Medium-high maturity continental shale oil is one of the hydrocarbon resources with the most potential for successful development in China. Nevertheless, the unique geological conditions of a multi-lithologic superposition shield the vertical propagation of hydraulic fractures and limit the longitudinal reconstruction in reservoirs, posing a great challenge for large-scale volumetric fracturing. Radial wellbore cross-layer fracturing, which transforms the interaction between the hydraulic fractures and lithologic interface into longitudinal multilayer competitive initiation, could provide a potential solution for this engineering challenge. To determine the longitudinal propagation behaviors of fractures guided by radial wellbores, true triaxial fracturing experiments were performed on multilayer shale–sandstone samples, with a focus on the injection pressure response, fracture morphology, and cross-layer pattern. The effects of the radial borehole length L, vertical stress difference Kv, injection rate Q, and viscosity ν of the fracturing fluid were analyzed. The results indicate that radial wellbores can greatly facilitate fracture initiation and cross-layer propagation. Unlike conventional hydraulic fracturing, there are two distinct fracture propagation patterns in radial wellbore fracturing: cross-layering and skip-layering. The fracture height guided by a radial wellbore is positively correlated with Kv, Q, and ν. Increasing these parameters causes a shift in the fracture initiation from a single root to an asynchronous root/toe end and can improve the cross-layer propagation capacity. Critical parameter thresholds exist for fracture propagation through and across interlayers under the guidance of radial boreholes. A parameter combination of critical cross-layering/skip-layering or alternating displacement/viscosity is recommended to simultaneously improve the fracture height and degree of lateral activation. The degree of correlation of different parameters with the vertical fracture height can be written as L > Q/ν > Kv. Increasing the radial wellbore length can effectively facilitate fracture cross-/skip-layer propagation and reduce the critical threshold of injection parameters, which is conducive to maximizing the stimulated reservoir volume.
Continental shale oil is one of the unconventional hydrocarbon resources in China with the most potential for successful development. According to the maturity of the organic matter, Ro, shale oil can be divided into two types: medium-high maturity (Ro > 1.0%) and medium-low maturity (Ro = 0.5%–1.0%) [1]. Medium–high maturity shale oil is generally considered to be the most realistic field for exploration and development in the near future, due to its higher degree of thermal evolution. China is rich in medium-high maturity shale oil reserves, with resources of 1.0 × 1010 tons [2], [3]. Recently, several development demonstration shale oil sites, including Jimsar in Xinjiang and Longdong in Changqing, have been successively put into practice, setting off a boom in shale oil exploration and development in China [4]. Realizing the efficient development of continental shale oil is of great significance for consolidating the foundation of China’s self-supplied energy and ensuring national energy security.
Large-scale volumetric fracturing of horizontal wells is the core engineering technology for the development of medium–high maturity shale oil reservoirs. This technology has played an important role in the development of marine shale reservoirs and triggered the US shale oil/gas revolution, turning the United States from an oil/gas importer into an exporter [5]. However, in comparison with the thick marine shale oil in North America, the geological condition of the continental shale oil in China is more complex and changeable, with multiple thin laminated production layers in the sedimentary direction [6], [7], as shown in Fig. 1(a). So-called “sweet spots” are generally distributed within inter-bedded shale layers, and the sandstone/mudstone interlayer between neighboring production layers and corresponding lithologic interfaces shields the vertical propagation of hydraulic fractures, limiting the fracturing height and longitudinal reconstruction of reservoirs and thereby posing a great challenge for volumetric stimulation [8], [9]. The issue of how to cross the high-strength interlayer and simultaneously stimulate multiple production layers in the longitudinal direction is the key for the engineering success of volumetric fracturing and in obtaining high and stable yields of continental shale oil reservoirs in China [6].
To address the engineering challenges described above, radial wellbore cross-layer fracturing (Fig. 1(b)) has been proposed for use in multi-lithologic superimposed shale oil reservoirs. This fracturing technology transforms the interaction between hydraulic fractures and the lithologic interface into competitive longitudinal multilayer initiation. In this technology, radial boreholes tens of meters long are first drilled perpendicular to the horizontal main wellbore by means of a high-pressure hydra-jet or flexible drilling tools [10], [11], in order to longitudinally penetrate the sandstone interlayers and lithologic interfaces and connect multiple shale oil production layers. Then, hydraulic fracturing is implemented on the radial boreholes, allowing the fracturing fluid to directly act on multiple production layers and promote the competitive initiation of fractures in the multilayer shale oil [12]. This technology is expected to address the issue of fracture height limitation by the interlayer/lithology interface, maximize the longitudinal fracturing zone of the production layer, and greatly improve the volumetric stimulation of multi-lithologic superimposed shale oil reservoirs. Unlike conventional horizontal well fracturing, radial borehole cross-layer fracturing converts the key scientific issue of penetrating the interlayer and lithology interface of hydraulic fractures into an issue of fracture competitive initiation in multiple longitudinal layers, which involves the joint disturbances of radial borehole stress reconstruction and the interlayer interface/weak bedding surface. The mechanism of radial wellbore guided fracture initiation and propagation in multi-lithology superimposed reservoirs is still unclear.
Lithologic interface and bedding planes (BPs) are unique features of laminated rock masses such as shale oil. Compared with thick monolith formations, the fracturing behavior in multi-lithologic superimposed formations is more complicated, affected by the interlayer heterogeneity [13], [14], [15], in situ stress [16], interface properties [17], [18], and injection parameters [19], [20]. To determine the interaction between the hydraulic fractures and the lithologic interface, researchers have made great efforts to investigate the vertical propagation of fractures in laminated rocks [21], [22], [23], [24], and the effects of geological parameters (i.e., geo-stress, interlayer thickness, and dip angle) [25], [26], [27] and engineering parameters (the pump rate and viscosity of fracturing fluid, etc.) [28], [29], [30] have been studied comprehensively. Indeed, the cross-layer propagation of hydraulic fractures can occasionally be achieved by enhancing the pump rate and fluid viscosity, but the same set of fracturing parameters generally cannot be applied to different reservoirs, depending on the geological conditions and the mechanical properties of the interlayer and lithology interface [31], [32]. That is, the conventional cross-layer fracturing method is not a universal method that can be followed by simply optimizing the fracturing parameters and fluid features [33], [34]. In addition, although many studies have been carried out on the cross-layer propagation of hydraulic fractures under the interference of a lithologic interface, none have considered the existence of radial boreholes. The mechanism of fracture initiation and propagation under the joint actions of radial boreholes and a lithologic interface remains to be revealed.
