Abstract Pumping tests are routinely performed to characterize aquifers. In particular, recovery tests involve analyzing the residual drawdown after the termination of pumping. Evaluating the radius of investigation of pumping tests is important for test design and interpretation. However, the radius of investigation during the recovery phase has rarely been discussed in the literature. Here, we derive exact (semi-analytical) and approximate (fully analytical) solutions for the radius of investigation during the recovery phase, and present a sensitivity analysis for typical parameter values. During recovery, the radius of investigation shows non-monotonic behavior: it first increases, then decreases, and eventually vanishes. The maximum radius can be up to five times larger than that at the end of the pumping phase in the investigated range of parameter values. However, the conditions yielding a large radius of investigation are such that the time at which the maximum occurs is relatively large: up to one hundred times the pumping duration, depending on the parameters. Thus, in practice, one may need to find a compromise between the size of the investigated area and the time required for the test. In addition to the aquifer parameters, we observe that the pumping rate and duration, and the apparent measurement resolution are key parameters controlling the radius of investigation during recovery. Finally, the approach is applied to a field example. This study provides fundamental insight on the radius of investigation of recovery tests as well as practical solutions, thereby facilitating the design and interpretation of recovery tests in practice.

中文翻译：

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恢复测试期间调查半径的演变

摘要 抽水试验通常用于表征含水层。特别是，采收率测试涉及分析泵送终止后的残余压降。评估抽水试验的调查半径对于试验设计和解释很重要。然而，文献中很少讨论恢复阶段的调查范围。在这里，我们推导出了恢复阶段调查半径的精确（半分析）和近似（全分析）解，并对典型参数值进行了敏感性分析。在恢复期间，调查半径表现出非单调行为：它首先增加，然后减少，最终消失。在所研究的参数值范围内，最大半径可以比泵送阶段结束时的半径大五倍。然而，产生大调查半径的条件是出现最大值的时间相对较大：根据参数的不同，可达抽水持续时间的 100 倍。因此，在实践中，人们可能需要在调查区域的大小和测试所需的时间之间找到折衷方案。除了含水层参数外，我们观察到抽水率和持续时间以及表观测量分辨率是控制恢复期间调查半径的关键参数。最后，将该方法应用于现场示例。这项研究提供了关于恢复测试调查半径的基本见解以及实用的解决方案，