Study on Near-Wellbore Fracture Initiation and Propagation with Fixed-Plane Perforation in Horizontal Well for Unconventional Reservoirs

Abstract

At present, in the process of volume fracturing for a tight reservoir, employing the spiral perforation method to induce the fracture propagation direction would always obtain an unsatisfactory effect, which causes the deflection and tortuosity of hydraulic fractures. Therefore, researchers presented the fixed-plane perforation method for enhancing the effect on volume fracturing. In this paper, the three-dimensional discrete lattice method is used to study the initiation and propagation law of horizontal well fixed-plane perforation in unconventional reservoirs under two different stress states. The results show that it is more suitable to use fixed-plane perforation for reducing the initiation pressure. When employing the fixed-plane perforation method, fracture always initiates in the perforation plane, presents as an irregular fan-shaped failure surface, and then propagates along the wellbore. The initiation pressure is highly correlated to the phasing angle between adjacent perforations under different conditions, and the rate of increase in the initiation pressure decreases by around 1.59~6.38% when the phasing angle reaches 30°. The fracturing pressure is inversely correlated with the diameter and tunnel length of the perforations and the horizontal stress difference. When the diameter increases to 17 mm, the tunnel length increases to 25 cm or the horizontal stress difference reaches 8 MPa. These results reveal an insignificant effect of the above parameters on the initiation pressure.

1. Introduction

There has been a growing focus on the study of oil and gas exploration in unconventional reservoirs, characterized by tight rock quality, extremely low porosity, and permeability. Conventional drilling or completion methods are insufficient to meet production demands; hence, many advanced technologies are commonly employed to enhance the migration channels for oil and gas within the reservoir, aiming to achieve increased production rates [1,2,3,4,5,6]. Perforation plays a crucial role in the hydraulic fracturing process for enhanced oil recovery as it not only establishes communication between the wellbore and the formation but also stimulates fracture initiation and propagation, thus garnering significant attention from researchers [7,8,9,10].

More and more theoretical and experimental studies have been carried out in order to clarify the effects of different factors on the morphology and law of fracture initiation and propagation for both vertical and horizontal wells under various conditions [11,12,13,14,15,16,17,18,19]. Daneshy [20] first discovered, through hydraulic fracturing experiments, that the arrangement and number of perforations have a significant impact on the fracture morphology and fracturing pressure. The application of spiral perforation technology was initially limited to vertical wells due to the occurrence of near-wellbore fracture distortion and the incomplete initiation of multi-cluster fractures in horizontal wells [21]. To address these issues, advanced techniques such as oriented perforation and definite plane perforation have been developed [22,23,24]. Li [25] proposed length-controlled and diameter-controlled oriented perforation methods. The research shows that the proposed methods can reduce the fracture initiation pressure and increase the fracture are, which can effectively solve the issue of uneven fracture initiation. By comparing the initiation pressure and fracturing morphology under different perforation methods, Huang [26] revealed the micro-scale mechanism of near-wellbore complexity through numerical modeling, and the results show that the perforation tunnels guide the generation of initial microcracks; however, the subsequent fracture propagation is controlled by the relative locations of the perforation tunnels and the stress interference among different perforation tunnels. According to the above research studies, the results show that the initiation pressure of definite plane perforation is lower than that of spiral perforation. However, the utilization of definite plane perforation also presents certain drawbacks as it may lead to the formation of random local fan-shaped cross fractures, thereby influencing the propagation of the main fracture. For deep reservoirs, the high formation stress and strength conditions make it even more difficult for the rock to crack; therefore, innovation and improvement are still needed for oriented perforation fracturing technology to be used extensively.