Inducing in situ stress reconstruction by drilling boreholes is an effective method for guiding and controlling fracture propagation in rock engineering and already has wide application in the anti-reflection of coalbed methane [12]. Radial wellbore fracturing is a stimulation method that creates high-conductivity fractures in reservoirs via the drilling of single or multiple radial boreholes. Under the guidance of these radial boreholes, hydraulic fractures can escape the control of the original in situ stress and propagate in a favorable direction [35], [36]. Regarding the mechanism of guided fracture propagation by means of a radial wellbore, both a true triaxial fracturing experiment and a finite-element numerical simulation have been reported in the literature, with the aim of studying the fracture morphology, conductivity, and productivity with the existence of a single or multiple radial wellbores [37], [38]. The influences of horizontal stress difference, radial wellbore size, and orientation have also been determined [35], [36], [37], [38], [39]. Moreover, it has been found that multi-branch radial boreholes with the same phase arrangement can better guide and control fractures, while multi-branch radial boreholes arranged in different phases can effectively improve the complexity of the fracture network [35]. The advantages of radial wellbores in reducing the fracture initiation pressure, guiding the fracture extension, and increasing the drainage area have been confirmed [38], [39]. However, previous studies on radial wellbore fracturing have mainly focused on homogeneous monolith rock, rarely considering the influence of the interlayer and lithology interface. Unlike that in a monolith layer, fracture propagation in multilayer reservoirs is subjected to the combined effect of radial borehole guidance and the interlayer/interface, and therefore is significantly different from conventional fracturing.
To determine the cross-layer characteristics of hydraulic fracturing assisted by radial boreholes in multilayered shale oil reservoirs, we performed true triaxial radial wellbore fracturing experiments on superimposed shale–sandstone samples. The fracture initiation and propagation behaviors guided by a radial borehole in laminated rock were investigated and contrasted with those in conventional horizontal well fracturing. In addition, the influences of the radial borehole length, vertical stress difference, injection rate, viscosity of fracturing fluid, and so forth were analyzed. The threshold conditions for cross-layering under different radial borehole lengths were captured as well, and the dependency of cross-layering on different geological and engineering parameters was evaluated based on a parameterization domain analysis. The key findings are expected to provide new scientific insights to solve the problem of fracture height limitation and introduce a new potential volumetric stimulation method for multi-lithologic superimposed shale oil reservoirs.
2. Material and methods
2.1. Sample preparation
The rock materials used in this work were shale and sandstone collected from the Chang 7 outcrops of the Yanchang Formation at the Ordos Basin in China, as shown in Figs. 2(a)–(c). Discontinuities and BPs are well-developed in the shale outcrops. The Chang 7 Member of the Yanchang Formation is a typical multi-lithologic superimposed continental shale oil reservoir that has developed tight sandstone interlayers at a depth of 500–2000 m. Three sub-members—namely, Chang 71, Chang 72, and Chang 73—can be identified in the Chang 7 Member based on well logging and sedimentation cycles, as shown in Fig. 3[9]. According to the stratigraphic well connection profile (Fig. 2(b)) and core samples (Fig. 3), Chang 71 is dominated by thick sandy lamina containing sparse intercalated thin black shale lamina, Chang 72 is oil shale lamina interbedded with thin sandstone lamina, and Chang 73 is characterized by thick tuffaceous sandstone lamina stratified by black shale lamina [9]. Among the three sub-members, Chang 72 is generally targeted as the preferable reservoir due to its high frequency of shale lamina and high organic content. However, conventional horizontal well multi-stage fracturing in this reservoir did not produce a satisfactory yield, due to the various lithologies and thin interbedding [40], [41], [42]. It is challenging to connect the multiple layers with vertical fractures in order to enhance the fracturing effectiveness.
X-ray diffraction (XRD) and basic mechanical property tests were performed on shale and sandstone outcrops, and the results were contrasted with those of downhole core samples from the Chang 7 Member reported in the Ref. [40]. As indicated in the ternary classification shown in Fig. 4[40], the sandstone is richer in brittle minerals such as quartz, feldspar, and pyrite (QFP) and carbonates (calcite, dolomite, and siderite) than in shale. The average brittleness indexes of the shale and sandstone outcrops are 85% and 73%, respectively, which are comparable to those of the downhole core samples. Triaxial compression tests with a confining pressure of 20 MPa and Brazil tests were conducted, following previous works [40]. As shown in Figs. 5(a)–(d), the shale and sandstone outcrops have average compressive strengths of 111.33 and 183.98 MPa, tensile strengths of 4.71 and 7.03 MPa, elastic moduli of 18.43 and 27.18 GPa, and Poisson’s ratios of 0.22 and 0.23, respectively. The mechanical properties of these outcrops fall within the range of the downhole core samples, substantiating the representability of the outcrops. Compared with the shale, the sandstone interlayer has a higher strength and thus may have a shielding effect on the vertical extension of the hydraulic fractures in the shale oil reservoir.
In this work, natural outcrop rock samples were collected to prepare artificial sandstone–shale multilayer samples. This was done because the downhole core is small in size and its samples are low in quantity, making it difficult to meet our needs for the laboratory experiments. To model the multilayer interbedding geological structure in the shale oil reservoir, we cut the shales and sandstones into square slabs with dimensions of 200 mm × 200 mm × 40 mm (Fig. 2(c)) and assembled the slabs into a five-layer shale–sandstone laminated specimen using epoxy adhesive according to the combination pattern shown in Fig. 2(d). A center hole with a diameter of 16 mm and a length of 120 mm was drilled at the side surface of the intermediate shale slab to simulate the horizontal main wellbore, as shown in Figs. 6(a) and (b). A stainless-steel casing extending 80 mm into the main wellbore was cemented using temperature-resistant planting adhesive, with a 40 mm open-hole section left for the injection of fracturing fluid. In the middle position of the open hole, two radial boreholes perpendicular to the main wellbore were drilled with a phase distribution of 180° to model two lateral boreholes vertically penetrating the shale–sandstone interface. The diameter ratio of the radial borehole to the main wellbore in the sample was consistent with the actual field conditions [10]. Based on a similarity ratio of 8:1, the diameter of the radial-branch borehole was set to 5 mm. Radial branches with three different lengths were set in our work in order to study the influence of the radial-branch length on the fracture initiation and cross-layer propagation, with branch tips extending into the internal shale layer, denoted as SH2 (L = 20 mm), the interlayer sandstone, denoted as SA1 and SA2 (L = 55 mm), and the outer shale layer, denoted as SH1 and SH3 (L = 80 mm), as shown in Fig. 6(b). According to the similarity relation [43], [44], the radial borehole lengths of 20, 50, and 80 mm in the experiment respectively corresponded to 5–15, 15–25, and 25–40 m in the field.
