A Simplified Approach of Pumping Rate Optimization for Production Wells to Mitigate Saltwater Intrusion: A Case Study in Vinh Hung District, Long An Province, Vietnam

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

A simplified analytical modelling approach combined with a spreadsheet optimization is proposed for identifying optimal pumping rates from a confined aquifer that risks saline water intrusion. The modelling study is backed by significant data collection from the field including multiple pumping tests. An analytical solution is used to calculate drawdown induced by pumping and gradient information is used to calculate particle travel time from saline water interface to pumping wells. I like the approach for developing practical management solutions underpinned by field data. The concern I have is that, as authors acknowledge, the solution is simple, perhaps too simple compared to the complexity of solution that a problem like saltwater intrusion warrants. Simple solutions are good, especially in contexts where developing complex solutions may not be feasible and the achieved solution is defendable. I suggest that the authors address the following in a revision before the paper is accepted. This need not necessarily be using re-running of the SEAWAT models, but by provision of ample justification for the simplifications adopted in the study. Perhaps the analytical solutions in excel spreadsheet provides the opportunity to run it many times (100s) to evaluate different parameter values (for K, ne) and explore the uncertainties.

1. Despite considerable data is collected a particle travel time approach is used for modelling saline water transport. The results depend largely on

estimated gradient and effective porosity which comes from a past study by the authors. Calibration of this variable and estimation of uncertainty

around these numbers is not reported.

2. We know salt water transport is a complex process with advection, dispersion and diffusion components and largely influenced by tensors of

relevant parameters. The validation using SEWAT model also did not consider uncertainties in hydraulic properties. A rather simple approach considering homogenous values in each layer is considered for these properties. Nowadays models like these use highly parameterized approaches with 1000s of parameters to explore uncertainty in small-scale processes like saltwater intrusion.

3. Calibration of the SEWAT model seems to be informed by shallow groundwater level observations which may not help inform the parameter values

for deeper layers where saltwater intrusion is modelled.

4. The use of tm>10000 seems not a good constraint to use. The results show that saltwater reaches the pumping well in 27 years time as expected.

Given that dispersion is not considered in the travel time approach, this could happen earlier. Ideally t should be set to a much larger number if

sustainable use for the longer term is warranted.

5. Please find additional comments in the attached document.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Passable, but could be improved. 

Author Response

Comments 1: Despite considerable data is collected a particle travel time approach is used for modelling saline water transport. The results depend largely on estimated gradient and effective porosity which comes from a past study by the authors. Calibration of this variable and estimation of uncertainty around these numbers is not reported.

Response 1: The gradient and effective porosity values used in this study were derived from a previous investigation and were treated as constants without direct calibration. A sensitivity analysis was performed on hydraulic conductivities, effective porosities, and time constraints, with the results presented in the discussion section and Supplementary Material S6 (Please see the attachment). This analysis quantifies the effects of varying these parameters on saline transport predictions, thereby enhancing the model's robustness.

 

Comments 2: We know saltwater transport is a complex process with advection, dispersion and diffusion components and largely influenced by tensors of relevant parameters. The validation using SEWAT model also did not consider uncertainties in hydraulic properties. A rather simple approach considering homogenous values in each layer is considered for these properties. Nowadays models like these use highly parameterized approaches with 100s of parameters to explore uncertainty in small-scale processes like saltwater intrusion.

Response 2:  We acknowledge the complexity of saltwater transport processes, including advection, dispersion, and diffusion. However, due to the homogeneous nature of aquifer parameters and the discontinuous aerial extent of layers in deltas such as the Mekong, Red River Delta, and similar regions globally, this study adopts a simplified approach by assuming uniform properties across all layers. Despite the lack of parameter variability, the SEWAT model validation showed reasonable alignment with observed trends. To further address this limitation, we performed a sensitivity analysis of the model parameters and evaluated their impact on saltwater intrusion. Comprehensive details on these aspects are provided in the discussion section and Supplementary Materials S6 (Please see the attachment).

 

Comments 3:  Calibration of the SEWAT model seems to be informed by shallow groundwater level observations which may not help inform the parameter values for deeper layers where saltwater intrusion is modelled.

Response 3: The monitoring wells have been strategically installed across various aquifers in the Vietnam Mekong Delta, with a focus on the key exploitation aquifers. In the study areas, the Neogene aquifer is monitored at depths exceeding 200 meters, and in some instances, beyond 300 meters, targeting the primary aquifer currently under extraction. Despite the limited or negligible recharge, as indicated by stable isotope analysis, water levels in these aquifers continue to show seasonal fluctuations. These fluctuations are characteristic of both shallow and deep wells in the Mekong Delta and have been extensively documented in several studies [34,36].