In recent years, the fixed-plane perforation method was suggested as a novel approach for achieving completion in the field of research because there will be more opportunities to generate a fan-shaped failure plane at the near-wellbore region [27,28,29]. Falser et al. [30] discussed the influences of perforation on the near-wellbore fracture morphology by large-scale triaxial fracturing experiments on tight sandstone, and the results show that the fixed-plane perforation method is beneficial for avoiding fracture tortuosity at the near-wellbore region and reducing the initiation pressure. Yuan et al. [31] conducted a series of fracturing experiments on cement rocks under high stress differentials in the normal faulted stress regime. Comparisons between the fixed-plane perforation and spiral perforation techniques revealed that fixed-plane perforation completion exhibited the capability to generate radial hydraulic fractures, resulting in a significant reduction in the breakdown pressure. Xie et al. [32] investigated the morphology of hydraulic fracture of shale samples with bedding planes and natural fractures in different fracturing perforation scenarios, and the results indicate that fixed-plane perforation is much more recommended under large horizontal stress difference condition. Wang et al. [33] proposed an interlaced fixed-plane perforation method and discussed the control method of near-wellbore fractures in different types of unconventional reservoirs. The research demonstrated that different types of microfractures occur around the perforation tunnel, and it can yield a more desirable fracture morphology when fixed-plane perforation is used.

Qin et al. [34] established a 2D global cohesive element model for the study of the fracture propagation path. The results show that hydraulic fracture propagation is more complex for considering the existence of laminae and microfractures. However, under the fixed-plane perforation condition, there are more chances for them to connect with each other and finally form a fan-like fracture, which leads to the near wellbore tortuosity being greatly reduced. Meanwhile, it was found that the fracture morphology in the near-wellbore region tends to be more complex than that in the far-field zone. This also suggests the importance of the fracture initiation morphology for fracture propagation. Wu et al. [35] introduced the fixed-plane perforation to the enhanced geothermal system (EGS) and numerically examined its heat extraction performance. By simulation research of the hydraulic fracturing process, various factors were discussed, such as the injection rate, Young’s modulus, in situ stress difference and initial fracture angle. Compared with single perforation, it was found that the fractures are much longer and the rock damage area is considerably larger by fixed-plane perforation. Through a comparison of the heat extraction rate under different perforation conditions during geothermal energy extraction process, it indicated that fixed-plane perforation fracturing is significantly higher than those of the unfractured model and the model stimulated by the single-perforation fracturing. In certain conditions, fixed-plane perforation can have the effect of increasing production. For example, Duan et al. [36] conducted a study about ultra-low-permeability reservoirs, in which a large amount of residual oil stayed because of the long-term water flooding process. Therefore, for recovering the remaining oil, fixed-plane perforation was used as an alternative plan. Considering the oil field application effects, fixed-plane perforation fracturing reconnects the longitudinal low-permeability reservoir, achieving a significant effect to excavate more remaining oil. Huang et al. [37] carried out a modeling study of hydraulic fracturing initiation and near-wellbore propagation for three different perforation methods, which are spiral perforation, oriented perforation and Tristim perforation. The numerical simulation results demonstrate that with the injection process, initial microcracks occurs at the roots of the perforation tunnels, and subsequent propagation is guided by the stress interference among different perforation tunnels. This shows that spiral perforation gives the highest breakdown pressure. The primary cause of pressure breakdown is the formation of extensive micro-annulus cracks, resulting in trans-wellbore fracture surfaces.

However, previous studies have predominantly focused on optimizing fixed-plane perforation based solely on the fracture initiation pressure, neglecting the influence of perforation parameters on the near-wellbore fracture extension patterns. Furthermore, there has been limited comparative research investigating the fracturing effects between fixed-plane and spiral perforations. Therefore, this study employs a combination of true triaxial physical simulation experiments and numerical simulations to investigate the fracturing patterns and propagation morphologies of fixed-plane perforation under different stress conditions associated with normal faults and strike-slip faults. Additionally, it reveals the impact of both perforation parameters and geological factors on the fracturing effect of fixed-plane perforation.

2. Experimental Setup

2.1. Specimen Preparation

Concrete specimens were utilized for conducting the simulation experiments. To closely replicate the mechanical properties of real shale, the proportions of various materials were continuously adjusted until a ratio scheme that met the experimental requirements was ultimately selected. The primary constituents of the specimens consisted of high-strength Portland cement whose grade was 62.5, 400-mesh high-purity quartz sand, and water. Additionally, metakaolin, silica powder, a water-reducing agent obtained through dilution of polycarboxylic acid-based high-performance water-reducing agent mother liquor, and a polyether defoamer were incorporated into the material to enhance the strength and compactness. Experimental cement specimens with dimensions of Φ 25 mm × 50 mm were prepared by varying the material ratios. Subsequently, the rock mechanics parameters of the specimens were measured following an appropriate curing period. By comparing these parameters with those obtained from natural cores, an initial determination regarding the water–cement ratio was made; the subsequent optimization formulas led to finalizing the experimental ratios for other materials, as presented in

Table 1. Mass proportion of constituents for the specimen.

