Breakthrough Investigation of Advective and Diffusive Transport in a Porous Matrix with a Crack

Round 1

Reviewer 1 Report

Methodological aspects should be incorporated more clearly, which in turn improves the research design.

Author Response

Thanks for reviewing and comment.

The revised version will take your concern into account. 

Reviewer 2 Report

Comments for Author

Review of Manuscript ID: fluids-1358887." Breakthrough Investigation of Advective and Diffusive Transport in a Porous Matrix with a Crack"  submitted to Fluids.

 

The manuscript presents a systematic investigation of fluid flow and transport process in fractured porous media using numerical simulation. This investigation has been carried out using COMSOL Multiphysics software.

The following are the comments on this manuscript before recommend it for publication.

 

Comments:

• The introduction section does not cover the main concepts in this manuscript. The author should give more explanation about fractures and cracks.
• In section1, there author just mentioned the references by its numbers without any explanation. Some important studies and findings from the literature should be presented in the introduction part.
• Description of the model including geometry of the region should be in Section2 or in separate section. In my opinion section 1 (introduction) must be revisited and presented in a better way.
• Paragraph (line 70—73) is not clear. What does the author mean by ( only one of governing variables is relevant for the characterization of the btc).
• The author has used Navier-Stokes equations to govern the flow through the crack. Is this assumption common or it is assumed by the author? Please explain and put some relevant references.
• All equations and variable transformations in the mathematical model in section2 must be cited and add some relevant references.
• Boundary conditions in lines (134—138) should be given mathematically.
• Although the author has used software packages. However, how to ensure validity of the used code. So, necessary to validate its own code by comparing with literature for some fixed values and without crack (L=0).
• Paragraph 1 page 2 (line 48—56) needs more explanation and why the author choosed 2D.
• The dimensionless variable (Pe) presented in line 117 of the manuscript. Please provide an explanation of the physical interpretation of Peclet number.
• ) To have a better context of this work, please provide range estimates of the non-dimensional numbers in real applications. This will be useful to get a better understanding of the figures.
• In most figures, the vertical axis is confusing me and not clears. Please clarify.
• In conclusion part (line 395). How did the author conclude this important point, and why Da and Re are not relevant?
• Line 393. For highly advection dominated flow, the btc cannot be reproduced by a 1D approach, while in line 48 the author mentioned that a 2D is considered. Please clarify.
• The shape of the crack is considered as ellipse. Is this common, or limited to this study. Please explain.

 

Minor comments

• Why the author use brackets in (line 29) and (line 36).
• Better to use section instead of chapter (Ex. Line 68).
• Reference velocity (v0) has different forms in the manuscript.
• Line 114, why the solute mass transport equation holds with (k=1).
• Line 212, full stop should be added.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

In this paper, the transport of components in porous matrix with cracks is studied systematically by numerical simulation.  The analytical description is simplified to five dimensionless parameters: geometric parameters α and d and parameter combinations Re, Pe and Da. For a further study of the additional effect on advection and diffusion the breakthrough curves were examined with respect to the 1D advection-diffusion model.  The following are the suggestions of the reviewer, which need you to make appropriate modifications and explanations, so that readers can better understand and carry out follow-up research.

1. In the second section of differential equations, there is a lack of relevant descriptions about T, v and ∇ in the equation. Meanwhile, Normalized to a reference length L and a reference velocity v₀, the rewriting of Darcy’s law equation (1), the Navier-Stokes equation (2) and advection-diffusion equation (7). The reader does not understand it well.
2. In the section 3, after establishing numerical models of water flow and transport, grids were divided, and grids were encrypted near and inside the crack. However, the influence of the number of grids on the results was missing, so grid independence verification should be supplemented.
3. In Section 4.1 Flow Pattterns, when the crack direction is perpendicular to the Flow direction, this factor is 1, i.e. there is no influence, but with the decrease of α, this factor increases. Advection may increase by 50% if the crack is aligned with the flow. This is only true when d is small. The size of fracture D will have an impact on the dependence of A. The larger the fracture is, the weaker the dependence on A is and the decrease is smaller.
4. In section 4.3 distribution of temperature and pressure, there is too little description about the schematic diagram of temperature distribution of the cold front entering from the left in FIG. 5 in three time periods, so it is suggested to supplement relevant explanations.
5. There are several instances in this article where parentheses are not used properly. Parentheses should be used in pairs.
6. In section 4.3 breakthrough curves, some explanations and phenomenon descriptions need to be added to describe the impact of inclination Angle, crack opening and parameter combinations, so that readers can better understand their impact.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf