Computational Approaches to Assess Flow Rate Efficiency During In Situ Recovery of Uranium: From Reactive Transport to Streamline- and Trajectory-Based Methods
, Nurlan Shayakhmetov 1,*, Daniar Aizhulov 2,*, Banu Abdullayeva 3 and Madina Tungatarova 1
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors1.Chapter 2 is titled "Materials and Methods", while Chapter 3 is labeled "Method for Determining Solution Balance" – this structure is inconsistent. It is recommended to adjust the article's structure: Chapter 2 should be titled "Materials and Methods" and Chapter 3 "Results and Discussion".
2.The three calculation methods used in the paper all depend on model parameters, so these parameters need to be specified. Streamline and trajectory calculations require parameters like permeability coefficients, while reaction transport models need chemical reaction-related parameters.
3.Figure 6 shows that the sulfuric acid concentration in the extraction well is 0 at 478 days, which seems inconsistent with practical conditions. The model parameters appear to be improperly set. The paper should provide actual observational data to validate the rationality of the simulation results. Additionally, the full configuration methods and parameters of the model must be presented to enable readers to assess the validity of both the model and its simulation outcomes.
4.The model used in the paper is a steady flow, where streamlines and trajectories are essentially the same in theory. The so-called "trajectory method" actually only considers particle flight time, which is easily influenced by permeability coefficients and aquifer thickness.
Comments on the Quality of English Languagenone
Author Response
We sincerely thank the reviewer for their valuable comments and constructive suggestions, which have helped improve the quality and clarity of the manuscript. We have considered each comment and made the necessary revisions accordingly. Below, we provide a point-by-point response, indicating how each comment has been addressed in the revised version of the manuscript.
1.Chapter 2 is titled "Materials and Methods", while Chapter 3 is labeled "Method for Determining Solution Balance" – this structure is inconsistent. It is recommended to adjust the article's structure: Chapter 2 should be titled "Materials and Methods" and Chapter 3 "Results and Discussion".
We agree with your observation and the structure of the manuscript has been revised: Chapter 2 remains titled "Materials and Methods", and Chapter 3 has been renamed to "Results and Discussion".
2.The three calculation methods used in the paper all depend on model parameters, so these parameters need to be specified. Streamline and trajectory calculations require parameters like permeability coefficients, while reaction transport models need chemical reaction-related parameters.
The value of hydraulic conductivity is presented in Table 1, and it can also be expressed in terms of permeability using the following equation:
Density, gravitational acceleration and viscosity being constant permeability and hydraulic conductivity are effectively interchangeable. Nevertheless, to enhance clarity, an explanatory note “In practice, due to the low concentration of the reagent in the leaching solution…” has been added after Formula (2).
Regarding the reaction rate constants used in the reactive transport model, the methodology for their determination and the corresponding values are provided in our previous work [9], which includes validation of the mathematical model using field data from the same site analyzed in this work. A more detailed description has been included in the revised manuscript (below formula 10).
3.Figure 6 shows that the sulfuric acid concentration in the extraction well is 0 at 478 days, which seems inconsistent with practical conditions. The model parameters appear to be improperly set. The paper should provide actual observational data to validate the rationality of the simulation results. Additionally, the full configuration methods and parameters of the model must be presented to enable readers to assess the validity of both the model and its simulation outcomes.
According to equations (10)–(11), the leaching agent reacts with the solid mineral, resulting in the formation of a mineral in dissolved form (pregnant solution). So, there are two types of the solution: leaching solution and pregnant solution, both include SO4 in form of either H2SO4 or UO2SO4. Figure 6 illustrates the spatial distribution of the reagent that has not yet reacted with the solid components (i.e., the mineral and other associated substances), and yes, in its pure form did not reach the well yet. However, you can observe on Figure 7 that pregnant solution with some product of the reaction between sulfuric acid solids has indeed reached the well and is not 0. Captions of figures 6 and 7 were amended to avoid the confusion.
4.The model used in the paper is a steady flow, where streamlines and trajectories are essentially the same in theory. The so-called "trajectory method" actually only considers particle flight time, which is easily influenced by permeability coefficients and aquifer thickness.
The main objective of this study is to identify balance zones without relying on a full mathematical model. A complete mathematical model typically involves two stages: first, the calculation of hydrodynamic behavior to determine the velocity field; and second, the reactive transport simulation, which accounts for reactions between the components. The second stage is significantly more computationally demanding, as it requires a detailed analysis of chemical reactions for each block of the field, including the determination of reaction rate constants. This has been observed by authors and described in work [9] Kurmanseiit et al 2022. Significant computational demands are impractical as per comments of on-site geotechnologists and accelerated solutions are required. This study proposes omitting the second stage in order to accelerate the process of balance zone identification. Data demonstrating the computational speed-up achieved through this approach have also been included in Conclusion (last paragraph).
