Experimental Study of Anisotropic Characteristics of a Specific Formation Shale

The bedding surfaces of shale in the Longmaxi formation are well developed. To study the influence of bedding surfaces on the mechanical properties of shale, we have carried out uniaxial and triaxial compression tests on shale specimens of Longmaxi formation in Southern Sichuan, China. The results shows that when the samples are subjected to compression, the properties of shale, including strength characteristics, elastic parameters, and fracture mode in the shale samples, are characterized by strong anisotropy. The confining pressure effect is due to the existence of well-developed bedding surfaces in shale. The results provide a theoretical basis for horizontal wellbore stability analysis and hydraulic fracturing design in shale gas wells.

1. INTRODUCTION

Shale gas mainly occurs in the dark shale or high-carbon shale, characterized by low porosity, ultra-low permeability, and high content of organic matter. The shale gas geological resources of the Longmaxi formation in South Sichuan, China, are as high as 2.25 × 10¹² m³. Some authors pointed to the huge economic benefits of shale gas deposits in the Longmaxi formation [3, 5, 17]. Shale gas exploitation is commonly executed by horizontal wells. Horizontal wells have the advantages of large drainage areas, high production per well, and large penetration. However, the horizontal section of a shale gas well is generally long, while the rock bedding surfaces in the reservoir are well developed. Moreover, some of the reservoirs have a high and steep inclination. In the drilling process, serious instability problems such as borehole wall collapse and drilling fluid loss can easily occur, which severly limits the efficiency of shale gas wells [16]. The porosity and permeability characteristics of shale gas reservoir are low, and the airflow resistance is much higher than that of conventional natural gas reservoirs. Therefore, the productive development of shale gas reservoirs requires the application of special measures of reservoir intensification such as acidification and fracturing [1, 9, 13].

At present, a large number of scholars have studied the anisotropy of layered rocks. Niandou et al. [11] studied the anisotropy of shale samples obtained from the Tournemire region. The results of triaxial compression tests showed that the fracture mode in samples differs and belongs to either shear failure or tensile failure type. Yan et al. [14] carried out uniaxial compressive strength tests on argillaceous siltstone and maroon mudstone samples. The study aimed to evaluate the anisotropic strength of samples before and after water immersion. Kuila et al. [8] studied the stress and wave velocity anisotropy of low-porosity shale. Cho et al. [2] conducted uniaxial compression tests on gneisses sample from the Asan region, shale samples from Baoning region, and schist samples from the Lianchum region. The results demonstrated that the minimum compressive strength was obtained at angles between 15° and 45°. Du et al. [4] conducted Brazilian disk splitting tests on carbonaceous shale samples and found that the strength gradually inceased with increase in the angle between bedding surfaces and loading direction. Some scholars carried out triaxial compression tests and systematically studied the anisotropy of mechanical properties of layered rock masses such as siltstone, schist, Himalayan schist, and sand slate [6, 7, 10, 15]. The test results demonstrated that the compressive strength of the samples depended on the angle between the bedding surfaces and the test loading direction.

Therefore, despite the large number of studies on the anisotropy of layered rocks, the understanding of the influence of bedding surfaces on mechanical parameters and strength characteristics of reservoir rock is relatively insufficient. The experimental research on shale, particularly of the black carbon shale of the Longmaxi formation, is important for the stability analysis of horizontal wells and the hydraulic fracturing construction design. Therefore, it is necessary to study the machanical parameters and anisotropy of the fracture mode of shale in the Longmaxi formation.

In this paper, we have studied the samples of shale of the Longmaxi formation in Southern Sichuan, China. Based on the different angles of bedding surfaces in uniaxial and triaxial compression tests, the anisotropy of the mechanical properties of shale was studied, and the fracturing mechanism was analyzed. Thus, the results would provide a theoretical basis for horizontal wellbore stability and hydraulic fracturing construction design of shale gas wells in the Longmaxi formation and support the efficient exploitation of shale gas reservoirs.

2. TEST PREPARATION

2.1. TEST SAMPLES PREPARATION

The shale samples were obtained from the Longmaxi formation in Southern Sichuan, China. The gas-bearing formation rock is constituted by the dark carbonaceous shale, buried to a depth of 2000-3500 m. When drilling the samples, the angles between the drilling direction and the bedding surfaces are 0°, 30°, 60°, and 90°, as shown in Fig. 1. The sample diameter is 25 mm, the length is 50 mm, the error is ± 0.5 mm, and the parallelism of faces is ± 0.02 mm. To ensure the reliability of the measured results, each group of samples consists of three samples, and the average value is taken as the measured value for the sample group.

