Study on Permeability Anisotropy of Bedded Coal Under True Triaxial Stress and Its Application

Abstract

Anisotropy is a very typical observation in the intrinsic bedding structure of coal. To study the influence of anisotropy of coal structure and stress state on the evolution of permeability, a newly developed multifunctional true triaxial geophysical apparatus was used to carry out mechanical and seepage experiments on bedded coal. The permeability and deformation of three orthogonal directions in cubic coal samples were collected under true triaxial stress. It has detected the significant permeability anisotropy, and the anisotropy is firmly determined by the bedding direction and stress state of coal. Based on the true triaxial mechanical and seepage test results, the coal with bedding was simplified to be represented by a cubic model, and the dynamic anisotropic (D-A) permeability model was derived by considering the influence of bedding and stress state. The rationality of the permeability model was verified by the experimental data. Comparing the permeability model with Wang and Zang (W–Z) model, Cui and Bustin (C–B) model and Shi and Durucan (S–D) model, it is found that the theoretical calculated values of the D-A permeability model are in better agreement with the experimental measured values, reflecting the superiority of the D-A permeability model. Based on incorporating the model of D-A permeability under the concept of multiphysics field coupling, the numerical simulation experiments of coal seam gas extraction with different initial permeability anisotropic ratios were carried out by using COMSOL multiphysics simulator. The influence of initial permeability anisotropy ratio on gas pressure distribution in coal seam during gas extraction was explored, which provides theoretical guidance for the optimization of borehole layout for gas extraction in coal mine.

Appendices

Appendix A: The relationship between the initial PAR and the anisotropy ratio of coals structure

According to the definition of coal fracture permeability, the permeability in all directions can be obtained as follows (Yang et al. 2016):

$$\left\{ \begin{array}{l} k_{x0} = \xi_{x0} ((\lambda_{yz} b_{z0} + \Delta b_{y} )^{3} + (b_{z0} + \Delta b_{z} )^{3} )/12 \hfill \\ k_{y0} = \xi_{y0} ((\lambda_{xz} b_{z0} + \Delta b_{x} )^{3} + (b_{z0} + \Delta b_{z} )^{3} )/12 \hfill \\ k_{z0} = \xi_{z0} ((\lambda_{yz} b_{z0} + \Delta b_{y} )^{3} + (\lambda_{xz} b_{z0} + \Delta b_{x} )^{3} )/12 \hfill \\ \end{array} \right.$$

(A-1)

It is assumed that the curvature of coal and rock in the initial state is equal in all directions, i.e., ξ_x0 = ξ_y0 = ξ_z0. The relationship between initial PAR and fracture width anisotropy λ can be obtained

$$\left\{ \begin{array}{l} {\text{PAR}}_{xz0} = \frac{{k_{x0} }}{{k_{z0} }} \approx \frac{{(\lambda_{yz}^{3} + 1)}}{{(\lambda_{xz}^{3} + \lambda_{yz}^{3} )}} \hfill \\ {\text{PAR}}_{yz0} = \frac{{k_{y0} }}{{k_{z0} }} \approx \frac{{(\lambda_{xz}^{3} + 1)}}{{(\lambda_{xz}^{3} + \lambda_{yz}^{3} )}} \hfill \\ {\text{PAR}}_{xy0} = \frac{{k_{x0} }}{{k_{y0} }} \approx \frac{{(\lambda_{yz}^{3} + 1)}}{{(\lambda_{xz}^{3} + 1)}} \hfill \\ \end{array} \right.$$

(A-2)

For coals with obvious bedding, it can be assumed that the anisotropy of fracture width in two horizontal directions is equal in the initial state. The anisotropy of fracture width in horizontal and vertical directions is λ_yz= λ_xz= λ. Therefore, the relationship between the initial permeability anisotropy and the initial fracture width anisotropy can be obtained

$$\left\{ \begin{aligned} & {\text{PAR}}_{xz0} = {\text{PAR}}_{yz0} = \frac{{\lambda^{3} + 1}}{{2\lambda^{3} }} \\ & {\text{PAR}}_{xy0} = 1 \\ \end{aligned} \right.$$

(A-3)

Therefore, the anisotropy of initial fracture width of coal with bedding effect

$$\lambda = \frac{1}{{\sqrt[3]{{2{\text{PAR}}_{xz0} - 1}}}}$$

(A-4)

Appendix B: W–Z (anisotropy), C–B and S–D permeability model formulas

The W–Z anisotropic permeability model under constant gas pressure can be obtained with zero increment of gas pressure (Wang et al. 2014; Zang and Wang 2016)

$$k_{i} = k_{i0} \left\{ {1 - \frac{1}{{\varphi_{x0} }}\left[ \begin{aligned} & \frac{{\Delta \sigma_{tj} - v_{jk}^{b} \Delta \sigma_{tk} - v_{ij}^{b} \Delta \sigma_{ti} }}{{E_{j}^{b} }} + \frac{{\Delta \sigma_{tk} - v_{ki}^{b} \Delta \sigma_{ti} - v_{jk}^{b} \Delta \sigma_{tj} }}{{E_{k}^{b} }} \\ & + \frac{{(F_{Ij} - F_{Ij0} )\varepsilon_{Lj} p_{0} }}{{p_{Lj} + p_{0} }} + \frac{{(F_{Ik} - F_{Ik0} )\varepsilon_{Lk} p_{0} }}{{p_{Lk} + p_{0} }} \\ \end{aligned} \right]} \right\}^{3} \begin{array}{*{20}c} {} & {(i \ne j \ne k)} \\ \end{array}$$

(B-1)

Cui and Bustin (Cui and Bustin 2005; Cui et al. 2007) found that the relationship between permeability change and average stress increment was exponential. The C–B permeability model was obtained as follows

$$k = k_{0} e^{{ - 3C_{f} \Delta \sigma_{m} }} = k_{0} e^{{ - 3C_{f} (\sigma_{m} - \sigma_{m0} )}}$$

(B-2)

And the mean stress is the average of three principal stresses.

$$\sigma_{m} = \frac{1}{3}(\sigma_{1} + \sigma_{2} + \sigma_{3} )$$

(B-3)

Shi and Durucan (2004) applies the fracture compressibility calculation method (Mckee et al. 1988) to the permeability model and obtains the modified S–D permeability model

$$k = k_{0} e^{{ - 3\bar{C}_{f} (\sigma - \sigma_{0} )}}$$

(B-4)

$$\bar{C}_{f} = \frac{{C_{f0} }}{{\alpha (\sigma - \sigma_{0} )}}(1 - e^{{ - \alpha (\sigma - \sigma_{0} )}} )$$

(B-5)