Brittleness Evaluation in Shale Gas Reservoirs and Its Influence On

energies

Article Brittleness Evaluation in Shale Gas Reservoirs and Its Inﬂuence on Fracability

Yapei Ye 1,2,3, Shuheng Tang 1,2,3,* and Zhaodong Xi 1,2,3

1 School of Energy Resources, China University of Geosciences, Beijing 100083, China 2 Key Laboratory of Marine Reservoir Evolution and Hydrocarbon Enrichment Mechanism, Ministry of Education, Beijing 100083, China 3 Key Laboratory of Strategy Evaluation for Shale Gas, Ministry of Land and Resources, Beijing 100083, China * Correspondence: [email protected]

Received: 23 December 2019; Accepted: 9 January 2020; Published: 13 January 2020

Abstract: The brittleness index (BI) is a key parameter used to identify the desirable fracturing intervals of shale gas reservoirs. Its correlation with fracability is still controversial. There have been a variety of methods proposed that can estimate BI. The brittleness evaluation method based on stress-strain curves according to the energy-balanced law is the most suitable and reliable in this study. Triaxial compression test, optical microscopy and scanning electron microscopy (SEM) observation, and X-ray diﬀraction analysis (XRD) were performed on nine drill core samples from well SY3 located in the peripheral regions of Sichuan Basin, China. These tests further evaluated several commonly used methods (brittleness indices based on rock elastic parameters, rock mineral compositions) and determined the relationship between brittleness, rock elastic parameters, and the content of minerals. The results obtained indicate that for sedimentary rocks, a higher Young’s modulus reduces the brittleness of rock, and Poisson’s ratio weakly correlates with brittleness. Excessive amounts of quartz or carbonate minerals can increase the cohesiveness of rock, leading to poor brittleness. Furthermore, the most suitable fracturing layers possess a high brittleness index and low minimum horizontal stress.

Keywords: brittleness; brittle minerals; Young’s modulus; Poisson’s ratio; fracability; in-situ stress

1. Introduction Shale gas reservoirs are remarkably different compared to conventional reservoirs due to their ultra-low porosity and permeability. It is of utmost importance to hydraulically fracture the unconventional oil and gas reservoirs for commercial production. Consequently, the identification of candidates for prospected fracturing in shale gas reservoirs is necessary to enhance gas productivity. Brittleness index is an essential mechanical parameter that has been used to evaluate whether shale gas reservoirs can easily form complex fracture networks [1,2]. Also, shales with high brittleness tend to close hydraulically created fractures slowly [3]. Therefore, the quantitative evaluation of brittleness is of considerable significance to the optimization of fracturing intervals. At present, there exists no unique and universally accepted definition for rock brittleness. Different definitions are based on their purpose. For example, brittleness has been described as the lack of ductility [4] or the destruction of internal cohesion [5], the ability for a rock to deform and fail with a low degree of inelastic behavior has also been used to define brittleness [6], along with the process by which sudden loss of strength occurs with little or no plastic deformation [7], and the rock’s capability to self-sustain fracturing [8]. Although there is no consensus on the definition, it is commonly believed that brittle rocks are characterized by the following features: (1) easily fractured with the formation of more cracks and (2) little plastic deformation under compression.

Energies 2020, 13, 388; doi:10.3390/en13020388 www.mdpi.com/journal/energies Energies 2020, 13, 388 2 of 22

Brittleness is a comprehensive response of a rock’s combined mechanical properties. The influencing factors of rock brittleness are divided into internal factors and external factors. The intrinsic factors mainly include composition (e.g., total organic carbon (TOC), minerals, water/gas/oil content), texture, and porosity of the rock. The external factors comprise the ambient pressure and temperature [9]. Considering different affecting factors, numerous quantification methods for evaluating rock brittleness have been proposed. The most widely used methods are categorized into three general groups:(1) brittleness indices based on rock elastic parameters [10], (2) brittleness indices attained from rock mineral compositions [11–13], and (3) brittleness indices derived from rock stress-strain curves [8,14]. The aim of this paper is to select the most suitable and reliable brittleness evaluation method as standard after analyzing these three methods. Through a series of experiments, the brittleness indices by means of these three methods are respectively calculated and compared with each other. Meanwhile, the relationship between standard brittleness index, rock elastic parameters, and the content of minerals are investigated. The role that brittleness plays in the selection of desired fracturing intervals is also discussed in this study. The primary motivation of brittleness evaluation is to select prospective gas and oil shales that can be efficiently fractured for profitable production. However, others believe that the brittleness parameter usually ignores the actual mechanisms of effective fracturing, failing to select the desired fracturing intervals [15–17]. Consequently, the “fracability index” is defined to select fracturing intervals by using the parameters affecting fracability beyond the brittleness index [18]. Accordingly, the correlation of brittleness index and fracability index is studied.

2. Reviewing and Evaluating the Existing Brittleness Indices

2.1. Brittleness Indices Based on Rock Elastic Parameters Brittleness is a property of a material correlated with elastic and plastic deformation. If a rock under stress has a broader region of elastic behavior and a smaller region of ductile behavior, it is considered more brittle [19]. Therefore, elastic parameters (Young’s modulus and Poisson’s ratio) are utilized to calculate the brittleness index of materials. Young’s modulus is a ratio of stress and strain. Poisson’s ratio is a ratio of radial strain over axial strain. Equation (1) proposed by [10] combines Young’s modulus and Poisson’s ratio to evaluate rock brittleness:

E + v BI = n n , (1) 2

E Emin vmax v En = − ; vn = − (2) Emax E vmax v − min − min where E and ν are Young’s modulus and Poisson’s ratio, respectively; En and νn are normalized Young’s modulus and Poisson’s ratio, respectively; min and max indices in the equation are the minimum and maximum of the elastic parameters in the study area, respectively. In this framework, the brittle rocks with a higher Young’s modulus and lower Poisson’s ratio experience less axial strain and less radial strain under the same applied force. This indicates that these brittle rocks can transform more absorbed energy into elastic energy to promote the initiation and extension of cracks. However, the controversial debate of whether Young’s modulus and Poisson’s ratio can be used to assess brittleness has intensified recently. These two parameters are elastic parameters only corresponding to non-permanent (or elastic) deformation, but the failure of materials refers to not only non-permanent deformation but also permanent deformation [16]. Furthermore, previous research works found that the brittleness indices calculated from this model tend to remain almost unchanged, or even increase, with an increase in confining pressure [15,20]. This observation conflicts with the fact that a decrease in confinement stress increases rock brittleness [7,21]. Therefore, the brittleness index based on elastic modulus is inappropriate to evaluate rock brittleness correctly. Energies 2020, 13, 388 3 of 22

2.2. Brittleness Indices Attained from Rock Mineral Compositions Minerals are regarded as the most significant factor in controlling brittle rock behavior. In this framework, it is universally regarded that brittle minerals (e.g., quartz, carbonate minerals) tend to promote rock brittleness while ductile matters (e.g., clay minerals, organic matter) diminish brittle rock characteristics. Consequently, the method based on rock mineral components is expressed as follows [11–13]: w BI = b , (3) wb + wd where Wb is the weight fraction of brittle minerals that tend to promote rock brittleness, Wd is the weight fraction of ductile minerals that diminish rock brittle characteristics. The content of rock minerals is easily obtained from laboratory tests or well-logging data, so it is convenient for researchers to understand this method and calculate the brittleness index. However, three problems exist in this methodology. First, the confirmation of brittle minerals fails to reach a consensus. Apart from quartz, it is controversial whether carbonate minerals, pyrite, and feldspar are “brittle” minerals. Therefore, the calculation formulas vary in different study areas. As a result, outcomes calculated by various formulas may be extremely different. Second, each mineral is assigned the same weight coefficient, which means that every mineral has the same contribution to rock brittleness. This lacks a sufficient scientific basis because there are apparent mechanical differences for various minerals [22]. Third, this method does not take other affecting factors into account, such as rock porosity and rock texture. In this formulation, the brittleness indices of rocks with the same mineral composition but different porosity are consistent. This contradicts the fact that brittleness decreases with increasing porosity [23]. Moreover, rock texture is primarily responsible for brittleness characteristics, such as the laminar structure of shales and the fine-grained micritic textures of carbonate rocks [17,24]. This implies that mineralogical compositions cannot solely be used to accurately estimate rock brittleness.

