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Groundwater Flow: Transient Radial Flow to a Well in a Leaky Aquifer (Hantush-Jacob Method)

 When a semi-confined aquifer receives vertical recharge through an overlying aquitard during pumping, drawdown $(s)$ is non-steady and governed by the Hantush-Jacob Well Function:

$s = \frac{Q}{4 \pi \cdot T} \cdot W\left(u, \frac{r}{B}\right)$

​Where $Q$ is pumping discharge, $T$ is aquifer transmissivity, $r$ is radial distance from the well, and $W(u, r/B)$ is the leaky well function integrated over parameter $u:$

$u = \frac{r^2 \cdot S}{4 \cdot T \cdot t}$

​The leakage factor $B = \sqrt{T \cdot b' / K'}$ accounts for aquitard thickness $(b')$ and vertical hydraulic conductivity $(K').$ At long pumping durations $(t \to \infty),$ the transient response stabilizes into De Glee’s steady-state condition where leakage balances extraction.

​In the basaltic and weathered-rock aquifer systems of Central India, semi-confining clay layers create leaky groundwater conditions that complicate yield estimations during crop irrigation cycles.

​Modern hydrogeological field investigations deploy automated pumping tests coupled with type-curve matching software (such as AQTESOLV). Engineers rapidly evaluate leakance parameters (K'/b'), preventing the over-estimation of sustainable well yields in over-exploited agricultural blocks.

​Note: This technical content was curated and structured with AI assistance to support technical education.

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