An Analytical Framework for Stress Shadow Analysis During Hydraulic Fracturing – Applied to the Bakken Formation, Saskatchewan, Canada
 ^{1}Geological Engineering, Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, Vancouver, BC, Canada
 ^{2}Geological Engineering, Department of Civil, Geological, and Environmental Engineering, University of Saskatchewan, Saskatoon, SK, Canada
 ^{1}Geological Engineering, Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, Vancouver, BC, Canada
 ^{2}Geological Engineering, Department of Civil, Geological, and Environmental Engineering, University of Saskatchewan, Saskatoon, SK, Canada
Abstract. This paper presents selected results of a broader research project pertaining to the hydraulic fracturing of oil reservoirs hosted in the siltstones and fine grained sandstones of the Bakken Formation in southeast Saskatchewan, Canada. The Bakken Formation contains significant volumes of hydrocarbon, but largescale hydraulic fracturing is required to achieve economic production rates. The performance of hydraulic fractures is strongly dependent on fracture attributes such as length and width, which in turn are dependent on insitu stresses.
This paper reviews methods for estimating changes to the insitu stress field (stress shadow) resulting from mechanical effects (fracture opening), poroelastic effects, and thermoelastic effects associated with fluid injection for hydraulic fracturing. The application of this method is illustrated for a multistage hydraulic fracturing operation, to predict principal horizontal stress magnitudes and orientations at each stage. A methodology is also presented for using stress shadow models to assess the potential for inducing shear failure on natural fractures.
The results obtained in this work suggest that thermo and poroelastic stresses are negligible for hydraulic fracturing in the Bakken Formation of southeast Saskatchewan, hence a mechanical stress shadow formulation is used for analyzing multistage hydraulic fracture treatments. This formulation (and a simplified version of the formulation) predicts an increase in instantaneous shutin pressure (ISIP) that is consistent with field observations (i.e., ISIP increasing from roughly 21.6 MPa to values slightly greater than 26 MPa) for a 30stage fracture treatment. The size of predicted zones of shear failure on natural fractures are comparable with the event clouds observed in microseismic monitoring when assumed values of 115°/65° are used for natural fracture strike/dip; however, more data on natural fracture attributes and more microseismic monitoring data for the area are required before rigorous assessment of the model is possible.

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Mostafa Gorjian et al.
Interactive discussion
Status: closed

RC1: 'Comment on se20211', Anonymous Referee #1, 24 Feb 2021
The Authors are encouraged to consider the following comments.
 Introduction line 55: What is the specific objective of the study? The author mentioned “a better understanding of the combined effects of mechanical, thermos and poroelastic stress shadows during the process of hydraulic fracturing.” But from the literature review, it is not clear what is the problem or gap in this area that this work is attempting to address. The paper’s objective is not the same with the discussion and conclusion. The abstract needs to reflect clearly the objective(s) of the study.
 The equations presented to the end of page 17 are all from the literature and well known. There is no need to present them all in the main body of the manuscript, as it distracts the reader to focus on the main objective of this work. If necessary they should be moved to the Appendix.
 It is not clear at all, what a is the new development in this work. Is it the algorithm which combines the use of the analytical methods and numerical simulations using Gohfer?
 What is the shortcoming or limitation of the cumulative stress shadow calculation method? For example. 1. The author assumed the i+1 stage stress shadow has no impact on the I stage stress shadow. 2. The author assumed the average value of fracture length and width.
 1 Workflow: Clear discussions need to be given regarding the GOHFER software and how it accommodates stress shadow distribution (magnitudes and direction). Simple example to clarify how it works and validation of results should be given before presenting a complex 30 stage fracturing example.
 2 Mechanical stress shadow equation 14: There is no explanation of parameters such as E, E’, , R, r, etc. It is not clear if it is proposed to modify the existing equation or solely reproducing the equations.
 3 Thermoelastic Stress Shadow: Phie (effective porosity) is better to be shown as Φ.
 Line 310: In the case study part. The author mentioned the results of sensitivity analysis from other research, but there is no citation. These results are not generally known.
 Line 330: Which figures in the Appendix are results of ‘’0 MPa for the thermoelastic and 0 for 330 the poroelastic” are not mentioned.
 Line 350: It will be useful to show the direction of the stresses in Figure 12 using arrows in Figure 1. That will help to understand why the stage 3 fracture orients 11 degree.
 Line 400: figure 18 (a) is not induced shear stress, it is minimum horizontal stress.
 It is important to show the results of GOHFER simulation, I didn’t see how GOHFER was used and what are the outcomes. No explanations are given on how GOHFER adopts and utilizes the stress distribution to predict the fracture geometry and orientation.
 There is no explanation on how to obtain the total stress shadow from each stage.