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper focuses on the assessment of flow rate efficiency during in-situ leaching (ISL) of uranium, taking the Budenovskoye deposit in Kazakhstan as the research object. It compares the applicability of traditional methods, streamline-based methods, and trajectory-based methods by establishing a reactive transport model, and proposes alternative schemes that can reduce computational costs while maintaining accuracy.
(1) There were too many keywords, please keep only 5-6 critical keywords.
(2) Figure 2, please add the full name of Pr and In as it was presented in other Figures.
(3) Line 127, the citation [32?].
(4) The manuscript points out that the trajectory method overestimates the acid overflow outside the block (348.24 tons vs. 239.12 tons in the reactive transport model, with a deviation of 45.6%), but fails to conduct in-depth analysis of the reasons. Is it due to unreasonable setting of time step (Δt_change) or failure to consider the impact of chemical reactions on flow rate? Mechanistic analysis needs to be supplemented.
(5) The existing comparison mainly focuses on acid distribution and uranium dissolution, lacking quantitative analysis of computational efficiency (such as comparison of calculation time and hardware requirements of the three methods). Meanwhile, the impact of geological heterogeneity (such as sudden change in permeability) on the accuracy of the three methods is not discussed, which limits the definition of applicable scenarios of the methods.
(6) Please provide more geological information of the ISL area, to explain the solution flow rate, as well as if there was solution leakage. During the leaching, was there underground water flew to this area?
(7) Please uniform the references format according to the standard of Minerals.
Author Response
Thank you for your thorough review and constructive comments, which have contributed to improving the clarity and quality of our manuscript. We have carefully considered each point and made the necessary revisions. Below, we provide detailed responses to each comment, explaining the changes implemented in the revised version.
(1) There were too many keywords, please keep only 5-6 critical keywords.
In accordance with your recommendation, the number of keywords has been reduced, focusing only on the most critical terms relevant to the content of the manuscript: Well Flow Rate Efficiency; Solution Imbalance; Reactive Transport Modeling; Streamline-based Method; Trajectory-based Method; Computing Acceleration.
(2) Figure 2, please add the full name of Pr and In as it was presented in other Figures.
Thank you for your comment. Figure 2 is intended solely as an illustrative example of the distribution of well flow rates and is not directly involved in the subsequent calculations. Including the names of all wells in this figure may reduce its readability and visual clarity. Therefore, we respectfully propose to retain the current format of the figure for the sake of clarity and emphasis on flow distribution patterns.
(3) Line 127, the citation [32?].
The citation on Line 127 has been corrected.
(4) The manuscript points out that the trajectory method overestimates the acid overflow outside the block (348.24 tons vs. 239.12 tons in the reactive transport model, with a deviation of 45.6%), but fails to conduct in-depth analysis of the reasons. Is it due to unreasonable setting of time step (Δt_change) or failure to consider the impact of chemical reactions on flow rate? Mechanistic analysis needs to be supplemented.
Thank you for the insightful comment. An expanded explanation has been added before Table 5 to address this issue in more detail: “This overestimation is justified by the fact that well pressures gradually increase since the operation commencement…”
(5) The existing comparison mainly focuses on acid distribution and uranium dissolution, lacking quantitative analysis of computational efficiency (such as comparison of calculation time and hardware requirements of the three methods). Meanwhile, the impact of geological heterogeneity (such as sudden change in permeability) on the accuracy of the three methods is not discussed, which limits the definition of applicable scenarios of the methods.
To address this, a quantitative analysis of computational efficiency has been added in the final paragraph of the Conclusion section: “For the block under consideration, which includes 22 wells and a production…”, providing a detailed comparison of calculation times for the full reactive model and the simplified methods.
(6) Please provide more geological information of the ISL area, to explain the solution flow rate, as well as if there was solution leakage. During the leaching, was there underground water flew to this area?
Additional information regarding groundwater conditions has been added to the manuscript before Figure 3. Specifically, it is noted that groundwater flow was excluded from the simulations based on the assumption that its velocity is significantly lower than the flow induced by well operations. Moreover, data on natural groundwater movement were not available in the reference sources. As such, potential groundwater inflow into the leaching area and possible solution leakage were not considered (but can be if appropriate data is available) in the current model.
