Identification of aquifer parameters from residual drawdowns: an optimization approach

Abstract

An optimization method based on nonlinear least squares is proposed for the identification of aquifer transmissivity and two storage coefficients, one for the pumping phase and the other for the recovery phase, using only residual drawdowns at an observation well. The method is applicable irrespective of whether pumping and recovery storage coefficients are the same or are different and the argument of well function during recovery is less than or greater than 0.01. The method can check for the changed value of storage coefficient during the recovery phase and can quantify this change. Use of the method is illustrated through examples, which show that the parameters are estimated reliably.Key words aquifer; drawdown; pumping test; optimization; parameter estimation; storage coefficient; transmissivity Identification de paramètres d'aquifère à partir de rabattements résiduels: une approche d'optimisationRésumé Une méthode d'optimisation basée sur les moindres carrés non-linéaires est proposée pour identifier la transmissivité de l'aquifère ainsi que deux coefficients de stockage, l'un pour la phase de pompage et l'autre pour la phase de relaxation, en n'utilisant que les rabattements résiduels au niveau d'un puits d'observation. La méthode est applicable que les coefficients de stockage en phases de pompage et de relaxation soient identiques ou différents, et que l'argument de la fonction de puits pendant la relaxation soit inférieur ou supérieur à 0.01. La méthode peut tenir compte de la modification de la valeur du coefficient de stockage lors de la phase de relaxation et peut quantifier cette modification. L'utilisation de cette méthode est illustrée par des exemples qui montrent que les paramètres sont estimés de manière satisfaisante. [-] u′ argument of well function during recovery [-] u i argument of well function during pumping for ith residual drawdown [-] u i ′ argument of well function during recovery for ith residual drawdown [-] α S′/S [-] Mots clefs

Estimation of aquifer parameters from residual drawdowns

“…When compared with other methods, the present method has yielded a more unbiased estimation of aquifer parameters with a low sum of squared errors (SSE). The present method also yielded a quick convergence (10 iterations) over the conventional algorithm (35 iterations) used by Singh (2006) for the same initial input guess values. Clearly, in the 75 years since Theis (1935), major improvements in the estimation of T and S are increasingly hard to find.…”

“…The same set of data has been analysed by other authors including Ballukaraya and Sharma (1991), Singh (1999), Chenaf and Chapuis (2002), Singh (2003), Zheng et al (2005) and Singh (2006). The residual drawdowns were measured in an observation well located 30 .…”

“…Dataset 2 was synthetically generated by Singh (2006) with Q ¼ 0 . 025 m 3 /s, r ¼ 150 m and t p ¼ 12 000 s by introducing random errors in proportion to drawdowns.…”

“…The residual drawdowns for three conditions (no errors, small errors, and large errors) from the instant of shutdown of pumping are given in Table 2. Singh (2006) used the conventional Levenberg-Marquardt algorithm (also, Marquardt algorithm) in estimating the aquifer parameters. The error in theoretical residual drawdowns from the two methods is shown in Figure 1.…”

“…The drawdowns measured in an observation well during pumping are commonly used to estimate the aquifer parameters such as storage coefficient and transmissivity (Ballukaraya and Sharma, 1991;Todd, 1980). Residual drawdowns, which are routinely measured during pumping tests are sometimes considered to be more reliable in the estimation of aquifer parameters (Singh, 2006). The recovery period begins from the time of shutting off the pump, during which drawdown begins to recoup (Banton and Bangoy, 1996).…”