In multi-lithologic superimposed reservoirs, weak planes between neighboring lithologic layers are the most important intrinsic features, as they have a great impact on the vertical propagation of hydraulic fractures. The question of how to model the interlayer interface was one of the key issues in our experiment. In this work, we adopted a strength-controlled epoxy adhesive to model the interface or transition zone between the shale–sandstone layers. Artificial samples with interfaces cemented with various mixing ratios of epoxy resin and curing agent, ranging from 5:1 to 3:1, were prepared and compared with the natural downhole cores, in order to optimize the similarity of the cementation strength to the natural interlayer interface. In total, 16 groups of Brazilian tests and 12 groups of direct shear tests were performed, as shown in Fig. 7. It was noted that the tensile strength and shearing strength were positively correlated with the mixing ratio of the curing agent. At a ratio of 4:1, the tensile strength and shearing strength of the artificial interface were the closest equivalents to those of the natural downhole cores. Thus, we used this mixing ratio for the cementing of the experimental sandstone–shale multilayer samples in our work.
2.2. Experimental setup and procedure
In this work, a true triaxial fracturing system (Figs. 8(a) and (b)) was used to perform the experiments. This fracturing equipment included four main modules: a fluid injection module (Fig. 8(c)), a confining triaxial stress-loading module, a rock confining unit (Fig. 8(d)) designed for the sample with the dimensions of 100–400 mm3, and a data acquisition and control system. Two fluid injection modes could be implemented: a constant pressure and a constant flow rate, with a maximum injection displacement of 100 mL·min−1. A triaxial stress of up to 50 MPa could be loaded onto the rock sample along the x-, y-, and z-axis with an accuracy of ± 0.1 MPa.
The stepwise procedure of the fracturing experiment was as follows.
(1) Place the five-layer shale–sandstone laminated sample in the confining unit and connect the injection line to the wellbore.
(2) Turn on the triaxial stress-loading device and simultaneously load the x-axis (vertical stress direction), y-axis (horizontal maximum stress direction), and z-axis (horizontal minimum stress direction) stresses to the minimum principal stress; then increase y- and z-axis stresses to the target values in sequence, so as to evenly load and avoid compression failure caused by a high stress difference in loading.
(3) Keep the rock sample in the confined state for 30 min to ensure that the stress loading of the physical model is sufficient and the matrix pore compaction is close to the formation condition.
(4) Start the injection system and the vacuum pump to fill the injection tank with dyed fracturing fluid.
(5) Start the data acquisition and control system to adjust the fracturing fluid injection mode, control the injection rate, and monitor the wellbore pressure changes.
(6) Set the injection rate, open the injection valve, and start the fracturing experiment.
(7) Stop the injection when the wellbore pressure falls back to stability; then save and export the data.
(8) Open the drain valve, remove the wellbore and liquid injection pipeline, release the triaxial stresses, and take out the rock sample for further fracture morphology analysis. This ends one set of the experiment.
After fracturing, constant low-rate reinjection tests were conducted on the fractured samples to monitor the reinjection pressure curves and obtain the pressure at a stable stage, which could be used for evaluating the conductivity of the fractures. According to a report by Yang et al. [45], the fracture conductivity equation for the fractured samples can be expressed as follows:
where kf is the fracture permeability; wf is the fracture aperture; Cf is fracture conductivity; qw is the reinjection rate; μ is viscosity of reinjected fluid; re is effective radius, which is equal to the half side-length of the specimen in this work; rw is wellbore radius; ΔPwf is pressure difference between the wellbore and fracture.
This equation accounts for the reinjected water flow from the wellbore to the fracture; in addition, a transport index is introduced to correlate the flux rate and the pressure difference between the wellbore and the fracture. The water flow in the fracture is governed by Darcy’s equation. A formula proposed by Peaceman [46] and well-fracture intersection modeling in embedded discrete fracture modeling (EDFM) is applied here [47], [48], [49]. A more detailed derivation procedure of this equation can be found in the appendix of Ref. [45].
To obtain the three-dimensional (3D) morphology of the fractures, computed tomography (CT) scanning was performed on the multilayer samples with different radial borehole lengths, using a high-energy microfocus industrial CT equipped with a 9 MeV accelerator. The maximum rock sample size allowed by this CT is 300–500 mm, with a resolution of 150–200 μm. Post-treated 2D slices of the fractures were obtained and stacked mathematically to reconstruct the 3D fracture structures using an interactive threshold segmentation approach.
2.3. Experiment scheme
As shown in Table 1, a total of 31 sets of fracturing experiments were performed under different conditions, including one comparison group designated as H (the base case)—that is, conventional horizontal well fracturing (without a radial branch)—and 30 cross-layer fracturing groups designated as R, with radial boreholes. Based on the radial borehole length, the multilayer specimens were divided into three sub-groups: L = 20, 55, and 80 mm, numbered as R-S#1–R-S#10, R-M#1–R-M#12, and R-L#1–R-L#8, whose branch tips extended into the internal shale layer SH2 (L = 20 mm), the interlayer sandstone SA1/SA2 (L = 55 mm), and the outer shale layer SH1/SH3 (L = 80 mm), respectively. Cross-over trials were designed in sub-groups to illuminate the effects of key geological and engineering parameters on the fracturing performance, such as the injection rate Q, viscosity ν, and vertical stress difference. Three different stress conditions, with the vertical stress difference coefficient Kv ranging from 0.33 to 1.67, were investigated to cover the in situ Kv in the Chang 7 Member in the Ordos Basin. According to the Refs. [9], [50], the Chang 7 Member has a normal fault stress mode—that is, σv > σH > σh—and the relationship between the in situ stress and the formation depth is fitted as follows:
where σv is vertical principal stress; σH is maximum horizontal principal stress; σh is minimum horizontal principal stress; h is the depth of formation.
Since the pore pressure cannot be considered in experimental specimens, the effective stress of the rock matrix—that is, the difference between the principal stress and the pore pressure—was used to calculate the stress difference coefficient. The Refs. [51], [52] indicate that the pore pressure of the Chang 7 Member ranges between 14.3 and 16.0 MPa, with an average of 15.0 MPa at a depth of 1750–2030 m, and the in situ stress difference coefficient range is 0.12–3.11. In our experiment, the vertical stress difference coefficient was set to 0.33–1.67, which falls within the in situ ranges and meets the stress similarity.