Fig. 1

Schematic diagram of directional shale sampling.

2.2. TEST EQUIPMENTS AND SCHEME

The measurements are carried out on the TAW-1000 deep-water pore pressure servo laboratory device. The testing equipment provides measurements of high accuracy. The axial displacement was controlled during the test, and the loading rate was 0.04 mm / min. The confining pressures were set at 0, 25, 40, and 50 MPa, respectively. The axial force, axial displacement, and radial displacement value were measured, and the compressive strength, Young’s modulus, and Poisson’s ratio of shale for different β and confining pressures were calculated.

3. TEST RESULTS AND ANALYSIS

The average values of strength and elastic parameters of shale samples for different angles are shown in Figs. 2 – 4.

Fig. 2

The relationship between compressive strength and confining pressure.

Fig. 3

The relationship between Young’s modulus and confining pressure.

Here, β is the angle between the sampling axis and the bedding surfaces; σ₃ is the confining pressure applied to the samples, MPa; σ_c is the compressive strength of the samples, MPa; E is the Young’s modulus of the samples, GPa; and μ is the Poisson’s ratio of the samples, dimensionless.

3.1. ANALYSIS OF MECHANICAL PROPERTIES ANISOTROPY

3.1.1 Compressive strength

According to the test results, the influence of shale bedding angle on the compressive strength is analyzed, and the results are shown in Fig. 5.

Fig. 4

The relationship between Poisson’s ratio and confining pressure.

As can be seen in Fig. 5, for each value of the angle, increase in confining pressure leads to a corresponding increase in the compressive strength. When the confining pressure is low (0.and 25 MPa), the compressive strength in the direction parallel to the bedding surfaces is higher than that in the vertical direction sampling, while at high confining pressures (40 and 50 MPa), the compressive strength in the parallel direction is smaller than that in the vertical direction. With increase in the angle â, the compressive strength of shale under the same confining pressure first decreases and then increases, with the minimum value around 30°. The results show that when drilling the horizontal wells in the Longmaxi formation shale and when the angle between the borehole axis and the surrounding strata is around 60°, the drilling tools colliding with the wellbore wall can easily cause problems of falling blocks and collapse in the surrounding rock of the wellbore.

Fig. 5

The relationship between compressive strength and the bedding angle for different confining pressures.

The effect of bedding surfaces on the compressive strength of shale is similar to the Hoek-Brown empirical strength criterion, which comprehensively considers the influence of rock mass strength, structural plane strength, and rock mass structure, and describes the shear failure mechanism of the rock mass. Therefore, the Hoek-Brown empirical strength criterion is applied to characterize shale with obvious anisotropy [12].

The Hoek-Brown empirical strength criterion is

$$ {\sigma}_1={\sigma}_3+{\sigma}_{c_0}{\left(m\frac{\sigma_3}{\sigma_{c_0}}+s\right)}^{\alpha } $$

(1)

where ${\sigma}_{c_0}$ is the uniaxial compressive strength of the rock; m reflects the soft and hard degree of the rock, and its value ranges from 0.001 to 25; s is related to the tensile strength and adhesion between particles in the rock, and its value ranges from 0 to 1; α is a constant related to the characteristics of the rock mass; α is 0.5 for dense rock mass.

The test samples consist of dense and hard rock mass, and the Hoek-Brown empirical strength criterion can be expressed as

$$ {\sigma}_1={\sigma}_3+{\sigma}_{c_0}{\left(m\frac{\sigma_3}{\sigma_{c_0}}+1\right)}^{0.5} $$

(2)

According to the Hoek-Brown empirical strength criterion, the compressive strength of samples for different is calculated, and the resulting fitting curves are shown in Fig. 6.

Fig. 6

The fitting curves of compressive strength.

According to the fitting results, the calculated values of the m index and fitting correlation coefficient at different are shown in Table 1, where R² is the correlation coefficient of the fitting curve, dimensionless.