Water–Cement Ratio	Cement–Sand Ratio	Water-Reducing Agent	Defoamer	Metakaolin	Silica Powder
0.4	1.6	0.3%	0.05%	15%	15%

Note: The proportion of the water-reducing agent, metakaolin, silica powder and defoamer is the proportion of cement paste.

.

After determining the formula, a 100 mm × 100 mm × 100 mm experimental specimen was fabricated, as shown in Figure 1. Simultaneously, as shown in Figure 2, a prefabricated steel pipe with an outer diameter of 8 mm and an inner diameter of 6 mm was inserted into the simulated wellbore at the bottom of the mold, along with a pre-drilled perforation diameter measuring 2 mm on the steel pipe. After pouring cement paste into the mold, it was subjected to constant temperature curing for 28 days until reaching standard strength. To facilitate comprehensive and clear observation of the fracture growth, the sample underwent cutting using a precision cutting machine post-fracturing.

2.2. Experimental Procedure

In order to investigate the impact of the perforation interval spacing, tunnel length, and phasing angle on the initiation and propagation of hydraulic fractures during perforation fracturing, we considered the parameter conditions of this experiment with the in situ stress selected as σ_V = 15 MPa, σ_H = 10 MPa, and σ_h = 5 MPa. The remaining parameters and specific experimental scheme are presented in

Table 2. Parameters for the hydraulic fracturing experiments.

Phasing Angle (°)	Perforation Length (cm)	Perforation Interval Spacing (mm)	Number of Perforation Tunnels	Injection Flow Rate (mL/min)
60	1.5	4	6	20

.

A tri-axial hydraulic fracturing physical simulation test system was employed in the study, as illustrated in Figure 3. During the fracturing process, the specimen was positioned on the operating platform and subjected to loads from hydraulic jacks at its bottom and surrounding areas to replicate anisotropic stress conditions. The magnitude of the stress was regulated by a confining pressure system utilizing hydraulic pressure, with a maximum application capability of 70 MPa. Simultaneously, fracturing fluid was injected into the specimen through a high-pressure pump and an intermediate vessel. Throughout injection process, both the pumping rate and injection volume could be precisely controlled via computer programming. In the process of liquid injection, the confining pressure was continuously stabilized at the set value to ensure the experimental accuracy.

2.3. Experimental Results

To ensure alignment with the actual fracturing construction on site, the spiral perforation and fixed-plane perforation experiments were conducted with a phasing angle of 60°, as illustrated in Figure 4.

As can be seen from Figure 4, conventional spiral perforation leads to distorted fractures in the near-wellbore region, resulting in multiple branch fractures. Additionally, controlling the fracture direction becomes challenging, as shown in Figure 4a. However, it can be seen in Figure 4b that with the implementation of fixed-plane perforation, only two main fractures and one branch joint are formed. Considering the morphology of the fractures, employing fixed-plane perforation effectively guides the fracture direction within the vicinity of the wellbore to propagate vertically and radially while promoting deep propagation for the formation of a complex fracture network in the near-wellbore region. Consequently, it enhances the fracturing stimulation effectiveness.

3. Numerical Modeling

Utilizing the discrete lattice method, this study uses the software Xsite 3.0 and investigates the impact of various parameters on fracture initiation and propagation under constant surface perforation conditions, as based on experimental phenomena and preliminary conclusions obtained from true tri-axial physical simulation experiments.

3.1. Numerical Method

The model consists of a series of randomly distributed particles connected by springs, similar to the particle structure in the discrete element model, as shown in Figure 5 [38]. A spring corresponds to a contact between particles, and a node with mass corresponds to a particle [39]. The elastic and strength parameters of the fracture are assigned to the spring in contact with the discontinuity. Both the mesoscopic damage to the rock mass and the relative slip of the rock matrix on the discontinuity plane can be simulated. The nodes at the joint are calculated using the smooth joint model, so the shear and normal forces of the spring at the joint are calculated with reference to the set direction of the joint surface, rather than the connection direction between the nodes. When the spring between the nodes is stressed beyond its strength, the fracture occurs and the micro-cracks are connected with each other to form macro-cracks. The gaps between nodes are defined as “pipes”, which are used to calculate the microscopic flow of fluid and apply fluid pressure to the rock matrix, while the deformation of the matrix causes changes in the pore pressure and pore size.

