Propagation Characteristics of Fractures Induced by Supercritical Carbon Dioxide Jet in Hard and Soft Layered Rocks

: The initiation and propagation behavior of fractures induced by supercritical carbon dioxide (SC-CO 2 ) jet fracturing is signiﬁcant to evaluate stimulated reservoir volume (SRV). However, the propagation characteristics of fractures induced by SC-CO 2 jet in layered rocks with layers having different mechanical properties have not yet been studied. In this study, four groups of artiﬁcial sandstones were used to conduct SC-CO 2 jet fracturing experiments and investigate the fracture initiation and propagation behavior in hard and soft layered rocks. A strain collection device was employed to monitor the strain changes of the specimens during the experiments, and after the experiments, a three-dimensional scanner was used to obtain the morphologies of the main fractures. Experimental results showed that the SC-CO 2 jet fracturing can be divided into the pressurization of the perforation pressure stage and fracture propagation stage, and the fractures initiation and propagation is intermittent. Three types of main fractures have been found—longitudinal fracture, transverse fracture and oblique fracture—and the formation mechanism of the main fractures has been elaborated. The rock strength can affect the number and complexity of fractures created and the fracturing rate, and the Young’s modulus of rock has an effect on fracture propagation length. The fractures mainly develop near the perforation and are difﬁcult to propagate to another layer with different mechanical properties. The result in our study is conducive to the application of SC-CO 2 jet fracturing technology in the ﬁeld.


Introduction
The development of unconventional resources (such as shale gas, tight sand gas and coalbed methane) is a hot issue in recent years, which can enable the fuel supply to satisfy the growing demand for energy [1][2][3].Because of the extremely low permeability and low porosity of the unconventional reservoirs, the traditional methods make it difficult to exploit these reservoirs efficiently.The fracturing technology is regarded as a major technology to stimulate unconventional gas reservoirs, which can create fractures and increase permeability to achieve economic productivity for resources exploitation [4,5].
The hydra-jet fracturing is a typical method of fracturing technology proposed by Surjaatmadja et al. [6].Hydra-jet fracturing is regarded as a unique, cost-effective and efficient well-stimulation treatment (Figure 1), which can accomplish a multi-stage pinpoint fracturing without using mechanical packers due to the effect of pressure stagnation and hydraulic isolation [6][7][8].This method can control the fracture initiation location accurately and isolate the wellbore effectively by utilizing the pressure boosting effect in perforation cavity and the hydrodynamic sealing effect in annulus [8,9].The SC-CO 2 fracturing has been proposed in recent years [10,11], gaining great attention due to its particular properties and encouraging results [12][13][14][15].The SC-CO 2 has unique properties, including a low viscosity similar to the gas state, a large density similar to the liquid state, a low surface tension, and a high diffusivity [11,13,[16][17][18].As a fracturing fluid, SC-CO 2 has many potential advantages, such as avoiding the problem caused by swelling of clays [19], enhancing desorption of CH 4 due to its greater adsorption capacity than that of CH 4 [20], reducing water usage and minimize environmental pollution [21].To combine the advantages of hydra-jet fracturing and SC-CO 2 fracturing, the SC-CO 2 jet fracturing has been proposed [12,21].
Appl.Sci.2022, 12, x FOR PEER REVIEW 2 of 21 accurately and isolate the wellbore effectively by utilizing the pressure boosting effect in perforation cavity and the hydrodynamic sealing effect in annulus [8,9].The SC-CO2 fracturing has been proposed in recent years [10,11], gaining great attention due to its particular properties and encouraging results [12][13][14][15].The SC-CO2 has unique properties, including a low viscosity similar to the gas state, a large density similar to the liquid state, a low surface tension, and a high diffusivity [11,13,[16][17][18].As a fracturing fluid, SC-CO2 has many potential advantages, such as avoiding the problem caused by swelling of clays [19], enhancing desorption of CH4 due to its greater adsorption capacity than that of CH4 [20], reducing water usage and minimize environmental pollution [21].To combine the advantages of hydra-jet fracturing and SC-CO2 fracturing, the SC-CO2 jet fracturing has been proposed [12,21].To investigate the feasibility of applying SC-CO2 jet fracturing to unconventional resources, researchers have done many numerical simulations and experimental studies.He et al. [21] found that SC-CO2 jet fracturing could achieve a better pressurization effect than the pressurization effect of water jet fracturing under conventional formation and operating conditions by using numerical simulation and laboratory experiments.Cai et al. [12] investigated the influence of the factors, including jet pressure, jet distance, nozzle diameter, perforation length and perforation diameter, on the effect of SC-CO2 jet fracturing by conducting experiments on organic glasses, and found the optimal jet distance and nozzle diameter were 10 mm and 2 mm, respectively.Wang et al. [19] and Tian et al. [22] investigated the perforation ability of SC-CO2 jet by laboratory experiments, and provided a theoretical foundation and experimental proven for field application of SC-CO2 jet perforation technology, which was beneficial to the integration of perforation and fracturing by SC-CO2 jet.Hu et al. [23] found that the pressurization effect of SC-CO2 could easily lead to fractures initiation and propagation at three locations (the root, the middle, and the tip of perforation) by numerical simulation.The above research mainly focuses on the principle of SC-CO2 jet fracturing and the influence of relevant parameters on fracturing To investigate the feasibility of applying SC-CO 2 jet fracturing to unconventional resources, researchers have done many numerical simulations and experimental studies.He et al. [21] found that SC-CO 2 jet fracturing could achieve a better pressurization effect than the pressurization effect of water jet fracturing under conventional formation and operating conditions by using numerical simulation and laboratory experiments.Cai et al. [12] investigated the influence of the factors, including jet pressure, jet distance, nozzle diameter, perforation length and perforation diameter, on the effect of SC-CO 2 jet fracturing by conducting experiments on organic glasses, and found the optimal jet distance and nozzle diameter were 10 mm and 2 mm, respectively.Wang et al. [19] and Tian et al. [22] investigated the perforation ability of SC-CO 2 jet by laboratory experiments, and provided a theoretical foundation and experimental proven for field application of SC-CO 2 jet perforation technology, which was beneficial to the integration of perforation and fracturing by SC-CO 2 jet.Hu et al. [23] found that the pressurization effect of SC-CO 2 could easily lead to fractures initiation and propagation at three locations (the root, the middle, and the tip of perforation) by numerical simulation.The above research mainly focuses on the principle of SC-CO 2 jet fracturing and the influence of relevant parameters on fracturing results.The effect of beddings on the propagation of fractures induced by SC-CO 2 jet have been studied by Liu et al. [24], but the influence of geological factors on the propagation of fractures induced by SC-CO 2 jet have not been studied clearly.
The initiation and propagation behavior of fractures induced by fracturing technology is complicated and difficult to predict.Various factors influence the initiation and propagation behavior of fractures, including engineering factors and geological factors.The engineering factors are controllable, and understanding the effects of engineering factors, such as fracturing fluid viscosity and injection rate, on the fracture initiation and propagation are important to maximize the stimulated reservoir volume (SRV) [25][26][27][28][29][30].The geological factors, such as in situ stress and discontinuities, have an impact on fractures initiation and propagation, which is uncontrollable, but the fractures propagation can be predicted through investigating the influence of geological factors on fracture propagation [31][32][33][34][35][36][37].
Previous studies mainly focus on the engineering factors on the propagation of fractures induced by SC-CO 2 jet, and few studies investigate the influence of geological factors on the propagation of fractures induced by SC-CO 2 jet.For most reservoirs, the formations of reservoirs are layered, and the mechanical properties of different layers can be different, which can affect the propagation of fractures.It is significant to investigate the propagation behavior of fracture induced by SC-CO 2 jetting in the layered reservoirs with different mechanical properties which, here, is called hard and soft layered rock.In this paper, four groups of artificial sandstones were prepared to investigate the fracture propagation behavior in hard and soft layered rocks by SC-CO 2 jet fracturing.A strain collection device was employed to monitor the strain changes of the specimens during the experiments.After the experiments, a three-dimensional scanner was used to get the morphologies of the main fractures.

