Dear Juan Antonio Añel,

Thank you for your comment regarding the Data and Code Availability Section. In the submitted manuscript, we evaluated the new functionality of GMSH for creating complex geological topologies. This functionality enables involving real geological models and their uncertainties in numerical simulations.

GMSH is a well-established code that undergoes regular updates, with the latest versions available at https://gitlab.onelab.info/gmsh/gmsh and https://gmsh.info/. The code has been maintained for several years and supports various platforms and programming languages. Regarding your helpful comment, the whole source code of GMSH will be added to the Zenodo repository created for this study.

We would like to clarify that our manuscript does not aim to further develop the existing TIGER code. Instead, our objective is to assess the thermohydraulic performance of high-temperature storage systems in realistic geological scenarios, moving beyond simplistic box-shaped reservoirs.

In the Code and data availability section, it is mentioned that:

        “Required data and developed workflow for running the model for one of the showcases (GGB) is fully documented and available in the GitHub (https://github.com/Ali1990dashti/GeoMeshPy/tree/main/Examples/Storage%20Model) and Zenodo (https://zenodo.org/record/7643506#.Y-znA3bMKUl) repositories of the first author.”

The Zenodo repository includes a dataset comprising 11 geological scenarios and all the necessary scripts in the form of a comprehensive Jupyter notebook for recreating the meshes with complex topologies. Once the meshes are created using the provided script, they can be imported into any numerical solver. To facilitate the replication of the presented simulations, we have also addressed the material properties of the models in Table 1.

In a revised manuscript, we will add the DOI of the created repository in Zenodo (10.5281/zenodo.7643506). Furthermore, we will add the existing source codes of GMSH to the Zenodo repository to ensure secure and permanent data storage.

Best regards,

Ali Dashti

On behalf of the co-authors

Dear Reviewer,

Thank you very much for your careful review of the manuscript and helpful comments. Authors appreciate your insights and suggestions, which have helped us to improve the quality of the work. All your comments are addressed below, and a new version of the manuscript with track changes will be uploaded.

This paper reports on a mesh-based numerical simulation approach to assess the effect of structural uncertainty in geothermal models. The method primarily relies on recent features of the GMSH library, and some THM simulation results are shown on various geological scenarios for two geothermal sites. The problem of mesh updating is challenging and the results are interesting, so I think this paper deserves publication in GMD. However, even though I agree that the proposed workflow has a lot of potential to investigate more advanced settings, the modelling hypotheses remain relatively simple, so I see this paper as closer to a proof of concept than to a conclusive study on the considered geothermal reservoirs, so I think that the conclusions of the sensitivity study should probably be moderated. Therefore, and for the reasons listed below, I recommend major revisions.

Thank you very much for your comments regarding our manuscript and for taking the time to review the manuscript.

Main comments

1. In the GGB case study, the independent depth perturbation of layer hanging wall and footwall and the reference isopach geometry seem like relatively strong modelling assumptions. Could it happen that the reservoir thickness is not constant, e.g., that the overall dip of either interface is subject to uncertainty? What if a larger variogram range was used? Could it happen that some faults be present in the reservoir? Is it consequential to assume constant permeability in the Malm patch reef deposits? Could that change the conclusion? Could you envision to use seismic line interpretations to locally reduce horizon uncertainties around these lines, and possibly use larger uncertainties away from the seismic sections? I don’t mean that all of these suggestions should be undertaken for the paper to be published, but I think the wording of the conclusions should be modulated and that the discussion should discuss the uncertainties more thoroughly.