(7) Please uniform the references format according to the standard of Minerals.
All references have been revised to conform to the formatting requirements of Minerals Journal.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe article titled “Computational Approaches to Assess Flow Rate Efficiency during In-Situ Leaching of Uranium: From Reactive Transport to Streamline- and Trajectory-based Methods” provides a technical and comparative overview of computational strategies for evaluating flow efficiency in uranium in-situ leaching (ISL) operations. The authors focus particularly on reactive transport modeling (RTM), streamline-based, and trajectory-based methods to understand and optimize fluid flow and uranium mobilization within porous geological formations. The manuscript correctly identifies a key challenge in uranium ISL: optimizing fluid injection and recovery schemes to maximize metal recovery while minimizing environmental impact. The integration of computational fluid dynamics, reactive geochemical modeling, and flow-path analysis offers a multi-scale perspective, which is highly valuable for both research and industrial applications. The work is highly relevant, well-cited, and demonstrates a sound grasp of the theoretical basis for each modeling approach.
However, the manuscript needs major revisions before it can be considered for publication. Some areas require attention:
- The manuscript is often hard to follow due to overly technical language and underdeveloped explanations of key terms and methodologies. Non-expert readers may struggle with the terminology.
- While the methods are introduced, the comparative evaluation between the three approaches is insufficient. It would be useful to see specific metrics (e.g., accuracy, computational cost, scalability) compared in tabular or graphical format.
- The lack of real-world or simulated case studies weakens the manuscript. Application to actual uranium leaching scenarios (or synthetic benchmarks) would significantly improve the practical value.
- The study would benefit from referencing some alternative and environmentally sustainable leaching methods, like bioleaching (Waste and Biomass Valorization, 14, 3377–3390), or any other in uranium leaching
- The figures are helpful but would benefit from clearer labels, colorbars, and captions. Diagrams of flow fields, especially streamlines, should be tied more explicitly to the text discussion.
This is a promising and valuable study that addresses an important and underexplored aspect of uranium ISL optimization using computational tools. The combination of modeling frameworks is conceptually strong, and the manuscript demonstrates technical depth. However, due to the issues outlined above, especially the lack of empirical validation, limited comparative assessment, and occasional lack of clarity, major revisions are necessary to improve its scientific impact and accessibility.
Author Response
We sincerely thank the reviewer for the thoughtful and constructive comments, which have greatly contributed to improving the clarity, quality, and overall presentation of the manuscript. We have considered each point raised and made the corresponding revisions throughout the text. Please find below a point-by-point responses explaining how each comment has been addressed in the revised manuscript.
- The manuscript is often hard to follow due to overly technical language and underdeveloped explanations of key terms and methodologies. Non-expert readers may struggle with the terminology.
Revisions have been made throughout the manuscript to improve clarity and readability. An additional explanations of key terms, their relationships with other terms and methodologies have been added to assist in understanding the content.
- While the methods are introduced, the comparative evaluation between the three approaches is insufficient. It would be useful to see specific metrics (e.g., accuracy, computational cost, scalability) compared in tabular or graphical format.
Thank you for this valuable comment. To improve the clarity of the comparative evaluation, we have added specific data on computational costs in the Conclusion section and expanded the discussion on scalability. In particular, we highlight that the proposed streamline and trajectory-based methods become increasingly effective when modeling a larger number of chemical components in the rock. Scalability is also influenced by the number of changes in well flow rates: more frequent changes increase the hydrodynamic calculation time in all methods. However, since full reactive transport modeling also requires hydrodynamic calculations at each step, the relative efficiency of the simplified methods remains favorable for both larger block or for blocks with more frequent regime changes.
Although a direct quantitative accuracy comparison is not feasible due to the inherent differences in methodological assumptions, a qualitative evaluation based on the ability of each method to identify imbalances in leaching solution distribution is included. For instance, the streamline and trajectory-based method enables the identification of specific well cells with insufficient leaching solution, a capability not offered by the traditional approach. This would provide geotechnologists with actionable insights to optimize well flow rates.
- The lack of real-world or simulated case studies weakens the manuscript. Application to actual uranium leaching scenarios (or synthetic benchmarks) would significantly improve the practical value.
The accuracy of the full mathematical model has already been validated using real field data in [9] (Kurmanseiit et al., 2022). Specifically, the model achieved an accuracy of 1.7% based on the Normalized Root Mean Square Deviation (NRMSD), as reported in our previous work [9], where the model was tested against actual production curves. Building on this validated model, the present study focuses on comparing different solution balance estimation methods, using the previously established model accuracy as a benchmark. Thus, while this paper does not introduce a new case study, it relies on a real-world validated model to evaluate and compare the performance of alternative computational approaches. Numerous references to the previous work were added throughout the article.
