A new stress-damage-flow coupling model and the damage characterization of raw coal under loading and unloading conditions
Introduction
With the rapid development of China's economy, the consumption of various energy sources has increased dramatically, so the development of new energy is an important prerequisite for maintaining stable economic development. As a kind of potential clean energy, coalbed methane has huge reserves of resources and is an important reserve resource to supplement and replace conventional natural gas resources. Compared to coal and oil, coalbed methane can release less carbon dioxide when it produces the same energy.1 In addition, coalbed methane is a strong greenhouse gas with a greenhouse effect of more than 20 times that of carbon dioxide.2 At present, there are two main types of coalbed methane extraction in China, one is extracting coalbed methane by ground drilling, the other is coal and gas (coalbed methane) simultaneous extraction in coal mine underground. There may be many dynamic disasters when coal and gas are extracted simultaneously in coal mine, among which coal and gas outburst is particularly destructive,3,4 especially when mining deep coal seams. Therefore, the development and utilization of coalbed methane can not only reduce greenhouse gas emissions, but also reduce the risk of coal and gas outburst in the process of coal mining. In view of this, the research focus of this paper is the evolution law of damage and permeability, especially the seepage characteristics after yield point. The research in this paper is of great significance to realize the simultaneous extraction of coal and gas.
In order to describe the seepage characteristics of coal seams qualitatively, a large number of permeability models have been established. Gray5 believed that the permeability of coal seams was directly related to the effective horizontal stress which was perpendicular to the coal cleat, and the permeability evolution model of coal mass was established earlier. Seidle et al.6 simplified the coal mass to the geometric structure of the ‘bundled matchstick’, obtained the relationship between the permeability of coal mass and the effective hydrostatic pressure, and deduced the exponential function form of permeability change from the theoretical point of view. Palmer and Mansoori7 assumed that the reservoir was in the condition of single-axis strain, and the permeability model of coal seams was established by combining the non-isothermal porous elasticity theory. Shi and Durucan8 found out the change of effective stress in the horizontal direction of coal seams which based on the hypothetical of uniaxial strain, and established the permeability model in the form of exponential function. Cui and Bustin9 considered the effect of the overall mean effective stress on the porosity and permeability of coal mass, and the permeability model of coal mass in the process of desorption was deduced by using the porous elastic constitutive equation. Zhang et al.10 considered the coal mass as the composition of solid particles and pore space, assumed that the pore space of coal also had adsorption strain, and established a generalized permeability model which based on porosity. Liu et al.11 believed that the permeability of coal mass was composed of matrix permeability and fracture permeability, and the expression of permeability was synthesized by considering the interaction between matrix and fracture. Zhang et al.1 determined the permeability function expressed by regression analysis of quasi-Newton algorithm, which based on Darcy's law and the constitutive equation of cracks. Tao et al.12 took into account the deformation of coal mass which caused by the adsorption expansion, temperature effect and the compression of gas, and established the porosity model of gas-containing coal under compression condition (before dilatancy). Zhu et al.13,14 assumed that the rock parameters conformed to the Weibull distribution, and the maximum tensile stress and Mohr-Coulomb criteria were used to judge the representative elementary volume failure of coal mass, the elastic damage constitutive model of coal mass was established. Yang et al.15 used the segmented function to establish the permeability function of coal mass under shrinkage and tensile conditions. Zhu et al.16 modified the cubic relationship equation of permeability and porosity, and added the damage action item in exponential form. Zheng et al.17 added damage items to the C–B model,9 and assumed the exponential relationship between permeability and damage variables. Xue et al.18 proposed to introduce an item in the post-peak stage to reflect the damage effect, and assumed that the permeability and damage variables in the post-peak stage were linearly related. Espinoza et al.19,20 proposed a transverse isotropic model for microporous solids and investigated the impact of adsorption, swelling strains and swelling stresses on fracture permeability. Okotie and Moore21 shared field observations and operating guidelines of a very-low-pressure coalbed-methane reservoir, and discussed the reservoir simulation to diagnose the causes of reduced well-production efficiency. Wang and Liu22 measured the methane diffusion coefficient by using the classic unipore model and particle method, and discussed the effect of gas diffusion on coalbed methane production, especially for the late-stage coalbed methane reservoir when both gas pressure and permeability were relative low. Shang et al.23 proposed a three-parameter permeability model and used it to describe the cracking effects of fractured rocks induced by changes in effective stress and temperature. Peng et al.24 investigated the thermal effect on permeability in a single granite fracture and proposed a coupled thermal-mechanical model which considered mechanical and thermal damage. Zhou et al.25 investigated the influence of three-dimensional stress condition and multi-field on permeability, and proposed a new anisotropic coal permeability model under the influence of stress, gas sorption and temperature.
