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An elastoplastic model for gas flow characteristics around drainage borehole considering post-peak failure and elastic compaction

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Abstract

The excavation and drainage drilling for underground mining induces stress redistribution around the gas drainage borehole, thus forming three physical zones: residual state zone, strain softening zone and elastic zone. The formation process of these zones contains complex interactions among deformation, natural gas flow, and coal seam damage. A better understanding of these interactions could provide better guidance for the gas drainage engineering. Extensive studies have focused on the effect of effective stress or effective strain on permeability variation based on the poroelastic theory. Meanwhile, as there is few permeability models taking the post-peak failure effect into account, previous permeability variation analysis seldom commonly considered the elastoplastic characteristic of coal seam, which results in the permeability misestimation. Therefore, this study proposes a new approach to analyze this interaction process. The innovation of this approach is that it takes into account the influence of coal permeability enhancement in failure zone and the volumetric compaction in elastic zone around the drainage borehole. In this approach, analytical solutions of stress and strain are developed to include both the strain softening around a gas drainage borehole and the compaction in elastic zone. These solutions thus remove the flaws that previous studies did not consider the compaction in elastic zone. Further, a new permeability model is proposed by the introduction of damage enhancement coefficient for post-peak failure. Third, the permeability distribution of coal around a gas drainage borehole is calculated based on the analytical solutions and the new permeability model. Fourth, the gas flow equation is numerically solved to obtain gas pressure profiles. The gas content computed by this approach is verified by field data. Finally, parametric study is carried out to investigate the effect of the damage enhancement coefficient, initial geo-stress, drilling volume, and uniaxial strength on the gas pressure and the permeability around the gas drainage borehole. Based on these numerical analyses, it is found that the evolution of permeability is closely related to the physical properties of coal and the geological condition of coal seam. Higher initial geo-stress and lower failure strength have larger unloading zone and higher permeability enhancement. This compaction helps the coal seam form a flow-shielding zone near the interface between plastic zone and elastic zone. The gas flow in the coal around the drainage borehole can be divided into four different zones.

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Abbreviations

R 0, R b, R p :

Radii of the borehole, residual state zone and strain softening zone (m)

\(\sigma _{\theta }^{{\text{p}}}\), \(\sigma _{{\text{r}}}^{{\text{p}}}\) :

Hoop and radial stress components in the strain-softening zone (MPa)

\({m_{\text{e}}}\), \({m_{\text{p}}}\), \({m_{\text{b}}}\) :

Dilatation coefficients in the elastic zone, the strain-softening zone and the residual state zone (–)

\(\sigma _{{\text{c}}}^{*}\) :

Uniaxial residual strength (MPa)

\({\sigma _{{R_{\text{p}}}}}\) :

Stress on the boundary between the strain-softening zone and the elastic zone (MPa)

\(\Delta \varepsilon _{\theta }^{{}}\) :

Increments of hoop strain (–)

\(E\) :

Young’s modulus of coal (MPa)

\({p_{\text{i}}}\) :

Initial geo-stress (MPa)

\(\alpha\) :

Biot coefficient (–)

\(b\) :

Fracture aperture (m)

\(\tau\) :

Tortuosity parameter (–)

\(\gamma\) :

Mutation coefficient (–)

\(\lambda\) :

Damage enhancement coefficient (–)

\({\vec {q}_{\text{g}}}\) :

Velocity (m/s)

\({\nu ^{\text{b}}}\) :

Volumetric strain in the residual state zone (–)

p :

Gas pressure (MPa)

\({Q_{\text{m}}}\) :

Gas source by injection (m3/s)

\({\rho _{{\text{ga}}}}\) :

Gas density at standard conditions (kg/m3)

\({\rho _{\text{c}}}\) :

Density of coal (kg/m3)

\({V_{{\text{sg}}}}\) :

Content of absorbed gas

K :

Bulk modulus of coal (MPa)

\({k_{\text{g}}}\) :

Permeability of coal (m2)

ϕ 0 :

Initial porosity (–)

k 0 :

Initial permeability (m2)

\(\sigma _{\theta }^{{\text{e}}}\), \(\sigma _{{\text{r}}}^{{\text{e}}}\) :

Hoop and radial stress components in the elastic zone (MPa)

\(\sigma _{\theta }^{{\text{b}}}\), \(\sigma _{{\text{r}}}^{{\text{b}}}\) :

Hoop and radial stress components in the residual state zone (MPa)

\({\nu ^{\text{e}}}\), \({\nu ^{\text{p}}}\), \({\nu ^{\text{b}}}\) :

Volumetric strain in elastic zone, the strain-softening zone and the residual state zone (–)

\(\sigma _{{\text{c}}}^{{\text{p}}}\) :

Uniaxial compressive strength (MPa)

\({R_{\text{p}}}\) :

Boundary between the strain-softening zone and the elastic zone (m)

\(\Delta {\varepsilon _{\text{r}}}\) :

Increments of radial strain (–)

\({p_{\text{s}}}\) :

Supporting traction of cavity (MPa)

\({k_{\text{s}}}\) :

Softening coefficient of coal (–)

\({K_{\text{p}}}\) :

Modulus of pores (MPa)

\({l_{\text{n}}}\) :

Sum of the lengths of the multi-fractures (m)

\(\Delta p\) :

Pressure difference (MPa)

\({c_{\text{f}}}\) :

Compression coefficient of fracture (MPa−1)

\({\sigma _{\text{e}}}\) :

Effective stress (MPa)

V L :

Adsorption capacity of coal (m3/kg)

P L :

Langmuir pressure constant (MPa)

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

Sorption-induced volumetric strain (–)

m :

Mass content (kg/m3)

ρ g :

Density of CH4 at standard condition (kg/m3)

\({p_0}\) :

Initial gas pressure (MPa)

K s :

Bulk modulus of coal grains (MPa)

t :

Time (s)

\(\phi\) :

Coal porosity (–)

\(\mu\) :

Gas dynamic viscosity (Pa s)

\(\varphi\) :

Internal friction angle of coal (°)

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Acknowledgements

This study is sponsored by the National Natural Science Foundation of China (no. 51679199), the China Postdoctoral Science Foundation (no. 2018M633549), the Special Funds for Public Industry Research Projects of the Ministry of Water Resources (no. 201501034-04 and 201201053-03), Initiation Fund of Doctor’s Research (no. 107-451117008) and the Key Laboratory for Science and Technology Coordination & Innovation Projects of Shaanxi Province (no. 2014SZS15-Z01).

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Authors and Affiliations

  1. State Key Laboratory of Eco-hydraulics in Northwest Arid Region, Xi’an University of Technology, Xi’an, 710048, China

    Yi Xue, Faning Dang, Fengyin Liu, Rongjian Li & Songhe Wang

  2. Institute of Geotechnical Engineering, Shaanxi Provincial Key Laboratory of Loess Mechanics and Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Yi Xue, Faning Dang, Fengyin Liu, Rongjian Li & Songhe Wang

  3. Deep Earth Energy Laboratory, Department of Civil Engineering, Monash University, Building 60, Melbourne, VIC, 3800, Australia

    P. G. Ranjith

  4. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 221116, China

    Zhengzheng Cao & Yugui Yang

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  1. Yi Xue
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  2. Faning Dang
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Xue, Y., Dang, F., Liu, F. et al. An elastoplastic model for gas flow characteristics around drainage borehole considering post-peak failure and elastic compaction. Environ Earth Sci 77, 669 (2018). https://doi.org/10.1007/s12665-018-7855-y

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