Review Reports - Comparative Evaluation of Flow Rate Distribution Methods for Uranium In-Situ Leaching via Reactive Transport Modeling

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents the development and implementation of a reactive transport model applied to an actual technological unit at the Budenovskoye deposit. Furthermore, six distinct strategies for reallocating well flow rates were assessed. The results of the reactive transport modeling demonstrate that multi- criteria optimization methods can substantially enhance the efficiency of in-situ leaching (ISL) while concurrently reducing operational costs. The study makes a valuable contribution to ISL optimization; however, several issues need to be addressed:

On page 5, second paragraph, line 5, the first letter of "reactive" should be capitalized.
Figure 2 lacks proper citation in the text and essential graphical elements. Specifically: (a) the phrase "as shown in Figure 2" appears without corresponding textual reference; (b) the x and y axes lack unit specifications and descriptive labels; (c) the color legend requires clear explanation of its significance and scale parameters.
The mathematical formulations presented in Section 2.2 require proper attribution and validation. The authors should clarify whether these weighting factor calculation methods (equations 17-30) represent novel contributions or adaptations of existing methodologies. If adapted, appropriate citations to seminal works are essential.
In the part of Results and Discussion, author carried out a serious of mathematical modelling based on a previously validated reactive transport model. Furthermore, six approaches for well flow rate redistribution were compared, based on different weighting factor calculationmethods, however, there is lack discussion of model uncertainties and sensitivity analysis for key parameters.
In the Results and Discussion section, there is a lack of summary regarding how to leverage the application value of six reallocated well flow rates in practical engineering.
The Conclusions section requires revision. The introduction to the study should be more concise, and the comparative analysis and summary of the effectiveness of various flow rate optimization methods should be further strengthened and clearly refined.

Author Response

Thank you for the careful evaluation and constructive comments. The suggestions have been thoroughly considered, and corresponding revisions have been made to improve the quality of the manuscript. Detailed responses to each point are provided below, with the revisions highlighted in italics.

On page 5, second paragraph, line 5, the first letter of "reactive" should be capitalized.
The capitalization has been fixed.
Figure 2 lacks proper citation in the text and essential graphical elements. Specifically: (a) the phrase "as shown in Figure 2" appears without corresponding textual reference; (b) the x and y axes lack unit specifications and descriptive labels; (c) the color legend requires clear explanation of its significance and scale parameters.
A reference to the figure as well as X, Y units were added to the article. You are correct, the legend is irrelevant here since all cells contain same concentration. The legend was removed, however caption was extended.
The mathematical formulations presented in Section 2.2 require proper attribution and validation. The authors should clarify whether these weighting factor calculation methods (equations 17-30) represent novel contributions or adaptations of existing methodologies. If adapted, appropriate citations to seminal works are essential.
Thank you for this valuable remark. Indeed the advanced traditional (AT) method has been adopted by the subsidiaries of JSC NAC Kazatomprom and described in the official methodological book “Geotechnology of Uranium” [Poezhaev, 2017]. An appropriate reference has been added. The rest of the methods mentioned in the article are approaches proposed by the authors, in order to account for the distance between wells.
In the part of Results and Discussion, author carried out a serious of mathematical modelling based on a previously validated reactive transport model. Furthermore, six approaches for well flow rate redistribution were compared, based on different weighting factor calculation methods, however, there is lack discussion of model uncertainties and sensitivity analysis for key parameters.
The reactive transport model used in this work has been previously validated on the same deposit and discussed in the works [Kurmanseiit 2024] and [Kurmanseiit 2025]. Your point is valid, the accuracy of the proposed approaches directly depend on the model with which they were verified. The convergence of the model has been studied on such sensitive parameters as flow velocity, reaction rate and grid size. An additional paragraph has been added, although to the end of subsection 2.1.
In the Results and Discussion section, there is a lack of summary regarding how to leverage the application value of six reallocated well flow rates in practical engineering.
At the design stage of the technological block, one of the main decisions a geotechnologist must make is determining the flow rates at each well. This decision directly affects the coverage of the subsurface by the leaching solution and the operational time required to achieve the desired recovery rate. Such decisions should be based on a physics-based methodology that accounts for as many parameters as possible. The current AT approach does not consider well spacing, let alone other geotechnological parameters. Alternative approaches, verified through reactive transport modeling, which is itself a computationally expensive method, would enable rapid forecasting of scenarios with reduced operational time and, consequently, lower OPEX, while ensuring that the solution is distributed uniformly throughout the domain. Based on the results it is recommended to exploit SD method, which does not require complex numerical computations, and provides higher efficiency in terms of lowering recovery time and OPEX. Time-of-flight based approaches are prospective, yet would require additional studies to be carried out. As per your valuable suggestion, this recommendation has been added to the Results and Discussion section.
The Conclusions section requires revision. The introduction to the study should be more concise, and the comparative analysis and summary of the effectiveness of various flow rate optimization methods should be further strengthened and clearly refined.
The Conclusions section has been revised to be more concise and focused. The comparative analysis was clarified, highlighting the higher efficiency of the SD method in reducing recovery time and OPEX, while noting that time-of-flight approaches remain prospective but require further study.