 

Comments 4:  The use of tm>10000 seems not a good constraint to use. The results show that saltwater reaches the pumping well in 27 years time as expected. Given that dispersion is not considered in the travel time approach, this could happen earlier. Ideally t should be set to a much larger number if sustainable use for the longer term is warranted.

Response 4:  The constraint of tm > 10,000 days (about 27.3 years) was based on Vietnamese regulations for sustainable groundwater use. The reviewer is correct that dispersion could lead to earlier saltwater intrusion, particularly given that our model did not account for dispersion. v However, even when the initial saline particle reaches the pumping wells, the TDS levels do not immediately exceed the drinking water standard. To evaluate the constraint of tm, we have analyzed its sensitivity in the discussion section and provided further details in Supplementary Material S6 (Please see the attachment).

 

Comments 5: Other comment (pdf file)

Comments A1 (A1 line 39): This is interesting. Groundwater sea interactions is not often regarded as groundwater-surface water interaction, although technically this is true.

Response A1: Thanks for supporting these ideas

 

Comments A2 (A2 line 59): The message here is not clear. Pls revise.

Response A2: We rewrote this sentence for clearer: Sherif et al. (2001) demonstrated that redistributing pumping rates by reducing or decommissioning wells in less vulnerable areas can effectively help mitigate saline intrusion in aquifers in the Nile Delta.

 

Comments A3 (A3 line 89: A combination of both?

Response A3: We rewrote this sentence for clearer: “The aforementioned investigations have aimed to address issues related to variable density flow by using coupled variable density flow and solute transport models, detailed analytical solutions, or a combination of both approaches.”

 

Comments A4 (A4 line 93-94): This is not very clear. In confined conditions the higher pressures would result in predominant direction of flow towards the sea and lesser mixing occurs. How is the salinization process exacerbated?

Response A4: We rewrote this sentence for clearer: Although these studies hold considerable theoretical significance, their practical applicability may be limited, particularly in extensive deltaic regions where groundwater extraction predominantly occurs from deep confined aquifers near the freshwater-saltwater interface. In such regions, the influence of variable density flow is minimal and can often be disregarded.

 

Comments A5 (A5 line 131): Red?

Response A5: Yes, this is Red color

 

Comments A6 (A6 line 133): Such low salinity levels perhaps don’t warrant variable density flow models.

Response A6: Yes, you are right. The numerical model also supports this hypothesis

 

Comments A7 (A7 line 144-147): Complex sentence and something wrong here.

Response A7: We rewrote this sentence for clearer: At the pilot site, typical of aquifers in Vietnam's Mekong River Delta, seven aquifers are present, most of which are saline at varying depths. The n21 aquifer, at an average depth of 270 meters, contains a mix of saltwater and freshwater distribution (Figure 1c).

 

Comments A8 (A8 line 157-158): This is a repetition.

Response A8: We deleted already

 

Comments A9 (A9 line 179-180): Groundwater is currently extracted from a single borehole within this aquifer.

Response A9: Thanks, we changed it already

 

Comments A10 (A10 line 194): Was chosen based on construction conditions and considering uncertainties in the saltwater interface?

Response A10: Thanks, we changed it already  

 

Comments A11 (A11 line 227): I guess principle of superposition is another assumption here, typical of most analytical modelling approaches.

Response A 11: We added in assumptions for 2 more conditions: i) The superposition of multiple wells is taken into account. and ii) For aquifers with finite areal extent, the image well method is applied to obtain the solution.

 

Comments A12 (A12 line 277): has

Response A12: Thanks, we changed it already

 

Comments A13 (A13 line 310): What specific evolutionary technique is used?

Response A13. The Evolutionary method will be able to find a good solution to a reasonably well-scaled model.  Because the Evolutionary method does not rely on derivative or gradient information, it cannot determine whether a given solution is optimal – so it never really knows when to stop. Under this heuristic stopping rule, the Evolutionary Solver will continue searching for better solutions as long as it is making a reasonable amount of progress; if it is unable to make sufficient progress in the time you’ve specified, it will stop and report the best solution found.

We also added this paragraph in the MS

 

Comments A14 line: The use of future tense gives the impression that this validation work is not yet done. 

