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Hydraulic fracturing initiation and near-wellbore nonplanar propagation from horizontal perforated boreholes in tight formation
Journal of Natural Gas Science and Engineering 55 (2018) 337–349
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Hydraulic fracturing initiation and near-wellbore nonplanar propagation from horizontal perforated boreholes in tight formation
T
Ruxin Zhang, Bing Hou∗, Qinglin Shan, Peng Tan, Yue Wu, Jie Gao, Xiaofeng Guo State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Perforated fracturing True triaxial experiment Fracture initiation Perforation parameter optimization Near-wellbore geometry
Tight formations, which are rich in reserves in China, have a high economic development value. Perforated fracturing would need to be used widely to exploit these formations because of reservoir characteristics such as low permeability, low porosity and high density, resulting in high fracture pressure, limited fracture propagation, and complex fracture geometry. To address these issues, the mechanism of fracture propagation under different construction conditions must be understood and described. Therefore, the effect of different perforation parameters (shot density, shot length, shot diameter, shot phase, and shot interval spacing) and different horizontal stress contrasts on fracture geometry, initiation, and propagation from perforated horizontal wells in tight formations is studied based on numerous triaxial hydraulic fracturing simulation experiments. Three types of fracture geometry are observed in these experiments: A single flat fracture can be created by an initiated perforation or more initiated perforations with good connectivity, spiral-shaped fractures are generated by a large perforation diameter or high perforation density, and multiple-parallel fractures are induced by a high perforation phase. Moreover, each fracture type has certain pressure behaviors corresponding to a fracture curve shape. The perforations are likely to initiate when the angle between the perforation and maximum horizontal stress is small, and the initiation position is most likely at the base of the perforation. It is difficult to predict the initiation order of perforations; however, the first initiated perforation can be ensured by the profile of the relief pressure. In addition, a higher horizontal stress contrast value results in more initiated perforations, lower fracture pressure, and shorter breakage time. Ultimately, a large perforation diameter, high perforation density, and perforation phase of 60° should be chosen for fracturing at low fracture pressure and simple fracture geometry in tight formations.
1. Introduction With the development of oil and gas exploration and exploitation, significant attention has been paid in recent years to unconventional reservoirs, such as tight reservoirs, shale gas reservoirs, and coalbed methane reservoirs. Tight formations have rich reserves and are deeply buried in China. However, it is difficult to exploit them without employing auxiliary processes owing to features such as high density, low permeability, low porosity, and high temperature (Hou et al., 2017). Perforation fracturing has been a valuable technique to stimulate these tight reservoirs. The perforations afford a channel between the wellbore and the reservoir for guiding oil flow to improve production (Feng and Gray, 2017). Behrmann and Elbel (1991) revealed that the fracture initiation position was at the base of the perforations or at the intersection of the plane normal to the minimum horizontal stress when fracturing with a 180° perforation phase in a vertical well. Abass et al. (1992) highlighted that perforation initiation was easier when the ∗
perforation angle with respect to the maximum horizontal stress was smaller. Moreover, Abass et al. (1994) proved that the oriented perforation could induce a single wide fracture and control sand production. Nevertheless, perforated fracturing faces numerous issues such as premature screen-outs, low linkup between the borehole and reservoir, high treatment pressure, high fracture tortuosity, and the occurrence of multiple fractures. Daneshy (1973a) was the first to determine that the perforations had an impact on fracture morphology and fracturing pressure. The perforated fracturing generated more complex fractures and a higher fracture pressure than in an open hole. Brumley and Abass (1996) claimed that nonplanar fractures and complex fractures resulted in premature screen-outs, high friction near the wellbore, and high treatment pressure when the wellbore orientation with respect to the in situ horizontal stress was different. Veeken et al. (1989) found that limited entry effects occurred because of poor communication between the wellbore and hydraulic fracture or the existence of multiple
Corresponding author. College of Petroleum Engineering, China University of Petroleum, Beijing 102249, China. E-mail address: [email protected] (B. Hou).
https://doi.org/10.1016/j.jngse.2018.05.021 Received 5 September 2017; Received in revised form 10 April 2018; Accepted 13 May 2018 1875-5100/ © 2018 Elsevier B.V. All rights reserved.
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test frame surrounded by pressurizing pistons that add pressure around and at the bottom of the sample. They are of the same size as the sample's surface to guarantee uniform pressure, which is controlled by adjustable hydraulic pressure with a maximum pressure output of 30 MPa. Meanwhile, the top of the sample was covered by a steel plate to simulate the in-situ stress. The injection power was supported by an MTS 816 servo booster with a maximum injection pressure of 140 MPa, and the maximum injection volume was 800 mL.
fractures. One of these issues might have a significant impact on other issues and more than one issue might originate from some common sources, which complicates the overall problem (Abass et al., 1994; Hossain et al., 2000). However, the above problems can be solved by rational design of perforated fracturing, which has proven effective for fracture initiation when the perforations are in phase with the anticipated fracture direction (Behrmann and Elbel, 1991). In addition, an effective and reasonable perforation parameter design could yield more initiated perforations and reduced complex fracture geometry and fracture pressure to improve the fracturing effect. Several laboratory experiments and numerical simulations on the effect of perforation parameters on fracture initiation and propagation have been performed in the past. Veeken et al. (1989) proposed a formula to predict the number of initiated perforations. They assumed that a large perforation diameter, high perforation density, or large perforation depth would increase the number of initiated perforations and enhance the connection among fractures. A single fracture with a minimum tortuosity at an achievable fracture initiation pressure is desired. Behrmann and Nolte (1998) indicated that short perforation length and high perforation density could yield more perforations to initiate and cause more fractures to link up, which could reduce the fracture tortuosity and prevent the occurrence of multiple fractures. Poor connection among fractures is observed when the perforation phase is high. In particular, induced fractures were not linked when perforation phase was 90°, resulting in multiple fractures. Furthermore, van de Ketterij and de Pater (1997) showed that small perforation spacing facilitated fractures connecting with each other to reduce fracture complexity. Most of the above experimental research on perforated fracturing focused on the effect of perforation orientation, perforation phase, and fracturing fluid viscosity and injection rate on fracture initiation, geometry, and pressure. However, other perforation parameters, such as perforation density, perforation diameter, perforation length, were discussed from the aspect of numerical simulation in most cases rather than through experiments. Furthermore, several numerical simulations focused on the effect of perforation parameters on fracture broken pressure or initiation pressure rather than the fracture initiation method and fracture geometry. Hossain et al. (2000) established a prediction model of fracture pressure to discuss the effect of perforation azimuth. Fallahzadeh et al. (2010) demonstrated that perforation orientation had an impact on fracture initiation pressure in a deviated borehole. Quattlebaum et al. (2012) confirmed that the actual diameter of each perforation and the differences in perforation diameter size had an impact on the fracture pressure by using a finite element method. In the meantime, Alekseenko et al. (2012) studied the effect of perforation orientation, perforation length, perforation diameter, and perforation shape on fracture initiation and fracture pressure with the boundary element method. Therefore, in this work, we conducted a large-scale true triaxial hydraulic fracturing simulation experiment to study the effect of different perforation parameters (shot density, shot length, shot diameter, shot phase, and shot interval spacing) and different horizontal stress contrast values on fracture initiation, geometry, and pressure from perforated horizontal wells in tight formations. Finally, the experimental results could offer a theoretical basis for optimizing perforation parameters and putting forward some suggestions about perforated fracturing operations in tight formations.
2.2. Wellbore design The horizontal wellbores were made of steel pipe, composed of a wellhead and a chamber. The wellhead had a length of 30 mm, an outer diameter of 16 mm, and an inner diameter of 10 mm. The chamber had a length of 230 mm, an outer diameter of 14 mm, and an inner diameter of 10 mm. All wellbores had uniform size specifications. Some holes were drilled with a spiral distribution in the steel pipe and paper tubes were inserted to simulate perforations. The perforation interval was ensured to be the middle of the chamber. Four wellbores were made with different shot diameters, shot densities, shot phases, and shot interval spacings according to the experimental scheme requirements. Furthermore, different shot lengths were simulated by different lengths of paper tubes. In addition, some grooves were cut between the bottom of wellhead and the first perforation to avoid channeling. Then, each perforation was numbered clockwise from the top to bottom of the wellbore as shown in Fig. 2. For example, 1-1 represented the first perforation of the first perforation interval, and 2–6 represented the sixth perforation of the second perforation interval. 2.3. Rock sample preparation The tests were conducted in blocks of hydrostone, measuring 300 mm × 300 mm × 300 mm. No cementing material was used between the wellbore and the rock. The wellbore was placed at the middle position inside the mold. Hydrostone, which was mixed with cement (model 325) and quartz sand (20–40 M) in a constant mass ratio of 1:1, was then poured around the wellbore to form the sample as shown in Fig. 3. This is a more robust way to bond the wellbore and rock (Daneshy, 1973a,b). In the meantime, the mold was struck by a hammer for a while to reduce bubbles inside the sample. The artificial samples were placed in a dry environment for half a month to air for developing adequate strength. The rock mechanics test and permeability test were performed by TAW-100 testing (Ge et al., 2010; Jin et al., 2011) to measure the parameters listed in Table 1. 2.4. Experimental scheme The experimental scheme was set by using a similarity criterion (Guo et al., 2016) according to the field data. The experiments were divided into three groups. Experiments in the first group (1-1 – 1-6) were conducted to study the effect of different spiral perforation parameters on fracture initiation, fracture propagation, and fracture pressure in the normal-faulting stress regime (in which the vertical stress was 30 MPa, the maximum horizontal stress was 24 MPa, and the minimum horizontal stress was 21 MPa). Experiments in the second group (2-1 – 2-4) were conducted for examining the influence of the horizontal stress contrast on fracture initiation, fracture propagation, and fracture pressure in another normal-faulting stress regime (in which the vertical stress was 30 MPa, the maximum horizontal stress was 27 MPa, and the minimum horizontal stress was 19 MPa). Furthermore, the third group experiment (3-1) was carried to investigate the horizontal stress contrast influencing (in which the vertical stress was 30 MPa, the maximum horizontal stress was 25 MPa, and the minimum horizontal stress was 13 MPa). The concrete experimental plan is given in Table 2. Guar with a viscosity of 3 mPa s was used as the fracturing fluid in
2. Experimental process and scheme 2.1. Experimental equipment The experiments were performed in a true triaxial pressure machine. The specific apparatus includes a true triaxial test frame, a triaxial hydraulic voltage source, an oil–water separator, an MTS pressurization controller, and a data acquisition and processing system as shown in Fig. 1. The 300-mm cubic model block was placed in the 338
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Fig. 1. Experimental equipment and flowchart (Tan et al., 2017).
these experiments. The fracturing fluid was injected at a rate of 60 ml/ min through the wellbore into the sample. Meanwhile, some fluorescent tracers were added to the fracturing fluid for better observation of the induced hydraulic fractures. The in-situ stress loading direction as shown in Fig. 4 was used to stimulate fracturing in the horizontal well.
