Nanoindentation-Based Three-Parameter Fracability Evaluation Method for Continental Shales

Shale fracturing evaluation is of great significance to the development of shale oil and gas resources, but the commonly used shale evaluation methods (e.g., the method using the brittleness index based on mineral composition or elastic parameters) have certain limitations. Fractures and beddings affecting fracturing are not considered in these methods. Therefore, it is necessary to develop a new method to evaluate fracturing more comprehensively. The samples used in this research were taken from four typical continental shale basins of China, namely the Bohai Bay Basin, the Ordos Basin, the Songliao Basin, and the Junggar Basin. From a microscopic point of view, a three-parameter evaluation method involving multi-dimensional factors has been developed based on the nanoindentation method. Then, the fracturing coefficient K2 is obtained by combining the ratio β of the fracture indentation to the total indentation and the uneven coefficient m. After that, the fracability coefficient K3 is the ratio of the elastic modulus parallel to bedding to that perpendicular to bedding. Finally, the correlation between fracability coefficients K1, K2, and K3 is used to evaluate the overall fracturing performance of shale. The results of this evaluation method are in good agreement with the actual fracturing performance. It can be concluded that this method is highly reliable and practical and well worthy of promoted applications.


INTRODUCTION
With the increasing demand for oil and gas resources all around the world, shale oil has become a key field for the exploration and development of unconventional oil and gas resources globally. The fracturing evaluation is of great significance to the development of shale oil and gas resources. Previous practice of shale fracability evaluation mostly uses the brittleness index to reflect the degree of difficulties in creating complex fracture networks (Ai et al., 2016;Li et al., 2017;Qin and Yang, 2019;Tang et al., 2019;Zhang et al., 2020). At present, two types of brittleness indexes are commonly used for shale, namely the mineral composition-based and rock mechanical parameter-based ones. However, during actual fracturing, the in-situ stress, the natural fracture development degree, bedding, and internal structure all have significant impacts on the shale fracability (Zhang et al., 2018a;Xie et al., 2020;Yang et al., 2020;Mao et al., 2021;Zhang et al., 2021).
In 2013, some scholars developed a fracability evaluation method using three rock mechanical parameters, namely the Young's modulus, Poisson's ratio, and uniaxial tensile strength, as the independent variables, and the fracability coefficient as a dependent variable, which yet ignored the impact of mineral composition (Yuan et al., 2013). In 2014, some scholars proposed a comprehensive evaluation method for shale gas fracability, which uses a radar chart of six geomechanical parameters to rank the fracability of shale gas reservoirs. However, this method cannot be used for quantitative analysis (Zhao et al., 2015). In 2015, some scholars proposed an evaluation method for shale gas fracability by integrating three features of shale (the brittleness, fracture toughness, and natural weak plane), but the impact of rock mechanical parameters was not addressed (Chen et al., 2017). In 2017, some scholars set up an evaluation system for shale fracability comprising five factors-the brittleness index, rock mineral content, cohesion, natural fractures, and porosity to evaluate the fracability of the Niutitang Formation. Nonetheless,    Frontiers in Earth Science | www.frontiersin.org December 2021 | Volume 9 | Article 797405 2 this research neglected the impact of organic matter and in-situ stress difference (Di et al., 2019).
The evaluation methods mentioned above mostly evaluate the fracability from a macro point of view, and rarely perform evaluation from a micro point of view. Over the past few years, many researchers have gradually applied the nanoindentation technique to studying the mechanical properties of rocks. Some scholars calibrated the indentation position by integrating the nanoidentation with the backscattered electron diffraction (BSE) and measured the mechanical property of kerogen at the nano scale. They found out that the elastic modulus of kerogen was 5-9 GPa, and higher kerogen content would reduce the overall elastic modulus of rock (Kumar et al., 2012;Shukla et al., 2015). Some scholars proposed a nanoindentation-based evaluation model for the fracture toughness of coal, which estimates the fracture energy and fracture area according to the brittle failure theory and the pop-in feature on the loading curve (Manjunath and Birendra, 2019). Some scholars obtained the mechanical properties of dry and saltwater-saturated coal samples at the nano scale through nanoindentation tests and compared them with the results of the traditional acoustic testing, based on which the limitations of the traditional acoustic testing are concluded (Zhang et al., 2018b).
The study addresses the typical continental shale of the Bohai Bay Basin, the Ordos Basin, the Songliao Basin, and the Junggar Basin in China. With the X-ray diffraction (XRD) test, scanning electron microscopy (SEM), and the nanoindentation test of the grid identation mode, the mechanical parameters of rocks such as elastic modulus, hardness, and fracture toughness are obtained. The evaluation results are in good agreement with the actual fracturing treatment performance and fracturing numerical simulation result. It is shown that this method is highly reliable and practical, and thus well worthy of promoted applications. This study provides an idea and technical method for evaluation of the continental shale and is valuable for revealing the mechanical behavior of shale and realizing efficient development of shale gas.