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript conducts research on the optimization of well flow allocation in the ISL operation of uranium mines. Taking the real technical block of the Budenovskoye deposit in Kazakhstan as an example, the author compared six flow redistribution methods using reactive transport modeling to minimize solution imbalance, reduce stagnation zones and lower operating costs. This method combines fluid mechanics modeling with the chemical kinetics of the interaction between sulfuric acid and uranium minerals.

The introduction has devoted a considerable amount of space to describing the reactive transport model. This part should be streamlined. The focus should be on elaborating on the application scope and effectiveness of the model.
This study mentions on page 4 that "porosity and permeability vary only slightly within the scale of a single block ". And in the conclusion, the potential advantages of the streamline method in "heterogeneous environments" were emphasized. If the hypothesis of this study is homogeneous, the advantages of the streamline method under heterogeneous conditions have not been fully demonstrated and discussed.

Author Response

The authors would like to thank the reviewer for the valuable comments and constructive suggestions, which have significantly contributed to improving the quality of this manuscript. All comments have been addressed, and corresponding revisions have been incorporated into the revised version. Point-by-point responses to the reviewers' comments are provided below, with the authors' responses highlighted in italics for clarity.

The introduction has devoted a considerable amount of space to describing the reactive transport model. This part should be streamlined. The focus should be on elaborating on the application scope and effectiveness of the model.

The part of the review, describing reactive transport simulation application for ISL has been compressed to be more streamline.

This study mentions on page 4 that "porosity and permeability vary only slightly within the scale of a single block ". And in the conclusion, the potential advantages of the streamline method in "heterogeneous environments" were emphasized. If the hypothesis of this study is homogeneous, the advantages of the streamline method under heterogeneous conditions have not been fully demonstrated and discussed.

This work assumes the absence of impermeable clay lenses based on the literature review. However, field observations, including those from the authors' experience, indicate that solution flow can be significantly redirected by local heterogeneities, affecting solution balance. While the mathematical model inherently accounts for such variability, the streamline approach requires separate validation for highly heterogeneous environments, which constitutes future work. Particular attention should be given to temporal permeability changes, as discussed in the Introduction. The Results and Conclusion sections have been revised to clarify that the streamline method's applicability to anomalously heterogeneous conditions and time-dependent geohydrochemical variations requires further investigation. Such variations affect effective total well flow rates, and thereby, conveniently, affect streamlines themselves, suggesting that this approach could provide a flexible tool for optimizing flow rate distribution in ISL operations.

Reviewer 3 Report

Comments and Suggestions for Authors

Kurmanseiit et al. present results about using modeling to predict the optimal solution delivery method for ISR using the Budenevskoye deposit as a case study. Overall, the manuscript is well written and conceived. I only have minor comments--I do not need to see this manuscript again.