The GGB case was designed in this study to evaluate the effect of thickness variations i.e. structural uncertainty on the performance of thick reservoirs. The reservoir is subjected to arbitrary uncertainty because the model is a generic one rather than a real case. We wanted to avoid falling into the realm of unknown unknowns. Our workflow is not uncertainty-dependent and for real cases, any source of realistic errors can be superposed to the structural models. For example, we can define a function for the error that has an inverse relation with the distance from the boreholes. References like Wellmann and Regenauer-Lieb (2012), Wellmann et al. (2010), Wellmann and Caumon (2018), etc. delved into the uncertainty topic. We rather want to quantify the impact of structural uncertainty using two cases. As you mentioned in the annotated version, ± 8 and 10 m are very optimistic for the GGB case. Therefore, we have changed the range to ± 10 and 15 m for the top and bottom contacts of the reservoir, respectively. It is assumed that available well data in the area of the 3D seismic survey allowed for a well-seismic tie. Countless degrees of freedom can be mentioned for the GGB case (and also DeepStor) but we tried to keep the parametrization similar to what exists in the literature. All your comments about the motivations behind our strategy for uncertainty are right. We should mention that in the submitted manuscript we introduced a tool that can be applied to far more complicated cases. The reservoir in the GGB case can also have fractures but such a setting has been out of our scope because then we could not compare our results to what has been done with Collignon et al., 2020. If we vary too many parameters, then it is not possible to control any specific one. Homogeneous permeability across a reservoir is not realistic but for the sake of modelling, we do not consider heterogeneities and give more consideration to the structural uncertainties of the reservoir geometry, i.e. particularly thickness variations of up to 25% at max.

The thermo-hydraulic influence of faults in thin reservoirs was evaluated for the DeepStor case. There, the reservoir is also slightly tilted which has a minor impact. The wording and structure of the manuscript will be completely modified to present our message more clearly.

2. In the DeepStor case study, it is great to see the addition of one fault into the model, but could it be that more faults exist? I suspect the conclusions would be quite different if the injector happened to be on a horst or a graben, even more so if there is compartmentalization. As in the previous case, there is also the question of the potential impact of sedimentary heterogeneity. This makes the regression part on pages 18-19 restricted to the relatively simple modelling assumptions. This should be acknowledged.

For the DeepStor, in 3D seismic data (not yet allowed to be published) no seismically major fault could be documented within the studied area (1 km × 1km × 250 m). We added one (arbitrary) sub-seismic fault to evaluate the impact on the reservoir’s storage performance with varying distances from the well. The heterogeneity of petrophysical properties in the thin reservoir matters as outlined by the sensitivity analysis of Stricker et al. (2020). We used the data of Stricker et al. (2020), which are based on a review of published petrophysical data from sandstones in the Meletta beds across the Upper Rhine Graben, which may best document their heterogeneities. However, we are aware that the data originate from samples taken in different areas and depths, which definitely matters (particularly the poro-perm properties). We are also aware of the fact that samples from boreholes undergo elastic unloading affecting their poro-perm properties. But we need something to start with. Model calibration can be done if hydraulic test data are available. The proposed regression is tightly linked to the parameterization we used in this study. We wanted to highlight relationships between pressure, temperature and the occurrence of possible (sub-seismic) faults as hydraulic boundary conditions for future hydraulic testing and operational data interpretation. This may be also used for other low-thickness heat storage reservoirs. New explanations will be added to the regression part to make the idea behind that regression more clearly and avoid misunderstandings.

3. Given the small amplitude of perturbation, could a simple mesh displacement be used in the GGB case study instead of a remeshing, as for instance done by (Tertois and Mallet, 2007)?

Thanks for this hint. Publications from Jean-Laurent Mallet and his colleagues are pivotal in the realm of meshing geological models. The mesh displacement (based on control points) can be a very useful option but in cases like GGB making two new surfaces in the Python API of GMSH is more robust. In addition, the mesh size has been refined close to the surface and it is computationally more efficient to first create the surface and then refine the mesh instead of moving the refined mesh based on the control points. In the second approach, we may lose the quality of the mesh or not follow the control point correctly. Another point is that we wanted to present this functionality which can be later used for cases with larger uncertainties. Based on your comment we increased the uncertainty range and the meshing process was fast and efficient.

