Numerical Simulation Study on Dynamic Interaction between Two Adjacent Wells during Hydraulic Fracturing

Abstract

The heterogeneity in fracture formation significantly influences the hydraulic fracture propagation among adjacent wells, underscoring the urgency to comprehend the underlying fracture mechanisms. Specifically, in shale gas or oil extraction fracturing operations, stress interactions among neighboring fracturing clusters, or mutual interference during the propagation of parallel fractures, are commonplace. At present, there is relatively little research on the sensitivity parameters of adjacent borehole fracture propagation morphology. Consequently, we employed ABAQUS software 2022 to construct a numerical model simulating the fracturing of adjacent boreholes in opposing directions. Upon validating the model’s fidelity, we systematically explored the influence of various engineering and geological factors on fracture morphology and propagation length. Our findings revealed a three-phase evolution: independent fracture propagation, subsequent mutual repulsion, and, ultimately, mutual attraction. It is worth noting that increasing the elastic modulus from 10 GPa to 80 GPa, and increasing the crack length by 16.30%, is beneficial for crack propagation, while the horizontal stress difference profoundly shapes the crack mode, but has a relatively small impact on the overall crack length. When HSD increases from 0 MPa to 15 MPa, the total crack length only changes by 1.24%. In addition, the filtration coefficient of the reservoir is a key determining factor that has a significant impact on the morphology and length of cracks generated by adjacent boreholes. Increasing the filtration coefficient from 1 × 10⁻¹⁴ m³/s/Pa to 5 × 10⁻¹² m³/s/Pa reduces the total length of cracks by 60.77%. Notably, an optimal injection rate exists, optimizing fracturing outcomes. Conversely, the viscosity of the fracturing fluid exerts a limited influence on fracture morphology and length within the confines of this simulation, allowing for the selection of a suitable viscosity to ensure smooth proppant transport during actual fracturing operations. In designing fracturing parameters, it is imperative to aim for sufficient fracture propagation length while harnessing “stress interference” to foster the development of intricate fracture networks. Ultimately, our research findings serve as a solid foundation for engineering practices involving hydraulic fracture propagation in adjacent boreholes undergoing opposing fracturing operations.

1. Introduction

Hydraulic fracturing has been extensively applied to both conventional and unconventional reservoir stimulation, as evidenced by numerous studies [1,2,3,4]. To enhance the stimulated reservoir volume, the well pad factory mode, involving the creation of multiple fractures, is employed in large-scale fracturing operations. However, when hydraulic fractures propagate in opposite directions, stress interferences are inevitable. This is due in particular to the complex interplay between geological factors and the physics of fluid injection, which can significantly influence fracture paths and ultimate outcomes.

Numerical simulations play a crucial role in characterizing hydraulic fractures. The foundational models in this field are the KGD model and the PKN model. Over time, numerous advanced numerical models for hydraulic fracture (HF) propagation have been proposed, which can be broadly classified into three categories: the discrete element method (DEM), the boundary element method (BEM), and the extended finite element method (XFEM) [5,6,7,8]. Given the intricate nature of fracturing tuning and deviating behavior, the XFEM has been particularly useful in studying curved fractures and stress interference. Sepehri et al. (2015) developed a model to investigate perforation effects on fracture reorientation. Their findings revealed that when two perforations are positioned closely together, stress interference can lead to the breakdown of one perforation. This underscores the importance of considering stress interference and perforation characteristics in predicting and managing fracture propagation in hydraulic fracturing operations [9]. Sircar and Maji (2021) employed the XFEM technique to investigate the influences of rock stiffness on the behavior of hydraulic fracture propagation, specifically when the rock mass is in a saturated condition. They also examined the variation of pore pressure within the fracture tip region. This study highlighted the significance of considering rock properties and pore pressure dynamics in understanding and predicting the behavior of hydraulic fractures, especially in formations where saturation conditions may play a crucial role. They suggested that a negative pore pressure distribution in the fracture process zone increased the length of fractures for stiffer rocks [5]. Luo et al., 2022 studied the heterogeneity of stress and properties among stages for the horizontal well using XFEM. In addition, they showed the non-uniform fluid partitioning is aggravated when injecting fracturing fluid with higher viscosity [10]. Cheng et al. (2024) developed an XFEM model for simulating non-planar hydraulic fracturing problems. Their simulations revealed four new intersection patterns considering the existence of vugs and natural fractures [11]. Deng et al. (2024) simulated hydraulic fracture propagation in laminated shales. They demonstrated that lamination weak interfaces can affect the fracture penetration tendency while creating more complex fracture geometry. Conversely, the tendency for deflection is strengthened when fractures propagate from soft to stiff rock [12]. These findings provide valuable insights into fracturing strategy optimization in laminated shale formations. According to former research, studies on hydraulic fracture propagation for a single horizontal well using the XFEM are numerous, while those on multiple fracture propagations in the opposite direction are rare. Hence, there is a demand to elucidate these mechanisms to better understand and predict fracture propagation with adjacent wells, with implications for enhancing the efficiency and safety of pad hydraulic fracturing operations.

