基于分数阶Maxwell蠕变模型的扩孔钻孔动态缩孔研究

    Research on dynamic shrinkage of hydraulic flushing borehole based on fractional Maxwell creep model

    • 摘要: 扩孔增透技术已经被广泛应用于松软煤层的瓦斯抽采。然而松软煤体强度低,极易发生蠕变变形,导致钻孔严重缩孔,影响瓦斯抽采效率。针对扩孔钻孔的缩孔问题,基于平面应变假设、煤体应变软化−扩容特性、分数阶Maxwell蠕变模型及Mohr-Coulomb准则等基本力学原理,推导了扩孔钻孔四周煤体的二维黏弹塑性应力−应变解析解,构建了扩孔钻孔半径动态演化模型,并采用COMSOL Multiphysics数值模拟软件对钻孔的动态缩孔机理及其影响因素进行了数值分析。研究结果表明:在蠕变效应作用下,扩孔钻孔成孔后,钻孔四周煤体所受径向应力和切向应力均不随时间发生明显变化,而径向应变不断增加,导致钻孔半径逐渐减小,即钻孔发生缩孔;钻孔刚刚成孔时(0 d),孔壁处煤体的径向应变仅为8.59%;成孔120 d时,孔壁处煤体的径向应变增加到35.17%,导致钻孔缩孔68.2%;钻孔缩孔受弹性模量、黏滞性系数、分数阶阶次、扩容系数和初始地应力等参数的影响较大;具体而言,弹性模量和黏滞性系数越小,分数阶阶次、扩容系数和初始地应力越大,钻孔四周煤体的径向应变越大,钻孔缩孔越严重。

       

      Abstract: Hydraulic flushing and permeability improving technology has been widely used in gas extraction in soft coal seams. However, the strength of soft coal is low, so creep deformation is easy to occur, resulting in serious borehole shrinkage and thus affecting gas extraction efficiency. Aiming at the shrinkage problem of hydraulic flushing borehole, firstly, we derived the 2D visco-elastoplastic stress-strain analytical solution of coal around the hydraulic flushing borehole based on the basic mechanical principles such as plane strain assumption, strain softening-expansion characteristics of coal, fractional Maxwell model and Mohr-Coulomb criterion, and then constructed the dynamic evolution model of borehole radius. Based on this model, the dynamic shrinkage mechanism of hydraulic flushing borehole was numerically analyzed by adopting the COMSOL Multiphysics numerical analysis software. The results show that the radial stress and tangential stress of the coal around the borehole do not change obviously with time after the borehole is constructed, while the radial strain increases continuously, resulting in a gradual decrease in borehole radius under the effect of creep. When the borehole was just constructed (0 d), the radial strain in the coal at the borehole wall was only 8.59%. However, when the borehole was constructed for 120 days, the radial strain in the coal at the borehole wall increased to 35.17%, the borehole shrinkage amplitude reaches 68.2%. At the same time, the borehole shrinkage is greatly affected by parameters such as elastic modulus, viscosity coefficient, fractional order, expansion coefficient and initial ground stress. Specifically, the smaller the elastic modulus and viscosity coefficient, the higher the fractional order, the expansion coefficient and the initial ground stress, the larger the radial strain of the coal around the borehole, and the more serious the borehole shrinkage.

       

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