A novel analytical model of fluid leakage through an abandoned well*

A non-plugged abandoned well may cause unwanted flows and solute transport between aquifers. This research provides a novel analytical model to calculate the leakage rate in an abandoned well between a confined aquifer and an unconfined aquifer under steady-state flow conditions. The abandoned well is treated as a passive preferential flow channel connecting a confined aquifer receiving injection from a separate well and an overlying unconfined aquifer; an impermeable aquiclude separates the two aquifers. A closed-form analytical solution for the steady-state leakage rate through an abandoned well is derived. The concerned abandoned well in this study fully penetrates the receiving unconfined aquifer but only penetrates the ceiling of the injecting confined aquifer with a very small screen length (with respect to the confined aquifer thickness). The injection well is sealed from the receiving unconfined aquifer and fully penetrating in the injecting confined aquifer. The solution developed in this study is compared with a previous solution by Avci (1994) (Avci, 1994. Evaluation of flow leakage through abandoned wells and boreholes. Water Resources Research, 30(9), 2565-2578). Compared to Avci (1994), this research has two different assumptions: (1) The Avci solution assumed that the leakage effect occurs between two confined aquifers, and leakage concerned in this research occurs between an injecting confined aquifer and a receiving unconfined aquifer. (2) The abandoned well in the Avci (1994) solution fully penetrates both the receiving and injecting confined aquifers, while the abandoned well in this research fully penetrates the receiving unconfined aquifer but only penetrates the ceiling of the injecting confined aquifer with a minor screen length. In both this study and the Avci (1994), the injecting well is isolated from the receiving aquifer and fully penetrating in the injecting aquifer. The results show that the two solutions have similarities in thin confined aquifers but are much different in relatively thick confined aquifers (with thickness greater than 10 m). Using the Sobol method for global sensitivity analysis, we tested controls of the hydraulic conductivity ratio between confined and unconfined aquifers, the transmissivity of the confined aquifer over the injection rate per unit screen length, and the aquifer thickness on model performance. The results show that the model is most sensitive to the transmissivity of the confined aquifer over the injection rate per unit screen length. This research can be applied in multiple applications, such as modeling the leakage effect among two aquifers involving stormwater recharge and using a monitoring well to detect the existence of abandoned wells when the abandoned wells are not visible on the surface or not documented, among others.