Experimental study of the effect of natural fracture curvature on hydraulic fracture propagation behavior

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To reveal the influence mechanism of natural fractures with different curvatures on hydraulic fracture propagation during the fracturing process, this study simulated the hydraulic fracture propagation patterns under natural fractures with different curvatures by carrying out large-size true triaxial hydraulic fracturing physical modeling experiments on artificial rock samples prefabricated with different curvatures of fractures. Results show that the injection rate of fracturing fluid and the curvature of natural fractures have important effects on the interaction between hydraulic fractures and natural fractures. When the approximation angle (the angle between the hydraulic fracture and the natural fracture) is 90°, with the gradual decrease of the fracturing fluid injection rate, the interaction between the hydraulic fracture and the natural fracture shows that the hydraulic fracture passes through the natural fracture directly, and gradually changes to the hydraulic fracture passes through the natural fracture and also extends along the natural fracture, and then in the end, only hydraulic fracture extends along the natural fracture occurs. When the injection rate is constant and the approximation angle is 90°, with the curvature of the natural crack gradually increasing (increasing curvature), the interaction between the hydraulic fracture and the natural fracture shows that the hydraulic fracture passes through the natural fracture and also partially extends along the natural fracture, and gradually changes to the hydraulic fracture extending only along the natural fracture, and then finally extends along the direction of the maximum horizontal principal stress. The results of the study are instructive for revealing the interaction mechanism between hydraulic fractures and natural cracks. Hydraulic fracturing Natural fracture Injection rate Curvature Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction Unconventional oil and gas reservoirs, due to their low porosity and low permeability characteristics, lead to the need for reservoir fracturing and stimulation in the process of oil and gas exploration to achieve the commercial development of oil and gas (Jarvie et al., 2007 ; Ross et al., 2009; Zou et al., 2010 ). Hydraulic fracturing technology is the core technology of reservoir stimulation and plays an important role in the process of oil and gas storage and production. The propagation pattern of hydraulic fractures during fracturing is affected by factors such as the material composition of the rock, diagenesis, geostress, temperature, discontinuity, fracturing fluid, proppant, and construction parameters, and these factors work together to make it difficult to accurately predict the propagation paths of hydraulic fractures during fracturing, which in turn restricts the volume of reservoir stimulation (Zhao et al., 2024; Li et al., 2017 ; Wang et al., 2019 ; Kamali et al., 2023 ; Zhou et al., 2023 ). Among them, the existence of discontinuities such as faults, fractures, and natural fractures is an important reason for the complexity and variability of hydraulic fracture propagation paths. It is found that when hydraulic fractures encounter discontinuities, they may undergo behaviors such as arrested, diverted, penetrated directly, and simultaneously penetrated and diverted (Zhang et al., 2022 ; Guo et al., 2021 ). The specific behavior that occurs is influenced by factors such as the strength of the natural fracture, production, friction characteristics, geostress, fracturing fluid, and construction parameters (Zou et al., 2021 ; Zhang et al., 2021 ; Hu et al., 2021; Lei et al., 2021 ; Zhang et al., 2023 ; Xie et al., 2022 ). Therefore, the complex propagation pattern of hydraulic fractures in discontinuities determines the complexity of the generated fracture network and leads to the difficulty of accurately predicting hydraulic fracture propagation paths. Discontinuities such as joints and natural fractures developed in rocks are often filled with various materials, and their pore permeability scales are much larger compared to the rock matrix, so they are more likely to be reactivated by hydraulic fractures during the fracturing process (Kresse et al., 2013 ; Tan et al., 2017 ; Cheng et al., 2015 ; Bakhshi et al., 2019 ). Meanwhile, the extending path of hydraulic fracture and its morphology will be complicated by the influence of natural fracture. Scholars conducted a systematic study on the interaction between hydraulic fractures and natural fractures during the fracturing process by using hydraulic fracturing physical experiments and found that during the interaction between hydraulic fractures and natural fractures, the hydraulic fracture may penetrate through the natural fractures directly, be arrested by the natural fractures, or extend along the natural fractures, etc., and the exact occurrence of which depends on the angle of approach (angle of intersection between the hydraulic fracture and natural fractures) and the horizontal principal stress difference (Blanton, 1982 , 1986 ; Warpinski et al., 1987). The specific situation depends on the approach angle (the angle of intersection between the hydraulic fracture and the natural fracture) and the value of the horizontal principal stress difference (Renshaw et al., 1995; Gu et al., 2010, 2012 ; Fisher et al., 2012), which establishes the propagation criterion of the hydraulic fracture encountering the natural fracture. Also, scholars conduct hydraulic fracturing tests at the mine site, and the obtained results are more consistent with the laboratory results, and the laboratory conclusions are well validated by using the field construction results (Brinkley et al., 2023 ; Fu et al., 2021 ). Besides external factors, the characteristics of natural fractures themselves, such as orientation, friction characteristics, strength, and size, also affect the results of their interaction with hydraulic fractures (Li et al., 2023 ; Li et al., 2022 ; Wang et al., 2023 ). As the strength of natural fractures increases, hydraulic fractures tend to penetrate directly through natural fractures. The increase in the size of natural fractures, in turn, is a prerequisite for the generation of a complex network of seams (Guo et al., 2023 ; Zeng et al., 2023 ; Pidho et al., 2023 ; Li et al., 2022 ). As a result of the factors, the complexity and variability of the propagation pattern of hydraulic fractures in discontinuities such as natural fractures and the unknown mechanism of propagation have brought serious difficulties in accurately predicting the propagation paths of hydraulic fractures, which, in turn, constrains the oil and gas production. Although scholars have conducted numerous studies on the interaction between hydraulic fractures and natural fractures, and have achieved certain conclusions and understanding (Zhou et al., 2008 ; Dehghan et al., 2015 ; Xiong et al., 2022; Li et al., 2022 ; Olson et al., 2012 ; Rahman et al., 2009 ). However, according to the field observation, a lot of natural fractures with different degrees of curvature are developed in the rock (Fig. 1 ), and less research work has been done on the influence of the degree of curvature of natural fractures on the propagation behavior of hydraulic fractures (Du et al., 2023 ; Zeng et al., 2024 ). Therefore, this paper firstly prefabricates natural fractures with different degrees of curvature in artificial rock samples, and then conducts true triaxial hydraulic fracturing physical experiments on them and investigates the interaction mechanism between hydraulic fractures and natural fractures with an approach angle of 90°. The results of the study provide some guidance for revealing the interaction mechanism between hydraulic fractures and natural fractures in the fracturing process. 