Test Samples
The test samples were obtained from the Bohai Bay, Ordos, Songliao, and Junggar Basins, respectively ( Figure 1). The Bohai Bay Basin is a faulted basin composed of a series of Paleogene half-graben sags. The Paleogene is a typical lacustrine sedimentary system having experienced two secondary cycles of lake transgression and regression. Located in the north of Xinjiang, the Junggar Basin covers an area of about 13 × 10 4 km 2 , which is a multi-stage superimposed basin occurring on an amalgamation block. Located in Northeast China, the Songliao Basin crosses over three provinces, Heilongjiang, Jilin, and Liaoning, and extends from NE to SW, with a NS length of about 820 km, a EW width of 350 km, and an area of about 26 × 10 4 km 2 , bounded by the Nenjiang Fault in the west and the Mudanjiang Fault in the east. It is a large Mesozoic-Cenozoic continental sedimentary basin. Located in the west of the North China Platform, the Ordos Basin covers an area of about 25 × 10 4 km 2 developing the Paleozoic and Mesozoic two petroleum systems. In this article, shale samples with parallel bedding and vertical bedding are prepared respectively. The "I/S" is illite/smectite mixed-layer, ""C/S ""is chlorite/smectite mixed-layer. tested shale sample is mixed curing with epoxy resin and curing agent, whose size is set as length of 5mm, width of 5 mm and thickness of 3 mm. Then, the cured samples will be polished by using the polished section with 15, 9, 3 and 0.5 μm to ensure the smoothness of sample.

XRD
The TTR III multifunctional X-ray diffractometer manufactured by Rigaku (Japan) was used for mineral composition analysis. Each mineral crystal has its specific X-ray diffraction spectrum,  Frontiers in Earth Science | www.frontiersin.org December 2021 | Volume 9 | Article 797405 4 whose characteristic peak intensity is positively related to the mineral content in a sample. The positive correlation (the K value) between the content of a mineral and the intensity of its characteristic diffraction peak can be determined as a prior by testing. Subsequently, the content of this mineral can be obtained by measure the intensity of its characteristic peak in an unknown sample.

SEM
The Apreo field-emission scanning electron microscope (FE-SEM), manufactured by FEI (America), was used for SEM, which is able to perform a fast qualitative or quantitative micro analysis for the multi-element composition by electron beam scanning. In the process of testing, information such as the sample number, accelerating voltage, scale, amplification factor, date, time, and working distance can be obtained. Researcher has established the correlation between shale pore structure, pore size distribution, and rock mechanical properties at the nano scale by the methodology based on the FE-SEM and digital image processing (Liu and Ostadhassan, 2017).

