基于速度势的多抽采钻孔干扰理论

Multiple Extraction Borehole Interference Theory Based on Velocity Potential

为得到多抽采钻孔干扰下瓦斯流场的基本特征,基于速度势理论及其叠加原理,对多钻孔共同抽采时的速度场确定方法进行了研究。推导得出等流量双钻孔互扰时的等势线族方程、流线族方程以及速度场分布函数,进而得到双钻孔干扰下的流线、等势线分布特征以及主流线和分流线上的速度变化规律,为钻孔抽采空白带位置计算提供了理论依据,并利用COMSOL Multiphysics进行了模拟验证。结果表明:两钻孔同时抽采时,从钻孔附近到远离钻孔的煤体深部,其等势线形状先是椭圆形,再为伯努利双纽线,最后逐渐趋近于圆形;其瓦斯流线或运动轨迹呈双曲线形式,与单一抽采钻孔流场特征有很大的不同。主流线上的流速最高,分流线上的速度先增大后减小,并在距平衡点1/2个钻孔间距位置达到最大值,钻孔外侧流速比内侧高。抽采空白区一般形成在平衡点位置附近,平衡点到两钻孔的距离之比与其流量成正比。

In order to obtain the basic characteristics of the gas flow field under the interference of multiple extraction boreholes,based on the velocity potential theory and its superposition principle,the determining method of the velocity field when multiple boreholes are jointly extracted was studied.The equipotential line family equation,streamline family equation and velocity field distribution function under the interference of equal-flow double borehole were derived.Then,the streamline,equipotential line distribution characteristics and the velocity variation laws on the mainstream line and shunt line under the interference of double boreholes were obtained.The theoretical basis for the calculation of the position of the blank zone of the double boreholes was provided,and the simulation verification was carried out by COMSOL Multiphysics.The results are concluded as follows.Firstly,when the double boreholes are extracted at the same time,from the vicinity of the borehole to the deep part of the coal body far away from the borehole,the shape of the equipotential line is elliptical first,then changes to the Bernoulli double lemniscate,and finally gradually approaches a circle.Secondly,the gas streamline or trajectory is hyperbolic,which is very different from the flow field characteristics of single extraction borehole.Thirdly,the velocity on the main flow line is the highest,but the velocity on the diversion line increases first and then decreases,and reaches the maximum at the position of 1/2 borehole spacing from the equilibrium point.The flow velocity inside the borehole is higher than the outside.Finally,the extraction blank area is generally formed near the equilibrium point,and the ratio of the distance from the equilibrium point to the two boreholes is proportional to its flow.