2. Experimental design and methodology 2.1 Experimental setup The experimental system used in this hydraulic fracturing physical model experiment mainly consists of a true-triaxial hydraulic fracturing experimental machine, a true-triaxial hydraulic voltage source, an MTS servo pressurization and control device, and a data acquisition and processing system (Fig. 2 ). As shown in Fig. 3 , a cubic rock sample with a side length of 300mm is placed in the groove of a true-triaxial hydraulic fracturing experimental machine, surrounded by a pressure piston to ensure that controllable pressure can be applied around the edges and bottom of the sample. The size of the piston is the same as the surface size of the sample, ensuring uniform pressure. The pressure can be controlled by the MTS pump pressure control system, with a maximum pressure output of 30 MPa. Meanwhile, the top of the sample is covered with steel plates to simulate in-situ stress. The injection power is controlled by an MTS816 servo booster, with a maximum injection pressure of 140MPa. The most injection volume is 800ml/min. Also, the acoustic emission monitoring system is used to collect acoustic emission event points during the experimental process, thereby locating the propagation morphology of hydraulic fractures during the fracturing process (Fig. 3 ). An acoustic emission system coupled with a true triaxial hydraulic fracturing system was used to characterize the initiation and propagation patterns of the hydraulic fractures in real time during the hydraulic fracturing process. The acoustic emission system has a total of 16 probes distributed on the four sides of the cubic rock sample, with four probes on each side, for a total of 16 probes, which are utilized to monitor the damage points in the rock sample during the hydraulic fracturing, and then, based on these acoustic emission data, the determination of the hydraulic fracture geometry is realized (Fig. 3 ). 2.2 Sample Preparation In this experiment, Chinese C80 cement and 40–60 mesh quartz sand were chosen to be mixed in the ratio of 1:1: and then the mixture was made into a cement slurry with water in the ratio of 3:2, and the prepared slurry was placed in a 300mm cube mould to prepare the rock samples. Moreover, natural fractures were simulated using pieces of hard paper having a length of 200 mm, a height of 100 mm, and a thickness of 0.8 mm. Among them, the curvature of the prefabricated natural fractures was defined as the ratio of the difference between the initial length of the prefabricated fracture minus the length of the prefabricated fracture after curving to its initial length (Fig. 4 c): $$C=\frac{{L}_{i}-{L}_{l}}{{L}_{i}} \left(1\right)$$ where \(C\) denotes curvature, dimensionless; \({L}_{i}\) denotes the initial original length of the prefabricated crack, mm; \({L}_{l}\) denotes the length of the prefabricated crack after bending, mm. In Eq. (1), the larger \(C\) is, the greater the degree of bending of the prefabricated crack. By changing the curvature \(C\) of the prefabricated natural fracture, the change in the morphology of the prefabricated natural fracture was achieved. In this experiment, the curvature \(C\) of prefabricated fracture was set to be 0.75, 0.5, 0.25, and 0. By prefabricating natural fractures with different curvatures, the influence of the morphology of natural fractures on the propagation morphology of hydraulic fractures was thus investigated. The location of the prefabricated cracks is shown in Fig. 4 , which is placed 100 mm from the center of the wellbore, the bottom surface is 100 mm from the bottom of the rock sample, the upper surface is 100 mm from the top of the rock sample, and the opening direction is back from the wellbore (Fig. 4 b). 2.3 Wellbore design After the rock sample is prepared, it is drilled into the middle of the sample for processing. Among them, a drilling tool with a diameter of 25mm was used for processing in this experiment, with a drilling depth of 170mm. Then, the sample was cased by using a wellbore with a length of 150 mm, where the open hole section was 20mm (Fig. 4 a, Fig. 4 b). 2.4 Experimental procedure The simulation of in-situ stress conditions is the key to hydraulic fracturing experiments. Therefore, this experiment was conducted under normal in-situ stress conditions, i.e., vertical stress > maximum horizontal stress > minimum horizontal stress (σ V > σ H > σ h ). In this case, the vertical stress, maximum horizontal stress, and minimum horizontal stress are 20 MPa, 15 MPa, and 10 MPa, respectively (Table 1 ). The fracturing fluid used in the experiment is clean water, and a green fluorescent powder is added to improve the detection ability of hydraulic fractures during the hydraulic fracturing. During the experiment, the injection rate of fracturing fluid remained constant at 30ml/min. As the fracturing fluid is injected, the wellbore pressure continues to increase until the wellbore pressure begins to decrease, surface rocks begin to initiate, hydraulic fractures begin to propagate, and then continue to be injected until the fracturing fluid flows out and the surface rock sample is crushed. After each fluid injection and hydraulic fracturing section of the experiment, the rock blocks should be inspected to determine the propagation morphology of hydraulic fractures. After visually inspecting the rock block, use a hammer and chisel to split it open and examine the propagation pattern of internal hydraulic fractures and their interaction with natural fractures. Finally, take some photos from each rock block slice and use these photos to analyze the propagation direction before, during, and after the interaction between hydraulic fractures and prefabricated natural fractures. Table 1 Summary of experimental conditions and results obtained Test σ V /MPa σ H /MPa σ h /MPa C Results gx-1 20 15 10 0 Crossing and Diversion gx-2 20 15 10 0.25 Crossing and Diversion gx-3 20 15 10 0.50 Diversion gx-4 20 15 10 0.75 Diversion 3. Experimental observations and results In this study, after each hydraulic fracturing experiment on the sample, a hammer and chisel were used to open the rock block along the hydraulic fracture, and the experimental results were observed and recorded. We use acoustic emission monitoring and tracer technology to characterize the morphology of generated hydraulic fractures in two-dimensional and three-dimensional spaces. By observing and analyzing the hydraulic fracture morphology generated during the fracturing process of each sample, the following conclusions can be drawn: The fracturing fluid injection rate is 30 ml/min and the angle of approach is 90° (the hydraulic fracture is vertically incident on the natural fracture) when the \(C\) is 0, i.e., the gx-1 rock sample exhibits the hydraulic fracture directly crossing the natural fracture simultaneously, some of the fracturing fluids flow along the natural fracture and the natural fracture is reactivated (Fig. 5 ). As the \(C\) increases, more and more fracturing fluid in the gx-2, gx-3 and gx-4 rock samples gradually tend to flow along the natural fractures, the natural fractures are reactivated and the ability of hydraulic fractures to cross the natural fractures directly decreases, and when the \(C\) is 0.5, i.e., all of the fracturing fluid flows along the natural fractures in the gx-3 rock samples, resulting in reactivation of the natural fractures while the direct crossing of the natural fracture behavior disappears (Fig. 6 ). In addition, according to the acoustic emission monitoring results and the post-pressure hydraulic fracture morphology analysis, it is found that during the hydraulic fracturing process, when the hydraulic fracture is not close to the natural fracture, it is easy to generate simple and straight symmetric bi-winged hydraulic fracture; when the hydraulic fracture interacts with the natural fracture, the morphology of hydraulic fracture becomes curved and complex, and the more complex the morphology of the natural fracture, the more complex is the morphology of the generated fracture network (Figs. 5 and 6 ) The experimental results are more consistent with the results obtained by Potluri et al.'s (Potluri et al, 2005 ) and Dehghan et al's (Dehghan et al, 2015 ) under normal ground stress. 4. Discussion Many scholars have conducted extensive research on the interaction mechanism between hydraulic fractures and natural fractures and proposed the interaction criteria, and Blanton (Blanton, 1982 , 1986 ), Warpinski and Teufel (Warpinski and Teufel, 1987 ) concluded from indoor hydraulic fracturing physical modeling experiments and hydraulic fracturing mine experiments, respectively, that when a hydraulic fracture encounters a natural fracture, the hydraulic fracture can cross the natural fracture, be arrested by the natural fracture and extend along the natural fracture, depending on the angle of approach and the magnitude of horizontal principal stress difference. The hydraulic fracture may cross the natural fracture, the hydraulic fracture is arrested by the natural fracture, and the hydraulic fracture extends along the natural fracture, depending on the angle of approach and the magnitude of the horizontal principal stress difference. However, this criterion mainly focuses on the initial interaction behavior when the hydraulic fracture encounters the natural fracture and does not take into account the later interaction behavior. Potluri et al (Potluri et al., 2005 ) evaluated the extension of the hydraulic fracture after its interaction with the natural fracture using the method of Warpinski and Teufel׳s (Warpinski and Teufel, 1987 ). Three main possible patterns were introduced, i.e., traversal and propagation starting from the tip of the natural fracture, as well as propagation and breakthrough at the weak points of the natural fracture surface. Zhou (Zhou et al., 2008 ) and Dehghan et al. (Dehghan et al., 2015 ) also observed three types of interactions between hydraulic fractures and natural fractures on an experimental basis, which is the same as that observed by Warpinski and Teufel׳s (Warpinski and Teufel, 1987 ). Moreover, Dehghan et al. (Dehghan et al., 2015 ) investigated the effect of the inclination and orientation of natural fractures on the propagation of hydraulic fractures and concluded that hydraulic fractures either propagate along the direction of the maximum horizontal geostress or the height of natural fractures under normal geostress conditions. Based on this, this paper analyses the influence of the morphology change of the natural fractures on the hydraulic fracture propagation behavior when the hydraulic fracture acts vertically on the natural fracture, and finds that the hydraulic fracture is more likely to generate simple, straight, and symmetric biplane hydraulic fractures when it does not encounter the natural fracture; when the hydraulic fracture interacts with the natural fracture, the morphology of hydraulic fracture becomes curved and complex, and the more complex the morphology of the natural fracture, the more complex the generated fracture network morphology is. The more complex the natural fracture morphology, the more complex the generated fracture network morphology (Figs. 5 and 6 ). The findings of Potluri et al.'s (Potluri et al., 2005 ) and Dehghan et al's (Dehghan et al., 2015 ) were confirmed by the study. In addition, when the injection rate is constant and the curvature is small, hydraulic fracture and natural fracture interactions mainly show hydraulic fracture crossing the natural fracture and extending partially along the natural fracture. As the degree of curvature of the natural fractures increases (i.e., the \(C\) increases), more fracturing fluid is diverted by the natural fractures, the natural fractures are reactivated, and the phenomenon of the hydraulic fractures crossing directly through the natural fractures diminishes. Further, when the curvature of the natural fracture is 0.5, the perpendicular interaction between the hydraulic fracture and the natural fracture exhibits that the hydraulic fracture extends along the natural fracture and then along the direction of the maximum horizontal principal stress, and the phenomenon of the hydraulic fracture crossing the natural fracture disappears. Therefore, under the normal state of geostress, the injection rate of fracturing fluid is constant, and the approach angle between hydraulic fracture and natural fracture is 90°, when the \(C\) is less than 0.5, when the hydraulic fracture extends to the natural fracture, it mainly occurs that the hydraulic fracture crosses the natural fracture directly and the hydraulic fracture crosses the natural fracture while the natural fracture is partially activated (Fig. 5 ); when the \(C\) is greater than or equal to 0.5, the hydraulic fracture and natural fracture interaction presents a hydraulic fracture turning along the natural fracture (Fig. 6 ). It can be inferred that when the injection rate is large and the approach angle between the hydraulic fracture and the natural fracture is 90°, the hydraulic fracture will directly cross the natural fracture when the hydraulic fracture extends to the natural fracture; keeping the angle of approach constant, with the gradual decrease of the injection rate, the hydraulic fracture gradually transforms from directly crossing the natural fracture to the hydraulic fracture crossing the natural fracture and simultaneously extending along the natural fracture. When the injection rate is constant and the approach angle is 90°, the hydraulic fracture gradually changes from extending along the natural fracture while crossing the natural fracture to extending only along the natural fracture as the natural fracture morphology becomes more and more curved ( \(C\) increases) and finally extends along the direction of the maximum horizontal principal stress. Therefore, when hydraulic fractures act vertically on natural fractures, the fluid injection rate and natural fracture morphology play an important role in controlling the interaction between hydraulic fractures and natural fractures, which in turn affects the complexity of the generated fracture network. 