Formation variables, including matrix permeability and mechanical properties, can significantly influence the fracture propagation path. With the help of stress and rock-property characterization tools, the effect of rock heterogeneity on fracture propagation can be determined for the fracturing stage on the horizontal wells. Several authors have discussed the impact of rock heterogeneity on fracture propagation. Ripudaman et al. (2018) investigated the influence of lateral mechanical property heterogeneity fracture propagation. They suggested that the lateral Young’s modulus can affect the fracture path during multiple fracture propagation. Moreover, they believed the stress shadowing effects can be strengthened by the increase in rock heterogeneity [13]. Li et al. (2022) examined the influence of vertical rock heterogeneity on fracture geometry and found that weak interfaces and interfacial mechanical properties have a considerable impact on fracture geometry, especially for the fracture width values along the fracture height [14]. Xie et al. (2018) established a hydraulic fracturing model for multi-fracture propagation and analyzed the influence of stress shadows on fracture propagation [15]. Wang et al. (2016) constructed numerical models for the hydraulic fracturing of brittle and ductile reservoir rocks based on an extended finite element analysis, and discussed the effects of fracture spacing and sorting on the interference of multiple hydraulic fractures [16]. Mojid et al. (2021) found that by adding viscoelastic surfactants (VES) to improve the load-bearing capacity of the proppants, the thickening of ScCO₂ can be achieved [17]. We have supplemented this in the manuscript. While these studies provide valuable insights, further investigation is needed to understand fracture propagation considering rock lateral heterogeneity for adjacent wells. This is crucial for optimizing fracturing strategies and improving the efficiency of hydrocarbon recovery in complex formations. The mutual interference and superposition of stress fields at the fracture tip change the distribution characteristics of local stress fields at the fracture tip, leading to changes in the propagation path of adjacent fractures. This stress interference can easily lead to the formation of complex fractures. Studying the mutual interference problem of multiple fractures is of great significance. In the case of shale gas or oil extraction fracturing, stress interference between adjacent fracturing clusters is often studied. However, in the actual fracturing process, there may be expansion of fracturing boreholes towards each other, and there is currently limited research in this area. Therefore, studying the dynamic interaction between two reverse fractures from adjacent fractured boreholes is of great significance.

In this study, a numerical simulation of hydraulic fractures in relation to the lateral rock heterogeneity difference was performed using the XFEM method. Additionally, the impact of rock mechanical characteristics, in situ stress variations, and engineering parameters on the fracture network shape were examined. This research can provide more insights into fracturing job design in heterogeneous formations on multiple wells.