 Figure 21. The orientation of each fracture is not clear. It looks like each fracture is parallel to the other and no stress shadow effect.
 There is a discussion on microseismic events on the early page but no further explanation in the main paper except onepage appendix. How the results of multistage fracturing simulations presented and the stress shadow effect was validated against microseismic data?

AC1: 'Reply on RC1', Mostafa Gorjian, 04 Apr 2021
We would like to thank the reviewers for their thoughtful comments and efforts towards improving our manuscript. Below is our response to the issues raised in the review:
 Introduction line 55: What is the specific objective of the study? The author mentioned “a better understanding of the combined effects of mechanical, thermo and poroelastic stress shadows during the process of hydraulic fracturing.” But from the literature review, it is not clear what is the problem or gap in this area that this work is attempting to address. The paper’s objective is not the same with the discussion and conclusion. The abstract needs to reflect clearly the objective(s) of the study.
Answer: The authors addressed two gaps related to Canadian Bakken Formation and stress shadow analysis: Lack of data specifically in core scale, and introducing the fast, simple, and realistic workflow.
The authors compiled/measured all the required data (e.g., thermal, hydraulic, mechanical properties, complete well logging set, etc.,.) for analyzing almost any geomechanical projects in the Canadian Bakken formation, and we have plan to put part of those data in the revised version. This lack of data was the first gap regarding Canadian Bakken Formation studied area.
Another gap was related to stress shadow analysis by itself. To the best of authors’ knowledge, most of prior analyses did not take most of real field complexities (e.g., different hydraulic fracture treatment schedule (proppant and fluid type), well trajectory, geologic structure, leakoff, process zone stress, etc.,). This is the reason of having reasonable match between our workflow output and DFIT field data.
We will definitely elaborate on each of them in the revised version.
 The equations presented to the end of page 17 are all from the literature and well known. There is no need to present them all in the main body of the manuscript, as it distracts the reader to focus on the main objective of this work. If necessary they should be moved to the Appendix.
Answer: We will move the formulation to the appendix in the revised version.
 It is not clear at all, what is the new development in this work. Is it the algorithm which combines the use of the analytical methods and numerical simulations using Gohfer?
Answer: The new development of this work is introducing the workflow (toolbox) to calculate thermohydromechanical stress shadow in tandem with a fully coupled three dimensional numerical fracture simulator. Despite the limitations, which is inherent in any method, this workflow considers the real field complexities. This workflow is simple and fast, and yet reliable as the result was verified by field data. Some of the real field complexities which were considered in our workflow are as follow:
 The rheological coupled behavior of frac fluid and proppant, the same as real treatment schedule. Rheological behavior of frac fluid was simulated based on the lab data, provided by service company.
 Calibration of treating pressure by modifying the frictional parameters such as pipe, and perforation friction, tortuosity factors.
 Considering the effect of real welltrajectory.
 Considering the real geological structure, which enables us to analyze horizontal heterogeneity.
 Determining type and amount of leakoff and PZS by analyzing DFIT test. The leakoff coefficient implicitly accounts for the existence of fissures, and secondary fractures around the hydraulic fracture. PZS is calculated by [i.e., ISIPclosure pressure], which is more realistic criteria for fracture propagation rather than fracture toughness, which is measured under dry laboratory condition.
 Updating fracture width according to proppant crushing strength at the end of the operation according to time lag.
 Verification of numerical simulation by applying pressurematching technique.
 And etc.,
To the best of authors knowledge, even measuring and compiling the data set for Canadian Bakken Formation is deemed as a new development, since lack of these data put hold on many major projects in this formation for more than a decade.
 What is the shortcoming or limitation of the cumulative stress shadow calculation method? For example. 1. The author assumed the i+1 stage stress shadow has no impact on the I stage stress shadow. 2. The author assumed the average value of fracture length and width.
Answer: As you mentioned in example 1 and 2. In our work, the effect of i+1 stage stress shadow on the stage i is not deemed important, since it was not simultaneous hydraulic fracturing.
 1 Workflow: Clear discussions need to be given regarding the GOHFER software and how it accommodates stress shadow distribution (magnitudes and direction). Simple example to clarify how it works and validation of results should be given before presenting a complex 30 stage fracturing example.
Answer: We will cover it in revised version.
 2 Mechanical stress shadow equation 14: There is no explanation of parameters such as E, E’, , R, r, etc. It is not clear if it is proposed to modify the existing equation or solely reproducing the equations.
Answer: We proposed to modify the existing equation, by considering the fact that fracture leaves open after hydraulic fracture due to existence of the proppant layers. The proposed equations consider the effect of propped fracture, as well.
 3 Thermoelastic Stress Shadow: Phie (effective porosity) is better to be shown as Φ.
Answer: we will correct it in the revised version.
 Line 310: In the case study part. The author mentioned the results of sensitivity analysis from other research, but there is no citation. These results are not generally known.