2.3. Energy-Based Brittleness Indices Derived from Rock Stress-Strain Curves The complete stress-strain curves of a rock sample under external loads show the deformation and rupture characteristics of the sample. Figure1 illustrates the internal micromechanical mechanisms of rock deformation and failure behaviors under compression loading. The entire failure process can be divided into ﬁve stages: (1) oa: Pre-existing micro-cracks and micro-pores close; this stage is terminated at crack closure stress (σcc). (2) ab: Linear elastic deformation of rock occurs with the tangent modulus of Young’s modulus until the crack initiation stress (σci) is reached. σci is the turning point of the rock from elasticity to plasticity, also known as the yield point. (3) bc: Micro-cracks stably propagate before crack damage stress (σcd). (4) cd: Cracks propagate in an unstable manner until the limit strength of the rock is reached at a stress level known as failure stress (σf). (5) de: At the peak stress (σf), the rock is in an unsteady state with high energy. The internal cracked surfaces of the rock intersect then form one or several macro-fracture surfaces. Subsequently, the rock mass slides along the macro-fracture surfaces, and the bearing capacity of the sample rapidly decreases until reaching the residual strength (σr). Energies 2020, 13, 388 4 of 22 Energies 2020, 13, x FOR PEER REVIEW 4 of 23

Figure 1. Typical compression stress-strain curve and associated deformation and failure characteristics Figure 1. Typical compression stress-strain curve and associated deformation and failure for brittle rocks. σcc: crack closure stress; σci: crack initiation stress; σcd: crack damage stress; σf: failure characteristics for brittle rocks. σcc: crack closure stress; σci: crack initiation stress; σcd: crack damage stress; σr: residual stress; εp: plastic strain; εcd: strain at crack damage threshold; εf: failure strain; εr: stress; σf: failure stress; σr: residual stress; εp: plastic strain; εcd: strain at crack damage threshold; εf: residual strain; E: Young’s modulus; H: hardening modulus and M: drop modulus (modified from [17]). failure strain; εr: residual strain; E: Young’s modulus; H: hardening modulus and M: drop modulus The(modified process from of[17]). rock failure is essentially a balancing process of energy absorption and release [17,25–29]. During the pre-peak stage, the rock undergoes elastic and plastic deformation. The process of rock failure is essentially a balancing process of energy absorption and release The total elastic energy (Wet) accumulated during elastic deformation increases the internal energy of [17,25–29]. During the pre-peak stage, the rock undergoes elastic and plastic deformation. The total rock. Also, plastic energy (Wp) dissipates during plastic deformation due to crack closure and frictional elastic energy (Wet) accumulated during elastic deformation increases the internal energy of rock. sliding. A more brittle rock can turn more the absorbed external energy into elastic energy instead Also, plastic energy (Wp) dissipates during plastic deformation due to crack closure and frictional of plastic energy, and the more elastic energy accumulated during loading favors rock rupture and sliding. A more brittle rock can turn more the absorbed external energy into elastic energy instead of fracture extension. plastic energy, and the more elastic energy accumulated during loading favors rock rupture and According to the characteristics of rock behavior in the post-peak region, the failure modes were fracture extension. classified into two types [30]. As Figure2 illustrates, the negative drop modulus ( M < 0) corresponds to According to the characteristics of rock behavior in the post-peak region, the failure modes Class I behavior, which means that additional energy is required to support rock failure as the amount were classified into two types [30]. As Figure 2 illustrates, the negative drop modulus (M < 0) of elastic energy from material is not sufficient. The positive drop modulus (M > 0) corresponds to corresponds to Class I behavior, which means that additional energy is required to support rock Class II behavior, which means that rock failure can be self-sustained and fully developed. The excess failure as the amount of elastic energy from material is not sufficient. The positive drop modulus (M energy (the yellow area in Figure2) in Class II failure is consumed to overcome the confinement > 0) corresponds to Class II behavior, which means that rock failure can be self-sustained and fully pressure and transformed into the failure process dynamics [8]. Hydrocarbon-bearing reservoirs are developed. The excess energy (the yellow area in Figure 2) in Class II failure is consumed to generally characterized by Class I behavior; therefore, Class II behavior is not discussed in this research. overcome the confinement pressure and transformed into the failure process dynamics [8]. Hydrocarbon-bearing reservoirs are generally characterized by Class I behavior; therefore, Class II behavior is not discussed in this research.

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FigureFigure 2. 2. Post-peakPost-peak energyenergy balancebalance for rocks of class Ⅰ I and class Ⅱ II,, EE:: Young’s Young’s modulus; modulus; MM: :drop drop modulusmodulus (modiﬁed (modified from from [ 8[8]).]).

AfterAfter thethe peak,peak, thethe accumulatedaccumulated elasticelastic energy is gradually released released to to form form macro-fractures. macro-fractures. However,However, because because of of the the plasticity plasticity of materialsof materials and and the etheffect effect of confining of confining pressure, pressure, the elastic the elastic energy storedenergy before stored the before peak isthe not peak enough is not for enough complete for self-sustainingcomplete self-sustaining rock failure. rock Therefore, failure. Therefore, additional energyadditional (the blueenergy area (the in Figureblue area2) provided in Figure by 2) loadingprovided is needed.by loading Compared is needed. to Compared brittle rocks, to ductilebrittle rocksrocks, require ductile more rocks additional require energymore toadditional maintain energy rupture. to At main the endtain ofrupture. the compression At the end experiment, of the therecompression is still some experiment, energy known there asis thestill residual some en elasticergy energyknown (Weras the) existing residual in theelastic rocks. energy (Wer) existingOverall, in the the rocks. stress-strain curves provide a comprehensive insight into rock deformation and brittle failureOverall, mechanisms the stress-strain under various curv loadinges provide conditions. a comprehensive Under certain insight ambient into rock conditions, deformation all of and the internalbrittle failure factors mechanisms affecting brittleness under canvarious be considered loading conditions. in this process. Under An certain accurate ambient brittleness conditions, evaluation all methodof the internal based on factors energy affecting balance brittleness rule can be can obtained be considered through in analyzing this process. the entire An accurate stress-strain brittleness curve. TheevaluationBI is defined method as follows based on [17 ]:energy balance rule can be obtained through analyzing the entire stress-strain curve. The BI is defined as follows [17]: 1 1 We We BI = (BI + BI ) = ( + ), (4) 21 1 2 2 1WrWe Wet +WeWp (4) BI = (BI + BI ) = ( + ) 2 1 2 2 Wr Wet +Wp 1 , Wet = σ2, (5) 2E f 1 2 (5) Wet = σ1 2 2 We = Wet Wer = (σf σr ), (6) − 2E2E ,f − Z 1 εr Wr = Wet + Wa Wer = (σ2 σ2) + σdε, (7) − 2E 1 f − 2r 2 (6) We = Wet −Wer = ( − ε)f σ f σ r Z 2E ε f 1 , Wp = Wt Wet = σdε σ2, (8) − − 2E f 0 ε 1 2 2 r (7) Wr = Wet +Wa −Wer = (σ −σ ) + σdε The corresponding definitions of the calculation parametersf r are presentedε in Figure1. We is the 2E  f consumed elastic energy, which is the difference between the total elastic energy, (Wet) and the residual elastic energy (Wer); Wt is the total consumed energy during the pre-peak stage; Wr represents the ε f 1 (8) rupture energy, which is the sum of the= total− elastic= energyσ ε − (Wet)σ and2 additional energy consumed Wp Wt Wet d f 0 by rock failure from loading the system (the blue area in Figure21E); and, Wp represents the dissipated plastic energy during the pre-peak region. The corresponding definitions of the calculation parameters are presented in Figure 1. We is the In this model, BI determines the extent to which the fracturing process occurs in a self-sustaining consumed elastic energy,1 which is the difference between the total elastic energy (Wet) and the manner. BI represents the fraction of the total absorbed energy during the pre-peak region released in residual elastic2 energy (Wer); Wt is the total consumed energy during the pre-peak stage; Wr the post-peak rupture process. These two values vary in the range from 0 to 1. Accordingly, the value represents the rupture energy, which is the sum of the total elastic energy (Wet) and additional of BI changes continuously from 0 to 1, and the degree of brittleness transforms from full ductility to energy consumed by rock failure from loading the system (the blue area in Figure 1); and Wp absoluterepresents brittleness. the dissipated plastic energy during the pre-peak region. 3. MaterialsIn thisand model, Measurements BI1 determines the extent to which the fracturing process occurs in a self-sustaining manner. BI2 represents the fraction of the total absorbed energy during the pre-peak 3.1.region Materials released in the post-peak rupture process. These two values vary in the range from 0 to 1. Accordingly, the value of BI changes continuously from 0 to 1, and the degree of brittleness Nine drill core samples from well SY3 underwent a series of laboratory tests (Figure3). Two of transforms from full ductility to absolute brittleness. the samples are from the Upper Ordovician Baota Formation. The remaining seven are from

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3. Materials and Measurements