Specimen Preparation
To investigate the growth behavior of SC-CO 2 induced fractures in hard and soft layered rocks, this research used artificial specimens which had two layers to conduct the SC-CO 2 jet fracturing experiments.As shown in Figure 2, the artificial specimen consisted of artificial sandstone and the casing.results.The effect of beddings on the propagation of fractures induced by SC-CO2 jet have been studied by Liu et al. [24], but the influence of geological factors on the propagation of fractures induced by SC-CO2 jet have not been studied clearly.
The initiation and propagation behavior of fractures induced by fracturing technology is complicated and difficult to predict.Various factors influence the initiation and propagation behavior of fractures, including engineering factors and geological factors.The engineering factors are controllable, and understanding the effects of engineering factors, such as fracturing fluid viscosity and injection rate, on the fracture initiation and propagation are important to maximize the stimulated reservoir volume (SRV) [25][26][27][28][29][30].The geological factors, such as in situ stress and discontinuities, have an impact on fractures initiation and propagation, which is uncontrollable, but the fractures propagation can be predicted through investigating the influence of geological factors on fracture propagation [31][32][33][34][35][36][37].
Previous studies mainly focus on the engineering factors on the propagation of fractures induced by SC-CO2 jet, and few studies investigate the influence of geological factors on the propagation of fractures induced by SC-CO2 jet.For most reservoirs, the formations of reservoirs are layered, and the mechanical properties of different layers can be different, which can affect the propagation of fractures.It is significant to investigate the propagation behavior of fracture induced by SC-CO2 jetting in the layered reservoirs with different mechanical properties which, here, is called hard and soft layered rock.In this paper, four groups of artificial sandstones were prepared to investigate the fracture propagation behavior in hard and soft layered rocks by SC-CO2 jet fracturing.A strain collection device was employed to monitor the strain changes of the specimens during the experiments.After the experiments, a three-dimensional scanner was used to get the morphologies of the main fractures.

Specimen Preparation
To investigate the growth behavior of SC-CO2 induced fractures in hard and soft layered rocks, this research used artificial specimens which had two layers to conduct the SC-CO2 jet fracturing experiments.As shown in Figure 2, the artificial specimen consisted of artificial sandstone and the casing.The artificial sandstone was a cylinder with a diameter of 100 mm and a length of 100 mm.The artificial sandstone had two layers which were made by mixtures consisting of cement, clay minerals, 20-40 mesh natural siliceous and water.As shown in    The artificial sandstone was a cylinder with a diameter of 100 mm and a length of 100 mm.The artificial sandstone had two layers which were made by mixtures consisting of cement, clay minerals, 20-40 mesh natural siliceous and water.As shown in Table 1, two mixtures of different ratios were used to make hard and soft layers, respectively.The lower and upper layers of the artificial stones were continuously poured, to avoid the occurrence of weak structural planes which can affect the fracture propagation.The artificial sandstones were cured over four weeks at a temperature of 25 • C. Four types of artificial sandstones were made by the mixtures: hard rock, soft rock, hard-soft rock, and soft-hard rock.The mechanical properties of the hard and soft rocks were obtained by the uniaxial compressive strength (UCS) test and direct simple shear (DSS) test listed in Table 2.A hole with a diameter of 6 mm and a length of 50 mm drilled in the center of each artificial sandstone to simulate the perforation.A steel casing plate with a 6 mm diameter hole at center of the casing was stuck to each artificial sandstone by epoxy glue to simulate the wellbore.The thickness and diameter of the casing were 2 mm and 90 mm, respectively, and the thickness of the epoxy resin was 0.5 mm.Two strain gages were stuck to each specimen by super glue, and a layer of polyethylene film was pasted on the surface of the strain gage to prevent external interference.One of the strain gages was 25 mm from the upper surface, and the other was 75 mm from the upper surface.Then, 18 completed specimens were kept in room temperature for one week.As shown in Table 3, four groups of specimens were prepared to study the growth behavior of fractures induced by SC-CO 2 jet fracturing in hard and soft layered rocks.Group A was hard rocks, for which the upper and lower layers were hard artificial sandstones; group B was soft rocks, in which the upper and lower layers were soft artificial sandstones; group C was hard-soft rocks, in which the upper layers were hard artificial sandstones, and the lower layers were soft artificial sandstones; group D was soft-hard rocks, in which the upper layers were soft artificial sandstones, and the lower layers were hard artificial sandstones.