Answer: We will cite it in a revised version.
 Line 330: Which figures in the Appendix are results of ‘’0 MPa for the thermoelastic and 0 for 330 the poroelastic” are not mentioned.
Answer: The authors meant the stress shadow at a point corresponding to Teta = 90° and R = fracture stage spacing for each stress shadow mechanism.
Figures A.2.b & B.2.b
 Line 350: It will be useful to show the direction of the stresses in Figure 12 using arrows in Figure 1. That will help to understand why the stage 3 fracture orients 11 degree.
Answer: We will try to accommodate it in the revised version.
 Line 400: figure 18 (a) is not induced shear stress, it is minimum horizontal stress.
Answer: We will correct it in the revised version.
 It is important to show the results of GOHFER simulation, I didn’t see how GOHFER was used and what are the outcomes. No explanations are given on how GOHFER adopts and utilizes the stress distribution to predict the fracture geometry and orientation.
Answer: we will show the results of verified GOHFER simulation, with explanation in the revised version.
 There is no explanation on how to obtain the total stress shadow from each stage.
Answer: We will explain it in the revised version.
 Figure 21. The orientation of each fracture is not clear. It looks like each fracture is parallel to the other and no stress shadow effect.
Answer: The red dashed lines are only the visual guide to show the location of each stage. We will try to fix it in the revised version. Fractures are not parallel in reality, and stress shadow effect is considered.
 There is a discussion on microseismic events on the early page but no further explanation in the main paper except onepage appendix. How the results of multistage fracturing simulations presented and the stress shadow effect was validated against microseismic data?
Answer: Comparison of the lateral extents of the zones of microseismic activity monitored at well L (Figure C1) against the predicted extents of shear failure zones for various scenarios of natural fracture orientation, used to validate (Table 2).

RC2: 'Comment on se20211', Anonymous Referee #2, 08 Mar 2021
The manuscript:
An Analytical Framework for Stress Shadow Analysis During Hydraulic Fracturing – Applied to the Bakken Formation, Saskatchewan, Canada
It is well written (as far as my English grammar knowledge allows) and deals with an interesting and uptodate subject, that involves both the economic development of tight reservoirs and the environment protection in such activities (this might be a suggestion to the Authors, from the general point of view…).
Despite these premises, the manuscript in its present form in not suitable for publications.
It is based on the application of a series of equations that are difficult to be understood (and to easily justify). Results produced by the application of the proposed equations are then compared with well results though time (or space?).
Among my perplexities, here are some substantial ones:
The Authors should make explicit how did they obtain the proposed equations (19) from the cited reference (Pollard & Segall 1987). This is important, since it is the base of the work presented in the manuscript.
The meaning of the term “Stage” is not enough explicit: does it refer to different time of application (line 280, Fig. 14) or does it represent a distance measure (Fig. 13)?
Computations are compared with experimental results that, as they maintain, strongly depend from the time lag between “stages”. Yet the presented equations do not take into account for the time variable, with the exception of the Thermoelastic model, where time is used as a mere computation of the amount of fluid injected (eq.12). Furthermore, the Authors demonstrated that this component is negligible in their computation.
On the other hand, the comparison between equations and experimental results deals with the relevance of the time lag between successive injection changes (stages, did I correctly understood?), that are not included in the used formulas.
The Author should make explicit how did they arrive to the simplified formulas (4546) from the proposed full form. Did they just summed the results from each stage by ignoring the dissipation/interference between stages? These formula contains fracture dimensions: how were they determined? Were they extracted from the experiment data, and how (line 444446)?
In my opinion, there is a general questionable point in their analysis: stress produced by fluid injection strongly depends on the rate of injection due to fluid viscosity and rock/fluid interaction (e.g. friction). This factor should be taken into consideration when computing produced stress and stress shadows. Cited Pollard models are based on a static approach, that is change in the fracture dimensions (i.e. L) is not considered during the computations, as they modify stress by the produced work, and geometry. And the prediction of enlargement of fractures is one of the goal of the presented work.
The computed average width of fractures with respect to their extension seems too large for the proposed properties (line 294295 and Tab. 1), with a width/length ratio of about 5.7 / 162 = 0.035 that is about 3 times what observed in nature (e.g. Walsh results). The authors should compare and comment on this.
As far as what mentioned, the manuscript requires a significant improvement before entering in the stage of a detailed and complete review.

AC2: 'Reply on RC2', Mostafa Gorjian, 04 Apr 2021
We truly appreciate the reviewer for the comments! Please find our responses as follow:
An Analytical Framework for Stress Shadow Analysis During Hydraulic Fracturing – Applied to the Bakken Formation, Saskatchewan, Canada
It is well written (as far as my English grammar knowledge allows) and deals with an interesting and uptodate subject, that involves both the economic development of tight reservoirs and the environment protection in such activities (this might be a suggestion to the Authors, from the general point of view…).