3.1. Materials

EnergiesNine2020 ,drill13, 388 core samples from well SY3 underwent a series of laboratory tests (Figure 3). Two6 of of 22 the samples are from the Upper Ordovician Baota Formation. The remaining seven are from the Upper Ordovician Wufeng Formation and Lower Silurian Longmaxi Formation, which are theimportant Upper shale Ordovician gas-bearing Wufeng layers Formation in the Sichuan and Lower Basin Silurian and its Longmaxiperipheral Formation, regions in whichsouthwest are importantChina. The shalepaleogeographic gas-bearing settings layers in of the these Sichuan format Basinions in and the its study peripheral area have regions been in reported southwest in China.previous The works paleogeographic [31,32]. Briefly, settings the upper of these member formations of the in theBaota study Formation area have mainly been reportedconsists inof previouslimestone works with [ 31polygonal,32]. Brieﬂy, reticulate the upper structures member of thedeveloped Baota Formation in a platform mainly consistsenvironment. of limestone The withWufeng-Longmaxi polygonal reticulate Formation structures can be developeddivided into in two a platform sections environment. according to their The Wufeng-Longmaxisedimentary facies. FormationThe Lower can Member be divided of the into Wufeng-Longmaxi two sections according Format to theirions sedimentary is dominantly facies. made The up Lower of deep Member black of thesiliceous Wufeng-Longmaxi shale, carbonaceous Formations shale, is dominantly and gray-b madelack up shale of deep [33], black indicating siliceous a shale, deep-water carbonaceous shelf shale,sedimentary and gray-black environment. shale [The33], primary indicating lithology a deep-water of the shelfUpper sedimentary Member of environment. the Longmaxi The Formation primary lithologyis gray, silty of the mudstone, Upper Member and argillaceous of the Longmaxi siltstone, Formation deposited is gray,in a shallow-water silty mudstone, shelf and sedimentary argillaceous siltstone,environment. deposited in a shallow-water shelf sedimentary environment.

Figure 3. GeologicalGeological drilling histograms of the Wufeng-Longmaxi Formations from well SY3. 3.2. Measurements 3.2. Measurements Triaxial compression tests were used to evaluate the failure characteristics of the rock samples. Triaxial compression tests were used to evaluate the failure characteristics of the rock samples. The external loading can be described as follows: The external loading can be described as follows:

σσσσ1 ==+σc + σa; σ2σσσ= ==σ3 = σc (9) 1ca; 23c where σ1, σ2, σ3 are the principal stresses; σa is the axial deviatoric stress; σc is the confining stress. A TAW-1000 stiff autonomous triaxial compression experimental machine (Aojin industry, Guangdong, China) with a loading capacity of 1000 KN and a maximum confining pressure up to 80 MPa is adopted as the testing apparatus. In this study, confining pressures of 30 MPa were designated for simulating true in-situ stress, and cylindrical samples were cored to 25 mm in diameter Energies 2020, 13, 388 7 of 22 and 60 mm in length. Defective rock samples caused during sample preparation were removed. To avoid the influence of the bedding planes and loading rate on rock failure behavior, all specimens were loaded at a strain rate of 0.12 mm/min, and bedding planes were perpendicular to the axis of the cylinders. After triaxial compression tests, the microstructures of the rock samples were also studied through various analytical methods such as optical microscopy, scanning electron microscopy (SEM). Also, the mineral compositions of the samples were determined by X-ray diffraction analysis (XRD), and the specific method of XRD analysis was consistent with that in reference [34]. The experimental results were shown in Table1.

Table 1. Summary of measured compositional properties of tested samples. Qz (quartz), Fsp (feldspar), Py (pyrite), Cb (carbonate minerals), TOC (total organic carbon).

Samples Formation Qz (wt%) Fsp (wt%) Cb (wt%) Clay (wt%) Py (wt%) TOC (wt%) 1 48.0 20.0 11.0 19.0 2.0 0.22 2Longmaxi 30.0 10.0 40.0 16.0 4.0 1.92 3 45.0 16.0 4.0 30.0 5.0 1.65 4 62.0 16.0 2.0 18.0 2.0 2.27 5 72.0 9.0 5.0 14.0 0 1.75 Wufeng 6 53.0 13.0 16.0 17.0 1.0 6.48 7 75.0 2.0 4.0 19.0 0 2.31 8 15.6 3.8 71.2 9.4 0 0.34 Baota 9 17.8 4.3 75.7 2.2 0 1.02

4. Results

4.1. The Diﬀerence of Mechanism between Diverse Brittleness Indices The energy-based brittleness indices derived from rock stress-strain curves of the rock samples vary from 0.18 to 0.78 (Table2). The post-peak curves of samples 1 and 4 sharply dropped from the peak stress (σf) to a low residual stress (σr) (Figure4). The residual elastic energy ( Wer) and post-peak fracture energy (Wr) of samples 1 and 4 are small, indicating that the total elastic energy (Wet) accumulated in pre-peak stage is mostly used for the fracture of samples, and less additional energy (Wa) is needed to maintain the fracture extension during the failure process. This type of rock is conducive to the formation of fractures. Consequently, samples 1 and 4 have high brittleness indices of 0.63 and 0.78, respectively. The post-peak curves of samples 7 and 9 smoothly dropped from the peak stress (σf) to a high residual stress (σr), and the residual elastic energy (Wer) and rupture energy (Wr) are relatively large. This indicates that the consumed elastic energy (We) is insuﬃcient to maintain fractures propagation, and additional (Wa) is necessary, so this type of rock is hard to form fractures. Therefore, samples 7 and 9 have low brittleness indices of 0.28 and 0.18, respectively.

4.2. The Effect of Confining Pressure on Brittleness According to the classification method of brittle and plastic minerals proposed in [13], sample 3 has a large weight fraction of clay minerals (30%). Sample 8 has a significant weight fraction of brittle minerals (17.8% quartz, 4.3% feldspar, 75.5% carbonate minerals) and low weight fraction of clay minerals (2.2%). However, these two samples both exhibit obvious plastic deformation before the peak, and the plastic energy of samples 3 and 8 are high, 147 and 98, respectively (Table2). Hence, rock plasticity is not only affected by clay mineral content but also high confining stress. This is consistent with the well-established fact that rocks tend to show higher plastic characteristics at elevated confining stresses [7,21]. In addition, the post-peak curves for all rock samples except for samples 1 and 4 slowly decreased from the peak stress (σf) to residual stress (σr) (Figure4). The applied confining pressure hinders the Energies 2020, 13, 388 8 of 22 radial dilation followed by further blocking the development of the macrocracks during the post-peak region, thus leading to decreased brittleness [35].

Table 2. Summary of mechanical parameters obtained from complete stress-strain curves of tested samples. E (Young’s modulus), ν (Poisson’s ratio), σf (failure stress), σr (residual stress), Wet (total elastic energy), Wer (residual elastic energy), We (consumed elastic energy), Wr (rupture energy), Wp (plastic energy), Wa (additional energy), BI1(We/Wr), BI2 (We/(Wet+Wp)), BI (brittleness index).

EnergiesSamples 2020, Formation13, x FOR PEERE (Gpa) REVIEWν σf (Mpa) σr (Mpa) Wet Wer We Wr Wp Wa BI1 BI2 BI8 of 23 1 22.4 0.21 123 60 31 7 23 33 12 9 0.72 0.55 0.63 is consistent2Longmaxi with the 31.7 well-established 0.30 242 fact 150that ro 102cks tend 39 to 63 show 114 higher 0 plastic 51 0.55 characteristics 0.62 0.58 at 3 35.3 0.28 266 90 140 16 124 266 147 142 0.46 0.43 0.45 elevated confining stresses [7,21]. 4 26.9 0.19 228 105 91 19 72 72 48 17 1.00 0.55 0.78 In5 addition, the 42.1post-peak 0.32 curves 262 for 100 all rock 52 samples 21 31 except 74 for 0 samples 43 0.43 1 and 0.48 4 0.45slowly Wufeng decreased6 from the peak 35.1 stress 0.16 (σf) 264to residual 173 stress 172 (σr 74) (Figure 98 4). 185 The 0applied 87 confining 0.50 0.56 pressure 0.53 7 56.7 0.22 275 200 96 51 45 188 39 143 0.24 0.32 0.28 hinders the radial dilation followed by further blocking the development of the macrocracks during 8 37.8 0.23 244 170 61 30 31 73 98 41 0.43 0.19 0.31 Baota the post-peak9 region, 55.5thus leading 0.23 to 269 decreased 225 brittleness 74 54 [35]. 20 182 0 162 0.10 0.26 0.18

