Applicable Investigation of SPH in Characterization of Fluid Flow in Uniform and Non-Uniform Periodic Porous Media
Round 1
Reviewer 1 Report
The authors explored numerically laminar fluid flow through uniform or non-uniform and periodic array of cylinders using the smoothed particle hydrodynamics (SPH) method to characterize properties of porous media and fluid properties, such as fluid velocity, permeability, streamlines, and hydraulic tortuosity.
The problem is very useful to the present scientific community. The used method (SPH) is a standard method for solving the equations.
Comments:
1. Give the clear motivation of the present study.
2. What are the applications of the present model. Give in detail.
3. The legend and axis values are not clear in Figures 3 and 11. Redraw it clearly.
4. In Figure 12, reduce the vertical axis range from 1 to 1.06 for clear view of profiles in the figure.
5. Fix the range (1 to 1.6) of vertical axis in figure 13.
6. Figure 14 and 15 are not clear. Redraw it clearly.
7. The references are inadequate.
Author Response
Response to Reviewer Comments
Point 1: Give the clear motivation of the present study.
Response 1: The motivation of the present study includes the following:
- Characterization of fluid flow through porous media and calculation of essential parameters such as permeability and tortuosity related to flow behavior.
- This type of study has been used widely by other CFD methods such as FEM and LB recently, but streamlines and tortuosity have not been studied with SPH in any previous study so far. So, we decided to study that.
- Investigation on the SPH potential in order to show the ability in modeling of characteristic laboratory experiments of porous media. Also, showing the possibility of using the SPH method instead of characteristic laboratory experiments of porous media.
Note: Relevant changes were made in the manuscript (Changes in the abstract and last paragraph of the introduction).
Point 2: What are the applications of the present model. Give in detail.
Response 2: The Application of the present study includes the following:
- Characterization of fluid flow through any desired porous media and extracting essential parameters of flow behavior such as permeability, velocity profiles, streamlines, tortuosity and shape factor (p) of porous.
- Using the SPH method to model pore and throat flow behavior with complex geometries and derive relationships such as permeability-porosity and tortuosity-porosity.
- The SPH method can be used for the primary characterization of the newly constructed porous media and the calculation of permeability and tortuosity for other applications.
- Using the SPH method to characterization of ideal porous produced by the packing method of regular particles or real media extracted by X-ray computed tomography (CT) images without conducting any flow experiments.
Note: Relevant changes were made in the manuscript (Changes in last paragraph of the introduction and conclusions).
Point 3: The legend and axis values are not clear in Figures 3 and 11. Redraw it clearly.
Response 3: Redraw the figure.
Point 4: In Figure 12, reduce the vertical axis range from 1 to 1.06 for clear view of profiles in the figure.
Response 4: Redraw the figure.
Point 5: Fix the range (1 to 1.6) of vertical axis in figure 13.
Response 5: Redraw the figure.
Point 6: Figure 14 and 15 are not clear. Redraw it clearly.
Response 6: Redraw the figure.
Point 7: The references are inadequate.
Response 7: As a result of changes in the manuscript (especially the introduction), 7 new references (references 23 - 29) were added and one older reference was deleted. Also, the last reference related to the characterization of porous media in interior and exterior flow field with the SPH method in 2020 was added (reference 28), which shows the importance of the present study and also declare that streamlines and tortuosity have not been studied with SPH in any previous study so far. On the other hand, reference 29 published in 2021, which shows the difficulty of laboratory methods to perform tortuosity calculations, was also added to the text. It shows the importance of the present study as a supplementary method for calculating hydraulic tortuosity in real porous media obtained from X-ray computed tomography (CT) images.
Author Response File: 
Author Response.docx
Reviewer 2 Report
1. In this manuscript, the authors studied permeability and tortuosity of uniform and non-uniform porous media with SPH, I think it's interesting. However, lin line 79, the authors stated that CFD methods, especially LB, needed for high initial parameters for modeling. What does the high initial parameters mean? What parameters does SPH need for modeling？
2. Line 100-102, the authors stated that streamlines and tortuosity had not been studied in any previous study so far. In this manuscript, the equation for simulating tortuosity is not difficult, why other researchers don't study it. Actually, the cited literature (Holmes et al.) was published in 2011. During the last decade, why other scholars didn't use SPH to simulate flow in porous media. I suggest the authors extend the reference. I really think some important literature is missing.
3. I suggest the authors stated SPH in detail. In current manuscript, it's difficult for readers undertanding how to simulate flow with SPH.
4. line 167, the "but" can be deleted.
