非达西效应下不稳定承压-无压井流的有限差分解

Finite difference solution for transient confined-unconfined flow with non-Darcian effect

在深部煤矿开采工程中,为了避免出现涌水现象,通常利用矿井排水使承压含水层水位低于采矿工作面,以确保煤炭开采的安全。因此,为了揭示承压含水层定流量抽水引起的不稳定承压-无压转换机理,提出了基于有限差分的非达西效应影响下不稳定承压-无压流的数值模型。该模型以Izbash方程为基础,提出了一种新的线性化方法来处理非达西问题,并进一步研究了非达西效应下非达西指数、准渗透系数和储水系数比对水位降深与无压区发展的影响。结果表明:在抽水期间,非达西指数和准渗透系数越大,则承压区的水位降深越大,无压区的水位降深越小,发生承压-无压转换的时间越晚;承压区的水位降深与储水系数比之间呈负相关关系,储水系数比越大意味着承压区存在较大的弹性储水量,对抽水井的补给水量也越大,导致水位降深越小。

To avoid the water inrush and ensure mining safety in deep coal mining engineering,it is common to use mine drainage to decrease the water level in the confined aquifer above the mine face.This paper proposes a new finite difference numerical solution to investigate the mechanism of transient confined-unconfined flow under the non-Darcian condition in the fully-penetrated confined aquifer.In order to use the finite difference method to solve the mathematical model,a new linearization method was developed to approximate the nonlinear terms of pumping-induced flow by using the Izbash’s equation.The model further investigated the non-Darcian effect represented by the non-Darcian index,hydraulic conductivity and the storativity ratio on drawdown simulation and development of the unconfined region.The results show that larger non-Darcian index and hydraulic conductivity can lead to a large drawdown in confined region,and a smaller drawdown in unconfined region and a later confined-unconfined conversion time;the storativity ratio has a negative effect on the drawdown and the development of the unconfined region;a large storativity ratio means a large storativity in the confined region and there is more water supply to the pumping well,leading to a smalle drawdown.