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Filling of brittle minerals such as quartz is one of the main factors affecting the initiation and propagation of reservoir fractures in shale fracturing, in order to explore the failure mode and thermal damage characteristics of quartz-filled shale under thermal-mechanical coupling. Combining the theory of damage mechanics and thermoelasticity, RFPA^{2D}-Thermal is used to establish a numerical model that can reflect the damage evolution of shale under thermal-solid coupling, and the compression test under thermal-mechanical coupling is performed. The test results show that during the temperature loading process, there is a temperature critical value between 60°C and 75°C. When the temperature is less than the critical temperature, the test piece unit does not appear obvious damage. When the temperature is greater than the critical temperature, the specimen unit will experience obvious thermal damage, and the higher the temperature, the more serious the cracking. Under the thermal-mechanical coupling of shale, the tensile strength and elastic modulus of shale show a decreasing trend with the increase of temperature. The failure modes of shale under thermal-solid coupling can be roughly divided into three categories: “V”-shaped failure (30°C, 45°C, and 75°C), “M”-shaped failure (60°C), and inverted “

With the rapid consumption of conventional energy such as petroleum, unconventional clean energy such as shale gas has become a current research focus [^{3}, ranking first in the world [

The fracturing of shale reservoirs uses high-pressure fluid to break the rock mass to form a complex fracture network with high permeability according to Jiang et al. [

Fractal theory has unique advantages in characterizing complex and irregular objects, and it provides a new theoretical basis for the evolution process of rock failure. Xie [

Shale is a kind of brittle rock formed by transportation and sedimentation in the process of geological structure evolution. The shale is filled with a large number of mineral particles. Under the action of temperature, the shape and content of mineral particles have a significant impact on the macro and micromechanical properties and fracture modes of shale [

This article uses statistical methods to describe the heterogeneity of quartz and shale matrix. Through the RFPA^{2D}-Thermal software, the shale is subjected to numerical simulation tests under constant confining pressure and different temperature conditions, and the compressive strength, elastic modulus and failure process of shale under different temperature conditions are studied in detail. Calculate the fractal dimension of the acoustic emission distribution map and analyze the relationship between the fractal dimension and the failure mode under different temperature conditions. The research results will have an important reference value for fracture mechanism, secondary crack initiation and propagation prediction, and enhanced oil recovery in shale fracturing.

Guizhou is one of my country’s oil and gas storage bases. The regional tectonic unit is divided into the Yangtze quasi-platform. Between hilly basins, the terrain is high in the west and low in the east and descends from the center to the north, east, and south. According to the distribution of surface structures, the metamorphic rock forms and structural combination styles of the area and other structural features. The study area has mainly experienced four tectonic cycles during the evolution of geological structure: Wuling tectonic movement, Caledonian-Xuefeng tectonic movement, Yanshan tectonic movement, and Himalayan tectonic movement. Among them, the Yanshanian period is the most intense tectonic movement, which is the main cause of the current topography. The Himalayan period superimposed and transformed the structures formed in the Yanshan period [

Area map of the third block of Fenggang, Qianbei, Guizhou [

The study of rock and mineral characteristics is an important factor that needs to be considered in the exploration and development of shale gas. The higher the content of brittle minerals in shale, the more likely it is to produce cracks under the action of tectonic stress or hydraulic fracturing, providing storage space and seepage channel for shale gas. It can be seen that the shale is filled with a large amount of quartz through the microsection identification. The identification process and results are shown in Figure

Verification diagram of microsection.

X-ray diffraction analysis of whole rock.

Mineral content map of shale reservoir.

Distribution map of shale mineral content [

Shale reservoirs have the characteristics of low permeability and micronano pore development. This low-permeability and microporosity feature has an important influence on the content and storage of shale gas. As the main storage space of gas reservoirs, shale micropores determine the enrichment degree of shale gas reservoirs. Generally speaking, the more developed the microfractures and pores of shale, the higher the flow capacity and the richer the gas reservoir. In this paper, the relaxation of nuclear magnetic resonance (NMR) technology is used to characterize the pore structure of shale. The experimental instrument model is MesoMR23-060H-I. Five groups of samples in the study area are selected for detection and analysis. The results show that the pore throats of the Lower Cambrian shale in Fenggang III block are mainly nanopores, which are distributed between 0 and 0.1

Pore size distribution diagram.

