Numerical modeling of physical and biochemical processes in the subsurface and their impacts on the self-potential signature

Liu, Xin; Zhang, Zengyu; Furman, Alex

doi:https://doi.org/10.5194/hess-2022-31

Preprints

https://doi.org/10.5194/hess-2022-31

Preprints

10 Mar 2022

| 10 Mar 2022

Status: this discussion paper is a preprint. It has been under review for the journal Hydrology and Earth System Sciences (HESS). The manuscript was not accepted for further review after discussion.

Numerical modeling of physical and biochemical processes in the subsurface and their impacts on the self-potential signature

Xin Liu, Zengyu Zhang, and Alex Furman

Abstract. Subsurface contamination is a significant problem due to excessive fertigation and industrial and domestic wastewater discharge. With numerical modeling and geophysical tool development, subsurface contaminant research has become easier to implement and study. However, there is still a gap in coupling the biochemical processes and geophysical signals. Such a coupling model is needed to facilitate understanding subsurface processes and provide further theoretical basis to practice and field monitoring. Thus, this research aims to simulate the self-potential (SP) signature in response to physical and biochemical dynamics in the subsurface. For the physico-bio-chemical model, the processes of water flow, solute transport, biochemical reactions, microbial dynamics, adsorption, and gas flow are considered. Specifically, the biochemical cycles related to C, N, Mn, Fe, and S are incorporated in the model. The physico-bio-chemical model is then coupled with the SP model. The SP model is addressed by Poisson’s continuity equation, based on streaming and redox potential contribution. The streaming potential is calculated by the effective excess charge density and the water flow velocity, while the Butler-Volmer equation solves the redox potential. The results show that redox processes dominate the SP signals. Oxygen and nitrate concentrations present positive relationships with redox potential and dominate the redox potential in the oxic and anoxic environment, respectively. Nitrification and dissolved organic carbon (DOC) aerobic oxidation rates show positive relationships with redox potential. In contrast, the denitrification rate presents a negative relationship. The higher reaction rates for different redox processes also correspond to their optimal redox potential ranges. The streaming potential affected by water content and flux contributes little to SP, and the negative values along with soil depth become less remarkable. Generally, the SP and redox potential model can better reflect redox species concentrations and reaction rates, while the streaming potential model can reflect the water content and flux dynamics. Thus, the research can guide the detection of redox-sensitive contamination and water leakage in the subsurface.

Received: 20 Jan 2022 – Discussion started: 10 Mar 2022

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Xin Liu, Zengyu Zhang, and Alex Furman

Status: closed

RC1:
'Comment on hess-2022-31', Andre Revil, 15 Mar 2022
This work starts with a great promise: a physics-based model for self-potential signals in complex environments with complex chemistry including biotic processes. Once this has been stated and after reading the manuscript, I got disappointed by some aspects of the modeling, which I believe are not correct. Here my criticisms. I hope the authors will take them in a positive spirit. I thank the authors for their wish to make the code available in HYDRUS 1D but this will need to be seriously corrected or errors will propagate in the literature.

The authors called Archie’s laws the conductivity equation, in which they neglect surface conductivity. Archie’s law is a relationship between the formation factor and the porosity or water content whatever surface conductivity can be neglected or not. This is NOT a conductivity equation. Surface conductivity CANNOT be neglected for soils. This assumption is therefore in contradiction with the corpus of knowledge developed in the realm of hydrogeophysics.

The authors neglect the diffusion/membrane polarization, which is related to the gradient in the electrochemical potential of the ionic charge carriers. However, this contribution is well-established and probably the major contributor of the observed signals. It is related to the Hittorf transport numbers of the ionic charge carriers, which depends in turn on the surface conductivity. Obviously, the authors have a lack of knowledge on how to compute this contribution and it was not discussed for that reason. This is not a good practice.

The redox potential contribution exist ONLY if a biotic or an abiotic (metallic in a broad sense including semi-conductors) electronic conductor is present in the material. This point is not well-discussed in the paper. The authors seems to mix electrodic potential associated with redox chemistry at the electrodes/ medium interface (which can be avoided with agar agar gel) and what specialists called self-potential signals (remotely measured without having the electrodes in contact with the medium in which the source of current occurs). I am glad that the authors modeled electrodic potentials but they should NOT be misled with self-potentials.

