Waterflooding Interwell Connectivity Characterization and Productivity Forecast with Physical Knowledge Fusion and Model Structure Transfer
, Jian Wang 2,*, Jianfa Han 4, Shiti Cui 4, Liming Zhang 1, Hanjun Zhao 5, Piyang Liu 3 and Honglin Song 6
Round 1
Reviewer 1 Report
This manuscript introduces a physical knowledge fusion neural network (PKFNN) to characterize waterflooding reservoir inter-well connectivity and forecast the productivity. PKFNN is developed on the material balance equation of the waterflooding process, and employs transfer learning algorithm to inherent the knowledge from the trained models. The authors have proved the effectiveness of PKFNN on several reservoir experiments. Generally, this manuscript provides an interesting way to combine the physical equations with data-driven models. It is recommended to improve some minor issues.
1) On page 1 line 40, “which aims to inverse the uncertain geological properties, (i.e., the permeability field)”, the comma after “properties” should be deleted.
2) “To make the inter-well connectivity analysis easy complement” on page 2, is there a misuse of the word “complement”, if not, please explain this sentence.
3) On page 2 line 81, “machine learning based” should be “machine-learning based”, and in page 5 line 201. “block based” should be “block-based”.
4) There is a grammar mistake of this sentence on page 6, “In other words, the value of this physical function can be recognized as a gate, which would be open for important variables and be close for variables contributing weakly to the learning task.”
5) There should be an indefinite article before the word “tight”, of the sentence on page 9 line 354, “This physical knowledge can be transferred as there is tight interlinkage between …”.
6) “The inter-well connectivity characterization results given by PKFNN is demonstrated in Figure 28” on page 26 line 718, should use a plural verb.
Author Response
Response to Reviewer 1’s comments
General Comments: This manuscript introduces a physical knowledge fusion neural network (PKFNN) to characterize waterflooding reservoir interwell connectivity and forecast productivity. PKFNN is developed on the material balance equation of the waterflooding process, and employs a transfer learning algorithm to inherit the knowledge from the trained models. The authors have proved the effectiveness of PKFNN on several reservoir experiments. Generally, this manuscript has sufficient research literature, detailed experimental data, and strong innovation, providing an interesting way to combine the physical equations with data-driven models, which is a referable work for researchers in petroleum engineering. Thus, it is recommended to improve some minor issues, and receive the manuscript directly after improvement.
Response: Many thanks for your insightful comments; we have revised our manuscript based on your suggestions.
Comment 1.1: On page 1 line 40, “which aims to inverse the uncertain geological properties, (i.e., the permeability field)”, the comma after “properties” should be deleted.
Response 1.1: Thank you so much for your suggestion and sorry for the mistake. We have changed this sentence. “which aims to inverse the uncertain geological properties, (i.e., the permeability field)” has been changed to “which aims to inverse the uncertain geological properties (i.e., the permeability field)”, please find the sentence on page 1 line 40.
Comment 1.2: “To make the inter-well connectivity analysis easy complement” on page 2, is there a misuse of the word “complement”, if not, please explain this sentence.
Response 1.2: Thanks a lot for your valuable comment and sorry for the mistake. There is an error in this sentence. “easy complement” has been changed to “easy to implement”, please find the sentence on page 2 line 53.
Comment 1.3: On page 2 line 81, “machine learning based” should be “machine-learning based”, and in page 5 line 201. “block based” should be “block-based”.
Response 1.3: Thank you for your suggestion. “block based” has been changed to “block-based”, please find the sentence on page 2 line 81.
Comment 1.4: There is a grammar mistake of this sentence on page 6, “In other words, the value of this physical function can be recognized as a gate, which would be open for important variables and be close for variables contributing weakly to the learning task.”
Response 1.4: Thank you for your suggestion and sorry for this mistake. We have revised this sentence. “In other words, the value of this physical function can be recognized as a gate, which would be open for important variables and be close for variables contributing weakly to the learning task.” has been changed to “In other words, the value of this physical function can be recognized as a gate, which would be opened for important variables, and closed for variables contributing weakly to the learning task.” Please find the sentence on page 6 line 258.
Comment 1.5: There should be an indefinite article before the word “tight”, of the sentence on page 9 line 354, “This physical knowledge can be transferred as there is tight interlinkage between …”.
Response 1.5: Thank you for your comment. We have added an indefinite article before the word “tight”, please find the sentence on page 9 line 354.
Comment 1.6: “The interwell connectivity characterization results given by PKFNN is demonstrated in Figure 28” on page 26 line 718, should use a plural verb.
Response 1.6: Thank you for your suggestion and sorry for this error. “The interwell connectivity characterization results given by PKFNN is demonstrated in Figure 28” has been changed to “The interwell connectivity characterization results given by PKFNN are demonstrated in Figure 28”, please find the sentence on page 36 line 718.
