# Rock Fracture Response Exposed to Hydraulic Fracturing: Insight into the Effect of Injection Rate on Aperture Pattern

Authors: Bo Zhang; Xinyi Cui; Linjun Wang; Xiaodi Fu
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

Injection rate is critical to hydraulic fracturing operation, especially to the hydraulic fracture aperture, which affects the proppant and methane migration. In this study, hydraulic fracturing experiments were carried out on shale specimens to investigate the influence of injection rate on hydraulic fracture aperture. According to the experimental results, when the injection rate increases, the average aperture of hydraulic fracture shows a significant linear increase. For different injection rate, the average aperture of stimulated natural fracture is always slightly greater than that of newly opened fracture. Compared with a low injection rate, the fracture apertures induced by the largest injection rate are evenly distributed in more intervals and approximately conform to the normal distribution. The research results can provide a theoretical basis for enhancing the fracture conductivity of hydraulic fracturing in shale reservoirs.


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## Body

## 1. Introduction

Hydraulic fracturing technology is critical in the unconventional energy field, especially for shale gas [1–3]. The hydraulic fracturing operation could stimulate the natural fractures and open the new fractures in the shale reservoir. The initiation, propagation, and coalescence of these fractures make up the network where the methane flow [4–8].Injection rate is one of the most important factors for the success of hydraulic fracturing operation [9–11]. De Pater et al. [12] conducted experiments and numerical simulations in early time, to investigate the influence of injection rate on fracture patterns. Using true triaxial test and high-energy CT scanning system, Guo et al. [13] and Zou et al. [14] showed that injection rates with intervals had different effects on fracture complexity in hydraulic fracturing for shale, and variable injection rate fracturing could increase the complexity of the fracture network. Wang et al. [15] indicated that the impact of injection rate on hydraulic fracturing treatment depends on the characteristics of the shale reservoir. Seong et al. [16] investigated the evolution of the breakdown pressure and the fracture initiation pressure, which indicated that high injection rate results in an increased value of the two kinds of pressures. For brittle rocks, the induced fractures are very sensitive to loading conditions [17, 18].The abovementioned research studies about injection rate in hydraulic fracturing focused on fracture complexity, rather than fracture aperture. The aperture of hydraulic fractures is essential for proppant and methane migration. However, the study published on it is very limited [19, 20]. In this work, hydraulic fracturing experiments of shale with different injection rates were conducted by a true triaxial test system. Then, a portable industrial electron microscope was utilized to measure the open aperture of fractures induced by hydraulic fracturing. Finally, the apertures of different types of fractures are calculated through mathematical statistics, and the relationship between the aperture and injection rate was established.


## 2. Experiment Equipment and Scheme

### 2.1. Experiment Equipment

In order to simulate the three-dimensional stress state of shale reservoirs, the hydraulic fracturing experiments are conducted in an electro-hydraulic servo true triaxial test system (Figure1). The triaxial pressure cell of this system could contain a cubic specimen with a side length of 30 cm, and each pair of pistons was pressurized independently with an oil pressure pump. The hydraulic fracturing pump pressure servo control system has a maximum displacement of 1 L/min and a maximum output pressure of 80 MPa.Figure 1
True triaxial hydraulic fracturing test system.