The viscosity of the fracturing fluid could be made to range from 1 to 100 mPa·s by adjusting the guar content. The injection rate was set at 10–50 mL·min−1, corresponding to 2.67–26.67 m3·min−1 onsite, according to the similarity criterion [44], [45]. Herein, the similarity criterion reported by Liu et al. [44] was employed, where the similarity coefficient c for the hydraulic fracturing simulation tests can be calculated using Eq. (5).
The similarity coefficient of the fracture height , is defined as follows:
where H represents the fracture height, and Ll and Lf are the fracture heights at laboratory scale and field scale, respectively.
The similarity coefficient of the fracturing time , is defined as follows:
where Tl and Tf are the fracturing times at laboratory scale and field scale, respectively.
The similarity coefficient of the injection rate , is defined as follows:
where Ql and Qf are the injection rates at laboratory scale and field scale, respectively.
By substituting Eqs. (6), (7), (8) into Eq. (5), we obtained the relationship between the injection rate at the laboratory scale and that at the field scale, which can be expressed as follows:
3. Results and analysis
3.1. Fracture morphology characteristics
To determine the probability that radial boreholes would guide the cross-layer propagation of the fractures in a multilayer shale oil reservoir, the shale–sandstone superimposed specimens R-S#5, R-M#7, and R-L#5 with different radial borehole lengths (20, 55, and 80 mm) were tested, and specimen H#1 was taken as a comparison group to conduct conventional horizontal well fracturing without radial boreholes. Fig. 9 shows six views of the fractured specimens, in which the leaking locations on the rock surface are marked to identify the fractures (the yellow dotted line in the figure). The purple and pink lines represent the open hole of the horizontal well and the radial boreholes relative to the given view, respectively. To better display the fracture in the rock, we split the fractured samples and reconstructed the 3D fracture morphology in a transparent view. In this reconstructed fracture view, the gray-black and yellow-brown backgrounds represent the shale and sandstone layers, respectively. The yellow, cyan, blue, and red surfaces represent the cementation interface cracking, BP cracking, longitudinal fractures in shale layers, and longitudinal fractures in sandstone layer, respectively. Fig. 10 shows the CT scanning results of the fractures. It can be seen that both the longitudinal hydraulic fracturing and the transverse bedding cracking can be well identified. The scanned 3D geometry of the fractures agrees with that obtained by mechanical splitting, substantiating the feasibility and reasonability of the mechanical splitting and reconstruction method. Higher fracture heights are generally expected from a stimulation to communicate with more production layers and create a larger simulated reservoir volume (SRV). Nevertheless, it is quite difficult for fractures to cross layers in multi-lithologic superimposed reservoirs, especially when high-strength interlayers exist. As shown in Figs. 9(a) and 10, under the conditions of Kv = 1, Q = 20 mL·min−1, and ν = 30 mPa∙s, the fracture initiates in the open-hole section of layer SH2 and then propagates longitudinally. Once it reaches the shale–sandstone interface, the fracture stops growing and passivation occurs. The BP of the intermediate shale layer, SH2, is cracked and causes the loss of fracturing fluid, which further weakens the capability of fracture height growth.
In contrast, the pattern of fracture propagation under the guidance of radial wellbores is significantly different. When the radial borehole L = 20 mm (sample R-S#5, as shown in Figs. 9(b) and 10), multiple fractures initiate at the root of the radial wellbore and extend longitudinally. Blocked by the high-strength sandstone, the fractures propagate laterally along the cementing surface after reaching the lithologic interface, and the fracture height stops increasing. When the radial borehole extends into the sandstone layer (L = 55 mm, sample R-M#7, as shown in Figs. 9(c) and 10), the fractures created at the root end of the radial borehole propagate radiatively in SH2, forming a crossed fracture network. Simultaneously, the stress concentration at the toe end of the radial borehole causes cracking in the SA2 layer, and the fracture extends vertically and crosses the sandstone–shale interface into the SH3 layer. Two sets of fractures created in the inner and outer shale layers are connected by radial boreholes, showing a unique skip-layer distribution pattern. Both cross-layer and skip-layer fractures exist in sample R-M#7, improving the effective fracture height in the shale reservoirs. At L = 80 mm (sample R-L#5, shown in Figs. 9(d) and 10), the radial borehole penetrates through the sandstone layer into the outer shale layers, and fracture initiation occurs at both the toe end and root end of the radial borehole, forming a unique skip-layer fracture pattern and leaving the high-strength unfractured sandstone interval. Therefore, it can be seen that radial boreholes are advantageous in guiding cross-layer or skip-layer fracture propagation, but the guiding effect is closely related to the radial borehole length. If radial boreholes with sufficient length are positioned in multi-layer reservoirs, the effective height of the fractures could be greatly increased by inducing cross-layer and skip-layer fractures and thereby stimulating multiple production layers in the reservoirs.
3.2. Injection pressure response and fracture conductivity
The fluctuation of the injection pressure curves generally align with the fracturing process and can provide direct feedback on the fracture initiation, cross-layer propagation, and post-fracturing closure stages [53]. Fig. 11(a) shows the pump pressure curves of horizontal well fracturing (sample H#1) and radial wellbore fracturing with different borehole lengths (samples R-S#5, R-M#7, and R-L#5). The pressure curve for the conventional horizontal well fracturing does not exhibit a sudden pressure drop in the ascending stage, as shown by the purple curve in the figure. However, there is a noticeable pressure drop on the curve for radial wellbore fracturing, which is attributed to the loss of fracturing fluid induced by the cracking of weak BPs. The abrupt pressure drop points could provide a basis for judging the fracture initiation and propagation behaviors in the laminated samples.
For radial wellbores with different lengths, the characteristics of the pumping curves vary due to different fracture propagation modes. At L = 20 mm (red line), when the pressure rises to 10.3 MPa, cracking preferentially occurs at the root end of the radial borehole due to the higher stress concentration [54] and forms the first peak. Then, the fracture further extends to the sandstone–shale interface, building the pressure to 10.1 MPa to generate the second peak, which corresponds to the shear failure of the interface and subsequent fluid loss. At L = 55 mm (blue line), the pumping pressure quickly rises to 12.8 MPa at first, and the toe end of radial borehole in the sandstone begin to crack; after that, the pressure growth rate drops sharply. Small fluctuations occur at a pressure of 13.9 MPa, which may indicate fracture cross-layering and agree with the results of the fracture propagation and morphology. At L = 80 mm (green line), due to the fluid leak-off induced by BP cracking, the growth rate of the pump pressure is relatively low and the curves show obvious fluctuations. The first pressure drop occurs at 8.4 MPa, indicating that the crack has begun to initiate. When the pressure reaches 13.7 MPa, the outer shale layer cracks and the pressure drops rapidly. It can be seen that the fracture initiation pressure in the presence of the radial branches is lower than that of the conventional horizontal well fracturing, and the initiation pressure (the first pressure drop point on the curve) decreases with increasing radial borehole length (10.3–8.4 MPa), which agrees with the findings of previous studies [37]. According to the feature points on the injection pressure curves, the cracking pressure at the root end is lower than that at the toe end (10.3 MPa < 12.8 MPa, 8.4 MPa < 13.7 MPa), indicating that the multilayer rock samples crack preferentially at the root end due to the higher stress concentration, instead of simultaneously cracking at the toe and root ends of the radial boreholes. In addition, based on the injection pressure curves and Eq. (1), we calculated the fracture conductivity, as shown in Fig. 11(b). As compared with that of the conventional horizontal well fracturing, the average fracture conductivity of the radial borehole fracturing was 111% higher, further substantiating the advantages of the latter technology in improving the fracture height and connectivity.