The experiments are poorly described. The paper of Zhang and Furman is not related to self-potential signals so I don’t have any idea on how the geophysical experiment was done. In addition, even in sand with organic matter and bacteria, surface conductivity can be strong, in contradiction with the basic assumption made in this paper. The CEC could have been estimated or measured.

Equation 28 is provided without any reference and associated assumptions. This is bad practice especially when this equation has already been discussed and developed in the literature. It was certainly not derived by the authors…Furthermore, equation 28 is valid ONLY in presence of an electronic conductor, this assumption is not discussed in the paper, see Rittgers J. B., A. Revil, M. Karaoulis, M. A. Mooney, L.D. Slater, and E.A. Atekwana, Self-potential signals generated by the corrosion of buried metallic objects with application to contaminant plumes, Geophysics, 78(5), EN65-EN82, 10.1190/GEO2013-0033.1, 2013, for details.[

For each figure, write clearly what is measured and what is computed.

Regardinh the statement “SP associated with redox processes is induced by electron transfer, where electron donors (e.g., organic carbon) deliver electrons to acceptors (e.g., oxygen or nitrate) driven by redox potential (Jouniaux et al., 2009).”, I cannot fond such statement in the cited paper. At the opposite, I am very surprise to see no citation of the excellent papers by Alexis Maineult on this subject. Also papers related to electrodic potentials should be cited as well.

Equation 25 is wrong. The current density is the effective charge density (defined through a dynamic volume averaging of the local current density, local charge time the local velocity) and the Darcy velocity, not the fluid velocity.

In the introduction, it is written that Poisson equation for the self-potential is a continuity equation. This is a field equation obtained by combining a continuity equation (conservation of charge in the quasi-static limit of the Maxwell equations) and a constitutive equation (generalized Ohm’s law). The authors should be more rigorous.

André Revil March 15^th 2022
Citation: https://doi.org/10.5194/hess-2022-31-RC1
- AC1:
  'Reply on RC1', Xin Liu, 03 May 2022
  
  We appreciate your constructive comments which help to build up a more rigorous SP model. We took all comments into consideration and made the corresponding responses in the Supplement.
  
  Citation: https://doi.org/10.5194/hess-2022-31-AC1
  - AC2: 'Reply on AC1', Xin Liu, 03 May 2022
    
    In the Response 4 of last Supplement , the unit of CEC should be meq/100g instead of meq/kg. I am so sorry about the mistake and make a revision this time.
    
    Citation: https://doi.org/10.5194/hess-2022-31-AC2
- RC3:
  'Reply on RC1', Andre Revil, 03 May 2022
  
  The authors decided not to reply to my comments or more precisely perhaps they did not provided a keyed reponse to my comments. They put their response in a suplement material. In my opinion, this is not the correct way to handle the review process and the comments I made were reaching the inner core of the paper and modeling, which in my opinion raise serious questions. I think the paper cannot be published in the present form.
  
  Citation: https://doi.org/10.5194/hess-2022-31-RC3
  - EC1: 'Reply to RC3', Gerrit H. de Rooij, 03 May 2022
    
    Dear Prof. Revil,
    The authors replied in detail to your comments. HESS permits comment to be published as supplements to allow more flexibiltiy in the formatting. The reply by the authors contains color figures, extensive text in different fonts, etc., so they had no choice but to place their reply in a supplement.
    Thank you,
    Gerrit de Rooij
    Editor
    
    Citation: https://doi.org/10.5194/hess-2022-31-EC1
    
    AC6: 'Reply on EC1', Xin Liu, 10 May 2022
    
    Dear Prof. Gerrit H. de Rooij
    Thank you very much for helping explain the reason.
    Sincerely,
    Xin Liu.
    
    Citation: https://doi.org/10.5194/hess-2022-31-AC6
  - AC5: 'Reply on RC3', Xin Liu, 10 May 2022
    
    Dear Prof. Andre Revil
    We appreciate your constructive comments and understand the paper and model need to be further improved. The reason that we put the responses in the supplement is to make our responses clear, not trying to aviod your comments. We will also improve the paper and model based on your comments and our responses in the next stage (revision stage).
    Thank you for your previous time and kindly consideration.
    Sincerely,
    Xin Liu.
    