5. Conclusion (1) When hydraulic fractures act vertically on natural fractures, the injection rate of fracturing fluid and the morphology of natural fractures during hydraulic fracturing play an important role in controlling the interaction behavior of hydraulic fractures with natural fractures. When the hydraulic fracture does not encounter the natural fracture, it is easier to generate simple, straight, and symmetric bi-wing hydraulic fracture; when the hydraulic fracture interacts with the natural fracture, the hydraulic fracture morphology becomes curved and complex, and the more complex the natural fracture morphology is, the more complex the morphology of the generated fracture network is. (2) Other conditions remain unchanged, when the hydraulic fracture acts vertically on the natural crack, with the increase of the degree of curvature of the natural crack (curvature increase), the hydraulic fracture gradually changes from crossing the natural fracture and expanding along the natural fracture to extending only along the natural fracture, and ultimately extending along the direction of the maximum horizontal principal stress. (3) Other conditions remain unchanged, when the hydraulic fracture acts perpendicularly on the natural fracture, with the decrease in the injection rate of fracturing fluid, the hydraulic fracture gradually changes from directly crossing the natural fracture to crossing the natural fracture and turning along the natural fracture simultaneously. Declarations Author Contribution Conceptualization, Jin Zhijun, Ma Xinhua,Gong Xun ; Formal Analysis, Gong Xun and Liu Yuyang; Resources, Jin Zhijun, Ma Xinhua, and Liu Yuyang; Data Curation, Gong Xun; Writing-Original Draft Preparation, Gong Xun; Writing-Review & Editing, Jin Zhijun, Ma Xinhua, Liu Yuyang, Li Guanfang; Visualization, Gong Xun; Supervision, Jin Zhijun, Ma Xinhua, Liu Yuyang, Li Guanfang; Project Administration,Ma Xinhua and Liu Yuyang. Acknowledgement This study was funded by the Project of R&D Department of Petrochina (No. 2021DJ2005 and No. 2021DJ2005). References Bakhshi E, Rasouli V, Ghorbani A, et al. 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Gong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFklEQVRIie3RsUrDQBjA8S8cXJYT1y9U2le4UNAl0Fe5UMgUgxAojpFApjxAoeozOBXcLgR0qZ2zNaWrQkoXQQcvoZtNyCh4/+GG4358xx2ATvcHOzfvIik4DiebXDY7WC+sg1hpnsnyxhlDQQXIPoQX3jQrK8+FgvF+BKTP1cVyYSzSw2GfQGDNhVF+JDC6ahFGtGpIQC7elpglEA5QEPshAfs5Ok2IkTYkpHC9BEXcRxR0cJaA4PI0oYQ1xE3B31VHYn51EUapUMRz5+hDfTF3oaaQLoKMSEWcMWcvl7haY2il29i6X6P91EImm228//zGITfjXXU7cwJ8nWbV+8wZtU35NVXUrwjH7+mX6H9Up9Pp/ks/7Bpjhm/t//kAAAAASUVORK5CYII=","orcid":"","institution":"Peking University","correspondingAuthor":true,"prefix":"","firstName":"Xun","middleName":"","lastName":"Gong","suffix":""},{"id":302486352,"identity":"abb7b903-c005-4bf2-ba0e-cbb8413f05b7","order_by":1,"name":"Zhijun Jin","email":"","orcid":"","institution":"Peking University","correspondingAuthor":false,"prefix":"","firstName":"Zhijun","middleName":"","lastName":"Jin","suffix":""},{"id":302486353,"identity":"b1ebaec7-f88b-4802-926c-3bea4f59851a","order_by":2,"name":"Xinhua Ma","email":"","orcid":"","institution":"Research Institute of Petroleum Exploration and Development (RIPED)","correspondingAuthor":false,"prefix":"","firstName":"Xinhua","middleName":"","lastName":"Ma","suffix":""},{"id":302486354,"identity":"b14f5310-70dc-4210-83a0-ebe18dbd74a6","order_by":3,"name":"Yuyang Liu","email":"","orcid":"","institution":"Research Institute of Petroleum Exploration and Development (RIPED)","correspondingAuthor":false,"prefix":"","firstName":"Yuyang","middleName":"","lastName":"Liu","suffix":""},{"id":302486355,"identity":"dde20571-8718-461e-bcd4-0346f76cb89a","order_by":4,"name":"Guanfang Li","email":"","orcid":"","institution":"Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Guanfang","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2024-05-11 04:08:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4403407/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4403407/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":57008868,"identity":"ebe8e1de-4989-457b-bfa5-84a6cc7a8435","added_by":"auto","created_at":"2024-05-23 10:45:33","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":198556,"visible":true,"origin":"","legend":"\u003cp\u003eNatural fractures developed in rocks with curved patterns (Zeng et al., 2024)\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4403407/v1/f6916e32781facc39f9d9a91.jpeg"},{"id":57009336,"identity":"514d6aea-cc4d-420a-96cd-6805e1588e32","added_by":"auto","created_at":"2024-05-23 10:53:33","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":189487,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of tri-axial experimental equipment (Zhou et al., 2008)\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4403407/v1/8480aeb1b31e00a4dc79b4e5.jpeg"},{"id":57008869,"identity":"4cd5a38d-e7ce-429d-8c03-c2367d929c20","added_by":"auto","created_at":"2024-05-23 10:45:33","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":294982,"visible":true,"origin":"","legend":"\u003cp\u003eTrue triaxial hydraulic fracturing test machine and acoustic emission system\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4403407/v1/e28b051d9ef88a08d6c092d1.jpeg"},{"id":57008867,"identity":"aee2102d-4803-4eae-a920-ef174102ed48","added_by":"auto","created_at":"2024-05-23 10:45:33","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":87736,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of artificial rock sample preparation\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4403407/v1/f888d29278606d7ca0b7a897.jpeg"},{"id":57008872,"identity":"13d92c7c-bd95-4733-ac48-c6b0d4f293cb","added_by":"auto","created_at":"2024-05-23 10:45:33","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":247027,"visible":true,"origin":"","legend":"\u003cp\u003eHydraulic fracture morphology of rock samples with a curvature of 0\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4403407/v1/5d73dd816dd994961ef986ab.jpeg"},{"id":57008870,"identity":"725a5b0a-e945-41ae-bcf0-dc5fa12fb1c5","added_by":"auto","created_at":"2024-05-23 10:45:33","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":256412,"visible":true,"origin":"","legend":"\u003cp\u003eHydraulic fracture morphology of rock samples with a curvature of 0.5\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4403407/v1/ffb6ef61eef1ff92bc54443e.jpeg"},{"id":57113784,"identity":"b936b478-b566-4298-b6e5-82095b18824e","added_by":"auto","created_at":"2024-05-24 22:16:35","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1623386,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4403407/v1/4b972c45-00d2-4ba5-b115-32df7a44d509.