Author Response
Response to Reviewer Comments
Point 1: In this manuscript, the authors studied permeability and tortuosity of uniform and non-uniform porous media with SPH, I think it's interesting. However, in line 79, the authors stated that CFD methods, especially LB, needed for high initial parameters for modeling. What does the high initial parameters mean? What parameters does SPH need for modeling？
Response 1: High means more. In fact, by CFD methods, we mean grid-based methods such as FDM and FEM, which require more initial parameters to modeling underground flow problems according to the type of formulation. Some of these parameters are location-dependent such as the cross-sectional area of each grid in all spacial directions for transmissibility of fluids and etc. The SPH method need less initial parameters such as model dimensions, resolution, fluid properties such as density, viscosity, equation of state (EOS) and boundary conditions (BC) to perform like the Lattice Boltzmann (LB) method.
Note: In order to apply the point, high was replaced by more, and the “especially LB” was deleted from the mentioned line.
Point 2: Line 100-102, the authors stated that streamlines and tortuosity had not been studied in any previous study so far. In this manuscript, the equation for simulating tortuosity is not difficult, why other researchers don't study it. Actually, the cited literature (Holmes et al.) was published in 2011. During the last decade, why other scholars didn't use SPH to simulate flow in porous media. I suggest the authors extend the reference. I really think some important literature is missing.
Response 2: After the cited literature (Holmes et al., 2011), a lot of literature on SPH and especially on using SPH to simulate fluid flow in porous media was published. Characterizing properties of porous media has not been completely performed in any SPH modeling studies and most studies have been limited to permeability calculation only. Although the SPH method has been used widely to study the multiphase flow problems in porous media recently. But streamlines and tortuosity have not been studied with SPH in any previous study so far. Recently, Wu et al., investigated the characterization of porous media in interior and exterior flow field with free surfaces, but their study does not include flow issues related to underground layers without free boundaries.
Note: Relevant changes were made in the manuscript (Changes in the last paragraph of the introduction).
Point 3: I suggest the authors stated SPH in detail. In current manuscript, it's difficult for readers understanding how to simulate flow with SPH.
Response 3: As mentioned in Basics and Formulation, the formulation introduced by Tartakovsky and Meakin, and especially Holmes et al., was used to model fluid flow in a porous media. Therefore, we decided to bring the general formulas here and avoid repetition. Also, important topics in the SPH method such as the kernel function, the method of searching for neighboring particles, the time integration method, formulas of dimensionless parameters, and every essential value for simulation of fluid flow with SPH have been mentioned.
Note: Some changes by adding some sentences, were made in the manuscript (Changes in the Smoothed Particle Hydrodynamics Method and its first subsection, Basics and Formulation).
Point 4: line 167, the "but" can be deleted.
Response 4: Was deleted.
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
My detailed comments are as follows:
1. Last time I mentioned that some details about SPH were missing. However in the revised version, the authors didn't make any changes. The authors explained the SPH was applied and studied by many scholars, so to avoid repetition, there was no need to explain this method it in detail. However, I don't think so. For a scientific paper, it should be described in detail. If the authors think the method is general and there is no any innovation of this method, I think the authors can describe the method in Appendix. If the authors just listed part equations in the manuscript, I don't think readers can understand this work.
2. The authors stated that most studies of SPH have been limited to permeability calculation only, and streamlines and tortuosity have not been studied with SPH in any previous study so far. However, I really think if one can obtain the permeability based on SPH, he can easily get the streamlines and tortuosity. So, what's the real innovation of this work?
Author Response
Response to Reviewer Comments
Point 1: Last time I mentioned that some details about SPH were missing. However in the revised version, the authors didn't make any changes. The authors explained the SPH was applied and studied by many scholars, so to avoid repetition, there was no need to explain this method it in detail. However, I don't think so. For a scientific paper, it should be described in detail. If the authors think the method is general and there is no any innovation of this method, I think the authors can describe the method in Appendix. If the authors just listed part equations in the manuscript, I don't think readers can understand this work.
Response 1: It is completely true that any scientific paper should be described in detail. In order to apply the point, relevant changes were made in the SPH method (Changes in Smoothed Particle Hydrodynamics Method and Adding Appendix A for basic concepts and detail of SPH plus its related references).
Point 2: The authors stated that most studies of SPH have been limited to permeability calculation only, and streamlines and tortuosity have not been studied with SPH in any previous study so far. However, I really think if one can obtain the permeability based on SPH, he can easily get the streamlines and tortuosity. So, what's the real innovation of this work?
Response 2: It is completely through that if SPH can estimate permeability one can also extractive other dynamic properties such as tortuosity based on streamlines length. In this regard, the second paragraph at page 3 (Line 3) rewords in order to avoid misunderstanding. Estimation of tortuosity from lab work presented by Jarrar et al. (2021) brought us to try estimating dynamic tortuosity using the SPH method.
