Using Cooper‐Jacob Approximation to Take Account of Pumping Well Pipe Storage Effects in Early Drawdown Data of a Confined Aquifer

Abstract

AbstractMost hydrogeology textbooks warn the reader that in order to avoid large errors the Cooper‐Jacob solution should only be applied when the u‐parameter of the Theis solution is less than 0.01 or 0.02. This paper proposes a graphical representation for visualizing and quantifying the difference between the two solutions. The graph of drawdown vs log (time) may be divided into three zones, the early one being influenced by storativity, pumping well pipe capacity and skin effects (among others), the latest by boundary effects, and the intermediate one by the transmissivity and storativity of the aquifer. The differences between the theoretical solutions are maximal in the early data zone. Because both solutions consider a pumping well of infinitesimal diameter, the early time data graph may be distorted by the influence of real well pipe storage capacity and, consequently, may yield a poor estimate of the parameters of the aquifer. The method of Papadopulos and Cooper is already available to take pumping well pipe storage into account in interpreting the pumping well drawdown data, but may result in unreliable S values due to the difficulty in curve matching. A more practical solution, which is also applicable to observation wells, is proposed and demonstrated with a worked example. This solution can be used when the Cooper‐Jacob approximation is valid and it does not require curve matching. Early drawdown data in the pumping well cannot provide a reliable estimate of storativity for many reasons. These early data can be used, however, to obtain a better estimate of storativity and transmissivity from the drawdown data of observation wells. The effect of pumping well pipe storage in the early drawdown data may be significant in cases of low transmissivity aquifers and low pumping rates, which are quite common in ground‐water remediation.