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Experimental study of the effect of natural fracture curvature on hydraulic fracture propagation behavior","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eUnconventional oil and gas reservoirs, due to their low porosity and low permeability characteristics, lead to the need for reservoir fracturing and stimulation in the process of oil and gas exploration to achieve the commercial development of oil and gas (Jarvie et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Ross et al., 2009; Zou et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Hydraulic fracturing technology is the core technology of reservoir stimulation and plays an important role in the process of oil and gas storage and production. The propagation pattern of hydraulic fractures during fracturing is affected by factors such as the material composition of the rock, diagenesis, geostress, temperature, discontinuity, fracturing fluid, proppant, and construction parameters, and these factors work together to make it difficult to accurately predict the propagation paths of hydraulic fractures during fracturing, which in turn restricts the volume of reservoir stimulation (Zhao et al., 2024; Li et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Kamali et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zhou et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Among them, the existence of discontinuities such as faults, fractures, and natural fractures is an important reason for the complexity and variability of hydraulic fracture propagation paths. It is found that when hydraulic fractures encounter discontinuities, they may undergo behaviors such as arrested, diverted, penetrated directly, and simultaneously penetrated and diverted (Zhang et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Guo et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The specific behavior that occurs is influenced by factors such as the strength of the natural fracture, production, friction characteristics, geostress, fracturing fluid, and construction parameters (Zou et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Hu et al., 2021; Lei et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Xie et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Therefore, the complex propagation pattern of hydraulic fractures in discontinuities determines the complexity of the generated fracture network and leads to the difficulty of accurately predicting hydraulic fracture propagation paths.\u003c/p\u003e \u003cp\u003eDiscontinuities such as joints and natural fractures developed in rocks are often filled with various materials, and their pore permeability scales are much larger compared to the rock matrix, so they are more likely to be reactivated by hydraulic fractures during the fracturing process (Kresse et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Tan et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Cheng et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Bakhshi et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Meanwhile, the extending path of hydraulic fracture and its morphology will be complicated by the influence of natural fracture. Scholars conducted a systematic study on the interaction between hydraulic fractures and natural fractures during the fracturing process by using hydraulic fracturing physical experiments and found that during the interaction between hydraulic fractures and natural fractures, the hydraulic fracture may penetrate through the natural fractures directly, be arrested by the natural fractures, or extend along the natural fractures, etc., and the exact occurrence of which depends on the angle of approach (angle of intersection between the hydraulic fracture and natural fractures) and the horizontal principal stress difference (Blanton, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1982\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1986\u003c/span\u003e; Warpinski et al., 1987). The specific situation depends on the approach angle (the angle of intersection between the hydraulic fracture and the natural fracture) and the value of the horizontal principal stress difference (Renshaw et al., 1995; Gu et al., 2010, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Fisher et al., 2012), which establishes the propagation criterion of the hydraulic fracture encountering the natural fracture. Also, scholars conduct hydraulic fracturing tests at the mine site, and the obtained results are more consistent with the laboratory results, and the laboratory conclusions are well validated by using the field construction results (Brinkley et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Fu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Besides external factors, the characteristics of natural fractures themselves, such as orientation, friction characteristics, strength, and size, also affect the results of their interaction with hydraulic fractures (Li et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Li et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). As the strength of natural fractures increases, hydraulic fractures tend to penetrate directly through natural fractures. The increase in the size of natural fractures, in turn, is a prerequisite for the generation of a complex network of seams (Guo et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zeng et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Pidho et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Li et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). As a result of the factors, the complexity and variability of the propagation pattern of hydraulic fractures in discontinuities such as natural fractures and the unknown mechanism of propagation have brought serious difficulties in accurately predicting the propagation paths of hydraulic fractures, which, in turn, constrains the oil and gas production.\u003c/p\u003e \u003cp\u003eAlthough scholars have conducted numerous studies on the interaction between hydraulic fractures and natural fractures, and have achieved certain conclusions and understanding (Zhou et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Dehghan et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Xiong et al., 2022; Li et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Olson et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Rahman et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). However, according to the field observation, a lot of natural fractures with different degrees of curvature are developed in the rock (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), and less research work has been done on the influence of the degree of curvature of natural fractures on the propagation behavior of hydraulic fractures (Du et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zeng et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Therefore, this paper firstly prefabricates natural fractures with different degrees of curvature in artificial rock samples, and then conducts true triaxial hydraulic fracturing physical experiments on them and investigates the interaction mechanism between hydraulic fractures and natural fractures with an approach angle of 90\u0026deg;. The results of the study provide some guidance for revealing the interaction mechanism between hydraulic fractures and natural fractures in the fracturing process.