Review Reports - Hydrodynamic and Mass-Transfer Modeling of Uranium Recovery in a Packed Ion-Exchange Column with a Conical Flow Distributor

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Presently, the underground leaching method is predominantly employed for the extraction of uranium from ore. In this article, researchers emphasised that high efficiency can be achieved by modifying the design of column furnaces when extracting uranium by the circulation method. This objective was realised through the substantiation of various patterns in theoretical calculations.
Nevertheless, the article has a number of shortcomings:
The process of digitisation was not executed in a sequential manner during the formulation of article formulas.
The article is riddled with grammatical and stylistic errors.
It is evident that there is an inaccuracy in the translation of the articles contained within the bibliography.
It was observed that words which had not been translated from Russian remained.
In consideration of the theoretical data obtained, it is imperative to elucidate the rationale behind the selection of specific indicators, namely β=120 h-1, φ=0.35, H=6m, and R=1.5m, during the course of the practical research. The extent to which the indicators would deviate if a larger or smaller size were to be extracted from the source material is a question that merits investigation.
The pH environment, liquid-to-solid ratio, and pulp feed rate for the uranium sorption process using this improved hopper have not been adequately substantiated.
The work demonstrates a high level of scientific validity and consistency.

Author Response

Comments and Suggestions for Authors

Reply to Reviewer 1

Thank you for pointing out the inaccuracies in the article. I have carefully checked and corrected the following:

Formula numbering in the article;
Grammatical and stylistic errors;
Inaccuracies in the translation of the titles of works cited in the bibliography.

The words remaining untranslated from Russian have been translated.

Regarding the selection of the specific parameter values β = 120 h⁻¹, φ = 0.35, H = 6 m, and R = 1.5 m used in this study, these values correspond to the actual operating characteristics of the sorbent and sorption columns currently employed at the production facilities of JSC “Kazatomprom”. (This is briefly discussed on page 20 or lines 278-279.) The use of these industrially relevant parameters was intended to demonstrate the practical applicability of the proposed mathematical and numerical modeling approach for the analysis and enhancement of real uranium oxide recovery processes from productive solutions.

With regards, A.Kaltayev

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript submitted by Kaltayev et al for consideration for publication in “Minerals” presents a model based analysis uranium sorption in a packed ion-exchange column equipped with a conical flow distributor. In my opinion, the manuscript has the potential to be published on Minerals after major revisions.

Key general comments

No information regarding how the code was implemented was given. Was it coded from scratch in FORTRAN, C, MATLAB, Python…? Or, was it created using a multiphysics tools like COMSOL or OpenFOAM? Please explain. If possible, it would nice to see the code, maybe if distributed through a public repository (e.g. GitHub).
More importantly, was a benchmark study conducted to ensure that the numerical results obtained here are correct? The authors are requested to prove that their method is validated against another tested method. Looking at the formulation, the model can be resolved using standard existing numerical open-source tools (e.g. MODFLOW + MT3DMS) and perhaps analytical solutions (for simplified geometries).
Reynolds number shown in Figure 4a are very high, posing questions about the validity of the Darcy’s law. How was this issue dealt with by the authors? Was any correction factor applied?
What is the initial concentration in the system for both mobile and immobile uranium species? Immobile concentrations of >23 g/l mean even much higher in the mobile phase, posing severe concerns regarding the validity of the assumption that the fluid is an incompressible Newtonian fluid with density and viscosity close to those of water! Buoyancy may become a critical issue! Please report mobile phase concentrations and discuss the possibile presence of density-driven effects on the flow field.