- The study would benefit from referencing some alternative and environmentally sustainable leaching methods, like bioleaching (Waste and Biomass Valorization, 14, 3377–3390), or any other in uranium leaching
Bioleaching is a promising approach in ISR of useful components. Specifically, few field studies have been conducted in the Semizbay deposit in northern Kazakhstan. Work conducted in (Waste and Biomass Valorization, 14, 3377–3390) as well as in https://doi.org/10.1016/j.hydromet.2019.07.002 and in https://doi.org/10.1016/j.egypro.2011.06.021 have been referenced in the manuscript as environmentally sustainable leaching methods implementing bioleaching.
- The figures are helpful but would benefit from clearer labels, colorbars, and captions. Diagrams of flow fields, especially streamlines, should be tied more explicitly to the text discussion.
The figures have been revised to include more informative captions.
Reviewer 4 Report
Comments and Suggestions for AuthorsKurmanseiit et al. present results about three different modeling approaches to optimize lixiviant delivery to cells in the Budenevskove uranium ISR operation in Kazakhstan. Overall, this is a strong paper; each section is well written, and this is one of the best submissions I have seen to an MDPI journal. The figures are high quality and the conclusions are supported by the data. However, some changes are needed before I can recommend this article for publication.
Major comments:
1.I understand the lack of precise U(VI) and U(IV) mineralogy given that uranium in roll front deposits is present at low concentrations (usually 0.1 weight%). At these concentrations, XRD may not be able to constrain uranium mineralogy.
However, the other impurities could certainly be quantified with XRD. For example, pyrite and calcite often appear at up to 4 weight percent in some roll-front deposits. Getting a couple of representative XRD patterns to even provide a semi-quantitative estimate of mineral impurities would greatly strengthen this paper. Kinetic rates of calcite and pyrite dissolution in acidic solutions are known in the literature and having better constraints on minerals that dissolve would allow this paper to be more applicable to other deposits.
2.The methods sections are all well written, however, it was not immediately clear to the reader how the accuracy of each method is being assessed. I think it would be helpful to have a short section before the reactive transport methods section that explicitly states the time-dependent measurements that are input to the model (flow rates, acidity, etc.), the initial model parameters (permeability, porosity, etc.), and how the relative accuracy of each model was assessed/validated.
Minor comments:
-Consider using the term “In situ recovery (ISR)” instead of “in situ leaching (ISL)”. The Australian and U.S. communities are now moving towards the term ISR because the word “leaching” can have negative connotations for the public.
-In the reactive transport methods section, there should be a sentence or two about grid spacing and possible effects of grid spacing on results.
-What reactive transport code/software was used? Please include this in the methods. Also, consider including your input file(s) as supplementary data (unless of course this is proprietary information). The past studies with HYTEC and other modeling software approaches don’t include code or input files, which can make it hard for other investigators to use and/or expand on this code to improve it. One major benefit of the peer review process is that it makes science/code open-source such that models can continue to be developed and improved.
-In section 2.1: Was Archie’s Law considered to calculate diffusion coefficients in porous media?
-Figure 4: Is the solution acidity measured in the injection or production fluid? I would assume the production fluid but it would be good to clarify.
Line 97: change “Key factor” to “A key factor”
Author Response
We sincerely appreciate the reviewer’s insightful and constructive feedback, which has significantly helped enhance the clarity and overall quality of our manuscript. We have addressed each of the comments and made the necessary revisions throughout the text. Below, we provide a point-by-point response outlining how each suggestion has been considered and incorporated into the revised version.
Major comments:
1.I understand the lack of precise U(VI) and U(IV) mineralogy given that uranium in roll front deposits is present at low concentrations (usually 0.1 weight%). At these concentrations, XRD may not be able to constrain uranium mineralogy.
However, the other impurities could certainly be quantified with XRD. For example, pyrite and calcite often appear at up to 4 weight percent in some roll-front deposits. Getting a couple of representative XRD patterns to even provide a semi-quantitative estimate of mineral impurities would greatly strengthen this paper. Kinetic rates of calcite and pyrite dissolution in acidic solutions are known in the literature and having better constraints on minerals that dissolve would allow this paper to be more applicable to other deposits.