Testing Principles and Steps
The nanoindentation technique uses the high-precision sensor to control the indenter to press into and out of a sample and record the changes in load and displacement during this process. Figure 2 illustrates the mechanism of indentation. As shown in Figure 3, a typical process of nanoindentation has three stages: loading, holding, and unloading. In the loading stage, the press-in depth increases with the increase in the pressing load, which is associated with elastic and plastic deformation. The holding stage is designed to eliminate the effect of the sudden force change on the calculation of mechanical parameters. In the unloading stage, the indentation partially recovers, with the reduction in load. It is assumed that only elastic deformation occurs in this stage, based on which the mechanical properties at the indentation point is calculated. In this study, the quasi-static nanoindentation test with a fixed maximum load was carried out, and the grid indentation method is used, with a total of 100 indentation points for each sample. Due to the high heterogeneity across the rock surface, a great number of indentation points were measured using the grid indentation mode, which allows for statistical analysis of the rock microscopic mechanical properties. During the test, the nanoindenter was pressed into the shale surface at a loading rate of 100 μN/s, held in place for 5 s as soon as the load reaches the maximum value of 1 mN, and then gradually popped out of the shale surface at an unloading rate of 100 μN/s. Its displacement-load path is shown in Figure 3.

Theory
According to the relationship between indentation and load (specifically, the proportional relationship between the maximum load F max adopted in the test and the contact area A c of sample) (Oliver and Pharr, 1992), the rock hardness H can be expressed as: where, F max is the maximum load in N, and A c is the projected contact area in m 2 .
The contact stiffness S of the sample can be obtained from the initial slope of the unloading section as: where S is the contact stiffness in kN/mm. Fracture toughness can be determined via the energy analysis (Cheng et al., 2002). In the operation process of nanoindentation, the total energy U is composed of elastic energy U e and plastic energy U p . As irreversible energy, U p can be further decomposed into pure plastic energy U pp and fracture energy U frac . Therefore, the following equation is obtained: where U is the total energy in J; U e is the elastic energy in J; U p is the plastic energy in J; U pp is the pure plastic energy in J; U frac is the fracture energy in J. U e and U p can be obtained from the diagram of load vs. displacement, as shown in Figure 4.
The relationship between U PP and U is as follows: The propagation of fractures generates U frac , and the corresponding critical energy release rate G c can be obtained using the following equation: where, G c is the critical energy release rate in N/m; A m is the maximum fracture area in m 2 , calculated using the relationship between the indenter depth and area. The fracture toughness K ic can be calculated using the following equation: TEST RESULTS

Mineral Analysis Results
The bulk mineral composition is listed in  Table 2 shows that there are remarkable differences in the relative composition of clay minerals. The samples from the Ordos and Songliao Basins have high relative content of I/S, while the samples from the Junggar Basin have smectite content high up to 72%. As for the samples from the Bohai Bay Basin, the C/S is the main component for clay minerals, reaching 58%. Figure 5 presents the histograms of the compositions of bulk minerals and clay minerals. The samples from the Songliao and Ordos Basins have similar compositions, which are greatly different from those of the samples from the other two basins.

