Quantitative study of 3D numerical simulation on optimizing borehole layout spacing of gas drainage
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摘要: 为了识别钻孔间距对煤层瓦斯抽采的影响及如何实现高效抽采，基于流固耦合模型，建立三维几何模型，使其更接近现场实际，借助COMSOL软件模拟某煤矿钻孔不同间距的瓦斯抽采过程，利用瓦斯压力为0.74 MPa等压面三维立体图使有效抽采区域可视化，通过计算有效抽采区域体积大小，量化分析钻孔间距对抽采效果的影响。结果表明：单一钻孔抽采120 d时，有效抽采半径约为1.5 m；当布置多个钻孔且钻孔间距d为5 m，抽采120 d时，瓦斯压力为0.74 MPa的等压面围绕所有钻孔近似呈圆柱状但向内部凹陷（即出现空白带）；钻孔间距d为2.1、3、4、5、6 m时，有效抽采区域体积V的大小顺序随着时间的增长而改变，抽采120 d时，Vd=5 m>Vd=4 m>Vd=3 m>Vd=2.1 m>Vd=6 m。综合分析瓦斯压力等压面三维立体图和有效抽采区域体积的大小顺序，确定该矿钻孔的较优间距为4 m。研究提出的以有效抽采半径、叠加效应、三维瓦斯压力等压面的形状及有效抽采区域体积大小为指标的钻孔间距数值计算考察方法，可为煤矿井下钻孔间距优化布置提供参考。Abstract: In order to optimize the spacing of boreholes and realize efficient drainage, based on the fluid solid coupling model, a three-dimensional geometric model was established to make it closer to the field reality, the gas drainage processes of a coal mine with different borehole spacing were simulated using COMSOL software. The results show that: the effective drainage area was visualized by the three-dimensional diagram of the isobaric surface with gas pressure of 0.74 MPa, and the influence of borehole spacing on the extraction efficiency was discussed. The results show that: the effective extraction radius is about 1.5 m during gas extraction with single borehole at 120 days; when the borehole spacing d was 5 m during gas extraction with multiple boreholes at 120 days, the isobaric surface with gas pressure of 0.74 MPa was approximately cylindrical around all the boreholes, but it was sunken to the interior(there is a blanking zone); when the borehole spacing were 2.1 m, 3 m, 4 m, 5 m and 6 m respectively, the order of the volumes of the effective drainage area V changed with the growth of time; at 120 days, the order was Vd=5 m>Vd=4 m>Vd=3 m>Vd=2.1 m>Vd=6 m. According to the three-dimensional diagram of gas pressure isobaric surface and the order of effective drainage area volumes, the optimal borehole spacing is determined to be 4 m. In this paper, a numerical investigation method for borehole spacing based on effective extraction radius, superposition effect, shape of isobaric surface of three-dimension of gas pressure and volume of effective extraction area was presented, providing reference for optimizing layout of borehole spacing in underground coal mines.
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图 2 不同试验点物理模拟和数值模拟瓦斯压力对比曲线
Fig. 2 Comparison curves of gas pressures in physical simulation and numerical simulation at different test points
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图 5 不同间距钻孔瓦斯抽采时煤层内点P的瓦斯压力与时间曲线
Fig. 5 Gas pressure and time curves of point p in coal seam during gas drainage with different borehole spacing
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图 6 不同间距钻孔抽采时瓦斯压力演化及有效抽采半径立体图
时间为1.036 8×107s，因变量为p，MPa
Fig. 6 Diagrams of gas pressure evolution and effective radius during gas drainage with different borehole spacing
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图 7 不同钻孔间距有效抽采区域体积变化曲线
Fig. 7 Volume variation curves of effective extraction area with different borehole spacing
表 1 模型参数取值
Table 1 The values of the model parameters
参数 数值 弹性模量E/Pa 2.8×109 煤基质弹性模量ES/ Pa 8.4×109 泊松比υ 0.3 煤基质密度s/(kg·m–3) 1.35×103 煤层初始孔隙率${\phi _0}$ 0.037 煤层裂隙初始渗透率k0/m2 8.6×10–17 瓦斯动力黏度g/(Pa·s) 1.08×10–5 初始瓦斯压力p0/Pa 1.0×106 Langmuir压力常数pL/Pa 3.03×106 Langmuir体积应变常数${\varepsilon _{\rm{L}}}$ 0.026 
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