    Citation: https://doi.org/10.5194/hess-2022-31-AC5
- AC4: 'Reply on RC1', Xin Liu, 03 May 2022
  
  I am so sorry to upload the Supplement again. This is because the equation numbers that directly cited from the revised text in the previous Supplement is automatic changes by linking with MathType. Thus, I disabled the function and revised equation numbers this time. I am so sorry to add troubles and make changes again.
  
  Citation: https://doi.org/10.5194/hess-2022-31-AC4
RC2:
'Comment on hess-2022-31', Anonymous Referee #2, 12 Apr 2022

The authors proposed a coupling model to simulate the complex bio-geochemical reactions in subsurface water flow and solte transport. The reactions are important and it is meanful to including these in a traditional model. However, I got lost in reading through the manuscript. The work is interest but I felt the authors were failed to present a clear consistent streamline from the model development to calculation, simulation and verification.

1. Abstract

The abstract seems too long and a bit of confusing. It is kind of hard to get your main contribution from this complicated abstract. Like you state that the development of the model is your research goal, but your results focus on detailed geochemical analysis and explanations. Thus which one is your most important point? The goal and results then are not logically consistent though for sure they are related. If the model is creative, it would be better to prove its accuracy and efficiency. If the bio-geochemical processes are the problem that need to be illustrated, then it is better to describe the significance of the geochemical environment. I suggest to modify your abstract to clearly present your contribution.

2. Introduction

Are there any try out of embracing SP to subsurface flow and transport modeling in previous studies? I am not an expert in SP model but can you directly tranfter this signial into geochemical variables in subsurface porous media?

3. Model development

The authors described a bunch of equations. Are the basic water flow and solute transport... are set up by own developed code or a business code such as comsol/hydrus? I saw the authors mentioned this in the end of the manuscript, but it is better to be cleared out in the paper.

The same as the previous concern, is the SP code constructed by the authors or an adopted module? It is really hard to tell which equation is cited from other papers and which one is that you derived. Meanwhile, the authors introduced the flow and SP separately, but how the two parts are connected ? How the variables in the two systems are connected? A section is needed here.

Many paramters and observations were enrolled in the modeling but how were they obtained from the physical-based experiment? And the model then has a high degree of reedom, how did you constrain your model in the simulation and verificaiton? Also, the uncertainty is greatly increased in this process as stated in the literature: "Bayesian performance evaluation of evapotranspiration models based on eddy covariance systems in an arid region. Hydrology and Earth System Sciences. 2019, 23(7):2877-2895".

4. Results

As the problem mentioned above, it is not quite clear the performance of developed model. It is hard to say whether the approach in valid or not. It would be better to show what are your inputs and what are your outputs as too many reactions are take into account here. How are the simulations compared with the observations for the most important parameters? And how the results performed by comparing to the model that ignoring the SP.

Citation: https://doi.org/10.5194/hess-2022-31-RC2
- AC3: 'Reply on RC2', Xin Liu, 03 May 2022
  
  We appreciate your constructive comments which help to make the paper’s expression and logic clearer. We took all the comments into consideration and made responses in the Supplement.
  
  Citation: https://doi.org/10.5194/hess-2022-31-AC3

Status: closed

RC1:
'Comment on hess-2022-31', Andre Revil, 15 Mar 2022
This work starts with a great promise: a physics-based model for self-potential signals in complex environments with complex chemistry including biotic processes. Once this has been stated and after reading the manuscript, I got disappointed by some aspects of the modeling, which I believe are not correct. Here my criticisms. I hope the authors will take them in a positive spirit. I thank the authors for their wish to make the code available in HYDRUS 1D but this will need to be seriously corrected or errors will propagate in the literature.

The authors called Archie’s laws the conductivity equation, in which they neglect surface conductivity. Archie’s law is a relationship between the formation factor and the porosity or water content whatever surface conductivity can be neglected or not. This is NOT a conductivity equation. Surface conductivity CANNOT be neglected for soils. This assumption is therefore in contradiction with the corpus of knowledge developed in the realm of hydrogeophysics.

The authors neglect the diffusion/membrane polarization, which is related to the gradient in the electrochemical potential of the ionic charge carriers. However, this contribution is well-established and probably the major contributor of the observed signals. It is related to the Hittorf transport numbers of the ionic charge carriers, which depends in turn on the surface conductivity. Obviously, the authors have a lack of knowledge on how to compute this contribution and it was not discussed for that reason. This is not a good practice.

