双重多孔介质中考虑井损的三维渗流方程的解析解

从六十年代开始,国内外就有许多学者从事裂隙-岩溶介质(以下简称双重介质)中的渗流问题研究,并提出许多双重介质渗流模型,见文献[1],[2],[3],[4],[5],[6]。但从可以看到的文献资料,还未见到考虑井损的双重介质渗流模型。可是,抽水时由于井损在井内和井壁附近的水流都呈现三维流态。本文建立了考虑井内偏流、井壁摩阻以及井内水流加速运动等水头损失的双重介质三维渗流模型,并给出了定解问题的解。解的结构由两部分组成:第一部分为双重介质中二维流水位降深;第二部分为双重介质中共损引起的水位降深。实践表明,根据本文理论解所作的曲线基本接近抽水井中水位变化曲线,即抽水初期有滞后现象。可知本文提出的解是符合双重多孔介质井流特征的。

An Analytic Solution of the Three-Dimensional Flow Equation for Well-Loss in Double Porous Media

Many scholars at home and abroad have been engaging in the study of fluidproblem in double porous media since 1960's, and a lot of models of fluid in doubleporous media have been proposed. But as yet the fluid model takingwell-loss in double porous media into consideration has not been seen in referencesavailable. However, the water flow in the well and near the wall of the wellappears in three-dimensional flow state due to well-loss resulting from pumpingground water. Considering the head loss resulting from the deflection current in a well, thefrictional resistance of the wall of a well and the accelerated motion of flow ina well, a three-dimensional flow model in double porous media is established inthis paper and a solution of this boundary value problem is given. The structureof the solution consists of two parts, the first part being a two-dimensional draw-down of the well in double porous media and the second part being the well-lossresulting from the drawdown of the well in double porous media. It has been shown by practice that the theoretical curve drawn according to the solution in this paper coincides with that of the change of water table in thepumping well, i.e. the drawdown of the well possesses the delay phenomenon in theinitial stage of pumping water. Thus, it can be seen that the solution provided inthis paper is feasible.