Answer: Thanks for the positive comments!
Despite these premises, the manuscript in its present form in not suitable for publications.
It is based on the application of a series of equations that are difficult to be understood (and to easily justify). Results produced by the application of the proposed equations are then compared with well results though time (or space?).
Among my perplexities, here are some substantial ones:
The Authors should make explicit how did they obtain the proposed equations (19) from the cited reference (Pollard & Segall 1987). This is important, since it is the base of the work presented in the manuscript.
answer: We will explain the method in the revised version. The authors cordially ask the reviewer to refer to Appendix C of “Ge, J. (2011). Modeling and analysis of reservoir response to stimulation by water injection (Doctoral dissertation, Texas A & M University)”. We need to cite this reference in the revised version, as well. It should be noted that one of the real field complexities which was considered by our toolbox is the effect of propped fracture due to the proppant layers remaining inside of the fracture after termination of each stage within the process of multistage hydraulic fracture. To do that, these equations were modified slightly.
The meaning of the term “Stage” is not enough explicit: does it refer to different time of application (line 280, Fig. 14) or does it represent a distance measure (Fig. 13)?
Answer: Stage is so common and broadly agreedupon term in the hydraulic fracturing field. It means the interval, which is pressurized to create hydraulic fracture. In multistage hydraulic fracturing presented in our paper, stages are from the toe (end of the horizontal leg) to the heel (back to the vertical part of the well). Figures 13 and 14 show the stage spacing (distance) and time lag (the time between finishing one stage and starting the next stage) within multistage hydraulic fracturing in well S.
Computations are compared with experimental results that, as they maintain, strongly depend from the time lag between “stages”. Yet the presented equations do not take into account for the time variable, with the exception of the Thermoelastic model, where time is used as a mere computation of the amount of fluid injected (eq.12). Furthermore, the Authors demonstrated that this component is negligible in their computation.
On the other hand, the comparison between equations and experimental results deals with the relevance of the time lag between successive injection changes (stages, did I correctly understood?), that are not included in the used formulas.
Answer: Figure 3 is the algorithm that was developed in our work. The attributes of the hydraulic fracture are simulated by 3D coupled numerical simulation and then those attributes are given to the stress shadow toolbox as an input to calculate stress shadow. The insitu stress is updated then accordingly. It should be mentioned that leakoff data were real, and analyzed through field DFIT test in the studied area.We will definitely elaborate on this part in the revised version.
The Author should make explicit how did they arrive to the simplified formulas (4546) from the proposed full form. Did they just summed the results from each stage by ignoring the dissipation/interference between stages? These formula contains fracture dimensions: how were they determined? Were they extracted from the experiment data, and how (line 444446)?
 We considered the effect of dissipation and interference between stages. Attributes of hydraulic fracture are obtained by doing 3D coupled numerical modeling. Please refer to the answer 4. The reason for extracting fracture attributes from numerical modelling was to consider maximum real field complexities (e.g., different hydraulic fracture treatment schedule (proppant and fluid which were rheologically modelled by using lab data), well trajectory, geologic structure, leakoff, process zone stress, etc.,) and analytical model cannot reflect that level of complexities.
In my opinion, there is a general questionable point in their analysis: stress produced by fluid injection strongly depends on the rate of injection due to fluid viscosity and rock/fluid interaction (e.g. friction). This factor should be taken into consideration when computing produced stress and stress shadows. Cited Pollard models are based on a static approach, that is change in the fracture dimensions (i.e. L) is not considered during the computations, as they modify stress by the produced work, and geometry. And the prediction of enlargement of fractures is one of the goal of the presented work.
 Answer: As we mentioned before, proppant type and rheological behavior of fluid according to laboratory data were simulated. Treatment pressure was calibrated by modifying the frictional parameters such as pipe, and perforation friction, tortuosity factors. It is worth noting that even the effect of proppant embedment on the surface of fracture was considered in this workflow. We will elaborate on them in the revised version of this paper.
The computed average width of fractures with respect to their extension seems too large for the proposed properties (line 294295 and Tab. 1), with a width/length ratio of about 5.7 / 162 = 0.035 that is about 3 times what observed in nature (e.g. Walsh results). The authors should compare and comment on this.
Answer: This well was actually completed by 30stages of hydraulic fracturing in the field, and each stage had 4 tonnes of proppant mixed with 32.9 m3 of fracture fluid (ELEStim for proppant stages and ELEStim 18cp for nonproppant stages) injected over a total time of 47 minutes for each stage. The ELEStim has initial viscosity of 111 cp and peak viscosity of 516 cp, and ELEStim18cp has initial viscosity of 11 cp and peak viscosity of 18 cp. Having more viscous fluid rather than conventional 1 cp fluid (e.g., fresh water) results wider and shorter fracture.