Figure 4. Stress-strain curves of diﬀerent samples under triaxial compression. Figure 4. Stress-strain curves of different samples under triaxial compression. 5. Discussion Table 2. Summary of mechanical parameters obtained from complete stress-strain curves of tested 5.1. Correlationssamples. E of(Young’s Brittleness modulus), and Elastic ν (Poisson’s Parameters ratio), σf (failure stress), σr (residual stress), Wet (total elastic energy), Wer (residual elastic energy), We (consumed elastic energy), Wr (rupture energy), The brittleness index based on elastic parameters are calculated by Equation (1) and compared Wp (plastic energy), Wa (additional energy), BI1(We/Wr), BI2 (We/(Wet+Wp)), BI (brittleness index). with the energy-based brittleness indices derived from rock stress-strain curves. There is a negative correlationSamples between Formation these E two (Gpa) types ν of𝝈𝒇 calculations (Mpa) 𝝈𝒓 (Mpa) (Figure Wet5 ).Wer In orderWe Wr to Wp explain Wa thisBI1 phenomenon,BI2 BI the relationship1 between the22.4 elastic0.21 parameters 123 60 (Young’s 31 modulus 7 23 33 and 12 Poisson’s 9 0.72 ratio)0.55 0.63 and the 2 Longmaxi 31.7 0.30 242 150 102 39 63 114 0 51 0.55 0.62 0.58 energy-based brittleness index derived from rock stress-strain curves are analyzed. 3 35.3 0.28 266 90 140 16 124 266 147 142 0.46 0.43 0.45 4 26.9 0.19 228 105 91 19 72 72 48 17 1.00 0.55 0.78 5 42.1 0.32 262 100 52 21 31 74 0 43 0.43 0.48 0.45 Wufeng 6 35.1 0.16 264 173 172 74 98 185 0 87 0.50 0.56 0.53 7 56.7 0.22 275 200 96 51 45 188 39 143 0.24 0.32 0.28 8 37.8 0.23 244 170 61 30 31 73 98 41 0.43 0.19 0.31 Baota 9 55.5 0.23 269 225 74 54 20 182 0 162 0.10 0.26 0.18

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5. Discussion

5.1. Correlations of Brittleness and Elastic Parameters The brittleness index based on elastic parameters are calculated by Equation (1) and compared with the energy-based brittleness indices derived from rock stress-strain curves. There is a negative correlation between these two types of calculations (Figure 5). In order to explain this phenomenon, the relationship between the elastic parameters (Young’s modulus and Poisson’s ratio) and the Energies 2020, 13, 388 9 of 22 energy-based brittleness index derived from rock stress-strain curves are analyzed.

Figure 5. ComparisonComparison between between the the energy-based energy-based BI andand elastic elastic BI..

The relationshiprelationship betweenbetween Young’s Young’s modulus modulus and an brittlenessd brittleness has been has discussedbeen discussed by many by scholars. many scholars.The brittleness The brittleness evaluation methodevaluation proposed method in [prop10] supposesosed in that[10] asupposes higher Young’s that a modulus higher resultsYoung’s in modulusa more brittle results rock. in Ina more [33], itbrittle is believed rock. thatIn [33], a formation it is believed with higherthat a Young’sformation modulus with higher values Young’s induces modulusmore microcracks, values induces which shows more amicrocracks, strong brittleness which inducing shows a morea strong complex brittleness hydraulic inducing fracture a system. more complexOn the contrary, hydraulic the fracture paper [ 36system.] proposes On the that contrary, rocks with the apaper high Young’s[36] proposes modulus that onlyrocks create with shortera high Young’sfracture aperturesmodulus foronly their create limited shorter deformation fracture ability. apertures In contrast, for their rocks limited with deformation a low Young’s ability. modulus In contrast,tend to formrocks fractures with a low with Young’s larger averagemodulus apertures. tend to form This fractures leads to with fracturing larger average fluids penetrating apertures. Thisthe fracture leads to tips fracturing quickly, fluids resulting penetrating in a greater the fracturefracture conductivity.tips quickly, resulting The experimental in a greater data fracture in this conductivity.study indicates The that experimental Young’s modulus data in is negativelythis study correlatedindicates that with Young’s energy-based modulus brittleness is negatively indices correlated(Figure6a). with As shown energy-based in Figure brittleness6b, samples indices 5, 7, 8, (Figur and 9,e which6a). As have shown higher in Figure Young’s 6b, modulus samples values, 5, 7, 8, andconsume 9, which less have elastic higher energy Young’s (We). Specifically, modulus values, the stored consume elastic less energy elastic in rocksenergy with (We higher). Specifically, Young’s themodulus stored valueselastic isenergy not enough in rocks to with self-sustain higher Youn the developmentg’s modulus values of cracks, is not leading enough to to the self-sustain reduction theof the development brittleness index.of cracks, The relationshipleading to the between reduct theion stress-strain of the brittleness curve and index. Young’s The modulus relationship also betweenfurther proves the stress-strain this conclusion curve (Figure and Young’s6c,d). Young’s modulu moduluss also further ( E) of proves the specimens this conclusion tend to increase(Figure with the increasing peak strength (σ ) (Figure7), which is also verified by others [ 37,38]. Therefore, 6c,d). Young’s modulus (E) of the specimensf tend to increase with the increasing peak strength (σf) (Figureassuming 7), otherwhich parameters is also verified remain by constant, others [37,38]. an increase Therefore, of Young’s assuming modulus other (E )parameters and peak strength remain (σ ) results in decreased the consumed elastic energy (the difference between total elastic energy (Wet) constant,f an increase of Young’s modulus (E) and peak strength (σf) results in decreased the consumedand residual elastic elastic energy energy (the (Wer differ)), andence additional between energytotal elastic (the sum energy of blue (Wet area) and and residual orange areaelastic as energyshown in(Wer Figure)), and6c,d) additional is necessary energy to maintain (the sum the of developmentblue area and of orange cracks. area This as results shown in in the Figure decreased 6c,d) isbrittleness necessary of to the maintain rocks. the development of cracks. This results in the decreased brittleness of the rocks.

Energies 2020, 13, 388 10 of 22 Energies 2020, 13, x FOR PEER REVIEW 10 of 23 Energies 2020, 13, x FOR PEER REVIEW 10 of 23

Figure 6. The relationship between brittleness index and Young’s modulus. (a) A negative Figure 6.6.The The relationship relationship between between brittleness brittlen indexess index and Young’s and Young’s modulus. modulus. (a) A negative (a) A correlation negative correlation of Young’s modulus and energy-based BI; (b) Samples 5, 7, 8, and 9 with higher Young’s correlationof Young’s of modulus Young’s and modulus energy-based and energy-basedBI;(b) Samples BI; (b) 5, Samples 7, 8, and 5, 9 7, with 8, and higher 9 with Young’s higher modulusYoung’s modulus consume less elastic energy (We, the difference between Wet and Wer); (c,d). The change of modulusconsume lessconsume elastic less energy elastic (We, energythe di (ﬀWe,erence the betweendifferenceWet betweenand Wer Wet); (c and,d). TheWer change); (c,d). ofThe energy change with of energy with the increase of Young’s modulus and peakWp strength (σf). Wp (plasticWet energy), Wet (total energythe increase with ofthe Young’s increase modulus of Young’s and modulus peak strength and peak (σf). strength(plastic (σ energy),f). Wp (plastic(total energy), elastic Wet energy), (total elastic energy), Wer (residual elastic energy). elasticWer (residual energy), elastic Wer (residual energy). elastic energy).

Figure 7. The relationship between Young’s modulus and peakpeak strength.strength. Figure 7. The relationship between Young’s modulus and peak strength. TheThe results do not indicate that all materials with a lower Young’s modulus are more brittle. The results do not indicate that all materials with a lower Young’s modulus are more brittle. Young’sYoung’s modulusmodulus measures measures a rock’sa rock’s hardness hardness rather rather than brittleness,than brittleness, so materials so materials with higher with Young’s higher Young’s modulus measures a rock’s hardness rather than brittleness, so materials with higher modulusYoung’s modulus are diﬃcult are todifficult break downto break simply down due simply to the due higher to the fracture higher initiationfracture initiation stress state stress needed, state Young’s modulus are difficult to break down simply due to the higher fracture initiation stress state forneeded, example, for example, diamond anddiamond granite and [39 granite]. On the [39]. other On hand, the other complicated hand, complicated networks of fracturesnetworks areof needed, for example, diamond and granite [39]. On the other hand, complicated networks of fractures are difficult to generate in materials with low Young’s modulus, such as rubber and wax. fractures are difficult to generate in materials with low Young’s modulus, such as rubber and wax.