Microscopic Pore Characteristics
SEM analysis is used to study different pore sizes, pore types, and micro-fractures. Figure 6 shows the typical SEM images of rock samples from four basins. Most of the pore sizes are at the micro/ nano scale and some organic matter also occurs. The pore types include residual intergranular pores and feldspar dissolution pores. There is also locally-developed calcite. There are prominent micro-fractures in some reservoir rocks. In addition to the initial pores on the surface of shale, there are also many pores caused by the whole or partial exfoliation of massive minerals. And beyond that, there are also microscopic fissures  Frontiers in Earth Science | www.frontiersin.org December 2021 | Volume 9 | Article 797405 8 developed at the edges of the mineral grains and pores throughout the mineral grains. The pore structure is affected by the sedimentary environment, and the geological structure has a great impact on the pore structure Lin et al., 2017). Figure 7 shows the calculated frequency distribution of the grid hardness for the four basins. For the Junggar Basin, the maximum hardness is 9.704 GPa, the minimum is 0.232 GPa, averaging 3.466 GPa, and the hardness is mainly distributed in the range of 0.232-4 GPa. For the Songliao Basin, the hardness presents a maximum of 6.231 GPa, and a minimum of 0.217 GPa, averaging 2.215 GPa, and is mainly distributed in the range of 0.2-1 GPa. For the Bohai Bay Basin, the maximum hardness is 5.692 GPa, the minimum is 0.296 GPa, averaging 3.225 GPa, and the hardness is mainly distributed in the range of 3.5-5 GPa. For the Ordos Basin, the maximum and minimum hardness is 8.614 and 0.176 GPa, respectively, with an average of 2.796 GPa, and the hardness is mainly distributed in the range of 0.176-3 GPa. It can be concluded that the Junggar Basin has the largest average hardness, while the Songliao Basin has the smallest average value. For the Bohai Bay Basin, the elastic modulus presents a maximum of 42.287 GPa and a minimum of 9.649 GPa, averaging 26.783 GPa; the elastic moduli are mainly distributed in the range of 20-35 GPa. For the Ordos Basin, the elastic modulus presents a maximum of 53.535 GPa and a minimum of 2.281 GPa, averaging 26.903 GPa; the elastic moduli are mainly distributed in the range of 15-40 GPa. It can be concluded that the Junggar Basin has the largest average elastic modulus, while the Songliao Basin has the smallest average value. Figure 9 shows the calculated frequency distribution of the grid fracture toughness for the four basins. For the Junggar Basin, the fracture toughness is associated with a maximum of 26.773 MPa m 1/2 and a minimum of 5.291 MPa m 1/2 , averaging 15.659 MPa m 1/2 ; the fracture toughness is mainly distributed in the range of 10-20 MPa m 1/2 . For the Songliao Basin, the fracture toughness is associated with a maximum of 17.117 MPa m 1/2 and a minimum of 4.913 MPa m 1/2 , averaging 10.396 MPa m 1/2 ; the fracture toughness is mainly distributed in the range of 5-13 MPa m 1/2 . For the Bohai Bay Basin, the fracture toughness is associated with a maximum of 19.707 MPa m 1/2 and a minimum of 5.832 MPa m 1/2 , averaging 14.624 MPa m 1/2 ; the fracture toughness is mainly distributed in the range of 14-20 MPa m 1/2 . For the Ordos Basin, the fracture toughness is associated with a maximum of 24.379 MPa m 1/2 and a minimum of 3.616 MPa m 1/2 , averaging 13.646 MPa m 1/2 ; the fracture toughness is mainly distributed in the range of 8-18 MPa m 1/2 . It can be concluded that the Bohai Bay Basin has the largest average fracture toughness, while the Songliao Basin has the smallest average value.