The discrete lattice method uses an explicit solution scheme [9]. Thus, the law of motion for translational degrees of freedom consists of the following central difference formulae for each node (assume that the acceleration of the node remains constant for ∆t):

$$v_i^{(t+\mathsf{\Delta }t/2)}=v_i^{(t-\mathsf{\Delta }t/2)}+{\displaystyle \frac{\mathsf{\Sigma }{F}_i^{(t)}\mathsf{\Delta }t}{m}},$$

(1)

where $v_i^{(t)}$ is the velocity of node i at time t, m/s; and ${\displaystyle \sum F_i^{(t)}}$ is the sum of all the force components i acting on the node of mass m with timestep ∆t, N.

At time t, the angular velocity ${\omega }_i$ of node i is calculated by the following difference equation:

$${\omega }_i^{(t+\mathsf{\Delta }t/2)}={\omega }_i^{(t-\mathsf{\Delta }t/2)}+{\displaystyle \frac{\mathsf{\Sigma }{M}_i^{(t)}\mathsf{\Delta }t}{I}},$$

(2)

where ${\omega }_i$ is the angular velocity, rad/s; M_i is the sum of all the moments acting on the particle, N⋅m; and I is the moment of inertia, kg⋅m².

The changes in the normal and shear forces of the spring can be determined by calculating the relative displacement of the nodes,

$$F_i^N\leftarrow F_i^N+{\dot{u}}_i^N{k}^N\mathsf{\Delta }t$$

(3)

$$F_i^S\leftarrow F_i^S+{\dot{u}}_i^S{k}^S\mathsf{\Delta }t$$

(4)

where $F_i^N$, $F_i^S$ are the normal and shear force, respectively, N; ${\dot{u}}_i^N$, ${\dot{u}}_i^S$ are, respectively, the velocity in the normal and shear direction, m/s; and $k^N$, $k^S$ are the normal and shear stiffness of the spring, N/m. If $F_i^N$ exceeds the tensile strength or $F_i^S$ exceeds the shear strength, the spring is judged to have tensile or shear failure.

The flow rate q along the pipe between two nodes (node “A” to node “B”) can be calculated based on the plane Poiseuille flow,

$$q=\beta K_r{\displaystyle \frac{a^3}{12\mu }}\left[P^A-P^B+{\rho }_{w}g\left(Z^A-Z^B\right)\right]$$

(5)

where q is the fluid flow rate, m³/s; β is the dimensionless coefficient; K_r is the relative permeability, m²; a is the hydraulic fracture width, m; μ is the viscosity of the fluid, Pa⋅s; P^A and P^B are the fluid pressures at nodes “A” and “B”, Pa; ρ_w is the fluid density, kg/m³; g is the gravitational acceleration, m/s²; and Z^A and Z^B are the elevations of fluid elements A and B, m.

The fluid pressure increment ΔP in the time step Δt_f of the fluid is expressed as follows:

$$\mathsf{\Delta }P={\displaystyle \frac{Q}{V}}{\overline{K}}_f\mathsf{\Delta }{t}_f$$

(6)

$$Q={\displaystyle \sum q_i}$$

(7)

where ∆P is the pressure increment, Pa; Q is the sum of all the flows of the pipelines connected to the nodes, m³/s; V is the node volume, m³; ${\overline{K}}_f$ is the apparent fluid bulk modulus, Pa; and ∆t_f is the fluid time step, s.

3.2. Numerical Model Establishment

A 3D fracturing model centered on a perforated wellbore is established, as shown in Figure 6. The dimensions of the rock mass model are 1.5 m × 2.5 m × 2.5 m. The wellbore is positioned at the geometric center of the model, with its axis parallel to the X-axis. The diameter of the perforation is D = 2 cm, and the tunnel length is L = 25 cm. Additionally, there exists a cement ring with a thickness of 4 cm and casing with a thickness of 1 cm surrounding the wellbore for reinforcement purposes. To ensure more uniform stress conduction, a soft soil layer measuring 0.125 m in thickness covers the boundary of the model. Meanwhile, the numerical simulation is carried out in two states, which are normal fault (σ_X = 38 MPa, σ_Y = 42 MPa, σ_Z = 48 MPa) and strike-slip fault (σ_X = 38 MPa, σ_Y = 48 MPa, σ_Z = 42 MPa).