### 2.2. Specimen Preparation

The shale blocks are taken from the outcrop of the Longmaxi Formation in China, where the natural fractures are very developed. In the Fenggang block of the Longmaxi formation, the high-angle fractures account for 56.4% of natural fractures, and the rest are low-angle fractures and parallel-bedded fractures [21]. These shale rocks were processed into standard specimen of 30 cm × 30 cm × 30 cm with a disk saw. A drill bit with an outer diameter of 12 mm was used to prefabricate a 15 cm deep borehole perpendicular to the bedding plane of shale specimens, to model the perforations in a horizontal well. A high-strength steel pipe with an outer diameter of 10 mm, an inner diameter of 6 mm, and a length of 13 cm is installed in the borehole to facilitate the injection of fracturing fluid into the specimen. High-strength epoxy resin glue is used to bond the steel pipe to the shale sample, and the final specimen is shown in Figures 2 and 3. It should be noted that the bottom of the steel pipe is wrapped with tissue paper and plastic wrap, to prevent epoxy resin from flowing into the borehole, causing a blockage at the end of the steel pipe. The physical and mechanical parameters of shale are shown in Table 1.Figure 2
The shale specimen after processing.Figure 3
Three-dimensional (3D) graph of shale specimen.Table 1
Physical and mechanical parameters of shale.
Cohesion stress (MPa)Friction angle (MPa)Tension stress (MPa)Elastic modulus (GPa)Poisson ratio31.626.87.632.30.23


### 2.3. Experiment Scheme

The confining pressure conditions for this experiment areσv = 12 MPa, σH = 14 MPa, and σh = 10 MPa. In this study, the direction of σv is perpendicular to the bedding (Figure 3), and the specific test parameters are shown in Table 2. The ordinary water is taken as fracturing fluids, which is injected into shale specimens at the constant injection rate.Table 2
Test conditions for hydraulic fracturing.
Specimen numberσv (MPa)σH (MPa)σh (MPa)Injection rate (ml/min)S112141040S2121410100S3121410150The specific test steps are as follows:(1)
Dip a clean towel with clean water, and wipe clean on the six surfaces of the shale specimen. Take pictures of the surfaces with a digital camera, and use drawing software to record the distribution of natural fractures before the test.(2)
Put the prepared shale specimen into the true triaxial stress loading chamber and complete the triaxial stress loading. At the same time, the hydraulic loading system of pumping is started, and the computer collects various test data in time.(3)
When the total volume of fracturing fluid is injected into 900 ml, the hydraulic fracturing experiment ends. The hydraulic loading system is stopped, and the stress in the true triaxial loading chamber is unloaded to zero.(4)
Disassemble the sample, use a digital camera to photograph each surface of the specimen after fracturing, and use drawing software for postprocessing of hydraulic fractures.(5)
Take a portable industrial electron microscope to measure the opening aperture of hydraulic fractures, including stimulated natural fractures and newly opened fractures.


## 2.1. Experiment Equipment

In order to simulate the three-dimensional stress state of shale reservoirs, the hydraulic fracturing experiments are conducted in an electro-hydraulic servo true triaxial test system (Figure1). The triaxial pressure cell of this system could contain a cubic specimen with a side length of 30 cm, and each pair of pistons was pressurized independently with an oil pressure pump. The hydraulic fracturing pump pressure servo control system has a maximum displacement of 1 L/min and a maximum output pressure of 80 MPa.Figure 1
True triaxial hydraulic fracturing test system.


## 2.2. Specimen Preparation

The shale blocks are taken from the outcrop of the Longmaxi Formation in China, where the natural fractures are very developed. In the Fenggang block of the Longmaxi formation, the high-angle fractures account for 56.4% of natural fractures, and the rest are low-angle fractures and parallel-bedded fractures [21]. These shale rocks were processed into standard specimen of 30 cm × 30 cm × 30 cm with a disk saw. A drill bit with an outer diameter of 12 mm was used to prefabricate a 15 cm deep borehole perpendicular to the bedding plane of shale specimens, to model the perforations in a horizontal well. A high-strength steel pipe with an outer diameter of 10 mm, an inner diameter of 6 mm, and a length of 13 cm is installed in the borehole to facilitate the injection of fracturing fluid into the specimen. High-strength epoxy resin glue is used to bond the steel pipe to the shale sample, and the final specimen is shown in Figures 2 and 3. It should be noted that the bottom of the steel pipe is wrapped with tissue paper and plastic wrap, to prevent epoxy resin from flowing into the borehole, causing a blockage at the end of the steel pipe. The physical and mechanical parameters of shale are shown in Table 1.Figure 2
The shale specimen after processing.Figure 3
Three-dimensional (3D) graph of shale specimen.Table 1
Physical and mechanical parameters of shale.
Cohesion stress (MPa)Friction angle (MPa)Tension stress (MPa)Elastic modulus (GPa)Poisson ratio31.626.87.632.30.23