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"2. Experimental design and methodology","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Experimental setup\u003c/h2\u003e \u003cp\u003eThe experimental system used in this hydraulic fracturing physical model experiment mainly consists of a true-triaxial hydraulic fracturing experimental machine, a true-triaxial hydraulic voltage source, an MTS servo pressurization and control device, and a data acquisition and processing system (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, a cubic rock sample with a side length of 300mm is placed in the groove of a true-triaxial hydraulic fracturing experimental machine, surrounded by a pressure piston to ensure that controllable pressure can be applied around the edges and bottom of the sample. The size of the piston is the same as the surface size of the sample, ensuring uniform pressure. The pressure can be controlled by the MTS pump pressure control system, with a maximum pressure output of 30 MPa. Meanwhile, the top of the sample is covered with steel plates to simulate in-situ stress. The injection power is controlled by an MTS816 servo booster, with a maximum injection pressure of 140MPa. The most injection volume is 800ml/min. Also, the acoustic emission monitoring system is used to collect acoustic emission event points during the experimental process, thereby locating the propagation morphology of hydraulic fractures during the fracturing process (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAn acoustic emission system coupled with a true triaxial hydraulic fracturing system was used to characterize the initiation and propagation patterns of the hydraulic fractures in real time during the hydraulic fracturing process. The acoustic emission system has a total of 16 probes distributed on the four sides of the cubic rock sample, with four probes on each side, for a total of 16 probes, which are utilized to monitor the damage points in the rock sample during the hydraulic fracturing, and then, based on these acoustic emission data, the determination of the hydraulic fracture geometry is realized (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Sample Preparation\u003c/h2\u003e \u003cp\u003eIn this experiment, Chinese C80 cement and 40\u0026ndash;60 mesh quartz sand were chosen to be mixed in the ratio of 1:1: and then the mixture was made into a cement slurry with water in the ratio of 3:2, and the prepared slurry was placed in a 300mm cube mould to prepare the rock samples. Moreover, natural fractures were simulated using pieces of hard paper having a length of 200 mm, a height of 100 mm, and a thickness of 0.8 mm. Among them, the curvature of the prefabricated natural fractures was defined as the ratio of the difference between the initial length of the prefabricated fracture minus the length of the prefabricated fracture after curving to its initial length (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec):\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$C=\\frac{{L}_{i}-{L}_{l}}{{L}_{i}} \\left(1\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C\\)\u003c/span\u003e\u003c/span\u003e denotes curvature, dimensionless; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({L}_{i}\\)\u003c/span\u003e\u003c/span\u003e denotes the initial original length of the prefabricated crack, mm; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({L}_{l}\\)\u003c/span\u003e\u003c/span\u003e denotes the length of the prefabricated crack after bending, mm.\u003c/p\u003e \u003cp\u003eIn Eq.\u0026nbsp;(1), the larger \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C\\)\u003c/span\u003e\u003c/span\u003e is, the greater the degree of bending of the prefabricated crack. By changing the curvature \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C\\)\u003c/span\u003e\u003c/span\u003e of the prefabricated natural fracture, the change in the morphology of the prefabricated natural fracture was achieved. In this experiment, the curvature \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C\\)\u003c/span\u003e\u003c/span\u003e of prefabricated fracture was set to be 0.75, 0.5, 0.25, and 0. By prefabricating natural fractures with different curvatures, the influence of the morphology of natural fractures on the propagation morphology of hydraulic fractures was thus investigated. The location of the prefabricated cracks is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, which is placed 100 mm from the center of the wellbore, the bottom surface is 100 mm from the bottom of the rock sample, the upper surface is 100 mm from the top of the rock sample, and the opening direction is back from the wellbore (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Wellbore design\u003c/h2\u003e \u003cp\u003eAfter the rock sample is prepared, it is drilled into the middle of the sample for processing. Among them, a drilling tool with a diameter of 25mm was used for processing in this experiment, with a drilling depth of 170mm. Then, the sample was cased by using a wellbore with a length of 150 mm, where the open hole section was 20mm (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Experimental procedure\u003c/h2\u003e \u003cp\u003eThe simulation of in-situ stress conditions is the key to hydraulic fracturing experiments. Therefore, this experiment was conducted under normal in-situ stress conditions, i.e., vertical stress\u0026thinsp;\u0026gt;\u0026thinsp;maximum horizontal stress\u0026thinsp;\u0026gt;\u0026thinsp;minimum horizontal stress (σ\u003csub\u003eV\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;σ\u003csub\u003eH\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;σ\u003csub\u003eh\u003c/sub\u003e). In this case, the vertical stress, maximum horizontal stress, and minimum horizontal stress are 20 MPa, 15 MPa, and 10 MPa, respectively (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe fracturing fluid used in the experiment is clean water, and a green fluorescent powder is added to improve the detection ability of hydraulic fractures during the hydraulic fracturing.\u003c/p\u003e \u003cp\u003eDuring the experiment, the injection rate of fracturing fluid remained constant at 30ml/min. As the fracturing fluid is injected, the wellbore pressure continues to increase until the wellbore pressure begins to decrease, surface rocks begin to initiate, hydraulic fractures begin to propagate, and then continue to be injected until the fracturing fluid flows out and the surface rock sample is crushed. After each fluid injection and hydraulic fracturing section of the experiment, the rock blocks should be inspected to determine the propagation morphology of hydraulic fractures. After visually inspecting the rock block, use a hammer and chisel to split it open and examine the propagation pattern of internal hydraulic fractures and their interaction with natural fractures.\u003c/p\u003e \u003cp\u003eFinally, take some photos from each rock block slice and use these photos to analyze the propagation direction before, during, and after the interaction between hydraulic fractures and prefabricated natural fractures.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of experimental conditions and results obtained\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eσ\u003csub\u003eV\u003c/sub\u003e/MPa\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eσ\u003csub\u003eH\u003c/sub\u003e/MPa\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eσ\u003csub\u003eh\u003c/sub\u003e/MPa\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eResults\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003egx-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCrossing and Diversion\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003egx-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCrossing and Diversion\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003egx-3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDiversion\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003egx-4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDiversion\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Experimental observations and results","content":"\u003cp\u003eIn this study, after each hydraulic fracturing experiment on the sample, a hammer and chisel were used to open the rock block along the hydraulic fracture, and the experimental results were observed and recorded. We use acoustic emission monitoring and tracer technology to characterize the morphology of generated hydraulic