An Application of Safety Assessment for Radioactive Waste Repository: Non-Equilibrium Transport of Tritium, Selenium, and Cesium in Crushed Granite with Different Path Lengths

Recommendation

Response

1. line 47: according to the description of radioactive waste before a repository, the radioactive waste should be formed in solid state or in vitrified glass, so why the authors deal with liquid waste, in addition what are the chemical compounds of Se and Cs in your lab?

The authors appreciate the reviewer’s comments.

For safety assessment (SA) in HLW disposal, the most possible scenario of released radionuclides is the groundwater intrusion into HLW repository due to the failure of surrounding barriers and vitrified glass after long-term storage (> 10,000 years). Toxic radionuclide would be soluble into groundwater and it migrate or transport to biosphere. Therefore, the possible pathway for radionuclide should be noticed or studied by combining an experimental results and numerical model.

The chemical compounds of Cs is CsCl, Se for SeO₂. Both Se and Cs were soluble in de-ionized water, and chemical form is Cs⁺ and Se(IV) for HSeO₃^- or SeO₃^2- according pH-Eh diagram.

2. lines 105-110: the definition of non-equilibrium physical models are not clear. Why in the mobile and immobile zones there only diffusion process, not advection effect especially for mobile zone?

To described the early solute breakthrough and tailing behaviors in experimental observation. Physical and/or chemical nonequilibrium models were frequently applied.

A physical nonequilibrium model is also called a two-region model. In the two-region model, water is divided into flowing (mobile) and stagnant/dead (immobile) regions. The approach assumes the advective-dispersive transport of solutes only occurs in the mobile region. Solute exchange between the two liquid phases is assumed to be a diffusion like process.

Materials and methods

3.Lines 133-134: What micro-pore or fracture in rock can be found by using the X-ray signal noise? what the noise of X-ray is defined?

Micro-X-ray computed tomography (micro-CT) is a non-destructive method used to detect differences in the X-ray attenuation between different micro pores and mineral components of a intact granite rock. Moreover, The X-ray image is expected to interact with different materials that signals intensity (or signal attenuation) is an important parameter. Therefore, micro-pores or fractures in intact granite would be easily to find out to adjust the contrast and signal/nosie ratio by image processing software (AVIZO or Slicer 3D).

4.The equation (4) should be more clear described, on the left side there is the change of a chemical element concentration per time, on the right side there are factor describing diffusion and the lost resulted from the pore dispersity?

The equation (4) is a classical advective-dispersive equation (ADE). The factor D is a combination of mechanical dispersion and molecular diffusion. In an ADE system, mechanical dispersion usually dominates the factor D.

5.The condition (6) and (7) should be concerned, according with this condition there is no concentration in whole space and time?

Thank you for your comments. We have modified the equation (5)~(7) as follows:

C(x,0) = 0

C(0, t) = C0

∂C(∞, t)/∂t = 0

6.The formula (8): what is physical meaning of the equation (8), what is R and T, the authors should more explain this equation. Without description there is very difficult to understand the formula.

Van Genuchten et al. (1981) applied dimensionless techniques to derived several analytical solutions for nonequilibrium models. In the studies, each parameter were explained in detailed. We will add this report as a reference [19.

Van Genuchten, M. TH (1981) Non-equilibrium transport parameters from miscible displacement experiments. Research Report No. 119, U. S. Salinity Lab., USDA, ARS, Riverside. CA.

7.line 187: What ADE installation -Advective-dispersion Equation installation? Or laboratory stand for conduct the experiments for determining the parameter of ADE?

8.The data for No1 and No3 on the Table 1 are missing?

The authors appreciate the reviewer’s comments. The manuscript has been corrected accordingly. No.1 No.2 and No.3 on the Table 1 were list the same value, i.e: bulk density (ρ, g/cm³) , porosity (θ), particle size (mm), flow rate (mL/min), radionuclide etc.

As like comment 6, we will add Van Genuchten et al. (1981) as a reference. Because the derivations of the functions are lengthy, it is not suitable to explained detailed description, and we would like to recommend to the interested reader to access the report and get more details.

9.Line 244 – there is mistake of the equation numbering.

10.The equation at the line 244 should be explained, what are the functions G(T), H(T), what is T and so on. The authors should make explanation for reader. What is the physical meaning of the equation, the authors should more interpret the equations.

11.Lines 252-260: totally not understand, where is immobile and mobile zones in the experimental columns?

It is impossible to identify the location of mobile or immobile regions. The main idea of a two-region model is that we assumed a fraction of rock/soil is stagnant. Further, we fitted the observation data to figure the fraction of immobile zone.