Table 1

As can be seen from Table 1, the m value decreases with increases in the correlation coefficient. In order to facilitate the study of the law of influence of bedding surfaces on the compressive strength of shale, m is regarded as a function of, that is,

$$ m=f\left(\beta \right) $$

First, β is expressed in radiants, that is,

$$ r=\frac{\beta \pi}{180} $$

where r is the angle in radians.

The obtained fitting curve of r (rad) and m is shown in Fig. 7.

Fig. 7

The fitting curve of m and r (rad).

Finally, we obtained the fitting equation, that is, 2

$$ m=-1.6596{\mathrm{rad}}^2-2.1677{\mathrm{rad}}^2+2.1677\mathrm{rad}+17.085 $$

(3)

and the correlation coefficient of the fitted curve is 0.961.

The fitting equation was substituted into Eq. (2) to obtain a new model for predicting the compressive strength of shale in the Longmaxi formation in Southern Sichuan, China:

$$ {\sigma}_c={\sigma}_3+{\sigma}_{c_0}{\left[\left(-1.6596{r}^2-2.1677r+17.085\right)\frac{\sigma_3}{\sigma_{c_0}}+1\right]}^{0.5} $$

(4)

The calculation results of the Hoek-Brown strength criterion and the new model of strength prediction are compared with the experimental results. The results are shown in Table 2.

Table 2

It can be seen from Table 2 that the correlation coefficient of both the Hoek-Brown empirical strength criterion and the new prediction model is higher than 0.98, which meets the accuracy requirements. The new model can be applied for the prediction of the compressive strength of shale for different angles under different confining pressures.

3.1.2 Young’s modulus

According to the test results, the values of the Young’s modulus under different confining pressures and different angles were measured, and the results are shown in Fig. 8.

Fig. 8

Young’s modulus under different confining pressures.

As can be seen from Fig. 8, the Young’s modulus increases with increase in confining pressure. When the compression is uniaxial, the Young’s modulus first decreases and then increases with increase in. When the compression is triaxial, the Young’s modulus decreases with increase in the angle, and the rate of decreasing first increases and then decreases. The Young’s modulus increase rate changes with the range as follows: moreover, the Young’s modulus of the samples at 90° is almost the same, which shows that the lateral deformation is inhibited by the effect of compaction of pores and microfractures between stratified planes under the confining pressure. However, in the vertical direction of sampling, the effect of the confining pressure on compaction is weak; therefore, the effect of bedding surfaces angle on the axial deformation in the samples is small, and the Young’s modulus is practically unchanged.

3.1.3 Poisson’s ratio

According to the results, the influence of the bedding angle on the Poisson’s ratio for different confining pressure is analyzed, and the results are shown in Fig. 9.

Fig. 9

Poisson’s ratio under different confining pressures.

It can be seen from Fig. 9 that, under the same confining pressure, with increase in the angle, the Poisson’s ratio first decreased and then increases; moreover, the Poisson’s ratio is the smallest for angles around 60°. However, when the confining pressure is 0 MPa, the poisson’s ratio of the samples varies significantly, which may be caused by the disintegration of pores and microcracks between the bedding surfaces. When the confining pressure is 25, 40, and 50 MPa, the Poisson’s ratio variation trend is similar, but the rate of change is much smaller. This may be caused by inhibition of the pore disintegration under high confining pressures.

3.1.4 Anistropy analysis

The anistropy coefficient δ_i is introduced to describe how the mechanical parameters of shale under compression condition are affected by the bedding surface angle, and the calculation formula is as follow:

$$ {\delta}_i=\sum \frac{\left|{x}_{\beta }-{x}_0\right|}{x_0} $$

(5)

where x_β is the mechanical parameter considering the angle β, and x₀ is the machanical parameter at β =0. The results of the anistropy coefficient calculated for different machanical parameters under different confining pressures are shown in Fig. 10.

Fig. 10

The value of under different confining pressures.

In Fig. 10, is the anistropy coefficient of compressive strength, is the anistropy coefficient of Young’s modulus, and is the anistropy coefficient of Poisson’s ratio.

It can be seen from the definition of that the larger the, the greater the fluctuation of the mechanical parameter value and the stronger the dependence of the parameter on bedding surface angle. It can be seen from the calculation results that, and decrease with increase in confining pressure, indicating that the increase of the confining pressure reduces the influence of bedding surfaces on various mechanical parameters in shale. The Poisson’s ratio anistropy coefficient is more sensitive to the confining pressure change.

