# Hantush H(u,β) Solution for Leaky Confined Aquifers

Hantush (1960) published a mathematical solution that is useful for determining the hydraulic properties (transmissivity and storativity of pumped aquifer; vertical hydraulic conductivity and storage coefficient of aquitard) of **leaky confined** (semi-confined) aquifers.

Evaluation of aquifer properties involves matching the Hantush **H(u,β)** well function to water-level drawdown data collected during a pumping test (aquifer test). The solution assumes storage in leaky compressible aquitard(s) and also accounts for partially penetrating wells (Hantush 1961a,b).

AQTESOLV provides visual and automatic methods for matching the Hantush H(u,β) solution to pumping test data. This easy-to-use and intuitive software promotes rapid and accurate determination of aquifer properties.

Other solution methods for leaky confined aquifers include the following:

- Hantush and Jacob (1955) - line source with incompressible aquitard
- Neuman and Witherspoon (1969) - line source with compressible aquitard and variable-head in source aquifer
- Moench (1985) - finite-diameter well with wellbore storage and wellbore skin for Hantush Cases 1, 2 and 3

## Assumptions

The following assumptions apply to the use of the Hantush β solution:

- aquifer has infinite areal extent
- aquifer is homogeneous, isotropic and of uniform thickness
- control well is fully or partially penetrating
- flow to control well is horizontal when control well is fully penetrating
- aquifer is leaky confined
- flow is unsteady
- water is released instantaneously from storage with decline of hydraulic head
- diameter of control well is very small so that storage in the well can be neglected
- aquitards have infinite areal extent, uniform vertical hydraulic conductivity and uniform thickness
- aquitards are overlain or underlain by an infinite constant-head plane source
- flow in the aquitards is vertical

## Solution

Options

AQTESOLV provides the following options for the Hantush and Jacob r/B solution for leaky confined aquifers:

- variable pumping rates
- multiple pumping wells
- multiple observation wells
- partially penetrating pumping and observation wells

## Benchmark

## References

Hantush, M.S., 1960. Modification of the theory of leaky aquifers, Jour. of Geophys. Res., vol. 65, no. 11, pp. 3713-3725.

Hantush, M.S., 1961a. Drawdown around a partially penetrating well, Jour. of the Hyd. Div., Proc. of the Am. Soc. of Civil Eng., vol. 87, no. HY4, pp. 83-98.

Hantush, M.S., 1961b. Aquifer tests on partially penetrating wells, Jour. of the Hyd. Div., Proc. of the Am. Soc. of Civil Eng., vol. 87, no. HY5, pp. 171-194.