4. I think it would be very useful to also publish the python scripts for the DeepStor project, as they would show a concrete example about how to use the non-manifold features of GMSH.

A fully explained Jupyter notebook is prepared to elaborate on how the mesh for the DeepStor has been generated. The notebook will be uploaded to the Zenodo and GitHub repositories. The only issue is the exact morphology of the reservoir in DeepStor. Again, authors are not yet allowed to publish the detailed structural model of the DeepStor. A thin layer (10 m like the reservoir in DeepStor) will be meshed in the uploaded example. The dimensions of the model in the published code are the same as the DeepStor model and only z values are replaced. The morphology of the presented synthetic model is even more complicated than the reservoir of the DeepStor and a fault also exists in that model.

5. In its present state, the discussion is mainly a summary of the findings and an extension of the results section (including a regression method to locate the fault based on the sensitivity analysis). I would recommend to move the regression part in the results section, and to improve the discussion section. Overall, structural uncertainty issues have been addressed in other reservoir contexts or with other methods before, so I recommend to integrate some more discussions on the method in the light of previous literature reviewed by (Wellmann and Caumon, 2018), especially : (Holden et al., 2003; Jolley et al., 2007; Seiler et al., 2010; Cherpeau et al., 2012; Irving et al., 2014; Julio et al., 2015; Huang et al., 2015; Patterson et al., 2020; Legentil et al., 2023). The last sentence of the conclusion on chemical processes would also probably better fit in the discussion.

In our manuscript, we have not added anything new to the ideas behind structural uncertainties (informative references are mentioned in your comment). In fact, we included them in two heat storage cases. In the first case (GGB), we wanted to document which level of uncertainty we could accept before investing time and money into the refinement of the subsurface data. This is section 4.1 of the discussion (Exploration campaign design). For the DeepStor case, we wanted to see the effect of errors (ignoring the sub-seismic fault) on the system’s behavior. As the sub-seismic fault has not been observed, we cannot be sure about its locations, and the regression part of the discussion wants to suggest a predictor for it. We cannot also simulate every possible location of the fault and such predictors can help us to avoid running thousands of simulations. Therefore, we presented our discussion around these aspects. However, to document our awareness of aspects that play a role beyond our modeling we modified the manuscript accordingly.

Form

1. I found the current structure of the manuscript a bit difficult to read. I could help to change the structure by considering first the methodology (current sections 2.3 and 2.4), then one section for each application case. This would make the simulation results closer to the geological settings, and probably avoid going back and forth in the manuscript. For instance, Table 1 gives some geological elements such as formation thicknesses, which would be useful in Section 2.1. I think such reorganization would also help to better separate the generic aspects of the method and the specific choices made for the two considered case studies.

Thanks for this hint. We tried to apply your suggestion, but we came back to the original structure. Presenting the information about each case in one section makes that section very long. In section 2 of the manuscript (Uncertainty and Numerical model developments) we first present the structural model and the idea behind the uncertainty of each case. Then the meshing process for both cases is explained and at the end, the details of simulations (like BCs) and material properties are presented. In section 2.1 we will refer to Table 1 for the thicknesses. We will also add more details about meshing for either case which makes the whole section longer.

2. Some parts of the methodology would call for a bit more details. For instance, did you constrain the geometry of the layer at the injector/ producer location in the GGB case? Do you assume a constant fault displacement in the DeepStor case? (Note that if the displacement is variable, I guess this reinforces the conclusions). What are the lateral boundary conditions in both case studies? Importantly, I don’t clearly understand when reading the manuscript how the fault is integrated into gmsh. Providing the python script doing this would be great, but additional details on the management of non-manifold lines and the displacement between the fault and the horizon cutoff lines would be welcome in the text, as this is a challenging problem. Another question is whether this displacement is applied so as to keep the block perforated by the well at the same depth? On the displacement, you may want to have a look at the following references: (Calcagno et al., 2008; Georgsen et al., 2012; Godefroy et al., 2018).

