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A Novel Damage-Based Permeability Model for Coal in the Compaction and Fracturing Process Under Different Temperature Conditions

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Abstract

Before a coal mining operation, it is necessary to carry out coal-bed methane (CBM) pre-extraction to prevent coal and gas explosions, causing accidents. However, gas extraction and coal mining will lead to coal damage, which results in a change in the gas migration law. Especially, under deep mining conditions, the gas migration mechanism is more complicated owing to a high ground temperature. Coal permeability is the most important constituent that determines gas flow properties. Therefore, the coal permeability evolutionary law related to damage-induced conditions under different temperatures should be further researched. In this paper, a series of triaxial seepage experiments during the whole stress-induced process, and in the changing of the effective stress process were carried out. The results have shown that during the whole stress–strain process, with an increase in axial strain, coal permeability gradually decreases to a minimum value at first, then increases sharply, and finally keeps nearly constant. A higher temperature resulted in a lower elastic modulus, peak strain, and peak strength, but it caused higher thermal damage. When the coal fractures, coal permeability increases with the increase in temperature. During a change in the effective stress process, higher temperatures resulted in higher permeability. Under higher effective stress, the impact of temperature on permeability was not significant. Based on the above results, a novel damage-based permeability model was developed to describe the permeability evolutionary law caused by damage-induced conditions under compaction, and in a fracturing situation. In the proposed model, an exponential function has been used for the combination between permeability and damage variable. The damage variable is composed of thermal damage and mechanical damage. In addition, the damage variable has been modified by introducing a modified function of the initial damage. Finally, the proposed model has been applied to fit two sets of experimental data available. The fitting results showed that the proposed permeability model could well reflect the permeability behaviors of damage-induced coal at different temperatures.

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Abbreviations

a :

Coal cleat spacing (cm)

A :

Cross section area (cm2)

Aa :

Pre-exponential coefficient (cm3/g)

A 0 :

Permeability area of the specimen (cm2)

b :

Coal cleat aperture (cm)

B :

Constitutive coefficient

c :

Maximum adsorption amount (mmol/g)

d :

Langmuir constant (MPa−1)

DT :

Thermal damage

D m :

Mechanical damage variable

E :

Elastic moduli of the equivalent coal (MPa)

E A :

The modulus of adsorption-induced expansion of coal (MPa)

E m :

Elastic moduli of the coal matrix (MPa)

E T :

Elastic moduli at temperature T (MPa)

E 0 :

Elastic moduli at room temperature (MPa)

E a :

Adsorption-induce energy (kJ/mol)

f s :

Total cleat length per unit cross section (cm−1)

f c 0 :

Compressive strength (MPa)

I d :

Initial damage coefficient

k :

Coal permeability (10–3 μm2)

k f :

Coal cleat permeability (10–3 μm2)

l :

Coal cleat height (cm)

l m :

Coal matrix width (cm)

L :

Coal matrix length (cm)

L 0 :

Length of specimen (cm)

p :

Gas pressure (MPa)

p 0 :

Initial gas pressure (MPa)

p 1 :

Inlet gas pressure (MPa)

p 2 :

Outlet gas pressure (MPa)

peff :

Effective confining pressure (MPa)

p p :

Pore pressure (MPa)

P 0 :

Standard atmospheric pressure (MPa)

q 1 :

Flow rate through this single cleat (cm3/s)

q n :

Flow rate through n cleats (cm3/s)

Q :

Gas flow rate (cm3/s)

R :

Universal gas constant

R m :

Elastic modulus reduction ratio

S :

Specific surface area of the solid (m2/g)

T :

Temperature (K)

u :

Displacement of the coal matrix (cm)

u*:

Displacement of the equivalent coal (cm)

V :

Gas volume adsorbed by coal (cm3)

V 0 :

Gas molar volume (L/mol)

V abs :

Gas absolute volume adsorbed by coal (cm3

ϕ f :

Coal cleat porosity

φ :

Internal friction angle (°)

μ :

Gas dynamic viscosity (Pa·S)

γ :

Deformation constant

γ d :

Damage-permeability coefficient

ρ c :

Solid body density (g/cm3)

λ c :

Residual strength coefficient

Γ :

Surface excess (mol/m2)

ε s :

Adsorption volumetric strain

Δεe :

Effective strain

Δεf :

Cleat strain

Δεtx :

Total strain in x or y direction

ε 1 :

Axial strain

ε c 0 :

Peak strain

ε cr :

Residual strain

ε cu :

Maximum residual strain

σ 1 :

Axial stress (MPa)

σ 3 :

Confining pressure (MPa)

Δσ :

Deviatoric stress (MPa)

Δσe :

Effective stress (MPa

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Acknowledgements

This study was financially supported by the National Natural Science Foundation of China (Grants No. 51804085, 51911530203 and 51874144), Guizhou Science and Technology Department (No. J2015-2049).

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Authors and Affiliations

  1. College of Mining, Guizhou University, Guiyang, 550025, People’s Republic of China

    Chonghong Ren, Bobo Li, Yao Zhang, Jianhua Li & Zheng Gao

  2. Guizhou Key Laboratory of Comprehensive Utilization of Non-Metallic Mineral Resources, Guiyang, 550025, People’s Republic of China

    Bobo Li

  3. National and Local Joint Laboratory of Engineering for Effective Utilization of Regional Mineral Resources From Karst Areas, Guizhou University, Guiyang, 550025, People’s Republic of China

    Bobo Li

  4. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400044, People’s Republic of China

    Jiang Xu

  5. Fujian Research Center for Tunneling and Urban Underground Space Engineering, Huaqiao University, Xiamen, 361021, People’s Republic of China

    Chonghong Ren & Jin Yu

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  1. Chonghong Ren
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  2. Bobo Li
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  3. Jiang Xu
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  4. Yao Zhang
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Correspondence to Bobo Li.

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Ren, C., Li, B., Xu, J. et al. A Novel Damage-Based Permeability Model for Coal in the Compaction and Fracturing Process Under Different Temperature Conditions. Rock Mech Rock Eng 53, 5697–5713 (2020). https://doi.org/10.1007/s00603-020-02236-7

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