Estimation of the equivalent elastic modulus in shale formation: Theoretical model and experiment

Gao, Chao; Xie, Lingzhi; Xie, Hui; He, Bo; Jin, Wencheng; Li, F.; Yang, Zhipeng; Sun, Yulin

doi:10.1016/j.petrol.2016.12.002

Cited by 27 publications

(9 citation statements)

References 32 publications

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“…The average UCS of the Longmaxi shale specimens is 135.21 MPa, which falls in the range of the UCS (81.9-157.2 MPa) measured by previous studies [14,41,42] using specimens (Ф50 mm× H100 mm) from the adjacent area. E values from current study (11.24 GPa in average, Table 1) are consistently smaller than the previously measured E values (14.9-44.5 GPa) using Ф50 mm × H100 mm specimens.…”

Section: Mechanical Property Measurementssupporting

confidence: 70%

Mechanical Property Measurements and Fracture Propagation Analysis of Longmaxi Shale by Micro-CT Uniaxial Compression

et al. 2018

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The mechanical properties and fracture propagation of Longmaxi shale loading under uniaxial compression were measured using eight cylindrical shale specimens (4 mm in diameter and 8 mm in height), with the bedding plane oriented at 0 • and 90 • to the axial loading direction, respectively, by micro computed tomography (micro-CT). Based on the reconstructed three-dimensional (3-D) CT images of cracks, different stages of the crack growth process in the 0 • and 90 • orientation specimen were revealed. The initial crack generally occurred at relatively smaller loading force in the 0 • bedding direction specimen, mainly in the form of tensile splitting along weak bedding planes. Shear sliding fractures were dominant in the specimens oriented at 90 • , with a small number of parallel cracks occurring on the bedding plane. The average thickness and volume of cracks in the 90 • specimen is higher than those for the specimen oriented at 0 • . The geometrical characterization of fractures segmented from CT scan binary images shows that a specific surface area correlates with tortuosity at the different load stages of each specimen. The 3-D box-counting dimension (BCD) calculations can accurately reflect crack evolution law in the shale. The results indicate that the cracks have a more complex pattern and rough surface at an orientation of 90 • , due to crossed secondary cracks and shear failure.Various experimental methods, e.g., electromagnetic radiation (EMR), acoustic emission (AE), micro-seismic (MS), infrared technique, high speed digital imaging, and computerized tomography (CT), have been used to analyze the mechanical behavior of rocks (including shale) during uniaxial or triaxial loading [15][16][17][18][19][20][21]. CT scanning has been widely applied in the investigation of damage propagation since 1997, due to the three-dimensional (3-D) visualization and high-resolution imaging [22][23][24][25][26][27][28]. Kawakata et al. used CT to study the initial mesoscopic damage characteristics of rock materials, and observed spatial fault development in granite undergoing compression [29,30]. In the experiment, only the damaged specimens, rather than the entire process from crack initiation to specimen destruction, were scanned, and then observed by 3-D reconstruction of X-ray CT images. To examine the entire process, Ge et al. investigated rock compression with a real-time CT test [23]. Through the use of the industrial CT images, the rock meso-damage propagation law was revealed. Rock failure started with micro-pore and micro-crack compression, growth, bifurcation, and development, followed by fracture. Sun et al. displayed real-time deformation in backfill body under loading using industrial CT in several slices, and provided insights into the process of faulting [31]. However, the relatively low spatial resolution and image quality of conventional industrial CT is not suitable for fine-grained rocks. Furthermore, the 3-D information was not fully captured or used, which limited the accuracy of further calculation ...

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Section: Mechanical Property Measurementssupporting

confidence: 70%

Mechanical Property Measurements and Fracture Propagation Analysis of Longmaxi Shale by Micro-CT Uniaxial Compression

et al. 2018

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“…Based on the test data from the above-mentioned studies, the uniaxial compressive strength (UCS) and triaxial compressive strength (TCS) variations with respect to bedding inclination are displayed in Strength under triaxial compression conditions is the key characteristic of rock material. Some tests are conducted under uniaxial compression [2,11,25,36,[77][78][79][80]85,86,95,106,107], and some tests are conducted under triaxial compression conditions [2,36,78,85,108]. The various shale specimens taken from different sampling sites in these studies display different magnitudes of strength, but their values all show a similar law of variation concerning the bedding inclination.…”

Section: Uniaxial and Triaxial Compression Testmentioning

confidence: 97%

Anisotropic Mechanical Behaviors of Shale Rock and Their Relation to Hydraulic Fracturing in a Shale Reservoir: A Review