fractures in two-dimensional and three-dimensional spaces. By observing and analyzing the hydraulic fracture morphology generated during the fracturing process of each sample, the following conclusions can be drawn:\u003c/p\u003e \u003cp\u003eThe fracturing fluid injection rate is 30 ml/min and the angle of approach is 90\u0026deg; (the hydraulic fracture is vertically incident on the natural fracture) when the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C\\)\u003c/span\u003e\u003c/span\u003e is 0, i.e., the gx-1 rock sample exhibits the hydraulic fracture directly crossing the natural fracture simultaneously, some of the fracturing fluids flow along the natural fracture and the natural fracture is reactivated (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). As the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C\\)\u003c/span\u003e\u003c/span\u003e increases, more and more fracturing fluid in the gx-2, gx-3 and gx-4 rock samples gradually tend to flow along the natural fractures, the natural fractures are reactivated and the ability of hydraulic fractures to cross the natural fractures directly decreases, and when the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C\\)\u003c/span\u003e\u003c/span\u003e is 0.5, i.e., all of the fracturing fluid flows along the natural fractures in the gx-3 rock samples, resulting in reactivation of the natural fractures while the direct crossing of the natural fracture behavior disappears (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn addition, according to the acoustic emission monitoring results and the post-pressure hydraulic fracture morphology analysis, it is found that during the hydraulic fracturing process, when the hydraulic fracture is not close to the natural fracture, it is easy to generate simple and straight symmetric bi-winged hydraulic fracture; when the hydraulic fracture interacts with the natural fracture, the morphology of hydraulic fracture becomes curved and complex, and the more complex the morphology of the natural fracture, the more complex is the morphology of the generated fracture network (Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) The experimental results are more consistent with the results obtained by Potluri et al.'s (Potluri et al, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2005\u003c/span\u003e) and Dehghan et al's (Dehghan et al, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) under normal ground stress.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eMany scholars have conducted extensive research on the interaction mechanism between hydraulic fractures and natural fractures and proposed the interaction criteria, and Blanton (Blanton, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1982\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1986\u003c/span\u003e), Warpinski and Teufel (Warpinski and Teufel, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e1987\u003c/span\u003e) concluded from indoor hydraulic fracturing physical modeling experiments and hydraulic fracturing mine experiments, respectively, that when a hydraulic fracture encounters a natural fracture, the hydraulic fracture can cross the natural fracture, be arrested by the natural fracture and extend along the natural fracture, depending on the angle of approach and the magnitude of horizontal principal stress difference. The hydraulic fracture may cross the natural fracture, the hydraulic fracture is arrested by the natural fracture, and the hydraulic fracture extends along the natural fracture, depending on the angle of approach and the magnitude of the horizontal principal stress difference. However, this criterion mainly focuses on the initial interaction behavior when the hydraulic fracture encounters the natural fracture and does not take into account the later interaction behavior. Potluri et al (Potluri et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2005\u003c/span\u003e) evaluated the extension of the hydraulic fracture after its interaction with the natural fracture using the method of Warpinski and Teufel׳s (Warpinski and Teufel, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e1987\u003c/span\u003e). Three main possible patterns were introduced, i.e., traversal and propagation starting from the tip of the natural fracture, as well as propagation and breakthrough at the weak points of the natural fracture surface.\u003c/p\u003e \u003cp\u003eZhou (Zhou et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) and Dehghan et al. (Dehghan et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) also observed three types of interactions between hydraulic fractures and natural fractures on an experimental basis, which is the same as that observed by Warpinski and Teufel׳s (Warpinski and Teufel, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e1987\u003c/span\u003e). Moreover, Dehghan et al. (Dehghan et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) investigated the effect of the inclination and orientation of natural fractures on the propagation of hydraulic fractures and concluded that hydraulic fractures either propagate along the direction of the maximum horizontal geostress or the height of natural fractures under normal geostress conditions. Based on this, this paper analyses the influence of the morphology change of the natural fractures on the hydraulic fracture propagation behavior when the hydraulic fracture acts vertically on the natural fracture, and finds that the hydraulic fracture is more likely to generate simple, straight, and symmetric biplane hydraulic fractures when it does not encounter the natural fracture; when the hydraulic fracture interacts with the natural fracture, the morphology of hydraulic fracture becomes curved and complex, and the more complex the morphology of the natural fracture, the more complex the generated fracture network morphology is. The more complex the natural fracture morphology, the more complex the generated fracture network morphology (Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). The findings of Potluri et al.'s (Potluri et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2005\u003c/span\u003e) and Dehghan et al's (Dehghan et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) were confirmed by the study.\u003c/p\u003e \u003cp\u003eIn addition, when the injection rate is constant and the curvature is small, hydraulic fracture and natural fracture interactions mainly show hydraulic fracture crossing the natural fracture and extending partially along the natural fracture. As the degree of curvature of the natural fractures increases (i.e., the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C\\)\u003c/span\u003e\u003c/span\u003e increases), more fracturing fluid is diverted by the natural fractures, the natural fractures are reactivated, and the phenomenon of the hydraulic fractures crossing directly through the natural fractures diminishes. Further, when the curvature of the natural fracture is 0.5, the perpendicular interaction between the hydraulic fracture and the natural fracture exhibits that the hydraulic fracture extends along the natural fracture and then along the direction of the maximum horizontal principal stress, and the phenomenon of the hydraulic fracture crossing the natural fracture disappears. Therefore, under the normal state of geostress, the injection rate of fracturing fluid is constant, and the approach angle between hydraulic fracture and natural fracture