2. XFEM Methodology

The Extended Finite Element Method (XFEM) offers significantly higher precision and accuracy in dealing with complex geometries and discontinuities such as fractures, holes, and material interfaces. This is achieved through the use of enriched shape functions, which capture the behavior of physical quantities near discontinuities without the need for mesh refinement [18,19,20]. In addition, XFEM has the ability to handle complex geometries and discontinuities, making it an attractive choice for simulating fracture propagation in real-world scenarios. Its enriched shape functions provide a more accurate representation of the physical behavior near discontinuities, leading to improved predictions of fracture propagation paths and rates [21].

$$u={\displaystyle \sum _{i=1}^N{N}_i(x)}\left[u_i+H(x)a_i+{\displaystyle \sum _{\alpha =1}^4{F}_{\alpha }(x)b_i^{\alpha }}\right]$$

(1)

The normal nodal shape function, denoted as N_i(x), is employed in conjunction with the nodal rate vector u_i and the product of the nodal-enriched degree of freedom vector, αi, to define the rate field. The inclusion of the Heaviside function H(x) and the product of nodal-enriched degrees of freedom biα accounts for discontinuities induced by fractures. Additionally, the fracture-tip functions Fα(x), which capture the elastic asymptotic behavior near fracture tips, were utilized.

In Equation (2), the discontinuous jump function can be expressed as,

$$H(\chi )=\left\{\begin{array}{c}1 \mathrm{when} (\chi -{\chi }^{\ast })·n\ge 0\\ -1 \mathrm{else}\end{array}\right.$$

(2)

Among them, χ is a Gaussian point; χ* is the point near the Gaussian point on the fracture surface; N is the unit vector perpendicular to the fracture face outward at point χ*.

The asymptotic fracture-tip functions F_α(x) can be written as:

$$F_{\alpha }(x)=\left[\sqrt{r}\sin {\displaystyle \frac{\theta }{2}},\sqrt{r}\cos {\displaystyle \frac{\theta }{2}},\sqrt{r}\sin {\displaystyle \frac{\theta }{2}}\sin \theta ,\sqrt{r}\cos {\displaystyle \frac{\theta }{2}}\sin \theta \right]$$

(3)

where (r, θ) is a polar co-ordinate system with its origin at the fracture tip, and θ = 0 is tangential to the fracture at the tip.

To track and delineate dynamic interfaces within a domain, the level set method was employed. Within a domain, Ω, we considered its division into two subdomains, Ω_A and Ω_B, separated by an interface denoted as Γ_d. Notably, the distinction between open and closed interfaces within Γ_d is significant, reflecting the varying material properties present in the domain. An open interface uniquely partitions the domain, with at least one extremity residing within the domain, a characteristic exemplified in fractured domains. Among the various level set functions, the signed distance function stands out as the most prevalent choice. It serves as a precise representation of the interface’s location, enabling accurate tracking and analysis of interface dynamics.

$$\phi (x)=‖x-x^{\ast }‖sign(n_{\mathsf{\Gamma }d}·(x-x^{\ast }))$$

(4)

The closest point projection of a point x onto the discontinuity, denoted as x*, lies along the normal vector nΓ_d to the interface at x*. The symbol ‖·‖ represents the Euclidean norm, quantifying the distance from point x to the discontinuity Γ_d as ‖x − x*‖.

$$\phi (x)=\left\{\begin{array}{ll}>0,& if x\in {\mathsf{\Omega }}_A\\ =0,& if x\in {\mathsf{\Gamma }}_d\\ <0,& if x\in {\mathsf{\Omega }}_B\end{array}\right.$$

(5)

Within this model, the kinematics of strong discontinuities are formulated based on the Heaviside function.

$$H(x)=\left\{\begin{array}{cc}-1,& if \phi (x)<0\\ 1,& if \phi (x)>0\end{array}\right.$$

(6)

The traction–separation relationship can used for the rock deformation during hydraulic fracturing, and the elastic and viscous behavior can be encapsulated by the elastic and viscous constitutive matrices, respectively.

$$t=\left\{\begin{array}{c}{t}_n\\ t_s\\ t_t\end{array}\right\}=\left[\begin{array}{ccc}{K}_{nn}& 0& 0\\ 0& K_{ss}& 0\\ 0& 0& K_{tt}\end{array}\right]\left\{\begin{array}{c}{\delta }_n\\ {\delta }_s\\ {\delta }_t\end{array}\right\}=K\delta$$

(7)

The nominal traction stress vector, t, comprises t_n, t_s, and t_t, representing the normal and two shear traction components, respectively. These tractions are associated with separations δ_n, δ_s, and δ_t.

