As for the key technology in fracturing completion, perforation has been paid more and more attention to in recent years. To exploit the unconventional oil and gas resources such as shale gas, tight gas, and coalbed methane, perforation was performed not only to connect the wellbore and formation rocks, but also to control the fracture propagation and promote the formation of fracture network^{[1,2,3,4,5,6]}.

In large-scale staged perforating and fracturing of long vertical horizontal wells, the commonly used perforating methods are helical perforation, directional perforation and conventional fixed plane perforation, which can reduce the fracturing pressure, control the expansion morphology of the main fracture and promote the formation of the fracture network^{[7,8,9,10,11,12]}. Adopting the fixed plane perforation technology combined with the equal aperture deep penetration perforation bullet can control the height of fracture and avoid the early penetration in the near wellbore area. Perforating the serious sanding horizontal well along the direction of the minimum stress difference with directional perforation technology can change the flow pattern of the near wellbore formation, which can make the stress evenly distributed and reduce the sand production. Combining the above three methods and adopting multi-stage composite perforation technology, we can obtain deep holes or fractures with high penetration, alleviate the serious pollution in the near wellbore area of horizontal wells and the deviation of wellbore trajectory from the reservoir. However, due to the complex fracture physical morphology, diverse connection patterns, unclear formation mechanism and propagation law of fractures around the perforating holes, there are many limitations in the above methods, such as lack of theoretical and experimental basis, poor stability of application effect, narrow application scope, etc. These limitations will seriously restrict the efficient and stable development of unconventional oil and gas reservoirs and complex conventional oil and gas reservoirs. So it is still an important problem in the research of perforating and fracturing that how to control the fractures near the wellbore by optimizing the perforation mode and parameters so as to improve the effect of fracturing.

In this paper, the perforation and fracturing process is divided into three stages first, and then we put forward an innovative perforation method of interlaced fixed plane perforation based on the analysis of the characteristics of fracture behavior of each stage and conventional perforation methods. By carrying out perforation experiments on large-scale rocks, we investigate the fracture morphology, propagation mechanism and propagation law of the near-wellbore fracture generated during the perforating process under different fixed angle and interlaced angle combinations. At last, we discuss the control method for near-wellbore fractures.

In order to put forward the concept of interlaced fixed plane perforation, we need to investigate the fracture behavior characteristics for every stage during perforation fracturing firstly. The perforation-fracturing process can be divided into three stages: (1) The stage of near-wellbore fractures formation^[13,14,15]. With the formation of perforation channels, there are a large number of micro-fractures around them, which will connect with each other by the stress concentration effect and further propagate to form complex near-wellbore fractures. Because of the fact that the high energy will release in a short time during the perforation, the formation of near-wellbore fractures in this stage is mainly determined by the perforation method and perforation parameters, and the influence of in-situ stress is small. (2) The stage of main fracture formation^[16,17]. In this stage, the hydraulic fracturing is carried out after the perforating operation. The complex near-wellbore fractures will further propagate to form main fractures. At the same time, under the effect of in-situ stress, the main fracture will twist and eventually extend along the direction perpendicular to the minimum in-situ stress. In this stage, the influence of perforation will be weakened and the influence of in-situ stress will be enhanced. (3) The stage of fracturing network formation^[18]. In this stage, every main fracture propagates along the direction perpendicular to the minimum in-situ stress driven by the hydraulic energy. Meanwhile, affected by the local in-situ stress change, reservoir heterogeneity, natural fractures and other influencing factors, these main fractures will bifurcate, divert, and interact with each other to form a complex fracturing network. In this stage, the influence of perforation factors is negligible. It can be found that the morphology and propagation law of the near-wellbore fractures in the first stage have a great influence on the formation and propagation of the main fractures. Generally, for increasing the oil drainage area, avoiding premature intersection of the main fracturing fractures, and promoting the main fractures in the second and third stages to extend further in the far-wellbore area under the condition that near-wellbore fractures are perpendicular to the wellbore axis and evenly distributed around the wellbore.

However, the conventional perforation methods (such as helical, directional and fixed plane perforation) are difficult to meet these requirements. The main reasons are as followings: when using the helical perforation method, the perforation holes are relatively isolated, the formation and propagation of fractures around the perforation tunnels are random with poor connectivity, so it is difficult to form near-wellbore fractures with controllable morphology and propagation law. When using the directional perforation method, with the change of the perforation azimuth angle, the penetration depth of the perforation tunnels tends to fluctuate drastically. Also the micro-fractures around the tunnels as well as the near-wellbore fractures are normally parallel to the wellbore axis, so it is difficult to form the main transverse fracture. When using the fixed-plane perforation method, the perforations in the same plane maybe closely linked, which are easy to form the local scalloped near-wellbore transverse fracture surface. However the connectivity between different scalloped transverse fracture surfaces is random, which makes it difficult to control, and fracturing accident such as uncontrolled propagation of main fracture often occurs.