One general comment I have for the authors is that these models would be substantially improved by having real mineralogy, even if it is generalized. Kinetic dissolution rates for ~30 uranium minerals are present in the literature and their dissolution rates vary by several orders of magnitude depending on the mineral. While using UO₂ and UO₃ is suitable for this manuscript, I encourage/challenge these authors to raise the bar for future modeling papers and try to better constrain the geochemistry. Especially if the authors plan to keep using Budenevskoye as a test case for modeling, getting uranium EXAFS data for core materials from this site would significantly improve the predictive modeling. Having XRD would also allow the authors to determine the amount of pyrite in core materials, which oxidizes more rapidly than uraninite, affecting both pH and oxidant concentrations.

Minor comments:

-What were the proportions of UO2 versus UO3 used for modeling?

-Is UO₂SO₄ the dominant aqueous species at the pH in this ISR operation? I would expect that UO₂²⁺ may also be a dominant species in this pH range. If UO22+ is the dominant species, it may be better to show this in the representative reactions to avoid these being possibly misleading.

-In figure 10, please increase the font size of the titles, labels (a, b, and c), and legend text if possible. This is a great figure but the text is very difficult to read.

-Figure 13. Change “interations” to “iterations”

-For Table 1, it may be better to report average deviation rather than total deviation. Because the change in uranium (in g/L) is reported as an average, it would be good to also average the deviations. That way, readers will not get confused and think that the deviation is larger than the average for each method.

-For Table 2, it would be clearer to readers if “Operation time” was changed to “Operation time to reach 90% recovery” or something similar. “Efficiency (%)” is also unclear. Efficiency relative to what? Changing this label would improve clarity. Maybe something like “Efficiency (% decrease in operational costs)”

Author Response

The authors appreciate the reviewers' insightful comments and suggestions. All concerns have been addressed in the revised manuscript. Responses to individual comments are provided below, with the authors' replies highlighted in italics.

One general comment I have for the authors is that these models would be substantially improved by having real mineralogy, even if it is generalized. Kinetic dissolution rates for ~30 uranium minerals are present in the literature and their dissolution rates vary by several orders of magnitude depending on the mineral. While using UO₂ and UO₃ is suitable for this manuscript, I encourage/challenge these authors to raise the bar for future modeling papers and try to better constrain the geochemistry. Especially if the authors plan to keep using Budenevskoye as a test case for modeling, getting uranium EXAFS data for core materials from this site would significantly improve the predictive modeling. Having XRD would also allow the authors to determine the amount of pyrite in core materials, which oxidizes more rapidly than uraninite, affecting both pH and oxidant concentrations.

The authors appreciate the valuable suggestions regarding future research directions. Overall mineralogy has been considered in previous works [Kurmanseiit 2022, Kurmanseiit 2024, Kurmanseiit 2025]; however, the main chemical interactions have been simplified. While multiple compounds react during ISL, not all significantly affect uranium recovery. For example, according to Gromov, the commonly cited reaction: UO₃ + H₂SO₄ → UO₂SO₄ + H₂O is not fully accurate. The hydrogen dissociates, and the following reaction occurs for UO₃ alone, not accounting for more complex UO₂: UO₃ + 2H⁺ → UO₂²⁺ + H₂O. In practice, solving the complete system of equations is computationally prohibitive, particularly when incorporating clogging reactions with calcium carbonate and catalytic effects from pyrolusite or hydrogen peroxide. The ultimate objective is to develop a practical tool for operational flow rate distribution. During authors’ implementation at mining sites, hydrochemical simulations required up to 24 hours per technological block scenario, rendering the approach impractical for industrial decision-making. Consequently, simplifications of kinetic equations were necessary, complemented by acceleration techniques including GPU parallel computing and neural networks for generating initial approximations. EXAFS and XRD data will be requested to refine the model in future work. The authors thank the reviewer for this valuable suggestion.

