Optimization of Well Locations and Trajectories: Comparing Sub-Vertical, Sub-Horizontal and Multi-Lateral Well Concepts for Marginal Geothermal Reservoir in The Netherlands

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript of E.G.D. Barros et al., "Optimization of Well Locations and Trajectories: Comparing Sub-Vertical, Sub-Horizontal and Multi-Lateral Well Concepts for Marginal Geothermal Reservoir in the Netherlands" is an article concerning the techno-economic performance of the geothermal doublet. This study can provide a suitable program for the target case study. However, there are additions/revisions that I feel could improve this paper. A more detailed list of my thoughts follows below.

 

1.       There are 7 keywords, 1 or 2 should be removed, and too many of them will result in a lack of focus in the article.

2.       In the Introduction Section, for the well location optimization in unconventional reservoirs, some researchers also consider the problem of induced seismicity. Please supplement it for completeness. Some published papers can be used for reference.

Hui G., Chen Z., Ryan S., et al. Intricate unconventional fracture networks provide fluid diffusion pathways to reactivate pre-existing faults in unconventional reservoirs. Energy. 2023, 282, 128803. https://doi.org/10.1016/j.energy.2023.128803.

3.       The article is not so well structured: the number of cases (“a total of 2600, 3100 and 3200 reservoir simulations”) should be placed in the section “3.3 Reservoir simulation model (and program design)”.

4.       The results of the optimization (Table 2) should have been placed in section “4.1 Optimization experiments” (before fig. 9~11) instead of the section “5.conclusions”.

5.       The optimization method used in the article is gradient stochastic trees, have other machine learning methods been considered?

6.       In optimization studies, we are often concerned with input parameters such as the location of the five-coordinate points of the well (x, y, z) rather than the output parameters of simulation results. It is the input parameters that are the reference to guide the drilling of the well, especially, if the output results are not validated.

7.       In the proposed, the validation of the output parameters NPV could not be shown with injection and production curves, or thermal diagrams in a geological model, but what are the correlation and error judgment criteria between the model input and output parameters? Correlation coefficient R2, root mean square error RMSE? Please explain it for clarity

8.       Some grammar or format errors should be revised.

(1)   Page 4 line 138: “the” should be deleted (“To the calculate the approximate gradient”).

(2)   Page 6 line 220: “2.3.1” should be “2.3.2”.

 

(3)   Page 6 line 220: “value” should be “values”.

Author Response

The authors would like to express our sincere gratitude for the time and effort you dedicated to reviewing our paper. We are pleased to inform you that all your comments have been carefully considered, and we have incorporated the suggested changes into the revised version of the manuscript. Below we provide the point-by-point responses.

Comments 1: There are 7 keywords, 1 or 2 should be removed, and too many of them will result in a lack of focus in the article.
Responses 1: Thank you for your suggestion. The number of keywords has been reduced from seven to four: two keywords have been removed, and two others have been merged into a single one.

Comments 2: In the Introduction Section, for the well location optimization in unconventional reservoirs, some researchers also consider the problem of induced seismicity. Please supplement it for completeness. Some published papers can be used for reference.
Hui G., Chen Z., Ryan S., et al. Intricate unconventional fracture networks provide fluid diffusion pathways to reactivate pre-existing faults in unconventional reservoirs. Energy. 2023, 282, 128803. https://doi.org/10.1016/j.energy.2023.128803.
Responses 2: Thank you for your comment. The abovementioned reference has been added to the Introduction section to emphasize this additional purpose for well placement optimization. The authors took the opportunity to highlight this aspect from one of their recently published papers (ref. [16], which was already cited in the original manuscript).

Comments 3: The article is not so well structured: the number of cases (“a total of 2600, 3100 and 3200 reservoir simulations”) should be placed in the section “3.3 Reservoir simulation model (and program design)”.
Responses 3: Thank you for your suggestion, but the authors disagree with it. Section 3.3 is about the description of the numerical simulated model used to represent the reservoir of the target case study, while the comment on the total number of simulations required to achieve the obtained results is to provide an indication / discussion of the computational cost of the automated optimization workflow. Moreover, the authors would like to clarify that the total number of reservoir simulations mentioned is not part of “program design”; this is not something that the end-user of the optimization workflow would know or define a-priori. The optimization runs as many iterations as needed until reaching one of the stopping / convergence criteria. So the total number of simulations reported in the text is a case-specific result of, not an user-input setting to the optimization procedure.