All your questions will be addressed in the new version of the manuscript. But some short answers here: in the structural model, it is assumed that in the points where the wells are touching the upper (-1100 m) and lower (-1200 m) contacts of the reservoir, the depth value is a certain data. We assumed a constant fault displacement for the DeepStor case to make the model as pessimistic as possible due to the purpose of simulations which is evaluating the system’s reaction in case of embedding a sealing fault in it. In all the 16 faulted scenarios the fault displacement exceeds the reservoir thickness. If we make it less and allow some contact between the reservoir on two sides of the fault, the impact of the fault as a confining barrier decreases. Neither temperature nor pressure BCs are set on the side faces, hence they follow the gradient. All the faces of the models are considered as open to flow. The meshing section for the DeepStor case is completely rewritten. Each step of meshing is elaborated and a new figure is added to make the meshing process more understandable. In the DeepStor case contact of the well with the top and bottom of the reservoir is fixed and certain.

3. In the case study presentations, it would be great to summarize the average thickness / poro / perm/ thermal conductivity of the various formations on a stratigraphic column or in a table.

Table 1 contains mentioned information about the basement, reservoir and caprock units for both the GGB and DeepStor. The data for both the cases are coming from the literature and a simple table can be more convenient than a stratigraphic column to present the values.

4. When giving the results timings, please mention the RAM, number of nodes and processors used for HPC computation.

The text will be updated.

5. I don’t understand the “time stepping details” (page 8 and 9). Does this refer to the CFL condition for the numerical time step, to the injection schedule, or both?.

This part is trying to explain the time discretization. The injection schedule is fixed, for example in GGB we have four months of injecting hot fluid in the hot well and producing from the cold well. Then, we have two months of rest (in which there is no injection and production) followed by four months of production in the hot well and cold fluid injection in the cold well. Then, to have reliable results from the FE solver, we started with very short time steps for each cycle and then increased the size gradually. This way, the solver (MOOSE) can converge more efficiently. In the first cycle (four months of injecting hot fluid in the hot well and producing from the cold well) the time step size increases from one hour to 10 days. Then, the time step size decreases to one hour at the start of the rest cycle (two months) and increases gradually to 20 days at the end of this rest period. At the start of the next four-month cycle, the time step size is forced to be one hour and increases to 10 days at the end.

6. Some figures could be improved: please show the well on Fig. 3. Fig. 7 would be easier to read by showing semi-transparent or cutoff horizons and fault. Fig. 7 and 8 could be merged, as they are essentially two ways to visualize the same thing. Caption should focus on describing the figure and do not need to stress how the chosen presentation helps to read the figure.

Fig. 3 and 7 will be updated. Captions will also be modified. Your handwritten comments on the manuscript are suggesting to merge Fig. 8 and 10. However, in Fig. 8 the pressure value across the reservoir unit is plotted while in Fig. 10 the pressure values are coming from one point (top of the open-hole section where injection and production are happening).

7. Please mind that the topology for all the GGB scenarios is always the same. Only the geometry changes.

Thanks for this comment. The terminology will be corrected accordingly.

8. More generally, the text has room for improvement in terms of grammar and style. Some sentences need revision or clarification. Some parts of the text read more like a commercial pitch than a scientific paper. Some redundancies could be reduced, especially in the results and discussion sections (e.g., page 13). I highlighted these problems in the attached annotated document.

The text will be revised thoroughly. We will remove all the redundancies to make the message of the paper concise, clear, and understandable. Thanks for your hints on the annotated file. Your comments will be considered.

Best regards

Ali Dashti (on behalf of the co-authors)

Dear Reviewer,

Thank you for your careful review of the manuscript and helpful comments. Authors appreciate your insights and suggestions, which have helped us to improve the quality of the work.