The failure mechanism consists of two parts: a damage initiation criterion and a damage evolution law. Specifically, under pure compression, damage does not initiate unless the traction reaches the cohesive strength T0 or the separation exceeds a critical damage rate δ0. Once δ surpasses δ0, the traction decreases linearly to zero as the rate increases, signifying complete failure of the cohesive element [22].

$$f=\left\{{\displaystyle \frac{{〈t_n〉}^2}{t_n^0}}\right\}+\left\{{\displaystyle \frac{{t_s}^2}{t_s^0}}\right\}+\left\{{\displaystyle \frac{{t_t}^2}{t_t^0}}\right\}$$

(8)

In this model, the damage law is described as follows [23].

$$t_n=\left\{\begin{array}{ll}(1-D){\overline{t}}_n,& \overline{t}\ge 0\\ {\overline{t}}_n,& \overline{t}\le 0\end{array}\right.$$

(9)

$$t_s=(1-D){\overline{t}}_s$$

(10)

$$t_t=(1-D){\overline{t}}_t$$

(11)

In this context, t_n represents the nominal stress in Pascals (Pa), ts denotes the first shear stress in Pa, and t_t signifies the second shear stress in Pa. Similarly, $t_n^0$, $t_s^0$, and $t_t^0$ are the peak values of the nominal, first shear, and second shear stresses, respectively, also measured in Pa. The Macaulay bracket notation <> employed in the normal direction emphasizes that pure compressive stresses do not initiate damage processes. The variable D encapsulates the overall damage within the material, accounting for the cumulative effects of all active damage mechanisms (Figure 1).

2.1. Model Implementation and Inputs

XFEM offers significantly higher precision and accuracy in dealing with complex geometries and discontinuities, such as fractures, holes, and material interfaces. This is achieved through the use of enriched shape functions, which capture the behavior of physical quantities near discontinuities without the need for mesh refinement. To verify the accuracy of the XFEM model in studying fracture propagation problems, the fracture propagation results of numerical simulations were compared with those of indoor true triaxial tests [23,24]. The physical and mechanical properties of the rock sample used in the experiment are shown in

Table 1. Input parameters for numerical simulation validation.

Parameter	Value
Elastic modulus/GPa	8
Poisson’s ratio	0.25
Uniaxial compressive strength/MPa	28
Tensile strength/MPa	2.6
Permeability/10−3 μm2	0.1
Porosity/%	1.85
Maximum horizontal principal stress/MPa	10
Minimum horizontal principal stress/MPa	8
Experimental rate/m3·s−1	2 × 10−8
Model dimension/m	0.3 × 0.3
Fracturing fluid viscosity/mPa·s	70

. The directions of the minimum (S_Hmin) and maximum (S_Hmax) in situ stresses coincide with the x–axis and y–axis, respectively. The comparison between the numerical simulations and lab true triaxial tests demonstrated that the XFEM model accurately captured the fracture propagation behavior observed in the experiments.

Figure 2a shows the fracture propagation path for the perforated well. Figure 2b shows the result obtained using the XFEM fracture propagation model. There can be seen that the numerical simulation method well reflects the phenomenon of fracture deflection caused by local stress change, and the two sets of results show good consistency. Although the indoor experimental samples are cemented rock samples, it cannot be guaranteed that the samples are completely homogeneous, resulting in asymmetric fracture propagation on the left and right wings. In contrast, the results of numerical simulations exhibit good symmetry.