Energies 2020, 13, x FOR PEER REVIEW 11 of 23

Therefore, Young’s modulus should have a reasonable range of values for ideal brittle materials. The relationship between Young’s modulus and brittleness can be determined by Equation. (10). When Energies 2020, 13, 388 11 of 22 the energy absorbed per unit surface area attains its critical value (GC), fractures propagate along the pre-existing fractures. Materials with lower Gc will generate more fractures, supposing the given energydifficult is tokept generate constant. in materialsThe critical with value low (Gc Young’s) is defined modulus, below such[13]: as rubber and wax. Therefore, Young’s modulus should have a reasonable(0.313 range+ 0 of.027 values× E) for2 ideal brittle materials. The relationship between Young’s modulusGc and= (1 brittleness−ν 2 ) can be determined×10 by3 Equation. (10). When the energy(10) E absorbed per unit surface area attains its critical value (GC), fractures propagate along the pre-existing fractures.When Materials Poisson’s with ratio lower (ν) remainsGc will constant, generate the more change fractures, in Young’s supposing modulus the can given then energy analyze is kept the relationshipconstant. The between critical valueGc and (Gc E). isAs defined Young’s below modulus [13]: increases, Gc first decreases then increases. When Young’s modulus is 11.6 GPa, Gc has reached its minimum value. However, the value of (0.313 + 0.027 E)2 Young’s modulus is generally greaterGc = (1 thanν2 )11.6 GPa under× in-situ 10stress3 for most sedimentary rocks(10) [13], hence rocks with a higher Young’s− modulus are difficultE to fracture.× Energy-basedWhen Poisson’s brittleness ratio (ν) indices remains do constant, not correlate the change with Poisson’s in Young’s ratio modulus (Figure 8). can Under then analyzetriaxial compression,the relationship the between applied confiningGc and E. pressure As Young’s tends modulus to hinder increases, the radialGc dilatifirst decreaseson during thenthe post-peak increases. region.When Young’s Consequently, modulus most is 11.6 Poisson’s GPa, Gc ratiohas reached values itsfluctuate minimum in a value. small However,range of 0.2 the to value 0.3, ofleading Young’s to themodulus weak iscorrelation generally greaterbetween than Poisson’s 11.6 GPa ratio under and in-situ brittleness. stress This for most observation sedimentary is also rocks confirmed [13], hence by othersrocks with[17,35]. a higher Young’s modulus are difficult to fracture. BecauseEnergy-based the energy-based brittleness indicesbrittleness do notindex correlate of rock with negatively Poisson’s correlates ratio (Figure with 8Young’s). Under modulus triaxial andcompression, weakly related the applied to Poisson’s confining ratio, pressure the brittlene tendsss to index hinder calculated the radial by dilation elastic duringparameters the post-peak is vastly differentregion. Consequently, from the actual most brittleness Poisson’s value, ratio that values is, the fluctuate energy-based in a small brittleness range of 0.2index to 0.3,in this leading study. to Therefore,the weak correlation the brittleness between evaluation Poisson’s method ratio and base brittleness.d on elastic This parameters observation has is severe also confirmed theoretical by defectsothers [that17,35 limit]. its application.

Figure 8. The relationship between brittleness index and Poisson’s ratio. Figure 8. The relationship between brittleness index and Poisson’s ratio. Because the energy-based brittleness index of rock negatively correlates with Young’s modulus 5.2.and Correlations weakly related of Brittleness to Poisson’s with ratio,Mineral the Composition brittleness index calculated by elastic parameters is vastly diﬀerentThe frombrittleness the actual index brittleness of samples value, based that on is,mineral the energy-based composition brittleness are calculated index following in this study. the formulaTherefore, proposed the brittleness by [13,40]: evaluation method based on elastic parameters has severe theoretical defects that limit its application. =+++ (11) BIWWWWWmi() Qz Fsp Cb Py/ Tot 5.2. Correlations of Brittleness with Mineral Composition where BImi is the mineral BI and is dimensionless; WQz is the weight fraction of quartz, %; WFsp is the weightThe fraction brittleness of feldspar, index of%; samplesWCb is the based weight on fraction mineral of composition carbonate minerals, are calculated %; WPyfollowing is the weight the fractionformula of proposed pyrite, %; by and [13, 40WTot]: is the weight fraction of total minerals, %. BImi = WQz + WFsp + WCb + WPy /WTot (11)

Energies 2020, 13, 388 12 of 22

where BImi is the mineral BI and is dimensionless; WQz is the weight fraction of quartz, %; WFsp is the Energiesweight 2020 fraction, 13, x FOR of feldspar, PEER REVIEW %; W Cb is the weight fraction of carbonate minerals, %; WPy is the12 weight of 23 fraction of pyrite, %; and WTot is the weight fraction of total minerals, %. InIn thisthis formula,formula, quartz, quartz, feldspar, feldspar, carbonate carbonate minerals, minerals, and pyriteand pyrite are regarded are regarded as brittle as minerals, brittle minerals,while clays while are regarded clays are as plasticregarded minerals. as plasti For thec minerals. method basedFor onthe mineral method compositions, based on mineral a higher compositions,content of brittle a higher minerals content and lower of brittle content minerals of plastic and minerals lower content leads to of a moreplastic brittle minerals rock (higherleads toBI a). moreThe calculated brittle rock brittleness (higher indices BI). The attained calculated from rock brittleness mineral compositionsindices attained are vastlyfrom higherrock mineral than the compositionsenergy-based are brittleness vastly higher index than (Figure the9 ).energy The mineral-based brittlenessBI of samples index 1, (Figure 2, 3, 4 and 9). The 6 are mineral in the rangeBI of samplesof 0.70–0.84, 1, 2, with3, 4 anand average 6 are in of the 0.8. range The energy-based of 0.70–0.84, brittlenesswith an average indices of of 0.8. these The five energy-based samples are brittlenessin the range indices of 0.45–0.78, of these with five an samples average ofare 0.6. in Althoughthe range there of 0.45–0 is not.78, a strong with positivean average correlation of 0.6. Althoughbetween thesethere twois not calculations a strong positive for these correlati five samples,on between generally these speaking, two calculations the differences for these between five samples,these two generallyBI are still speaking, within the a reasonable differences range. between The these minor two di BIfference are still may within be influenceda reasonable by range. other Thefactors, minor such difference as rock texture,may be theinfluenced content by of other organic fact matterors, such and as porosity. rock textur However,e, the content it is worth of organic noting matterthat the and mineral porosity.BI of However, samples 5,it 7,is 8,worth and 9noting are high, that inthe the mineral range ofBI 0.81–0.98,of samples with 5, 7, an 8, averageand 9 are of high,0.89, butin the their range energy-based of 0.81–0.98, brittleness with an indicesaverage are of low,0.89, inbut a rangetheir energy-base of 0.18–0.45,d with brittleness an average indices of 0.28.are low,There in is aa range considerable of 0.18–0.45, difference with betweenan average the of two 0.28. calculation There is methods a considerable for these difference four samples between (marked the twoby a calculation red dotted methods line in Figure for these9). four samples (marked by a red dotted line in Figure 9).

FigureFigure 9. 9. ComparisonComparison between between the the energy-based energy-based BIBI andand the the mineral mineral BIBI..

TheThe quartz quartz and and carbonate carbonate contents contents in in samples samples 5, 5, 7, 7, 8, 8, and and 9 9are are high, high, exceeding exceeding 70% 70% (Table (Table 2).2). TheThe Young’s Young’s modulus modulus of of these these four four samples samples is also is also relatively relatively high, high, with with an average an average of 48 ofGPa. 48 This GPa. indicatesThis indicates that they that have they havea stronger a stronger cohesive cohesive strength. strength. Based Based on the on SEM the SEMresults results (Figure (Figure 10), the10), mineralsthe minerals in these in these four four samples samples are aretightly tightly structured structured and and cemented, cemented, and and there there are are few few weak weak mechanicalmechanical interfaces interfaces in in these these rocks rocks (Figure (Figure 10a).10a). The The cracks cracks that that do do exist exist terminate terminate into into the the uniform uniform andand compact compact rock rock texture texture (Figure (Figure 10b).10b). This This indicates indicates why why the the four four specimens specimens are are so so hard hard to to be be fractured,fractured, which which is is a a result result of of their their excessive excessive amount amount of of single single brittle brittle mineral mineral (quartz (quartz or or carbonate carbonate minerals).minerals). By contrast, althoughalthough the the sample sample 1, 1, 2, 4,2, and4, and 6 mainly 6 mainly consist consist of quartz, of quartz, the content the content of quartz of quartzis less is than less 70%. than 70%. In addition, In addition, appropriate appropriate content content of various of various brittle brittle minerals minerals and and clay clay minerals minerals in inthese these four four samples samples form form many many weak weak mechanical mechanical planes planes existing existing at the at boundaries the boundaries of diﬀ oferent different grains grains(Figure (Figure 10c). These 10c). weak These structural weak surfacesstructural are surfac conducivees are to conducive crack initiation, to crack then initiation, the generated then cracks the generatedbypass mineral cracks particles bypass andmineral extend particles to interact and with extend other to cracks, interact leading with toother the formationcracks, leading of a complex to the formationnetwork cracking of a complex system network (Figure 10 crackingd). Overall, system the excessive(Figure 10d). content Overall, of quartz the orexcessive carbonate content minerals of quartzhinder or fracture carbonate initiation minerals and hinder propagation. fracture initiation and propagation.

