Anomalous Solute Transport in a Cylindrical Two-Zone Medium with Fractal Structure

Round 1

Reviewer 1 Report

 

Reviewed paper deals with the investigation of anomalous solute transport in a cylindrical two-zone medium with fractal structure. The subject of the paper well fits the scope of Applied Sciences. The paper contains new results and can be considered for publication in Applied Sciences after revision taking into account the following comment:

1. The phrase “here and futher 1 stands for the macropore and 2 for the micropore” from line 145 should appear much earlier, when the indices 1 and 2 appear for the first time.
2. Most of the calculations from Section 3 could be transferred to Appendix?
3. In all the figures, the range along the “r” coordinate is from 0 to 1.5 m. But, according to Figure 1 and the values of the parameters used (line 173), the range should be up to 2 m. If this is done for better visualization of the figures, it should be mentioned.
4. Based on the formula 27 and the values of the used parameters listed in lines 170-173, as well as the length of the computational domain in x direction, which can be seen in the figures - 1.5 m, the number of grid nodes in x direction is 15 , in “r” direction in the range from 0 to “a” (inner cylinder) - 15, and in the region of the outer cylinder (from “ba” to “b”) - 35. Is this a sufficient grid? Maybe the grid near the boundary of the layers it should be refined?
5. In paragraph 174-181 it is written that at the boundary of the layers, i.e. at r = a, a surface kink is observed, and the value of “a” is 0.75 m (line 173). But in the figures, a kink is observed at r of about 0.5 m, or even at slightly smaller r.

 

Author Response

Responses to comments

Reviewer 1

 

1. The phrase “here and further 1 stands for the macropore and 2 for the micropore” from line 145 should appear much earlier, when the indices 1 and 2 appear for the first time.

Answer: We moved this phrase to line 127, where the indices 1 and 2 appeared for the first time.

 

2. Most of the calculations from Section 3 could be transferred to Appendix?

Answer: We have transferred a part of the calculations from Section 3 to the Appendix A.

 

3. In all the figures, the range along the “r” coordinate is from 0 to 1.5 m. But, according to Figure 1 and the values of the parameters used (line 173), the range should be up to 2 m. If this is done for better visualization of the figures, it should be mentioned.

Answer: In line 173 values of parameters a and b were incorrect. We corrected values of parameters a from 0.75 to 0.5 and b from 1.25 to 1.5, so range of r is from 0 to 1.5.

 

4. Based on the formula 27 and the values of the used parameters listed in lines 170-173, as well as the length of the computational domain in x direction, which can be seen in the figures - 1.5 m, the number of grid nodes in x direction is 15 , in “r” direction in the range from 0 to “a” (inner cylinder) - 15, and in the region of the outer cylinder (from “ba” to “b”) - 35. Is this a sufficient grid? Maybe the grid near the boundary of the layers it should be refined?

Answer: We changed values of grid parameters as following: h₁ from 0.1 to 0.01, h₂  from 0.05 to 0.005 and τ from 1 to 0.1. Now number of grid nodes is great enough.

 

5. In paragraph 174-181 it is written that at the boundary of the layers, i.e. at r = a, a surface kink is observed, and the value of “a” is 0.75 m (line 173). But in the figures, a kink is observed at r of about 0.5 m, or even at slightly smaller r.

Answer: As we mentioned above in answer 3, value of parameter a  was given wrong. We corrected this mistake. So it is true that kinks are at about 0.5 m.

 

All added and corrected parts of the manuscript we marked with different color.

 

We thank the Reviewer 1 for his (her) valuable and helpful comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

(1) Please clarify what this research will contribute to and emphasis the impact of the paper. 

 

(2) This paper didn't do any comparisons with experiment, and there was no validation of the model. I couldn't understand how useful the model is. 

Author Response

Responses to comments

 

Reviewer 2

 

1. Please clarify what this research will contribute to and emphasis the impact of the paper.

 

Answer: We added some information into introduction part in order to explain the aim and scientific novelty of the paper.

 

2. This paper didn't do any comparisons with experiment, and there was no validation of the model. I couldn't understand how useful the model is.

Answer: There are some papers in which laboratory experiments two-zone cylindrical form porous media are given. In most of them, the surrounding porous media (micropore) are not permeable. In this paper we considered two zones in each of them liquid is mobile, one of them is high permeable, the other one is low permeable for the liquid. For instance, we analyzed the following papers:

1) Haws N.W.; Paraskewich M.R.Jr.; Hilpert M.; Ball W.P. Effect of fluid velocity on model-estimated rates of radial solute diffusion in a cylindrical macropore column. Water Resources Research, 2007, 43, W10409. doi:10.1029/2006WR005751.

2)  Sharma P. K., Shukla S. K., Rahul Choudhary & Deepak Swami (2016): Modeling for solute transport in mobile–immobile soil column experiment, ISH Journal of Hydraulic Engineering, DOI: 10.1080/09715010.2016.1155181

 

Nevertheless, we hope, our results are physically reasonable and meaningful. We also added some information into results and conclusion parts to explain how useful the model is.

All added and corrected parts of the manuscript we marked with different color.

 

We thank the Reviewer 2 for his (her) valuable and helpful comments.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The manuscript was improved.