2.2. Geometric Model and Parameter Settings

A numerical model was established for the stress interaction for two adjacent wells. To reduce computational costs, a two-dimensional model was established using ABAQUS software, with dimensions of 15 m × 10 m, as shown in Figure 3. In the initial fracture stage, there is no distinct fracture deflection, and fluid pressure on its surface is much smaller than that in the non-fracture area. Therefore, the wellbore tunnel can be characterized by initial fractures that are perpendicular to the maximum horizontal stress direction, and the initial fracture length is about 1 cm in this numerical simulation model. In the proposed model, a shale reservoir at a depth of approximately 2500 m was simulated. For this depth of reservoir, the three principle stresses, including the maximum horizontal principal stress, minimum horizontal principal stress, and vertical principal stress were set to 20 MPa, 15 MPa, and 25 MPa, respectively. A low-viscosity fracturing fluid was used, with a viscosity of 1 × 10⁻⁵ Pa s, a fracturing time of 600 s, and a rate of 0.0005 m²/s. Other main parameters are shown in

Table 2. Model geometric parameters and construction parameters.

Parameter	Value
Initial fracture length/m	0.01
Density/×103 kg	2.8
Elastic modulus/GPa	42
Poisson’s ratio	0.25
Tensile strength/MPa	10
Normal fracture energy/J	25
Tangential fracture energy/J	25
Pore ratio	0.2
Liquid viscosity/mPa·s	0.001
Saturation	1.0
Injection time/s	600
Maximum injection rate/m3/s	0.005

. In this model, the boundary and pore pressures are fixed. The standard for selecting the CPE4P grid partitioning is to appropriately increase the global grid size while ensuring that there are no swept grids (poor grid partitioning quality).

3. Numerical Simulation Results

3.1. Evolution of Fracture Propagation

Figure 4 illustrates the fracture propagation at different time steps. In the baseline model, the propagation of fractures emanating from adjacent boreholes was examined under specific conditions: a fracturing fluid viscosity of 1 × 10⁻⁵ Pa·s, a stress differential of 5 MPa, an elastic modulus of 42 GPa, a filtration coefficient of 1 × 10⁻¹² m³/s/Pa, and a fracturing fluid injection rate of 0.0005 m²/s. The figure reveals that, initially, two fractures initiate and propagate concurrently. Due to the globally partitioned grid configuration, these fractures experience minimal mutual influence at the onset. Notably, the left-side fracture exhibits a slightly greater length compared to the right-side fracture, with minimal interference observed between them during the initial 100 s of the simulation.

However, the left fracture can still deflect upwards and move away from the right fracture. When the simulation time reaches 200 s, the upper fracture begins to deflect downwards, while the lower fracture has basically not deviated at this time, and the expansion of the fractures on both sides is not completely the same. When the simulation time reaches 300 s, the two fractures deflect towards each other, and the vertical distance between the tips of the two fractures decreases, showing a phenomenon of mutual attraction. During the simulation period of 450–600 s, the change in fracture propagation was minimal. It is speculated that during this time, there was a significant loss of fracturing fluid due to fracture deflection, resulting in slower changes in fracture propagation. The fracture propagation of adjacent boreholes went through three stages: independent propagation, mutual repulsion, and mutual attraction. The propagation of fractures is influenced by various factors, which is also an issue we need to consider and will be discussed in depth in the next step.

Three geological factors, namely elastic modulus (E), horizontal stress difference (HSD), and filtration coefficient (F), as well as two engineering factors, namely fracturing fluid rate (I) and fracturing fluid viscosity (μ), making a total of five influencing factors on fracture propagation were investigated. The values of elastic Young’s modulus are 10 GPa, 20 GPa, 42 GPa, and 80 GPa, respectively. The horizontal stress difference is maintained at a minimal level, while the vertical stress value remains constant. Variations in the maximum horizontal principal stress are introduced to assess their influence on fracture propagation. Specifically, the horizontal stress differences examined are 0 MPa, 5 MPa, 10 MPa, and 15 MPa, respectively. Furthermore, the filtration coefficient, a crucial parameter governing fracturing fluid leakage, significantly impacts on-site fracturing operations. In this simulation, we explored filtration coefficient values of 1 × 10⁻¹⁴ m³/s/Pa, 1 × 10⁻¹³ m³/s/Pa, 1 × 10⁻¹² m³/s/Pa, and 1 × 10⁻¹² m³/s/Pa, respectively. The fracturing fluid viscosity and injection rate need to be adjusted for various engineering backgrounds. The fracturing fluid viscosity values studied ranged from 0.001 mPa·s to 1 mPa·s, encompassing 0.001 mPa·s, 0.01 mPa·s, 0.1 mPa·s, and 1 mPa·s. To isolate the effect of fracturing fluid injection rate, simulations were conducted while ensuring a constant total volume of fracturing fluid, leading to varying fracturing durations. The injection rates were set at 0.0004 m³/s, 0.0005 m³/s, 0.0006 m³/s, and 0.0007 m³/s, corresponding to simulation times of 750 s, 600 s, 500 s, and 428 s, respectively.