Energies 2020, 13, 388 13 of 22 Energies 2020, 13, x FOR PEER REVIEW 13 of 23

FigureFigure 10. 10.Microstructural Microstructural characteristics characteristics ofof rockrock samples in in SEM. SEM. (a (a) )Sample Sample 5 5mainly mainly consists consists of ofone one brittlebrittle mineral, mineral, and and there there are are few few weak weak structural structural planes; planes;( (bb)) AA crackcrack bypassesbypasses a particle and and extends extends a shorta short distance distance around around the grain, the grain, and then and isthen terminated is terminated due to due the uniformto the uniform and compact and compact rock texture rock in sampletexture 5; (inc) sample Sample 5; 4 is(c) made Sample up 4 of is appropriate made up of content appropriate of various content brittle of various minerals, brittle so thereminerals, are many so weakthere structural are many planes weak between structural diﬀ planeserent mineral between particles; different (d mineral) When theparticles; crack propagates,(d) When the it connectscrack thepropagates, weak structural it connects surface the existing weak structural along the surface edge of ex theisting grains, along leading the edge to of a longerthe grains, distance leading extension to a in samplelonger distance 4. extension in sample 4.

BecauseBecause an an excessive excessive amount amount of single of single brittle bri mineralsttle minerals (quartz (quartz or carbonate or carbonate minerals) minerals) diminishes rockdiminishes brittleness, rock the brittleness, relationship the relationship between the betw brittlenesseen the brittleness and various and minerals various minerals (quartz, carbonate(quartz, minerals,carbonate feldspar minerals, and feldspar clay minerals) and clay are minerals) further are analyzed. further analyzed. As Figure As 11 aFigure illustrates, 11a illustrates, when the when quartz contentthe quartz is less content than 70%, is less the rockthan brittleness70%, the rock increases brittleness with theincreases increase with of thethe quartzincrease content. of the However,quartz whencontent. quartz However, content iswhen greater quartz than content 70%, rock is greater brittleness than 70%, suddenly rock brittleness decreases. suddenly The variation decreases. tendency The of Young’svariation modulus tendency of a of rock Young’s with increasing modulus quartzof a rock contents with increasing is the opposite quartz of contents the brittleness is the opposite index. This of is consistentthe brittleness with the index. results This discussed is consistent in Section with 5.1the (Figureresults 11discussedb). In general, in Section the content5.1 (Figure of terrigenous 11b). In mineralsgeneral, (quartz, the content feldspar, of terrigenous and clay minerals) minerals in(qua sedimentaryrtz, feldspar, rocks and is clay positively minerals) correlated in sedimentary with each other.rocks Furthermore, is positively correlated the excessive with each amount other. of Furt quartzhermore, is mainly the excessive authigenic amou quartznt of quartz (Figure is mainly12a) [41 ], andauthigenic the content quartz of authigenic (Figure 12a) quartz [41], is and unrelated the content to the of content authigenic of terrigenous quartz is unrelated minerals to [42 the]. Therefore,content whenof terrigenous the content minerals of quartz [42]. is lowTherefore, (<20%), when such the as co samplesntent of 8quartz and 9 is (Figure low (<20%), 12b), thesuch content as samples of other 8 and 9 (Figure 12b), the content of other terrigenous minerals (feldspar and clay minerals) are also terrigenous minerals (feldspar and clay minerals) are also low. This indicates that the rock consists of low. This indicates that the rock consists of carbonate minerals, and the compact texture of this type carbonate minerals, and the compact texture of this type of rock leads to poor rock brittleness. When the of rock leads to poor rock brittleness. When the quartz content is 20–70%, the existence of quartz content is 20–70%, the existence of terrigenous quartz indicates that the rocks also contain a terrigenous quartz indicates that the rocks also contain a moderate amount of other terrigenous moderate amount of other terrigenous minerals (feldspar and clay) (Figure 12c), along with variable minerals (feldspar and clay) (Figure 12c), along with variable amounts of carbonate minerals. In this amountscase, the of rock carbonate contains minerals. many weak In thismechanical case, the structural rock contains surfaces, many hence weak brittleness mechanical increases structural with surfaces,the increase hence of brittleness quartz content. increases When with quartz the increase content ofexceeds quartz 70% content. in rocks, When such quartz as samples content 5 and exceeds 7 70% in rocks, such as samples 5 and 7 (Figure 12d), the excessive amount of quartz can enhance Young’s modulus, leading to decreased rock brittleness. Energies 2020, 13, x FOR PEER REVIEW 14 of 23 Energies 2020, 13, x FOR PEER REVIEW 14 of 23

(Figure 12d), the excessive amount of quartz can enhance Young’s modulus, leading to decreased Energies(Figure2020 12d),, 13, 388the excessive amount of quartz can enhance Young’s modulus, leading to decreased14 of 22 rockrock brittleness. brittleness.

Figure 11. (a) Relationship between energy-based BI and quartz content; (b) Relationship between FigureFigure 11.11.( a(a)) Relationship Relationship betweenbetween energy-basedenergy-basedBI BIand andquartz quartzcontent; content;( b(b)) Relationship Relationship between between Young’s modulus and quartz content. Young’sYoung’s modulus modulus and and quartz quartz content. content.

Figure 12. Microstructural characteristics of rock samples under an optical microscope and SEM; Qz FigureFigure 12. 12. Microstructural Microstructural characteristics characteristics of of rock rock sample samples sunder under an an optical optical microscope microscope and and SEM; SEM; Qz Qz (quartz); Fsp (feldspar); Cb (carbonate minerals). (a) Amount of authigenic quartz developed in sample (quartz);(quartz); FspFsp (feldspar);(feldspar); CbCb (carbonate(carbonate minerals).minerals). ( a(a) )Amount Amount of of authigenic authigenic quartz quartz developed developed in in sample5; (b) Sample 5; (b) 9Sample mainly 9 consists mainly ofconsists carbonate of carbonate minerals (75.7%), minerals leading (75.7%), to highleading cohesion, to high and cohesion, the rhombic and sample 5; (b) Sample 9 mainlyc consists of carbonate minerals (75.7%), leading to high cohesion, and thecleavage rhombic of calcite cleavage is visible; of calcite ( ) Microstructural is visible; (c) characteristicsMicrostructural of samplecharacteristics 3 in SEM, of sample sample 3 is3 madein SEM, up ofthe the rhombic ideal content cleavage of variousof calcite minerals is visible; (45% (c quartz,) Microstructural 16% feldspar, characteristics and 30% clay of minerals),sample 3 andin SEM, the sample 3 is made up of the ideal content of various minerals (45% quartz, 16% feldspar, and 30% clay amountsample of3 is weak made mechanical up of the structuralideal content surfaces of variou in thes minerals rock is conducive (45% quartz, to the 16% development feldspar, and of fractures. 30% clay minerals), and the amount of weak mechanical structural surfaces in the rock is conducive to the (dminerals),). Under SEM,and the an excessiveamount of amount weak mechanical of quartz (72%) structural in sample surfaces 5 makes in the it hard rock to is form conducive fractures. to the developmentdevelopment of of fractures. fractures. ( d(d).). Under Under SEM, SEM, an an excessive excessive amount amount of of quartz quartz (72%) (72%) in in sample sample 5 5 makes makes it it hardAshard Figure to to form form 13 fractures. afractures. illustrates, when the carbonate mineral content is low (<15%), there is no signiﬁcant correlation between the brittleness index and carbonate mineral content. In this case, when the rocks are mainly composed of quartz, they show poor brittleness, such as samples 5 and 7. By contrast, when Energies 2020, 13, x FOR PEER REVIEW 15 of 23

As Figure 13a illustrates, when the carbonate mineral content is low (<15%), there is no Energiessignificant2020, 13correlation, 388 between the brittleness index and carbonate mineral content. In this15 case, of 22 when the rocks are mainly composed of quartz, they show poor brittleness, such as samples 5 and 7. By contrast, when the quartz content of rocks is in an appropriate range of 20–70%, the rocks show thegood quartz brittleness, content such of rocks as samples is in an 1 appropriate and 4. For sample range of 2, 20–70%, the carbonate the rocks mineral show content good brittleness, was 40%, such and asrock samples brittleness 1 and was 4. For 0.58, sample indicating 2, the carbonatethat an appropriate mineral content amount was of 40%, carbonate and rock minerals brittleness benefit was rock 0.58, indicatingbrittleness. that For an samples appropriate 8 and amount 9, which of carbonateboth have minerals a high content beneﬁt rockof carbonate brittleness. minerals For samples (>70%), 8 andthe 9,brittleness which both coefficients have a high suddenly content decrease. of carbonate Similarly, minerals the (> Young’s70%), the modulus brittleness of coesamplesﬃcients 8 and suddenly 9 are decrease.also relatively Similarly, high the(Figure Young’s 13b). modulus of samples 8 and 9 are also relatively high (Figure 13b).