Therefore, the main hydraulic fractures could be divided into three categories: single flat fractures, spiral-shaped fractures, and multipleparallel fractures. The resulting description of each sample is given in Table 3.
3.1. Fracture geometry 3. Experimental results and interpretation 3.1.1. Single flat fractures An ideal perforation for fracture initiation would create only a single fracture with minimum tortuosity (Behrmann and Nolte, 1998). It could be created when a single perforation initiated and propagated along the direction of the maximum horizontal stress, such as test 1-1 and test 1–2. In addition, a single fracture with minimum tortuosity could also be formed when more perforations are initiated with good connection and fractures overlap as in test 2-1. To observe the fracture morphology vividly and objectively, fracture morphology was reconstructed in a three-dimensional space as shown in Fig. 5. However, because the probability of each initiated perforation is random, it was difficult to interpret the number of initiated perforations that occurred during fracturing. Further, it was difficult to identify the connections among initiated perforations and overlapping ones among fractures during fracture propagation. A single flat fracture is desired,
After fracturing, each sample was opened carefully along the induced hydraulic fracture and split slowly into two part by a hammer and chisel, without any additional sectioning on crack surface, to observe fracture initiation characteristics and the form of propagation. All hydraulic fractures were transverse fractures that propagated along the maximum horizontal principal stress direction (perpendicular to the wellbore) in our experiments. These fracture morphologies were consistent with the existing understanding that hydraulic fractures always initiate perpendicular to the direction of the minimum principal stress and propagate along the direction of maximum horizontal stress (Hou et al., 2014; Feng et al., 2016). However, owing to the different perforation parameters and different horizontal stress contrast values, the induced fractures were not always a single, planar main fracture with minimum tortuosity. Nonplanar fractures appeared in the experiments.
Fig. 2. Schematic of wellbore design. a. Photograph of real wellbore to show wellbore design, including wellhead and chamber. The size of each part is marked on the image. Perforations are simulated by paper tubes. b. Schematic of the distribution of perforation positions on the wellbore and the serial number of each perforation. 339
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Fig. 3. Schematic of artificial rock sample fabrication process. a. Schematic of a wellbore inserted inversely into the middle of the mold. b. Schematic of a sample cast process. All samples were made by using this process.
strongly, resulting in a large overlapping area. Ultimately, these fractures would become one main fracture propagating along the direction of the maximum horizontal stress to the sample edge. In addition, the spiral amplitude of sample 1–4 was larger than that of sample 1–3. Because the vertical distance between the first initiated perforations and the last initiated perforations was greater in sample 1–4 (five initiated perforations) than in sample 1–3 (only three initiated perforations), as shown in Fig. 6. Sample 2-2 also had a spiral-shaped fracture with a large spiral amplitude. The area and boundary of three induced fractures were observed, as shown in Fig. 6. Two reasons could account for this fracture geometry. High density could explain why the fractures had tortuosity rather than being multiple parallel. High density shortened the spacing between each adjacent perforation to enhance interaction between initiated fractures. Each induced fracture tended to overlap and form a main fracture. However, the high horizontal stress contrast (8 MPa) shortened the time fractures interacted and linked up with each other. Induced fractures propagated independently along the direction of the maximum horizontal stress. This phenomenon was also found in the study of van de Ketterij and de Pater (1997). Behrmann and Elbel (1991) had claimed that fractures had more time to initiate and interact at lower stress levels. Therefore, under the influence of these two factors, a large spiral amplitude fracture was generated with obvious boundaries of three fractures.
Table 1 Mechanical parameters of the artificial sample. Parameter
Value
Units
Elasticity Modulus Poisson's Ratio Compressive Strength Tensile Strength Permeability Porosity
7.86 0.2 20.89 1.53 0.1 1.54%
GPa – MPa MPa mD –
but its creation is not always possible, and nonplanar fractures were normally induced in many cases.
3.1.2. Spiral-shaped fractures Spiral-shaped fractures might be created in helix perforated fracturing with a large shot diameter or high shot density. These spiralshaped fractures are always regarded as the cause of high fracture pressure, high friction near the wellbore, or premature screen-outs. Sample 1–3 showed that three perforations acted as the fracture initiation source and a spiral-shaped fracture was created in helix perforated fracturing with a large shot diameter (4 mm). Each fracture propagated away from the wellbore to the sample edge. Fractures interacted with each other and some parts overlapped to form a main fracture with a spiral shape as shown in Fig. 6. Sample 1–4 showed that a spiral-shaped fracture was induced from five initiated perforations in helix perforated fracturing with a high shot density (18 holes/cm). It was difficult to identify the area and boundary of each fracture, because these fractures communicated and connected
3.1.3. Multiple-parallel fractures Multiple-parallel fractures also appeared in helix perforated fracturing owing to high shot phase, such as in samples 1–5 and 2–3. More initiated perforations with poor connection in horizontal or deviated
Table 2 Hydraulic fracture spiral perforation experimental scheme. Test
Shot Length (cm)
Shot Diameter (mm)
Shot Density (holes/cm)
Shot Phase (°)
Shot Interval Spacing (cm)
σv (MPa)
σH (MPa)
σh (MPa)
1–1 1–2 1–3 1–4 1–5 1–6 2–1 2–2 2–3 2–4 3–1
3 4 3 3 3 3 3 3 3 3 3
2 2 4 2 2 2 2 2 2 2 2
12 12 12 18 12 12 12 18 12 12 12
60 60 60 60 90 60 60 60 90 60 60
2 2 2 2 2 4 2 2 2 4 2
30 30 30 30 30 30 30 30 30 30 30
24 24 24 24 24 24 27 27 27 27 25
21 21 21 21 21 21 19 19 19 19 13
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addition, he found another initiated position of perforations at the intersection of the plane normal to the minimum horizontal stress that passes through the axis of the wellbore and the wellbore surface in the vertical well. However, this phenomenon could not be found, because the experiments conducted in this study were for a horizontal well in which all fractures were transverse fractures perpendicular to the wellbore. Second, perforations initiated depend on the size of the angle between the perforation direction and the maximum horizontal stress direction. Daneshy (1973a,b) was the first to establish this rule. He pointed out that 0° was the best angle for perforations to initiate and that 90° was the worst angle. The fractures may be initiated from all shots only when the angle was ≤10° (Behrmann and Elbel, 1991). In addition, Abass et al. (1992) summarized that the initiation pressure increased with angle by taking eight types of angle into consideration. This rule was applicable to our experiments as well; that is, perforations were easier to initiate when the angle was smaller. The angle of the initiated perforations ranged from 20° to 60°. Third, it was difficult to ensure the perforation initiation order. Whereas, Abass et al. (1992) proposed that the profile of the relief in pressure (RIP) could provide useful information to ensure that the wellbores were in phase or out of phase relative to the fracture direction, he pointed out that the pressure in the RIP region was a function of the angle between the wellbore direction and the maximum horizontal stress direction. The angle increased, resulting in the slope of the pressure immediately declining as shown in Fig. 8. The treatment pressure declined slowly and smoothly when the angle increased. Brumley and Abass (1996) claimed that the larger wellbore orientations yielded a smaller rate and a smaller magnitude of RIP. Further, the angle between each perforation direction and the maximum horizontal stress direction can be regarded as the angle between the wellbore direction and the maximum horizontal stress direction, as shown in Fig. 9. Therefore, the RIP region of the fracture curve could be used to ensure the perforation initiation order of each sample. Samples 1-1 and 1–2 were not analyzed because they only had one initiated perforation. Hence, sample 2-1 was chosen as an example. Two sharp points are observed in the curve, as shown in Fig. 10. The slope of the first sharp point was lower than that of the second sharp point (i.e., the angle of the first sharp point was greater than that of the second sharp point). Therefore, perforation 1–2 with an angle of 90° initiated earlier than perforation 1–3 with an angle of 30°, as shown in Fig. 5. However, problems arose when the rest of samples were analyzed using this rule. Fracture curves for samples 1–3, 1–4, 1–5, 1–6, 2-2, and 2–4 were more complex than those for samples 2-1 and 2–3. The large degrees of fluctuations of the curve resulted in many sharp points owing to the fracturing fluid flowing with high friction in uneven nonplanar fractures, the existence of a pressure-out phenomenon, and the dominating fracture opening and closing frequently (Zhou et al., 2010). It is difficult to identify which one represented the initiated perforation. Although the perforation initiation order was difficult to ascertain, the first initiated perforation can be identified from the fracture curve according to the RIP profile. Conversely, fracturing pressure is defined as the time at which the treatment pressure reaches its maximum value. However, fracture initiation typically occurs before this breakdown point (Lhomme, 2005; Fallahzadeh et al., 2015). Therefore, the first sharp point of the fracture curve must represent the point at which the breakdown of rock and perforation has initiated. The first initiated perforation of each sample can then be inferred based on the RIP profile of the first sharp point in the fracture curve, as given in Table 4. RIP region analysis is a practical and effective method to recognize the first initiated perforation and the order of perforation initiation when the fracture curve is simple. However, it remains a difficult task to determine the specific order of perforation initiation when the fracture curve is complex. Additional studies are needed to optimize this method.
Fig. 4. Schematic of the in-situ stress direction. The direction of the minimum horizontal principal stress is loaded along the direction of the wellbore to simulate horizontal well fracturing. Table 3 Hydraulic fracture spiral perforation experimental results. Sample Number
Initiated Shot Number
Fracture Pressure (MPa)
Fracture Shape
1–1 1–2 1–3 1–4 1–5 1–6 2–1 2–2 2–3 2–4
1 1 3 5 2 2 2 3 3 5
22.46 18.7 24.89 26.57 25.82 26.45 21.4 18.7 22.27 24.8
3–1
2
14.3
A single flat fracture A single flat fracture Spiral-shaped fracture Spiral-shaped fracture Multiple-parallel fracture Multiple-parallel fracture A single flat fracture Spiral-shaped fracture Multiple-parallel fracture Multiple-parallel fracture + a single flat fracture Multiple-parallel fracture
well fracturing could be a cause of forming such multiple-parallel fractures (e.g., sample 1–6). This fracture geometry should be responsible for a narrow fracture width near the wellbore, resulting in difficulty in adding sand, high fracture pressure, and high friction near the wellbore (Abass et al., 1992; Behrmann and Nolte, 1998). Both samples with a shot phase of 90° in our experiments (samples 1–5 and 1–6) showed that multiple-parallel fractures were created from two or three adjacent initiated perforations. These fractures propagated from their initiated position to the sample edge along the maximum horizontal stress direction without any interaction and linkup, as shown in Fig. 7 van de Ketterrij and de Patter (1997) also found that the probability of linkup among fractures was restricted when the shot phase was 90°. Furthermore, wall waviness or roughness was observed on the fracture surface.