Experimental Apparatuses
The SC-CO 2 jet fracturing experiments in this study were conducted by the SC-CO 2 jet fracturing experimental system which was introduced in detail by Cai and Wang et al. [12,38].As Figure 3 shows, the system is composed of the SC-CO 2 generating device, the high pressure jet kettle, and the strain collection device.The SC-CO 2 generating device consists of a de-sander, CO 2 cylinder, refrigeration, a storage tank, plunger pump, buffer tank, and a water bath heater.Firstly, the gas CO 2 from CO 2 cylinder and the recycled CO 2 from de-sander is cooled by refrigeration, and then stored in a storage tank in a liquid state.Secondly, the liquid CO 2 will be pressurized by triple plunger pump to 15-40 MPa, and stores in a buffer tank which is heated by a water bath heater to 50 • C. Thirdly, the CO 2 in the buffer tank will change to a supercritical state when its temperature and pressure exceed 31.26

Experimental Apparatuses
The SC-CO2 jet fracturing experiments in this study were conducted by the SC-CO2 jet fracturing experimental system which was introduced in detail by Cai and Wang et al. [12,38].As Figure 3 shows, the system is composed of the SC-CO2 generating device, the high pressure jet kettle, and the strain collection device.The SC-CO2 generating device consists of a de-sander, CO2 cylinder, refrigeration, a storage tank, plunger pump, buffer tank, and a water bath heater.Firstly, the gas CO2 from CO2 cylinder and the recycled CO2 from de-sander is cooled by refrigeration, and then stored in a storage tank in a liquid state.Secondly, the liquid CO2 will be pressurized by triple plunger pump to 15-40 MPa, and stores in a buffer tank which is heated by a water bath heater to 50 °C .Thirdly, the CO2 in the buffer tank will change to a supercritical state when its temperature and pressure exceed 31.26°C and 7.38 MPa, respectively.The strain collection device consists of a static-dynamic strain indicator, computer, and strain gage, which has been well used in the experiments of Cai et al. [39,40].The strain indicator is suitable for static and dynamic strain test with frequencies below 5000 Hz, the strain measurement range is ±38,000 με, and strain resolution is 0.1 με.The strain gage is connected with strain indicator by 1/4 bridge connection method, and each specimen has two strain gages connected to the compensation strain gage.Jet fracturing is a low-frequency shock, so the strain is detected at a frequency of 1000 Hz in this experiment.The strain gage used in this experiment is BX120-3AA strain gage, and its base size and wire grid size are 6.6 × 3.3 mm and 3.0 × 2.3 mm, respectively.The resistance of the strain gage is 120 Ω, with ±0.5 Ω error.The strain collection device consists of a static-dynamic strain indicator, computer, and strain gage, which has been well used in the experiments of Cai et al. [39,40].The strain indicator is suitable for static and dynamic strain test with frequencies below 5000 Hz, the strain measurement range is ±38,000 µε, and strain resolution is 0.1 µε.The strain gage is connected with strain indicator by 1/4 bridge connection method, and each specimen has two strain gages connected to the compensation strain gage.Jet fracturing is a lowfrequency shock, so the strain is detected at a frequency of 1000 Hz in this experiment.The strain gage used in this experiment is BX120-3AA strain gage, and its base size and wire grid size are 6.6 × 3.3 mm and 3.0 × 2.3 mm, respectively.The resistance of the strain gage is 120 Ω, with ±0.5 Ω error.

Experimental Procedure
The SC-CO 2 jet fracturing experiments were conducted in the SC-CO 2 jet fracturing kettle (see Figure 4).Firstly, the specimen was put into the kettle, and the strain gages were connected to the static-dynamic strain indicator.The target distance (S) was set to 10 mm, and the diameter of the nozzle (d n ) selected was 2 mm, because under these parameters, the effect of SC-CO 2 jet fracturing was better according to the study of Cai et al. [12].Secondly, valve 2 was opened by computer, and CO 2 from buffer tank entered the kettle via side nozzle to increase ambient pressure.When the ambient pressure (P am ) reached the value needed, valve 2 was shut down.In the experiments, the ambient pressure was constant at 5 MPa, and the ambient temperature was constant at 50 • C in the kettle which was maintained by circulating hot water from the water bath heater.Thirdly, the triple plunger pump would raise the pressure in the buffer tank to the value needed which was the injection pressure, and the injection pressures are listed in Table 3. Fourthly, valve 1 was opened by computer, and the jet fracturing started with the strain data recorded by computer in the meantime.Lastly, the emptying valve was opened, and the high pressure CO 2 would drain out, and then the specimen was taken out.During the SC-CO 2 jet fracturing experiments, data of all sensors were monitored and recorded by computer.

Experimental Procedure
The SC-CO2 jet fracturing experiments were conducted in the SC-CO2 jet fracturing kettle (see Figure 4).Firstly, the specimen was put into the kettle, and the strain gages were connected to the static-dynamic strain indicator.The target distance (S) was set to 10 mm, and the diameter of the nozzle (dn) selected was 2 mm, because under these parameters, the effect of SC-CO2 jet fracturing was better according to the study of Cai et al. [12].Secondly, valve 2 was opened by computer, and CO2 from buffer tank entered the kettle via side nozzle to increase ambient pressure.When the ambient pressure (Pam) reached the value needed, valve 2 was shut down.In the experiments, the ambient pressure was constant at 5 MPa, and the ambient temperature was constant at 50 °C in the kettle which was maintained by circulating hot water from the water bath heater.Thirdly, the triple plunger pump would raise the pressure in the buffer tank to the value needed which was the injection pressure, and the injection pressures are listed in Table 3. Fourthly, valve 1 was opened by computer, and the jet fracturing started with the strain data recorded by computer in the meantime.Lastly, the emptying valve was opened, and the high pressure CO2 would drain out, and then the specimen was taken out.During the SC-CO2 jet fracturing experiments, data of all sensors were monitored and recorded by computer.

Characteristics of Fracture Propagation
Investigating the characteristics of fracture propagation is crucial to understand the formation mechanism of fractures and evaluate the effect of SC-CO2 jet fracturing.In this section, unfolded images of fractures taken by a digital camera and morphologies of fractures obtained by a three-dimensional scanner were used to evaluate the fractures.The typical results of fractures propagation in some specimens were shown in Figure 5. Through observation, the fracture patterns of each group were different, but the fracture patterns of the specimens from the same group were similar.

Characteristics of Fracture Propagation
Investigating the characteristics of fracture propagation is crucial to understand the formation mechanism of fractures and evaluate the effect of SC-CO 2 jet fracturing.In this section, unfolded images of fractures taken by a digital camera and morphologies of fractures obtained by a three-dimensional scanner were used to evaluate the fractures.The typical results of fractures propagation in some specimens were shown in Figure 5. Through observation, the fracture patterns of each group were different, but the fracture patterns of the specimens from the same group were similar.

Characteristics of Main Fractures
The characteristics of main fractures is one of the significant aspects to study the fracture propagation.According to the observation, the main fractures can be divided into three types (Figure 6): (1) type-A is a longitudinal fracture which is parallel to the axial direction of perforation; (2) type-B is a transverse fracture developing in the transition zone of hard-soft and soft-hard rocks which is perpendicular to the axial direction of perforation, and cutting through the whole specimen; (3) type-C is an oblique fracture developing in the upper layer of the specimen which is oblique to the axial direction of perforation and only cuts through part of the specimen.

