Approximation of Well Function and Identification of Leaky Aquifer Parameters

The existing equation for leaky aquifers is transformed into a nondimensional form using new parameters and a scaled well function for leaky aquifers is proposed. A computationally simple function is developed for accurately approximating the scaled well function for the practical range of the parameters. Utilizing this function (approximation), an optimization method is proposed for identifying the leaky-aquifer parameters from observed drawdowns. The new function has an enhanced utility when a repetitive numerical evaluation of the well function for leaky aquifers is needed, e.g., while estimating the aquifer parameters using optimization or Kalman filter or artificial neural network methods. The application of the proposed method is illustrated using a few sets of published data. The proposed method outperforms the extended Kalman filter method, based on the reported results in the literature.