12.Lines 262-267: What this paragraph is meaning?

After a dimensionless process, governing equations of the two-region and two-site model will become identical. However, dimensionless parameters in these two models stand for different physical or chemical process. After the fitting processes are completed, we can derive the dimensional parameters using the fitted dimensionless parameters. Such a process is very helpful to figure out solute transport behaviors in an experimental column.

13.Line 279: Why based on the figures 2bc, the authors stated that the biotite was responsible for sorption of Se (IV) and Cs?

In our manuscript , 2 previous works [19, 20] have been finished by different material analysis i.e: SEMEDS, Polar-microscopy etc. The results showed the biotite was responsible for sorption of Se (IV) and Cs , and it also have a agreement with several literature and reports [27].

19. Lee, C. P.; Tsai, S. C.; Wu, M. C.; Tsai, T. L.; Tu, Y. L.; Kang, L. J.: A comparative study on sorption and diffusion of Cs in crushed argillite and granite investigated in batch and through-diffusion experiment. Journal of Radioanalytical and Nuclear Chemistry 2017 , 311,1155-1162,

20. Shi, Y.; Lee, C. P.; Yu, H.; Hu, Y.; Liu, H.; Tien, N. C.; Wang, Y.; Liu, W.; Kong, J. Study on Advection-Dispersion Behavior for Simulation of HTO and Se Transport in crushed granite. Journal of Radioanalytical and Nuclear Chemistry 2021, 328 , 1329–1338

27. Mckinley, J. P.; Zachara, J.M.; Heald, S.M.; Dohnalkova, A.; Newville, M.G.; Sutton, S.R. Microscale Distribution of Cesium Sorbed to Biotite and Muscovite. Environ. Sci. Technol. 2004, 38, 1017-1023

14.Figures 3d, 3e and 3f should be clearly described.

The authors appreciate the reviewer’s modifications and suggestions.

In an ADE experiment, diffusion is usually not important, since mechanical dispersion will generally dominate the dispersion process. Also, dispersion coefficient could be calculated by D=α*V. From the relationship, it is not difficult to know the advection term.

15.All the figures 4 require explanation, because the reader can't understand. I see that the BTCs curves fitting to the experiment points using the sum of squared residuals. What the fitted data of the advection, diffusion parameters?

Discussion

16.Lines 331-333: The statement was not before considered. To have the mentioned statement the R, D should be considered as a functions of porosity, what is dependence of these parameters on the porosity.

The authors thank the reviewer for giving us a good suggestion for discussion in text. Values of R and D are obtained from fitting the observation. Inherently, the parameters have include the effects of porosity. However, for example, if one wants to know the sorption coefficient Kd. The following equation could be applied

R=1+Kd*ρ/ɵ(=porosity)

Then, truly, Kd depends on porosity.

17.This chapter should be far more discussed, the authors should conduct the discuss focus on the results in detail. In my opinion the discussion is very shallow.

Conclusion

18.Lines 372-374 “In the physical non-equilibrium models, the increase in α with increases in D may have been caused by an increase in the amount of immobile water, and hence by an increase in the diffusion length for the radionuclides from mobile to immobile center”. What is immobile and mobile waters?

The authors appreciate the reviewer’s comments.

A physical nonequilibrium model is also called a two-region model. In the two-region model, water is divided into flowing (mobile) and stagnant/dead (immobile) regions.

19.The conclusions should be after particular discussion of the data summarized on the tables 3 and 4

Recommendation

Response

1. Introduction – this paragraph is too long in comparison with the whole text, in addition in this paragraph the important the composition of nuclear wastes and their classification (light, medium and heavy waste). But authors most focused on the nuclear power. Why the authors deal with Cs, Se and tritium? There is no description.

The authors thank the reviewer’s comments. In our manuscript, there are several paragraphs from Line 48 to 77 to state the high-level radioactive waste (HLW). Moreover, there is no HLW repository operation now, and there are over 40 intermediate or low-level radioactive waste(ILLW or LLW) repository around the world. In fact, HLW disposal has become the most difficult issue for nuclear power development. Therefore, we discuss the safety assessment for HLW disposal in this work for radionuclide migration in deep geology, especially for granite, a common host rock in the geosphere.   

Line 88 to 93 present the Cs and Se importance for SA in HLW due to long half-life and chemical property (cation and anion. Tritium would be applied as a radiotracer to represent water in our work.

2. Materials and methods – in this paragraph authors mention only the XRD method for determining the mineral composition in the crushed granite, but not described in detail how to determine using this method, especially they determined the porosity comparing with  X-ray attenuation background? It seems to me the method is new, but it was totally ignored.