As you correctly noted, due to the low uranium concentrations in roll-front deposits, direct identification of U(VI) and U(IV) mineral phases using XRD is challenging. However, in our previous work (Kurmanseiit et al., 2022) [9], we addressed this limitation by modeling various U(VI)/U(IV) ratios and calibrating the simulations against field production data to infer the most likely initial speciation.
Regarding other mineral phases, we agree that their quantification could significantly enhance the applicability of reactive transport models. The concentrations of these components were investigated in the referenced work (Kurmanseiit et al., 2022) [9] and averaged, with the resulting mean values incorporated into the model via Equation (R3) (Minerals).
2.The methods sections are all well written, however, it was not immediately clear to the reader how the accuracy of each method is being assessed. I think it would be helpful to have a short section before the reactive transport methods section that explicitly states the time-dependent measurements that are input to the model (flow rates, acidity, etc.), the initial model parameters (permeability, porosity, etc.), and how the relative accuracy of each model was assessed/validated.
We have clarified the input data and validation approach in the manuscript. While individual well flow rates are not available in open sources, the total flow rates for both injection and production wells (as shown in Figure 4) were taken from the field data presented by Patrin [34] and Podrezov [35]. The distribution of flow rates among wells was performed using the method illustrated in Figure 2 and described in the corresponding text. Acidity variation over time, which was identical for all wells, is shown in Figure 4.
Initial model parameters, such as permeability and porosity, are provided in Table 1. The accuracy of the model was validated against field production curves, as previously demonstrated in Kurmanseiit et al. (2022) [9]. Additional clarification on the relation between permeability and hydraulic conductivity has also been included in the revised manuscript.
Minor comments:
Consider using the term “In situ recovery (ISR)” instead of “in situ leaching (ISL)”. The Australian and U.S. communities are now moving towards the term ISR because the word “leaching” can have negative connotations for the public.
Based on your recommendation, the term In Situ Recovery (ISR) has been adopted throughout the manuscript. For clarity and broader reader recognition, the alternative term In Situ Leaching (ISL) has also been mentioned at first use.
In the reactive transport methods section, there should be a sentence or two about grid spacing and possible effects of grid spacing on results.
Detailed information on grid spacing, mesh resolution, and their potential influence on simulation results is provided in our previous works (Kurmanseiit et al., 2021 [9], 2023 [21], 2024 [28]), where the full mathematical model was developed and validated against field data. As the present article focuses primarily on the evaluation of balance calculation methods rather than the underlying numerical modeling, grid resolution effects are not discussed in detail here.
What reactive transport code/software was used? Please include this in the methods. Also, consider including your input file(s) as supplementary data (unless of course this is proprietary information). The past studies with HYTEC and other modeling software approaches don’t include code or input files, which can make it hard for other investigators to use and/or expand on this code to improve it. One major benefit of the peer review process is that it makes science/code open-source such that models can continue to be developed and improved.
The reactive transport simulations in this study were performed using custom software developed by the authors. However, the source code and input files cannot be shared due to copyright restrictions established in collaboration with JSC NAC Kazatomprom, who co-financed the development of the software. Despite this limitation, the key input parameters and modeling assumptions are fully described in the manuscript to ensure transparency and to allow comparison with other modeling approaches. Information about the software has also been included in the main text of the article (under equation 12).
In section 2.1: Was Archie’s Law considered to calculate diffusion coefficients in porous media?
In this study, all relevant data, including permeability and porosity, were used in their final interpreted form and obtained from geophysical well log analysis, as reported in the studies by Patrin and Podrezov [34, 35]. Therefore, Archie’s Law was not explicitly applied to calculate diffusion coefficients. Moreover, the primary aim of this article is not to compare simulation results with measured field data, as this comparison was already performed and discussed in our previous publication (Kurmanseiit et al., 2022) [9], which forms the basis for the present study. In any case, any prospective model encapsulated in a software package will import already interpreted data from geological and production databases available on-site at mining enterprises.
Figure 4: Is the solution acidity measured in the injection or production fluid? I would assume the production fluid but it would be good to clarify.
The acidity shown in Figure 4 refers to the leaching solution at the injection wells as per the data that is usually provided by the industry. This clarification has been added both in the figure caption and in the main text of the manuscript.
Line 97: change “Key factor” to “A key factor”
Text has been fixed.
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsI think the author has revised it according to the comments and it is suitable for publication
Reviewer 3 Report
Comments and Suggestions for AuthorsAccept in present form
Reviewer 4 Report
Comments and Suggestions for AuthorsGood job and I appreciate the thorough responses to comments! This manuscript is now suitable for publication.