As far as what mentioned, the manuscript requires a significant improvement before entering in the stage of a detailed and complete review.
Answer: We trust the foregoing answers are satisfactory, and we would greatly appreciate your reconsideration of our paper.

AC2: 'Reply on RC2', Mostafa Gorjian, 04 Apr 2021

EC1: 'Comment on se20211', Federico Rossetti, 07 Apr 2021
Dear Authors,
Your manuscript is a potentially interesting contribution. However, both reviewers’ reports indicate that the manuscript is not suitable for publication as it stands. Much work is needed to improve its internal structure and to better focus the scientific rationale. In particular, it is necessary (i) to elucidate the scope of the paper, (ii) to justify and discuss more in detail the proposed work flow and assumptions made in the study; and (iii) to provide an exhaustive validation of the presented results.
Submission of a revised version is thus only encouraged if the above points will be carefully considered during manuscript revision. In any case, the revised manuscript will be subject to a further revision round.
Federico Rossetti
Interactive discussion
Status: closed

RC1: 'Comment on se20211', Anonymous Referee #1, 24 Feb 2021
The Authors are encouraged to consider the following comments.
 Introduction line 55: What is the specific objective of the study? The author mentioned “a better understanding of the combined effects of mechanical, thermos and poroelastic stress shadows during the process of hydraulic fracturing.” But from the literature review, it is not clear what is the problem or gap in this area that this work is attempting to address. The paper’s objective is not the same with the discussion and conclusion. The abstract needs to reflect clearly the objective(s) of the study.
 The equations presented to the end of page 17 are all from the literature and well known. There is no need to present them all in the main body of the manuscript, as it distracts the reader to focus on the main objective of this work. If necessary they should be moved to the Appendix.
 It is not clear at all, what a is the new development in this work. Is it the algorithm which combines the use of the analytical methods and numerical simulations using Gohfer?
 What is the shortcoming or limitation of the cumulative stress shadow calculation method? For example. 1. The author assumed the i+1 stage stress shadow has no impact on the I stage stress shadow. 2. The author assumed the average value of fracture length and width.
 1 Workflow: Clear discussions need to be given regarding the GOHFER software and how it accommodates stress shadow distribution (magnitudes and direction). Simple example to clarify how it works and validation of results should be given before presenting a complex 30 stage fracturing example.
 2 Mechanical stress shadow equation 14: There is no explanation of parameters such as E, E’, , R, r, etc. It is not clear if it is proposed to modify the existing equation or solely reproducing the equations.
 3 Thermoelastic Stress Shadow: Phie (effective porosity) is better to be shown as Φ.
 Line 310: In the case study part. The author mentioned the results of sensitivity analysis from other research, but there is no citation. These results are not generally known.
 Line 330: Which figures in the Appendix are results of ‘’0 MPa for the thermoelastic and 0 for 330 the poroelastic” are not mentioned.
 Line 350: It will be useful to show the direction of the stresses in Figure 12 using arrows in Figure 1. That will help to understand why the stage 3 fracture orients 11 degree.
 Line 400: figure 18 (a) is not induced shear stress, it is minimum horizontal stress.
 It is important to show the results of GOHFER simulation, I didn’t see how GOHFER was used and what are the outcomes. No explanations are given on how GOHFER adopts and utilizes the stress distribution to predict the fracture geometry and orientation.
 There is no explanation on how to obtain the total stress shadow from each stage.
 Figure 21. The orientation of each fracture is not clear. It looks like each fracture is parallel to the other and no stress shadow effect.
 There is a discussion on microseismic events on the early page but no further explanation in the main paper except onepage appendix. How the results of multistage fracturing simulations presented and the stress shadow effect was validated against microseismic data?

AC1: 'Reply on RC1', Mostafa Gorjian, 04 Apr 2021
We would like to thank the reviewers for their thoughtful comments and efforts towards improving our manuscript. Below is our response to the issues raised in the review:
 Introduction line 55: What is the specific objective of the study? The author mentioned “a better understanding of the combined effects of mechanical, thermo and poroelastic stress shadows during the process of hydraulic fracturing.” But from the literature review, it is not clear what is the problem or gap in this area that this work is attempting to address. The paper’s objective is not the same with the discussion and conclusion. The abstract needs to reflect clearly the objective(s) of the study.
Answer: The authors addressed two gaps related to Canadian Bakken Formation and stress shadow analysis: Lack of data specifically in core scale, and introducing the fast, simple, and realistic workflow.
The authors compiled/measured all the required data (e.g., thermal, hydraulic, mechanical properties, complete well logging set, etc.,.) for analyzing almost any geomechanical projects in the Canadian Bakken formation, and we have plan to put part of those data in the revised version. This lack of data was the first gap regarding Canadian Bakken Formation studied area.