Figure 13.13. (a) Relationship betweenbetween energy-basedenergy-based BI and carbonate mineral content;content; ((b)) RelationshipRelationship between Young’s modulusmodulus andand carbonatecarbonate mineralsminerals content.content.

Feldspar content is positively correlated with the energy-based brittleness index (Figure 14).14). WhenWhen thethe contentcontent ofof feldsparfeldspar isis lowlow ((<10%),<10%), such as samples 5, 7, 8, and 9, because a large proportion of feldspar is of terrigenousterrigenous origin, the content of clay minerals from the samesame terrigenousterrigenous source is also relatively low (Figure (Figure 15).15). This This indicates indicates that that the the rock rock contains contains an an excessive excessive amount amount of ofquartz quartz or orcarbonate carbonate minerals, minerals, resulting resulting in inpoor poor brittleness brittleness of of the the rock. rock. With With the the increase increase of feldspar content ((>10%),>10%), thethe contentcontent of of terrigenous terrigenous clay clay minerals minerals and and quartz quartz in rocks in rocks also also increases. increases. In this In case, this thecase, rocks the arerocks no are longer no longer dominated dominated by a single by a single mineral, mineral, and many and many weak weak mechanical mechanical structural structural surfaces surfaces exist Energies 2020, 13, x FOR PEER REVIEW 16 of 23 betweenexist between diﬀerent different mineral mineral boundaries boundaries in the rocks. in the This rocks. leads This to theleads enhancement to the enhancement of rock brittleness. of rock brittleness. As Figure 16 illustrates, when the clay mineral content is low (<20%), rock brittleness indices increase with the increase of clay mineral content. It should be noted that this phenomenon is mainly caused by the existence of quartz or carbonate minerals, instead of the increase of clay mineral content. This variation tendency and its reasons are the same as that of feldspar. However, when the content of clay minerals exceeds 20%, such as in sample 3, the brittleness suddenly decreases, which indicates that clay minerals decrease the brittleness of rocks. It is concluded that quartz can appropriately characterize the shale brittleness among all minerals. Shale brittleness increases with the increase of quartz content, but an excessive amount of quartz (> 70%) decreases shale brittleness.

Figure 14. The relationship between energy-based BI and feldspar content. Figure 14. The relationship between energy-based BI and feldspar content.

Figure 15. The relationship between the content of clay minerals and feldspar content.

Figure 16. The relationship between energy-based BI and the content of clay minerals.

Energies 2020, 13, x FOR PEER REVIEW 16 of 23

Energies 2020, 13, 388 16 of 22 Figure 14. The relationship between energy-based BI and feldspar content.

Figure 14. The relationship between energy-based BI and feldspar content.

Figure 15. The relationship between the content of clay minerals and feldspar content.

As Figure 16 illustrates, when the clay mineral content is low (<20%), rock brittleness indices increase with the increase of clay mineral content. It should be noted that this phenomenon is mainly caused by the existence of quartz or carbonate minerals, instead of the increase of clay mineral content. This variation tendency and its reasons are the same as that of feldspar. However, when the content of clay minerals exceeds 20%, such as in sample 3, the brittleness suddenly decreases, which indicates that clay mineralsFigure 15. decrease The relationship the brittleness between of the rocks. content of clay minerals and feldspar content.

Figure 16. The relationship between energy-based BI and the content of clay minerals.

Figure 16. TheThe relationship relationship between energy-based BI and the content of clay minerals.

It is concluded that quartz can appropriately characterize the shale brittleness among all minerals. Shale brittleness increases with the increase of quartz content, but an excessive amount of quartz (>70%) decreases shale brittleness.

5.3. Correlation of Brittleness and Fracability As research continues, some have argued that it is not enough to merely use the brittleness index to select fracturing layers [15–17]. The ‘fracability index (FI)’ is a new term that can evaluate the degree to which shale gas and oil reservoirs can be fractured [18]. In recent years, numerous quantification methods for evaluating the fracability of unconventional oil and gas reservoirs have been proposed [43–45]. In these methods, apart from BI, other main factors controlling fracability are Energiesselected2020 to, 13calculate, 388 formation fracability, such as fracture toughness, diagenesis, natural 17crack of 22 density, differential horizontal stress, and so on. However, it should be noted that there are several withproblems these with methods. these First,methods. the BIFirst,derived the BI from derived rock mineralfrom rock compositions mineral compositions or elastic parameters or elastic areparameters utilized are to calculateutilized toFI calculatein these FI methods, in theseyet methods, this has yet been this provenhas been to proven be incorrect to be inincorrect previous in sectionsprevious of sections this paper. of this Second, paper. it isSecond, hard to it develop is hard anto edevelopffective quantificationan effective quantification method of fracability method byof randomlyfracability selectingby randomly the parameters.selecting the Formation parameters. fracability Formation is afracability complicated is a functioncomplicated of various function rock of compositional,various rock compositional, textural, physical, textural, and mechanicalphysical, an propertiesd mechanical under properties specific in-situ under temperatures specific in-situ and pressures.temperatures Other and dominant pressures. factors Other may dominant be neglected factors in thesemay methods.be neglected Third, in thesethese fracability-relatedmethods. Third, factorsthese fracability-related are not independent factors and canare havenot independent a similar impact and oncan fracturing have a similar behavior. impact For example,on fracturing rock elasticbehavior. parameters For example, are closely rock elasti correlatedc parameters with the are mineral closely composition correlated with and subjectedthe mineral to in-situcomposition stress. Consequently,and subjected into thesein-situ methods, stress. Consequently, the effect of rock in mineralthese methods, content onthe fracability effect of rock is calculated mineral content repeatedly, on whichfracability is not is reasonable.calculated repeatedly, Hence, to determinewhich is not the reasonable. correlation Hence, of brittleness to determine and fracability, the correlation we need of tobrittleness assess formation and fracability, fracability we onneed the to premise assess form of evaluatingation fracability the brittleness on the premise index scientifically, of evaluating rather the thanbrittleness randomly. index scientifically, rather than randomly. It can bebe statedstated thatthat scientificscientific fracabilityfracability evaluationevaluation needs toto comprehensivelycomprehensively combine all aaffectingffecting factors according to rockrock failurefailure mechanisms.mechanisms. Fracability is determined by not only the petrophysical propertiesproperties of rockof rock but alsobut geological also geological conditions, conditions, including ambientincluding pressure, ambient temperature, pressure, andtemperature, pre-existing and (natural) pre-existing fractures. (natural) The influencefractures.of The petrophysical influence of properties petrophysical on fracability properties can on be expressedfracability bycan energy-based be expressed BI, by which energy-based has been provenBI, which correct has inbeen this proven paper. correct The next in step thisis paper. to discuss The thenext impact step is ofto geologicaldiscuss the conditions impact of ongeological fracability. conditions on fracability.

5.3.1. In-Situ Earth Stresses

In thethe principal principal stress stress of threeof three directions, directions, the minimum the minimum horizontal horizontal stress (S hstress) is extremely (Sh) is signiﬁcantextremely whensignificant designing when fracturing designing treatments fracturing [46 ].treatmen The simulatedts [46]. fracturesThe simulated will grow fractures perpendicular will grow to Sh, whichperpendicular urges the to inducedSh, which fracture urges the to close.induced In fracture addition, to asclose. the SInh increases,addition, as the the rock Sh increases, failure mode the changesrock failure from mode tensile changes failure tofrom shear tensile failure failure (Figure to 17shear), limiting failure the (Figure vertical 17), growth limiting of fractures the vertical [47]. Therefore,growth of fractures for formations [47]. Therefor with highere, forSh formations, it is diﬃcult with for higher fractures Sh,to it is extend difficult vertically for fractures to connect to extend other pre-existingvertically to connect fractures other [48]. pre-existing fractures [48].

Figure 17. Inﬂuence of minimum horizontal stress (Sh) on failure mode. Figure 17. Influence of minimum horizontal stress (Sh) on failure mode. The minimum horizontal stresses can be estimated using the following equation [49,50]: The minimum horizontal stresses can be estimated using the following equation [49,50]: ν Eνε Sh =𝑆 = ×(S𝑆V −𝛼𝑃αPP)++𝛼𝑃αPP++ (12) 1 ν × − 1ν2 − − where ν is Poisson’s ratio; SV is the vertical stress, psi; α is the Biot’s constant and is a dimensionless where ν is Poisson’s ratio; SV is the vertical stress, psi; α is the Biot’s constant and is a dimensionless value; 𝜀 is the tectonic strain parameter, psi; PP is pore pressure, psi. value; ε is the tectonic strain parameter, psi; PP is pore pressure, psi.