XRD spectra for granite have been published in previous works, it is used to cite it in this paper.  XRD spectra always have been compared with an international mineral database developed in past decades. According to the database, several minerals in granite have been found and identified. We correct Figure 1 for polar microscopy, and it has been published in previous work. In the following pages, we will put it for reference.

3. The theory of the ADE was very shallow and very weak related to the experiments. In the differential equations (formulas 4-7) C was mentioned, but in the solution (8) there is Ce, suggest dissension. In addition the formula 8 is written in the excel form not math one and without physical interpretation of this formula.

The authors appreciate the reviewer’s suggestions. We revised and correct it in our manuscript.

4. In table 1, the data at the columns 1 and 3 are missing, if the data were the same as column 2, the authors should add asterisk.

The authors appreciate the reviewer’s suggestions. We correct it in Table1.

5. During the experiments authors used the LSC method, but this method was ignored in description. Additionally authors stated that efficiency of LSC is 90%. It not true, because of the efficiency of LSC method depends on the every isotope, it chemical compound and the kind of the scintillation cocktail. In may opinion the efficiency of LSC for tritium (where E_bmax=18 keV) is much lower than for Cs-137 (E_bmax=514 keV).

The authors appreciate the reviewer’s professional comments. After check the LSC manual(as following page), the efficiency of LAS for H-3 is 51%, and we perform it in counting HTO activity.  Moreover, Se and Cs were analyzed by FAAS and ICPOES.

6. The functions H and G at the Formula (9) were not explained

The authors appreciate the reviewer’s suggestions. We revised and correct it in our manuscript.

7. Results: Based on the color of the micro CT-photo, authors stated that biotite is responsible for the sorption of Cs and Se(IV). The statement is without scientific justification.

8. Again the authors make mistake in numbering the formula in the text –, the number of the formula at the page 8 should be 10 but not 8. This error suggest the authors have not tried to improve their paper. In addition the formula is in the excel form?

9. Retardation coefficient R for HTO is 1, this result is obvious, because of HTO is the water.

Yes, HTO would be applied as a radiotracer to represent water in our work. In fact, there may be heterogeneous or dead-end pores when we compacted crushed granite in our column. Therefore, HTO (R=1) is a non-reactive radiotracer for water to understand the pore distribution in our column according to fit BTCs. If it happened that R<1 or R>1 for HTO, it may be a bias for our following Cs and Se experiments. Therefore, HTO is really good indicator or physical calibration for a ADE column system before reactive tracer.       

10. Discussion: The authors stated that the dispersion and retardation coefficients are depended on the porosity, but what is a relation. This problem is ignored in the text.

The authors appreciate the reviewer’s suggestions. We revised and correct it in our manuscript.

11. Lines 345-346: this statement has not hard scientific background.

The authors appreciate the reviewer’s suggestions. We revised and correct it in our manuscript.

12. Conclusions: The episode from the line 360 to 363 is inconsistence (the second phrase is opposite to the first one).

13. The statement at the lines 380-381 is unsubstantiated.

Recommendation

Response

1. In the paragraph §2.3 the authors used a synthetic ground water (GW) to fill up the columns, and sampled every 30’ to measure the Na, Mg, Ca and K. So in my opinion the authors could make the breakthrough curves (BTCs) for these elements and compare with that of Cs and Se. If there is good relation, the HLW could be less used in the laboratory. Additionally in water there are also negative ions such as HCO₃^-, Cl^- and SO₄^2-, which could be also measure.

The authors appreciate the reviewer’s comments.

(1) In fact, the variation of Na, Mg, Ca and K.in GW by ICPOES detection is a little higher, and we observed that water saturation had been reached at 1 P.V(pore volume) after C/C₀≒1. Generally, the water saturation before ADE experiments continuous to 3 hours (about 5-10 P.V). Because elution about 60mL (Q=2mL/min) every 30 min, for 2 and 4 cm columns , P.V >1 P.V, and 8 cm column almont ≒ 1 P.V, The results is similar with HTO, therefore, we didn’t put it in our manuscript and it is a good suugestion for us to record the data and show it to compare with important radionucldies in HLW.

(2) The egative ions such as HCO₃^-, Cl^- and SO₄² could be detected by ion chromatography (IC) with a conductivity detector. Generally, the affinity of anion exchange column for different anion is quite different, and SO₄^2- showed a higher adsorption affinity for anion exchange and slower retention time than Cl^- in the elution process. On the other hand . it could be achieved to select different anion column to change the eluting process.

2. The formula at the line 300, the equations (18) expressing the RMSE should be written in the math form not in excel ones.

The authors appreciate the reviewer’s comments. The manuscript has been corrected accordingly.