Therefore, in order to achieve more effective control of the near-wellbore fractures, strengthen the connectivity between perforation tunnels and promote the orderly propagation of fractures around them, an innovative perforation method of interlaced fixed plane perforation is proposed (Fig. 1). The fixed angle represents the angle between two adjacent perforation tunnels in the same fixed plane, similar to the phase angle for the helical perforation. The interlaced fixed angle represents the angle between the first perforation tunnels of adjacent fixed planes. Interlaced fixed plane perforation is based on conventional fixed plane perforation, which introduces fixed plane interlaced angle, so that the adjacent fixed plane formed by three perforations is interlaced. It can not only guarantee close connection between perforations in the same fixed plane and easy connection of micro fractures around the perforation of conventional fixed plane perforation technology, but also enhance the connection between perforations in adjacent fixed planes, promote the connection between micro fractures of fixed planes, which is conducive to the formation of orderly connection and expansion of near-wellbore fractures.

To make it easy to understand, Fig. 1 arranges the three perforation bullets in the same plane, which is not completely consistent with the actual operation. In the actual perforation arrangement, the 3 perforating bullets in the same plane are arranged continuously from top to bottom in the perforating gun. If the plane perpendicular to the wellbore is regarded as the reference plane, then from top to bottom, the first perforation bullet inclines downward by 10°-13°, and the included angle with the reference plane is 10°-13°; the second perforation bullet is vertical to the wellbore and the included angle with the reference plane is 0°; the third perforation bullet inclines upward by 10°-13° and the included angle with the reference plane is 10°-13°. The three perforating bullets form a plane approximately.

To further explore the near-wellbore fracture morphology, formation mechanism and propagation law of interlaced fixed plane perforation, a large-scale perforation test was designed (Fig. 2). Two kinds of perforating bullets were used to perforate four shale targets to simulate the interlaced fixed perforation process. After perforation, the target body was split and the perforation channels and near-wellbore fractures were observed.

The two kinds of perforating bullets are DP44RDX38-1 deep penetrating perforating bullet and GH46RDX43-1 large aperture perforating bullet produced by Shuanglin Perforating Bullet Factory in Jilin Province. The perforation effects of these two kinds of perforating bullets are obviously different with small aperture and deep penetrating, large aperture and small penetrating respectively. The standard target aperture of DP44RDX38-1 bullet is about 11 mm, the penetration depth is about 1.5 m, and the standard target aperture of the GH46RDX43-1 perforating bullet is about 20 mm and the penetration depth is about 0.8 m.

Four shale targets, numbered 115#-118#, are cast with cement mortar in a water-lime-sand ratio of 0.52:1.00:2.50. They are all cylindrical with homogeneity, 1.4 m high and 2.5 m in diameter. Due to the limited experimental conditions, there are no natural fractures and bedding planes in the rock target. The effective perforation section is 1 m long. A casing with outer diameter of 139.7 mm and the wall thickness of 9.7 mm is reserved in the center of each shale target. The perforating gun is placed in the middle of the casing. The outer wall of the casing is directly connected with the target. In perforation experiments, the uniaxial compressive strength of the targets is 35.2-37.6 MPa, the modulus of elasticity is 39.5-41.7 GPa, and the Poisson's ratio is 0.29-0.31. The targets are similar with shale in physical property and can be used to simulate the shale formation with 1000-3000 m depth.

Four perforating guns, numbered 115#-118#, corresponding to 115#-118# shale targets respectively. The effective perforating section length of each gun is 1 m, 15 perforating bullets (1#-15#) are evenly arranged, and five groups of fixed planes are set up from top to bottom. Each fixed plane consist of three bullets, the distance between adjacent fixed planes is 200 mm in the axial direction (the law of well-bore fracture propagation is obvious with little interference and close connection between bullets when the distance is set at 200 mm). All the fixed planes are perpendicular to the axial direction of the wellbore. The gun 115# uses large aperture GH46RDX43-1 perforating bullets with fixed angle of 60°, and the five groups of interlaced fixed angles from top to bottom are 30°, 60°, 90° and 120° respectively. The gun 116# uses deep penetrating DP44RDX38-1 perforating bullets with the same fixed angle and interlaced angle as the gun 115#. The gun 117# uses large aperture GH46RDX43-1 perforating bullets with fixed angle of 90°, and five groups of interlaced fixed angles from top to bottom are 45°, 90°, 135° and 180° respectively. The gun 118# uses deep penetrating DP44RDX38-1 perforating bullets with fixed angle and interlaced angle the same as the gun 117#. After the perforation experiments, the shale targets will be split, some channels will be marked with red pigments, and some cracks around the holes will be marked with yellow pigments.