In the manuscript with the title “Developing meshing workflows for Geologic Uncertainty Assessment in High-Temperature Aquifer Thermal Energy Storage”, the authors present approach to combine geological modelling, uncertainties, mesh, generation, and geothermal simulations within one workflow. The work contains a combination of previous developments around automated meshing approaches in combination with two dedicated applications to aquifer thermal heat storage (ATES).

• We appreciate the careful review of the manuscript and constructive comments. All comments (and also the comments from another reviewer) are implemented with track changes in the modified version of the manuscript. In the following also your comments are discussed and replied.

Even though the work has many important aspects, the overall aim is not entirely clear: a main focus is to test the influence of geological uncertainties on ATES simulations. This was partly evaluated in previous work (if I am not mistaken?) and here mostly extended to the consideration of a fault. The question then also arises if the fault can be detected or not (which is also a question of sensitivity) - and this aspect is then quite similar to the work of Konrad et al., e.g.:

Konrad, F., Savvatis, A., Degen, D., Wellmann, F., Einsiedl, F., & Zosseder, K. (2021). Productivity enhancement of geothermal wells through fault zones: Efficient numerical evaluation of a parameter space for the Upper Jurassic aquifer of the North Alpine Foreland Basin. Geothermics, 95, 102119.

Degen, D., Veroy, K., Freymark, J., Scheck-Wenderoth, M., Poulet, T., & Wellmann, F. (2021). Global sensitivity analysis to optimize basin-scale conductive model calibration–A case study from the Upper Rhine Graben. Geothermics, 95, 102143.

(And maybe also others)

A main difference is that, in this work presented here, the (re-)meshing is actually automated - this is different to the approach of Konrad et al, where different scenarios were tested. However, the analysis itself in the manuscript is also only shown for discrete scenarios (e.g. Fig. 8, 10, 11) - and therefore, the advantage of an automated workflow is somewhat diminished (as it could equally be established with a completely manual or semi-automated approach in a reasonable time).

• As stated by the reviewer (re-)meshing for complex geological models is the main focus of this study. Previous studies on GGB (Collignon et al. (2020)) and DeepStor (Stricker et al. (2020)) mainly focused on the sensitivity analysis in simplified reservoir geometries. For the GGB case we had indeed no limitations to make new scenarios as we can generate unlimited number of scenarios and test them. In the updated notebooks of GGB (https://github.com/Ali1990dashti/GeoMeshPy/tree/main/Examples/Storage_Models/GGB_Case and https://zenodo.org/records/10256834), 101 different geometries are generated and can be meshed. In this study we only presented three of them because the considered range of uncertainty (updated to be ± 10 and ± 15 m for the top and bottom contact of the reservoir, respectively) did not affect the temperature and pressure fields. We argued that this result can be used to design a financially efficient exploration campaign (see text for further details). For DeepStor we have implemented the fault in different parts of the model reservoir according to the varying spacing from the injection well and obtained results for them. A new section is added to the manuscript which provides details implementing the fault in the model. In DeepStor we have some limitations for the location of the fault: we can only locate the fault at places where we have a point grid. In fact, we had to stick to the resolution of our vertices (in x direction) as derived from the geological model. Two notebooks (uploaded in Zenodo: https://zenodo.org/records/10256834 and Github: https://github.com/Ali1990dashti/GeoMeshPy/tree/main/Examples/Storage_Models) explains how the mesh for the DeepStor case was generated.

A more significant contribution could be achieved if the geological parameters of the fault (position, dip, fault permeability) were implemented in a real sensitivity analysis. This would also help to clarify the contribution: in the manuscript, it is partly difficult to follow the logic of the work and to see where exactly the novelties lie. If a clear QoI would be defined and, subsequently, a structured SA would be performed (ideally a global SA, see also ref above, which may be difficult due to computational issues), the contribution of the work would be much clearer.

