地下水流有限差分模型开采井内水位的校正试验

Correction of drawdown in a pumping well for Finite Difference Models of groundwater flow

许多地下水流数值模拟的初学者往往将有限差分法求得的格点(结点)水位当作相同位置开采井的水位,这是一种错误做法。本文根据前人研究,系统阐明了由有限差分法计算出的格点(结点)水位只能代表该格点(结点)所在均衡区域的某种平均水位,必须减去用普勒凯特(Prickett)公式计算出的校正降深和井损之后,才能得出井内水位的合理模拟值。针对这个问题,设计了室内沙箱阶梯流量抽水试验,采用均匀正方形网格有限差分法进行模拟,并做出井中水位校正。试验结果表明,用有限差分法得到的开采井降深明显偏小,相对误差可达60%,而经校正之后精度显著提高,相对误差一般小于3%。

Newcomers on numerical modeling of groundwater flow tend to use nodal groundwater level obtained with Finite Difference Method （FDM） as the groundwater level in a pumping well. It is a mistake. According to existing studies, in this presentation the causes and correction of this mistake is clearly demonstrated. The nodal groundwater level calculated with FDM can only represent an average in the vicinity of the grid node. To obtain the correct groundwater level within the pumping well, an additional drawdown needs to be calculated by Priekett formula and the well loss must be taken into account. In particular in this study, an experimental pumping test has been carried out in a sandbox with step-variable flow rate. The test is simulated with FDM and then corrected. It is indicated that the nodal drawdown as the output of the numerical model is obviously small with a relative error up to 60%. However, the corrected drawdown is closes to the observed drawdown within the pumping well with a relative error generally less than 3%.