3.2. Perforation initiation characteristics Some characteristics of perforation initiation were obtained based on the above experimental results. First, the fractures almost initiated at the base of the perforations. The fracturing fluid was always distributed along the base of the initiated perforations and then extended along the direction of perforation in our experiments. This phenomenon could prove our viewpoint about the position of perforation initiation. Behrmann obtained the same experimental results in 1991 and 1998. In 341
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Fig. 5. Single flat fracture induced with different perforation parameters under different horizontal stress contrast values. a. Schematic of a single flat fracture shape of sample 1-1 in three dimensions to improve understanding of the fracture shape. b. One perforation initiated to form a single flat fracture under conventional perforation parameters and a horizontal stress contrast of 3 MPa c. A single flat fracture induced with one perforation initiation under a perforation length of 4 cm and a horizontal stress contrast of 3 MPa d. Two perforations initiated to form a single main fracture under conventional perforation parameters and a horizontal stress contrast of 8 MPa.
fracture pressure and shortened the initiation time effectively, as shown in Fig. 12. Because the pressure-out phenomenon disappeared and the fracturing fluid flowed with less friction in the smooth fracture surface, fractures could propagate quickly with less friction from the sample edge. Therefore, the main reason for different fracture pressure in our experiments was the co-effect of two factors: perforation parameters and horizontal stress contrast. In addition, traditional theoretical models (Haimson and Fairhurst, 1967; Hossain et al., 2000) were not applied well to calculate fracture pressure of our experiments. Many scholars indicated that the calculation result was not consistent with the experimental result (Zoback et al., 1977; Guo et al., 1993; Morita et al., 1996). Because fracture pressure was not only controlled by in-situ stresses, but also dependent on Young's modulus of the formation, wellbore size and type of the drilling fluids (Zhang et al., 2018). Too many factors had an impact on fracture pressure, resulting in difficulty prediction. Future work was required to modify and improve the theoretical model, considering the effect of multiple factors, such as perforation parameters, fluid viscosity, pump rate.
3.3. Fracture curve The treatment pressure responses were different under different fracturing conditions, as shown in Figs. 11 and 12. With a low horizontal stress contrast, the fracture pressure was high and the initiation time was long (comparing samples 1-1 to 1–6 with samples 2-1 to 2–4). The increase in perforation length leaded to low fracture pressure (comparing sample 1–2 with sample 1-1). The result was consistent with the study result of Alekseenko et al. (2012). The increase of the perforation length decreased fracture initiation pressure in the case of highly misaligned perforations. However, the increase in perforation diameter or density resulted in high fracture pressure and long initiation time (comparing samples 1–3 and 1–4 with sample 1-1), as shown in Fig. 11, which was supposed to reduce the fracture pressure and shorten the initiation time (Daneshy, 1973a; Behrmann and Elbel, 1991). This abnormal phenomenon was a result of many factors. For instance, the existence of pressure-out phenomenon during the process of fracture propagation would raise the treatment pressure; fracturing fluid flows in uneven nonplanar fracture could lead to high fluctuation of treatment pressure; and breakdown pressure could be higher for increased tunnel numbers with a low horizontal stress contrast (Liu et al., 2016). A high horizontal stress contrast, whereas, reduced the 342
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Fig. 6. Spiral-shaped fracture induced with different perforation parameters under different horizontal stress contrast values. a. Schematic of a spiral-shaped fracture shape of sample 1–3 in three dimensions to improve understanding of the fracture shape. b. Three perforations initiated to form a spiral-shaped fracture under a perforation diameter of 4 mm and a horizontal stress contrast of 3 MPa c. Five perforations initiated to generate a spiral-shaped fracture of small tortuosity under a perforation density of 18 holes/cm and a horizontal stress contrast of 3 MPa d. Three perforations initiated to form a spiral-shaped fracture of large tortuosity under a perforation density of 18 holes/cm and a horizontal stress contrast of 8 MPa.
4. Discussion
density or perforation diameter shortened PS. Moreover, the decrease in PS was conducive to induce more initiated perforations and improve connection among fractures to reduce fracture complexity and fracture pressure. Therefore, several initiated perforations formed a main fracture rather than an initiated perforation with a main fracture (comparing samples 1–3 and 1–4 with sample 1-1). However, the increase in perforation phase increased PS. Poor connection among induced fractures resulted in fractures propagating independently, forming multiple-parallel fractures (comparing sample 1–5 with sample 1-1). The change in perforation length and perforation interval spacing had no impact on PS; therefore, the fracture shape was the same as that of sample 1-1. 2) A single flat main fracture with minimum tortuosity at an achievable fracture initiation pressure was desired (Behrmann and Nolte, 1998), but multiple-parallel fractures and spiral-shaped fractures were created in most cases, resulting in a narrow fracture width, high friction near the wellbore, difficulty in adding sand, premature screen-out, and high fracture pressure (Abass et al., 1992; Surjaatmadja et al., 1994; Behrmann and Nolte, 1998). However, low fracture pressure, many initiated perforations, and simple fracture geometry could be a result of perforated fracturing with optimized perforation parameters. The increase in perforation
1) The change in perforation parameters causes different fracture geometries and fracture pressures. However, the mechanism of this change remains unclear. An interesting phenomenon was observed when we tried to identify this mechanism. To clarify it, two adjacent perforations were taken as a two-dimensional simplified model, as shown in Fig. 13. Here, the vertical distance between two perforation centers is L1, the horizontal distance between two perforation centers is L 2 , and the diameter of the perforation is defined as d . L1 decreased as the perforation density increased, L 2 increased as the perforation phase increased, and d increased as the perforation diameter increased. However, the perforation length and perforation interval spacing did not change with changes in the above three factors. Different perforation parameters affect different factors, but all were related to perforation spacing (PS). PS was defined as the distance between A and B, as shown in Fig. 13; therefore, the change in perforation parameters could be converted into the influence on PS. Yew et al. (1999) also revealed that two induced fractures, initiated from two adjacent perforations, influenced each other during propagation process. The influence degree was depended on the distance of two adjacent perforations. The increase of perforation
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Fig. 7. Multiple-parallel fracture induced with different perforation parameters under different horizontal stress contrast values. a. Schematic of a multiple-parallel fracture shape of sample 1–5 in three dimensions to improve understanding of the fracture shape. b. Two perforations initiated to form a multiple-parallel fracture under a perforation phase of 90° and a horizontal stress contrast of 3 MPa c. Two perforations initiated to form a multiple-parallel fracture under a perforation cluster spacing of 4 cm and a horizontal stress contrast of 3 MPa d. Three perforations initiated to form a multiple-parallel fracture under a perforation phase of 90° and a horizontal stress contrast of 8 MPa.
Fig. 8. Schematic of the relationship of pressure decline after breakdown and angle (Abass et al., 1992). a. Results of qualitative analysis showing that different angles between wellbore direction and the maximum horizontal stress direction have different RIP profiles. b. Results of quantitative analysis showing that the angle increase results in the slope of the pressure immediately declining. 344
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Fig. 9. a. Schematic showing different angles between different wellbore orientations and the direction of the maximum horizontal stress. b. Schematic showing how a perforation can be regarded as a wellbore by changing the direction of in situ stress.
density generated different results under different horizontal stress contrast values. The fracture surface exhibited small tortuosity but high fracture pressure under a horizontal stress contrast of 3 MPa. However, the fracture surface exhibited large tortuosity but low fracture pressure under a horizontal stress contrast of 8 MPa (comparing sample 2-2 to sample 2-1). Therefore, to reduce the fracture pressure rather than the fracture tortuosity, low perforation density should be used under low horizontal stress contrast and high perforation density should be used under high horizontal stress contrast. In contrast, if we focus on fracture tortuosity rather than fracture pressure, high perforation density should be used under low horizontal stress contrast and low perforation density should be used under high horizontal stress contrast. However, high perforation density would result in casing damage by compromising casing strength. Moreover, a large perforation diameter was the best choice for perforated fracturing. It not only reduced fracture pressure but also decreased perforation friction. The size and concentration of the proppant also depend on the size of the perforation diameter, because large perforation diameter could prevent bridge blinding of proppant near the perforation hole (Li et al., 1998). Furthermore, a small tortuosity fracture with a large drainage area was induced by a
Table 4 First initiated perforation of each sample. Sample Number
First Initiated Perforation
Angle (°)
1–3 1–4 1–6 2–2 2–3
2–3 2–8 2–4 2–6 Three shots initiated at the same time
60 20 40 0 0, 60
The angle was between the perforation direction and the maximum horizontal stress direction.