• The introduced fault is considered not to be detected by 2D-/3D-seismic surveys. We assumed that its strike will be parallel with the major N-S striking faults. Simulations are done in a way to represent the worst case scenarios in which the fault will make a barrier throughout the model. For this purpose, changing the dipping angle does not make a big difference because we want to have offsets higher than the reservoir thickness. This way, the fault surface will make an impermeable boundary for the reservoir layer by juxtaposing it with the impermeable basement. We can superpose more levels of uncertainty to the model but then it cannot possible to track the influence of each one.

Please also note that the meshing software MeshIt (Cacace & Blöcher) also enables an automation of mesh generation to a certain degree (reasonably fixed topology). Please specify the difference/ advantages of the approach taken here:

Cacace, M., & Blöcher, G. (2015). MeshIt—a software for three dimensional volumetric meshing of complex faulted reservoirs. Environmental Earth Sciences, 74, 5191-5209.

• MeshIt is a great tool for making meshes in complex geometries. However, in MeshIt the user still needs to do some manual work compared to the proposed workflow in this study. For example in the case of GGB we developed a workflow in which the user should only push a point cloud into GMSH and the mesh will be generated automatically without any manual adjustment like selecting the border points and so on. The workflow also leverages functionalities of Python for automating the mesh generation in GMSH. For example, it is required in MeshIT to import each surface as a single input file (as .txt,.csv, etc.) but in Python API of GMSH a single numpy array or a nested list can contain all the surfaces of all the realizations that we need and there is no limitation for the number of surfaces and realizations (all the details are also explained in the notebook uploaded in Zenodo(https://zenodo.org/records/10256834) and Github(https://github.com/Ali1990dashti/GeoMeshPy/tree/main/Examples/Storage_Models)). This way, one single for loop enables making several meshes even without looking into the import, surface generation, meshing, refinement, embedment, physical properties assignment and export processes. The recently uploaded notebook for DeepStor also shows how fast and automated the workflow is for embedding fault planes in the mesh with the least amount of manual adjustments.

Another option would be a full forward UQ with hundreds of draws from the prior distributions - even if this is mentioned in the paper at some points (“a myriad of watertight FE meshes”, “workflow exports as much [sic] as required stochastic geological meshes”), it is not actually shown. Examples which really show the results of automatically generated meshes over a wide range of parameters would help to see the general suitability of the method.

• Thanks for this suggestion but it has been beyond the focus of this manuscript. This suggestion can be considered as an outlook for us. Such sentences (“a myriad of watertight FE meshes”, …) are written to introduce the capabilities of the presented workflow. For the GGB case it did not matter if we change the top and bottom surfaces three times one 100 times. Meshing is the bottleneck between geological models and numerical simulations and we tried to solve. For the DeepStor also we moved the fault 15 times (due to the resolution of the geological model).

In any case, a more structured analysis would not only help to highlight the contribution of the work (and the advantage of using an automated meshing methods), but also clarify the structure of the paper and increase the readability.

• Thanks for this comments. The whole structure of the manuscript is revised and rewritten to clarify our message more clearly.

Very important to note is that, in this manuscript, only geometric parameters are considered - and the rock properties remain fixed. Requires explanation or, at least, clarification from the beginning onwards - and also in the discussion and conclusion!

• It is added to the new version.

Please find below some more comments to specific sections in the text. The manuscript also contains several grammatically wrong, incomplete, and partly unclear sentences. Some of these are mentioned below, but these are by far not all of them - a thorough revision wrt grammar and logic is suggested.

• The whole text is revised and corrected.

49-50: Please provide more reasoning or a reference for this claim.

• The text is corrected.

55: A (conceptual) sketch about ATES systems, the structural and petrophysical elements, and their respective uncertainties would be helpful at this point.

• We have added a new figures about how the mesh has been generated for GGB and DeepStor. Petrophysical elements are coming from the literature and we mentioned them in a table. Fig. 1 also shows the reservoir geometry for one of the scenarios from the GGB case.

