Review Reports - Heat Transfer Modeling on High-Temperature Charging and Discharging of Deep Borehole Heat Exchanger with Transient Strong Heat Flux

Round 1

Reviewer 1 Report

However this is a good study but following comments will improve the quality of this paper

1. Why assumption 3 is considered? Please elaborate the reason.

2. Please provide the references for important equations used.

3. On page 8, equations are not numbered.

4. In figure 7, relative error limit taken as 5%. Why?

5. Section 4 is general, try to improve it or can be removed.

6. Shorten abstract also.

7. Add some qualitative results in the conclusion section.

8. Nomenclature is missing. 9. Please add some qualititive results in abstract section. 10. There is much difference in simulation cost between OGS and your study. Please elaborate it. It is a good study.

Author Response

Comments and Suggestions for Authors

However this is a good study but following comments will improve the quality of this paper

Why assumption 3 is considered? Please elaborate the reason.

Reply: Thank you for the valuable comment. This assumption originates from geological observation and in-situ field test of the deep drilling project. As is mentioned in the paper, deep borehole heat exchanger (DBHE) is featured with much deeper drilling depth underground. It could reach up to 1000~3000 m and far exceeds the depth of traditional shallow BHEs (around 100m). In general, DBHE can be constructed almost anywhere and does not require natural hydrothermal reservoirs or special geological formations (Daniel 2016). It is an ideal substitute towards sustainable exploitation of geothermal resources especially in areas where no groundwater exists. The environmental issues caused by imbalanced groundwater extraction and injection of hydrothermal technology could be properly avoided. Therefore, assumption 3 is usually adopted for heat transfer modeling of DBHE.

Please provide the references for important equations used.

Reply: Thank you for the valuable comment. All the important equations cited from literature are all properly added with the references. The left equations without citations are carefully deduced by the authors.

On page 8, equations are not numbered.

Reply: Thank you for the valuable comment. We have checked the equations in page 8. It is a ordinary differential equation set numbered as Eq.(9) shown below.

In figure 7, relative error limit taken as 5%. Why?

Reply: Thank you for the valuable comment. This relative error basically satisfies accuracy requirement of engineering application. We have also set the limit lower than 5% as 1% and 0.5%. The simulation result is not so sensitive to the error limit. The error limit in Fig 7 is applied to judge the imbalance between heat extraction from rock and the heat gained by circulating water. Because real-time outlet temperature of circulating water is the key performance indicator of DBHE system rather than heat extraction or heat release rate. As heat capacity of water is so large being 4200 J/kg/°C, simulation error of heat extraction or heat release rate within 5% would not lead to significant error of outlet temperature of the circulating water.

So we set the commonly acceptable error limit of 5% for simulation.

Section 4 is general, try to improve it or can be removed.

Reply: Thank you for the valuable comment. Section 4 has been improved to be more concrete with quantitative conclusion from the Figures and Tables above, we did not delete it because necessary discussion is required in the template.

Shorten abstract also.

Reply: Thank you for the valuable comment. The abstract has been properly refined to be concise enough.

Add some qualitative results in the conclusion section.

Reply: Thank you for the valuable comment. The quantitative results has been included in the conclusion.

Nomenclature is missing.

Reply: Thank you for the valuable comment. The nomenclature has been included in the Appendix A.

Please add some qualititive results in abstract section.

Reply: Thank you for the valuable comment. The quantitative results has been included in the abstract.

There is much difference in simulation cost between OGS and your study. Please elaborate it.

Reply: Thank you for the valuable comment. The distinctive comparison of simulation cost reflect high efficiency of our model. OGS software is a commonly applied simulation tool for geothermal community, but it is based on traditional numerical solution based on finite element method. So it would be time consuming for this challenging problem featured with strong heat flux. Because local mesh refinement and demanding time step are required to capture the intense heat transfer in face of high temperature gradient near the borehole of DBHE. Unlike traditional numerical approach which are quite computationally inefficient, we schematically presented analytical formulations of the heat front propagation and heat flux density distribution along depth for the unsteady heat transfer in the rock zone. These analytical formulations are critical to relieve computational effort without resort to local mesh refinement or demanding time step. It is critical to achieve robust and accelerated computation for the problem. To our knowledge, it is the first time to analytically reveal the heat flux density distribution along borehole depth of DBHE under so extreme heat transfer condition.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper entitled “Heat transfer modeling on high temperature charging and dis charging of deep borehole heat exchanger with transient strong heat flux” it’s presented new Heat transfer modeling for deep borehole heat exchanger. The paper is interesting and well written. However, I have the following comments:

1- Citation of all information and equation in section 2 are missing.