Comments 4: The results of the optimization (Table 2) should have been placed in section “4.1 Optimization experiments” (before fig. 9~11) instead of the section “5. Conclusions”.
Responses 4: Thank you for your suggestion. The authors agree to this, Table 2 is now placed in section 4.1.

Comments 5: The optimization method used in the article is gradient stochastic trees, have other machine learning methods been considered?
Responses 5: Thank you for your question. The method used in the study is not a machine learning method. It is an approximated gradient method, more specifically, the stochastic gradient approach, applied to model-based optimization (which uses high-fidelity physics-based numerical simulation models throughout the entire procedure, not data-driven / statistical models). The authors found it to be out of scope of this work to apply machine learning methods. The stochastic gradient method was chosen due to its demonstrated efficiency in terms of the required number of model simulations, making it well-suited for the problem at hand. This is explained in the first paragraph of section “2.2. Numerical optimization framework” in the manuscript.

Comments 6: In optimization studies, we are often concerned with input parameters such as the location of the five-coordinate points of the well (x, y, z) rather than the output parameters of simulation results. It is the input parameters that are the reference to guide the drilling of the well, especially, if the output results are not validated.
Responses 6: Thank you for your remark. The authors present the resulting optimal well trajectories and locations (Figures 7 and 8) along with their performance in terms of the maximum objective function (Figures 10 and 11, and Table 2). A list / table with exact coordinates for the well trajectories were not included, as the authors believe this information would not be meaningful to the reader. However, in practical applications, exact coordinates are always provided to drilling engineers. The authors are using optimization to find solutions that improve the techno-economic performance compared to initial guess, and therefore NPV is used as assessment of well locations and trajectories.

Comments 7: In the proposed, the validation of the output parameters NPV could not be shown with injection and production curves, or thermal diagrams in a geological model, but what are the correlation and error judgment criteria between the model input and output parameters? Correlation coefficient R2, root mean square error RMSE? Please explain it for clarity.
Response 7: Thank you for your question. The plots with production temperature and generated heat power have been corrected in Figure 11. In addition, the text clarifying that the gain in NPV for multilateral-wells comes from multilateral solution allowing for more aggressive heat power generation. Reiterating the message of the reply to comment 5 above, statistical machine learning algorithms are not being used in this work. A model-based optimization approach is being used (based on high-fidelity physics-based numerical simulation models, not data-driven / machine learning / statistical models), taking as input our workflow are initial well locations and trajectories. Optimized solutions are found through optimization workflow involving representative subsurface flow simulations. Therefore, outputs are improved well locations and trajectories leading to higher NPV.

Comments 8: Some grammar or format errors should be revised.
a. Page 4 line 138: “the” should be deleted (“To the calculate the approximate gradient”).
b. Page 6 line 220: “2.3.1” should be “2.3.2”.
c. Page 6 line 220: “value” should be “values”.
Responses 8: The text is changed for corrections (a) and (b), but no issues have been found by the authors with the word "value" in the original manuscript.

 

Reviewer 2 Report

Comments and Suggestions for Authors

 

Lines 69–72: Could the author clarify what specific type of computer-assisted optimization has been used? The description here is somewhat vague.

For the Stochastic Simplex Approximate Gradient (StoSAG) optimization technique, while the author provides a citation for this method, it would enhance readability and understanding to include a brief introduction or explanation of the algorithm.

Lines 215–217: In addition to the target and kick-off points, are there any other boundary conditions applied during the optimization process?

 

Regarding the multi-lateral wells, how does the optimization algorithm account for avoiding crossover between different lateral wellbores? A detailed explanation would be appreciated.

 

 

Author Response

The authors would like to express our sincere gratitude for the time and effort you dedicated to reviewing our paper. We are pleased to inform you that all your comments have been carefully considered, and we have incorporated the suggested changes into the revised version of the manuscript. Below we provide the point-by-point responses.