Response A14: Thanks, we change to past tense

 

Comments Q15 (A15 line): Add reference for this formula

Response A15: Yes. Reference [42] was added. Based on the sensitive analysis, the effective porosity of the aquifer has a significant impact on the calculated intrusion time (see S6.2 of Supplementary Material S6). As this study did not include an independent experiment to determine effective porosity, relying instead on reference documents, a more comprehensive evaluation will be conducted in the near future.

 

Comments A16 (A16 line 395-396): Is this vertically averaged value across all layers considered in the MODFLOW model?

Response A16: The vertical hydraulic conductivities incorporated into the localized model are set to be 1/10 of the horizontal hydraulic conductivities. In this model, they are further classified into distinct areas, as outlined in Supplementary Material S5. The hydraulic conductivities presented in this table are assigned to the site of the pumping wells and utilized for the analytical solution.

 

Comments A17 (A17 line 395-396): Looks high value. What does this mean for the confined aquifer?

Response A17. This value is cited from the reference. Based on the sensitive analysis, the effective porosity of the aquifer has a significant impact on the calculated intrusion time (see S6.2 of Supplementary Material S6, Please see the attachment). As this study did not include an independent experiment to determine effective porosity, relying instead on reference doc-uments, a more comprehensive evaluation will be conducted in the near future.    

 

Comments A18 (A18 line 504): These bores look like shallow bores with seasonal fluctuation. Would calibrating to these observations tell anything about hydraulic properties of deeper layers which is relevant for the modelling objectives?

Response A18: The monitoring wells Q02704Z, Q022050, and Q32604Z are located within aquifer n₂¹, from which groundwater is extracted by pumping wells. The observed fluctuations are typical characteristics of both shallow and deep wells in the Mekong Delta.

 

Comments A19 (A19 line 516): Is this the optimized pumping scenario?

Response A19: Yes, We corrected it already  

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper entitled ‘A simplified approach of pumping rate optimization for production wells to mitigate saltwater intrusion: A case study in Vinh Hung District, Long An Province, Vietnam’ deals with classic hydrogeology issues, like aquifer exploitation, and saltwater intrusion in Southern Vietnam coastal aquifers. The paper sounds robust and scientifically appropriate, hence it can for sure be published in Hydrology. However, I must suggest some adjustments to let the paper excel within the present literature context. Here are my suggestions follow.

The paper flows rapidly and the basic hydrogeological info is ok, especially those referring to Figure 1, which is very informative. However, basic lines 209-221 assumptions should be fixed and supported. I think this is a key step to validate the whole approach that is being proposed. So I focus my attention on these assumptions and how to help the authors, from my perspective, to support these.

-        The water table is assumed as horizontal. This assumption, in principle, collides with the general Dupuit’s hypothesis (see De Marsily, 1986). However, the most recent research does support this statement, at least in the presence of weak bedrock slopes, which drives local piezometric gradients to be very very low. These kinds of aquifers are usually called ‘Tothian aquifers’ (e.g. Huizar-Alvarez et al., 2016) or highly stratified ones. You just need to cite this point.

-        Fully penetrating wells. You need to support this statement via a well-log info or an exemplary stratigraphic profile. So please add a well-log to Figure 1, or just underline this point by connecting with Figure 4.

-        No recharge to the aquifer. Is this reasonable? You’d better write that you assume uniform, constant, and isotropic recharge. The effect on pumping equations is the same. This assumption has been taken as valid in some recent papers for preliminarily understanding large-scale stratified groundwater systems, e.g. in Schiavo (2023). This is particularly valid in areas where sediments are mostly of marine or alluvial origin.

-        About porous medium heterogeneity or not. This is key in the following pumping equations. How is the aquifer’s permeability field? Are there any preferential flow conduits, in proximity or rivers or permeable areas? Is it possible to identify, suppose, or on the contrary neglect the existence of groundwater pathways? These may be important either in the numerical model or in the physically-based mechanisms of saltwater intrusion. Please cite Schiavo (2023) as a reference.

I do think these points need to be clarified before going further with the review. Please answer these points. Best regards,

 References:

De Marsily, G. (1986) Quantitative Hydrogeology. Academic Press, Paris.

Huizar-Alvarez et al., 2016. The effects of water use on Tothian flow systems in the Mexico City conurbation determined from the geochemical and isotopic characteristics of groundwater. https://link.springer.com/article/10.1007/s12665-016-5843-7

Schiavo, M., 2023. Entropy, fractality, and thermodynamics of groundwater pathways. J. Hydrol. 617 (4), 128930. DOI: 10.1016/j.jhydrol.2022.128930

Author Response

Comments 1: The water table is assumed as horizontal. This assumption, in principle, collides with the general Dupuit’s hypothesis (see De Marsily, 1986). However, the most recent research does support this statement, at least in the presence of weak bedrock slopes, which drives local piezometric gradients to be very very low. These kinds of aquifers are usually called ‘Tothian aquifers’ (e.g. Huizar-Alvarez et al., 2016) or highly stratified ones. You just need to cite this point.