large perforation diameter in sample 1–3. However, a high perforation phase induced multiple-parallel fractures easily under low or high horizontal stress contrasts (samples 1–5 and 2–3). These results agree with those of Daneshy (1973a,b) and Behrmann and Nolte (1998). van de Ketterij and de Patter (1997) also assumed that it was difficult for fractures to connect with each other when the perforation phase was 90°. A perforation phase of 60° was the optimal phase for perforated fracturing because this phase could ensure that most perforations had a suitable angle with respect to the
Fig. 10. Fracture curve of sample 2-1. Left panel. Two sharp points can be seen inside the fracture curve. Right panel. Enlarged area to observe more clearly the two angle values and the slope of each sharp point. 345
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maximum horizontal stress direction for initiation (Daneshy, 1973a,b; Abass et al., 1992). In addition, the fracture pressure of the perforation phase with 45° or 60° was lower than that of the perforation phase with 90° or 120° when perforated fracturing was employed in the Yuanba gas field, Sichuan Basin (Tang, 2015). However, the increase in perforation length or perforation interval spacing had negligible effect on fracture geometry in our experiments. This result is consistent with the viewpoint of Yew and Li (1987). Therefore, based on the effect of perforation on casing strength, on-site engineers should adopt high perforation density, large perforation diameter, and low perforation phase for fracturing. Li et al. (1998) claimed that perforated fracturing was improved when the perforation density of 18 holes/m and perforation phase of 90° were changed to 20 holes/m and 45°, respectively. Another field example of horizontal wells in southeast Sichuan, China, verifies this result. The in-situ stresses of target formation were σV = 110.12 MPa, σH = 124.53 MPa, and σh = 101.27 MPa and the pore pressure was Pp = 76.67 MPa. Two horizontal wells were drilled along the minimum horizontal stress and perforated with a perforation phase of 60°. Slick water was injected at a low pump rate at first for approximately 1 h and then at a high pump rate of 10–11 m3/min, as shown in Fig. 14. A horizontal well with a perforation density of 16 holes/m and a perforation diameter of 10 mm had a high treatment pressure and low sand concentration, resulting in a poor fracturing effect. However, a large perforation diameter of 14 mm and a high perforation density of 22 holes/m were adopted for fracturing in another horizontal well, leading to a low treatment pressure and a high sand concentration, as shown in Fig. 14. Because small tortuosity fracture or planar fracture was induced by large perforation diameter and high perforation density, the fracturing fluid flowed with less friction along this fracture surface, resulting in low treatment pressure. Moreover, proppants entered into the induced fractures easily owing to the fracture geometry. 3) One key point in the fracture curve is the sharp point. It reflects perforation initiation patterns: only one sharp point indicates that perforations initiate at the same time; more than one sharp point indicates a sequence. Furthermore, the perforation initiation order could be inferred by analyzing its slope (RIP region). Another key point is the fracture curve shape, which corresponds to the fracture geometry in our experiments, as shown in Fig. 15. A single flat fracture has an even and smooth surface with less friction, resulting in the fracture propagating quickly to the sample edge. Therefore, the fracture curve shape is simple, with the pressure dropping fast and the extension pressure being smooth without any fluctuation, as seen with samples 1-1, 1–2, and 2-1. Nevertheless, the fracture curve shape of spiral-shaped fractures has a large degree of fluctuation. Fractures interact and overlap with each other to form a main fracture, opening and closing frequently (Zhou et al., 2010), and fracturing fluids flow in this uneven spiral fracture surface with high friction, leading to extension pressure fluctuation. The above two reasons caused the complex shape of the fracture curves, as seen in samples 1–3, 1–4, and 2-2. In addition, multiple-parallel fractures have planar fracture surfaces but are not smooth. Wall waviness was observed on the fracture surface. Fracturing fluids flowed under rough surfaces, resulting in small extension pressure fluctuation. Consequently, the fracture curves exhibited a small degree of fluctuation, as seen in samples 1–5, 1–6, and 2–4. This corresponding relationship between fracture geometry and the fracture curve was summarized qualitatively by our experiments in tight formations. It was difficult to quantize this relationship owing to the many factors that could affect the fracture curve. Whether this relationship can be applied to other heterogeneous formations, such as shale formations with beddings and natural fractures, requires further studies in the future. 4) The horizontal stress contrast has a crucial and decisive impact on fracture geometry and fracture pressure. High horizontal stress
Fig. 11. Fracture curve for each sample under a horizontal stress contrast of 3 MPa.
Fig. 12. Fracture curve for each sample under a horizontal stress contrast of 8 MPa.
Fig. 13. Two-dimensional simplified model of two adjacent perforations. The vertical distance between two perforation centers is labeled L1, the horizontal distance between two perforation centers is labeled L2, and the diameter of the perforation is defined as d.
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Fig. 14. Fracture curves for different perforation sections with different perforation parameters. a. Fracture curve with a perforation diameter of 10 mm and a perforation density of 16 holes/m. b. Fracture curve with a perforation diameter of 14 mm and a perforation density of 22 holes/m.
under high horizontal stress contrast. The low treatment pressure would be gained during perforated fracturing operation.
contrast promotes more perforations to initiate and induce fractures to propagate faster and farther, whereas it shortens the connection time of fractures, resulting in fractures independently propagating without connection and overlapping, as shown in Fig. 16. Multipleparallel fractures or a single fracture with a smooth fracture surface are more likely generated in the case with unchanged PS, such as samples 2-1, 2–3, 2–4, and 3-1. If PS decreased, a spiral-shaped fracture with a large spiral amplitude might be induced under a high horizontal stress contrast (e.g., sample 2-2). This phenomenon is a result of high horizontal stress contrast, preventing induced fractures from connecting. Therefore, optimizing perforation parameters for ideal fracture geometry does not achieve the desired results under high horizontal stress contrast. However, low fracture pressure and short breakdown time would be observed under high horizontal stress contrast. The pressure-out phenomenon does not exist because the fractures propagate quickly to the sample edge
5. Conclusion Laboratory experiments were performed to study the effect of different helix perforation parameters on fracture initiation, propagation, and pressure under different horizontal stress contrast values in tight formations. The following conclusions are drawn by comparing and analyzing the experimental results: (1) The induced fracture geometry can be categorized into three types based on different perforation parameters: A single flat fracture, an ideal fracture, can be created by only one initiated perforation or more initiated perforations with good overlapped; spiral-shaped fractures can be induced by a high perforation density or large
Fig. 15. Corresponding relation between fracture geometry and fracture curve shape. a. A single flat fracture has smooth and flat fracture curve. b. A spiral-shaped fracture leads to a fracture curve with a large degree of fluctuation. c. A multiple-parallel fracture results in a fracture curve with a small degree of fluctuation. 347
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Fig. 16. Fracture geometry under different horizontal stress contrast values and different perforation parameters. a. A multiple-parallel fracture in the first perforation interval of sample 2–4 with a perforation interval spacing of 4 cm and a horizontal stress contrast of 8 MPa b. A single flat fracture in the second perforation interval of sample 2–4. c. A multiple-parallel fracture in sample 3-1 with a horizontal stress contrast of 12 MPa.
perforation diameter; and multiple-parallel fractures can be generated by a perforation phase of 90°. In addition, each fracture geometry has its own pressure behavior, corresponding to the fracture curve. A single flat fracture has a smooth and flat fracture curve; spiral-shaped fractures lead to fracture curves with a large degree of fluctuation; and multiple-parallel fractures result in fracture curves with a small degree of fluctuation. (2) Reducing the angle between the direction of perforation and the maximum horizontal stress as much as possible can promote perforation initiation. High perforation density, large perforation diameter, and low perforation phase are recommended for perforated fracturing, whereas changing the perforation parameters leads to different results under different horizontal stress contrast values. To obtain low fracture pressure or small tortuosity of the fracture surface, we suggest the following optimal perforation parameter combination: a perforation length of 30 mm, a perforation diameter of 4 mm, a perforation density of 12 holes/cm, a perforation phase of 60°, and a perforation interval spacing of 20 mm under low horizontal stress contrast; however, a perforation length of 30 mm, a perforation diameter of 4 mm, a perforation density of 18 holes/ cm, a perforation phase of 60°, and a perforation interval spacing of 40 mm would be used under low horizontal stress contrast. (3) The fracture pressure is affected deeply by the horizontal stress contrast rather than the perforation parameters. High horizontal stress contrast always reduces the fracture pressure in tight formations.
Daneshy, A.A., 1973b. A study of inclined hydraulic fractures. Soc. Petrol. Eng. J. 13 (2), 61–68. Fallahzadeh, S.H., Shadizadeh, S.R., Pourafshary, P., 2010. Dealing with the challenges of hydraulic fracture initiation in deviated-cased perforated boreholes. In: Paper SPE 132797, Presented at the Trinidad and Tobago Energy Resources Conference Held in Port of Spain, Trinidad, June 27–30. Fallahzadeh, S.H., Rasouli, V., Sarmadivaleh, M., 2015. An investigation of hydraulic fracturing initiation and near-wellbore propagation from perforated boreholes in tight formations. Rock Mech. Rock Eng. 48, 573–584. Feng, Y.C., Gray, K.E., 2017. Modeling near-wellbore hydraulic fracture complexity using coupled pore pressure extended finitie element method. In: Paper ARMA 17-352, Presented at the 51th US Rock Mechanics and Geomechanics Symposium, San Francisco, California, USA, June 25-28. Feng, Y.C., Jones, J.F., Gray, K.E., 2016. A review on fracture-initiation and -propagation pressures for lost circulation and wellbore strengthening. SPE Drill. Complet. 1–11. Ge, W.F., Chen, M., Jin, Y., 2010. Analysis of the external pressure on casings induced by salt-gypsum creep in build-up sections for horizontal wells. Rock Mech. Rock Eng. 44, 711–723. Guo, F., Morgenstern, N.R., Scott, J.D., 1993. An experimental investigation into hydraulic fracture propagation - part 2 single well tests. International Journal of Rock Mechanism and Mine Science 30, 189–202. Guo, T.K., Liu, X.Q., Gu, Q.L., 2016. Deduction of similarity laws of hydraulic fracturing simulation experiments for perforated wells. Chinese Offshore Oil and Gas 27 (3), 108–112. Haimson, B.C., Fairhurst, C., 1967. Initiation and extension of hydraulic fractures in rocks. SPE J. 7, 310–318. Hossain, M.M., Rahaman, M.K., Rahman, S.S., 2000. Hydraulic fracture initiation and propagation: roles of wellbore trajectory, perforation and stress regimes. J. Petrol. Sci. Eng. 27 (3), 129–149. Hou, B., Chen, M., Li, Z.M., 2014. Propagation area evaluation of hydraulic fracture networks in shale gas reservoirs. Petrol. Explor. Dev. 41 (6), 833–838. Hou, B., Diao, C., Li, D.D., 2017. An experimental investigation of geomechanical properties of deep tight gas reservoirs. J. Nat. Gas Sci. Eng. 47, 22–33. Jin, Y., Yuan, J.B., Chen, M., Chen, K.P., Lu, Y.H., Wang, H.Y., 2011. Determination of rock fracture toughness kiic and its relationship with tensile strength. Rock Mech. Rock Eng. 44, 621–627. Lhomme, T.P.Y., 2005. Initiation of Hydraulic Fractures in Natural Sandstones. Delft University of Technology. Li, H.T., Wang, Y.Q., Li, H.J., Ge, Y.W., 1998. An optimum perforation design method for prefracturing wells. Nat. Gas. Ind. 18 (2), 43–46. Liu, Z.Y., Jin, Y., Chen, M., Hou, B., 2016. Analysis of non-planar multi-fracture propagation from layered-formation inclined-well hydraulic fracturing. Rock Mech. Rock Eng. 49, 1747–1758. Morita, N., Black, A.D., Fuh, G.F., 1996. Borehole breakdown pressure with drilling fluids—I. Empirical results. International Journal of Rock Mechanism and Mine Science 33, 39–51. Quattlebaum, C.C., Borgen, K., Xue, Z.Y., Wilkinson, P., 2012. Optimizing perforating charge design for stimulation. In: Paper SPE 159085, Presented at the SPE Annual Technical Conference and Exhibition Held in San Antonio, Texas, USA, October 8–10. Surjaatmadja, J.B., Abass, H.H., Brumley, J.L., 1994. Elimination of near-wellbore tortuosities by means of hydrojetting. In: Paper SPE 28761, Presented at the Asia Pacific Oil& Gas Conference, Melboumo, Austrslia, 7–10 November. Tan, P., Jin, Y., Han, K., Hou, B., Chen, M., Guo, X.F., Gao, J., 2017. Analysis of hydraulic fracture initiation and vertical propagation behavior in laminated shale formation. Fuel 206, 482–493. Tang, R.J., 2015. Optimization of fracturing technology for low-permeability tight sandstone gas reservoirs in the yanba gas field, Sichuan Basin. Nat. Gas. Ind. 35 (7), 55–59. van de Ketterij, R.G., de Pater, C.J., 1997. Experimental study on the impact of perforations on hydraulic fracture tortuosity. In: Paper SPE 38149, Presented at the SPE European Formation Damage Conference, the Hague, The Netherlands, June 2–3. Veeken, C.A.M., Davies, D.R., Walter, J.V. s, 1989. Limited communication between hydraulic fracture and (deviated) wellbore. In: Paper SPE 18982, Presented at the SPE Joint Rocky Mountain Regional/Low Permeability Reservoirs Symposium and
Acknowledgments The authors are grateful for the Project Support of NSFC (No. 51574260, No. 51490651 and No. 51521063). References Abass, H.H., Saeed, Hedayati, Meadows, D.L., 1992. Nonplanar fracture propagation from a horizontal wellbore: experimental study. In: Paper SPE 24823, Presented at the SPE Annual Technical Conference and Exhibition Held in Washington, DC, Oct. 4–7. Abass, H.H., Meadows, D.L., Brumley, J.L., Hedayati, S., Venditto, J.J., 1994. Oriented perforations – a rock mechanics view. In: SPE 28555, Presented at the SPE Annual Technical Meeting Held in New Orleans, Louisiana, Sept. 25–28. Alekseenko, O.P., Potapenko, D.I., Cherny, S.G., Esipov, D.V., Kuranakov, D.S., Lapin, V.N., 2012. 3D modeling of fracture initiation from perforated noncemented wellbore. Soc. Petrol. Eng. J. 1–12. Behrmann, L.A., Elbel, J.L., 1991. Effect of perforations on fracture initiation. J. Petrol. Technol. 43 (05), 608–615. Behrmann, L.A., Nolte, K.G., 1998. Perforating requirements for fracture stimulations. In: Paper SPE 39453, Presented at the International Symposium on Formation Damage Control Held in Lafayette, Louisians, February 18–19. Brumley, J.L., Abass, H.H., 1996. Hydraulic fracturing of deviated wells: interpretation of breakdown and initial fracture opening pressure. In: Paper SPE 37363, Presented at the Eastern Regional Meeting Held in Columbus, Ohio, October 23–25. Daneshy, A.A., 1973a. Experimental investigation of hydraulic fracturing through perforations. In: Paper SPE 4333, Presented at the SPE-aime European Spring Meeting, London, April 2–3.