Comments 1: Lines 69–72: Could the author clarify what specific type of computer-assisted optimization has been used? The description here is somewhat vague.
Responses 1: Thank you for your question. The authors have specified in the Introduction section which computer-assisted optimization method is used (i.e., stochastic gradient method). And that method is further detailed in the Methodology section (more specifically in sections 2.2 and 2.3).

Comments 2: For the Stochastic Simplex Approximate Gradient (StoSAG) optimization technique, while the author provides a citation for this method, it would enhance readability and understanding to include a brief introduction or explanation of the algorithm.
Responses 2: Thank you for your suggestion. The authors believe the current description, provided in two paragraphs, is sufficient given the applied nature of this paper. Since this is not a mathematical paper and the authors do not proposed a new algorithm, a detailed explanation of the StoSAG algorithm is beyond its scope. However, the StoSAG method is already presented with all its mathematical details in publications referred to in the text (i.e., Chen et al., 2009 [27], Fonseca et al., 2017 [19]). The authors are currently preparing another paper that will provide a full algorithmic description of the method and its application in their optimization tool (EVEREST™), but it is not ready for citation.

Comments 3: Lines 215–217: In addition to the target and kick-off points, are there any other boundary conditions applied during the optimization process?
Responses 3: Thank you for your question. The geometric constraints considered in the optimization process are:
- Fixed surface drilling location
- The maximum allowed dog-leg severity (i.e. measure of curvature) = 4°/100 ft
Although there is no constraint on the maximum well length, longer wells are penalized by higher drilling costs, as visible in economic formulation in section “3.4. Economic model”. The text has been updated to include exact dogleg value in section “3.1. Surface drilling location”. And the surface drilling location is now marked in Figure 8.

Comments 4: Regarding the multi-lateral wells, how does the optimization algorithm account for avoiding crossover between different lateral wellbores? A detailed explanation would be appreciated.
Responses 4: Thank you for your suggestion. There is no explicitly defined constraint to avoid cross-overs in the current approach. However, cross-overs are not expected to occur because the cost for well length included in the objective function ensures implicitly that the legs are optimized to increase contact with the reservoir, which is not the case if they cross. The authors have added an explanation to the manuscript in section 2.3.2 to clarify this.

 

Reviewer 3 Report

Comments and Suggestions for Authors

1: The abstract of this study is rather vague in describing the experimental results. The lack of quantitative data makes it difficult to describe in detail the model constructed by the authors for optimizing the well locations and trajectories of various wells. In addition, the authors did not provide detailed keywords for the geological conditions of various wells in the geothermal reservoir, which requires the authors to summarize and add.

2: Figure 1 lacks the most basic direction indicator or compass orientation icon required for map drawing. What could be the reason why the red dot area marked on the map does not completely correspond to the good indication area? In addition, the introduction section does not make a detailed and complete analysis of the current status of various well locations and trajectories for geothermal reservoir exploitation. The author needs to explore it more deeply.

3: Another sentence was added to express the "The drilling or fracturing process affects the reservoir well location"in the introduction section, It needs to be supported by some previous papers: ----The Carrying Behavior of Water-Based Fracturing Fluid in Shale Reservoir Fractures and Molecular Dynamics of Sand-Carrying Mechanism. -----A Numerical Investigation on Kick Control with Displacement Kill Method during Well Test in Deep-water Gas Reservoir: Case Study.

4: In Figure 3, the same yellow circles are used to represent Pp and Ph. This makes it impossible to accurately distinguish the two parameters in the diagram. The author needs to make appropriate changes to the way Pp and Ph are represented in Figure 3. At the same time, what kind of parameters do the stepped distributions of different colors in Figure 6 represent? This cannot be accurately distinguished in the legend?

5: In which part of Figure 1 are the wells shown in Figures 7 and 8 located? At the same time, the best well locations shown in the above two figures belong to which of the nearly vertical wells, nearly horizontal wells, and multi-branch wells mentioned in the abstract? In addition, the detailed geological and wellbore information about the initial and optimal solution well locations is not shown in the original article or figure 7 and 8.

6: There are large differences in the parameters of the reservoir wells in the initial stage between Figure 10a and Figure 10c, but the optimized well parameters show completely different effects. What factors may be the cause? In addition, the reason why the initial parameters and optimized parameters of Exp3 in Figure 10b are so different requires detailed analysis by the author.

