An analytical solution for non-Darcian flow in a confined aquifer using the power law function
An analytical solution for non-Darcian flow in a confined aquifer using the power law function
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DOI：
10.1016/j.advwatres.2007.06.002
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发表时间：
2008-01
影响因子：
4.7
通讯作者：
Z. Wen;Guanhua Huang;Hongbin Zhan
中科院分区：
文献类型：
--
作者：
Z. Wen;Guanhua Huang;Hongbin Zhan
本文提出了一种新的方法来分析承压含水层中非达西渗流。这种方法是基于非达西流方程的线性化近似和拉普拉斯变换的组合。得到了稳态压降和后期压降的解析解。利用Stehfest数值逆拉普拉斯变换，计算了任意距离和时间的压降的半解析解。在Darcian流的特殊情况下，本文的结果与前人的Theis解和Papadopulos及库珀解完全一致。以往常用于求解非达西流问题的玻尔兹曼变换，在研究径向非达西流问题时存在问题。通过我们提出的方法和玻尔兹曼变换方法得到的压降比较表明，玻尔兹曼变换方法在早期和中期不同于线性化方法，并且在后期产生与线性化方法相似的结果。幂指数n和准水力传导系数k越大，后期压降越小，与井筒储存无关。当n较大时，流动更早地接近稳定状态。稳定状态下的水位降深近似与r1−n成正比，其中r是距抽油井的径向距离。后期压降是稳态解和与t（1−n）/（3−n）成比例的负的时间相关项的叠加，其中t是时间。
We have developed a new method to analyze the power law based non-Darcian flow toward a well in a confined aquifer with and without wellbore storage. This method is based on a combination of the linearization approximation of the non-Darcian flow equation and the Laplace transform. Analytical solutions of steady-state and late time drawdowns are obtained. Semi-analytical solutions of the drawdowns at any distance and time are computed by using the Stehfest numerical inverse Laplace transform. The results of this study agree perfectly with previous Theis solution for an infinitesimal well and with the Papadopulos and Cooper’s solution for a finite-diameter well under the special case of Darcian flow. The Boltzmann transform, which is commonly employed for solving non-Darcian flow problems before, is problematic for studying radial non-Darcian flow. Comparison of drawdowns obtained by our proposed method and the Boltzmann transform method suggests that the Boltzmann transform method differs from the linearization method at early and moderate times, and it yields similar results as the linearization method at late times. If the power index n and the quasi hydraulic conductivity k get larger, drawdowns at late times will become less, regardless of the wellbore storage. When n is larger, flow approaches steady state earlier. The drawdown at steady state is approximately proportional to r1−n, where r is the radial distance from the pumping well. The late time drawdown is a superposition of the steady-state solution and a negative time-dependent term that is proportional to t(1−n)/(3−n), where t is the time.