## 2.3. Experiment Scheme

The confining pressure conditions for this experiment areσv = 12 MPa, σH = 14 MPa, and σh = 10 MPa. In this study, the direction of σv is perpendicular to the bedding (Figure 3), and the specific test parameters are shown in Table 2. The ordinary water is taken as fracturing fluids, which is injected into shale specimens at the constant injection rate.Table 2
Test conditions for hydraulic fracturing.
Specimen numberσv (MPa)σH (MPa)σh (MPa)Injection rate (ml/min)S112141040S2121410100S3121410150The specific test steps are as follows:(1)
Dip a clean towel with clean water, and wipe clean on the six surfaces of the shale specimen. Take pictures of the surfaces with a digital camera, and use drawing software to record the distribution of natural fractures before the test.(2)
Put the prepared shale specimen into the true triaxial stress loading chamber and complete the triaxial stress loading. At the same time, the hydraulic loading system of pumping is started, and the computer collects various test data in time.(3)
When the total volume of fracturing fluid is injected into 900 ml, the hydraulic fracturing experiment ends. The hydraulic loading system is stopped, and the stress in the true triaxial loading chamber is unloaded to zero.(4)
Disassemble the sample, use a digital camera to photograph each surface of the specimen after fracturing, and use drawing software for postprocessing of hydraulic fractures.(5)
Take a portable industrial electron microscope to measure the opening aperture of hydraulic fractures, including stimulated natural fractures and newly opened fractures.


## 3. Experiment Results and Analysis

### 3.1. Pump Pressure-Time Curve

Specimen S1 was injected with fracturing fluid with a constant injection rate of 40 ml/min, and the breakdown pressure was 45.4 MPa. As shown in Figure4(a), the pump pressure curve of S1 is rapidly to point A, then the specimen broke and the pump pressure decreased (point B). After the natural fractures were stimulated, the pump pressure dropped (point D), and the pump pressure fluctuated only slightly.Figure 4
Pumping pressure-time curve for hydraulic fracturing experiments: (a) S1; (b) S2; (c) S3.
(a)(b)(c)S2 was injected with fracturing fluid with a constant injection rate of 100 ml/min, and the breakdown pressure was 61 MPa. The pump pressure-time curve is shown in Figure4(b). The reason for the curve pattern may be as follows. When the breakdown pressure is reached (point A), the primary hydraulic fracture of the shale sample is initiated, which makes the fluid flow into the hydraulic fracture rapidly, resulting in the decrease of pump pressure (point B). Then, due to the existence of highly cemented and closed natural fractures in the sample, the propagation of hydraulic fractures was blocked, and the pump pressure was raised again (point C). When the natural fractures were stimulated, the fluid further leaked into these fractures, causing the pump pressure to drop (point D).S3 was injected with fracturing fluid with a constant injection rate of 150 ml/min, and the breakdown pressure was 58.8 MPa. As shown in Figure4(c), the pump pressure curve of S3 was significantly different from that of S1 and S2. The fluctuation times of S3 are less than that of S1, and the pump pressure of S3 could still be maintained at a higher pressure (about 40 MPa) after the pump pressure dropped.


