Hantush and Jacob Step Drawdown Test Solution for Leaky Confined Aquifers

Well-aquifer configuration for Hantush and Jacob (1955) step-drawdown test solution for leaky confined aquifers

Mahdi S. HantushHantush 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:

sw = Q 4 π T [ w u,r/B + 2 b 2 π 2 l - d 2 n = 1 1 n 2 sin n π l b - sin n π d b 2 · w u , (r/B)2 + K z / K r n π rw b 2 + 2Sw ] + CQP     (1) u = r w 2 S 4 T t     (2)

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]
  • Kr is the radial (horizontal) hydraulic conductivity [L/T]
  • Kz 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]
  • rw is well radius [L]
  • sw is drawdown in the pumped well [L]
  • S is storativity [dimensionless]
  • Sw is wellbore skin factor [dimensionless]
  • t is elapsed time since start of pumping [T]
  • T is transmissivity [L²/T]
  • w(u,β) is the Hantush and Jacob well function for leaky confined aquifers [dimensionless]

The exponent, P, in the nonlinear well loss term, CQP, 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
  • 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

Solution
Options

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

Example

Analysis of a step-drawdown test in a leaky confined aquifer
Estimation of aquifer properties and well loss by matching Hantush and Jacob (1955) type-curve solution to time-drawdown data from a step-drawdown test assuming a leaky confined aquifer (data from Clark 1977).

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.