the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 23 Aug 2022
Semi-continuum modelling of unsaturated porous media flow to explain the Bauters' paradox
Abstract. In gravity-driven free infiltration of a wetting liquid into a homogeneous unsaturated porous medium, the flow pattern is known to depend significantly on the initial saturation. Point-source infiltration of a liquid into an initially dry porous medium produces a single finger with an oversaturated tip and an undersaturated tail. In an initially wet medium, a diffusion-like plume is produced with a monotonic saturation profile. We present a semi-continuum model based on a proper scaling of the retention curve which is discrete in space and continuous in time. We show that the semi-continuum model is able to describe this transition and to capture the experimentally observed dependence of the saturation overshoot and the finger velocity on the initial saturation.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(14496 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(14496 KB) - Metadata XML
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2022-673', Anonymous Referee #1, 04 Oct 2022
The manuscript describes a modeling approach of the flow in unsaturated sand in order to explain so-called Bauters’ paradox. A semi-continuum model approach is presented that can imitate the finger flow phenomena with the oversaturation in the tip and the whole transition towards a diffusion-type infiltration plume as function of the initial soil moisture condition. The model was successfully tested by description of the Bauters’ experiment.
General Comments
The manuscript tackles an important problem that is in the focus of the journal. Methods and results are novel and can much contribute to progress in describing unsaturated flow phenomena. My main critical comment is that for in-depth understanding the physical basis of the modeling approach and finally also of the results, a better explanation of the semi-continuum’s model concept would help.
In addition, I found the introduction is much too far reaching, of course, everything is somehow connected. The review on global water cycle, the flow phenomena, sample volume dependency, REV concepts and Richards’ equations, and other aspects, all does not help much to better understand the problem, and are not discussed later any more.
What I did not understand was the semi-continuum model concept, especially what is different from a numerical discretization of a continuum model? Perhaps you did it already in other papers. It seems relatively simple and more empirical because of the block size selection and the scaling relations. Maybe it helps to include an illustration? The idea of scaling the retention function with block size is also unclear to me. I did not read the cited references, but the present paper seems to apply the previously developed model concept to describe the specific experiment, yes? It is suggested in the manuscript that the initial water saturation is the variable controlling the finger formation. What about the wettability (i.e., surface tension), which is of course connected with water saturation but can change with time?
Overall, this valuable contribution could become even better if more focussed and with more specific explanations on the physical basis of the approaches.
Citation: https://doi.org/10.5194/egusphere-2022-673-RC1 - AC1: 'Reply on RC1', Jakub Kmec, 17 Jan 2023
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RC2: 'Comment on egusphere-2022-673', Anonymous Referee #2, 23 Dec 2022
The paper analyses the process of infiltration of a liquid into an unsaturated porous medium, which is characterized by different regimes depending on the level of saturation. The liquid is assumed to be wettable with respect to the homogeneous medium. Then, the authors introduce a semi-continuum model that lends itself well to the interpretation of the infiltration regime.
The topic is of interest and deals with a process that even in extremely simple situations reveals a degree of complexity.
However, I see the major limitation in the absence of experimental validation: the numerical scheme, although of interest, appears limited in its interpretation of physical reality. Moreover, and this is a second major issue, there is a lack of sensitivity analysis, since the only estimator comes from repeating the numerical tests by changing only the intrinsic permeability distribution. In this sense, it is necessary for the authors to thoroughly analyse the uncertainty of the parameters (viscosity, degree of saturation, etc.) and analyse the variability of the governed quantities.
There is one point of particular interest: if Bauter's paradox occurs even when intrinsic permeability is homogeneous, how does the proposed model behave in this situation?
Last, the authors tell us about the behavior of their model, but the interpretation of why appears to be missing.
Minor comments
Figure 3: specify units for the colorbar
Figures 5-6: add the frame to panel b diagram
Citation: https://doi.org/10.5194/egusphere-2022-673-RC2 - AC2: 'Reply on RC2', Jakub Kmec, 17 Jan 2023
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RC3: 'Comment on egusphere-2022-673', Anonymous Referee #3, 05 Feb 2023
Please see the pdf.
As there are several points unclear to me, I wanted to skip ticking the points 1), 2) and 3) above. This did not work out, so I just ticked "Good" everywhere. This is just to proceed.