Table 3. Main simulation parameters of the rock mass.

Parameter	Value
Tensile strength (MPa)	7.2
Compressive strength (MPa)	110
Young’s modulus (GPa)	30
Poisson’s ratio	0.221
Permeability (10−15 m2)	1.7
Fracture toughness (MPa·m0.5)	0.98
Density (kg/m3)	2650

presents the basic parameters for the numerical simulation.

4. Analysis of Modeling Results

4.1. Comparison of Fracture Initiation and Propagation with Different Perforation Methods

In order to investigate the fracture initiation and propagation laws of spiral perforation and fixed-plane perforation, the perforation models shown in Figure 6b,c are used to simulate two stress states of normal fault and strike-slip fault. Referring to previous studies, the phasing angle of spiral perforation is 60°, the tunnel density is 20 holes/m, the phasing angle of fixed-plane perforation is θ = 30°, and the number of perforations is 6.

It can be seen from Figure 7a that under the normal fault stress state, the initiation pressure of fixed-plane perforation is 94.1 MPa, and it is lower than that of spiral perforation, which is 96.2 MPa. At the same time, it can be seen in Figure 7b that #1, #2, #3 and #6 perforations did not crack, only #4 was fully cracked, #5 was incomplete cracked, and #4 fracture was seriously deflected along the wellbore axis. However, in the case of fixed-plane perforation, all six perforations fully fractured, forming two vertical wellbore fracture surfaces that propagate radially along the wellbore.

The numerical modeling results of a strike-slip fault are illustrated in Figure 8, revealing that the initiation pressure for fixed-plane perforation is comparatively lower than that for spiral perforation, with values of 95.1 MPa and 99.4 MPa, respectively. When spiral perforation was used, perforations #1 and #6 did not crack, perforations #2, #3 and #4 did not fully propagate, and perforations #2 and #4 were twisted and propagated axially along the wellbore, and only perforations #5 were fully fractured. However, when using fixed-plane perforation, all the perforations were fully fractured, and the fractures did not cross torsional in the near-wellbore region and propagated generally perpendicular to the wellbore.

For normal faults and strike-slip faults, spiral perforation results in high initiation pressure, incomplete perforation or insufficient perforation, and cross-twisting of fractures in the near-wellbore region, making it difficult to control the fracture propagation. This is basically consistent with the results obtained from previous experiments. In contrast, the fixed-plane perforation causes a lower initiation pressure and can effectively guide the propagation direction of fractures in the near-well region, making them basically expand vertically and radially along the wellbore, and pushing them to expand deep to form a complex fracture network in the far-field, which is basically consistent with the conclusions obtained from physical simulation experiments.

4.2. Influence of Perforation Diameter on Fracture Initiation and Propagation Under Fixed-Plane Perforation

The perforation diameters were set to be 10 mm, 17 mm, and 24 mm, and the perforation phasing angles were set to be 15°, 30°, and 45°, respectively.

In the normal fault stress state, under a constant perforation diameter, the rock initiation pressure exhibits a positive correlation with the phasing angle, as shown in Figure 9a. This relationship arises due to an increase in the perforation interval spacing as the phasing angle increases, leading to a reduced stress concentration between each perforation and subsequently higher initiation pressure. However, when the angle reaches 30°, the rate of increase in the initiation pressure diminishes. Conversely, when keeping the phasing angle unchanged, increasing the perforation diameter facilitates a reduction in the initiation pressure. This is attributed to the decreased perforation interval spacing within the plane as the perforation diameter increases, resulting in a more pronounced stress concentration effect between perforation tunnels, and consequently, lower initiation pressure. For instance, at a phasing angle of 45° and with a perforation diameter of 10 mm, the initiation pressure measures 102 MPa, whereas for a perforation diameter of 17 mm, it decreases by 15.6 MPa or 15.3% to reach 86.4 MPa; further reducing to 84.2 MPa for a perforation diameter of 24 mm, it represents a decrease of only 2.28%. Henceforth, it should be noted that increasing the perforation diameter can only reduce the initiation pressure within certain limits.