91: Randomised noise: what exactly does this mean? Are (vertical position) uncertainties added to the nodes, which are then sampled IID (seems so, considering line 95)? Very important in a geological/ geophysical context: spatial correlation! The variations are by no means independent. Please explain in more detail how exactly the surfaces are modified and which rational is behind choosing or not choosing spatial correlations. Note that uncorrelated noise will typically lead to lower effects of the uncertainty!

• The GGB case is generic and we followed the parametrization and geometry proposed by Collignon et al. (2020). In our model we assumed that 3D seismic data is giving a grid of points representing a surface and also two boreholes drilled into the reservoir were seismic well tie can be done. We started from a box with flat planes representing the top and bottom of the reservoir and we are certain about four points which are the contact of two boreholes with the reservoir. We can define a function in which the noise has a direct relation with the distance from the boreholes. This way, we may generate a reservoir with concave or convex surfaces. In our study we wanted to show the level of the irregularity that can be meshed. As Fig. 1 show the mesh for GGB contains a lot of small hills and depressions. If we correlate the noise, there would be a relation between them and making the surface can be easier than what we have generated via the random noise. We have increased the level of uncertainty to be ± 10 and ± 15 m for the top and bottom contact of the reservoir, respectively and results did not change. The text is updated based on this comment.

93: Points are just points - what makes a surface is the connection between them, i.e. the topology.

• Thanks for this hint. It is added to the manuscript.

133: See comments above: why only so few scenarios? If the process is automated: why no distributions and random samples? Choosing scenarios is adding significant bias to the analysis!

• The process is automated but still limitations exist. For example the vertical fault should be positioned at locations that a point grid exist there and we had to deal with the resolution of the available model (~14 m in x direction and ~26 m in y direction). The whole fault embedment is elaborated in the uploaded notebook and a lot details are also added to the updated version of the manuscripts. Regarding the scenarios for DeepStor we were biased to choose the worst case bases. Therefore, we put the fault in as much as possible locations in the eastern side of the well.

158: Adding functionality for more complex topologies is certainly a key aspect of the approach! So, do you mean to say that, in this work, the complexity is extended through the consideration of a fault? Please be more specific on the level of complexity that can be achieved: would it also work for fault networks with multiple intersections, pinching out of layers, finite faults?

• In the previous study (Dashti et al. (2023)) a geological model with very simple surfaces were tested but at the moment the surface fitting method is so robust that can be used for any type of geometries. It can work for fault networks but the relation between the networks should be identified beforehand. An example in Github (https://github.com/Ali1990dashti/GeoMeshPy/tree/main/Examples/No_Fault) can explain how to transfer from generated fault networks in GemPy to correctly discretized meshes in GMSH. Dashti et al. (2023) published a Python library (GeoMeshPy) to link GemPy with GMSH which works for some types of the models. GemPy can generated a wide variety of geological models (with onlap relation, pinch out, etc.) which cannot be handled by GeoMeshPy and GMSH. But in case of adjusting the input into readable and correct format for GMSH, it can be done.

191: Mesh sensitivity: results?

• Results are not presented to keep the manuscript short. Otherwise, two extra figure for mesh sensitivity of each case can be provided.

196: General-purpose PDE environment

• Is added.

199: of TIGER

• Is corrected.

200: Is this functionality (mixed meshes) actually used?

• It is used. In our meshes boreholes are represented by 1D lines and fault planes by 2D surfaces. Then, we can add another dimension in the input file to it. For example a thickness will be added to the fault plane to make it a volume.

204: Repetition

• Is corrected.

Sec. 2.4 in general: as simulations take a prominent part, more information about physics required in the form of employed equations and coupling.

• New explanation about TIGER are added. We could add the governing equations that TIGER uses to solve fluid-flow and heat-transfer but all of the details are already mentioned in publications like Gholami Korzani et al., 2020.

223: Repetition

• Is corrected.

257: Unclear sentence

• Is corrected.