is 90\u0026deg;, when the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C\\)\u003c/span\u003e\u003c/span\u003e is less than 0.5, when the hydraulic fracture extends to the natural fracture, it mainly occurs that the hydraulic fracture crosses the natural fracture directly and the hydraulic fracture crosses the natural fracture while the natural fracture is partially activated (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e); when the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C\\)\u003c/span\u003e\u003c/span\u003e is greater than or equal to 0.5, the hydraulic fracture and natural fracture interaction presents a hydraulic fracture turning along the natural fracture (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). It can be inferred that when the injection rate is large and the approach angle between the hydraulic fracture and the natural fracture is 90\u0026deg;, the hydraulic fracture will directly cross the natural fracture when the hydraulic fracture extends to the natural fracture; keeping the angle of approach constant, with the gradual decrease of the injection rate, the hydraulic fracture gradually transforms from directly crossing the natural fracture to the hydraulic fracture crossing the natural fracture and simultaneously extending along the natural fracture. When the injection rate is constant and the approach angle is 90\u0026deg;, the hydraulic fracture gradually changes from extending along the natural fracture while crossing the natural fracture to extending only along the natural fracture as the natural fracture morphology becomes more and more curved (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C\\)\u003c/span\u003e\u003c/span\u003e increases) and finally extends along the direction of the maximum horizontal principal stress. Therefore, when hydraulic fractures act vertically on natural fractures, the fluid injection rate and natural fracture morphology play an important role in controlling the interaction between hydraulic fractures and natural fractures, which in turn affects the complexity of the generated fracture network.\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003e(1) When hydraulic fractures act vertically on natural fractures, the injection rate of fracturing fluid and the morphology of natural fractures during hydraulic fracturing play an important role in controlling the interaction behavior of hydraulic fractures with natural fractures. When the hydraulic fracture does not encounter the natural fracture, it is easier to generate simple, straight, and symmetric bi-wing hydraulic fracture; when the hydraulic fracture interacts with the natural fracture, the hydraulic fracture morphology becomes curved and complex, and the more complex the natural fracture morphology is, the more complex the morphology of the generated fracture network is.\u003c/p\u003e \u003cp\u003e(2) Other conditions remain unchanged, when the hydraulic fracture acts vertically on the natural crack, with the increase of the degree of curvature of the natural crack (curvature increase), the hydraulic fracture gradually changes from crossing the natural fracture and expanding along the natural fracture to extending only along the natural fracture, and ultimately extending along the direction of the maximum horizontal principal stress.\u003c/p\u003e \u003cp\u003e(3) Other conditions remain unchanged, when the hydraulic fracture acts perpendicularly on the natural fracture, with the decrease in the injection rate of fracturing fluid, the hydraulic fracture gradually changes from directly crossing the natural fracture to crossing the natural fracture and turning along the natural fracture simultaneously.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eConceptualization, Jin Zhijun, Ma Xinhua,Gong Xun ; Formal Analysis, Gong Xun and Liu Yuyang; Resources, Jin Zhijun, Ma Xinhua, and Liu Yuyang; Data Curation, Gong Xun; Writing-Original Draft Preparation, Gong Xun; Writing-Review \u0026amp; Editing, Jin Zhijun, Ma Xinhua, Liu Yuyang, Li Guanfang; Visualization, Gong Xun; Supervision, Jin Zhijun, Ma Xinhua, Liu Yuyang, Li Guanfang; Project Administration,Ma Xinhua and Liu Yuyang.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThis study was funded by the Project of R\u0026amp;D Department of Petrochina (No. 2021DJ2005 and No. 2021DJ2005).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBakhshi E, Rasouli V, Ghorbani A, et al. 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Computers and Geotechnics; 2021;135: 104165.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Hydraulic fracturing, Natural fracture, Injection rate, Curvature","lastPublishedDoi":"10.21203/rs.3.rs-4403407/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4403407/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe interaction mechanism between hydraulic fractures and natural fractures has been the focus of hydraulic fracturing research. To reveal the influence mechanism of natural fractures with different curvatures on hydraulic fracture propagation during the fracturing process, this study simulated the hydraulic fracture propagation patterns under natural fractures with different curvatures by carrying out large-size true triaxial hydraulic fracturing physical modeling experiments on artificial rock samples prefabricated with different curvatures of fractures. Results show that the injection rate of fracturing fluid and the curvature of natural fractures have important effects on the interaction between hydraulic fractures and natural fractures. When the approximation angle (the angle between the hydraulic fracture and the natural fracture) is 90\u0026deg;, with the gradual decrease of the fracturing fluid injection rate, the interaction between the hydraulic fracture and the natural fracture shows that the hydraulic fracture passes through the natural fracture directly, and gradually changes to the hydraulic fracture passes through the natural fracture and also extends along the natural fracture, and then in the end, only hydraulic fracture extends along the natural fracture occurs. When the injection rate is constant and the approximation angle is 90\u0026deg;, with the curvature of the natural crack gradually increasing (increasing curvature), the interaction between the hydraulic fracture and the natural fracture shows that the hydraulic fracture passes through the natural fracture and also partially extends along the natural fracture, and gradually changes to the hydraulic fracture extending only along the natural fracture, and then finally extends along the direction of the maximum horizontal principal stress. The results of the study are instructive for revealing the interaction mechanism between hydraulic fractures and natural cracks.\u003c/p\u003e","manuscriptTitle":"Experimental study of the effect of natural fracture curvature on hydraulic fracture propagation behavior","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-05-23 10:45:28","doi":"10.21203/rs.3.rs-4403407/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d17ace9a-475a-49d6-a35f-92822c986ab4","owner":[],"postedDate":"May 23rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-05-24T22:08:28+00:00","versionOfRecord":[],"versionCreatedAt":"2024-05-23 10:45:28","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4403407","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4403407","identity":"rs-4403407","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}