Another gap was related to stress shadow analysis by itself. To the best of authors’ knowledge, most of prior analyses did not take most of real field complexities (e.g., different hydraulic fracture treatment schedule (proppant and fluid type), well trajectory, geologic structure, leakoff, process zone stress, etc.,). This is the reason of having reasonable match between our workflow output and DFIT field data.
We will definitely elaborate on each of them in the revised version.
 The equations presented to the end of page 17 are all from the literature and well known. There is no need to present them all in the main body of the manuscript, as it distracts the reader to focus on the main objective of this work. If necessary they should be moved to the Appendix.
Answer: We will move the formulation to the appendix in the revised version.
 It is not clear at all, what is the new development in this work. Is it the algorithm which combines the use of the analytical methods and numerical simulations using Gohfer?
Answer: The new development of this work is introducing the workflow (toolbox) to calculate thermohydromechanical stress shadow in tandem with a fully coupled three dimensional numerical fracture simulator. Despite the limitations, which is inherent in any method, this workflow considers the real field complexities. This workflow is simple and fast, and yet reliable as the result was verified by field data. Some of the real field complexities which were considered in our workflow are as follow:
 The rheological coupled behavior of frac fluid and proppant, the same as real treatment schedule. Rheological behavior of frac fluid was simulated based on the lab data, provided by service company.
 Calibration of treating pressure by modifying the frictional parameters such as pipe, and perforation friction, tortuosity factors.
 Considering the effect of real welltrajectory.
 Considering the real geological structure, which enables us to analyze horizontal heterogeneity.
 Determining type and amount of leakoff and PZS by analyzing DFIT test. The leakoff coefficient implicitly accounts for the existence of fissures, and secondary fractures around the hydraulic fracture. PZS is calculated by [i.e., ISIPclosure pressure], which is more realistic criteria for fracture propagation rather than fracture toughness, which is measured under dry laboratory condition.
 Updating fracture width according to proppant crushing strength at the end of the operation according to time lag.
 Verification of numerical simulation by applying pressurematching technique.
 And etc.,
To the best of authors knowledge, even measuring and compiling the data set for Canadian Bakken Formation is deemed as a new development, since lack of these data put hold on many major projects in this formation for more than a decade.
 What is the shortcoming or limitation of the cumulative stress shadow calculation method? For example. 1. The author assumed the i+1 stage stress shadow has no impact on the I stage stress shadow. 2. The author assumed the average value of fracture length and width.
Answer: As you mentioned in example 1 and 2. In our work, the effect of i+1 stage stress shadow on the stage i is not deemed important, since it was not simultaneous hydraulic fracturing.
 1 Workflow: Clear discussions need to be given regarding the GOHFER software and how it accommodates stress shadow distribution (magnitudes and direction). Simple example to clarify how it works and validation of results should be given before presenting a complex 30 stage fracturing example.
Answer: We will cover it in revised version.
 2 Mechanical stress shadow equation 14: There is no explanation of parameters such as E, E’, , R, r, etc. It is not clear if it is proposed to modify the existing equation or solely reproducing the equations.
Answer: We proposed to modify the existing equation, by considering the fact that fracture leaves open after hydraulic fracture due to existence of the proppant layers. The proposed equations consider the effect of propped fracture, as well.
 3 Thermoelastic Stress Shadow: Phie (effective porosity) is better to be shown as Φ.
Answer: we will correct it in the revised version.
 Line 310: In the case study part. The author mentioned the results of sensitivity analysis from other research, but there is no citation. These results are not generally known.
Answer: We will cite it in a revised version.
 Line 330: Which figures in the Appendix are results of ‘’0 MPa for the thermoelastic and 0 for 330 the poroelastic” are not mentioned.
Answer: The authors meant the stress shadow at a point corresponding to Teta = 90° and R = fracture stage spacing for each stress shadow mechanism.
Figures A.2.b & B.2.b
 Line 350: It will be useful to show the direction of the stresses in Figure 12 using arrows in Figure 1. That will help to understand why the stage 3 fracture orients 11 degree.
Answer: We will try to accommodate it in the revised version.
 Line 400: figure 18 (a) is not induced shear stress, it is minimum horizontal stress.
Answer: We will correct it in the revised version.
 It is important to show the results of GOHFER simulation, I didn’t see how GOHFER was used and what are the outcomes. No explanations are given on how GOHFER adopts and utilizes the stress distribution to predict the fracture geometry and orientation.
Answer: we will show the results of verified GOHFER simulation, with explanation in the revised version.
 There is no explanation on how to obtain the total stress shadow from each stage.
Answer: We will explain it in the revised version.