Observing the four targets of 115#-118#, it can be found that the perforation bullets are injected into the rocks to form channels, which is accompanied by the generation of micro-fractures^[15]. These micro-fractures can be divided into three types according to their relationship with perforation: (1) Type I micro-fracture, also called radial micro-fractures, as shown in Figs. 3a-3c, the fracture plane extends in the direction of the perforation channel (radial in the wellbore), and the perforations have a good control effect. Type I micro-fracture is the most common one, it is more obvious with single shot in shale rock (Fig. 3c). (2) Type II micro-fracture, also known as skew micro-fracture, as shown in Figs. 3d-3e, the fracture plane intersect with the perforation propagation direction at an angle, and the perforation has a weakened control effect on the expansion. (3) Type III micro-fracture, also known as divergent micro-fracture at the perforation tip, is shown in Fig. 3f. When the tip of the perforation hole is blocked, it is often accompanied by the formation of type III fractures. Because type Ⅲ fracture has the characteristics of low probability of occurrence, small scale, complex shape with no regularity, no schematic diagram has been made. The type I, II and III micro-fractures in this study are different from the type I open fractures, type II shear fractures and type III tear fractures defined in fracture mechanics.

These three kinds of fractures around the perforation holes interact and connect to form complex near-wellbore fractures and networks, as shown in Fig. 4. (1) When the type I micro-fracture connect to each other, type I-I fractures around the perforation holes are formed. At this time, the interaction between the perforation holes is strong, and the perforation holes have good control on the propagation of these fractures. (2) When the type I and the type II micro-fractures connect to each other, I-II distorted fractures around the perforation holes are formed. At this time, the interaction between the perforation holes is weakened, and the perforation holes have a weakened ability to control the propagation of these fractures. (3) When the hole type II and type II micro-fractures connect to each other, type II-II type fractures with perforation channel at certain skew angles are formed. At this time, the interaction between the perforation holes is the weakest, and the control ability of the perforation drops rapidly. (4) When the type I-I, type I-II, and type II-II fractures coexist, a complex near- wellbore crack network is formed. Since the type III micro-cracks have a low frequency and a small scale, it is unnecessary to study it.

3.2.1. Propagation law of near-wellbore fractures for the deep penetration perforating bullet

Due to the small opening cone angle of the charge liner of deep penetration perforating bullet DP44RDX38-1, the high-energy metal fluid flow formed is long and thin, and the energy release is relatively concentrated, so that when the perforation tunnels are formed, the type I micro-fractures are mainly developed around the tunnels, the type II micro-fractures are less developed, the tunnels are generally complete, rarely broken, and the rocks around the casing are basically intact. When the fixed angle is 60° and the interlaced angle is 30° (Fig. 5a-5c), it can be found that the three perforations in the same fixed plane have poor connectivity in the loop direction and are independent of each other. However, the two perforations on adjacent fixed planes in adjacent phase communicate with each other through the type I-I fracture plane. When multiple type I-I fractures exist at the same time, a diamond-shaped transverse fracture perpendicular to the vertical wellbore axis will be formed. The diamond- shaped transverse fracture will propagate deep along the channel extension direction. During this process, type I-I fractures rarely distort and type I-II fractures rarely appear.

With the increasing interlaced angles of fixed planes to 60°, 90° and 120°, type I-I fractures between the perforation channels in the same or adjacent phase between adjacent fixed planes gradually decrease, and mainly propagate along the direction parallel or nearly parallel to the axis of wellbore. Some type I-I fracture planes will twist and deform into type I-II fracture planes, while the others will be broken by type II-II fractures formed by the connection of type II fractures around the hole, resulting in losing control of perforation channels on near-wellbore fractures gradually, and the propagation direction is more random, which makes it difficult to form transverse fracture perpendicular to the wellbore (Fig. 5d-5f).