### 3.2. Analysis of Fracture Aperture of Specimens

Electron microscope was utilized in order to scan and measure the fracture apertures of the shale specimens after hydraulic fracturing. Taking the fractures in surface 2′ of S3 as an example, the types of fractures are shown in Figure5. The green, red, and white lines represent, respectively, newly opened fracture (NOF), stimulated natural fracture (SNF), and natural fracture (NF).Figure 5
Various types of fracture of the shale specimens after hydraulic fracturing.After statistics of the fracture apertures of each specimen, the average aperture of 159 fractures which contain 43 NOFs and 116 SNFs, was calculated and listed in Table3 according to the type of fracture. In this study, the hydraulic fracture (HF) contains both of NOF and SNF.Table 3
Aperture of fractures on the surfaces of specimens.
Fracture typeThe average aperture of S1 (μm)The average aperture of S2 (μm)The average aperture of S3 (μm)NOF54.67110.32152.33SNF68.94119.37165.29HF65.48115.88163.35Ratio of SNF/NOF1.261.081.09It can be seen from Table3 that the average value of the fracture aperture of all types of fractures increases with the injection rate. When the injection rate increases from 40 ml/min to 150 ml/min, the HF apertures corresponding to S1 to S3 also increase significantly, from 65.48 μm to 163.35 μm. In addition, the average value of fracture aperture of SNF is greater than that of NOF, with a ratio of 1.08 to 1.26. The reason for this could be that the SNF is generally induced by the shear mechanism, and this process is always accompanied by shear dilatancy. As shown in Figure 6, there is a significant linear relationship between injection rate and average aperture, and the linear equations are described as follows:(1)an=0.8891Q+19.824,as=0.8747Q+33.308,a=0.8881Q+29.055,where an represents the average aperture of NOF, as represents the average aperture of SNF, a represents the average aperture of HF, and Q represents the injection rate.Figure 6
Relation between injection rate and fracture aperture: (a) relation between injection rate and average aperture of NOF; (b) relation between injection rate and average aperture of SNF; (c) relation between injection rate and average aperture of HF.
(a)(b)(c)It can be seen from Figure7 that, for S1, the HF apertures are mainly concentrated in the three intervals of 1–50 μm, 51–100 μm, and 101–150 μm, and the sum of the frequencies is 90.8%. Especially, in the interval 1–50 μm, the frequency is 53.9%. For S2, the HF apertures are also concentrated in these three intervals, and the maximum interval of the aperture is 101–150 μm. For S3, unlike the first two specimens, the apertures are more evenly distributed in seven intervals and close to the normal distribution. In these intervals, the three intervals of 101–150 μm, 151–200 μm, and 201–250 μm are the most, with frequencies of 27%, 18.9%, and 21.6%, respectively.Figure 7
Distribution frequency of HF aperture.


## 3.1. Pump Pressure-Time Curve

Specimen S1 was injected with fracturing fluid with a constant injection rate of 40 ml/min, and the breakdown pressure was 45.4 MPa. As shown in Figure4(a), the pump pressure curve of S1 is rapidly to point A, then the specimen broke and the pump pressure decreased (point B). After the natural fractures were stimulated, the pump pressure dropped (point D), and the pump pressure fluctuated only slightly.Figure 4
Pumping pressure-time curve for hydraulic fracturing experiments: (a) S1; (b) S2; (c) S3.
(a)(b)(c)S2 was injected with fracturing fluid with a constant injection rate of 100 ml/min, and the breakdown pressure was 61 MPa. The pump pressure-time curve is shown in Figure4(b). The reason for the curve pattern may be as follows. When the breakdown pressure is reached (point A), the primary hydraulic fracture of the shale sample is initiated, which makes the fluid flow into the hydraulic fracture rapidly, resulting in the decrease of pump pressure (point B). Then, due to the existence of highly cemented and closed natural fractures in the sample, the propagation of hydraulic fractures was blocked, and the pump pressure was raised again (point C). When the natural fractures were stimulated, the fluid further leaked into these fractures, causing the pump pressure to drop (point D).S3 was injected with fracturing fluid with a constant injection rate of 150 ml/min, and the breakdown pressure was 58.8 MPa. As shown in Figure4(c), the pump pressure curve of S3 was significantly different from that of S1 and S2. The fluctuation times of S3 are less than that of S1, and the pump pressure of S3 could still be maintained at a higher pressure (about 40 MPa) after the pump pressure dropped.