Minor comments:

-What were the proportions of UO2 versus UO3 used for modeling?

The proportions were taken as 1 to 1. This generalized ratio was obtained through experimentation with varying proportions of uranium oxides [Kurmanseiit 2022] and comparison with laboratory experiments. The corresponding description was added after equation 12.

-Is UO₂SO₄ the dominant aqueous species at the pH in this ISR operation? I would expect that UO₂²⁺ may also be a dominant species in this pH range. If UO22+ is the dominant species, it may be better to show this in the representative reactions to avoid these being possibly misleading.

Yes, models incorporating pH dynamics exist, however, the proposed mathematical model employs simplified chemical representations to accelerate calculations, design processes, and forecasting. Comprehensive models accounting for such factors require cluster-based computing infrastructure, which is impractical for remotely located mining sites. The primary objective of the proposed instrument is to provide rapid calculations with sufficient accuracy for operational decision-making.

-In figure 10, please increase the font size of the titles, labels (a, b, and c), and legend text if possible. This is a great figure but the text is very difficult to read.

The figure has been amended to be more readable and split into 3.

-Figure 13. Change “interations” to “iterations”

Misspelling has been fixed.

This is not the total deviation, but the sum of the average deviations. The corresponding change was made: From Total deviation to Sum of average deviation.

The recommendations you provided have been implemented.

Reviewer 4 Report

Comments and Suggestions for Authors

Page 3 (Introduction)

The introduction is comprehensive, but please explicitly state how your comparison adds to recent surrogate modeling and machine learning optimization approaches (e.g., refs [15], [21]). A short statement distinguishing your contribution would strengthen novelty.
Consider adding a brief note linking your sulfuric acid focus to other lixiviant systems (e.g., CO₂+O₂, ref [22]) so readers see broader applicability.

Pages 7–9 (Methods – Equations 4–6)

Ensure consistency in equation notation: “Oxidant” and “Reductant” in Eq. (5) should be more clearly defined, and confirm whether cUO2SO4c_{UO_2SO_4} participates in w3w_3 as written.
A summary table listing all fixed parameters (Kf, porosity, dispersion coefficient, reaction rate constants with units) would greatly improve reproducibility.

Page 12–14 (Flow distribution methods)

When describing the LD, SD, and AQ methods, please clarify whether weighting is normalized per block or per cell. This is implied but not fully explicit.
For AQ (quadrilateral area method), a worked numerical example of the area calculation would help readers replicate the method.

Page 15–16 (Streamline-based methods)

In the TOFmin/TOFavg descriptions, specify the relaxation factor and stopping criterion for convergence (also relevant to Fig. 13).
Add a short discussion explaining why TOF methods did not outperform SD under homogeneous assumptions, and emphasize that their main benefit arises in heterogeneous media.

Page 18–19 (Results – Figure 11 & Table 1)

Figure 11: The zoomed-in view should indicate the exact time range shown (e.g., 500–545 days). Adding labels for the key recovery times (511, 512, 514, 515, 521, 542 days) directly on the curves would improve clarity.
Table 1: Add units in column headers (e.g., “Solid mineral concentration [g/L]”). Clarify that “Avg. by cells” is the mean of the four production well cells.

Page 20 (Results – Figure 12)

Consider adding scale bars or consistent colorbar limits across subplots so readers can compare uranium concentrations directly between AT and SD methods.

Page 21 (Results – Figure 13)

State the convergence iteration number more clearly in the caption (e.g., “converged after ~15 iterations for AT initialization, ~8 for AQ”).

Page 22–23 (Discussion & Conclusions)

The discussion rightly points to SD as most efficient, but please add one short paragraph giving practical guidance: e.g., “Under homogeneous block assumptions, SD or AQ are recommended; under heterogeneous conditions, TOF methods should be preferred.”
Language polishing recommended: standardize phrasing (“redistribution of flows” vs. “flow rate redistribution”), and add articles (“the SD method”).