- AC3: 'Reply on RC3', Jakub Kmec, 15 Feb 2023
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2022-673', Anonymous Referee #1, 04 Oct 2022
The manuscript describes a modeling approach of the flow in unsaturated sand in order to explain so-called Bauters’ paradox. A semi-continuum model approach is presented that can imitate the finger flow phenomena with the oversaturation in the tip and the whole transition towards a diffusion-type infiltration plume as function of the initial soil moisture condition. The model was successfully tested by description of the Bauters’ experiment.
General Comments
The manuscript tackles an important problem that is in the focus of the journal. Methods and results are novel and can much contribute to progress in describing unsaturated flow phenomena. My main critical comment is that for in-depth understanding the physical basis of the modeling approach and finally also of the results, a better explanation of the semi-continuum’s model concept would help.
In addition, I found the introduction is much too far reaching, of course, everything is somehow connected. The review on global water cycle, the flow phenomena, sample volume dependency, REV concepts and Richards’ equations, and other aspects, all does not help much to better understand the problem, and are not discussed later any more.
What I did not understand was the semi-continuum model concept, especially what is different from a numerical discretization of a continuum model? Perhaps you did it already in other papers. It seems relatively simple and more empirical because of the block size selection and the scaling relations. Maybe it helps to include an illustration? The idea of scaling the retention function with block size is also unclear to me. I did not read the cited references, but the present paper seems to apply the previously developed model concept to describe the specific experiment, yes? It is suggested in the manuscript that the initial water saturation is the variable controlling the finger formation. What about the wettability (i.e., surface tension), which is of course connected with water saturation but can change with time?
Overall, this valuable contribution could become even better if more focussed and with more specific explanations on the physical basis of the approaches.
Citation: https://doi.org/10.5194/egusphere-2022-673-RC1 - AC1: 'Reply on RC1', Jakub Kmec, 17 Jan 2023
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RC2: 'Comment on egusphere-2022-673', Anonymous Referee #2, 23 Dec 2022
The paper analyses the process of infiltration of a liquid into an unsaturated porous medium, which is characterized by different regimes depending on the level of saturation. The liquid is assumed to be wettable with respect to the homogeneous medium. Then, the authors introduce a semi-continuum model that lends itself well to the interpretation of the infiltration regime.
The topic is of interest and deals with a process that even in extremely simple situations reveals a degree of complexity.
However, I see the major limitation in the absence of experimental validation: the numerical scheme, although of interest, appears limited in its interpretation of physical reality. Moreover, and this is a second major issue, there is a lack of sensitivity analysis, since the only estimator comes from repeating the numerical tests by changing only the intrinsic permeability distribution. In this sense, it is necessary for the authors to thoroughly analyse the uncertainty of the parameters (viscosity, degree of saturation, etc.) and analyse the variability of the governed quantities.
There is one point of particular interest: if Bauter's paradox occurs even when intrinsic permeability is homogeneous, how does the proposed model behave in this situation?
Last, the authors tell us about the behavior of their model, but the interpretation of why appears to be missing.
Minor comments
Figure 3: specify units for the colorbar
Figures 5-6: add the frame to panel b diagram
Citation: https://doi.org/10.5194/egusphere-2022-673-RC2 - AC2: 'Reply on RC2', Jakub Kmec, 17 Jan 2023
-
RC3: 'Comment on egusphere-2022-673', Anonymous Referee #3, 05 Feb 2023
Please see the pdf.
As there are several points unclear to me, I wanted to skip ticking the points 1), 2) and 3) above. This did not work out, so I just ticked "Good" everywhere. This is just to proceed.
- AC3: 'Reply on RC3', Jakub Kmec, 15 Feb 2023
Peer review completion
Journal article(s) based on this preprint
Data sets
Simulation data for: Semi-continuum modelling of unsaturated porous media flow to explain the Bauters' paradox Jakub Kmec, Miloslav Šír, Tomáš Fürst, Rostislav Vodák https://doi.org/10.5281/zenodo.6860668
Model code and software
The semi-continuum model for unsaturated porous media flow Jakub Kmec https://doi.org/10.5281/zenodo.6837742
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Cited
1 citations as recorded by crossref.
Miloslav Šír
Tomáš Fürst
Rostislav Vodák
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(14496 KB) - Metadata XML