3.3. Effects of key geological and engineering parameters
3.3.1. Vertical stress difference
The vertical stress difference coefficient (Kv) is an important parameter affecting the longitudinal propagation behavior of hydraulic fractures under the guidance of a radial wellbore. To investigate the effect of Kv on the vertical propagation characteristics of fractures, three vertical stress difference coefficients (0.33, 1.00, and 1.67) were tested on samples with different radial borehole lengths, as shown in Fig. 12. As Kv increases from 0.33 to 1.67, the ability of the radial wellbore to guide the cross-layer propagation of the fracturing increases. A high vertical stress difference coefficient is conducive to improving the vertical propagation of fractures and increasing the effective fracture height. Under low-Kv conditions (e.g., Kv = 0.33), as shown in Figs. 12(c), (f), and (j), the fracture height is dominated by the shale–sandstone interface. Fractures occur only in the intermediate shale, accompanied by significant bedding and interface cracking, and cannot effectively cross the sandstone interval in the longitudinal direction. As Kv increases to 1.00, the radial borehole can better control vertical fracture propagation. Radial boreholes with L = 55 mm start to guide the fractures to penetrate through the sandstone layer (Fig. 12(e)), forming a cross-layer fracture pattern and increasing the effective fracture height in the rock sample, although the fractures still cannot penetrate the high-strength sandstone interlayer under the condition of L = 20 mm (Fig. 12(b)). Moreover, a longer radial borehole is more advantageous in improving the cross-layer propagation of the fracturing, which agrees with the findings in Section 2.1. When Kv increases to 1.67, the vertical propagation of the fracturing is further enhanced; thus, cross-layer fractures occurred in the samples with radial boreholes of L = 20 and 55 mm (Figs. 12(a) and (d), respectively). Unlike the samples in the S and M group, under long radial borehole conditions (L = 80 mm, as shown in Figs. 12(g) and i), fractures tend to initiate at both the root and toe ends and form a unique skip-layer pattern, instead of initiating at the single root end. Two sets of fractures skip over the in-between high-strength sandstone interlayer and propagate competitively in multiple shale production layers, increasing the effective fracture height in the reservoir.
Competition occurs between the longitudinal propagation of hydraulic fractures and the horizontal cracking of weak planes. Under high vertical stress, weak plane structures are subjected to greater effective normal stress, which makes them more difficult to crack and thereby facilitates the longitudinal propagation of fractures, enhancing the radial wellbores’ ability to guide cross-layer propagation. Fig. 13 shows the number of activated shale and sandstone layers by hydraulic fracturing under different vertical stress differences in samples with different radial borehole lengths. The number of activated layers and the corresponding fracture heights are positively correlated with Kv. The sandstone layers of the samples in the S and M groups are more easily activated, showing the characteristics of a cross-layer pattern. In contrast, the samples in the L group are mainly characterized by multiple initiations of shale production layers, showing a skip-layer pattern, with the average fracture height of the production zone being respectively 27.4% and 50.4% higher than those in the S and M groups. In such a skip-layer pattern, all the hydraulic energy can be applied to the production layer, which assists in improving the effective stimulation performance of the shale layer.
Figs. 14(a)–(c) show the effect of Kv on the pump pressure of samples with different borehole lengths. In general, the pressure first increases to the peak and then declines. However, a great vertical stress difference will cause the crack to propagate too fast, making it difficult to distinguish the feature points of fracture initiation and propagation on the curves. For the three radial borehole lengths, the fracture initiation pressure at the root end grows with increasing Kv (L = 20 mm: 16.9 MPa > 14.3 MPa > 11.6 MPa; L = 55 mm: 12.5 MPa > 11.6 MPa > 9.4 MPa; L = 80 mm: 5.6 MPa > 5.2 MPa). The cross-layer pressure is 13.6%–25.9% higher than the initiation pressure at the root end. The pump pressure curves of the long-radial-borehole samples clearly fluctuate after the peak, which may be attributed to competitive initiation and propagation of the fractures in multiple layers. Although a high Kv can enhance cross-layer propagation in radial borehole fracturing, it is not conducive to the opening of weak surfaces, so the fracture morphology tends to be simple, decreasing the fracture conductivity, as shown in Fig. 14(d).
3.3.2. Injection rate
To study the effect of injection rate on radial borehole fracturing, true triaxial fracturing experiments were performed at rates of 10, 20, and 50 mL·min−1. There is a positive correlation between the injection rate and the ability of a radial borehole to induce the cross-layer propagation of fractures. In group S, the injection rate of Q = 20 mL·min−1 could not achieve layer penetration under the condition of Kv = 1, as shown in Fig. 15(a). When Q increased to 50 mL·min−1 (Fig. 15(b)), the fracture initiated at the root end in the SH2 layer and extended through the high-strength interlayer under the guidance of the radial well, forming a single-wing cross-layer fracture. In group M, the longer radial borehole was better able to guide the fracture propagation, so the threshold injection rate required for cross-layering was reduced. At L = 55 mm (Figs. 15(c) and (d)), fractures initiated from both the root and toe ends at injection rates of Q = 20 and 50 mL·min−1. The toe-end fracture extended through the lithologic interface into the SH3 layer and was connected with the root-end fracture by the radial wellbore, forming a hybrid cross-layer/skip-layer fracture mode. When the radial wellbore length was further increased to L = 80 mm, the threshold injection rate further decreased to 10 mL·min−1 (Fig. 15(e)). The fractures successively initiated in the SH2 layer (root end) and SH1/3 layers (toe end) and propagated separately in their own layer, exhibiting a skip-layer fracture mode. The longitudinal fracture in each layer did not cross into the sandstone interlayer. At a higher injection rate of 20 mL·min−1 (Fig. 15(f)), the cracking of weak planes was suppressed, and hydraulic fractures were created in all three shale layers, stimulating multiple sweet spots.