Based on the theory of continuum mechanics, shale is considered to be an ideal linear elastic body, which satisfies the generalized Hooke’s law under external load [

where

This article considers the high temperature and high-pressure environment of shale, which involves the coupling relationship between temperature field and stress field. Through the control equations of stress field and temperature field, the damage evolution process of shale under external force and the influence of damage on stress field and temperature field are considered. Under the coupling effect of temperature field and stress field, microcracks in shale begin to sprout, and the damage of shale in turn affects the elastic modulus, compressive strength, and thermal conductivity of shale. Considering the effect of thermal stress on shale deformation caused by the temperature field, the stress-strain relationship of shale can be expressed as Equation (

where

The thermal conductivity of shale is closely related to temperature and reflects the unevenness of shale temperature field. Regarding the thermophysical properties of the shale microscopic unit, when the damaged unit is not initiated, the thermal conductivity

In the formula,

In the numerical model established in this paper, the mutual conversion between thermal energy and mechanical energy is ignored, and the energy conservation equation is calculated according to Equation (

where

RFPA^{2D}-Thermal is based on finite element theory and statistical damage theory. Considering the inhomogeneity of the rock, we simplified the complicated macro-nonlinear problem into a fine-to-microlinear problem and combined the assumption of random distribution of the inhomogeneity with numerical calculation methods. The numerical simulation of the nonuniform rock failure process can be realized [

In the formula,

In order to study the influence of temperature on the mechanical properties and failure modes of shale, this paper uses the RFPA^{2D}-Thermal software to establish a numerical model and carries out simulation tests at different temperatures. In the numerical model, the larger the elastic modulus of the mineral particles, the brighter the color, which can be used to characterize the quartz mineral particles and the shale matrix. According to the physical experiments, the mechanical parameters and thermodynamic parameters of the quartz mineral and shale matrix in the model are shown in Table

Numerical model parameters.

Elastic modulus | Compressive strength | Poisson’s ratio | Friction angle (°) | Thermal conductivity/J.(m.s.°C)^{-1} | Heat capacity/(J.(kg.°C)^{-1}) | Thermal expansion coefficient/(10^{-6}.°C^{-1}) | |
---|---|---|---|---|---|---|---|

Shale | 51600 | 145 | 0.22 | 35 | 1250 | 1250 | 1.36 |

Quartz | 96000 | 375 | 0.08 | 60 | 700 | 700 | 1.1 |

This experiment establishes a numerical model of quartz-filled shale at different temperatures. The quartz content in the model is 62.09%. Shale pores are mostly nanosized pores and a small amount of microsized pores. This test does not consider the influence of shale primary pores. The loading model is shown in Figure

Model loading diagram.

Shale is often filled with brittle minerals such as quartz. Because the thermal expansion coefficients of brittle mineral particles and shale matrix are different, the thermal expansion at the boundary between quartz and shale matrix is inconsistent, resulting in tensile or compressive thermal stress in the junction between quartz particles and shale matrix. Figure

Thermal damage evolution process diagram of shale.

Acoustic emission number is the elastic wave signal of element damage initiation and release of shale specimen under thermal stress, reflecting the damage evolution process of specimen. Figure

Variation of acoustic emission number with temperature

During the displacement loading process, the thermal-mechanical coupling effect of shale has a significant effect on the compressive strength and elastic modulus of shale filled with quartz minerals. Table

Compressive strength and elastic modulus of shale under thermomechanical coupling.

Temperature/°C | Elastic modulus/GPa | Compressive strength/MPa |
---|---|---|

30 | 84.92 | 79.79 |

45 | 79.82 | 67.32 |

60 | 77.31 | 52.59 |

75 | 62.05 | 30.71 |

90 | 54.88 | 10.15 |

Compressive strength and elastic modulus of shale under thermal-mechanical coupling.

Figure

Damage evolution process diagram of shale under thermal-mechanical coupling.

In the acoustic emission diagram, yellow represents the tensile failure initiated at the current step, red represents the shear damage caused by the current step, and black represents the damaged unit. Looking at the acoustic emission diagram, it can be seen that the shale specimens are mainly tensile-shear failure. The cracks when the specimen is instability and failure are connected by a tensile damage unit and a compression-shear damage unit. The cumulative damage development trend of microunits directly reflects the macrofailure mode of shale specimens. The joint action of thermal stress and external stress will cause tensile damage when the tensile strength of the specimen is first reached. As the loading process reaches the critical value of the Mohr-Coulomb strength criterion, the specimen unit appears compression-shear failure. The above results indicate that the heterogeneous microstructure of the quartz filled in shale under thermal-mechanical coupling has a significant impact on its damage evolution process and failure mode.

Figure

The relationship between stress level and AE energy under thermal-mechanical coupling.

Fractal theory can quantitatively describe complex objects in the world. It is widely used in the field of rock failure and helps to reveal the law of damage and fracture of rocks. In this paper, the fractal dimension of the image is calculated by the box dimension, and the fractal dimension program is written on the MATLAB software platform. Binarize the acoustic emission diagrams under different stress levels obtained in the experiment, and import the calculation program to obtain the fractal dimension of the acoustic emission diagrams. The formula is defined as follows:

where

Table

AE energy and fractal dimension values.