Author Response

The authors would like to express our sincere gratitude for the time and effort you dedicated to reviewing our paper. We are pleased to inform you that all your comments have been carefully considered, and we have incorporated the suggested changes into the revised version of the manuscript. Below we provide the point-by-point responses.

Comments 1: The abstract of this study is rather vague in describing the experimental results. The lack of quantitative data makes it difficult to describe in detail the model constructed by the authors for optimizing the well locations and trajectories of various wells. In addition, the authors did not provide detailed keywords for the geological conditions of various wells in the geothermal reservoir, which requires the authors to summarize and add.
Responses 1: Thank you for your suggestion. The abstract does contain a summary of the main conclusions and findings derived from the experimental results. The authors did not include quantitative data in the abstract because an appropriate explanation of those would not be possible within the 200-word limit from the guideline to authors of the Energies journal. Regarding the details of geological settings, there is already a section fully dedicated to describe it (section “3.2. Geological characterization”). However, the authors have added more information to this section. There is also a reference [31] for more information on the creation of static geological model. Moreover, the authors would like to point out that the optimization methodology is independent of the geological setting, and therefore prefer not to limit the message of manuscript to show benefits of the methodology to specific geological conditions.

Comments 2: Figure 1 lacks the most basic direction indicator or compass orientation icon required for map drawing. What could be the reason why the red dot area marked on the map does not completely correspond to the good indication area? In addition, the introduction section does not make a detailed and complete analysis of the current status of various well locations and trajectories for geothermal reservoir exploitation. The author needs to explore it more deeply.
Responses 2: Thank you for your comments. An arrow indicating the north direction has been added. The authors would like to clarify that Figure 1 is not a result of the presented optimization study – it has been extracted from the publicly available ThermoGIS portal (https://thermogis.nl) related to mapping the Netherland's geothermal potential. We used it to highlight the importance and the challenges of geothermal energy production as a resource for urban heat demand in the Netherlands. The fact that not all the red dot areas (i.e. large urban areas) coincide with the good geothermal potential areas is exactly the point that the authors would like to make to motivate the importance of this work. The Netherlands need solutions to make geothermal energy production viable in poor quality (also called “marginal”) reservoirs, because sometimes those are the only alternative available in the vicinity of high heat demand areas. The paper studies not the full Netherlands geothermal fields, but only a single geothermal site. Therefore the authors find to suggestion of providing a deeper analysis of the whole Netherlands to be out of the scope of this manuscript. The selected (candidate) geothermal site lies within an area where high heat demand is expected (city with 100,000+ inhabitants) but with limited geothermal potential present – either by poor properties of the subsurface formation derived from existing measurements or by lack of more exploration and characterization data in the area. For more detailed information, we refer to https://thermogis.nl. The caption of Figure 1 has been enhanced to give more information about the different elements of the map.

Comments 3: Another sentence was added to express the "The drilling or fracturing process affects the reservoir well location" in the introduction section, It needs to be supported by some previous papers: ----The Carrying Behavior of Water-Based Fracturing Fluid in Shale Reservoir Fractures and Molecular Dynamics of Sand-Carrying Mechanism. -----A Numerical Investigation on Kick Control with Displacement Kill Method during Well Test in Deep-water Gas Reservoir: Case Study.
Responses 3: Thank you for your remark. The authors could not find the quoted sentence in the Introduction section. Still, the authors clarify that the presented study is about decision on planning of drilling location and well concept selection, not the detailed modelling of the drilling / completion process. The outcome of a study such as the one presented in this manuscript is to provide target locations and well shapes to the drillers.