Brittleness Index K 1
In the elastic deformation stage of materials, the stress is directly proportional to the strain, which conforms to the Hooke's Law. The ratio of the two is termed the elastic modulus E r of the material. The greater the E r value is, the higher the shale fracability is, which indicates a positive correlation between the two. Hardness H refers to the ability of shale to resist hard materials pressing into its local surface. The greater the H value is, the higher the shale fracability (also a positive correlation). Fracture toughness K c refers to the ability of shale to prevent the crack from progagating and is a quantitative indicator to measure the toughness of materials. The greater the K c value is, the lower the shale fracability is (a negative correlation). According to the relationships between the above relevant variables and shale fracability, the shale fracability is positively correlated with the brittleness index K 1 defined as below: As shown in Eq. 6, the dimension of the fracability coefficient K 1 is m −1 . For convenience of the subsequent analysis and discussion, K 1 has multiplied with a unit length to obtain a  Frontiers in Earth Science | www.frontiersin.org December 2021 | Volume 9 | Article 797405 10 dimensionless index. Figure 10 shows the distribution of mechanical parameters for the four basins. The K 1 values for all of the four basins are obtained, which are shown in Table 3.
Based on the brittleness index K 1 calculated using the above equation, a comprehensive evaluation was made for the fracability of the shale in the four basins. The shale in the Junggar Basin has high fracability coefficient K 1 values mainly of 0.4-0.6 (averaging 0.49), due to that it has the largest elastic modulus and hardness. The shale in the Bohai Bay Basin has low fracability coefficient K 1 values mainly of 0.3-0.5 (averaging 0.4), owing to its lower elastic modulus and hardness. The shale in the Songliao Basin is associated with the fracability coefficient K 1 of 0.3-0.8 (averaging 0.45), and that in the Ordos Basin has the fracability coefficient K 1 values of 0.3-0.5 (averaging 0.39, the lowest). However, the average K 1 values of the shale in the four basins are found with only minor differences.
Brittleness Index K 2 m is a parameter for the Weibull distribution, known as the Weibull modulus. In this research, the higher the m values of  corresponding mechanical parameters (such as elastic modulus and hardness) are, the less the discreteness of parameter x is, which implies less discreteness of corresponding mechanical parameters of rock and thus lower rock heterogeneity. Therefore, the higher the 1/m value is, the higher the heterogeneity is. β represents the proportion of special loaddisplacement curves featuring fractures and pores to the total curves. The larger the β value is, the stronger the heterogeneity is.
Hence, β/m is used to evaluate the heterogeneity-the larger the β/m value is, the greater the heterogeneity is.
K 2 β m (8) Figures 11 and 12 show the heterogeneity coefficient β and m for the four regions, respectively. And then the brittleness index K 2 is calculated, as shown in Table 4. The samples from the Bohai Bay Basin have the largest proportion of curves featuring fractures and pores, and thus higher heterogeneity. The calculated fracability coefficient K 2 of the shale is the highest in the Bohai Bay Basin (7.01) and the lowest in the Songliao Basin (4.08).

Brittleness Index K 3
The brittleness index characterizes the difficulties in creating complex fracture networks by hydraulic fracturing. With a higher brittleness index, the reservoir is more sensitive to fracturing and the resultant fractures are more complex. The elastic modulus reflects the ability of shale to preserve the fractures after being fractured. Some researchers analyzed the kerogen morphology and nanomechanical properties of oil shale cored in different directions (parallel and perpendicular to the bedding plane) (Alstadt et al., 2016).
As shown in Figures 13, 14, there is usually a great difference between the elastic moduli in the horizontal and vertical bedding directions. A greater difference is preferred for fractures to propagate along the bedding plane.
The ratio between the elastic moduli in the directions in relation to the bedding plane is directly related to the fracability, so the ratio of the elastic modulus parallel to the bedding plane to that perpendicular to the bedding plane can be used to represent brittleness. Therefore, the fracability coefficient K 3 is defined as below: FIGURE 16 | Fracability based on mineral composition.
FIGURE 17 | Microscopic comprehensive evaluation for shale oil producibility (Jin et al., 2021). where E h is the elastic modulus along the bedding plane, and E v is the elastic modulus perpendicular to the bedding. Based on upscaling and analysis of the nanoindentation test data, the elastic moduli of shale parallel and perpendicular to beddings at the centimeter scale were obtained, and a new model to calculate the brittleness index was established. The calculated brittleness index K 3 is shown in Table 5. For samples from the Ordos Basin, there is a great difference between samples parallel and perpendicular to beddings, and the fracability coefficient K 3 is the largest (2.01). For samples from the Songliao Basin, the difference between samples parallel and perpendicular to beddings is the smallest, and the fracability coefficient K 3 is thus the lowest (1.27).