2- In section 2, the authors need to present the new of their model compared to the literature and what is the benefits

3- In the result section, section 3. Authors need to add an introduction describing the case studies and procedure for getting the results.

4- In section 4, the authors need to link the discussion to the results (table and figures) with more descriptions

Author Response

Comments and Suggestions for Authors

Citation of all information and equation in section 2 are missing.

Reply: Thank you for the valuable comment. Citations for the information have been updated. All the equations cited from literature are all properly added with the citation. The left equations without citations are carefully deduced by the authors.

In section 2, the authors need to present the new of their model compared to the literature and what is the benefits

Reply: Thank you for the valuable comment. Model setup in the literature is quite cumbersome, which would lead to extraordinarily high computational overhead. It is not good for wider applications. In section 2, we detailed our model, this model is applicable to both charging and discharging process of DBHE with strong heat flux.

The new of our model are listed as following, which are presented in Page 5:

Firstly, unlike traditional numerical approach which are quite computationally inefficient, we schematically presented analytical formulations of the heat front propagation and heat flux density distribution along depth for the unsteady heat transfer in the rock zone. These analytical formulations are critical to relieve computational effort without resort to local mesh refinement or demanding time step. To our knowledge, it is the first time to analytically reveal the heat flux density distribution along borehole depth of DBHE under so extreme heat transfer condition.

Secondly, this model highlights tight coupling between heat transfer inside and outside of the borehole during the transient heat transfer through heat flux at the interface. As for quasi-steady heat transfer inside the borehole, both heat extraction and heat stor-age conditions of DBHE are formulated in detail.

The benefits of our model are summarized in Page.8 as following:

“ Spatiotemporal formulation of heat flux distribution is especially beneficial to achieve efficient simulation with large time step for the extreme heat transfer of high temperature charging and discharging. Since it is analytical solution, there is no stability issue to capture the intense heat transfer despite of the high temperature gradient. Neither time-consuming iterations for the discretized heat conduction equations set nor mesh refinement are required for the simulation. More importantly, this formulation proves applicable to both charging and discharging scenarios of DBHE, which would be validated in the model evaluation.”

In the result section, section 3. Authors need to add an introduction describing the case studies and procedure for getting the results.

Reply: Thank you for the valuable comment. Section 3 carries out case studies from one typical high temperature heat storage case from the literature and an in-situ field test of a pilot demonstration project in China.

(1). Introduction describing the first case from literature has been clearly presented in section 3.1 and Table 1.

(2). Introduction describing the second case from a pilot demonstration project has been clearly presented in section 3.2.1 and 3.2.2, moreover, detailed design and operational parameters of the case are summarized in Table 5-8.

Procedures for getting the results could refer to Fig.7, which demonstrates overall heat transfer simulation procedure of deep BTES system under charging or discharging phases.

In section 4, the authors need to link the discussion to the results (table and figures) with more descriptions

Reply: Thank you for the valuable comment. More descriptions about necessary link between discussion and tables or figures have been updated in section 4.

Author Response File: Author Response.pdf

Reviewer 3 Report

This manuscript discussed a modeling study on heat transfer in a deep borehole with strong heat flux. The study is of great interest to the mining industry. Throughout the whole manuscript, the modeling building and situations considering are very detailed. The authors considered the heat flux during heat storage and heat extraction modes and built in detailed geology facts, moreover, the authors verified the modeling accuracy and efficiency by key performance indicators. The language is proper and accurate, only very minor spell check is needed.

Author Response

Comments and Suggestions for Authors

Reply:

Thank you for the valuable comment. We have carefully revised this paper and performed the minor spell check.