The redox potential contribution exist ONLY if a biotic or an abiotic (metallic in a broad sense including semi-conductors) electronic conductor is present in the material. This point is not well-discussed in the paper. The authors seems to mix electrodic potential associated with redox chemistry at the electrodes/ medium interface (which can be avoided with agar agar gel) and what specialists called self-potential signals (remotely measured without having the electrodes in contact with the medium in which the source of current occurs). I am glad that the authors modeled electrodic potentials but they should NOT be misled with self-potentials.

The experiments are poorly described. The paper of Zhang and Furman is not related to self-potential signals so I don’t have any idea on how the geophysical experiment was done. In addition, even in sand with organic matter and bacteria, surface conductivity can be strong, in contradiction with the basic assumption made in this paper. The CEC could have been estimated or measured.

Equation 28 is provided without any reference and associated assumptions. This is bad practice especially when this equation has already been discussed and developed in the literature. It was certainly not derived by the authors…Furthermore, equation 28 is valid ONLY in presence of an electronic conductor, this assumption is not discussed in the paper, see Rittgers J. B., A. Revil, M. Karaoulis, M. A. Mooney, L.D. Slater, and E.A. Atekwana, Self-potential signals generated by the corrosion of buried metallic objects with application to contaminant plumes, Geophysics, 78(5), EN65-EN82, 10.1190/GEO2013-0033.1, 2013, for details.[

For each figure, write clearly what is measured and what is computed.

Regardinh the statement “SP associated with redox processes is induced by electron transfer, where electron donors (e.g., organic carbon) deliver electrons to acceptors (e.g., oxygen or nitrate) driven by redox potential (Jouniaux et al., 2009).”, I cannot fond such statement in the cited paper. At the opposite, I am very surprise to see no citation of the excellent papers by Alexis Maineult on this subject. Also papers related to electrodic potentials should be cited as well.

Equation 25 is wrong. The current density is the effective charge density (defined through a dynamic volume averaging of the local current density, local charge time the local velocity) and the Darcy velocity, not the fluid velocity.

In the introduction, it is written that Poisson equation for the self-potential is a continuity equation. This is a field equation obtained by combining a continuity equation (conservation of charge in the quasi-static limit of the Maxwell equations) and a constitutive equation (generalized Ohm’s law). The authors should be more rigorous.

André Revil March 15^th 2022
Citation: https://doi.org/10.5194/hess-2022-31-RC1
- AC1:
  'Reply on RC1', Xin Liu, 03 May 2022
  
  We appreciate your constructive comments which help to build up a more rigorous SP model. We took all comments into consideration and made the corresponding responses in the Supplement.
  
  Citation: https://doi.org/10.5194/hess-2022-31-AC1
  - AC2: 'Reply on AC1', Xin Liu, 03 May 2022
    
    In the Response 4 of last Supplement , the unit of CEC should be meq/100g instead of meq/kg. I am so sorry about the mistake and make a revision this time.
    
    Citation: https://doi.org/10.5194/hess-2022-31-AC2
- RC3:
  'Reply on RC1', Andre Revil, 03 May 2022
  
  The authors decided not to reply to my comments or more precisely perhaps they did not provided a keyed reponse to my comments. They put their response in a suplement material. In my opinion, this is not the correct way to handle the review process and the comments I made were reaching the inner core of the paper and modeling, which in my opinion raise serious questions. I think the paper cannot be published in the present form.
  
  Citation: https://doi.org/10.5194/hess-2022-31-RC3
  - EC1: 'Reply to RC3', Gerrit H. de Rooij, 03 May 2022
    
    Dear Prof. Revil,
    The authors replied in detail to your comments. HESS permits comment to be published as supplements to allow more flexibiltiy in the formatting. The reply by the authors contains color figures, extensive text in different fonts, etc., so they had no choice but to place their reply in a supplement.
    Thank you,
    Gerrit de Rooij
    Editor
    
    Citation: https://doi.org/10.5194/hess-2022-31-EC1
    
    AC6: 'Reply on EC1', Xin Liu, 10 May 2022
    
    Dear Prof. Gerrit H. de Rooij
    Thank you very much for helping explain the reason.
    Sincerely,
    Xin Liu.
    