The variations of shale mechanical parameters at different confining pressures and different angles show that the occurrence of the bedding surfaces is the cause of the mechanical weakness of shale. Besides, the pores and microfractures in the rock between the bedding surfaces are relatively small in size, and the capillary force is large. Therefore, in the process of drilling, the drilling fluid invades the rock along the bedding surfaces, resulting in a reduction of the strength of the surrounding rock. Moreover, the longer the surrounding rock is soaked in contact with the drilling fluid, the higher the damage will be. At the same time, the collision of drilling tools and the effect of high viscosity drilling fluid will damage the surrounding rock and may easily cause accidents such as rock failure and borehole collapse. In the process of hydraulic fracturing, with the injection of the fracturing fluid, the fluid will first infiltrate into the reservoir rock along the weak planes, initiating the fractures along the weak bedding surfaces. Due to the strong anistropy of shale, a fracture network structure is not easily formed, which seriously affects the fracturing effect and fails to meet the expected production requirements.

3.2. FRACTURE MODE ANALYSIS

Under the compressive condition, the mechanical parameters of shale are affected by the bedding surfaces and show obvious anistropy. Anistropy of the machanical parameters causes the differences of fracture mode on the macro level. In this paper, we have analyzed the mode of fracturing in a shale sample after compaction damage and the influence surfaces on fracture mode in the sample.

3.2.1 Fracture mode under uniaxial compression

When a sample is a subjected to uniaxial compression, the fracture morphology of shale rock has the obvious failure characteristics of layered hard brittle rock. When the axial stress gradually increases to the peak strength, the shale sample starts to disintegrate. At this point, the energy is released instantaneously, and the shale sample is penetrated by multiple macroscopic cracks, forming multiple tensile and shear fracture surfaces. The morphology of the fracture surfaces after the failure of shale samples at various angles is shown in Fig. 11.

Fig. 11

Shale fracture surface characteristics under uniaxial compression.

The fracture mode of the samples at different angles is as follows:

(1) b = 0°: Tensile splitting failure of multiple parallel bedding surfaces is formed. With increase in axial stress, the lateral tension applied on the sample increases, and then a series of tensile fracture surfaces develops in the shale sample, running through both ends of the shale and parallel to the bedding surfaces. The sample is broken into thin slices but retains sufficient pressure bearing capacity in this state. In the process of continuous loading, the pressure load would cause in the thin section of rock to bend, and buckling instability finally occurs, resulting in parallel fracture development.

(2) b =30°: Slide shear failures is formed along the bedding surfaces. An obvious shear slip occurs along the 30° bedding surfaces, fun forming a flat fracture surface that runs through the entire sample.

(3) b =60°: Tensile shear failure is formed through the bedding surfaces, and sliding shear failure is formed along the bedding surfaces. First, a shear fracture surface develops through the bedding surfaces on both sides of the near end faces, and the angle between the fracture surface and the bedding surfaces is about 45°. With increase in axial stress, the fracture surfaces gradually expands to the middle of the sample, forming, the sliding shear failure along the bedding surfaces in the middle of the sample after penetrating multiple bedding surfaces. Then the fracture surfaces at both ends are connected, forming a composite shear failure in the sample.

(4) β = 90°: Tensile failure through the bedding surfaces, and sliding shear failure is formed along the bedding surfaces. With increase in axial, the lateral tension in the sample increase, and the sliding shear failure ifs formed along the bedding surfaces when the tensile overcomes the interlaminar friction. At this moment, the sample retains sufficient bearing capacity. When the axial stress continues to increase and reaches the compressive strength limit of the bedding surfaces in the sample, tensile failure is formed through the bedding surfaces.

3.2.2 Fracture mode under triaxial compression

Under triaxial compression, the fracture mode of shale consist mainly of shear failure cracks, including single shear and multiple shear (or conjugate shear) failure fractures. With increase in confining pressure, the shale sample becomes more plastic, the brittle fracture characteristics gradually weaken, and the number of fracture surfaces gradually decreases. The morphology of the fracture surfaces after the failure in shale samples at various angles is shown in Fig. 12.

Fig. 12

Shale fracture surface characteristics under triaxial compression.

The fracture modes of samples of different angles can be divided into the following two types.

