Finiteness of steady state plumes
Finiteness of steady state plumes
复制标题
DOI：
10.1029/2005wr004000
复制
发表时间：
2005-12
影响因子：
5.4
通讯作者：
R. Liedl;A. Valocchi;P. Dietrich;P. Grathwohl
中科院分区：
文献类型：
--
作者：
R. Liedl;A. Valocchi;P. Dietrich;P. Grathwohl
通过开发和采用一种新的分析解决方案来确定稳态污染物羽流的有限最大长度，该解决方案克服了与现有方法相关的两个缺点。首先，我们考虑了在前沿发生的瞬时二元反应中，污染物（“电子供体”）和一些电子受体完全消耗所引起的尖锐前沿。这种方法不是基于纯粹的保守或一阶退化模型，这些模型会导致理论上无限的羽流，此外，还依赖于浓度阈值。其次，选择厚度有限的含水层垂直截面作为模型，以便更好地代表电子受体的供给，这些电子受体主要从顶部进入含水层。这种类型的设置允许研究含水层厚度对烟柱长度的影响。在有限垂直域中，供体-受体前沿的隐式表示先前需要潜在的平流-分散-反应方程的数值解；我们首次给出了这个二维输运问题的解析解。羽流的长度由供体-受体前缘与含水层底部的交点决定。此外，导出了一个相当简单和高度精确的近似计算稳态羽流长度。综合敏感性分析表明，含水层厚度对结果的影响最大，其次是垂直横向分散性，化学反应参数对结果的影响较小。纵向色散对羽流长度几乎没有影响，线速度对羽流长度的影响为零。关于在野外尺度上的地下水风险评估，同样重要的是要注意到，目前的方法旨在提供实际羽流长度的上限。进一步的研究活动可以通过考虑例如羽流内部的降解和污染源的有限垂直范围来指导改进传输模型。
The finite maximum length of a steady state contaminant plume is determined by developing and employing a new analytical solution which overcomes two drawbacks associated with existing approaches. First, we account for a sharp front caused by the complete consumption of the pollutant (“electron donor”) and some electron acceptor in an instantaneous binary reaction occurring at the front. This approach is not based on purely conservative or first‐order degradation models which lead to theoretically infinite plumes and, in addition, depend on a concentration threshold. Second, a vertical aquifer cross section with finite thickness is selected as a model in order to better represent the supply of electron acceptors mostly entering the aquifer from the top. This type of setting allows investigation of the impact of aquifer thickness on plume length. An implicit representation of the donor‐acceptor front in a finite vertical domain previously required numerical solutions of the underlying advection‐dispersion‐reaction equation; we provide for the first time an analytical solution of this two‐dimensional transport problem. The length of the plume is found to be given by the point of intersection of the donor‐acceptor front and the aquifer bottom. Furthermore, a rather simple and highly accurate approximation is derived to compute the steady state plume length. A comprehensive sensitivity analysis reveals that results are most strongly influenced by aquifer thickness, followed by vertical transverse dispersivity and, to a somewhat lesser extent, by chemical reaction parameters. Longitudinal dispersivity has practically no effect on plume length, and furthermore, there is zero impact of linear velocity. With regard to groundwater risk assessment at the field scale it is also important to note that the present approach is meant to provide an upper bound on the actual plume length. Further research activities may be directed to refine the transport model by considering, for instance, degradation inside the plume and the limited vertical extent of the contaminant source.