Fig. 6 shows that when the fixed angle increases to 90°, with the interlaced angles of 45°, 90°, 135° and 180°, the space distance of perforation channels increases. As a result, the three perforations in the same plane no longer develop I-I fractures in the circumferential direction, and type I-I fractures between the perforations in the same and adjacent phase between adjacent fixed planes greatly decrease, while perforations in the same phase and adjacent phase between non-adjacent fixed planes begin to form type I-I fractures across multiple fixed planes, which are parallel or nearly parallel to the axis of wellbore.

3.2.2. Propagation law of near-wellbore fractures for the large aperture perforating bullet

The large-aperture perforating bullet GH46RDX43-1, the opening cone angle of the liner increases with the increase of explosive quantity, resulting in short and thick liquid metal flow and relatively divergent energy release. When the fixed angle is 60° and interlaced angles are set as 30° and 60° respectively, the space distance between perforations is relatively close, which makes the formation of each channel show the phenomenon of explosion. In the experiment, several obvious characteristics are as follows: the perforation channel is broken and the penetration depth is reduced with twisted fractures around the perforation channel. The wall rock around the casing is severely fractured, and the target body appears large-scale fragmentation. These phenomena all indicate that there are a large number of type I and type II micro-fractures around the channel during the formation and extension of the channel. A part of type I and II micro-fractures are interconnected to form multiple types I-I, I-II and II-II fractures. Finally, the three types coexist to form a network around the perforation, resulting in target fragmentation (Fig. 7a-7c). Type III micro-fractures are also developed in individual perforations, which further aggravates the complexity of near-wellbore fracture network.

With the increase of the interlaced angle of the fixed plane to 90° and 120°, the bursting phenomenon of each channel decreases and well-formed channels appear, which indicates the decrease of type II fractures around the perforation. At the same time, the adjacent fixed-plane perforation has more complete type I-I fractures which coincide with or nearly coincide with the direction of perforation extension. Some type I-I fractures are connected with each other to form transverse fractures which are nearly perpendicular to the axis of the wellbore, but they soon twist and evolve into type I-II fractures (Fig. 7d-7f).

Fig. 8a-8c show that when increasing the fixed angle to 90°, the space distance between perforations is increased and the independence of perforation is enhanced. There are both type I and type II micro-fractures around the perforation holes and they propagate randomly. When the interlaced angles are 45° and 90°, the perforation channels in the adjacent phase of adjacent fixed planes will connect through type I-I fractures. These type I-I fractures will propagate along the extending direction of the channels and continuously communicate with type II micro-fractures, which gradually evolve into type I-II fractures, and eventually spread to deep rock in a random divergent form.

Fig. 8d-8f show that when the interlaced angle increases to 135° and 180°, the independence of perforations further increases, most perforations are no longer interconnected, the development and expansion of type I and II micro-fractures around the perforations are more random, the near-wellbore fractures are more distorted. Some channels are broken by type II micro-fractures around the holes.

3.2.3. Propagation law of near-wellbore fractures under different combinations of fixed angle and interlaced angle

Through analyzing Figs. 5-8 comprehensively, the propagation law of fractures near wellbore developed by two types of perforating bullets with different combinations of fixed angle and interlaced angle can be summarized as follows. For the deep penetration perforating bullet DP44RDX38-1: (1) When the fixed angle is 60° and interlaced angle is 30°,transverse fractures are formed nearly perpendicular to the axis of the wellbore. (2) When the fixed angle is 60° and interlaced angle is 60°, perforations on adjacent fixed planes form small parallel fractures parallel to the axial direction of the wellbore. (3) When the fixed angle is 60° and interlaced angles are 90° or 120°, the release of perforation energy is more divergent and there are random divergent fractures appear around the perforation hole. A small number of perforation channels are connected through I-II type fractures, which is similar to the helical perforation. (4) When the fixed angle is 90° and interlaced angles are 45°, 90°, 135° or 180°, large parallel fractures parallel to the axis of wellbore are formed between non-adjacent fixed-plane perforations, which are similar to directional perforations. The propagation law is as Fig. 9.

For the large aperture perforating bullet GH46RDX43-1: (1) When the fixed angle is 60° and interlaced angles are 30° and 60°, the fracture network near the wellbore is formed, that is, the rocks near the wellbore are broken up by the explosion of perforating bullet. (2) When the fixed angle is 60° and interlaced angles are 90° and 120°, or fixed angle of 90° with interlaced angles of 45° and 90°, small transverse fractures perpendicular to the wellbore appear, but distort quickly. (3) When the fixed angle is 90° and interlaced angles are 135° and 180°, perforations are independent of each other, the release of perforation energy is more divergent. A small number of small parallel fractures appear, which is similar to helical perforation (Fig. 10).