Characteristics of Main Fractures
The characteristics of main fractures is one of the significant aspects to study the fracture propagation.According to the observation, the main fractures can be divided into three types (Figure 6): (1) type-A is a longitudinal fracture which is parallel to the axial direction of perforation; (2) type-B is a transverse fracture developing in the transition zone of hard-soft and soft-hard rocks which is perpendicular to the axial direction of perforation, and cutting through the whole specimen; (3) type-C is an oblique fracture developing in the upper layer of the specimen which is oblique to the axial direction of perforation and only cuts through part of the specimen.

Characteristics of Main Fractures
The characteristics of main fractures is one of the significant aspects to study the fracture propagation.According to the observation, the main fractures can be divided into three types (Figure 6): (1) type-A is a longitudinal fracture which is parallel to the axial direction of perforation; (2) type-B is a transverse fracture developing in the transition zone of hard-soft and soft-hard rocks which is perpendicular to the axial direction of perforation, and cutting through the whole specimen; (3) type-C is an oblique fracture developing in the upper layer of the specimen which is oblique to the axial direction of (a) In hard rocks (group A), both the main fractures of specimen A1 and A3 were longitudinal fractures, and the longitudinal fractures propagated completely through the specimens and cut the specimens to two pieces (Figure 5a), and the figures of the fractures in group A were approximately symmetrical.
In soft rocks (group B), longitudinal and oblique fractures were well-developed in three specimens (Figure 5b).The longitudinal fractures terminated when they extended to the oblique fractures.The oblique fractures only developed in the upper layers of specimens and propagated through part of upper layers at the direction oblique to the axial direction.
In hard-soft rocks (group C), the specimen C1-1, C1-2, and C2-2 had no fractures due to the low injection pressure that had not reached the breakdown pressure of specimens.The specimens with fractures had the common characteristic that the fractures were transverse at the middle of specimens (Figure 5c).The transverse fractures initiated from the perforation tip and extended to the surface along a radial direction.
In soft-hard rocks (group D), all three types of fractures were created (Figure 5d).All specimens in group D had longitudinal and transverse fractures, and longitudinal fractures terminated when they extended to the transverse fractures, and the transverse fractures propagated through the whole specimens.The oblique fractures were found in the upper layers of specimen D1-1 and D3-2 which propagated through part of the upper layers.In hard rocks (group A), both the main fractures of specimen A1 and A3 were longitudinal fractures, and the longitudinal fractures propagated completely through the specimens and cut the specimens to two pieces (Figure 5a), and the figures of the fractures in group A were approximately symmetrical.
In soft rocks (group B), longitudinal and oblique fractures were well-developed in three specimens (Figure 5b).The longitudinal fractures terminated when they extended to the oblique fractures.The oblique fractures only developed in the upper layers of specimens and propagated through part of upper layers at the direction oblique to the axial direction.
In hard-soft rocks (group C), the specimen C1-1, C1-2, and C2-2 had no fractures due to the low injection pressure that had not reached the breakdown pressure of specimens.The specimens with fractures had the common characteristic that the fractures were transverse at the middle of specimens (Figure 5c).The transverse fractures initiated from the perforation tip and extended to the surface along a radial direction.
In soft-hard rocks (group D), all three types of fractures were created (Figure 5d).All specimens in group D had longitudinal and transverse fractures, and longitudinal fractures terminated when they extended to the transverse fractures, and the transverse fractures propagated through the whole specimens.The oblique fractures were found in the upper layers of specimen D1-1 and D3-2 which propagated through part of the upper layers.
The fracturing results have been summarized in Table 4. Generally, the fractures developing in soft rocks and soft-hard rocks are complicated, and the fractures in hard rocks and hard-soft rocks are simple.The fracture branches are a group of secondary fractures near the main fractures [41], and the observation of fracture branches is another crucial aspect to investigate the fracture propagation.Generally, fracture branches mainly occurred in the soft rocks (group B) and soft-hard rocks (group D).According to the observation of fracture branches, three types of fracture branches were found on the surfaces of specimens (Figure 7).Type-I fracture branches occurred on the surfaces of specimen B2 and B3, and they initiated from a main fracture at a low angle and then converged to the main fracture.Type-II fracture branches were most common in the results; they occurred on every specimen listed in Figure 7, and they connected two main fractures.Type-III fracture branches occurred on the surfaces of specimen D1-2 and D3-1, and they initiated from a main fracture connecting no fractures.The fracture branches are a group of secondary fractures near the main fractures [41], and the observation of fracture branches is another crucial aspect to investigate the fracture propagation.Generally, fracture branches mainly occurred in the soft rocks (group B) and soft-hard rocks (group D).According to the observation of fracture branches, three types of fracture branches were found on the surfaces of specimens (Figure 7).Type-I fracture branches occurred on the surfaces of specimen B2 and B3, and they initiated from a main fracture at a low angle and then converged to the main fracture.Type-II fracture branches were most common in the results; they occurred on every specimen listed in Figure 7, and they connected two main fractures.Type-III fracture branches occurred on the surfaces of specimen D1-2 and D3-1, and they initiated from a main fracture connecting no fractures.The fracture branches are a group of secondary fractures near the main fractures [41], and the observation of fracture branches is another crucial aspect to investigate the fracture propagation.Generally, fracture branches mainly occurred in the soft rocks (group B) and soft-hard rocks (group D).According to the observation of fracture branches, three types of fracture branches were found on the surfaces of specimens (Figure 7).Type-I fracture branches occurred on the surfaces of specimen B2 and B3, and they initiated from a main fracture at a low angle and then converged to the main fracture.Type-II fracture branches were most common in the results; they occurred on every specimen listed in Figure 7, and they connected two main fractures.Type-III fracture branches occurred on the surfaces of specimen D1-2 and D3-1, and they initiated from a main fracture connecting no fractures.The fracture branches are a group of secondary fractures near the main fractures [41], and the observation of fracture branches is another crucial aspect to investigate the fracture propagation.Generally, fracture branches mainly occurred in the soft rocks (group B) and soft-hard rocks (group D).According to the observation of fracture branches, three types of fracture branches were found on the surfaces of specimens (Figure 7).Type-I fracture branches occurred on the surfaces of specimen B2 and B3, and they initiated from a main fracture at a low angle and then converged to the main fracture.Type-II fracture branches were most common in the results; they occurred on every specimen listed in Figure 7, and they connected two main fractures.Type-III fracture branches occurred on the surfaces of specimen D1-2 and D3-1, and they initiated from a main fracture connecting no fractures.The fracture branches are a group of secondary fractures near the main fractures [41], and the observation of fracture branches is another crucial aspect to investigate the fracture propagation.Generally, fracture branches mainly occurred in the soft rocks (group B) and soft-hard rocks (group D).According to the observation of fracture branches, three types of fracture branches were found on the surfaces of specimens (Figure 7).Type-I fracture branches occurred on the surfaces of specimen B2 and B3, and they initiated from a main fracture at a low angle and then converged to the main fracture.Type-II fracture branches were most common in the results; they occurred on every specimen listed in Figure 7, and they connected two main fractures.Type-III fracture branches occurred on the surfaces of specimen D1-2 and D3-1, and they initiated from a main fracture connecting no fractures.

