Retracted: A Single Recovery Type Curve from Theis' Exact Solution

Abstract

The Theis type curve matching method and the Cooper-Jacob semilog method are commonly used for estimation of transmissivity and storage coefficient of infinite, homogeneous, isotropic, confined aquifers from drawdown data of a constant rate pumping test. Although these methods are based on drawdown data, they are often applied indiscriminately to analyze both drawdown and recovery data. Moreover, the limitations of drawdown type curve to analyze recovery data collected after short pumping times are not well understood by the practicing engineers. This often may result in an erroneous interpretation of such recovery data. In this paper, a novel but simple method is proposed to determine the storage coefficient as well as transmissivity from recovery data measured after the pumping period of an aquifer test. The method eliminates the dependence on pumping time effects and has the advantage of employing only one single recovery type curve. The method based on the conversion of residual drawdown to recovered drawdown (buildup) data plotted versus a new equivalent time (delta(t) x t(p)/t(p) + delta(t)). The method uses the recovery data in one observation point only, and does not need the initial water level h0, which may be unknown. The accuracy of the method is checked with three sets of field data. This method appears to be complementary to the Cooper-Jacob and Theis methods, as it provides values of both storage coefficient and transmissivity from recovery data, regardless of pumping duration.

An Improved Straight‐Line Fitting Method for Analyzing Pumping Test Recovery Data

“…All methods listed in Table 1 gave comparable results, which does not enable us to differentiate the performance of these methods. However, the unique features of our approach become obvious when we compare the straight‐line plot in Figure 1 with straight‐line fitting reported by others, e.g., Chenaf and Chapuis (2002, Figures 2 to 5) and Samani and Pasandi (2003, Figure 5b). In our Figure 1, all the points transformed from the recovery data fall onto a straight line nicely except for a couple of late time points, which may be due to measurement errors.…”

“…All other plots reported in Table 1 showed deviation from a straight‐line fit for early‐time data. In fact, both Chenaf and Chapuis (2002) and Samani and Pasandi (2003) adopted the Cooper‐Jacob approximation to arrive at linear relations that require both u 1 and u 2 to be no more than 0.01. For the application described in the previous section, we plotted the values of u 1 and u 2 vs. the corresponding t ′ in a semilog graph (Figure 2).…”

“…Department of the Interior (USDI) (1977, p. 120) to estimate T and S . This set of data has been analyzed by others, including Goode (1997), Chenaf and Chapuis (2002), and Samani and Pasandi (2003).…”

“…Since then, many have developed simplified methods for estimating T and S from recovery data by approximating the exact Theis solution. Detailed surveys of these methods can be found in Chapuis (1992), Banton and Bangoy (1996), Chenaf and Chapuis (2002), Agarwal (1980), Samani and Pasandi (2003, also see Ground Water 42, no. 1, for Notice of Plagiarism with regard to this paper), and Singh (2003).…”

Recent advances in modeling of well hydraulics

“…The analysis of residual drawdown data can estimate the transmissivity and provide an independent check on the hydrogeological parameters found from the previous drawdown data analysis. There are many studies associated with the data analyses of water level recovery after a pumping at a constant rate in confined aquifers with neglecting well radius [68,69] or considering well radius [70], leaky aquifers [71], unconfined aquifers [72], as well as for head recovery after a packer test in unsaturated fractured media [73]. Shapiro et al [74] presented a model based on the solutions of Papadopulos and Cooper [75] and Cooper et al [57] to determine the earlytime recovering water level following the shut down of a constant pumping in wells with turbulent head losses.…”