Three-Parameter Evaluation
The three fracability coefficients K 1 , K 2, and K 3 based on the nanoindentation test are all dimensionless and the sum of them can characterize the overall fracability of shale. In addition, weight factors α 1 , α 2 and α 3 should be defined for the summation to represent the impact degree of each fracability coefficient on the overall fracability. To this end, four cases are discussed in this research. First, assuming α 1 +α 2 +α 3 1 and all the three indexes produce the same impact (in other words, α 1 K 1 α 2 K 2 α 3 K 3 ), then α 1 0.75, α 2 0.05 and α 3 0.2. When the impact of K 1 is more significant, we have α 1 K 1 2α 2 K 2 2α 3 K 3 and thus α 1 0.85, α 2 0.03, and α 3 0.12. When the impact of K 2 is more significant, we have 2α 1 K 1 α 2 K 2 2α 3 K 3 and then α 1 0.7, α 2 0.1, and α 3 0.2. When the impact of K 3 is more significant, we have 2α 1 K 1 2α 2 K 2 α 3 K 3 and then α 1 0.6, α 2 0.05, and α 3 0.35. Rational weight factors can be determined in accordance with the field conditions, to characterize the impact degree of the three indexes on the fracability. Thus, the ultimate brittleness index is obtained as: The calculated brittleness index B with different α 1 , α 2, and α 3 values for each basin is shown in Table 6 and Figure 15. Except for Case 4, the Bohai Bay Basin has the most distinctive fracability. In Cases 1 and 3, there is little difference in fracability between the Junggar and Ordos Basins. In Figure 16, the fracability based on the mineral composition analyzed from the rock cutting are compared. Figure 17 shows the microscopic comprehensive evaluation for the producibility of the continental shale oil in the four basins by previous research (Jin et al., 2021). Comparison shows that Case 2 is more consistent with the field conditions. Therefore, α 1 0.85, α 2 0.03, and α 3 0.12 are used, and the above equation is rewritten as: As shown in Figure 18, the fracability of the shale reservoir is determined from the perspectives of the point (K 1 ), area (K 2 ), and volume (K 3 ) parameters and the 3D distribution of fracability is obtained. The redder the color in the figure is, the greater the fracability is; the bluer the color is, the lower the fracability is.

CONCLUSION
This research addresses the typical continental shale of the Bohai Bay, Ordos, Songliao, and Junggar Basins in China. via the XRD mineral analysis, SEM, and nanoindentation test using the grid indentation testing mode, the elastic modulus, hardness, and fracture toughness of rocks are obtained. Furthermore, the three fracability parameters K 1 , K 2, and K 3 are obtained by analyzing the measured mechanical parameters, resulting in the ultimate fracability coefficient B 0.7K 1 +0.1K 2 +0.2K 3.
1) The point fracability coefficient is obtained: K 1 E r H/K 2 c . In the Junggar Basin, the average fracability coefficient K 1 of shale is 0.49, indicating the highest point fracability among the four basins. In the Bohai Bay Basin, the average fracability coefficient K 1 of shale is 0.4, and the point compressibility K 1 shows no great difference from the other three basins.
2) The area fracability coefficient is obtained: K 2 β/m. Among the four regions, the samples from the Bohai Bay Basin have the largest proportion of curves featuring fractures and pores, and a high degree of heterogeneity. The calculated fracability coefficient K 2 of the shale is the highest (7.01) in the Bohai Bay Basin, and the lowest (4.08) in the Songliao Basin.
3) The volume fracability coefficient is obtained: K 3 E h /E v . For the samples from the Ordos Basin, there is a great difference between the elastic moduli parallel and perpendicular to beddings, and the fracability coefficient K 3 is the largest (2.01). For the samples from the Songliao Basin, the difference between the elastic moduli parallel and perpendicular to beddings is the smallest, and the fracability coefficient K 3 is also the lowest (1.27). 4) With the sum of the three subordinate fracability coefficients, the overall fracability of shale is characterized. In addition, weight factors α 1 , α 2, and α 3 should be defined for the summation to represent the impact degrees of the three parameters on fracability. With the composition of minerals taken into account, the weight factors are finally determined as: α 1 0.85, α 2 0.03, and α 3 0.12, and in other words, the ultimate fracability index B 0.85K 1 +0.03K 2 +0.12K 3 .

DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.