# In Situ Deformation Analysis of a Fracture in Coal under Cyclic Loading and Unloading

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## Abstract

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## 1. Introduction

## 2. Cyclic Stress Sensitivity Experiment of a Coal Sample

#### 2.1. Experimental Method and Equipment

_{i}(x), at time t:

#### 2.2. Core Sample Preparation

#### 2.3. Experimental Procedures

- Prior to the experiments, the experimental device for loading and unloading is first connected, and as mentioned previously, the core is placed in the core holder, and then the core holder is fixed.
- According to the connection diagram shown in Figure 2, the pipelines are connected to the core holder to start the first cycle step-up experiments. Open the valve and gradually increase the confining pressure according to the sequence of 0 MPa, 0.5 MPa, 1 MPa, 1.5 MPa, 2 MPa, 3 MPa, 5 MPa, 7 MPa and 10 MPa. After the pressure is stabilized for 30 min, the valve is closed, and the pipelines are disassembled for CT scanning to obtain the digital core images.
- Then, the first cycle depressurization experiment is carried out. The valve is opened, and the pressure is gradually reduced in the order of 7 MPa, 5 MPa, 3 MPa, 1.5 MPa and 0 MPa. After the confining pressure is stabilized for 1h, the valve is closed, the pipeline is disassembled and CT scanning is performed to obtain the digital core images.
- Similar to the above steps, the second cycle loading and unloading experiments are carried out: the confining pressure is increased in the order of 0 MPa, 0.5 MPa, 1.5 MPa, 3 MPa, 5 MPa and 10 MPa, and the confining pressure is reduced in the order of 5 MPa, 3 MPa, 1.5 MPa and 0 MPa.
- To reduce the time of image processing, we extract the subvolume from the scanning results as the research object, and then we carry out image processing. Based on this, we can get the change of fracture aperture with confining pressure at the same position in different cycles. Then, the 3D digital core of the fracture can be obtained by image segmentation, and the dimensionless permeability of the fracture can be obtained by LBM simulation.

## 3. Results and Discussions

#### 3.1. In Situ Quantitative Characterization of Fracture Aperture

#### 3.2. LBM Simulation Results

#### 3.3. Discussions

## 4. Conclusions

- The deformation of the fracture changes significantly under cyclic loading and unloading. The variation law of fracture aperture in the first and second cycle is similar, namely regardless of loading or unloading, the fracture aperture changes greatly under low effective stress. However, the effect of different cyclic stress on fracture aperture is different, the stress sensitivity of the first cycle core is stronger, and the change range of the loading stage is larger, but the recovery of aperture in the second cycle is stronger.
- The variation of permeability with cyclic stress is similar to that of fracture aperture with cyclic stress, that is, under low effective stress, the permeability decreases faster, and the influence of the first cycle on fracture aperture and permeability is more severe. In addition, the recovery of permeability in the second cycle is also stronger. At the end of the first cycle, when the confining pressure is reduced to 0 MPa, permeability decreases to 94.6% of the initial time. Permeability of the end of the second cycle decreases to 50.8% of the starting of the second cycle.
- Compared with the first cycle, the deformation of the second cycle fracture is weaker, and the coal sample has certain “elastic” characteristics during the loading and unloading process. Based on the experimental results, the variations of core parameters of coal with an artificial fracture under cyclic stress are divided into three stages: initial rapid deformation stage, transition stage and final stable deformation stage. Hence, special attention should be paid to taking appropriate measures to prevent the rapid closure of fractures in the first cycle.
- For the pore area connected with the artificial fracture, the compaction under high confining pressure (10 MPa) and cyclic confining pressure does not significantly change its shape; moreover, when the fracture is gradually closed, it is obvious that the pore structure can be a beneficial flow channel.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Desorption and migration of CBM: (

**a**) desorption from surface; (

**b**) migration in pores and fractures; (

**c**) flowing into the well bore through fractures.

**Figure 2.**Schematic diagram of in situ X-ray CT characterization system of cyclic stress sensitivity.

**Figure 3.**A slice of a coal sample: (

**a**) original grayscale image, (

**b**) after image smoothing and denoising.

**Figure 5.**The 2D images of the same position in the first cycle (with the increase in confining pressure).

**Figure 7.**The 2D images of the same position in the second cycle (with the increase in confining pressure).

**Figure 8.**The 2D images of the same position in the second cycle (with the decrease in confining pressure).

**Figure 12.**The digital core and streamlines of the first 0 MPa: (

**a**) the digital core, (

**b**) the streamlines.

**Figure 13.**The relationship between permeability and confining pressure: (

**a**) the first cycle, (

**b**) the second cycle.

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**MDPI and ACS Style**

Liu, Z.; Yang, Y.; Li, Y.; Li, J.
In Situ Deformation Analysis of a Fracture in Coal under Cyclic Loading and Unloading. *Energies* **2021**, *14*, 6474.
https://doi.org/10.3390/en14206474

**AMA Style**

Liu Z, Yang Y, Li Y, Li J.
In Situ Deformation Analysis of a Fracture in Coal under Cyclic Loading and Unloading. *Energies*. 2021; 14(20):6474.
https://doi.org/10.3390/en14206474

**Chicago/Turabian Style**

Liu, Zhihui, Yongfei Yang, Yingwen Li, and Jiaxue Li.
2021. "In Situ Deformation Analysis of a Fracture in Coal under Cyclic Loading and Unloading" *Energies* 14, no. 20: 6474.
https://doi.org/10.3390/en14206474