Author Response

The authors sincerely thank the reviewers for their thorough evaluation and constructive comments, which have substantially improved the quality of this manuscript. All concerns have been addressed, and corresponding revisions have been incorporated into the manuscript. Point-by-point responses to each comment are provided below, with the authors' responses highlighted in italics.

Page 3 (Introduction)

The introduction is comprehensive, but please explicitly state how your comparison adds to recent surrogate modeling and machine learning optimization approaches (e.g., refs [15], [21]). A short statement distinguishing your contribution would strengthen novelty.

The authors have previously integrated ISL simulation software at several uranium mining enterprises in Southern Kazakhstan. The primary challenge encountered during ISL modeling is excessive computational time, particularly for hydrochemical simulations, which require up to 24 hours per production scenario even with GPU-accelerated parallel computing. Such computational costs are impractical during production operations and even design stages, especially for timely decision-making regarding flow rate adjustments. Currently, site geotechnologists employ the AT approach to address solution imbalances, however, this method lacks physical basis and does not account for inter-well distances. The proposed approaches aim to reduce computation time, a critical factor for forecasting and operational decision-making accounting for distance between wells, and, for streamline approaches, accounting for time-of-flight. While AI was not employed in the present work, it may be incorporated in future studies following the approach demonstrated in authors’ previous publications [Aizhulov 2024, Kurmanseiit 2024], where AI accelerated hydrodynamic calculations by generating initial approximations. Mining sites possess extensive historical production data, including flow rates, reagent concentrations, and recovery metrics. As suggested by you, these datasets could serve as useful training data for machine learning methods to support decision-making processes in a timely manner.

Consider adding a brief note linking your sulfuric acid focus to other lixiviant systems (e.g., CO₂+O₂, ref [22]) so readers see broader applicability.

Other lixiviant systems were mentioned before equation (4), and yes, depending on subsurface geochemistry, additional agents may be involved in the production process. In some cases, clogging can occur due to gypsum precipitation in the presence of carbonates, or supplemental reagents may be required to intensify the process. The chemical equation system presented in this work is traditional for the Chu-Sarysu basin in the Turkestan region of Kazakhstan. The main uranium leaching equation itself has been simplified to reduce computational costs by disregarding hydrogen dissociation and its direct reaction with uranium oxide.

Pages 7–9 (Methods – Equations 4–6)

Ensure consistency in equation notation: “Oxidant” and “Reductant” in Eq. (5) should be more clearly defined, and confirm whether cUO2SO4c_{UO_2SO_4}cUO2SO4 participates in w3w_3w3 as written.

You are correct that c_{UO₂SO₄} is incorporated into the mathematical model through w₃ (omega). Since the primary objective is to model acid consumption and these intermediate species are not extraction targets, the mathematical formulation has been simplified accordingly to reduce computational complexity while maintaining accuracy for the parameters of interest. Since reaction occur at redox front, adding oxidant and reductant in equations were to follow standard notation.

A summary table listing all fixed parameters (Kf, porosity, dispersion coefficient, reaction rate constants with units) would greatly improve reproducibility.

All parameters are defined within the article text. The authors believe that consolidating them into a separate table would disrupt the narrative flow for the reader. Parameters such as porosity, hydraulic conductivity, and uranium content, etc. represent initial conditions for the model and are introduced when the model setup is described. Conversely, parameters like reaction rates were obtained through the modeling process itself and are therefore presented later in the text where their derivation can be properly explained.

Page 12–14 (Flow distribution methods)

When describing the LD, SD, and AQ methods, please clarify whether weighting is normalized per block or per cell. This is implied but not fully explicit.

In general, since one node of acid distribution unit is assigned per block, total flow rates are determined per same block. However, the distribution framework can be scaled to other levels (e.g., field-wide implementation) if required for operational or optimization purposes. The text has been clarified with the explanation above, inserted before equation 13.

