If the Theis graphical method is used for determining the hydraulic constants of an aquifer under water-table conditions, the observed drawdowns should be corrected for the decrease in saturated thickness. This is especially true if the drawdown is a large fraction of the original saturated thickness, for then the computed coefficient of permeability is highly inaccurate if based on observed, rather than corrected, water levels. Wenzel's limiting formula, a modification of the Theis graphical method, is useful where u=r2s/4Tt is less than about 0.01. However, a shorter procedure for determination of the coefficient of transmissibility, as well as the coefficient of storage, consists of plotting the values of the corrected drawdowns against the values of the logarithm of r.
Wenzel (1942) suggested that observation wells be situated on lines that extend upgradient and downgradient from the pumped well. However, a detailed analysis of aquifer-test results indicates that such a restriction is unnecessary. The gradient method for determining permeability should yield the same results as the Thies method. The former, when applied for a distance within the range of applicability of the latter, is merely a duplication of effort or, at best, a crude check. Because of the limitations of accuracy in plotting, the gradient method is much less satisfactory. That Wenzel (1942) obtained identical results from the two methods is regarded as a coincidence.
Failure to take into consideration the fact that the pumped well does not tap the full thickness of the aquifer leads to an apparent coefficient of permeability that is much too low, especially if the aquifer consists of stratified sediments. The average coefficient of permeability computed from uncorrected drawdowns may be only a little more than half of the true value.