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fracture propagation and fracture breakdown pressure. Journal of Petroleum Science and Engneering 164, 164–173. Zhou, J., Jin, Y., Chen, M., 2010. Experimental investigation of hydraulic fracturing in random naturally fractured blocks. Int. J. Rock Mech. Min. Sci. 47, 1193–1199. Zoback, M.D., Rummel, F., Jung, R., Raleigh, C.B., 1977. Laboratory hydraulic fracturing experiments in intact and pre-fractured rock. International Journal of Rock Mechanism and Mine Science 14, 49–58.
Exhibition Held in Denver, Colorado, March 6–8. Yew, C.H., Li, Y., 1987. Fracturing of a deviated well. In: Paper SPE 16930, Presented at the SPE Annual Technical Conference and Exhibition Held in Dallas, Sept. 27–30. Yew, Y.W., Schmidt, J.H., Yi, L.U., 1999. On fracture design of deviated wells. In: Paper SPE 19722, Presented at the Annual Technical Conference and Exhibition Held in San Antonio, Texas, USA, October 8–10. Zhang, Y.S., Zhang, J.C., Yuan, B., Yin, S.X., 2018. In-situ stresses controlling hydraulic
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Hydraulic fracturing initiation and near-wellbore nonplanar propagation from horizontal perforated boreholes in tight formation
T
Ruxin Zhang, Bing Hou∗, Qinglin Shan, Peng Tan, Yue Wu, Jie Gao, Xiaofeng Guo State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Perforated fracturing True triaxial experiment Fracture initiation Perforation parameter optimization Near-wellbore geometry
Tight formations, which are rich in reserves in China, have a high economic development value. Perforated fracturing would need to be used widely to exploit these formations because of reservoir characteristics such as low permeability, low porosity and high density, resulting in high fracture pressure, limited fracture propagation, and complex fracture geometry. To address these issues, the mechanism of fracture propagation under different construction conditions must be understood and described. Therefore, the effect of different perforation parameters (shot density, shot length, shot diameter, shot phase, and shot interval spacing) and different horizontal stress contrasts on fracture geometry, initiation, and propagation from perforated horizontal wells in tight formations is studied based on numerous triaxial hydraulic fracturing simulation experiments. Three types of fracture geometry are observed in these experiments: A single flat fracture can be created by an initiated perforation or more initiated perforations with good connectivity, spiral-shaped fractures are generated by a large perforation diameter or high perforation density, and multiple-parallel fractures are induced by a high perforation phase. Moreover, each fracture type has certain pressure behaviors corresponding to a fracture curve shape. The perforations are likely to initiate when the angle between the perforation and maximum horizontal stress is small, and the initiation position is most likely at the base of the perforation. It is difficult to predict the initiation order of perforations; however, the first initiated perforation can be ensured by the profile of the relief pressure. In addition, a higher horizontal stress contrast value results in more initiated perforations, lower fracture pressure, and shorter breakage time. Ultimately, a large perforation diameter, high perforation density, and perforation phase of 60° should be chosen for fracturing at low fracture pressure and simple fracture geometry in tight formations.
1. Introduction With the development of oil and gas exploration and exploitation, significant attention has been paid in recent years to unconventional reservoirs, such as tight reservoirs, shale gas reservoirs, and coalbed methane reservoirs. Tight formations have rich reserves and are deeply buried in China. However, it is difficult to exploit them without employing auxiliary processes owing to features such as high density, low permeability, low porosity, and high temperature (Hou et al., 2017). Perforation fracturing has been a valuable technique to stimulate these tight reservoirs. The perforations afford a channel between the wellbore and the reservoir for guiding oil flow to improve production (Feng and Gray, 2017). Behrmann and Elbel (1991) revealed that the fracture initiation position was at the base of the perforations or at the intersection of the plane normal to the minimum horizontal stress when fracturing with a 180° perforation phase in a vertical well. Abass et al. (1992) highlighted that perforation initiation was easier when the ∗
perforation angle with respect to the maximum horizontal stress was smaller. Moreover, Abass et al. (1994) proved that the oriented perforation could induce a single wide fracture and control sand production. Nevertheless, perforated fracturing faces numerous issues such as premature screen-outs, low linkup between the borehole and reservoir, high treatment pressure, high fracture tortuosity, and the occurrence of multiple fractures. Daneshy (1973a) was the first to determine that the perforations had an impact on fracture morphology and fracturing pressure. The perforated fracturing generated more complex fractures and a higher fracture pressure than in an open hole. Brumley and Abass (1996) claimed that nonplanar fractures and complex fractures resulted in premature screen-outs, high friction near the wellbore, and high treatment pressure when the wellbore orientation with respect to the in situ horizontal stress was different. Veeken et al. (1989) found that limited entry effects occurred because of poor communication between the wellbore and hydraulic fracture or the existence of multiple
Corresponding author. College of Petroleum Engineering, China University of Petroleum, Beijing 102249, China. E-mail address: [email protected] (B. Hou).
https://doi.org/10.1016/j.jngse.2018.05.021 Received 5 September 2017; Received in revised form 10 April 2018; Accepted 13 May 2018 1875-5100/ © 2018 Elsevier B.V. All rights reserved.
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test frame surrounded by pressurizing pistons that add pressure around and at the bottom of the sample. They are of the same size as the sample's surface to guarantee uniform pressure, which is controlled by adjustable hydraulic pressure with a maximum pressure output of 30 MPa. Meanwhile, the top of the sample was covered by a steel plate to simulate the in-situ stress. The injection power was supported by an MTS 816 servo booster with a maximum injection pressure of 140 MPa, and the maximum injection volume was 800 mL.
fractures. One of these issues might have a significant impact on other issues and more than one issue might originate from some common sources, which complicates the overall problem (Abass et al., 1994; Hossain et al., 2000). However, the above problems can be solved by rational design of perforated fracturing, which has proven effective for fracture initiation when the perforations are in phase with the anticipated fracture direction (Behrmann and Elbel, 1991). In addition, an effective and reasonable perforation parameter design could yield more initiated perforations and reduced complex fracture geometry and fracture pressure to improve the fracturing effect. Several laboratory experiments and numerical simulations on the effect of perforation parameters on fracture initiation and propagation have been performed in the past. Veeken et al. (1989) proposed a formula to predict the number of initiated perforations. They assumed that a large perforation diameter, high perforation density, or large perforation depth would increase the number of initiated perforations and enhance the connection among fractures. A single fracture with a minimum tortuosity at an achievable fracture initiation pressure is desired. Behrmann and Nolte (1998) indicated that short perforation length and high perforation density could yield more perforations to initiate and cause more fractures to link up, which could reduce the fracture tortuosity and prevent the occurrence of multiple fractures. Poor connection among fractures is observed when the perforation phase is high. In particular, induced fractures were not linked when perforation phase was 90°, resulting in multiple fractures. Furthermore, van de Ketterij and de Pater (1997) showed that small perforation spacing facilitated fractures connecting with each other to reduce fracture complexity. Most of the above experimental research on perforated fracturing focused on the effect of perforation orientation, perforation phase, and fracturing fluid viscosity and injection rate on fracture initiation, geometry, and pressure. However, other perforation parameters, such as perforation density, perforation diameter, perforation length, were discussed from the aspect of numerical simulation in most cases rather than through experiments. Furthermore, several numerical simulations focused on the effect of perforation parameters on fracture broken pressure or initiation pressure rather than the fracture initiation method and fracture geometry. Hossain et al. (2000) established a prediction model of fracture pressure to discuss the effect of perforation azimuth. Fallahzadeh et al. (2010) demonstrated that perforation orientation had an impact on fracture initiation pressure in a deviated borehole. Quattlebaum et al. (2012) confirmed that the actual diameter of each perforation and the differences in perforation diameter size had an impact on the fracture pressure by using a finite element method. In the meantime, Alekseenko et al. (2012) studied the effect of perforation orientation, perforation length, perforation diameter, and perforation shape on fracture initiation and fracture pressure with the boundary element method. Therefore, in this work, we conducted a large-scale true triaxial hydraulic fracturing simulation experiment to study the effect of different perforation parameters (shot density, shot length, shot diameter, shot phase, and shot interval spacing) and different horizontal stress contrast values on fracture initiation, geometry, and pressure from perforated horizontal wells in tight formations. Finally, the experimental results could offer a theoretical basis for optimizing perforation parameters and putting forward some suggestions about perforated fracturing operations in tight formations.