Stress level temperature | 10% | 20% | 30% | 40% | 50% | 60% | 70% | 80% | 90% | 100% |
---|---|---|---|---|---|---|---|---|---|---|

30°C AE | 0 | 0 | 0 | 0 | 0 | 0.00011 | 0.00182 | 0.01169 | 0.07182 | 0.31024 |

0 | 0 | 0 | 0 | 0 | 0.1632 | 0.4466 | 0.7057 | 0.9033 | 1.071 | |

45°C AE | 0 | 0 | 0 | 0.00006 | 0.00078 | 0.00276 | 0.01097 | 0.0372 | 0.12476 | 0.4857 |

0 | 0 | 0 | 0.1818 | 0.3542 | 0.1754 | 0.6621 | 0.7938 | 0.9432 | 1.113 | |

60°C AE | 0 | 0.00006 | 0.0002 | 0.0008 | 0.00352 | 0.00859 | 0.02739 | 0.07412 | 0.19217 | 0.634 |

0 | 0.1516 | 0.2137 | 0.4754 | 0.572 | 0.6931 | 0.8288 | 0.9183 | 1.127 | 1.262 | |

75°C AE | 0.00047 | 0.00143 | 0.00306 | 0.00553 | 0.01325 | 0.02197 | 0.04228 | 0.08221 | 0.17565 | 0.50713 |

0.5432 | 0.6164 | 0.6677 | 0.7051 | 0.7926 | 0.8448 | 0.92 | 0.9928 | 1.072 | 1.189 | |

90°C AE | 0.01787 | 0.04349 | 0.06711 | 0.08616 | 0.11039 | 0.1587 | 0.22617 | 0.34097 | 0.4221 | 0.53713 |

1.024 | 1.051 | 1.072 | 1.086 | 1.101 | 1.129 | 1.154 | 1.193 | 1.212 | 1.231 |

Relationship between stress level and fractal dimension under thermo-mechanical coupling.

Stress leveltemperaturefractal dimension relationship diagram.

Shale is often filled with quartz minerals, and the difference in thermal expansion between quartz particles and shale matrix is an important influencing factors of rock fracture under thermal-mechanical coupling. In this paper, the thermal-solid coupling model is established to study the influence of temperature on the mechanical properties and damage evolution process of quartz-filled shale, and the following rules are summarized:

(1) The quartz content of the Niutitang Formation shale in the III District of Fenggang is 35.79%~92.49%, with an average content of 62.09%. As the depth of burial increases, the overall quartz content gradually increases. Shale pore throats are mainly nanopores distributed between 0 and 0.1

(2) The effect of temperature has a significant effect on the thermal damage of shale filled with a large amount of quartz. The evolution process of thermal damage can be divided into nondamage stage, microdamage stage, and damage stage. There is a critical temperature value. When the temperature is greater than the critical temperature, the specimen unit will experience obvious thermal cracking. The higher the temperature, the more serious the cracking. The thermal-mechanical coupling effect has a significant effect on the compressive strength and elastic modulus of shale filled with quartz minerals. With the increase of temperature, the tensile strength and elastic modulus of shale show a decreasing trend

(3) Temperature has a significant influence on the damage evolution and failure modes of shale under thermo-solid coupling. The failure modes can be roughly divided into three categories. When the temperature is 30°C, 45°C, and 75°C, it is a “V”-shape failure; when the temperature is 60°C, it is an “M”-shape failure; when the temperature is 90°C, it is an inverted “

(4) Using the self-similarity of the spatial distribution of acoustic emission points, we quantitatively analyze the influence of thermal-mechanical coupling on the failure mode of shale specimens based on fractal theory. The larger the fractal dimension, the more complicated the failure mode of the specimen and the more serious the internal damage. When the temperature is 60°C, the fractal dimension is the largest, which is 1.262, and the corresponding failure mode is the most complicated “M” shape. The fractal dimension is between 1.071 and 1.189, and the corresponding failure mode is “V” shape. The fractal dimension is 1.231, and the corresponding failure mode is inverted “

The data used to support the study is available within the article.

The authors declare that they have no conflicts of interest.

This study was supported by the Talent Introduction Project of Special Fund for Science and Technology of Water Resources Department of Guizhou Province (Project No. KT201804), Guizhou Postgraduate Innovation Fund (Project No. YJSCXJH[2020]087), Guizhou Science and Technology Fund (Project No. [2020]4Y046, Project No. [2019]1075, and Project No. [2018]1107), the National Natural Science Foundation of China (Project Nos. 51964007 and 51774101), and Project Scientific Research Project of Guiyang Rail Transit Line 2 Phase I Project (Project No. D2(I)-FW-YJ-2019-001-WT). This study is also funded by the Teaching reform project of Guizhou University (Project No. JG201990) and Guizhou Province Mine Dynamic Disaster Early Warning and Control Technology Innovation Talent Team Project (Project No. [2019]5619).