3.2. The Influence of Elastic Modulus

Figure 5 shows the fracture propagation morphology under different elastic moduli E. The main parameters of its model are shown in Table 2, with only the elastic modulus changed. The parameters were fracturing fluid viscosity 1 × 10⁻⁵ Pa s, stress difference 5 MPa, filtration coefficient 1 × 10⁻¹² m³/s/Pa, and fracturing fluid rate 0.0005 m²/s. When the elastic modulus value was small, the reservoir was not tight, relatively speaking, resulting in a large amount of drilling fluid leakage, and the fractures extended in a straight direction, with less stress interference. When the elastic modulus increased further, the reservoir became denser, and the extension and expansion of fractures improved. As the elastic modulus increased, the fracture tips became more attractive to each other, and the fracture length became longer, which is consistent with field experiments where the reservoir is denser and the fracture length extends further.

Figure 6 is a statistical graph quantifying the simulation results of the lengths of the upper and lower fractures under varying elastic modulus (E) conditions. When the elastic modulus was 10 GPa, 20 GPa, 42 GPa, and 80 GPa, the corresponding upper fracture lengths were 7.69 m, 9.06 m, 9.18 m, and 9.19 m, respectively, and the lower fracture lengths were 8.32 m, 8.79 m, 9.26 m, and 9.44 m, respectively. The total fracture lengths were 16.01 m, 17.94 m, 18.45 m, and 18.62 m, respectively, and the total fracture length increased by 16.30%. The elastic modulus can mainly affect the fracture length, which should be taken into consideration for the hydraulic fracturing design for adjacent wells.

3.3. The Influence of Horizontal Stress Difference

Figure 7 illustrates the variations in fracture propagation morphology under varying degrees of horizontal stress difference (HSD), with the key model parameters detailed in Table 2. Notably, only the HSD varied, while the fracturing fluid viscosity was maintained at 1 × 10⁻⁵ Pa·s, the elastic modulus at 42 GPa, the filtration coefficient at 1 × 10⁻¹² m³/s/Pa, and the fracturing fluid injection rate at 0.0005 m²/s. The figure clearly demonstrates that the HSD exerts a pronounced effect on the fracture morphology. Specifically, when the HSD was very small (0 MPa), the two hydraulic fractures propagated relatively towards each other, significantly influenced by the absence of stress disparity. Conversely, when HSD became excessively large, the fractures propagated in straight lines, minimizing the likelihood of stress interference between them.

To quantify the simulation results, Figure 8 is a statistical graph under different horizontal stress difference (HSD) conditions. The simulation of fractures emanating from opposing adjacent boreholes reveals that, while the horizontal stress difference significantly influences the fracture morphology, it exerts a comparatively limited effect on the total length of the fractures. When the horizontal stress difference was 0 MPa, 5 MPa, 10 MPa, and 15 MPa, the corresponding upper fracture lengths were 8.74 m, 9.18 m, 8.89 m, and 8.94 m, respectively, and the lower fracture lengths were 9.01 m, 9.26 m, 8.99 m, and 8.59 m, respectively. The total fracture lengths were 17.75 m, 18.44 m, 17.88 m, and 17.53 m, respectively, and the total fracture length decreased by 1.24%. However, in practical field operations, the excessively high stress difference encountered within reservoirs poses a challenge to the development of intricate fracture networks. This finding is congruent with the actual fracturing conditions observed on-site, validating the relevance and applicability of the research outcomes.