As shown in Figure 9b, when the phasing angle is 15°, no fracture bifurcation occurs; when the phasing angle is 30°, fracture bifurcation only occurs when the perforation diameter is 10 mm; and when the phasing angle is 45°, slight fracture bifurcation occurs in the near-wellbore region, as shown in Figure 9b. This indicates that under normal fault stress conditions, an increase in the phasing angle leads to a higher probability of fixed-plane perforation fracture bifurcation close to the wellbore. Simultaneously, it can be observed from Figure 10 that in a normal fault stress state, the rock mass initially fractures at the perforation plane during the early stages of initiation and gradually forms a fan-shaped failure plane with continuous fracturing fluid injection before expanding radially along the wellbore.

Similarly, as shown in Figure 11a, under a strike-slip fault stress state, the initiation pressure increases with an increase in the phasing angle when the perforation diameter is constant, but it decreases once the phasing angle reaches 30°. When the phasing angle remains unchanged, there exists a negative correlation between the initiation pressure and the perforation diameter, as shown in Figure 12. For instance, at a phasing angle of 45° and a perforation diameter of 10 mm, the initiation pressure is 102.8 MPa; however, increasing the perforation diameter to 17 mm results in a decrease in the initiation pressure by 21.7 MPa or by 14.1%. Further increasing it to 24 mm leads to only a slight reduction (1.8%) in the initiation pressure. Therefore, under the strike-slip fault stress condition, increasing the perforation diameter cannot indefinitely reduce the initiation pressure.

As shown in Figure 11b, when the phasing angle is 15°, perforations with diameters of 10 mm and 17 mm are fully fractured, while those with a diameter of 24 mm do not achieve full fracture. At a phasing angle of 30°, only perforations with a diameter of 17 mm experience complete fracture, whereas those with diameters of 10 mm and 24 mm do not fully crack. When the phasing angle reaches 45°, all the perforations demonstrate insufficient fracture initiation. Therefore, with the increase of the phasing angle, the possibility of full perforation fracture decreases. Additionally, as shown in Figure 12, under strike-slip fault stress conditions, the perforation tunnel also initially cracks in the perforation plan, forming a fan-shaped failure plane and propagating radially along the wellbore.

4.3. Influence of Perforation Tunnel Length on Fracture Initiation and Propagation Under Fixed-Plane Perforation

The perforation tunnel length was set to 15 cm, 25 cm, and 35 cm, respectively. The perforation phasing angle was 15°, 30° and 45°, respectively.

In Figure 13a, under the normal fault stress state, when the perforation tunnel length is constant, the initiation pressure also increases as the phasing angle enlarges, and the increase reduces after reaching 30°. Under certain circumstances and for a given phasing angle of 30°, increasing the perforation tunnel length has a significant effect on reducing the initiation pressure. Because the area of the inner wall of the tunnel increases with the increase of the tunnel length, the greater the load effect on the inner wall of the tunnel length under the same fluid pressure, the lower the initiation pressure. For instance, when the perforation tunnel length is 15 cm, the initiation pressure is measured at 87.9 MPa, whereas for a length of 25 cm, it decreases to 83.3 MPa (a decrease of 6.3 MPa or 5.2%). When considering a perforation diameter of 35 cm, there is only a marginal decrease in the initiation pressure to approximately 83.1 MPa (0.24% reduction). Therefore, it can be concluded that increasing the perforation tunnel length does not indefinitely reduce the initiation pressure; beyond a length of 25 cm, further increases have no significant effect.

Meanwhile, at a phasing angle of 45°, the initiation of #1 perforation is insufficient and exhibits slight bifurcation near the wellbore at various perforation tunnel lengths, as shown in Figure 13b and Figure 14. This observation indicates that under the normal fault stress condition, the phasing angle of the perforation is excessively large, resulting in the fracture bifurcation near the well in the early stage.