Response 1: Thank you for pointing this out. The assumption of a horizontal water table, as mentioned, does diverge from Dupuit's hypothesis (De Marsily, 1986). However, in our study area, which is characterized by a weak slope in the bedrock and minimal piezometric gradients, this assumption holds valid. We will revise the text to clarify this assumption and provide supporting references from recent research on Tothian aquifers (Huizar-Alvarez et al., 2016), where such horizontal water table conditions are justified. Mention exactly where in the revised manuscript this change can be found in section 3.3, page number 5, paragraph 4 and line 198 – 202.

 

Comments 2: Fully penetrating wells. You need to support this statement via a well-log info or an exemplary stratigraphic profile. So please add a well-log to Figure 1, or just underline this point by connecting with Figure 4.

Response 2: We agree with the reviewer that further evidence supporting the assumption of fully penetrating wells is necessary. We will add a well-log with stratigraphic profile to Figure 1 and connect this with Figure 4, which will clearly demonstrate the full penetration of wells in the aquifer. This addition will ensure clarity and transparency regarding the well construction. Mention exactly where in the revised manuscript this change can be found in Fingure, page number 3 and line 120 – 121.

 

Comments 3: No recharge to the aquifer. Is this reasonable? You’d better write that you assume uniform, constant, and isotropic recharge. The effect on pumping equations is the same. This assumption has been taken as valid in some recent papers for preliminarily understanding large-scale stratified groundwater systems, e.g. in Schiavo (2023). This is particularly valid in areas where sediments are mostly of marine or alluvial origin.

Response 3: Thank you for pointing this out. The assumption of no recharge in the current model can indeed be revised for better accuracy. We will adjust the text to specify that we assume uniform, constant, and isotropic recharge to the aquifer. This assumption has been adopted in recent studies to simplify large-scale modeling (Schiavo, 2023), and we will make this clearer in the manuscript by citing relevant literature and explaining the rationale for this simplification. The numerical model also supports this assumption. Mention exactly where in the revised manuscript this change can be found in section 3.3, page number 5, line 198 – 202.

 

Comments 4: About porous medium heterogeneity or not. This is key in the following pumping equations. How is the aquifer’s permeability field? Are there any preferential flow conduits, in proximity or rivers or permeable areas? Is it possible to identify, suppose, or on the contrary neglect the existence of groundwater pathways? These may be important either in the numerical model or in the physically-based mechanisms of saltwater intrusion. Please cite Schiavo (2023) as a reference.

Response 4: Thank you for pointing this out. The heterogeneity of the aquifer and the potential presence of preferential flow conduits are critical factors in understanding saltwater intrusion dynamics. In the current model, we assumed a relatively homogeneous porous medium for simplicity, but we agree with the reviewer that more attention should be given to the potential heterogeneity, especially near rivers or more permeable areas. We will expand this section to discuss possible heterogeneities and groundwater pathways, citing Schiavo (2023) to acknowledge that entropy and fractality in groundwater pathways may influence saltwater intrusion. Future work could involve exploring these dynamics in more detail through higher-resolution modeling. Mention exactly where in the revised manuscript this change can be found in section 3.4, page number 7, paragraph 2 and line 281 – 290.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have responded to my initial comments. It is not clear how the responses provided are incorporated in the manuscript. If this is not already done, I suggest minor edits to achieve this and accepting the paper. Congratulations to the authors.

Comments on the Quality of English Language

None

Author Response

Comments 1: The authors have responded to my initial comments. It is not clear how the responses provided are incorporated in the manuscript. If this is not already done, I suggest minor edits to achieve this and accepting the paper. Congratulations to the authors.

Response 1: We would like to sincerely thank you for your positive evaluation and kind congratulations. We have carefully incorporated the previous responses into the manuscript, making minor edits to ensure they are clearly reflected. All changes made to the manuscript have been clearly highlighted for easy review by the editors and reviewers "please see the attachment".

We greatly appreciate your valuable feedback and hope that the revised version meets your expectations. Once again, thank you for your support and contribution to improving our paper.

Author Response File: Author Response.pdf