Evolution of the radius of investigation during recovery tests

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.