Line by line comments

Figures must be improved. Some of them have hand-written labels or marks (such as Fig1b - alpha and omega are handwritten). Captions do not include an explanation of the acronyms or variables within the figure.
L127 “delta” must be indicated after line 129 .
Line 129 contains two equations: why not numbering them?
L136 what is phi in Eq1 ? This is the link with the sorption
L145 why a ratio of 5 between longitudinal and transversal alphas? Usually a value of 10 is used if not tracer-based experiment is conducted. Ideally, both alphas should be calibrated and a sensitivity analysis presented.
L157 eq2’ is not defined. You mean Eq2?
L159, L168 , L182 and elsewhere: why bold font? Not needed.
L188 fix Cyrillic symbol , Kd has no units
L191-262 : this part could be moved to the Appendix. It contains general mathematical information regarding the numerical solution, which are not needed here. It is sufficient to indicate (1) what the grid discretization in the FDM and (2) what are the boundary conditions.
I have no detailed comments regarding the results, until the major comments presented above are resolved.
The “Discussion” section contains no discussion (except the few lines containing “future research”). It starts with a summary and then provides a mix of summary and conclusions. This is not acceptable. The Discussion section should compare the results obtained here against other experiments, methods, previous findings, or anything which is useful debate. I am no expert of uranium recovery, but as a scientist I would be curious to see how this study improves the state of the art. For example, I quickly found a few works on “uranium recovery ion exchange” on the web https://www.sciencedirect.com/science/article/abs/pii/S0892687505002001; https://www.sciencedirect.com/science/article/abs/pii/S1226086X1930468X; https://www.sciencedirect.com/science/article/abs/pii/S0304386X18302822 and it seems that flow velocity is not considered as a critical issue. But maybe, in light on the present study, it should be? Or, at lines 41-43 the authors write “Existing studies on uranium sorption mainly focus on modeling transport processes and sorption kinetics in fixed-bed columns, considering advection, hydrodynamic dispersion, and physicochemical interactions between uranium species and sorbents [10-13].” How the present findings improve the findings from those previous studies cited here?

Author Response

Please see the attachmen

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

The introduction is relatively brief and does not sufficiently explain the necessity or significance of this manuscript. The authors are encouraged to expand this section by clearly outlining the research gap, the motivation behind the study, and its potential contributions to the field.
The column design used in the numerical study should be described in greater detail. Key parameters such as dimensions, boundary conditions, operating variables, and assumptions applied in the model should be clearly specified to improve transparency, reproducibility, and overall understanding of the study.

Author Response

We thank the reviewer for this valuable comment.

Comment 1

The Introduction has been expanded to better emphasize the scientific motivation, research gap, and novelty of the study. In particular, the limitations of conventional 1D fixed-bed models for industrial-scale sorption columns have been clarified, and the contribution of the present multidimensional modeling approach has been explicitly highlighted.

Comment 2

The description of the numerical study method has been substantially revised to improve transparency and reproducibility.

The main modeling assumptions have been summarized in a separate paragraph at the beginning of Section 2.3. A summary table of geometric dimensions, operating conditions, and model parameters has been added. The boundary and initial conditions were clarified, and the description of the numerical research method, including the fictitious region method, was revised and moved to Appendix.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript has been partly revised and things have been clarified (such as the initial concentrations, which now explain why mobile and immobile concentrations are those reported in the graphs). I detected some remaining inaccuracies which should be fixed. These include:

The authors say that they “will discuss placing their Fortran code in an open repository with the potential client.” There is no indication in the manuscript that it will happen, so no guarantee in that regard. Please, indicate it clearly in the manuscript and include a repository - or just say "it will not be available".
The authors indicate that “the available literature does not provide detailed three-dimensional numerical data, let alone analytical solutions, for the distribution of uranium oxide concentrations in the mobile and immobile phases within sorption columns of complex geometry comparable to that investigated in the present study.” While this is true ( I have not checked that carefully), the authors could have created new data using existing codes, such as those mentioned in the previous revision.
That said, the authors mentioned that “the fictitious domain method (FDM) has been applied by the authors to a significantly more complex physicochemical problem described by the dynamically incompressible Navier–Stokes equations (where the thermodynamic or mean pressure depends only on time, Pt(t)=ρRT): namely, to the simulation of flame propagation in a domain with obstacles. “. To support this statement, they mentioned a study [A.Kaltayev, Zh.Ualiev. Simulation of flame propagation in closed vessel with obstacles. Springer. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Volume 93. Advances in High Performance Computing and Computational Sciences, 2005, pp.113-125. 10.1007/978-3-540-33844-4 ]. This paper does not appear in the revised manuscript. Please, add it to the paper in a "validation" statement to support the validation of the code.
Kd usually has units of m3/g, i.e. inverse to a concentration. If Kd is dimensionless, please explain why.
The Discussion and Conclusions still do not contain a solid comparison against existing studies!

I recommend a further round of revision to fix these and other remaining problems, such as typos. For example, letters are still in Cyrillic, for instance in the figure and caption of several figures. Units are missing in many figures and graphs, such as those related to the concentrations.

Author Response

Please see the attachment

Author Response File: Author Response.pdf