(1) Multiple shear surfaces (or conjugate shear surfaces). The disintegration of shale sample subjected to pressure causes the formation of more than two shear fractures in the sample. The two sets of fracture surfaces are roughly parallel to each other, and the fracture surfaces develop through the sample and divide the sample into several pieces, thus forming a conjugate shear fracture surface. The pattern of the fracture surfaces on the sample surface is similar to the letter “w”. The formation of multiple shear surfaces is typical for samples with a 0° angle and subjected to a confining pressure of 25~50 MPa.

(2) Single shear plane. The main shear fracture surface is formed in all shale sample after the compression failure, but the morphology of the shear fracture surface depends on the angle. Under different confining pressures, the shear fracture surfaces in the sample at 30° is relatively flat and runs along the bedding surfaces through both ends of the sample. The main shear fracture surfaces in the sample at 60° is curved; it runs through both ends of the sample, forming an angle of about 35° with the bedding surfaces. The shear fracture surface of the sample at 90° is slightly bent, and it forms an angle of about 50° with the bedding surfaces.

Comparing the fracture modes in shale with different angles of the bedding surfaces, it can be seen that two main factors control the fracture formation in shale: one is defined by the weakness of the bedding surfaces. On the macro level, the former determines the formation of fracture surfaces along the weak bedding surfaces, while the latter determines the formation of fracture surfaces through the bedding surfaces. The analysis results of the major controlling factors and fracture models in shale samples are shown in Table 3.

Table 3

Generally speaking, when the samples are subjected to uniaxial compression, the fracture modes are divided into four types, which are mainly affected by the weakness of the bedding surfaces. When the samples are subjected to triaxial compression, the fracture modes are divided into three types, dominated mainly by the properties of the matrix in the bedding surfaces. By comparing the fracture modes of uniaxial and triaxial compression and their main control factors, it can be seen that when subjected to confining pressure, the plasticity of shale is enhanced, the fracture characteristics of layered brittle rock are weakened, and the main factor controlling the fracturing in shale changes from the bedding surfaces weakness to the matrix properties.

4. CONCLUSIONS

• (1) The mechanical properties of shale of the Longmaxi formation in Southern Sichuan, China show obvious anisotropy.

• (2) With increase in the angle between the sampling axis and shale bedding surfaces, the Young's modulus of shale decreases gradually, Poisson's ratio first decreases and then increases, and the compressive strength shows a “U” shaped variation pattern, with a minimum value in the middle of the range. A new strength prediction model has been established, considering the m parameter in the Hoek-Brown empirical strength criterion as a function of the angle. The new model can quickly and accurately predict the compressive strength of shale at different angles under different confining pressures.

• (3) The fracture mode in shale under compression depends on the bedding angle and confining pressure. When subjected to malarial compression, the shale sample at 0° is mainly affected by the weakness of the bedding surfaces, resulting in a tensile fracture surface formation along the weak planes. When the angle is 30°, shear slip fracture surfaces are formed along the weak bedding surfaces. When the angle is 60°, shear slip fracture surfaces are formed along the bedding surfaces and through the bedding surfaces under the influence of the matrix properties of the bedding surfaces. When the angle is 90°, the tensile splitting fracture surfaces are formed through the bedding surfaces. The fracture mode is affected by the properties of the matrix. Under triaxial compression, the shale sample at 0° demonstrates the formation of conjugate shear fracture surfaces through the bedding surfaces, which is affected by the properties of the matrix. When the angle is 30°, the shear slip fracture surfaces are formed along the bedding surfaces in the shale sample, affected by the weak bedding surfaces. In shale samples at 60° and 90°, the shear fracture surfaces are formed through the bedding surfaces affected by the matrix properties of the bedding surfaces.

• (4) The increase in confining pressure can reduce the influence of the bedding surfaces on the mechanical parameters and fracture mode in shale.

• (5) The bedding surfaces are the weak planes in shale. The shale layered sedimentary structure and weak cementation between the bedding surfaces are the main reasons causing the anisotropy of mechanical properties and strength characteristics. On the macro level, the anisotropy of mechanical parameters is demonstrated by the change of the fracture mode. The friction between the bedding surfaces is relatively small, and the strength is relatively low. Thus, sliding shear fractures tend to occur along the bedding surfaces, causing disintegration and formation of the rock fragments. In serious cases, the shale fracturing may cause accidents such as downhole tools getting stuck and borehole wall collapsing.