Tortuosity of the Longitudinal Fractures
In order to study the main fractures quantitatively, a parameter called tortuosity is introduced by Chen et al. [26], which is defined as the total length of a fracture divided by the shortest length of the two ends of the fracture along the surface, and it has been used by Jia et al. [42] and Zhao et al. [43].In this section, tortuosity of the longitudinal fractures on the vertical surfaces of the specimens in group A, B and D is calculated by following equation [26,42,43]: T (dimensionless) is fracture tortuosity, Lf (m) is the sum of total fracture lengths on the vertical surface; L (m) is the sum of linear lengths between the two ends of the fracture's pathway.The Lf and L are calculated by the following equation: Lfi (m) is the trace length of the i-th fracture; Li (m) is the linear length between the two ends of the i-th fracture pathway.Vertical surfaces of specimens are digitized (see Figure 8) to calculate the fracture lengths (black lines) and the linear lengths (red lines).

Tortuosity of the Longitudinal Fractures
In order to study the main fractures quantitatively, a parameter called tortuosity is introduced by Chen et al. [26], which is defined as the total length of a fracture divided by the shortest length of the two ends of the fracture along the surface, and it has been used by Jia et al. [42] and Zhao et al. [43].In this section, tortuosity of the longitudinal fractures on the vertical surfaces of the specimens in group A, B and D is calculated by following equation [26,42,43]: T (dimensionless) is fracture tortuosity, L f (m) is the sum of total fracture lengths on the vertical surface; L (m) is the sum of linear lengths between the two ends of the fracture's pathway.The L f and L are calculated by the following equation: L fi (m) is the trace length of the i-th fracture; L i (m) is the linear length between the two ends of the i-th fracture pathway.Vertical surfaces of specimens are digitized (see Figure 8) to calculate the fracture lengths (black lines) and the linear lengths (red lines).The characteristics of transverse and oblique fractures cannot be measured by tortuosity, so only the longitudinal fractures are evaluated quantitatively in this part.The calculated tortuosity of longitudinal fractures on vertical surfaces of the specimens in group A (hard rocks), B (soft rocks) and D (soft-hard rocks) is shown in Figure 9. Generally, the effect of injection pressure on the tortuosity of longitudinal fractures is not obvious.The tortuosity of longitudinal fractures in soft rocks (group B) is apparently the highest, indicating that the longitudinal fractures in soft rocks are the most complicated among the three groups.The characteristics of transverse and oblique fractures cannot be measured by tortuosity, so only the longitudinal fractures are evaluated quantitatively in this part.The calculated tortuosity of longitudinal fractures on vertical surfaces of the specimens in group A (hard rocks), B (soft rocks) and D (soft-hard rocks) is shown in Figure 9. Generally, the effect of injection pressure on the tortuosity of longitudinal fractures is not obvious.The tortuosity of longitudinal fractures in soft rocks (group B) is apparently the highest, indicating that the longitudinal fractures in soft rocks are the most complicated among the three groups.The characteristics of transverse and oblique fractures cannot be measured by tortuosity, so only the longitudinal fractures are evaluated quantitatively in this part.The calculated tortuosity of longitudinal fractures on vertical surfaces of the specimens in group A (hard rocks), B (soft rocks) and D (soft-hard rocks) is shown in Figure 9. Generally, the effect of injection pressure on the tortuosity of longitudinal fractures is not obvious.The tortuosity of longitudinal fractures in soft rocks (group B) is apparently the highest, indicating that the longitudinal fractures in soft rocks are the most complicated among the three groups.

Morphologies of the Main Fracture Surfaces
Since tortuosity is difficult to evaluate transverse and oblique fractures, a threedimensional scanner is used to get the morphologies of the main fracture surfaces and evaluate their roughness.Raw coordinate data points of the main fracture surface can be obtained by three-dimensional scanning and a digital surface is reconstructed by the Geomagic Studio software.The morphologies of typical fracture surfaces are shown in Figure 10.
To quantitatively analyze the roughness of main fractures, Area Ratio (AR) is introduced which is defined as the ratio of actual area to projected area of the main fracture surface.In this work, the actual area can be calculated by the reconstructed surface, and the projected area is the fracture surface on its best fitting surface.A higher AR signifies that the main fracture surface is rougher.Table 5 shows the values of AR of the main fracture surfaces.To quantitatively analyze the roughness of main fractures, Area Ratio (AR) is introduced which is defined as the ratio of actual area to projected area of the main fracture surface.In this work, the actual area can be calculated by the reconstructed surface, and the projected area is the fracture surface on its best fitting surface.A higher AR signifies that the main fracture surface is rougher.Table 5 shows the values of AR of the main fracture surfaces.Comparing the AR of longitudinal fractures in hard (group A), soft (group B) and softhard (group D) rocks (Figure 11a), the result is consistent with the tortuosity of longitudinal fractures in the three different types of rocks (Figure 9), which indicates that the longitudinal fracture in soft rocks is the roughest.The overall AR is the weighted average of each main fracture AR in the rock with actual area as the weight, shown in Table 5 and Figure 11b.The injection pressure has no significant effect on the overall AR of specimens in the same group, and the overall AR of main fractures in soft rocks (group B) is obviously higher than that of other specimens, which means the main fractures in soft rocks are the roughest.
gitudinal fractures in the three different types of rocks (Figure 9), which indicates that the longitudinal fracture in soft rocks is the roughest.The overall AR is the weighted average of each main fracture AR in the rock with actual area as the weight, shown in Table 5 and Figure 11b.The injection pressure has no significant effect on the overall AR of specimens in the same group, and the overall AR of main fractures in soft rocks (group B) is obviously higher than that of other specimens, which means the main fractures in soft rocks are the roughest.

Analysis of Strain Response
Strain monitoring is a useful and reliable method to record the state of rock, and it has been used in the experiments of Cai et al. [39] and Liang et al. [44].In the experiments, the strain gages measured circumferential strain, and the strain was negative when the side surface was subjected to tensile stress in a circumferential direction.