## 3.2. Analysis of Fracture Aperture of Specimens

Electron microscope was utilized in order to scan and measure the fracture apertures of the shale specimens after hydraulic fracturing. Taking the fractures in surface 2′ of S3 as an example, the types of fractures are shown in Figure5. The green, red, and white lines represent, respectively, newly opened fracture (NOF), stimulated natural fracture (SNF), and natural fracture (NF).Figure 5
Various types of fracture of the shale specimens after hydraulic fracturing.After statistics of the fracture apertures of each specimen, the average aperture of 159 fractures which contain 43 NOFs and 116 SNFs, was calculated and listed in Table3 according to the type of fracture. In this study, the hydraulic fracture (HF) contains both of NOF and SNF.Table 3
Aperture of fractures on the surfaces of specimens.
Fracture typeThe average aperture of S1 (μm)The average aperture of S2 (μm)The average aperture of S3 (μm)NOF54.67110.32152.33SNF68.94119.37165.29HF65.48115.88163.35Ratio of SNF/NOF1.261.081.09It can be seen from Table3 that the average value of the fracture aperture of all types of fractures increases with the injection rate. When the injection rate increases from 40 ml/min to 150 ml/min, the HF apertures corresponding to S1 to S3 also increase significantly, from 65.48 μm to 163.35 μm. In addition, the average value of fracture aperture of SNF is greater than that of NOF, with a ratio of 1.08 to 1.26. The reason for this could be that the SNF is generally induced by the shear mechanism, and this process is always accompanied by shear dilatancy. As shown in Figure 6, there is a significant linear relationship between injection rate and average aperture, and the linear equations are described as follows:(1)an=0.8891Q+19.824,as=0.8747Q+33.308,a=0.8881Q+29.055,where an represents the average aperture of NOF, as represents the average aperture of SNF, a represents the average aperture of HF, and Q represents the injection rate.Figure 6
Relation between injection rate and fracture aperture: (a) relation between injection rate and average aperture of NOF; (b) relation between injection rate and average aperture of SNF; (c) relation between injection rate and average aperture of HF.
(a)(b)(c)It can be seen from Figure7 that, for S1, the HF apertures are mainly concentrated in the three intervals of 1–50 μm, 51–100 μm, and 101–150 μm, and the sum of the frequencies is 90.8%. Especially, in the interval 1–50 μm, the frequency is 53.9%. For S2, the HF apertures are also concentrated in these three intervals, and the maximum interval of the aperture is 101–150 μm. For S3, unlike the first two specimens, the apertures are more evenly distributed in seven intervals and close to the normal distribution. In these intervals, the three intervals of 101–150 μm, 151–200 μm, and 201–250 μm are the most, with frequencies of 27%, 18.9%, and 21.6%, respectively.Figure 7
Distribution frequency of HF aperture.


## 4. Conclusion

Injection rate is critical for hydraulic fracturing operation because it can influence the characteristics of hydraulic fractures, such as aperture, scale, and complexity. In this study, hydraulic fracturing experiments were carried out on shale specimens to investigate the influence of injection rate on hydraulic fracture aperture. The following conclusions can be drawn:(1)
The injection rate has an obvious positive effect on hydraulic fracture aperture. When the injection rate increases, the average aperture of hydraulic fracture, both of NOF and SNF, shows a significant linear increase. The equation of average aperture and injection rate can be obtained by linear fitting.(2)
For different injection rate, the average aperture of SNF is always greater than that of NOF, with a ratio of 1.08 to 1.26. The reason could be that the SNF is generally induced by the shear dilatancy mechanism.(3)
For the largest injection rate, 150 ml/min, its corresponding fracture apertures are evenly distributed in more intervals and approximately conform to the normal distribution.



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*Source: 9431143-2022-03-20.xml*