Increasing the injection rate can effectively improve the radial wellbore’s ability to guide fracturing through and across layers and to increase the fracture height, as shown in Fig. 16. A long radial borehole can facilitate cross-layer and skip-layer propagation and reduce the threshold injection rate. Nevertheless, a low injection rate helps to open the horizontal weak surface of the shale intersecting with vertical hydraulic fractures to form a fracture network, which is conducive to improving the fracture complexity. Therefore, in actual engineering operations, it is recommended to maximize the radial well extension length and use a high-low rate-alternating injection method, as follows: First, a high displacement is used to increase the vertical height of the fracture; then, a low displacement injection is used to induce the cracking of weak BPs, so as to maximize the reconstruction volume of the reservoir.
In terms of the fracturing curve response, the pressure in the well grows faster as the injection rate increases, and the fracture initiation pressure rises accordingly, as shown in Figs. 17(a)–(c). In a long radial wellbore, the growth amplitude of the initiation pressure is greater. Compared with the pressure curves of groups S and M, the pressure curve of group L fluctuates more obviously, indicating that multiple fractures are competing to initiate. The fracture conductivity is positively correlated with the displacement (Fig. 17(d)), and the fracture conductivity increases by 54.6%–151.2% as the injection rate increases.
3.3.3. Viscosity of fracturing fluid
In laminated formations, the fluid viscosity directly determines the opening of weak planes and the filtration loss, so it has an important influence on vertical fracture propagation. Fig. 18 illustrates the effects of fluid viscosity on the fracture morphology of samples with different radial borehole lengths. As shown in Figs. 18(a) and (c), low-viscosity fracturing fluid tends to create complex fractures at the root end of a radial wellbore, accompanied by the opening of BPs. Hydraulic fractures are passivated at the interlayer interface, and it is difficult for fractures to pass through the interlayer. At a high viscosity of 100 mPa·s (Figs. 18(b) and (d)), the cross-layering of the fracture is improved. The fracture passes through the interlayer SA2 to the outer layer SH3, forming a single-wing cross-layer fracture. Although high-viscosity fluid is conducive to improving the cross-layering of fractures and the fracture height (Fig. 19), it is not beneficial to the activation of natural weak surfaces such as BPs, so it results in a decrease in fracture complexity. Therefore, in actual engineering operations, alternating the injection of high- and low-viscosity fracturing fluid is recommended to maximize the stimulation performance.
As shown in Figs. 20(a)–(c), the fracture initiation pressure increases significantly with increasing viscosity. When injected with low-viscosity fluid, the fracture fluctuation is significant, with a low-pressure building rate, which corresponds to natural bedding cracking in the fracturing process. There is a positive correlation between the fluid viscosity and fracture conductivity, as shown in Fig. 20(d). As the viscosity of the fracturing fluid increases, the fracture width increases significantly due to the growing flow resistance, which improves the fracture conductivity by 2.00–61.93 times.
3.4. Parameterization domain analysis
3.4.1. Fracture propagation pattern plates
To more intuitively demonstrate the comprehensive influence of multiple parameters on the longitudinal propagation of fractures as guided by a radial wellbore and to identify the critical zone for cross-layering and the optimal parameter combination, all the results from the experimental fracture morphology were summarized and plotted into a 2D plate, as shown in Figs. 21(a)–(c). Based on the second theorem of similarity, also known as the π theorem, the governing equation of the propagation of full 3D hydraulic fracturing can be normalized to bridge the corresponding relationship between physical model experiments of hydraulic fracturing and field fracturing [43], [55]. It can be further taken as an up-scale law to apply experimental results to reservoirs. According to this similarity equation, the injection rates of 10, 20, and 30 mL·min−1 in the experiment correspond to 2.67–5.33, 5.33–10.67, and 10.67–26.67 m3·min−1 in the field scale, respectively. The radial borehole lengths of 20, 55, and 80 mm in the experiment correspond to lengths of 5–15, 15–25, and 25–40 m in the field, respectively, representing three different cross-layer cases with radial boreholes. The blue area in the lower left part of Fig. 21 is the passivation domain, where the fracture cannot cross through the lithologic interlayer under relatively low parameter conditions. The pink area in the upper right part of the chart represents the cross-layer domain; the parameter values in this zone are higher, which is conducive to strengthening the cross-layering guided by the radial wellbore. The green area is the skip-layer domain, where multiple groups of fractures spread separately in each shale layer across the intermediate high-strength sandstone interlayers. At high Kv, the required critical injection rate and viscosity of the fracturing fluid for fracture cross-layering or skip-layering are relatively low. However, at lower Kv, the injection rate and viscosity need to be increased to achieve multilayer fracturing. A longer radial wellbore can effectively facilitate the cross-layering of fractures, reducing the corresponding critical threshold of various parameters for multilayer fracturing. For example, when Kv = 0.33, the critical cross-layering conditions of the samples in group S are Q = 50 mL·min−1 and ν = 100 mPa∙s, as shown in Fig. 21(b), while the critical injection parameters of the samples in groups M and L (Figs. 21(a) and (c)) respectively decrease to Q = 20 mL·min−1 and ν = 50 mPa∙s and to Q = 10 mL·min−1 and ν = 30 mPa∙s. With a short radial well (group S, L = 20 mm, with the toe end located in the intermediate shale layer), when the parameter exceeds the critical threshold condition, the fracture penetrates through the sandstone layer to form a single-wing cross-layer morphology. Under medium length conditions (group M, L = 55 mm, with the toe end located in the sandstone interlayer), there is a transition zone (yellow area) between the passivation and the cross-layer domain. In this zone, the fractures initiate at both the toe end and root end, and the toe end fractures extend outward through the interface into the outer shale layers, forming a unique hybrid cross-/skip-layer pattern. However, with a long radial well (group L, L = 80 mm, with the toe end located in the outer shale layer), the fracture transforms into a single skip-layer initiation mode as the parameters increase, without a cross-layer mode, which is advantageous in applying more hydraulic energy to the production layer and increasing the effective fracture height.