Comments 4: In Figure 3, the same yellow circles are used to represent Pp and Ph. This makes it impossible to accurately distinguish the two parameters in the diagram. The author needs to make appropriate changes to the way Pp and Ph are represented in Figure 3. At the same time, what kind of parameters do the stepped distributions of different colors in Figure 6 represent? This cannot be accurately distinguished in the legend?
Responses 4: Thank you for your comment. The authors do not fully understand the remark of the reviewer. In Figure 3, there is a clear distinction between the 5 yellow filled circles and the many white filled circles. This is to highlight that only 5 guide points are directly controlled by the optimizer, while all the many other points are derived through smart interpolation of those 5 target points. This is explained in the text in section ”2.3.1 Standard wells”, however authors added explicit references in the text to the points in the figure. The authors do not follow why the reviewer cannot distinguish Pp from “Ph” (i.e. Pk in fact), they are clearly distinct points (i.e. not overlapping) in the schematic drawing. Based on the limited understanding of what was meant with the remarks, the authors have made an attempt in improving the text and figure caption describing Figure 3 to clarify the differences between the various points. Regarding Figure 6, the caption clearly indicates that the maps are showing the porosity distribution. The authors have added the word “porosity” next to the colorbar to make it even more explicit.

Comments 5: In which part of Figure 1 are the wells shown in Figures 7 and 8 located? At the same time, the best well locations shown in the above two figures belong to which of the nearly vertical wells, nearly horizontal wells, and multi-branch wells mentioned in the abstract? In addition, the detailed geological and wellbore information about the initial and optimal solution well locations is not shown in the original article or Figures 7 and 8.
Responses 5: Thank you for your comments.
First question: The specific locations considered in this study are not on the national-scale map depicted in Figure 1, which serves mainly the purpose to illustrate the overall context and relevance of the work. The optimized well locations within the area of the interest of the optimization study (much smaller than national scale) are not shown on the Figure 1 also because at this stage they remain as planned / candidate drilling locations and the site owners request to keep them anonymized until the project is confirmed and in development. A red rectangle was added in Figure 1 to highlight approximately the area of interest.
Second question: It is included in section 4.1 which optimization experiment corresponds to each well concept (exp 1: nearly vertical, exp 2: nearly horizontal, exp 3: multi-laterals), and the colors of the well trajectories for these experiments are also indicated in Figures 7 and 8 (see top left corner). The authors clarified this by updating text in section 2.1 and by explaining the colors in the captions of Figures 7, 8 and 9.
Third question: The initial and optimal wellbore locations are displayed in Figures 7 and 8, however a list / table with exact coordinates for the planned well trajectories was not included, as the authors believe this information would not be meaningful to the reader.. Finally, the detailed geological information is not depicted because 50 realizations of the detailed geological model are considered. It would be impractical to display geological details along with well trajectories in 3D for all the 50 realizations. The authors added more geological information in section “3.2. Geological characterization” and there is also a reference [31] to work on generating static geological model. On Figures 7 and 8 the wellbore geometries (initial vs. optimized) are displayed on top of a grey picture of the 3D model so that the reader can focus on inspect the results in terms of geometry (wellbore vs. model grid) instead of the geological property details. Figure 6 gives a flavor of the geological details present in the model, along with the degree of variability across realizations.

Comments 6: There are large differences in the parameters of the reservoir wells in the initial stage between Figure 10a and Figure 10c, but the optimized well parameters show completely different effects. What factors may be the cause? In addition, the reason why the initial parameters and optimized parameters of Exp3 in Figure 10b are so different requires detailed analysis by the author.
Responses 6: Figures 10a (top left panel) and 10c (bottom left panel) do not depict any well parameters, but the CDF plots of techno-economic indicators (NPV and LCOE) associated with the initial and optimized solutions for each well concept (exp 1: sub-vertical, exp 2: sub-horizontal, exp 3: multi-laterals). The authors believe that the comment of the reviewer is trying to highlight and request an explanation for the fact that the CDF plots of the 3 initial solutions are much more different from each other than the CDF plots of the 3 optimized solutions. The initial placements of the three different well shapes were kept similar, as seen in Figure 8. Therefore the difference in initial performance of each concept is due mostly to the shape of the wells. The significantly lower NPV for initial multilateral case compared to the other two scenarios is due to higher drilling costs for similar achievable well rates and production temperatures. This is explained in section “4.1. Optimization experiments”.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I have carefully checked the modified manuscript and the response to the reviewers. I think the author has properly addressed all the comments, which in turn greatly improves the quality of the paper. Therefore, I would like to recommend this manuscript for publication.

Reviewer 3 Report

Comments and Suggestions for Authors

accepted