For AQ (quadrilateral area method), a worked numerical example of the area calculation would help readers replicate the method.

You are correct that the formula may not be intuitively clear at first glance. An additional formulation has been added as equation (25) to describe the geometric calculation process for S_{i,j}.

Page 15–16 (Streamline-based methods)

In the TOFmin/TOFavg descriptions, specify the relaxation factor and stopping criterion for convergence (also relevant to Fig. 13).

Stopping criteria for relaxation has been added after Figure 9. Figure 13 (now it is Figure 15) has been edited in accordance with your suggestion.

Add a short discussion explaining why TOF methods did not outperform SD under homogeneous assumptions, and emphasize that their main benefit arises in heterogeneous media.

This is an important observation. The comparison essentially contrasts length-based versus area-based metrics. While streamlines follow the path of least resistance, TOFmin accounts for time-of-flight along the shortest flow path, conceptually similar to LD, but expressed in temporal rather than spatial terms. Consequently, TOFmin does not account for the leaching area or the influence of neighboring injection wells. Conversely, TOFavg incorporates these factors, however, it suffers from instability issues because streamline distributions change significantly after some specific iteration, particularly for streamlines with the longest time-of-flight values. These limitations render both TOF-based approaches less efficient than SD and AQ. Results from all methods except AT and LD fall within a narrow, practically insignificant range. Differences of merely a few days in recovery time would require flow rate precision unattainable under field conditions. An additional discussion and figure (Figure 16) have been added to address this point, thanks to your insightful comment.

Page 18–19 (Results – Figure 11 & Table 1)

Figure 11: The zoomed-in view should indicate the exact time range shown (e.g., 500–545 days). Adding labels for the key recovery times (511, 512, 514, 515, 521, 542 days) directly on the curves would improve clarity.

Your valuable suggestion has been implemented in Figure 13 (numeration has changed).

Table 1: Add units in column headers (e.g., “Solid mineral concentration [g/L]”). Clarify that “Avg. by cells” is the mean of the four production well cells.

Units were added.

Page 20 (Results – Figure 12)

Consider adding scale bars or consistent colorbar limits across subplots so readers can compare uranium concentrations directly between AT and SD methods.

Colorbar was added.

Page 21 (Results – Figure 13)

State the convergence iteration number more clearly in the caption (e.g., “converged after ~15 iterations for AT initialization, ~8 for AQ”).

The change has been made.

Page 22–23 (Discussion & Conclusions)

The discussion rightly points to SD as most efficient, but please add one short paragraph giving practical guidance: e.g., “Under homogeneous block assumptions, SD or AQ are recommended; under heterogeneous conditions, TOF methods should be preferred.”

The amendments have been put in place.

Language polishing recommended: standardize phrasing (“redistribution of flows” vs. “flow rate redistribution”), and add articles (“the SD method”).

Language polishing has been made.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Carefully review the entire text to ensure it meets the requirements of the journal.

Reviewer 3 Report

Comments and Suggestions for Authors

Good job addressing comments!

Reviewer 4 Report

Comments and Suggestions for Authors

The authors have carefully and comprehensively addressed all the previous review comments.
The revised version shows significant improvement in clarity, structure, and methodological transparency.

The introduction now provides clear context and highlights the novelty of the study relative to recent works on surrogate and deep-learning models.
The methods section has been improved with consistent notation and clearer descriptions of reaction equations and parameters.
The results and figures are now well-presented, with improved captions, consistent units, and better readability.
The discussion provides stronger justification for the performance differences between geometric and streamline-based approaches, as previously suggested.
Minor language and formatting issues have been corrected, and the manuscript reads fluently.

Overall, the revisions satisfactorily resolve all earlier concerns. The paper now presents a clear, well-supported, and methodologically sound contribution to the field of uranium in-situ leaching optimization.

I recommend this manuscript be accepted in its present form.