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Impact of Effective Stress and Matrix Deformation on the Coal Fracture Permeability

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Abstract

The permeability of coal is an important parameter in mine methane control and coal bed methane exploitation because it determines the practicability of methane extraction. We developed a new coal permeability model under tri-axial stress conditions. In our model, the coal matrix is compressible and Biot’s coefficient, which is considered to be 1 in existing models, varies between 0 and 1. Only a portion of the matrix deformation, which is represented by the effective coal matrix deformation factor \(f_\mathrm{m}\), contributes to fracture deformation. The factor \(f_\mathrm{m}\) is a parameter of the coal structure and is a constant between 0 and 1 for a specific coal. Laboratory tests indicate that the Sulcis coal sample has an \(f_\mathrm{m}\) value of 0.1794 for \(\hbox {N}_{2}\) and \(\hbox {CO}_{2}\). The proposed permeability model was evaluated using published data for the Sulcis coal sample and is compared to three popular permeability models. The proposed model agrees well with the observed permeability changes and can predict the permeability of coal better than the other models. The sensitivity of the new model to changes in the physical, mechanical and adsorption deformation parameters of the coal was investigated. Biot’s coefficient and the bulk modulus mainly affect the effective stress term in the proposed model. The sorption deformation parameters and the factor \(f_\mathrm{m}\) affect the coal matrix deformation term.

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Abbreviations

\(\varepsilon _\mathrm{e}\) :

Coal bulk strain caused by the effective stress (dimensionless)

\(\varepsilon _\mathrm{eP}\) :

Fracture strain caused by the effective stress (dimensionless)

\(V_\mathrm{e}\) :

Coal bulk volume caused by the effective stress (mL)

\(V_\mathrm{ef}\) :

Fracture volume caused by the effective stress (mL)

\(V\) :

Coal bulk volume (mL)

\(V_\mathrm{P}\) :

Coal pore volume (mL)

\(\bar{{\sigma }}\) :

Mean stress (MPa)

\(K\) :

Coal bulk modulus (MPa)

\(K_\mathrm{P}\) :

Coal pore system modulus (MPa)

\(\alpha \) :

Biot’s coefficient (dimensionless)

\(K_\mathrm{m}\) :

Coal matrix modulus (MPa)

\(\beta \) :

Effective coefficient of fracture (dimensionless)

\(\phi \) :

Fracture porosity of coal (dimensionless)

\(\varepsilon _\mathrm{m}\) :

Coal matrix strain (dimensionless)

\(\varepsilon _\mathrm{s}\) :

Coal matrix strain due to sorption (dimensionless)

\(\varepsilon _\mathrm{mP}\) :

Coal matrix strain due to gas pressure compression (dimensionless)

\(\varepsilon _{\mathrm{max}}\) :

Maximum adsorption strain (dimensionless)

\(P\) :

Gas pressure (MPa)

\(P_\mathrm{L}\) :

Langmuir’s pressure (MPa)

\(P_\mathrm{R}\) :

Rebound pressure (MPa)

\(V_{\mathrm{mf}}\) :

Fracture volume deformation due to coal matrix deformation (mL)

\(V_{\mathrm{mv}}\) :

Bulk volume deformation due to matrix deformation (mL)

\(V_\mathrm{m}\) :

Coal matrix volume (mL)

\(k\) :

Coal permeability (mD)

\(E\) :

Elastic modulus (MPa)

\(v\) :

Poisson’s ratio (dimensionless)

\(M\) :

Constrained axial modulus (MPa)

\(f_\mathrm{m}\) :

Effective coal matrix deformation factor (dimensionless)

\(f\) :

Empirical parameter for P–M model (dimensionless)

\(\gamma \) :

Matrix compressibility (\(\hbox {MPa}^{-1}\))

\(C_\mathrm{f}\) :

Fracture compressibility (\(\hbox {MPa}^{-1}\))

\(C_{0}\) :

Initial fracture compressibility (\(\hbox {MPa}^{-1}\))

\(\theta \) :

Decline rate of fracture compressibility with increasing effective stress (\(\hbox {MPa}^{-1}\))

0:

Initial or reference state

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Acknowledgments

The authors are grateful for the support of the National Foundation of China (Nos. 51004106, 41202118, 51204173, 51304204), the National Basic Research Program of China (973 Program, No. 2011CB201204) and China Postdoctoral Science Foundation and project funded by the priority academic program development of Jiangsu Higher education institutions (PAPD).

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Correspondence to Yuanping Cheng.

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Guo, P., Cheng, Y., Jin, K. et al. Impact of Effective Stress and Matrix Deformation on the Coal Fracture Permeability. Transp Porous Med 103, 99–115 (2014). https://doi.org/10.1007/s11242-014-0289-4

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