2.2. Wellbore design The horizontal wellbores were made of steel pipe, composed of a wellhead and a chamber. The wellhead had a length of 30 mm, an outer diameter of 16 mm, and an inner diameter of 10 mm. The chamber had a length of 230 mm, an outer diameter of 14 mm, and an inner diameter of 10 mm. All wellbores had uniform size specifications. Some holes were drilled with a spiral distribution in the steel pipe and paper tubes were inserted to simulate perforations. The perforation interval was ensured to be the middle of the chamber. Four wellbores were made with different shot diameters, shot densities, shot phases, and shot interval spacings according to the experimental scheme requirements. Furthermore, different shot lengths were simulated by different lengths of paper tubes. In addition, some grooves were cut between the bottom of wellhead and the first perforation to avoid channeling. Then, each perforation was numbered clockwise from the top to bottom of the wellbore as shown in Fig. 2. For example, 1-1 represented the first perforation of the first perforation interval, and 2–6 represented the sixth perforation of the second perforation interval. 2.3. Rock sample preparation The tests were conducted in blocks of hydrostone, measuring 300 mm × 300 mm × 300 mm. No cementing material was used between the wellbore and the rock. The wellbore was placed at the middle position inside the mold. Hydrostone, which was mixed with cement (model 325) and quartz sand (20–40 M) in a constant mass ratio of 1:1, was then poured around the wellbore to form the sample as shown in Fig. 3. This is a more robust way to bond the wellbore and rock (Daneshy, 1973a,b). In the meantime, the mold was struck by a hammer for a while to reduce bubbles inside the sample. The artificial samples were placed in a dry environment for half a month to air for developing adequate strength. The rock mechanics test and permeability test were performed by TAW-100 testing (Ge et al., 2010; Jin et al., 2011) to measure the parameters listed in Table 1. 2.4. Experimental scheme The experimental scheme was set by using a similarity criterion (Guo et al., 2016) according to the field data. The experiments were divided into three groups. Experiments in the first group (1-1 – 1-6) were conducted to study the effect of different spiral perforation parameters on fracture initiation, fracture propagation, and fracture pressure in the normal-faulting stress regime (in which the vertical stress was 30 MPa, the maximum horizontal stress was 24 MPa, and the minimum horizontal stress was 21 MPa). Experiments in the second group (2-1 – 2-4) were conducted for examining the influence of the horizontal stress contrast on fracture initiation, fracture propagation, and fracture pressure in another normal-faulting stress regime (in which the vertical stress was 30 MPa, the maximum horizontal stress was 27 MPa, and the minimum horizontal stress was 19 MPa). Furthermore, the third group experiment (3-1) was carried to investigate the horizontal stress contrast influencing (in which the vertical stress was 30 MPa, the maximum horizontal stress was 25 MPa, and the minimum horizontal stress was 13 MPa). The concrete experimental plan is given in Table 2. Guar with a viscosity of 3 mPa s was used as the fracturing fluid in
2. Experimental process and scheme 2.1. Experimental equipment The experiments were performed in a true triaxial pressure machine. The specific apparatus includes a true triaxial test frame, a triaxial hydraulic voltage source, an oil–water separator, an MTS pressurization controller, and a data acquisition and processing system as shown in Fig. 1. The 300-mm cubic model block was placed in the 338
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Fig. 1. Experimental equipment and flowchart (Tan et al., 2017).
these experiments. The fracturing fluid was injected at a rate of 60 ml/ min through the wellbore into the sample. Meanwhile, some fluorescent tracers were added to the fracturing fluid for better observation of the induced hydraulic fractures. The in-situ stress loading direction as shown in Fig. 4 was used to stimulate fracturing in the horizontal well.
Therefore, the main hydraulic fractures could be divided into three categories: single flat fractures, spiral-shaped fractures, and multipleparallel fractures. The resulting description of each sample is given in Table 3.
3.1. Fracture geometry 3. Experimental results and interpretation 3.1.1. Single flat fractures An ideal perforation for fracture initiation would create only a single fracture with minimum tortuosity (Behrmann and Nolte, 1998). It could be created when a single perforation initiated and propagated along the direction of the maximum horizontal stress, such as test 1-1 and test 1–2. In addition, a single fracture with minimum tortuosity could also be formed when more perforations are initiated with good connection and fractures overlap as in test 2-1. To observe the fracture morphology vividly and objectively, fracture morphology was reconstructed in a three-dimensional space as shown in Fig. 5. However, because the probability of each initiated perforation is random, it was difficult to interpret the number of initiated perforations that occurred during fracturing. Further, it was difficult to identify the connections among initiated perforations and overlapping ones among fractures during fracture propagation. A single flat fracture is desired,
After fracturing, each sample was opened carefully along the induced hydraulic fracture and split slowly into two part by a hammer and chisel, without any additional sectioning on crack surface, to observe fracture initiation characteristics and the form of propagation. All hydraulic fractures were transverse fractures that propagated along the maximum horizontal principal stress direction (perpendicular to the wellbore) in our experiments. These fracture morphologies were consistent with the existing understanding that hydraulic fractures always initiate perpendicular to the direction of the minimum principal stress and propagate along the direction of maximum horizontal stress (Hou et al., 2014; Feng et al., 2016). However, owing to the different perforation parameters and different horizontal stress contrast values, the induced fractures were not always a single, planar main fracture with minimum tortuosity. Nonplanar fractures appeared in the experiments.
Fig. 2. Schematic of wellbore design. a. Photograph of real wellbore to show wellbore design, including wellhead and chamber. The size of each part is marked on the image. Perforations are simulated by paper tubes. b. Schematic of the distribution of perforation positions on the wellbore and the serial number of each perforation. 339
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Fig. 3. Schematic of artificial rock sample fabrication process. a. Schematic of a wellbore inserted inversely into the middle of the mold. b. Schematic of a sample cast process. All samples were made by using this process.
strongly, resulting in a large overlapping area. Ultimately, these fractures would become one main fracture propagating along the direction of the maximum horizontal stress to the sample edge. In addition, the spiral amplitude of sample 1–4 was larger than that of sample 1–3. Because the vertical distance between the first initiated perforations and the last initiated perforations was greater in sample 1–4 (five initiated perforations) than in sample 1–3 (only three initiated perforations), as shown in Fig. 6. Sample 2-2 also had a spiral-shaped fracture with a large spiral amplitude. The area and boundary of three induced fractures were observed, as shown in Fig. 6. Two reasons could account for this fracture geometry. High density could explain why the fractures had tortuosity rather than being multiple parallel. High density shortened the spacing between each adjacent perforation to enhance interaction between initiated fractures. Each induced fracture tended to overlap and form a main fracture. However, the high horizontal stress contrast (8 MPa) shortened the time fractures interacted and linked up with each other. Induced fractures propagated independently along the direction of the maximum horizontal stress. This phenomenon was also found in the study of van de Ketterij and de Pater (1997). Behrmann and Elbel (1991) had claimed that fractures had more time to initiate and interact at lower stress levels. Therefore, under the influence of these two factors, a large spiral amplitude fracture was generated with obvious boundaries of three fractures.
Table 1 Mechanical parameters of the artificial sample. Parameter
Value
Units
Elasticity Modulus Poisson's Ratio Compressive Strength Tensile Strength Permeability Porosity
7.86 0.2 20.89 1.53 0.1 1.54%
GPa – MPa MPa mD –
but its creation is not always possible, and nonplanar fractures were normally induced in many cases.