Fig. 4 and 5: no difference visible, figures in this form not helpful. Suggestions: 2-D instead of 3-D (third dimension does not help in Flg 4 but rather distract); show a single example and maybe a difference plot, if there are any differences visible?

• 4 is presenting also a 3D view into three different reservoir geometries. With the 3D figure the reader can have a better view on the different reservoir geometries. As mentioned there is no difference in the heat plume in Fig. 4 hence we presented a line plot to check for any difference between three scenarios and nothing is noticed. We used this observation in our discussion to argue about the decision making for the required levels of accuracy in our data.

Fig. 7: Same consideration

• This figure is updates. As another reviewer commented, we added the cutoff of the fault plane to it. In Fig. 7 the 3D view and also cross section in middle of the model are observable. Dimension of the heat plum in y direction is also completely different for the scenario with a fault in 4 m in the east of the well.

Fig. 8: best figure in the paper (as clearly some aspects are visible and marked). Numerical question: what is the reason for the negative “bump” just before the increase (and at other locations) in     E? Please explain, comment on numerical validity of result.

• The negative “bump” is a negligible mesh effect. We tried to solve it via refining the mesh on the fault plane but it was adding a huge amount of computational cost without so much improve. The fault in the model was considered as a big plane and refinement on it can add a lot of more elements. The pressure values go back normal just meters before and after the fault plane. We refined the mesh on the fault plane and also boreholes up to levels that results stabilized. Regarding the validity of the results, unfortunately we have not any measured data to calibrate the model with. However, the results especially in Fig. 8 make sense. We can see that everything is happening between the borehole and the fault plane. For example in the scenario E, the eastern side of the fault stays in the initial conditions or for B, C and D the western side of the faults is unperturbed.

336: Uncertainties - into what?

• Is corrected, into numerical simulations.

340: Automation mentioned - but not really used (and shown) in the paper - see comments above. “As much”: “as many”. How many? What is the reasoning behind the choice here?

• The text is corrected to avoid misunderstandings.

342: “Any type of data”? Please explain!

• Is corrected and explanations are added.

349: Usually, it is not of interests to broaden the uncertainty. I guess you mean to say: extend the consideration of uncertain parameters/ consider more aspects of uncertainty?

• Thanks for this hint, the text is corrected.

352: Topological uncertainty: really considered? Seems to me that topology (at least of the geology) remains fixed. Please review concepts on topology.

• Thanks for this hint, the text is corrected.

361: Statement would only be true in the range of the assumptions taken here.

• The text is corrected.

368: A bit confusing: you write above that uncertainties about structures do not matter - here they do. The difference is due to the two examples - but here the important point: a more clearly structured SA would help!

• The text is corrected to be clearer. For the GGB case the uncertainty did not matter so much (of course this conclusion is specific to the parametrization we have chosen from the literature) whereas for the DeepStor the real geological model in which the reservoir was inclined and the sub-seismic fault mattered. Stricker et al. (2020) presented a detailed SA for the DeepStor. Collignon et al. (2020) also presented the same for GGB. Here we chose to the base case parametrization and modify the structural model.

385-390: Why this analysis? Also Fig. 11: not clear why results are relevant. Please explain/ expand.

• This part of the discussion want to say that we can use pressure data to get some ideas about the geological model. Fig. 11 shows the correlation between pressure data and the distance of the sealing fault. Such strategy allows us to rebuild or at least revise the structural model after getting some measure data. Of course the assumption is that we are certain (!) about the material properties. Typically the geological models are in the simulations and parameters are tuned in a way to match the measurements but in this manuscript we want to see what happens if we change the geological model. New explanations are added to present the message in a more clear way.

417: “a myriad”: see comments above.

• The text is corrected.

423: Unclear sentence.

• The text is corrected.

Based on the comments we replied here and also comments from the first reviewer, the text and structure of the manuscript is revised thoroughly.

Best regards

Ali Dashti (on behalf of the co-authors)