    Citation: https://doi.org/10.5194/hess-2022-31-AC6
  - AC5: 'Reply on RC3', Xin Liu, 10 May 2022
    
    Dear Prof. Andre Revil
    We appreciate your constructive comments and understand the paper and model need to be further improved. The reason that we put the responses in the supplement is to make our responses clear, not trying to aviod your comments. We will also improve the paper and model based on your comments and our responses in the next stage (revision stage).
    Thank you for your previous time and kindly consideration.
    Sincerely,
    Xin Liu.
    
    Citation: https://doi.org/10.5194/hess-2022-31-AC5
- AC4: 'Reply on RC1', Xin Liu, 03 May 2022
  
  I am so sorry to upload the Supplement again. This is because the equation numbers that directly cited from the revised text in the previous Supplement is automatic changes by linking with MathType. Thus, I disabled the function and revised equation numbers this time. I am so sorry to add troubles and make changes again.
  
  Citation: https://doi.org/10.5194/hess-2022-31-AC4
RC2:
'Comment on hess-2022-31', Anonymous Referee #2, 12 Apr 2022

The authors proposed a coupling model to simulate the complex bio-geochemical reactions in subsurface water flow and solte transport. The reactions are important and it is meanful to including these in a traditional model. However, I got lost in reading through the manuscript. The work is interest but I felt the authors were failed to present a clear consistent streamline from the model development to calculation, simulation and verification.

1. Abstract

The abstract seems too long and a bit of confusing. It is kind of hard to get your main contribution from this complicated abstract. Like you state that the development of the model is your research goal, but your results focus on detailed geochemical analysis and explanations. Thus which one is your most important point? The goal and results then are not logically consistent though for sure they are related. If the model is creative, it would be better to prove its accuracy and efficiency. If the bio-geochemical processes are the problem that need to be illustrated, then it is better to describe the significance of the geochemical environment. I suggest to modify your abstract to clearly present your contribution.

2. Introduction

Are there any try out of embracing SP to subsurface flow and transport modeling in previous studies? I am not an expert in SP model but can you directly tranfter this signial into geochemical variables in subsurface porous media?

3. Model development

The authors described a bunch of equations. Are the basic water flow and solute transport... are set up by own developed code or a business code such as comsol/hydrus? I saw the authors mentioned this in the end of the manuscript, but it is better to be cleared out in the paper.

The same as the previous concern, is the SP code constructed by the authors or an adopted module? It is really hard to tell which equation is cited from other papers and which one is that you derived. Meanwhile, the authors introduced the flow and SP separately, but how the two parts are connected ? How the variables in the two systems are connected? A section is needed here.

Many paramters and observations were enrolled in the modeling but how were they obtained from the physical-based experiment? And the model then has a high degree of reedom, how did you constrain your model in the simulation and verificaiton? Also, the uncertainty is greatly increased in this process as stated in the literature: "Bayesian performance evaluation of evapotranspiration models based on eddy covariance systems in an arid region. Hydrology and Earth System Sciences. 2019, 23(7):2877-2895".

4. Results

As the problem mentioned above, it is not quite clear the performance of developed model. It is hard to say whether the approach in valid or not. It would be better to show what are your inputs and what are your outputs as too many reactions are take into account here. How are the simulations compared with the observations for the most important parameters? And how the results performed by comparing to the model that ignoring the SP.

Citation: https://doi.org/10.5194/hess-2022-31-RC2
- AC3: 'Reply on RC2', Xin Liu, 03 May 2022
  
  We appreciate your constructive comments which help to make the paper’s expression and logic clearer. We took all the comments into consideration and made responses in the Supplement.
  
  Citation: https://doi.org/10.5194/hess-2022-31-AC3

Xin Liu, Zengyu Zhang, and Alex Furman

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https://doi.org/10.5194/hess-2022-31-supplement

Xin Liu, Zengyu Zhang, and Alex Furman

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Short summary

This paper built a systematic model to simulate geophysical signals in response to soil physico-bio-chemical dynamics based on the subsurface natural environment. The results show that geophysical signals can better reflect the typical contamination (i.e., C and N) concentration and degradation. Additionally, the signals are also sensitive to water content and flux. Thus, the research can guide the detection of typical contamination and water leakage in the subsurface.


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