section “5. Conclusions” and written “In this study, the breakthrough time and saturation time were efficiently solved using the fzero command of MATLAB 2023b, while the equilibrium loading, breakthrough capacity and saturation capacity were determined by its int command. These process parameters were essential for evaluating the performance of the fixed-bed column. The Yoon–Nelson model provided a poor fit for the modeling of the breakthrough curves from phosphate adsorption on the Ca-Fe-La composite because of its symmetry. Error statistics and AIC/BIC analysis indicated that the parallel sigmoidal model was optimal. The predicted equilibrium loadings were 101.11, 116.69 and 129.50 mg g−1 respectively at the adsorbent mass of 0.1, 0.3 and 0.5 g. This study effectively bridged the gap between the undetermined parameters of empirical breakthrough models and the process parameters of the fixed-bed column, significantly enhancing their practical applicability” in the revised manuscript (Lines 307-318).
- The English of the manuscript needs to be revised.
Reply: Thanks for your suggestion. We corrected the English grammars of the manuscript carefully. The revised portion was marked in red.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe manuscript aims to investigate the empirical models of breakthrough curves in a fixed-bed column. The experimental data were published earlier, here the modeling part was presented. The topic is very interesting and important, it is related to the profile of the journal; nevertheless, the structure of the manuscript should be reconsidered, moreover, the aim and concluions should be more elaborated, to be useful for other researchers. Section 2 is a bit confusing; it presents the theoretical background of fitting models - the fitting results don’t fit here, they should be moved to Results and discussion part.
Generally, the Title is informative, the Abstract well summarized the results of the work: a list of abbreviations should be very useful. Introduction section is well written, it reveals the importance and novelty of the topic. Methods part should contain a short description of the adsorption circumstances, as the adsorbent mass is a
meaningless value without the other parameters. The manuscript should be understandable on its own, without the previous article.
Results and discussion section, Fig 2. Before presenting the results,/figures please, specify the aim and the parameters you were investigated.
lines 262-272: the technical procedure of modelling should be moved to Methods section. Here the evaluation should be presented, please, explain here what can be concluded form AIC and BIC values?
The English of the manuscript seems to be good and understandable; few spelling mistakes were found; please check it carefully. The indices must be corrected through the manuscript. (The referee is not a native English speaker).
The manuscript is recommended for publication after major revision.
Author Response
Response to Reviewer #2
The manuscript aims to investigate the empirical models of breakthrough curves in a fixed-bed column. The experimental data were published earlier, here the modeling part was presented. The topic is very interesting and important, it is related to the profile of the journal; nevertheless, the structure of the manuscript should be reconsidered, moreover, the aim and conclusions should be more elaborated, to be useful for other researchers. Section 2 is a bit confusing; it presents the theoretical background of fitting models - the fitting results don’t fit here, they should be moved to Results and discussion part.
Reply: Thanks for your suggestion. In the revised manuscript, the theoretical backgrounds of the empirical breakthrough models have been moved to section “3. Results and discussion”. Moreover, we explained the objective of this study clearly in the abstract (Lines 27-29) and we written “This study aimed to conveniently obtain the critical process parameters through MATLAB software using the empirical breakthrough models, thereby providing the reliable information for the design and optimization of the fixed-bed adsorbers”. We added a section “5. Conclusions” and written “In this study, the breakthrough time and saturation time were efficiently solved using the fzero command of MATLAB 2023b, while the equilibrium loading, breakthrough capacity and saturation capacity were determined by its int command. These process parameters were essential for evaluating the performance of the fixed-bed column. The Yoon–Nelson model provided a poor fit for the modeling of the breakthrough curves from phosphate adsorption on the Ca-Fe-La composite because of its symmetry. Error statistics and AIC/BIC analysis indicated that the parallel sigmoidal model was optimal. The predicted equilibrium loadings were 101.11, 116.69 and 129.50 mg g−1 respectively at the adsorbent mass of 0.1, 0.3 and 0.5 g. This study effectively bridged the gap between the undetermined parameters of empirical breakthrough models and the process parameters of the fixed-bed column, significantly enhancing their practical applicability” in the revised manuscript (Lines 307-318).
Generally, the Title is informative, the Abstract well summarized the results of the work: a list of abbreviations should be very useful. Introduction section is well written, it reveals the importance and novelty of the topic. Methods part should contain a short description of the adsorption circumstances, as the adsorbent mass is a meaningless value without the other parameters. The manuscript should be understandable on its own, without the previous article.
Reply: Thanks for your suggestion. We provided a list of abbreviations and a short description of the fixed-bed adsorption experiments, and written “According to the previous study [14], the fixed-bed adsorption experiments were conducted using a cylindrical column with an internal diameter of 1.0 cm and a length of 10 cm. The column was packed with a mixture of the Ca-Fe-La composite and quartz sands in a ratio of 1:9. The breakthrough curves were generated by varying the adsorbent mass (0.1, 0.3 and 0.5 g) while keeping other conditions constant: an initial phosphate concentration of 30 mg L⁻¹, a flow rate of 2.5 mL min⁻¹ and a pH value of 5.12. The effluent phosphate concentration was measured using a UV/vis spectrophotometer at a wavelength of 700 nm” in the revised manuscript (Lines 78-85).
Results and discussion section, Fig 2. Before presenting the results,/figures please, specify the aim and the parameters you were investigated.
Reply: Thanks for your suggestion. We added “To further evaluate fitting quality of these empirical models, four error statistics (RSS, Adj. R2, χ2 and RMSE) were used” in the revised manuscript (Lines 209-210).
lines 262-272: the technical procedure of modelling should be moved to Methods section. Here the evaluation should be presented, please, explain here what can be concluded form AIC and BIC values?
Reply: Thanks for your suggestion. In the revised manuscript, the technical procedure of modelling has been moved to “2. Methods”. We written “The primary objective of AIC and BIC was to identify a model that best explained the experimental results while containing the least parameters. A lower value of AIC or BIC indicated that the estimated model achieved a compromise between the goodness of fit and the model complexity, making it the preferred model” in the revised manuscript (Lines 113-117).
The English of the manuscript seems to be good and understandable; few spelling mistakes were found; please check it carefully. The indices must be corrected through the manuscript. (The referee is not a native English speaker).
Reply: Thanks for your suggestion. We corrected the English grammars of the manuscript carefully. The revised portion was marked in red.
The manuscript is recommended for publication after major revision.
Reply: Thanks for your suggestion. We carefully revised the manuscript point by point. The revised portion was marked in red. We appreciate for your warm work earnestly, and hope that the corrections will meet with approval.
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsThe manuscript was significantly improved according to reviewer's quiery. Now it is recommend for publication.
