Consider the well-known Theis solution for a constant-rate pumping test in a nonleaky confined aquifer of infinite extent:
where s is drawdown [L], Q is pumping rate [L³/T], T is transmissivity [L²/T], t is time [T], r is radial distance [L] and S is storage coefficient [-].
The Cooper and Jacob method approximates the Theis well function, w(u), by truncating the infinite series in (4) after the first two terms:
How small should u be for (5) to be valid? The threshold for IARF (i.e., when Cooper and Jacob becomes valid) is often given as u ≤ 0.05 (Driscoll 1986) or u ≤ 0.01 (Kruseman and de Ridder 1994); however, we can see for ourselves when (5) is valid by plotting w(u) versus 1/u (dimensionless drawdown versus dimensionless time) on semilog axes and looking for a constant logarithmic derivative plateau (Figure 1).
|Figure 1. Theis (1935) solution (blue curve) plotted as w(u) versus 1/u on semilog axes. Logarithmic derivative shown by red curve.|
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