For the state of strike-slip fault stress, the initiation pressure can be significantly reduced by increasing the length of the perforation tunnel, but this effect is only evident within a certain range. As shown in Figure 15a, taking a phasing angle of 15° as an example, when the length of the perforation tunnel is 15 cm, the initiation pressure is 81.0 MPa. However, with an increase in the tunnel length to 25 cm, the initiation pressure decreases to 75.8 MPa, with a reduction of 5.2 MPa or approximately 6.4%. Further increasing the perforation tunnel length to 35 cm results in a decrease in the initiation pressure to 75.5 MPa, which represents a decrease of only about 0.39%. Therefore, it should be noted that there are limitations on reducing the initiation pressure solely through an increase in the perforation tunnel length beyond approximately 25 cm.

When the phasing angle is 45° or the length of the perforation tunnel is 35 cm, asymmetric fracture propagation occurs on both sides of the wellbore, as illustrated in Figure 15b. This observation indicates that under the strike-slip fault stress state, higher phasing angles and longer perforation tunnel lengths are more likely to result in asymmetric propagation. The underlying reason lies in the fact that excessive tunnel lengths or phasing angles lead to dispersed stress between perforations, thereby causing insufficient initiation of certain perforations.

4.4. Influence of Horizontal Stress Difference on Fracture Initiation and Propagation Under Fixed-Plane Perforation

The effect of the horizontal stress difference (K) on the fracture initiation of fixed-plane perforation was investigated by assuming σ_X = 36 MPa, σ_Y = 46 MPa, and σ_Z = 48 MPa under the normal fault stress condition, and σ_X = 36 MPa, σ_Y = 48 MPa, and σ_Z = 46 MPa under the strike-slip fault stress condition. The horizontal stress difference was varied by changing σ_X to values of 6 MPa, 8 MPa, and 10 MPa.

As shown in Figure 16a, under the normal fault stress condition, the crack initiation pressure decreases as the horizontal stress difference increases while keeping the phasing angle constant. This phenomenon can be attributed to the weakening of the interference effects from the minimum horizontal principal stress on fracture propagation with an increasing horizontal stress difference, resulting in a lower crack initiation pressure. For instance, at the phasing angle of 30°, when the horizontal stress difference is 6 MPa, the crack initiation pressure is measured at 89.1 MPa. However, when this difference increases to 8 MPa, there is a decrease in the crack initiation pressure of 4.3 MPa or 4.8%, reaching a value of 84.8 MPa. A further increase in the horizontal stress difference to 10 MPa leads to a slight reduction in the crack initiation pressure to 83.3 MPa (decrease of approximately 1.76%). Hence, it can be concluded that a high horizontal stress difference does not indefinitely reduce the crack initiation pressure and its impact becomes negligible once this difference reaches around 8 MPa.

It can be seen from Figure 17a that under the stress state of strike-slip fault, the initiation pressure increases with an increase in the phasing angle under a constant horizontal stress difference. Similarly, when the phasing angle remains constant, an increase in the horizontal stress difference also contributes to a reduction in the initiation pressure. For instance, at the phasing angle of 45°, increasing the horizontal stress difference from 6 MPa to 8 MPa results in a decrease in the initiation pressure from 92.7 MPa to 89.0 MPa, representing a decline of 3.9%. Furthermore, at a stress difference of 10 MPa, the crack initiation pressure decreases to 88.1 MPa by approximately 1.01%. Henceforth, the increase in the horizontal stress difference in the strike-slip fault stress state also has a significant effect on reducing the initiation pressure, but only in a certain range.

Simultaneously, the fracture deflection along the axial direction of the wellbore is maximized when the phasing angle is 15° and the stress difference is 6 MPa. With a constant phasing angle, the degree of fracture deflection weakens as the stress difference increases, leading to vertical and symmetrical propagation of fractures along the axial direction. Additionally, as shown in Figure 16b and Figure 17b, at the phasing angle of 45°, incomplete initiation occurs in all conditions. Hence, in the strike-slip fault stress stage, smaller phasing angles and lower horizontal stress differences correspond to more obvious axial deflection along the wellbore of fractures.

