Cooper-Jacob Solution for Confined Aquifers
Description
The Cooper and Jacob (1946) solution (Jacob modified nonequilibrium method) is useful for determining the hydraulic properties (transmissivity and storativity) of nonleaky confined aquifers. Analysis involves matching a straight line to drawdown data as a function of the logarithm time since the start of pumping.
The Cooper and Jacob solution is a large-time approximation of the Theis nonequilibrium method. The approximation involves truncation of an infinite series expression for the Theis well function that is valid when the variable u (=r²S/4Tt) is small. AQTESOLV includes a feature to verify that u is sufficiently small for proper application of the Cooper-Jacob modified nonequilibrium method.
AQTESOLV provides visual and automatic methods for matching the Cooper and Jacob solution to pumping test data. This easy-to-use and intuitive software promotes rapid and accurate determination of aquifer properties.
AQTESOLV includes Jacob's correction for partial dewatering of water-table aquifers, thereby allowing use of the Cooper and Jacob solution for unconfined aquifers.
For variable rate pumping tests, the implementation of the Cooper and Jacob solution in AQTESOLV is equivalent to the method of Birsoy and Summers (1980) which applies the principle of superposition to the Cooper-Jacob approximation of the Theis equation.
Assumptions | Solution Options | Benchmark | References
Assumptions
The following assumptions apply to the use of the Cooper and Jacob solution:
- aquifer has infinite areal extent
- aquifer is homogeneous, isotropic and of uniform thickness
- control well is fully penetrating
- flow to control well is horizontal
- aquifer is 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 control well can be neglected
- values of u are small (i.e., r is small and t is large)
Solution Options
AQTESOLV provides the following options for the Cooper and Jacob modified nonequilibrium method:
- variable pumping rates
- multiple observation wells
Benchmark
Benchmark of Cooper and Jacob (1946) straight-line solution to time-drawdown data (squares) collected in an observation well during a constant-rate pumping test in a nonleaky confined aquifer. The derivative shown on the plot (crosses) guides the fit of the straight line to drawdown data from the infinite-acting radial flow period (data from Walton 1962).
References
Cooper, H.H. and C.E. Jacob, 1946. A generalized graphical method for evaluating formation constants and summarizing well field history, Am. Geophys. Union Trans., vol. 27, pp. 526-534.
See also: solution methods, pumping tests