3.1.2. Spiral-shaped fractures Spiral-shaped fractures might be created in helix perforated fracturing with a large shot diameter or high shot density. These spiralshaped fractures are always regarded as the cause of high fracture pressure, high friction near the wellbore, or premature screen-outs. Sample 1–3 showed that three perforations acted as the fracture initiation source and a spiral-shaped fracture was created in helix perforated fracturing with a large shot diameter (4 mm). Each fracture propagated away from the wellbore to the sample edge. Fractures interacted with each other and some parts overlapped to form a main fracture with a spiral shape as shown in Fig. 6. Sample 1–4 showed that a spiral-shaped fracture was induced from five initiated perforations in helix perforated fracturing with a high shot density (18 holes/cm). It was difficult to identify the area and boundary of each fracture, because these fractures communicated and connected
3.1.3. Multiple-parallel fractures Multiple-parallel fractures also appeared in helix perforated fracturing owing to high shot phase, such as in samples 1–5 and 2–3. More initiated perforations with poor connection in horizontal or deviated
Table 2 Hydraulic fracture spiral perforation experimental scheme. Test
Shot Length (cm)
Shot Diameter (mm)
Shot Density (holes/cm)
Shot Phase (°)
Shot Interval Spacing (cm)
σv (MPa)
σH (MPa)
σh (MPa)
1–1 1–2 1–3 1–4 1–5 1–6 2–1 2–2 2–3 2–4 3–1
3 4 3 3 3 3 3 3 3 3 3
2 2 4 2 2 2 2 2 2 2 2
12 12 12 18 12 12 12 18 12 12 12
60 60 60 60 90 60 60 60 90 60 60
2 2 2 2 2 4 2 2 2 4 2
30 30 30 30 30 30 30 30 30 30 30
24 24 24 24 24 24 27 27 27 27 25
21 21 21 21 21 21 19 19 19 19 13
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addition, he found another initiated position of perforations at the intersection of the plane normal to the minimum horizontal stress that passes through the axis of the wellbore and the wellbore surface in the vertical well. However, this phenomenon could not be found, because the experiments conducted in this study were for a horizontal well in which all fractures were transverse fractures perpendicular to the wellbore. Second, perforations initiated depend on the size of the angle between the perforation direction and the maximum horizontal stress direction. Daneshy (1973a,b) was the first to establish this rule. He pointed out that 0° was the best angle for perforations to initiate and that 90° was the worst angle. The fractures may be initiated from all shots only when the angle was ≤10° (Behrmann and Elbel, 1991). In addition, Abass et al. (1992) summarized that the initiation pressure increased with angle by taking eight types of angle into consideration. This rule was applicable to our experiments as well; that is, perforations were easier to initiate when the angle was smaller. The angle of the initiated perforations ranged from 20° to 60°. Third, it was difficult to ensure the perforation initiation order. Whereas, Abass et al. (1992) proposed that the profile of the relief in pressure (RIP) could provide useful information to ensure that the wellbores were in phase or out of phase relative to the fracture direction, he pointed out that the pressure in the RIP region was a function of the angle between the wellbore direction and the maximum horizontal stress direction. The angle increased, resulting in the slope of the pressure immediately declining as shown in Fig. 8. The treatment pressure declined slowly and smoothly when the angle increased. Brumley and Abass (1996) claimed that the larger wellbore orientations yielded a smaller rate and a smaller magnitude of RIP. Further, the angle between each perforation direction and the maximum horizontal stress direction can be regarded as the angle between the wellbore direction and the maximum horizontal stress direction, as shown in Fig. 9. Therefore, the RIP region of the fracture curve could be used to ensure the perforation initiation order of each sample. Samples 1-1 and 1–2 were not analyzed because they only had one initiated perforation. Hence, sample 2-1 was chosen as an example. Two sharp points are observed in the curve, as shown in Fig. 10. The slope of the first sharp point was lower than that of the second sharp point (i.e., the angle of the first sharp point was greater than that of the second sharp point). Therefore, perforation 1–2 with an angle of 90° initiated earlier than perforation 1–3 with an angle of 30°, as shown in Fig. 5. However, problems arose when the rest of samples were analyzed using this rule. Fracture curves for samples 1–3, 1–4, 1–5, 1–6, 2-2, and 2–4 were more complex than those for samples 2-1 and 2–3. The large degrees of fluctuations of the curve resulted in many sharp points owing to the fracturing fluid flowing with high friction in uneven nonplanar fractures, the existence of a pressure-out phenomenon, and the dominating fracture opening and closing frequently (Zhou et al., 2010). It is difficult to identify which one represented the initiated perforation. Although the perforation initiation order was difficult to ascertain, the first initiated perforation can be identified from the fracture curve according to the RIP profile. Conversely, fracturing pressure is defined as the time at which the treatment pressure reaches its maximum value. However, fracture initiation typically occurs before this breakdown point (Lhomme, 2005; Fallahzadeh et al., 2015). Therefore, the first sharp point of the fracture curve must represent the point at which the breakdown of rock and perforation has initiated. The first initiated perforation of each sample can then be inferred based on the RIP profile of the first sharp point in the fracture curve, as given in Table 4. RIP region analysis is a practical and effective method to recognize the first initiated perforation and the order of perforation initiation when the fracture curve is simple. However, it remains a difficult task to determine the specific order of perforation initiation when the fracture curve is complex. Additional studies are needed to optimize this method.
Fig. 4. Schematic of the in-situ stress direction. The direction of the minimum horizontal principal stress is loaded along the direction of the wellbore to simulate horizontal well fracturing. Table 3 Hydraulic fracture spiral perforation experimental results. Sample Number
Initiated Shot Number
Fracture Pressure (MPa)
Fracture Shape
1–1 1–2 1–3 1–4 1–5 1–6 2–1 2–2 2–3 2–4
1 1 3 5 2 2 2 3 3 5
22.46 18.7 24.89 26.57 25.82 26.45 21.4 18.7 22.27 24.8
3–1
2
14.3
A single flat fracture A single flat fracture Spiral-shaped fracture Spiral-shaped fracture Multiple-parallel fracture Multiple-parallel fracture A single flat fracture Spiral-shaped fracture Multiple-parallel fracture Multiple-parallel fracture + a single flat fracture Multiple-parallel fracture
well fracturing could be a cause of forming such multiple-parallel fractures (e.g., sample 1–6). This fracture geometry should be responsible for a narrow fracture width near the wellbore, resulting in difficulty in adding sand, high fracture pressure, and high friction near the wellbore (Abass et al., 1992; Behrmann and Nolte, 1998). Both samples with a shot phase of 90° in our experiments (samples 1–5 and 1–6) showed that multiple-parallel fractures were created from two or three adjacent initiated perforations. These fractures propagated from their initiated position to the sample edge along the maximum horizontal stress direction without any interaction and linkup, as shown in Fig. 7 van de Ketterrij and de Patter (1997) also found that the probability of linkup among fractures was restricted when the shot phase was 90°. Furthermore, wall waviness or roughness was observed on the fracture surface.
3.2. Perforation initiation characteristics Some characteristics of perforation initiation were obtained based on the above experimental results. First, the fractures almost initiated at the base of the perforations. The fracturing fluid was always distributed along the base of the initiated perforations and then extended along the direction of perforation in our experiments. This phenomenon could prove our viewpoint about the position of perforation initiation. Behrmann obtained the same experimental results in 1991 and 1998. In 341
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Fig. 5. Single flat fracture induced with different perforation parameters under different horizontal stress contrast values. a. Schematic of a single flat fracture shape of sample 1-1 in three dimensions to improve understanding of the fracture shape. b. One perforation initiated to form a single flat fracture under conventional perforation parameters and a horizontal stress contrast of 3 MPa c. A single flat fracture induced with one perforation initiation under a perforation length of 4 cm and a horizontal stress contrast of 3 MPa d. Two perforations initiated to form a single main fracture under conventional perforation parameters and a horizontal stress contrast of 8 MPa.
fracture pressure and shortened the initiation time effectively, as shown in Fig. 12. Because the pressure-out phenomenon disappeared and the fracturing fluid flowed with less friction in the smooth fracture surface, fractures could propagate quickly with less friction from the sample edge. Therefore, the main reason for different fracture pressure in our experiments was the co-effect of two factors: perforation parameters and horizontal stress contrast. In addition, traditional theoretical models (Haimson and Fairhurst, 1967; Hossain et al., 2000) were not applied well to calculate fracture pressure of our experiments. Many scholars indicated that the calculation result was not consistent with the experimental result (Zoback et al., 1977; Guo et al., 1993; Morita et al., 1996). Because fracture pressure was not only controlled by in-situ stresses, but also dependent on Young's modulus of the formation, wellbore size and type of the drilling fluids (Zhang et al., 2018). Too many factors had an impact on fracture pressure, resulting in difficulty prediction. Future work was required to modify and improve the theoretical model, considering the effect of multiple factors, such as perforation parameters, fluid viscosity, pump rate.
3.3. Fracture curve The treatment pressure responses were different under different fracturing conditions, as shown in Figs. 11 and 12. With a low horizontal stress contrast, the fracture pressure was high and the initiation time was long (comparing samples 1-1 to 1–6 with samples 2-1 to 2–4). The increase in perforation length leaded to low fracture pressure (comparing sample 1–2 with sample 1-1). The result was consistent with the study result of Alekseenko et al. (2012). The increase of the perforation length decreased fracture initiation pressure in the case of highly misaligned perforations. However, the increase in perforation diameter or density resulted in high fracture pressure and long initiation time (comparing samples 1–3 and 1–4 with sample 1-1), as shown in Fig. 11, which was supposed to reduce the fracture pressure and shorten the initiation time (Daneshy, 1973a; Behrmann and Elbel, 1991). This abnormal phenomenon was a result of many factors. For instance, the existence of pressure-out phenomenon during the process of fracture propagation would raise the treatment pressure; fracturing fluid flows in uneven nonplanar fracture could lead to high fluctuation of treatment pressure; and breakdown pressure could be higher for increased tunnel numbers with a low horizontal stress contrast (Liu et al., 2016). A high horizontal stress contrast, whereas, reduced the 342
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Fig. 6. Spiral-shaped fracture induced with different perforation parameters under different horizontal stress contrast values. a. Schematic of a spiral-shaped fracture shape of sample 1–3 in three dimensions to improve understanding of the fracture shape. b. Three perforations initiated to form a spiral-shaped fracture under a perforation diameter of 4 mm and a horizontal stress contrast of 3 MPa c. Five perforations initiated to generate a spiral-shaped fracture of small tortuosity under a perforation density of 18 holes/cm and a horizontal stress contrast of 3 MPa d. Three perforations initiated to form a spiral-shaped fracture of large tortuosity under a perforation density of 18 holes/cm and a horizontal stress contrast of 8 MPa.
4. Discussion
density or perforation diameter shortened PS. Moreover, the decrease in PS was conducive to induce more initiated perforations and improve connection among fractures to reduce fracture complexity and fracture pressure. Therefore, several initiated perforations formed a main fracture rather than an initiated perforation with a main fracture (comparing samples 1–3 and 1–4 with sample 1-1). However, the increase in perforation phase increased PS. Poor connection among induced fractures resulted in fractures propagating independently, forming multiple-parallel fractures (comparing sample 1–5 with sample 1-1). The change in perforation length and perforation interval spacing had no impact on PS; therefore, the fracture shape was the same as that of sample 1-1. 2) A single flat main fracture with minimum tortuosity at an achievable fracture initiation pressure was desired (Behrmann and Nolte, 1998), but multiple-parallel fractures and spiral-shaped fractures were created in most cases, resulting in a narrow fracture width, high friction near the wellbore, difficulty in adding sand, premature screen-out, and high fracture pressure (Abass et al., 1992; Surjaatmadja et al., 1994; Behrmann and Nolte, 1998). However, low fracture pressure, many initiated perforations, and simple fracture geometry could be a result of perforated fracturing with optimized perforation parameters. The increase in perforation
1) The change in perforation parameters causes different fracture geometries and fracture pressures. However, the mechanism of this change remains unclear. An interesting phenomenon was observed when we tried to identify this mechanism. To clarify it, two adjacent perforations were taken as a two-dimensional simplified model, as shown in Fig. 13. Here, the vertical distance between two perforation centers is L1, the horizontal distance between two perforation centers is L 2 , and the diameter of the perforation is defined as d . L1 decreased as the perforation density increased, L 2 increased as the perforation phase increased, and d increased as the perforation diameter increased. However, the perforation length and perforation interval spacing did not change with changes in the above three factors. Different perforation parameters affect different factors, but all were related to perforation spacing (PS). PS was defined as the distance between A and B, as shown in Fig. 13; therefore, the change in perforation parameters could be converted into the influence on PS. Yew et al. (1999) also revealed that two induced fractures, initiated from two adjacent perforations, influenced each other during propagation process. The influence degree was depended on the distance of two adjacent perforations. The increase of perforation
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Fig. 7. Multiple-parallel fracture induced with different perforation parameters under different horizontal stress contrast values. a. Schematic of a multiple-parallel fracture shape of sample 1–5 in three dimensions to improve understanding of the fracture shape. b. Two perforations initiated to form a multiple-parallel fracture under a perforation phase of 90° and a horizontal stress contrast of 3 MPa c. Two perforations initiated to form a multiple-parallel fracture under a perforation cluster spacing of 4 cm and a horizontal stress contrast of 3 MPa d. Three perforations initiated to form a multiple-parallel fracture under a perforation phase of 90° and a horizontal stress contrast of 8 MPa.