Yin,

Yang,

Ranjith

2024

Energies

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Shale gas is an important supplement to the supply of natural gas resources and plays an important role on the world’s energy stage. The efficient implementation of hydraulic fracturing is the key issue in the exploration and exploitation of shale gas. The existence of bedding structure results in a distinct anisotropy of shale rock formation. The anisotropic behaviors of shale rock have important impacts on wellbore stability, hydraulic fracture propagation, and the formation of complex fracture networks. This paper briefly reviews previous work on the anisotropic mechanical properties of shale rock and their relation to hydraulic fracturing in shale reservoirs. In this paper, the research status of work addressing the lithological characteristics of shale rock is summarized first, particularly work considering the mineral constituent, which determines its physical and mechanical behavior in essence. Then the anisotropic physical and mechanical properties of shale specimens, including ultrasonic anisotropy, mechanical behavior under uniaxial and triaxial compression tests, and tensile property under the Brazilian test, are summarized, and the state of the literature on fracture toughness anisotropy is discussed. The concerns of anisotropic mechanical behavior under laboratory tests are emphasized in this paper, particularly the evaluation of shale brittleness based on mechanical characteristics, which is discussed in detail. Finally, further concerns such as the effects of bedding plane on hydraulic fracturing failure strength, crack propagation, and failure pattern are also drawn out. This review study will provide a better understanding of current research findings on the anisotropic mechanical properties of shale rock, which can provide insight into the shale anisotropy related to the fracture propagation of hydraulic fracturing in shale reservoirs.

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“…The literature uses an energy principle to obtain the relationship between the effective elastic modulus, effective Poisson's ratio and crack density of fractured rocks [35][36][37][38][39] :…”

Section: Theoretical Derivation Of the Relationship Between The Longi...mentioning

confidence: 99%

“…The literature uses an energy principle to obtain the relationship between the effective elastic modulus, effective Poisson's ratio and crack density of fractured rocks 35–39 :

\frac{\bar{E}}{E}={\left[1+\frac{16}{45}\frac{(1-{\nu }^{2})(10-3\nu )}{(2-\nu )}f\right]}^{-1},

\frac{\bar{\nu }}{\nu }=\frac{\bar{E}}{E}\left[1+\frac{16}{45}\frac{(1-{\nu }^{2})}{(2-\nu )}f\right],

where

\bar{E}

and

\bar{\nu }

are, respectively, the effective elastic modulus and effective Poisson ratio of the fractured rock, E and ν are respectively the elastic modulus and Poisson ratio of rock without fissure, and f is the crack density parameter of fractured rock.…”

Section: Relationship Between the Longitudinal Wave Velocity And Dens...mentioning

confidence: 99%

Method of defining rock damage variable on the basis of wave impedance

Li,

Fang,

Gao

et al. 2023

Energy Science & Engineering

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A method of determining rock damage variable from wave impedance, which is suitable for the study of dynamics, is presented. The determined variable provides a more reasonable quantitative description of the degree of rock damage. First, the Taylor model of mesoscopic damage mechanics is used to derive the relationship between the velocity of longitudinal waves and the density of rock materials. Based on the measured data of rock samples with different lithology and the same lithology, the relationship between the longitudinal wave velocity and density of rock materials is studied. It is demonstrated that using the wave impedance to define the rock damage variable has advantages over using the P‐wave velocity. Second, the relationship between the wave impedance and degree of damage to the rock material is studied using an electron microscope and ultrasonic testing technology, and the microstructure of rock samples with a wave impedance gradient and time–frequency‐domain characteristics of the ultrasonic signals are compared and analyzed. It is found that it is feasible to determine the damage degree of the rock from the wave impedance. Finally, a method of defining rock damage variable with the wave impedance is further proposed and its rationality verified. The research results show that there is a good positive correlation between the longitudinal wave velocity and density of rock materials, and there is a strong correlation between the degree of rock damage and its wave impedance. The damage variable defined by wave impedance can better reflect the damage state and damage evolution process of rock.

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Estimation of the equivalent elastic modulus in shale formation: Theoretical model and experiment

Cited by 27 publications

References 32 publications

Mechanical Property Measurements and Fracture Propagation Analysis of Longmaxi Shale by Micro-CT Uniaxial Compression

Mechanical Property Measurements and Fracture Propagation Analysis of Longmaxi Shale by Micro-CT Uniaxial Compression

Anisotropic Mechanical Behaviors of Shale Rock and Their Relation to Hydraulic Fracturing in a Shale Reservoir: A Review

Method of defining rock damage variable on the basis of wave impedance

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