 Figure 21. The orientation of each fracture is not clear. It looks like each fracture is parallel to the other and no stress shadow effect.
Answer: The red dashed lines are only the visual guide to show the location of each stage. We will try to fix it in the revised version. Fractures are not parallel in reality, and stress shadow effect is considered.
 There is a discussion on microseismic events on the early page but no further explanation in the main paper except onepage appendix. How the results of multistage fracturing simulations presented and the stress shadow effect was validated against microseismic data?
Answer: Comparison of the lateral extents of the zones of microseismic activity monitored at well L (Figure C1) against the predicted extents of shear failure zones for various scenarios of natural fracture orientation, used to validate (Table 2).

RC2: 'Comment on se20211', Anonymous Referee #2, 08 Mar 2021
The manuscript:
An Analytical Framework for Stress Shadow Analysis During Hydraulic Fracturing – Applied to the Bakken Formation, Saskatchewan, Canada
It is well written (as far as my English grammar knowledge allows) and deals with an interesting and uptodate subject, that involves both the economic development of tight reservoirs and the environment protection in such activities (this might be a suggestion to the Authors, from the general point of view…).
Despite these premises, the manuscript in its present form in not suitable for publications.
It is based on the application of a series of equations that are difficult to be understood (and to easily justify). Results produced by the application of the proposed equations are then compared with well results though time (or space?).
Among my perplexities, here are some substantial ones:
The Authors should make explicit how did they obtain the proposed equations (19) from the cited reference (Pollard & Segall 1987). This is important, since it is the base of the work presented in the manuscript.
The meaning of the term “Stage” is not enough explicit: does it refer to different time of application (line 280, Fig. 14) or does it represent a distance measure (Fig. 13)?
Computations are compared with experimental results that, as they maintain, strongly depend from the time lag between “stages”. Yet the presented equations do not take into account for the time variable, with the exception of the Thermoelastic model, where time is used as a mere computation of the amount of fluid injected (eq.12). Furthermore, the Authors demonstrated that this component is negligible in their computation.
On the other hand, the comparison between equations and experimental results deals with the relevance of the time lag between successive injection changes (stages, did I correctly understood?), that are not included in the used formulas.
The Author should make explicit how did they arrive to the simplified formulas (4546) from the proposed full form. Did they just summed the results from each stage by ignoring the dissipation/interference between stages? These formula contains fracture dimensions: how were they determined? Were they extracted from the experiment data, and how (line 444446)?
In my opinion, there is a general questionable point in their analysis: stress produced by fluid injection strongly depends on the rate of injection due to fluid viscosity and rock/fluid interaction (e.g. friction). This factor should be taken into consideration when computing produced stress and stress shadows. Cited Pollard models are based on a static approach, that is change in the fracture dimensions (i.e. L) is not considered during the computations, as they modify stress by the produced work, and geometry. And the prediction of enlargement of fractures is one of the goal of the presented work.
The computed average width of fractures with respect to their extension seems too large for the proposed properties (line 294295 and Tab. 1), with a width/length ratio of about 5.7 / 162 = 0.035 that is about 3 times what observed in nature (e.g. Walsh results). The authors should compare and comment on this.
As far as what mentioned, the manuscript requires a significant improvement before entering in the stage of a detailed and complete review.

AC2: 'Reply on RC2', Mostafa Gorjian, 04 Apr 2021
We truly appreciate the reviewer for the comments! Please find our responses as follow:
An Analytical Framework for Stress Shadow Analysis During Hydraulic Fracturing – Applied to the Bakken Formation, Saskatchewan, Canada
It is well written (as far as my English grammar knowledge allows) and deals with an interesting and uptodate subject, that involves both the economic development of tight reservoirs and the environment protection in such activities (this might be a suggestion to the Authors, from the general point of view…).
Answer: Thanks for the positive comments!
Despite these premises, the manuscript in its present form in not suitable for publications.
It is based on the application of a series of equations that are difficult to be understood (and to easily justify). Results produced by the application of the proposed equations are then compared with well results though time (or space?).
Among my perplexities, here are some substantial ones:
The Authors should make explicit how did they obtain the proposed equations (19) from the cited reference (Pollard & Segall 1987). This is important, since it is the base of the work presented in the manuscript.
answer: We will explain the method in the revised version. The authors cordially ask the reviewer to refer to Appendix C of “Ge, J. (2011). Modeling and analysis of reservoir response to stimulation by water injection (Doctoral dissertation, Texas A & M University)”. We need to cite this reference in the revised version, as well. It should be noted that one of the real field complexities which was considered by our toolbox is the effect of propped fracture due to the proppant layers remaining inside of the fracture after termination of each stage within the process of multistage hydraulic fracture. To do that, these equations were modified slightly.
