裂隙分形维数对孔周煤体瓦斯非Darcy渗流特征参数的影响

Influence of fractal dimensions of fissures on characteristic parameters of non-Darcy seepage of coal gas in peripore coal bodies

  • 摘要: 钻孔孔周煤体的裂隙分形维数可有效反映孔周煤体裂隙网络的几何特征,它影响着孔周裂隙煤体瓦斯非Darcy渗流特征。为了探究预抽钻孔孔周裂隙煤体瓦斯非Darcy渗流特征,制作了含有2到4条贯穿裂隙共5种几何特征的含孔煤样,运用孔周煤体裂隙结构的分形维数量化表征孔周裂隙网络几何特征,并利用自主设计的瓦斯径向渗流系统开展孔周裂隙煤体侧限压缩径向渗流试验,模拟瓦斯在孔周裂隙煤体中的渗流过程,结合Forchheimer方程分析孔周裂隙煤体瓦斯径向渗流的非线性特征及其作用原理。结果表明:① 孔周裂隙煤体具有较好的分形特征,煤样孔周裂隙网络的二维分形维数D2在1.321~1.442之间,三维分形维数D3在2.321~2.442之间,孔周裂隙煤体分形维数的不同能够综合表征其表面裂隙率Rsc、裂隙交点个数Nj、裂隙条数Nseg、裂隙总长度Lsum、裂隙平均长度Lav和裂隙平均宽度e等基本几何指标的不同;② 气体在孔周裂隙煤体内的径向渗流受到局部粗糙度效应、流体内部的摩擦效应和曲折流效应这三重效应的影响,在同一压力梯度下,煤样孔周裂隙网络的分形维数越大,孔周裂隙网络中通过的流量越小;③ 孔周裂隙煤体的渗流速度随压力梯度的增加而增加,且逐渐偏离线性,孔周裂隙煤体的渗流速度越大,非线性越明显;煤样孔周裂隙网络的分形维数越大,所能达到的最大渗流速度越小;④ 随着孔周裂隙网络分形维数的增加,孔周裂隙煤体的渗透率降低,其关系式满足1011k= 4.6D32−23.9D3+ 31.9,同时非Darcy流β因子增大;此外,非Darcy流β因子随渗透率k的增大而减小。结合以上结论,在顺煤层钻孔预抽瓦斯工作中,观测孔周煤体裂隙网络的分形维数,进而掌握孔周裂隙煤体的渗透率大小,对于预抽钻孔布孔参数的设计具有重要的理论指导意义。

     

    Abstract: The fractal dimension of fractures surrounding the borehole in coal can effectively reflect the geometrical characteristics of the fracture network, which impacts the non-Darcy gas seepage characteristics in fractured coal around the borehole. To investigate these characteristics, five types of coal samples with one to four through-going fractures were prepared, representing distinct geometrical features. The fractal dimension of the fracture network around the borehole was employed to quantitatively characterize its geometry, and a self-designed radial gas seepage system was utilized to conduct laterally confined radial seepage tests on fractured coal around the borehole, simulating the gas seepage process. The nonlinear characteristics and mechanisms of radial gas seepage in fractured coal around the borehole were analyzed using the Forchheimer equation. The results indicated: ① The fractured coal around the borehole exhibits robust fractal characteristics, with two-dimensional fractal dimensions (D2) ranging from 1.321 to 1.442 and three-dimensional fractal dimensions (D3) ranging from 2.321 to 2.442. Variations in the fractal dimension comprehensively reflect differences in fundamental geometric indices such as surface fracture rate (Rsc), number of fracture intersections (Nj), number of fracture segments (Nseg), total fracture length (Lsum), average fracture length (Lav), and average fracture width (e). ② Radial gas seepage in fractured coal around the borehole is influenced by three effects: local roughness, internal fluid friction, and tortuous flow. Under the same pressure gradient, a higher fractal dimension of the fracture network results in a lower flow rate through the network. ③ The seepage velocity of fractured coal around the borehole increases with the pressure gradient, gradually deviating from linearity. Greater seepage velocities lead to more pronounced nonlinearity. A higher fractal dimension of the fracture network limits the maximum achievable seepage velocity. ④ As the fractal dimension of the fracture network increases, the permeability of fractured coal around the borehole decreases, following the relationship 1011k = 4.6D32−23.9D3 + 31.9. Simultaneously, the β factor for non-Darcy flow increases. Moreover, the β factor decreases as permeability (k) increases.In summary, observing the fractal dimension of the fracture network around the borehole in gas pre-drainage operations along coal seams can provide crucial insights into the permeability of fractured coal, guiding the design of borehole layout parameters.

     

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