Regarding the fracture complexity, although a fracturing fluid with a high injection rate and viscosity and a high vertical stress differential coefficient are conducive to improving the ability of the radial wellbore to guide fracture cross layers and to achieving an effective fracture height, the use of high parameters for cross-layering could weaken the activation of transverse BPs, resulting in a single main fracture, which assists in improving the overall SRV and fracture complexity. With a long radial wellbore, cross-layering can be achieved by using relatively low parameters, which results in the activation of more transverse BPs and creates a 3D fracture network. Therefore, considering the longitudinal height and complexity of the fracture, it is recommended to extend the radial branch length as much as possible; moreover, a critical parameter combination of cross-/skip-layering assists in achieving a good stimulation performance. In actual engineering, the adoption of a combination scheme of high viscosity/high displacement and low viscosity/low displacement is suggested to enhance the fracture height guided by a radial wellbore, while activating weak surfaces such as BPs to improve the transverse stimulation of the production layer, forming 3D complex fracture networks.
Fig. 22 shows the feature points of the pump pressure curves under different parameter combinations, where blue dots and red dots represent the fracture initiation pressure PRI (at the root end) under passivation conditions and cross-layer/skip-zone conditions, respectively, while yellow dots represent the fracture initiation pressure PTI (at the toe end) under skip-layer conditions. The contour was plotted according to the initiation pressure at the root end to illuminate its variation trend with the parameters. Unlike single-root initiation under short-radial-wellbore conditions (Fig. 22(a), L = 20 mm), when the radial borehole length increases to L = 55 and 80 mm (Figs. 22(b) and (c)), the fracture initiates asynchronously from the root and toe ends, and two corresponding feature points can be captured, in which the initiation pressure at the toe end is higher than that at the root end. However, when parameters such as the injection rate and viscosity are significantly higher than the critical threshold, the hydraulic energy accumulates too quickly, and both ends of the radial wellbore crack at almost the same time, showing only one feature point (red dot) on the curves. With an increase in Kv, Q, and ν, the fracture initiation pressure for the three well lengths increases gradually. According to the corresponding critical threshold parameter conditions of the cross-layering and skip-layering under different vertical stress differences, the fracture initiation pressure under critical conditions was determined and compared, as shown in Fig. 22(d). Increasing the radial wellbore length facilitates fracture initiation and reduces the critical pump pressure for cross-layering/skip-layering, which further substantiates the superiority of long radial wellbores.
3.4.2. Parameter correlation analysis
In order to quantitatively evaluate the influence of the vertical stress difference Kv, fracturing fluid injection rate Q, viscosity ν, and radial wellbore length L on the fracture height and to determine the main controlling factors, the number of activated layers NL by fracture and root/toe initiation pressure PRI and PTI under different parameter combinations were determined, and three algorithms (i.e., Pearson, Spearman, and Kendall [56]) were used for a correlation coefficient (CC) analysis, as shown in Fig. 23. The CC ranges from −1 to 1. CC > 0 indicates a positive correlation, while CC < 0 indicates a negative correlation. Absolute CC values in the ranges of 0–0.1, 0.1–0.3, 0.3–0.5, and 0.5–1.0 represent no correlation, weak correlation, intermediate correlation, and strong correlation, respectively. When L = 20 mm (Figs. 23(a)–(c)), Q has the most significant influence on NL and PRI (CC = 0.707–0.929), followed by viscosity ν (CC = 0.471–0.651), and finally Kv (CC = 0.196–0.366). When L = 55 mm (Figs. 23(d)–(f)), Kv has a weak influence on NL (CC = 0.180–0.258), but a strong correlation with PRI (CC = 0.845–0.926). ν has the best correlation with NL (CC = 0.514–0.698), followed by Q (CC = 0.371–0.578). When L = 80 mm (Figs. 23(g) and (h)), the correlation with Kv and Q is weak, with absolute values that are basically less than 0.3. It was found that, among the three parameters Kv, Q, and ν, the influence of Q and ν on the fracture height in multilayer shales is often greater than that of Kv. However, with an increase in the radial wellbore length, the effects of the Kv, Q, and ν parameters on the vertical fracture propagation weakens, and the correlation of each parameter decreases significantly. Fig. 23(i) indicates that the radial wellbore length L and NL exhibit a strong positive correlation (CC = 0.667–0.836), which is the most important factor dominating the fracture height. L has a strong negative correlation with PRI (CC = −1.000–−0.994) and a medium negative correlation with PTI (−0.333), indicating that radial wells can greatly reduce the initiation pressure, increase the fracture height, and reduce the engineering difficulty during construction. Therefore, the radial well length should be increased as much as possible in field construction to achieve multilayer initiation, improve the fracture height, effectively activate natural weak surfaces such as BPs, and improve the fracture complexity and SRV.
4. Discussion
In multi-lithologic superimposed reservoirs such as shale oil reservoirs, horizontal well fracturing is an important technique for creating a volumetric fracture network. However, natural weak surfaces such as BPs in laminated rocks ((i) in Fig. 24) and the sand–shale lithologic interface ((ii) in Fig. 24) in continental shale oil formations are easily damaged, resulting in transverse secondary fractures. According to the mechanical tests shown in Fig. 7, the interface has very low tensile strength, at only 2–3 MPa, which makes it liable to be activated by stress disturbance or fluid seepage. In the fracturing process, the stress around the interface is disturbed by the vertical propagation of the hydraulic fractures, and the seepage and filtration of fracturing fluid at the interface can further weaken the strength of the interface and induce interface cracking, although the hydraulic pressure does not exceed the vertical normal stress. Moreover, according to the pressure curves, the peak pressure of the fracturing in our work is within 10.0–18.7 MPa, while the interfacial shear strength is within 13–18 MPa (as shown in Fig. 7), just falling into the peak pressure ranges. Considering the inherent heterogeneity of rock samples, the increase in pore pressure induced by fluid filtration, and the stress disturbance during fracturing, there is a possibility that the interface will activate via shear failure.
Cross-layer behavior in the fracturing process is a very complicated problem that is affected by many factors, such as the physical properties of the fracturing fluid, the injection rate, in situ stress, and the mechanical properties of the rock. On the one hand, the fluid overcomes the minimum principal stress, promotes the longitudinal extension of the fracture, and penetrates through the high-strength interlayer barrier; on the other hand, the fluid activates the bedding and the weak interlayer surface, causing the fluid to filter out laterally and preventing the fracture from penetrating the layer longitudinally. Therefore, the cross-layer flow effect is essentially a competitive process between longitudinal fracture extension and transverse interface activation. The large hydraulic energy dissipation of transverse fractures makes it difficult to maintain the pressure [57], which limits the extension of fracture height and then affects the cross-layer performance of the hydraulic fractures. Only the use of a large injection rate and high viscosity can trigger cross-layer behaviors; however, this will hinder the activation of transverse fractures and is not conducive to forming a volumetric fracture network [58]. Moreover, rather than initiating in high-strength sandstone interlayers, fractures preferentially initiate in shale layers during fracturing [59]. It is difficult for fractures to penetrate through the interlayer. Fractures passivate and transform into T-shaped structures at the lithologic interface ((ii) in Fig. 24), limiting the longitudinal engineering stimulation of reservoirs.