The meaning of the term “Stage” is not enough explicit: does it refer to different time of application (line 280, Fig. 14) or does it represent a distance measure (Fig. 13)?
Answer: Stage is so common and broadly agreedupon term in the hydraulic fracturing field. It means the interval, which is pressurized to create hydraulic fracture. In multistage hydraulic fracturing presented in our paper, stages are from the toe (end of the horizontal leg) to the heel (back to the vertical part of the well). Figures 13 and 14 show the stage spacing (distance) and time lag (the time between finishing one stage and starting the next stage) within multistage hydraulic fracturing in well S.
Computations are compared with experimental results that, as they maintain, strongly depend from the time lag between “stages”. Yet the presented equations do not take into account for the time variable, with the exception of the Thermoelastic model, where time is used as a mere computation of the amount of fluid injected (eq.12). Furthermore, the Authors demonstrated that this component is negligible in their computation.
On the other hand, the comparison between equations and experimental results deals with the relevance of the time lag between successive injection changes (stages, did I correctly understood?), that are not included in the used formulas.
Answer: Figure 3 is the algorithm that was developed in our work. The attributes of the hydraulic fracture are simulated by 3D coupled numerical simulation and then those attributes are given to the stress shadow toolbox as an input to calculate stress shadow. The insitu stress is updated then accordingly. It should be mentioned that leakoff data were real, and analyzed through field DFIT test in the studied area.We will definitely elaborate on this part in the revised version.
The Author should make explicit how did they arrive to the simplified formulas (4546) from the proposed full form. Did they just summed the results from each stage by ignoring the dissipation/interference between stages? These formula contains fracture dimensions: how were they determined? Were they extracted from the experiment data, and how (line 444446)?
 We considered the effect of dissipation and interference between stages. Attributes of hydraulic fracture are obtained by doing 3D coupled numerical modeling. Please refer to the answer 4. The reason for extracting fracture attributes from numerical modelling was to consider maximum real field complexities (e.g., different hydraulic fracture treatment schedule (proppant and fluid which were rheologically modelled by using lab data), well trajectory, geologic structure, leakoff, process zone stress, etc.,) and analytical model cannot reflect that level of complexities.
In my opinion, there is a general questionable point in their analysis: stress produced by fluid injection strongly depends on the rate of injection due to fluid viscosity and rock/fluid interaction (e.g. friction). This factor should be taken into consideration when computing produced stress and stress shadows. Cited Pollard models are based on a static approach, that is change in the fracture dimensions (i.e. L) is not considered during the computations, as they modify stress by the produced work, and geometry. And the prediction of enlargement of fractures is one of the goal of the presented work.
 Answer: As we mentioned before, proppant type and rheological behavior of fluid according to laboratory data were simulated. Treatment pressure was calibrated by modifying the frictional parameters such as pipe, and perforation friction, tortuosity factors. It is worth noting that even the effect of proppant embedment on the surface of fracture was considered in this workflow. We will elaborate on them in the revised version of this paper.
The computed average width of fractures with respect to their extension seems too large for the proposed properties (line 294295 and Tab. 1), with a width/length ratio of about 5.7 / 162 = 0.035 that is about 3 times what observed in nature (e.g. Walsh results). The authors should compare and comment on this.
Answer: This well was actually completed by 30stages of hydraulic fracturing in the field, and each stage had 4 tonnes of proppant mixed with 32.9 m3 of fracture fluid (ELEStim for proppant stages and ELEStim 18cp for nonproppant stages) injected over a total time of 47 minutes for each stage. The ELEStim has initial viscosity of 111 cp and peak viscosity of 516 cp, and ELEStim18cp has initial viscosity of 11 cp and peak viscosity of 18 cp. Having more viscous fluid rather than conventional 1 cp fluid (e.g., fresh water) results wider and shorter fracture.
As far as what mentioned, the manuscript requires a significant improvement before entering in the stage of a detailed and complete review.
Answer: We trust the foregoing answers are satisfactory, and we would greatly appreciate your reconsideration of our paper.

AC2: 'Reply on RC2', Mostafa Gorjian, 04 Apr 2021

EC1: 'Comment on se20211', Federico Rossetti, 07 Apr 2021
Dear Authors,
Your manuscript is a potentially interesting contribution. However, both reviewers’ reports indicate that the manuscript is not suitable for publication as it stands. Much work is needed to improve its internal structure and to better focus the scientific rationale. In particular, it is necessary (i) to elucidate the scope of the paper, (ii) to justify and discuss more in detail the proposed work flow and assumptions made in the study; and (iii) to provide an exhaustive validation of the presented results.
Submission of a revised version is thus only encouraged if the above points will be carefully considered during manuscript revision. In any case, the revised manuscript will be subject to a further revision round.
Federico Rossetti
Mostafa Gorjian et al.
Mostafa Gorjian et al.
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