Methods for interpreting tracer tests often rely on equations assuming a natural regional flow which is straight and uniform. The main purpose of this project was to develop more realistic equations for the advective part of contaminant transport, by including the flow lines distortion occurring in the vicinity of the injection well. The complex potential of the flow during a tracer test was calculated by superimposing the complex potential of a natural, straight and uniform flow distorted by the presence of a passive well, and the complex potential of a radial flow corresponding to an isotropic injection alone. The equations were developed for a horizontal plan and the calculated complex potential yielded a groundwater velocity field, and after that a formula connecting the position of the advancing front of the tracer plume to the injection duration. These new equations were then tested with numerical simulations. A two-dimensional aquifer plan was modeled and set in order to numerically solve particle tracking and travel time computation of the moving front within a reasonable calculation time. This model provided a comparison of times needed to fully recover the tracer plume previously injected, the one calculated with the new equations and the one calculated with former equations neglecting the impact of the well presence on the groundwater flow field. The results showed that the new equations are significantly more precise, in particular when the injection rate is sufficiently low compared to the natural regional flow rate, with a relatively large well diameter and in the vicinity of the injection well. Three different plume shapes could be visualized numerically, and those shapes depend on the value of a parameter △ which compares the velocity component caused by the injection in the well and the component caused by the natural regional flow.

解释示踪剂测试的方法通常依赖于假设自然区域流动是直线且均匀的方程。该项目的主要目的是通过包括在注入井附近发生的流线畸变，为污染物输送的对流部分开发更现实的方程式。在示踪剂测试期间，通过将自然，笔直和均一的流动的复数电势（由于被动井的存在而变形）与径向流的复数电势（仅与各向同性注入相对应）相叠加，可以计算出示踪剂测试期间的复数电势。这些方程是为平面图开发的，计算出的复数势产生了地下水速度场，然后是一个公式，将示踪剂羽状物的前移位置与注入持续时间联系起来。然后用数值模拟测试这些新方程。对二维含水层计划进行建模和设置，以便在合理的计算时间内以数值方式解决运动前沿的粒子跟踪和行进时间计算。该模型提供了完全恢复先前注入的示踪羽流所需时间的比较，该时间是用新方程式计算的，而前一个方程式是计算的，而忽略了井的存在对地下水流场的影响。结果表明，新的方程式更加精确，尤其是当注入速率与自然区域流量相比足够低时，具有相对大的井径并且在注入井附近。可以用数字方式显示三种不同的羽状形状，这些形状取决于参数△的值，该值将井中注入引起的速度分量与自然区域流动引起的分量进行比较。