Hantush-Jacob r/B Solution for Leaky Confined Aquifers
Description
A mathematical solution by Hantush and Jacob (1955) is useful for determining the hydraulic properties (transmissivity and storativity of aquifer; vertical hydraulic conductivity of aquitard) of leaky confined (semi-confined) aquifers.
Analysis involves matching the Hantush-Jacob w(u,r/B) well function for leaky confined aquifers to drawdown data collected during a pumping test (aquifer test). The solution assumes no storage in incompressible leaky aquitard(s) and can account for partially penetrating wells (Hantush 1961a,b).
Kruseman and de Ridder (1994) refer to the curve-fitting procedure using the Hantush-Jacob solution as Walton's method (Walton 1962) and use the symbol w(u,r/L) for the Hantush-Jacob well function for leaky confined aquifers.
AQTESOLV provides visual and automatic methods for matching the Hantush-Jacob r/B solution to pumping test and recovery test data. This easy-to-use and intuitive aquifer test software promotes rapid and accurate determination of aquifer properties.
Other solution methods for leaky confined aquifers include the following:
- Hantush (1960) - line source with compressible 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 | Solution Options | Benchmark | References
Assumptions
The following assumptions apply to the use of the Hantush and Jacob r/B pumping test 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
- aquitards are incompressible (no storage)
- 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
- boundaries
Benchmark
Comparison of AQTESOLV (blue line) and published Hantush-Jacob (1955) well function values (symbols) for r/B=0.01.
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.
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.
See also: solution methods, pumping tests