The Strain Differences between Two Layers
The characteristics of strain curves were significantly different between two layers.Taking the strain curves of specimen A1 and B1 for example, the two strain gages are at the middle of the upper and lower layers, respectively (Figure 12).The strain response of the upper strain gage was more intense than the lower strain gage, and the initial response time of the lower gage was later than that of upper gage, because the stress waves produced by the pressurization of perforation pressure propagated to the upper gage first.So, the strain curve of upper gage could better reflect the propagation of the fractures, and in the later section, only strain curves of upper gage were used to analyze the results of experiments.

Analysis of Strain Response
Strain monitoring is a useful and reliable method to record the state of rock, and it has been used in the experiments of Cai et al. [39] and Liang et al. [44].In the experiments, the strain gages measured circumferential strain, and the strain was negative when the side surface was subjected to tensile stress in a circumferential direction.

The Strain Differences between Two Layers
The characteristics of strain curves were significantly different between two layers.Taking the strain curves of specimen A1 and B1 for example, the two strain gages are at the middle of the upper and lower layers, respectively (Figure 12).The strain response of the upper strain gage was more intense than the lower strain gage, and the initial response time of the lower gage was later than that of upper gage, because the stress waves produced by the pressurization of perforation pressure propagated to the upper gage first.So, the strain curve of upper gage could better reflect the propagation of the fractures, and in the later section, only strain curves of upper gage were used to analyze the results of experiments.

Characteristics of Strain Curve
According to the strain curve of specimens, the SC-CO2 jet fracturing can be divided into two stages, the pressurization of the perforation pressure stage and fracture propagation stage: In the stage of pressurization, the pressure in the perforation increased with the inletting and expanding of SC-CO2, and when the perforation pressure reached breakdown pressure of specimen, fracture initiated, and the strain reached a peak value.When the fracture initiates, the strain energy released, so at the earlier stage of fracture propagation, the value of the strain would decrease immediately.With the SC-CO2 entering into fractures and expanding, the pressure in the perforation and fractures increased, and then

Characteristics of Strain Curve
According to the strain curve of specimens, the SC-CO 2 jet fracturing can be divided into two stages, the pressurization of the perforation pressure stage and fracture propagation stage: In the stage of pressurization, the pressure in the perforation increased with the inletting and expanding of SC-CO 2 , and when the perforation pressure reached breakdown pressure of specimen, fracture initiated, and the strain reached a peak value.
When the fracture initiates, the strain energy released, so at the earlier stage of fracture propagation, the value of the strain would decrease immediately.With the SC-CO 2 entering into fractures and expanding, the pressure in the perforation and fractures increased, and then new fractures initiated, and old fractures propagated.According to the strain curve in the stage of facture propagation, the fractures initiation and propagation was intermittent.
A parameter is defined to evaluate the rate of jet fracturing called fracturing time, which starts with a dramatic change in strain and ends with stabilization of the strain (see Figure 13).Comparing the fracturing times of specimens in group A and B (see Figure 14), it is indicated that the hard rocks (group A) need more time to be fractured than soft rocks (group B) due to their high rock strength.With the increasing of injection pressure, the fracturing time needed decreases, and the rate of jet fracturing increases.It is clear that both the injection pressure and the rock strength can influence the rate of jet fracturing.

Characteristics of Strain Curve
According to the strain curve of specimens, the SC-CO2 jet fracturing can be divided into two stages, the pressurization of the perforation pressure stage and fracture propagation In the stage of pressurization, the pressure in the perforation increased with the inletting and expanding of SC-CO2, and when the perforation pressure reached breakdown pressure of specimen, fracture initiated, and the strain reached a peak value.When the fracture initiates, the strain energy released, so at the earlier stage of fracture propagation, the value of the strain would decrease immediately.With the SC-CO2 entering into fractures and expanding, the pressure in the perforation and fractures increased, and then new fractures initiated, and old fractures propagated.According to the strain curve in the stage of facture propagation, the fractures initiation and propagation was intermittent.
A parameter is defined to evaluate the rate of jet fracturing called fracturing time, which starts with a dramatic change in strain and ends with stabilization of the strain (see Figure 13).Comparing the fracturing times of specimens in group A and B (see Figure 14), it is indicated that the hard rocks (group A) need more time to be fractured than soft rocks (group B) due to their high rock strength.With the increasing of injection pressure, the fracturing time needed decreases, and the rate of jet fracturing increases.It is clear that both the injection pressure and the rock strength can influence the rate of jet fracturing.

Formation Mechanism of the Main Fractures
It is important to understand the formation mechanism of the main fractures which is beneficial to the prediction of fracture propagation.By observing the fracture morphologies (Figure 6), three types of main fractures have been found in the experiments: longitudinal fracture, transverse fracture, and oblique fracture.The formation mechanisms of the three types of main fractures are different.
Hu et al. [23] simulated the stress field of the hollow cylindrical shale fractured by SC-CO2 jet, and they found that the fractures could easily generate at three locations: the root, the middle, and the tip of perforation (Figure 15).Our results are well matched with the simulation results that the transverse fractures initiate from the tip of perforation, and the longitudinal and oblique fractures initiate from the middle of perforation.The casings of the specimens were separated from artificial sandstones in the experiments, due to the

