潜水稳定井流的剖面二维数值模拟方法  

Sectional 2D numerical modelling method for steady state well-flow in an unconfined aquifer

作　　者：王旭升[1] 谢永桦 陈崇希 Wang Xusheng;Xie Yonghua;Chen Chongxi(Key Laboratory of Groundwater Conservation of Ministry of Water Resources(in preparation),Beijing 100083,China;School of Water Resources&Environment,China University of Geosciences(Beijing),Beijing 100083,China;School of Environment Studies,China University of Geosciences(Wuhan),Wuhan 430078,China)

机构地区：[1]中国地质大学(北京)水利部地下水保护重点实验室(筹),北京100083 [2]中国地质大学(北京)水资源与环境学院,北京100083 [3]中国地质大学(武汉)环境学院,武汉430078

出　　处：《地质科技通报》2023年第4期27-36,共10页Bulletin of Geological Science and Technology

基　　金：国家自然科学基金项目(41972263,41772249)。

摘　　要：经典Dupuit井流模型与考虑入渗的改进Dupuit井流模型,都受到Dupuit假定的影响,可能存在系统误差。建立反映三维流或轴对称二维流特性的潜水井流数值模型,是检验Dupuit模型可靠性的重要手段。提出一种模拟潜水稳定井流的剖面二维数值模拟方法,通过参数转换把柱坐标系的渗流方程变换为等效的直角坐标系方程,利用MODFLOW方体网格有限差分模型实现剖面二维流场模拟。数值模型以抽水井的井中水位为已知条件,渗出面的排水量按照Darcy定律差分公式计算,潜水面则通过MODFLOW对干-湿单元的处理加以识别,抽水流量经水均衡计算得到。通过采用精细化网格建立典型案例模型,获得模拟精度很高的结果,使反算抽水井流量的相对误差不超过0.2%。以此检验Dupuit井流模型,发现解析公式得到的水位线总体与数值模拟结果一致,仅在抽水井附近由于没有考虑水跃而偏低,且误差受到含水层渗透系数各向异性的影响。在有入渗的情况下,分水岭附近的渗流违反Dupuit假定。然而,改进的Dupuit井流公式计算的分水岭水位相对误差低于1%。这一数值模拟方法简单实用,但也受到MODFLOW本身局限性的约束。[Objective]Both the classical Dupuit model and the modified Dupuit model including infiltration are influenced by Dupuit’s assumption and have potential systematic errors.Building a numerical model of well flow in an unconfined aquifer by characterizing the three-dimensional or axisymmetric two-dimensional(2D)flow is an essential approach to verify the performance of Dupuit-type models.[Methods]In this study,a 2D numerical model is proposed for the steady state well-flow in an unconfined aquifer,in which the control equation of seepage in the cylindrical coordinates is transformed equivalently to the Cartesian coordinates through parameter transformation,and the sectional 2D modelling is implemented via the MODFLOW finite-difference grid of cubic blocks.In the numeric model,the water level in the pumping well is a given condition,the flux across the seepage face is estimated by difference equation according to Darcy’s law,the phreatic surface is identified by the treatment of dry and wet cells in MODFLOW,and the pumping rate is determined from the water debug calculation.[Results]Fine grids are constructed innumerical models of typical cases to obtain high-precision results,in which the relative error of the backwards estimated pumping rate is no more than 0.2%.This numerical model is used to check the Dupuit-type well-flow models.As indicated,the groundwater level estimated from the analytical formulas generally agrees well with the numerical modelling results,except that near the well,where the analytical solution underestimates the groundwater level due to ignoring the waterjump and the errors depend on the anisotropic permeability of the aquifer.When infiltration exists,the flow in the vicinity of watershed does not follow Dupuit’s assumption.However,the estimated groundwater level on the watershed by modified Dupuit well-flow equation has a low level of relative error,which is less than 1%.[Conclusion]This numerical method is simple and practical however it is also influenced by limitations in MODFLOW.

关 键 词：Dupuit假定 抽水井 入渗补给 渗出面 潜水面 各向异性 有限差分法 

分 类 号：P641[天文地球—地质矿产勘探]