3.4. The Influence of Filtration Coefficient

Figure 9 displays the results of fracture propagation morphology under varying filtration coefficients (F), with the key model parameters outlined in Table 2. Notably, only the filtration coefficient was varied, keeping the fracturing fluid viscosity at 1 × 10⁻⁵ Pa·s, the elastic modulus at 42 GPa, the horizontal stress difference (HSD) at 5 MPa, and the fracturing fluid injection rate at 0.0005 m²/s. The filtration coefficient of the reservoir significantly influences practical operations, as a lower coefficient translates into reduced fracturing fluid leakage. Theoretically, this leads to longer fractures. As evident from the Figure, when the filtration coefficient is low, the fracture propagation morphology undergoes minimal changes, but the attraction between fracture tips intensifies, resulting in longer fractures. Conversely, as the filtration coefficient increases, the fracture morphology undergoes notable alterations, with decreased attraction at the fracture tips. Notably, when the filtration coefficient escalates by 500 times, substantial fracturing fluid leakage occurs, hindering further fracture expansion and confining them to independent propagation stages, as depicted in Figure 9d.

Figure 10 is a statistical graph quantifying the simulation results of the lengths of the fractures under different filtration coefficient (F) conditions. For filtration coefficients of 1 × 10⁻¹⁴ m³/s/Pa, 1 × 10⁻¹³ m³/s/Pa, 1 × 10⁻¹² m³/s/Pa, and 5 × 10⁻¹² m³/s/Pa, the corresponding upper fracture lengths were 11.75 m, 11.64 m, 9.18 m, and 4.36 m, respectively, and the lower fracture lengths were 11.24 m, 11.17 m, 9.26 m, and 4.66 m, respectively. The total fracture lengths were 22.99 m, 22.81 m, 18.45 m, and 9.02 m, respectively, reducing the total fracture length by 60.77%. The increase in leakage coefficient significantly reduces the length of fracture propagation. Furthermore, this underscores the rationale behind the suboptimal fracturing outcomes encountered during actual operations in leaky formations, naturally fractured zones, or karst regions. The filtration coefficient plays a pivotal role in shaping the fracture geometry and influencing the propagation length of fractures emanating from adjacent boreholes.

3.5. The Influence of Fracturing Fluid Rate

Figure 11 exhibits the fracture propagation morphology under varying fracturing fluid injection rates (I), with the model’s primary parameters detailed in Table 2. Notably, only the fracturing fluid rate was altered, maintaining a constant viscosity of 1 × 10⁻⁵ Pa·s, an elastic modulus of 42 GPa, a horizontal stress difference (HSD) of 5 MPa, and a filtration coefficient of 1 × 10⁻¹² m³/s/Pa. To isolate the rate of effect, the total fracturing fluid volume was held constant, necessitating variations in fracturing time. Specifically, the injection rates were set at 0.0004 m³/s, 0.0005 m³/s, 0.0006 m³/s, and 0.0007 m³/s, corresponding to simulation durations of 750 s, 600 s, 500 s, and 428 s, respectively. The figure reveals that a smaller fracturing fluid rate, owing to a longer fracturing duration, results in increased filtration, leading to a notable reduction in both the length and width of the induced fractures. Conversely, an excessively high rate causes more leakage under elevated pressures, imposing stricter demands on field equipment. Theoretically, an optimal rate exists that balances these factors. Empirical simulations have demonstrated that a larger rate shortens the independent propagation distance between fractures and intensifies the attraction between fracture tips.

To quantify the simulation results, Figure 12 is a statistical graph of the lengths of the upper and lower fractures, and the total length of the fractures under different fracturing fluid flow rates (I). When the fracturing fluid rate was 0.0004 m³/s, 0.0005 m³/s, 0.0006 m³/s, and 0.0007 m³/s, the corresponding upper fracture lengths were 8.86 m, 9.18 m, 9.75 m, and 10.06 m, respectively, and the lower fracture lengths were 8.57 m, 9.26 m, 9.44 m, and 9.95 m, respectively. The total fracture lengths were 17.44 m, 18.44 m, 19.19 m, and 20.02 m, respectively, and the total fracture length increased by 14.79%. During on-site construction, a low flow rate of fracturing fluid is not conducive to construction. When the flow rate of the fracturing fluid is high, the requirements for construction equipment are high and leakage is significant. Therefore, there exists an optimal fracturing fluid rate.

