Modelling Interactions between Three Aquifer Thermal Energy Storage (ATES) Systems in Brussels (Belgium)

Round 1

Reviewer 1 Report

This paper used coupled flow and heat transport simulation to evaluate the effect of a third building injection/production into a deeper reservoir on the performance of existing two building injection/production in a shallower reservoir. The contents look good to me. I just have a few minor comments/suggestions to the authors.

1.     In section 2.3.2, why the vertical component of the flow can be neglected? Did the authors only simulate horizontal flow within each layer?

2.     In this work, the authors neglected the geothermal heat flux in the height direction but set a fixed temperature boundary condition along the lateral boundaries, why choosing this setup? Why not consider the geothermal heat flux in the height direction as well? The lateral boundary condition may not have an effect since the modeled area is very big, but the vertical heat flux will affect the results.

3.     What is the model grid size? It seems the development region is just a very small section in the numerical model. So, will the model has enough resolution near building 1, 2, 3? It is suggested that the authors add a model grid setup in the zoom-in view of building 1, 2, 3.

Author Response

Thank you very much for your review. Here below you will find our answers to your useful comments:

1) the vertical component of the groundwater flow is not neglected but the 3D architecture of the model is described with 'layers' where systematically (and on the basis of the general experience in Belgium about those different geological layers) a ratio of 10 is chosen between the horizontal and the vertical hydraulic conductivity values. This is explicitly mentioned in section 3.1. A sentence has been added in section 2.3.2.

2) Correct, we neglected the mean deep geothermal energy flux as this last has a negligeable influence on this type of shallow geothermal systems (see the refs 3 and 34). This influence of the vertical heat flux from deep can be seen as negligeable with respect to the local lateral and vertical heat flux transported by conduction and advection.  This fact has been observed in different similar circumstances (refs 26, 27, 28, 30). The fact that the BC's are far from the simulated systems is an advantage in terms of relaibility of the model and does not change this assumption.

3) Yes, the modelled zone is relatively large as we wanted to avoid too much biasing influence from the prescribed BC's. It is difficult to insert a new figure of the local grid but we added useful information about the finite element sizes in the local area of interest. Details have been introduced in the paper. For your information, finite element sizes are from a few cm (near the wells) to a few meters in the area of interest. In fact, in the area of interest there are 21,726 finite elements/layer (434,520 in total) while there are 62,421 finite elements/layer (1,248,420 in total) in the whole model!

Thank you

Reviewer 2 Report

I suggest to accept the mauscript in presented form.

Author Response

Thank you very much for your positive review.

Reviewer 3 Report

I've listed some comments to improve the quality of your research:

1-I suggest adding a graphical abstract that can improve the quality of your research and represent the core idea with key findings.  you can find examples of graphical abstracts here:

https://www.elsevier.com/authors/tools-and-resources/visual-abstract

2-The key findings, including the main quantitative results, should be reflected in the abstract as well.

3-Please rescale the y-axis in Fig 11. It can start from 6 dergreeC.

4-It's better to change the color of the cold well (scenario 1) in Fig 11 and Fig 12.

5-The following two references can be referred to within the introduction as an example of reinjection technologies and modelling approaches.

https://doi.org/10.1016/j.applthermaleng.2023.120018

6-All the assumptions for density, conductivity, and other constants should be listed in the table with a clear reference.

7-The time step must be clearly mentioned and discussed.

8-Does your model include the static head along the injection well? If not, please clarify and discuss the supporting idea.

9-There are some typos in the manuscript. Just on page 2, I've found some as below:

"hydraulic gradint" 

"charcteristics" 

"cost constrains"

10-All the parameters should be clearly defined right after the equations or in the nomenclature list.

Please check the units for equation 2. I couldn't balance the left and right sides of the equation.

According to your definition, the unit of the term on the left (??? [kg/m3*(1/s)] is not the same as the term on the right ??? ?ℎ/?t [kg/m3 (m/s].

Author Response

Thank you very much for your useful and detailed review. Here below you will find the answers to your comments/suggestions:

1) a graphical abstract could be a nice idea as this is done usually in Elsevier journals. Unfortunately, I fear that it is not foreseen in this journal.

2) We have added a sentence in the abstract mentionning quantitative results especially for the added ATES (the third one in the deeper aquifer).

3) It is done. Thank you

4) It is done. Thank you

5) Thank you for having mentionned these references. They have been added in section 2.1.

6) There is no specific assumptions taken in terms of density and viscosity. They are not considered as constant. On the contrary, it is actually a huge avantage of using the Feflow software that considers fully the variation of groundwater density and viscosity with temperature. The hydraulic conductivity variation with the temperature can be neglected for so small changes in temperature. This has been explicitly added/mentioned in section 2.3.1 and 2.3.2 respectively.

7) Thank you, this is very important. We have added two sentences about it in section 3.2: 'The time steps of the heat transport simulations can vary from about 1 second until 15 days. In fact, very short time steps are automatically adopted by the software Feflow© when required for numerical stability and convergence needs'. 

8) We are not sure to understand exactly what the reviewer expressed in this comment. The model calculates the piezometric head in each well whether it is used for pumping and/or reinjection.  Indeed, very locally, a lowering or raising of the head is calculated influencing the local groundwater flow conditions.

9) Thank you. They are now corrected and we have reviewed also the whole paper in order to avoid others (as far as possible).

10) OK we have now checked (and added when needed) for having all parameters and variables rigorously defined. We checked equation 2 that is actually correct with terms expressed in  [kg/m3*(1/s)] units because Ss is in 1/m

We are deeply greatful to the reviewer for his useful remarks, comments and suggestions. He  has allowed us to improve the paper. Thank you.