After analyzing these models, it is concluded that the previous permeability models are mainly established by the assumption of the single-axis strain condition and the constant load. These models are primarily suitable for extracting coalbed methane by ground drilling. However, in the process of coal and gas simultaneous extraction, the stress characteristics of coal seams are different from that of extracting coalbed methane by ground drilling. In the process of working face propulsion, the coal in front of working face is subjected to the change of the stress path, the support stress in the vertical direction increases gradually and then decreases, the stress in the horizontal direction decreases continuously, and the stress of coal seams presents the typical three-direction stress change.26, 27, 28 Therefore, the previous permeability models cannot be fully applicable to the conditions of coal and gas simultaneous extraction. The experiments were performed by using the laboratory-fabricated ‘thermal-hydro-mechanical coupled with triaxial servo controlled seepage apparatus for gas-containing coal’,29 and investigated the deformation and seepage characteristics of raw coal under loading and unloading conditions. On this basis, combined with X-ray tomography images and Avizo software, three-dimensional reconstruction of raw coal samples before and after the experiment was carried out, the porosity was calculated by using the method of image grayscale level,30 and a new damage characterization parameter was proposed according to the information entropy theory. Finally, based on the basic definition of porosity, a dynamic evolution model of permeability considering damage, gas adsorption expansion and Klinkenberg effect was proposed. The model accurately predicted the permeability of raw coal under loading and unloading conditions.
Section snippets
Characteristics and preparation of coal samples
The coal samples used in experiments were taken from the Baijiao mine in Yibin, Sichuan Province, Southwest China. The main exploitable coal seams in the Baijiao coal mine were in the Xuanwei Formation, which contained B2, B3, and B4 coal seams. All of our coal samples were collected from the B2 coal seam. Large intact raw coal blocks were drilled from the working face, then these blocks were transported to the laboratory and directly cut into cylindrical samples for the seepage experiments.
Effect of loading and unloading conditions on stress-strain-permeability behavior
In order to study the permeability evolution in the process of coal seam mining, the permeability of raw coal under loading and unloading conditions was measured in this experiment. The deviatoric stress-strain curves and permeability-strain curves are analyzed, as shown in Fig. 3. The deviatoric stress-strain curves and permeability-strain curves of four coal samples show similar laws in Fig. 3. First, with the increasing of deviatoric stress, the permeability decreases rapidly, mainly because
Basic assumptions
- (1)
It is assumed that the sample is isotropic medium, namely the mechanical properties are the same in three directions.
- (2)
It is assumed that the sample is in the compaction stage when the hydrostatic pressure is applied, and the sample is in the elastic stage after the hydrostatic pressure is applied.
- (3)
It is assumed that only single-phase saturated gas flow in the sample.
- (4)
The gas flow complies with Darcy's law.
Development of gas permeability model
First, according to the basic definition of porosity, porosity Ø can be expressed by the
Discussion
In the process of coal seam mining, coal and gas outburst is a quite serious hazard, which is mainly caused by the combination of ground stress, coalbed methane flow and coal seam mechanical properties. Different mining layouts will cause differences in the stress path and gas pressure experienced in the coal seam, so the mining layouts have a significant impact on coal and gas outburst. Under loading and unloading conditions, with the increase of axial stress and the decrease of radial stress,
Conclusion
Aiming at the need of coal and gas simultaneous extraction, this paper studies the seepage characteristics and damage characteristics of raw coal samples under loading and unloading conditions by using ‘thermal-hydro-mechanical coupled with triaxial servo controlled seepage apparatus for gas-containing coal’ and X-ray tomography equipment. The permeability, stress-strain curves and CT scan images of coal samples are measured and recorded under loading and unloading conditions. Based on the
Declaration of competing interest
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “A new stress-damage-flow coupling model and the damage characterization of raw coal under loading and unloading conditions”.
Acknowledgments
This study was financially supported by the National Natural Science Foundation of China (52074044, 51674048), Entrepreneurship & Innovation Support Program for Chongqing Overseas Returnees (cx2020112), and Scientific Research Foundation of Key Laboratory of Mining Disaster Prevention and Control (MDPC202012).
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2023, FuelCitation Excerpt :The crack propagation in the coal determines the macroscopic stress–strain characteristics. How to establish appropriate mathematical and mechanical models to accurately describe the deformation and failure process caused by the crack propagation of coal under CO2 adsorption, so as to provide technical research guidance for engineering analysis, is an important issue in the basic theoretical research of deep rock mechanics [15]. Material damage is a phenomenon in which the development of micro-defects in the material leads to the deterioration of the mechanical properties [16,17].