3.6. The Influence of Fracturing Fluid Viscosity on Fracture Propagation

Figure 13 depicts the fracture propagation morphology under varying fracturing fluid viscosities (μ), with the model’s core parameters outlined in Table 2. Notably, only the fracturing fluid rate was varied, keeping the elastic modulus at 42 GPa, horizontal stress difference (HSD) at 5 MPa, filtration coefficient at 1 × 10⁻¹² m³/s/Pa, and the fluid rate fixed at 0.0005 m³/s. The graph underscores the field-adjustable nature of fluid viscosity and rate. As the viscosity of the fracturing fluid escalates, its influence on fracture propagation morphology remains relatively muted. To substantiate this observation, Figure 14 provides a statistical analysis of the lengths of the upper and lower fractures, along with their combined total, across different fluid flow rates (I). Specifically, when the viscosity ranged from 0.001 mPa·s to 1 mPa·s, the upper fracture lengths were 9.18 m, 9.00 m, 9.21 m, and 9.19 m, respectively, while the lower fracture lengths were 9.26 m, 9.05 m, 9.26 m, and 9.27 m. Consequently, the total fracture length hovers around 18.45 m, 18.05 m, 18.47 m, and 18.44 m, respectively, indicating a negligible overall change. This underscores the minimal effect of fracturing fluid viscosity on simulated fracture morphology and length. In practical fracturing operations, it is imperative to prioritize the smooth transport of proppant while selecting an appropriate fluid viscosity to optimize performance.

4. Conclusions

There is limited research on simulating the opposite fracturing of adjacent boreholes. Based on this, we established a numerical model for the opposite fracturing of adjacent boreholes using ABAQUS. Based on validating the model, we designed engineering and geological factors, and studied their effects on the morphology and length of fracture propagation. The obtained conclusions can be seen.

• The fracture propagation of adjacent boreholes has gone through three stages: independent propagation, mutual repulsion, and mutual attraction. In general, when the elastic modulus value is small, the reservoir is relatively loose, resulting in a large amount of drilling fluid leakage, and the fractures extend straight, with less stress interference. When the elastic modulus further increases, the reservoir becomes more brittle, thus resulting in a better fracture extension area and larger stress interference. The too large horizontal stress difference is negative for the complexity of complex fracture networks, but can migrate the stress interference.
• The filtration coefficient increased from 1 × 10−14 m³/s/Pa to 5 × 10−12 m³/s/Pa, reducing the total fracture length by 60.77%. The increase in filtering coefficient significantly shortens the length of fracture propagation. This also explains why the fracturing effect is poor when encountering leaking formations, natural fracture formations, or karst formations in actual fracturing operations. The filtration coefficient of the reservoir affects the shape and length of the fractures supported by adjacent wellbore fractures.
• When the rate of the fracturing fluid is small, due to the longer fracturing time, there is more filtration of fracturing fluid, resulting in a smaller length and significantly reduced width of the fractures being compressed. However, when the fracturing fluid rate is too large, leakage will occur under higher pressure.
• The viscosity of the fracturing fluid has a relatively small impact on the fracture morphology and length in this simulation. In actual fracturing construction, to ensure the smooth carrying of the proppant, the viscosity of the fracturing fluid should be selected carefully. The effect of stress difference on the total length of fractures is relatively small (HSD increased from 0 to 15 MPa, and the total fracture length decreased by 1.24%), but it significantly affects the fracture morphology.
• In the design of fracturing parameters, it is necessary to ensure that the fracture propagation length is large enough and to use “stress interference” to form a complex fracture network.

In future research, we will consider the impact of adding adjacent drilling methods (horizontal drilling distance and vertical drilling distance) on crack propagation, with the maximum transformation area as the objective function, and optimize it using machine learning algorithms.