Formation Mechanism of the Main Fractures
It is important to understand the formation mechanism of the main fractures which is beneficial to the prediction of fracture propagation.By observing the fracture morphologies (Figure 6), three types of main fractures have been found in the experiments: longitudinal fracture, transverse fracture, and oblique fracture.The formation mechanisms of the three types of main fractures are different.
Hu et al. [23] simulated the stress field of the hollow cylindrical shale fractured by SC-CO 2 jet, and they found that the fractures could easily generate at three locations: the root, the middle, and the tip of perforation (Figure 15).Our results are well matched with the simulation results that the transverse fractures initiate from the tip of perforation, and the longitudinal and oblique fractures initiate from the middle of perforation.The casings of the specimens were separated from artificial sandstones in the experiments, due to the fractures propagating at the root of perforation and destroying the cement between the casing and artificial sandstone.
is beneficial to the prediction of fracture propagation.By observing the fracture morphologies (Figure 6), three types of main fractures have been found in the experiments: longitudinal fracture, transverse fracture, and oblique fracture.The formation mechanisms of the three types of main fractures are different.
Hu et al. [23] simulated the stress field of the hollow cylindrical shale fractured by SC-CO2 jet, and they found that the fractures could easily generate at three locations: the root, the middle, and the tip of perforation (Figure 15).Our results are well matched with the simulation results that the transverse fractures initiate from the tip of perforation, and the longitudinal and oblique fractures initiate from the middle of perforation.The casings of the specimens were separated from artificial sandstones in the experiments, due to the fractures propagating at the root of perforation and destroying the cement between the casing and artificial sandstone.Cai et al. [12] conducted the SC-CO2 jet fracturing experiments on the organic glasses, and three types of fractures were found: surface fracture, longitudinal fracture, and transverse fracture (Figure 16).The surface fracture, the longitudinal fracture, and the transverse fracture were mainly caused by SC-CO2 jet flow impacting on the casing surface, the pressurization of SC-CO2 in perforation, and the stagnation pressure pressing on the tip Cai et al. [12] conducted the SC-CO 2 jet fracturing experiments on the organic glasses, and three types of fractures were found: surface fracture, longitudinal fracture, and transverse fracture (Figure 16).The surface fracture, the longitudinal fracture, and the transverse fracture were mainly caused by SC-CO 2 jet flow impacting on the casing surface, the pressurization of SC-CO 2 in perforation, and the stagnation pressure pressing on the tip of the perforation, respectively.The fracture initiation position in our experiments was consistent with his study.In our study, the longitudinal fracture was caused by the pressurization of SC-CO2 in perforation.As for transverse fracture, which only occurred in hard-soft rocks and softhard rocks where the upper and lower layers were different, there were three factors contributing to it: the strong heterogeneity [45] at the middle of specimens, the stress concentration on the tip of perforation due to discontinuity of structure, and the stagnation pressure pressing on the tip of the perforation.The oblique fracture occurred in soft rocks and soft-hard rocks for which the upper layers were soft, and it was caused by the pressurization of SC-CO2 in the perforation.In our study, the longitudinal fracture was caused by the pressurization of SC-CO 2 in perforation.As for transverse fracture, which only occurred in hard-soft rocks and soft-hard rocks where the upper and lower layers were different, there were three factors contributing to it: the strong heterogeneity [45] at the middle of specimens, the stress concentration on the tip of perforation due to discontinuity of structure, and the stagnation pressure pressing on the tip of the perforation.The oblique fracture occurred in soft rocks and soft-hard rocks for which the upper layers were soft, and it was caused by the pressurization of SC-CO 2 in the perforation.

Effect of Rock Mechanical Properties on Fracture Propagation
The fracture patterns in hard and soft rocks are different (Figure 5a,b).The uniaxial compressive strength and shear strength of soft rocks are significantly lower than that of hard rocks, which means less energy needed to create a fracture in soft rock, so under the same conditions, more fractures and fracture branches can be created in soft rocks (Table 4), and the AR of main fractures in soft rocks is obviously higher than that of main fractures in hard rocks (Table 5, Figure 11).According to Figure 14, the soft rocks require less time to be fractured compared with hard rocks, which means the soft rock is more easily destroyed.Generally, the rock strength has great impact on fracture propagation, which can affect the number and complexity of fractures created and the fracturing rate.
Notably, the longitudinal fractures in hard rocks propagate through the whole specimens (Figure 5a), and the longitudinal fractures in soft rocks terminate when they encounter the oblique fractures (Figure 5b).Compared with longitudinal fractures in soft rocks, the extended distances of longitudinal fractures in hard rocks are longer.There is an inverse relationship between the fracture toughness and Young's modulus [46], and the Young's modulus of hard rock is larger than that of soft rock, so the fracture toughness of hard rocks is lower than that of soft rocks.The lower fracture toughness of hard rock makes fracture is easier to propagate longer, which is the reason why the longitudinal fractures in hard rocks can propagate through the whole specimens.It is clear that the Young's modulus of rock has an effect on fracture propagation length.Generally, the rock mechanical properties can affect the development of fractures.

Fracture Propagation Behavior in Hard and Soft Layered Rocks
Notably, the transverse fractures only develop in hard-soft rocks and soft-hard rocks (Figure 5), and they have not developed in homogeneous rocks (hard rocks and soft rocks), so the effect of the stress concentration on the tip of perforation due to discontinuity of structure and the stagnation pressure pressing on the tip of perforation are not enough to create a transverse fracture.Tang et al. [47] found that increasing heterogeneity of the rock would cause stress inhomogeneity or concentration and the critical micro-fracture density will be reached at lower levels.Blair and Cook [45] found that increasing local stress heterogeneity would lower the mean ultimate strength of rock.According to their study, the strong heterogeneity at the transition area of the hard-soft rocks and soft-hard rocks causes the local stress concentration when the rocks are loaded, which is the primary reason for the development of transverse fracture.Generally, fractures are prone to develop in the transition area of hard-soft rocks and soft-hard rocks.
Through observing the fractures created in hard-soft rocks and soft-hard rocks, the fractures mainly develop in transition areas of hard-soft rocks (Figure 5c), and the fractures in soft-hard rocks mainly develop in the upper layers and transition areas (Figure 5d).The fractures tend to develop near the perforation and are difficult to propagate to another layer with different mechanical properties, and a complicated fracture network can be created when perforation position is at soft layer, which is conductive to the selection of perforation location in the actual field.

Conclusions
Based on experimental results and discussion, the following conclusion can be drawn: (1) Three types of main fractures are observed, and their formation mechanism has been discussed.The longitudinal fractures and oblique fractures were caused by the pressurization of SC-CO 2 in perforation.The transverse fractures were caused by the combined effect of the strong heterogeneity at the transition areas of hard-soft and soft-hard rocks, the stress concentration on the tip of perforation due to discontinuity of structure, and the stagnation pressure pressing on the tip of perforation.
(2) The SC-CO 2 jet fracturing can be divided into two stages, the pressurization of the perforation pressure stage and fracture propagation stage, and the fractures initiation and propagation is intermittent.Through the strain curve, the fracturing time can be obtained, which can evaluate the rate of jet fracturing, and the rate of jet fracturing can be enhanced by increasing injection rate.(3) The rock mechanical properties have great impact on fracture propagation.The rock strength can affect the number and complexity of fractures created and the fracturing rate.When the rock strength is low, more fractures can be created, and the fracturing rate is high.The Young's modulus of rock has an effect on fracture propagation length.(4) The fractures mainly develop near the perforation and are difficult to propagate to another layer with different mechanical properties, and the fractures are prone to develop in the transition areas of hard-soft rocks and soft-hard rocks due to the stress concentration caused by the strong heterogeneity of transition areas.When the perforation position is at the soft layer, complicated fracture networks can be created, which is conductive to the selection of perforation location in the actual field.