5.3.2. Temperature Eﬀects

Due to thermally activated deformation mechanisms, for instance, the dislocation slide of clay minerals, temperature influences the brittleness of shales. Typically, shales show a transition from brittle to more ductile only when temperature increases by several tens of degrees [3,20]. However, the vertical thickness of the target interval in a region is typically not large enough (<100 m). Assuming a geothermal gradient of 25 ◦C/km (uncertainty <30%), temperature varies only slightly in the objective Energies 2020, 13, 388 18 of 22 layers, which yields no significant change of rock mechanics. Accordingly, the effect of temperature on formation fracturing can be neglected.

5.3.3. Natural Fractures During hydraulic fracturing treatment, natural fractures can facilitate the leakage of fracturing fluid into reservoirs to generate complex hydraulic fractures network, constituting the high-speed path of shale gas output [51,52]. Therefore, to some extent, formations with denser natural fractures are equivalent to a higher fracability. Natural cracks are not taken into consideration in the fracability quantification model in this study. That does not mean that pre-existing fractures are neglected during the process of hydraulic fracturing; rather, formations with denser natural fractures are considered separately. The reasons are as follows. First, the crack density and its effect on fracability is extremely difficult to be quantitatively evaluated [13,53]. Second, fractured strata can be detected by engineering techniques, such as tiltmeters, well logging, and micro-seismic events. These formations should not simply be considered as good fractured layers but should be judged whether they intersect aquifer formations and faults to prevent the upward migration of shale gas. Third, under the same crustal stress state, brittle rocks may contain more abundant fractures compared to ductile rocks [54]. In the history of structural geology, if there is no substantial difference in the tectonic stress between different strata, the degree of fracture development depends on the brittleness characteristic of the rock. In this regard, to some extent, the brittleness of the rock represents the degree of development of natural fractures. Overall, natural cracks are no longer considered as a separate factor in our analysis. In conclusion, the energy-based brittleness index derived from stress-strain curves and minimum horizontal stress are the essential parameters for fracability. Therefore, a new method of fracability evaluation is proposed as follows: BIn + Sh_n FI = , (13) 2

BI BImin BIn = − , (14) BImax BI − min Sh_max Sh S = − , (15) h_n S S h_max − h_min where BIn and Sh_n are normalized brittleness and normalized minimum horizontal stresses. Max and min are the maximum and minimum values of corresponding variables for the investigated formation, respectively. FI is in the range of 0 to 1.0. A formation with FI = 1.0 is the best candidate for hydraulic fracturing, and a formation with FI = 0 is the worst candidate for hydraulic fracturing. In this framework, the most suitable fracturing layers possess a high brittleness index and low minimum horizontal stress. The formation with lower BI and higher Sh compared to the adjacent formations is regarded as a fracture barrier. The main purpose of fracture design is not only the detection of potential layers but also fracture barriers [47]. Fracture barriers not only limit the vertical growth of hydraulic fractures but can also prohibit hydraulic fractures from invading water-bearing layers or fault zones. The minimum horizontal stress and fracability index of the formations in which the nine samples located are calculated and summarized in Table3. Additionally, according to the formula for Sh (Equation (12)), the minimum horizontal stress increases with the increased Poisson’s ratio which ranges between 0.1 and 0.45. The Poisson’s ratio of the nine samples are positively correlated with the minimum horizontal stress of the formations in which the samples are located (Figure 18). Small ﬂuctuation in Poisson’s ratio can also cause substantial changes in the minimum horizontal stress. Therefore, Poisson’s ratio indirectly aﬀects the fracability through controlling the minimum horizontal stress, and the fracability index decreases with an increasing Poisson’s ratio (Figure 19). Energies 2020, 13, x FOR PEER REVIEW 19 of 23 Energies 2020, 13, x FOR PEER REVIEW 19 of 23 The minimum horizontal stress and fracability index of the formations in which the nine The minimum horizontal stress and fracability index of the formations in which the nine samples located are calculated and summarized in Table 3. Additionally, according to the formula samples located are calculated and summarized in Table 3. Additionally, according to the formula for Sh (Equation (12)), the minimum horizontal stress increases with the increased Poisson’s ratio for Sh (Equation (12)), the minimum horizontal stress increases with the increased Poisson’s ratio which ranges between 0.1 and 0.45. The Poisson’s ratio of the nine samples are positively correlated which ranges between 0.1 and 0.45. The Poisson’s ratio of the nine samples are positively correlated with the minimum horizontal stress of the formations in which the samples are located (Figure 18). with the minimum horizontal stress of the formations in which the samples are located (Figure 18). Small fluctuation in Poisson’s ratio can also cause substantial changes in the minimum horizontal Small fluctuation in Poisson’s ratio can also cause substantial changes in the minimum horizontal stress. Therefore, Poisson’s ratio indirectly affects the fracability through controlling the minimum stress. Therefore, Poisson’s ratio indirectly affects the fracability through controlling the minimum horizontalEnergies 2020 ,stress,13, 388 and the fracability index decreases with an increasing Poisson’s ratio (Figure19 19). of 22 horizontal stress, and the fracability index decreases with an increasing Poisson’s ratio (Figure 19).

Table 3. The value of Sh and fracability index of nine samples. Table 3. The value of Sh andand fracability fracability index index of of nine nine samples. Sample Sh (Mpa) Sh_n BI BIn FI SampleSample SSh (Mpa) SSh_n BI BI n FIFI 1 h 23 0.72h_n 0.63 0.76n 0.74 1 23 0.72 0.63 0.76 0.74 12 2336 0.720.32 0.580.63 0.67 0.76 0.50 0.74 2 36 0.32 0.58 0.67 0.50 23 3632 0.320.43 0.450.58 0.45 0.67 0.44 0.50 3 32 0.43 0.45 0.45 0.44 34 3221 0.430.79 0.780.45 1.00 0.45 0.89 0.44 4 21 0.79 0.78 1.00 0.89 45 2146 0.790.00 0.450.78 0.45 1.00 0.22 0.89 55 46 0.00 0.45 0.45 0.45 0.22 0.22 6 14 0.99 0.53 0.58 0.79 66 14 0.99 0.53 0.58 0.58 0.79 0.79 7 24 0.68 0.28 0.17 0.42 77 24 0.68 0.28 0.17 0.17 0.42 0.42 8 28 0.56 0.31 0.22 0.39 88 28 0.56 0.31 0.22 0.22 0.39 0.39 9 32 0.45 0.18 0.00 0.22 99 32 0.45 0.18 0.00 0.00 0.22 0.22

Figure 18. The relationship between minimum horizontal stress and Poisson’s ratio. FigureFigure 18. 18. TheThe relationship relationship between between minimum minimum horizontal horizontal stress and Poisson’s ratio.

FigureFigure 19. TheThe relationship relationship between between fracabi fracabilitylity index index and Poisson’s ratio. Figure 19. The relationship between fracability index and Poisson’s ratio. 6. Conclusions

The following conclusions are drawn from this study: The brittleness index assessment methods based on rock elastic parameters and mineral • compositions lack a scientific theory basis. The brittleness index derived from stress-strain curves according to energy conservation law is reliable because it can comprehensively reflect the deformation and rupture characteristic of rock. For rocks with a higher Young’s modulus, the consumed elastic energy (We) is insufficient to • generate a complex fracture network, leading to the reduced rock brittleness index. Because the Energies 2020, 13, 388 20 of 22

surrounding stress limits the radial dilation of rocks, there are weak correlations between Poisson’s ratio and brittleness. When a rock is composed of a variety of brittle minerals of moderate content, many weak structural • planes exist between diﬀerent mineral particles, which contributes to the development of cracks. Therefore, this type of rock is more brittle. By contrast, rocks which mainly consist of excessive amount of quartz or carbonate minerals are characterized by high cohesiveness. There are few weak structural planes in this type of rock, which leads to poor brittleness. The premise of fracability evaluation is to accurately assess rock brittleness. Apart from the • brittleness index, the minimum horizontal principal stress should also be regarded as an essential parameter in selecting potential fracturing layers. The most suitable fracturing layers possess a high brittleness index and low minimum horizontal stress. Poisson’s ratio positively correlates with the minimum horizontal stress. Therefore, with the increased Poisson’s ratio, the minimum horizontal stress increases, resulting in a reduced fracability index.

Author Contributions: Y.Y. conceived and designed the experiments; Y.Y. and Z.X. performed the experiments; Y.Y. wrote the paper; S.T. and Z.X. revised the paper. All authors have read and agreed to the published version of the manuscript. Funding: The authors would like to thank National Science and Technology Major Project of China (grant no. 2017ZX05035) and Project funded by China Postdoctoral Science Foundation (grant no. 2019M660737). Acknowledgments: The authors gratefully acknowledge the China National Administration of Coal Geology for sample support and their permission to publish the results of this study. We also greatly thank the anonymous reviewers and editors for their critical comments and valuable suggestions, which were very helpful to improve the manuscript. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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