Reviewer 2 Report
Very good piece of work. Combining the ANN and mass balance equations to find relations between injection wells and production wells seems a novel idea. More importantly, the results are very promising. Perhaps the authors want to use other ML or AI models in their future works. Based on these, I recommend its publication in youir journal.
Author Response
Many thanks for your insightful comments, positive judgment of our work and great effort in the revision. We have revised our manuscript and hope our work could provide some ideas to new readers.
Reviewer 3 Report
Overall comments: The authors propose a physical knowledge fusion neural network (PKFNN) by combining the merits of both physical and machine learning approaches. The results demonstrate that the proposed method is effective to forecast productivity and characterize the interwell connectivity. In brief, the current topic is creative and essential, and the methodology and the results have been fully discussed and analyzed. Therefore, this manuscript could be accepted after the following minor revisions considered.
Specific comments:
-1- Abstract: “Firstly, based on the physical control law, the ordinary differential equation (ODE) of the material balance equation), we endow the model with highly transparent modular architectures in the framework of feedforward neural network” (on page 1 line 27), should only use acronyms, ODE, and remove the redundant right parenthesis.
-2- Keywords: The “reservoir characterization” is too general, and it would be replaced by “interwell connectivity characterization”.
-3- Preliminary knowledge: The first line below the equation (1), (2) and (4) (line186, 190 and 194), should not have an indentation.
-4- Methodology: “Assume that the input data are WIRs of m injector” (on page 5 line 239), should use “M”.
-5- Discussion and Conclusions: More explanation and discussion about two blocks of PKFNN are suggested in the conclusion, which helps readers understand the work easily.
Author Response
Response to Reviewer 3’s comments
General Comments: Waterflooding Interwell Connectivity Characterization and Productivity Forecast with Physical Knowledge Fusion and Model Structure Transfer
Overall comments: The authors propose a physical knowledge fusion neural network (PKFNN) by combining the merits of both physical and machine learning approaches. The results demonstrate that the proposed method is effective to forecast productivity and characterize the interwell connectivity. In brief, the current topic is creative and essential, and the methodology and the results have been fully discussed and analyzed. Therefore, this manuscript could be accepted after the following minor revisions considered.
Response: Many thanks for your valuable comments; we have revised our manuscript based on your suggestions.
Comment 1.1: Abstract: “Firstly, based on the physical control law, the ordinary differential equation (ODE) of the material balance equation), we endow the model with highly transparent modular architectures in the framework of feedforward neural network” (on page 1 line 27), should only use acronyms, ODE, and remove the redundant right parenthesis.
Response 1.1: Thank you so much for your suggestion and sorry for the mistake. We have changed this sentence. “Firstly, based on the physical control law, the ordinary differential equation (ODE) of the material balance equation), we endow the model with highly transparent modular architectures in the framework of feedforward neural network” has been changed to “Firstly, based on the physical control law, the ODE of the material balance equation, we endow the model with highly transparent modular architectures in the framework of feedforward neural network”, please find the sentence on page 1 lines 26-27.
Comment 1.2: Keywords: The “reservoir characterization” is too general, and it would be replaced by “interwell connectivity characterization”.
Response 1.2: Thanks for your valuable suggestion. “reservoir characterization” has been changed to “interwell connectivity characterization”, please find them on page 1 line 34.
Comment 1.3: Preliminary knowledge: The first line below the equation (1), (2) and (4) (line186, 190 and 194), should not have an indentation.
Response 1.3: Thank you for your comments and sorry for this mistake. We have removed the indentation, please find the revision on page 4 line 186, 190 and page 5 line 194.
Comment 1.4: Methodology: “Assume that the input data are WIRs of m injector” (on page 5 line 239), should use “M”.
Response 1.4: Thank you for your suggestion and sorry for this mistake. We have revised this sentence, please find the sentence on page 5 line 239.
Comment 1.5: Discussion and Conclusions: More explanation and discussion about two blocks of PKFNN are suggested in the conclusion, which helps readers understand the work easily.
Response 1.5: Thank you for your comments. We have added more discussions about these two blocks of PKFNN: “In detail, the knowledge-distillation block employs a physical evaluation function to extract the knowledge (the nonlinear relationships between injectors and producers). With given water injection rates data, this block could calculate the total inflow rate from all injectors to each targeted producer. Assisted with the ANNs, the mapping-transfer block is designed to simulate the fluid change rate among the control volume, using the BHP and liquid production rates data. Under the guidance of material balance equation, PKFNN can generate the modeled production rate and water cut by the outputs of two blocks.” Please find these sentences on page 27 lines 744-751.