Limitations and Future Work
The findings of this study have to be seen in light of some limitations.In this paper, in order to simply study the propagation effect of fractures in hard and soft layered rock samples, artificial rock samples were used for the experiment.However, there are structural planes such as joints and bedding in the actual rock samples.Therefore, in future research work, real rock samples should be used to conduct experiments, so as to study the influence of different structural planes on fracture propagation, which is closer to the actual situation.In addition, there is still a lack of further theoretical research and quantitative analysis on the mechanism of fracture propagation induced by SC-CO 2 jet fracturing.In the next step, we need to carry out theoretical modeling in this aspect and quantitatively analyze the fracture initiation and propagation through numerical solution.

Figure 2 .
Figure 2. The preparation of specimens.(a) A schematic diagram of the cylindrical specimen; (b) the completed specimen.

Figure 2 .
Figure 2. The preparation of specimens.(a) A schematic diagram of the cylindrical specimen; (b) the completed specimen.

Figure 3 .
Figure 3.A schematic diagram of the SC-CO2 jet fracturing experimental system.

Figure 3 .
Figure 3.A schematic diagram of the SC-CO 2 jet fracturing experimental system.

Figure 4 .
Figure 4.A schematic diagram of the SC-CO2 jet fracturing kettle.

Figure 4 .
Figure 4.A schematic diagram of the SC-CO 2 jet fracturing kettle.

Figure 5 .
Figure 5.The unfolded images of fractures on the surfaces of specimens after experiments.(a) Experimental results of group A; (b) experimental results of group B; (c) experimental results of group C; (d) experimental results of group D.

Figure 5 .
Figure 5.The unfolded images of fractures on the surfaces of specimens after experiments.(a) Experimental results of group A; (b) experimental results of group B; (c) experimental results of group C; (d) experimental results of group D.

Four
type-A fractures, one type-B fracture and one type-C fracture Type-Ⅱ and type-Ⅲ D3-2 Three type-A fractures extended to the middle, and one type-B fracture Type-Ⅱ 3.1.2.Analysis of Fracture Branches

21 Table 4 .Four
A fractures and three type-C fractures None Appl.Sci.2022, 12, x FOR PEER REVIEW 10 of The fracturing results of each specimen.type-A fractures, one type-B fracture and one type-C fracture Type-Ⅱ and type-Ⅲ D3-2 Three type-A fractures extended to the middle, and one type-B fracture Type-Ⅱ 3.1.2.Analysis of Fracture Branches

B2 21 Table 4 .Four
Four type-A fractures and two type-C fractures Type-I and type-II B3 Three type-A fractures and one type-C fracture Type-I and type-II C C1-1 None None Appl.Sci.2022, 12, x FOR PEER REVIEW 10 of The fracturing results of each specimen.type-A fractures, one type-B fracture and one type-C fracture Type-Ⅱ and type-Ⅲ D3-2 Three type-A fractures extended to the middle, and one type-B fracture Type-Ⅱ 3.1.2.Analysis of Fracture Branches

21 Table 4 .Four
type-A fractures, one type-B fracture and one type-C fracture Type-II Appl.Sci.2022, 12, x FOR PEER REVIEW 10 of The fracturing results of each specimen.type-A fractures, one type-B fracture and one type-C fracture Type-Ⅱ and type-Ⅲ D3-2 Three type-A fractures extended to the middle, and one type-B fracture Type-Ⅱ 3.1.2.Analysis of Fracture Branches type-A fractures, one type-B fracture and one type-C fracture Type-II and type-III D3-2 Three type-A fractures extended to the middle, and one type-B fracture Type-II 3.1.2.Analysis of Fracture Branches

Figure 7 .
Figure 7.The digital images of fracture branches on the surfaces.Three types of fracture branches were summarized: type-I, initiating from a main fracture at a low angle and then converging to the main fracture; type-II, connecting two main fractures; type-III, initiating from a main fracture and connecting no fractures.

Figure 7 .
Figure 7.The digital images of fracture branches on the surfaces.Three types of fracture branches were summarized: type-I, initiating from a main fracture at a low angle and then converging to the main fracture; type-II, connecting two main fractures; type-III, initiating from a main fracture and connecting no fractures.

Figure 8 .
Figure 8.A schematic of the fracture tortuosity calculation.

Figure 9 .
Figure 9.The tortuosity of longitudinal fractures on the vertical surfaces of specimens in group A, B and D.3.1.4.Morphologies of the Main Fracture Surfaces Since tortuosity is difficult to evaluate transverse and oblique fractures, a three-dimensional scanner is used to get the morphologies of the main fracture surfaces and evaluate their roughness.Raw coordinate data points of the main fracture surface can be obtained by three-dimensional scanning and a digital surface is reconstructed by the Geomagic Studio software.The morphologies of typical fracture surfaces are shown in Figure 10.

Figure 8 .
Figure 8.A schematic of the fracture tortuosity calculation.

21 Figure 8 .
Figure 8.A schematic of the fracture tortuosity calculation.

Figure 9 .
Figure 9.The tortuosity of longitudinal fractures on the vertical surfaces of specimens in group A, B and D.3.1.4.Morphologies of the Main Fracture Surfaces Since tortuosity is difficult to evaluate transverse and oblique fractures, a three-dimensional scanner is used to get the morphologies of the main fracture surfaces and evaluate their roughness.Raw coordinate data points of the main fracture surface can be obtained by three-dimensional scanning and a digital surface is reconstructed by the Geomagic Studio software.The morphologies of typical fracture surfaces are shown in Figure 10.

Figure 9 .
Figure 9.The tortuosity of longitudinal fractures on the vertical surfaces of specimens in group A, B and D.

Figure 11 .
Figure 11.(a) The AR of longitudinal fractures in group A, B and D; (b) the overall AR of different rock specimens.

Figure 11 .
Figure 11.(a) The AR of longitudinal fractures in group A, B and D; (b) the overall AR of different rock specimens.

Figure 12 .
Figure 12.Strain differences between upper and lower layers of (a) specimen A1 and (b) specimen B1.

Figure 12 .
Figure 12.Strain differences between upper and lower layers of (a) specimen A1 and (b) specimen B1.

Figure 14 .
Figure 14.The fracturing times of specimens in group A and B.

Figure 14 .
Figure 14.The fracturing times of specimens in group A and B.
Appl.Sci.2022, 12, x FOR PEER REVIEW 17 of 21 of the perforation, respectively.The fracture initiation position in our experiments was consistent with his study.

Table 1 .
The mixtures composition ratio of the hard and soft layers.

Table 2 .
The mechanical properties of artificial sandstone.

Table 3 .
The experimental parameters.

Table 4 .
The fracturing results of each specimen.

Table 4 .
The fracturing results of each specimen.

Table 5 .
The Area Ratio (AR) of the main fracture surfaces.

Table 5 .
The Area Ratio (AR) of the main fracture surfaces.