Estimating formation properties from early-time oscillatory water levels in a pumped well

Hydrologists often attempt to estimate formation properties from aquifer te sts for which only the hydraulic responses in a pumped well are available. Borehole storage, turbulent head losses, and borehole skin, however, can ma sk the hydraulic behavior of the formation inferred from the water level in the pumped well. Also, in highly permeable formations or in formations at significant depth below land surface, where there is a long column of water in the well casing, oscillatory water levels may arise during the onset of pumping to further mask formation responses in the pumped well. Usually bo rehole phenomena an confined to the early stages of pumping or recovery, an d late-time hydraulic data can be used to estimate formation properties. In many instances, however, early-time hydraulic data provide valuable inform ation about the formation, especially if there are interferences in the lat e-time data. A mathematical model and its Laplace transform solution that a ccount for inertial influences and turbulent head losses during pumping is developed for the coupled response between the pumped borehole and the form ation. The formation is assumed to be homogeneous, isotropic, of infinite a real extent, and uniform thickness, with leakage from an overlying aquifer, and the screened or open interval of the pumped well is assumed to fully p enetrate the pumped aquifer. Other mathematical models of aquifer flow can also be coupled with the equations describing turbulent head losses and the inertial effects on the water column in the pumped well. The mathematical model developed in this paper is sufficiently general to consider both unde rdamped conditions for which oscillations arise, and overdamped conditions for which then ale no oscillations. Through numerical inversion of the Lapl ace transform solution, type curves from the mathematical model are develop ed to estimate formation properties through comparison with the measured hy draulic response in the pumped well. The mathematical model is applied to e stimate formation properties from a singlewell test conducted near Waialua, Oahu, Hawaii. At this site, both the drawdown and recovery showed oscillat ory water levels in the pumped well, and a step-drawdown test showed that a pproximately 86% of the drawdown is attributed to turbulent head losses. An alyses at this site using late-time drawdown data were confounded by the no ise present in the measured water levels due primarily to nearby irrigation wells and ocean tides. By analyzing the early-time oscillatory recovery da ta at the Waialua site, upper and lower bounds were placed on the transmiss ivity, T, storage coefficient, S, and the leakance of the confining unit, K '/B'. The upper and lower bounds on T differ by a factor of 2. Upper and lo wer bounds on S and K'/B' are much larger, because drawdown stabilized rela tively quickly after the onset of pumping. (C) 2000 Published by Elsevier S cience B.V.