Hantush and Jacob Step Drawdown Test Solution for Leaky Confined Aquifers
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:
- is aquifer thickness [L]
- is nonlinear well loss coefficient [TP/L3P-1]
- is the depth to the top of pumping well screen [L]
- is the radial (horizontal) hydraulic conductivity [L/T]
- is the vertical hydraulic conductivity [L/T]
- is the depth to the bottom of pumping well screen [L]
- is pumping rate [L³/T]
- is well radius [L]
- is drawdown in the pumped well [L]
- is storativity [dimensionless]
- is wellbore skin factor [dimensionless]
- is elapsed time since start of pumping [T]
- is transmissivity [L²/T]
- is the Hantush and Jacob well function for leaky confined aquifers [dimensionless]
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
- flow is unsteady
- 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
AQTESOLV 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
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.