5. Discussion

5.1. Research Implications

In this paper, based on the 3D lattice method, we establish a fixed-plane perforation hydraulic fracturing model in a horizontal well. By comparing the experimental and numerical simulation results, the fidelity of the numerical model is suggested. According to the morphology of fractures in the experimental section, it shows that with the implementation of fixed-plane perforation, the fracture direction can be guided effectively, which can enhance the fracturing stimulation effectiveness, and this result agrees with Wang et al. [33]. One of the objectives in optimizing the parameters for perforated fracturing in the field is to minimize the near-wellbore fracture complexity and promote the formation of simple plane fractures. Therefore, according to the research findings in this paper, fixed-plane perforation has more obvious advantages than conventional spiral perforation. The simulation results demonstrate that the implementation of fixed-plane perforation can significantly reduce the degree of fracture distortion, and Qin et al. [34] also came to similar conclusions. Currently, there have been some applications of fixed-face perforation fracturing. The ultra-low-permeability Chang 6 oil reservoir in Ansai was stimulated using fixed-plane perforation fracturing, resulting in an average daily oil increase of 1.80 t/d per well and a decrease in water cut by 43.0%. As shown in Figure 18, in comparison to conventional fracturing, the average daily oil increment per well increased by 0.70 t/d, while the reduction in the water cut reached 20.0% [36].

5.2. Model Limitation

Despite the study’s findings showing the advantages of fixed-plane perforation, it should be noted that hydraulic fracture initiation and propagation in the near-wellbore region represent a complex multiscale geo-mechanical problem. The fracturing effect is influenced by several other key factors, such as the injection schemes, heterogeneity of the rock matrix, presence of natural fracture network and other relevant parameters. Therefore, there are still some unsolved issues in this study.

At the same time, in unconventional reservoirs, there might exist a natural fracture network even in the near-wellbore region. This will obviously increase the complexity of fracture initiation and propagation [35]. In addition, the mechanical properties of the cement ring may also affect the fracture initiation, which may mean that fracture initiates along the interface between the cement ring and the wellbore. Moreover, fixed-plane perforation technology requires that all tunnels be in a same plane, which brings a challenge for the perforation process. However, the factors above are not the focus of this article.

When the numerical model was established, to more clearly illuminate the initiation and propagation morphology of fractures, a group of perforations was set within only one cluster. However, when multi-cluster fracturing is employed, hydraulic fracture will be affected by the stress shadow [26]. With a small horizontal principal stress difference, the stress shadowing effect of multiple fractures is obvious, and the deflection angle of the fractures will be enlarged due to the increase in the induced stress field between the fractures. Therefore, the findings and numerical model presented in this paper provide a foundation for future research in the field, highlighting the need for further investigation.

6. Conclusions

The initiation and propagation of hydraulic fracture pose a highly nonlinear liquid–solid coupling problem, encompassing various factors, such as the in situ stress condition, perforation structure and direction, multi-fracture interaction, properties of the casing cement and cement–rock interfaces, as well as the rock mechanical properties. The combined influence of these factors continues to present significant challenges to the study of fracture initiation pressure and its morphology in the near-wellbore region.

• Under the normal fault stress state and strike-slip fault stress state, the utilization of spiral perforation leads to the deflection of fractures near the wellbore as well as incomplete initiation. However, when employing fixed-plane perforation, a lower fracture initiation pressure is observed, enabling complete initiation and propagation. Consequently, the fracture surface is predominantly perpendicular to the wellbore, facilitating propagation of fractures to form a complex fracture network in the far-field.
• For the normal fault stress state and strike-slip fault stress state, fractures initiate along the perforation plane and subsequently propagate radially along the wellbore to form a fan-shaped failure plane. There exists a positive correlation between the initiation pressure and the phasing angle of perforation. However, the rate of increase in the initiation pressure decreases as the phasing angle increases to 30°, which is around 1.59~6.38%.
• When the phasing angle remains constant, there exists a negative correlation between the initiation pressure and the perforation diameter, perforation tunnel length, as well as horizontal stress difference. Increasing the perforation diameter and perforation tunnel length can effectively reduce the initiation pressure. However, once the perforation diameter reaches 17 mm or the perforation tunnel length reaches 25 cm, the rock initiation decreases when increasing the perforation diameter or tunnel length. Additionally, when the stress difference exceeds 8 MPa, the decline of the rock initiation pressure decreases.
• When employing fixed-plane perforation, under the normal fault stress stage, if the phasing angle is excessively large, it may result in incomplete initiation or bifurcation in the near-wellbore region, which is not conducive to fracture propagation toward the far-field. In the stress state of strike-slip fault, the smaller phasing angle of the perforation, the larger perforation tunnel length and the smaller horizontal stress difference will cause a greater degree of axial deflection along the wellbore.