In comparison with conventional horizontal well fracturing, radial wellbores reduce the difficulty of cross-layering and achieve cross-layer propagation with relatively weak parameters. This can effectively improve the fracture height and enhance the activation of horizontal BPs, addressing the issue of a simple fracture morphology under strong cross-layer injection parameters in traditional horizontal well fracturing and greatly improving the fracture complexity and SRV. Unlike conventional horizontal well fracturing, radial wellbore fracturing essentially transforms the issue of the hydraulic fracture penetrating through the interlayer/lithology interface into an issue of the radial-wellbore-guided cross-layering and longitudinal competitive initiation of fractures in multilayer reservoirs. The process of fracture initiation and propagation involves the joint disturbance of the radial-borehole-induced stress reconstruction and the lithology interface. Based on the experiments in this paper, two typical modes can be identified in radial wellbore fracturing—namely, the cross-layer and skip-layer modes—accompanied by two kinds of transverse fractures and four kinds of longitudinal fractures, as shown in Fig. 24. When the radial branch does not reach the interlayer, it is difficult for the fracture to penetrate through the high-strength interlayer, arresting the vertical propagation of fractures ((iii) in Fig. 24). When the radial branch is drilled into the interlayer, the fracture initiates at both the toe end and root end due to the stress concentration, and the toe end fracture crosses the interface to communicate with the upper reservoir. Since this toe-end fracture is not connected with the root-end fracture, it forms a hybrid cross- /skip-layer fracture ((iv) in Fig. 24). Nevertheless, as the injection rate and viscosity of the fracture fluid increase, the root-end and toe-end fractures will be connected to form a typical cross-layer pattern ((v) in Fig. 24). In fact, skip-layer and cross-layer behaviors are mutually restrictive. With long radial boreholes, the fractures preferentially initiate in multiple low-strength shale layers ((vi) in Fig. 24), while cross-layering basically does not occur. The skip-layer pattern has the advantage of applying more hydraulic energy to the production layer and increasing the effective fracture height, avoiding the hydraulic energy consumption of cross-layers in the high-strength sandstone interlayer. Thus, the use of long radial boreholes is suggested in order to achieve better fracturing performance in the field. In addition, although improving the injection parameters (Q and ν) and vertical stress difference is conducive to strengthening the longitudinal cross-layering of the fractures, it weakens the degree of transverse activation of weak surfaces and reduces fracture complexity. Therefore, considering the fracture height and complexity, it is recommended to adopt a combination of parameters under the critical condition of cross-layering or an injection method of alternating high/low displacement/viscosity to obtain the optimal SRV.
Although this paper confirms the technical advantages of radial wellbore fracturing in guiding fracture cross-layering and competitive initiation in multilayers, this only applies to radial boreholes vertical to the stratum. In fact, radial boreholes generated by hydra-jets or flexible drilling tools may not be completely perpendicular to the formation and may be at an angle to the in situ stress in the engineering field [60]. The non-plane propagation characteristics of radial-well-induced fractures in multilayer reservoirs at different dip angles is a key problem that requires further study in the future.
5. Conclusions
To determine the longitudinal propagation behavior of fractures guided by a radial wellbore in a multi-lithologic superimposed reservoir, we performed true triaxial radial wellbore cross-layer fracturing experiments on multilayered shale-sandstone samples. We studied the fracture initiation and propagation characteristics, with a focus on the injection pressure response, fracture morphology, and cross-layer pattern. The effect of the radial borehole length L, vertical stress difference Kv, injection rate Q, and viscosity ν of the fracturing fluid were investigated using a parameter domain analysis. The correlation between various parameters and the fracture height was quantitatively evaluated to illuminate the dominant factors. The main conclusions are as follows:
Compared with conventional horizontal well fracturing, radial wellbores can effectively reduce the fracture initiation pressure, facilitate cross-layer propagation, and improve the fracture height and the activation of transverse weak BPs, thereby enhancing the complexity and SRV of the fracture network.
Radial-wellbore-assisted hydraulic fracturing has two typical fracture-propagation modes: cross-layering and skip-layering. A short radial wellbore generally induces cross-layer fractures that penetrate through the interlayer. In contrast, a long radial wellbore is mainly characterized by skip-layer fractures, skipping the intermediate high-strength interlayer, activating multiple production layers, and improving the effective fracture height and flow conductivity.
In a multi-lithology superimposed reservoir, the capacity of radial wellbores to guide cross-layer/skip-layer propagation is positively correlated with Kv, Q, and ν. As these parameters increase, the fracture initiation pressure grows accordingly, with the initiation location shifting from a single root end to asynchronous root/toe ends. A high injection rate, viscosity, and vertical stress difference are advantageous in enhancing the cross-layer performance and fracture height, but they may weaken the transverse activation of BPs.
Critical parameter thresholds exist for the cross-layer and skip-layer propagation of fractures guided by radial wellbores. Under the conditions of a low injection rate and low-viscosity fracturing fluid, weak BPs in shale are prone to cracking, resulting in a filtration loss of fracturing fluid and slow boosting of the pump pressure with frequent fluctuations, which limits longitudinal fracture propagation. The use of strong parameters that are much higher than the critical threshold can greatly enhance the cross-layering of fractures; however, the cracking of transverse secondary fractures is inhibited, resulting in a simple fracture geometry with low complexity. Thus, a critical parameter combination for cross-/skip-layer modes or alternating Q/ν is recommended to improve the longitudinal fracture height and the complexity of the fracture networks.
The degree of correlation of different parameters with the vertical fracture height can be written as L > Q/ν > Kv. The radial wellbore length is the most dominant factor controlling fracture initiation and the propagation mode. Increasing the radial wellbore length can effectively facilitate cross-/skip-layer fracture propagation, decrease the fracture initiation pressure, and significantly reduce the critical threshold of the injection rate, viscosity, and vertical stress difference coefficient, which is conducive to improving the longitudinal fracture height and transverse fracture activation.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (52421002, U24B6001, 52204019, and 52192624) and the Open Foundation of the Shanxi Key Laboratory of Carbon Dioxide Sequestration and Enhanced Oil Recovery.
Compliance with ethics guidelines
Xiaoguang Wu, Zhongwei Huang, Tengda Long, Gensheng Li, Shouceng Tian, Haizhu Wang, Ruiyue Yang, Kun Li, and Zikang Wang declare that they have no conflict of interest and financial conflicts to disclose.
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