# Hantush and Jacob Step Drawdown Test Solution for Leaky Confined Aquifers

Related Solution Methods

Hantush and Jacob (1955) developed a mathematical solution for determining the hydraulic properties of leaky confined aquifers. Hantush (1961a, b) subsequently introduced equations for partially penetrating wells. For step-drawdown tests, the Hantush and Jacob solution can be modified to include linear and nonlinear well losses in the pumping well (Jacob 1947; Rorabaugh 1953; Ramey 1982). Analysis involves matching a curve to drawdown data collected during a step-drawdown test.

The Hantush and Jacob model for a partially penetrating pumping well in an anisotropic leaky confined aquifer, adapted for step-drawdown tests to include linear and nonlinear well loss, is given by the following equation:

where

• $b$ is aquifer thickness [L]
• $C$ is nonlinear well loss coefficient [TP/L3P-1]
• $d$ is the depth to the top of pumping well screen [L]
• ${K}_{r}$ is the radial (horizontal) hydraulic conductivity [L/T]
• ${K}_{z}$ is the vertical hydraulic conductivity [L/T]
• $l$ is the depth to the bottom of pumping well screen [L]
• $Q$ is pumping rate [L³/T]
• ${r}_{\mathrm{w}}$ is well radius [L]
• ${s}_{\mathrm{w}}$ is drawdown in the pumped well [L]
• $S$ is storativity [dimensionless]
• ${S}_{\mathrm{w}}$ is wellbore skin factor [dimensionless]
• $t$ is elapsed time since start of pumping [T]
• $T$ is transmissivity [L²/T]
• $\text{w}\left(u,\beta \right)$ is the Hantush and Jacob well function for leaky confined aquifers [dimensionless]

The exponent, $P$, in the nonlinear well loss term, $C{Q}^{P}$, is generally taken to be 2 as originally proposed by Jacob (1947); however, Rorabaugh (1953) postulated that $P$ may range between 1.5 and 3.5.

## Assumptions

The following assumptions apply to the use of the Hantush and Jacob step test solution:

• aquifer has infinite areal extent
• aquifer is homogeneous, isotropic and of uniform thickness
• pumping well is fully or partially penetrating
• aquifer is leaky confined
• water is released instantaneously from storage with decline of hydraulic head
• diameter of pumping 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
• aquitards are incompressible (no storage)
• flow in the aquitards is vertical

## SolutionOptions

provides the following options for the Hantush and Jacob step test solution for leaky confined aquifers:

• variable pumping rates
• multiple pumping wells
• multiple observation wells
• partially penetrating pumping and observation wells
• boundaries

## References

Hantush, M.S. and C.E. Jacob, 1955. Non-steady radial flow in an infinite leaky aquifer, Am. Geophys. Union Trans., vol. 36, no. 1, pp. 95-100.

Jacob, C.E., 1947. Drawdown test to determine effective radius of artesian well, Trans. Amer. Soc. of Civil Engrs., vol. 112, paper 2321, pp. 1047-1064.

Ramey, H.J., 1982. Well-loss function and the skin effect: A review. In: Narasimhan, T.N. (ed.) Recent trends in hydrogeology, Geol. Soc. Am., special paper 189, pp. 265-271.

Rorabaugh, M.J., 1953. Graphical and theoretical analysis of step-drawdown test of artesian well, Proc. Amer. Soc. Civil Engrs., vol. 79, separate no. 362, 23 pp.

Bear, J., 1979. Hydraulics of Groundwater, McGraw-Hill, New York, 569p.