Fig. 8. Schematic of the relationship of pressure decline after breakdown and angle (Abass et al., 1992). a. Results of qualitative analysis showing that different angles between wellbore direction and the maximum horizontal stress direction have different RIP profiles. b. Results of quantitative analysis showing that the angle increase results in the slope of the pressure immediately declining. 344
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Fig. 9. a. Schematic showing different angles between different wellbore orientations and the direction of the maximum horizontal stress. b. Schematic showing how a perforation can be regarded as a wellbore by changing the direction of in situ stress.
density generated different results under different horizontal stress contrast values. The fracture surface exhibited small tortuosity but high fracture pressure under a horizontal stress contrast of 3 MPa. However, the fracture surface exhibited large tortuosity but low fracture pressure under a horizontal stress contrast of 8 MPa (comparing sample 2-2 to sample 2-1). Therefore, to reduce the fracture pressure rather than the fracture tortuosity, low perforation density should be used under low horizontal stress contrast and high perforation density should be used under high horizontal stress contrast. In contrast, if we focus on fracture tortuosity rather than fracture pressure, high perforation density should be used under low horizontal stress contrast and low perforation density should be used under high horizontal stress contrast. However, high perforation density would result in casing damage by compromising casing strength. Moreover, a large perforation diameter was the best choice for perforated fracturing. It not only reduced fracture pressure but also decreased perforation friction. The size and concentration of the proppant also depend on the size of the perforation diameter, because large perforation diameter could prevent bridge blinding of proppant near the perforation hole (Li et al., 1998). Furthermore, a small tortuosity fracture with a large drainage area was induced by a
Table 4 First initiated perforation of each sample. Sample Number
First Initiated Perforation
Angle (°)
1–3 1–4 1–6 2–2 2–3
2–3 2–8 2–4 2–6 Three shots initiated at the same time
60 20 40 0 0, 60
The angle was between the perforation direction and the maximum horizontal stress direction.
large perforation diameter in sample 1–3. However, a high perforation phase induced multiple-parallel fractures easily under low or high horizontal stress contrasts (samples 1–5 and 2–3). These results agree with those of Daneshy (1973a,b) and Behrmann and Nolte (1998). van de Ketterij and de Patter (1997) also assumed that it was difficult for fractures to connect with each other when the perforation phase was 90°. A perforation phase of 60° was the optimal phase for perforated fracturing because this phase could ensure that most perforations had a suitable angle with respect to the
Fig. 10. Fracture curve of sample 2-1. Left panel. Two sharp points can be seen inside the fracture curve. Right panel. Enlarged area to observe more clearly the two angle values and the slope of each sharp point. 345
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maximum horizontal stress direction for initiation (Daneshy, 1973a,b; Abass et al., 1992). In addition, the fracture pressure of the perforation phase with 45° or 60° was lower than that of the perforation phase with 90° or 120° when perforated fracturing was employed in the Yuanba gas field, Sichuan Basin (Tang, 2015). However, the increase in perforation length or perforation interval spacing had negligible effect on fracture geometry in our experiments. This result is consistent with the viewpoint of Yew and Li (1987). Therefore, based on the effect of perforation on casing strength, on-site engineers should adopt high perforation density, large perforation diameter, and low perforation phase for fracturing. Li et al. (1998) claimed that perforated fracturing was improved when the perforation density of 18 holes/m and perforation phase of 90° were changed to 20 holes/m and 45°, respectively. Another field example of horizontal wells in southeast Sichuan, China, verifies this result. The in-situ stresses of target formation were σV = 110.12 MPa, σH = 124.53 MPa, and σh = 101.27 MPa and the pore pressure was Pp = 76.67 MPa. Two horizontal wells were drilled along the minimum horizontal stress and perforated with a perforation phase of 60°. Slick water was injected at a low pump rate at first for approximately 1 h and then at a high pump rate of 10–11 m3/min, as shown in Fig. 14. A horizontal well with a perforation density of 16 holes/m and a perforation diameter of 10 mm had a high treatment pressure and low sand concentration, resulting in a poor fracturing effect. However, a large perforation diameter of 14 mm and a high perforation density of 22 holes/m were adopted for fracturing in another horizontal well, leading to a low treatment pressure and a high sand concentration, as shown in Fig. 14. Because small tortuosity fracture or planar fracture was induced by large perforation diameter and high perforation density, the fracturing fluid flowed with less friction along this fracture surface, resulting in low treatment pressure. Moreover, proppants entered into the induced fractures easily owing to the fracture geometry. 3) One key point in the fracture curve is the sharp point. It reflects perforation initiation patterns: only one sharp point indicates that perforations initiate at the same time; more than one sharp point indicates a sequence. Furthermore, the perforation initiation order could be inferred by analyzing its slope (RIP region). Another key point is the fracture curve shape, which corresponds to the fracture geometry in our experiments, as shown in Fig. 15. A single flat fracture has an even and smooth surface with less friction, resulting in the fracture propagating quickly to the sample edge. Therefore, the fracture curve shape is simple, with the pressure dropping fast and the extension pressure being smooth without any fluctuation, as seen with samples 1-1, 1–2, and 2-1. Nevertheless, the fracture curve shape of spiral-shaped fractures has a large degree of fluctuation. Fractures interact and overlap with each other to form a main fracture, opening and closing frequently (Zhou et al., 2010), and fracturing fluids flow in this uneven spiral fracture surface with high friction, leading to extension pressure fluctuation. The above two reasons caused the complex shape of the fracture curves, as seen in samples 1–3, 1–4, and 2-2. In addition, multiple-parallel fractures have planar fracture surfaces but are not smooth. Wall waviness was observed on the fracture surface. Fracturing fluids flowed under rough surfaces, resulting in small extension pressure fluctuation. Consequently, the fracture curves exhibited a small degree of fluctuation, as seen in samples 1–5, 1–6, and 2–4. This corresponding relationship between fracture geometry and the fracture curve was summarized qualitatively by our experiments in tight formations. It was difficult to quantize this relationship owing to the many factors that could affect the fracture curve. Whether this relationship can be applied to other heterogeneous formations, such as shale formations with beddings and natural fractures, requires further studies in the future. 4) The horizontal stress contrast has a crucial and decisive impact on fracture geometry and fracture pressure. High horizontal stress
Fig. 11. Fracture curve for each sample under a horizontal stress contrast of 3 MPa.
Fig. 12. Fracture curve for each sample under a horizontal stress contrast of 8 MPa.
Fig. 13. Two-dimensional simplified model of two adjacent perforations. The vertical distance between two perforation centers is labeled L1, the horizontal distance between two perforation centers is labeled L2, and the diameter of the perforation is defined as d.
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Fig. 14. Fracture curves for different perforation sections with different perforation parameters. a. Fracture curve with a perforation diameter of 10 mm and a perforation density of 16 holes/m. b. Fracture curve with a perforation diameter of 14 mm and a perforation density of 22 holes/m.
under high horizontal stress contrast. The low treatment pressure would be gained during perforated fracturing operation.
contrast promotes more perforations to initiate and induce fractures to propagate faster and farther, whereas it shortens the connection time of fractures, resulting in fractures independently propagating without connection and overlapping, as shown in Fig. 16. Multipleparallel fractures or a single fracture with a smooth fracture surface are more likely generated in the case with unchanged PS, such as samples 2-1, 2–3, 2–4, and 3-1. If PS decreased, a spiral-shaped fracture with a large spiral amplitude might be induced under a high horizontal stress contrast (e.g., sample 2-2). This phenomenon is a result of high horizontal stress contrast, preventing induced fractures from connecting. Therefore, optimizing perforation parameters for ideal fracture geometry does not achieve the desired results under high horizontal stress contrast. However, low fracture pressure and short breakdown time would be observed under high horizontal stress contrast. The pressure-out phenomenon does not exist because the fractures propagate quickly to the sample edge
5. Conclusion Laboratory experiments were performed to study the effect of different helix perforation parameters on fracture initiation, propagation, and pressure under different horizontal stress contrast values in tight formations. The following conclusions are drawn by comparing and analyzing the experimental results: (1) The induced fracture geometry can be categorized into three types based on different perforation parameters: A single flat fracture, an ideal fracture, can be created by only one initiated perforation or more initiated perforations with good overlapped; spiral-shaped fractures can be induced by a high perforation density or large
Fig. 15. Corresponding relation between fracture geometry and fracture curve shape. a. A single flat fracture has smooth and flat fracture curve. b. A spiral-shaped fracture leads to a fracture curve with a large degree of fluctuation. c. A multiple-parallel fracture results in a fracture curve with a small degree of fluctuation. 347
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Fig. 16. Fracture geometry under different horizontal stress contrast values and different perforation parameters. a. A multiple-parallel fracture in the first perforation interval of sample 2–4 with a perforation interval spacing of 4 cm and a horizontal stress contrast of 8 MPa b. A single flat fracture in the second perforation interval of sample 2–4. c. A multiple-parallel fracture in sample 3-1 with a horizontal stress contrast of 12 MPa.
perforation diameter; and multiple-parallel fractures can be generated by a perforation phase of 90°. In addition, each fracture geometry has its own pressure behavior, corresponding to the fracture curve. A single flat fracture has a smooth and flat fracture curve; spiral-shaped fractures lead to fracture curves with a large degree of fluctuation; and multiple-parallel fractures result in fracture curves with a small degree of fluctuation. (2) Reducing the angle between the direction of perforation and the maximum horizontal stress as much as possible can promote perforation initiation. High perforation density, large perforation diameter, and low perforation phase are recommended for perforated fracturing, whereas changing the perforation parameters leads to different results under different horizontal stress contrast values. To obtain low fracture pressure or small tortuosity of the fracture surface, we suggest the following optimal perforation parameter combination: a perforation length of 30 mm, a perforation diameter of 4 mm, a perforation density of 12 holes/cm, a perforation phase of 60°, and a perforation interval spacing of 20 mm under low horizontal stress contrast; however, a perforation length of 30 mm, a perforation diameter of 4 mm, a perforation density of 18 holes/ cm, a perforation phase of 60°, and a perforation interval spacing of 40 mm would be used under low horizontal stress contrast. (3) The fracture pressure is affected deeply by the horizontal stress contrast rather than the perforation parameters. High horizontal stress contrast always reduces the fracture pressure in tight formations.
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