For different types of perforation bullets, when the combination of fixed angle and interlaced angle is changed, the near-wellbore fractures present a specific shape and propagation law, which will have a significant impact on the subsequent fracturing. Therefore, for unconventional reservoirs with different characteristics, we can try to promote the formation of near-wellbore fractures by adopting interlaced fixed-plane perforation method with optimized type of perforation bullet and the combination of fixed angle and interlaced angle. In this way, we can control the formation and propagation of subsequent main fractures effectively.

(1) Promoting the formation of 360° transverse fractures near wellbore. For shale reservoirs with good geological conditions, small dip change, large thickness, the wellbore axis is generally pass through the reservoir center line. It is better to form main transverse fracture perpendicular to the vertical wellbore axis, thus slowing down the near wellbore effect and “controlling the near and propagating the far”. This goal may be achieved when using deep penetrating perforation bullets DP44RDX38-1 with the combination of fixed angle of 60° and interlaced angle of 30°, and adopting the arrangement of one-way spiral encircling the wellbore in each fixed plane. As shown in Fig. 11, when perforating detonation occurs, the adjacent fixed planes near the wellbore are connected by diamond-shaped transverse fractures and surrounded the wellbore by 360°. Thus, during subsequent fracturing, these transverse fractures near wellbore are easier to propagate and develop into a large transverse fracture around the wellbore.

(2) Promoting the formation of directional transverse fractures near wellbore. For shale reservoirs with special geological conditions, large dip changes or special engineering requirements, the wellbore axis sometimes passes above or below the reservoir. It is better to form fractures more on one side of the reservoir, so as to maximize the use of hydraulic energy and improve productivity. This goal may be achieved when using deep penetrating perforation bullets DP44RDX38-1 with the combination of fixed angle of 60° and interlaced angle of 30°, and adopting the two-way arrangement of continuous “W” shape on one side of wellbore in each fixed plane. As shown in Fig. 12, when perforation detonation occurs, adjacent planes near the wellbore will be connected by diamond-shaped transverse fractures and twisted on one side of the wellbore in accordance with the shape of "W", thus forming directional transverse fractures near the wellbore. In subsequent fracturing, the controllable directional large-scale transverse fractures near the wellbore are easier to develop.

(3) Promoting the formation of multi-directional transverse fractures near wellbore. For shale reservoirs with complex geological condition and sharp dip changes, the borehole axis is often inclined to one side of the reservoir or out of the reservoir. It is better to form main fracture with extension direction along the reservoir position closely. At this time, as shown in Fig. 13, the goal may be achieved by using deep penetrating perforation bullets DP44RDX38-1 with the combination of fixed angle of 60° and interlaced angle of 30°, and adopting the mixed arrangement of one-way spiral and two-way continuous "W" shape in each fixed plane according to the reservoir location.

(4) Promoting the formation of near-wellbore fracture network. For complicated reservoirs, such as thin and poor reservoirs, oil and gas reservoirs with edge and bottom water, heavy oil reservoirs and sanding reservoirs, it is better to obtain larger oil release area directly on the wellbore by perforation and reduce reservoir fracture pressure and form near-wellbore fracture network system. At this time, the goal may be achieved by using large-aperture perforating bullet GH46RDX43-1 with the combination of fixed angle of 60° and interlaced angle of 30°, and adopting the arrangement of one-way spiral encircling the wellbore in each fixed plane. Under these perforation parameters, the rock around the perforation will break up during the perforation detonation due to the close distance between perforations and the concentration of energy release, thus directly forming the near-wellbore fracture network.

By introducing the interlaced fixed angle based on conventional fixed perforation, the interlaced fixed plane perforation strengthens the connectivity between the perforation tunnels not only of the same fixed plane but also of the adjacent fixed plane, making it easier to form the connecting fracture and propagate in order.

There are three kinds of micro-fractures developed around the perforation tunnels, namely type I radial fracture, type II oblique fracture and type III divergent fractures around perforation tip. These three fractures are interconnected to form more complex near-wellbore fractures. For the interlaced fixed perforation, under the different fixed angle and interlaced angle combinations and different types of perforation bullets, the near-wellbore fracture morphology and propagation law formed are also different. By adjusting the combination of fixed angle and interlaced angle and perforation bullet types according to reservoir characteristics, arranging each fixed plane at specific modes, we can not only obtain the near-wellbore fractures in demand, but also improving the fracturing fractures control ability.