Author(s): Hund-Der Yeh; Chih-Tse Wang; Mo-Hsiung Chuang
Linked Author(s):
Keywords: Ground water; Wells; Numerical analysis; Shanks transform
Abstract: Papadopulos and Cooper [1967. Drawdown in a well of large diameter. Water Resour. Res. 3 (1), 241-244] developed a dimensionless drawdown solution due to a constant-rate pumping at a large-diameter well. Their solution contains an integral with the limits from zero to infinitive and many terms of the products of zero-order and first-order Bessel functions. This solution is however complicated to be accurately evaluated due to the alternately oscillatory nature of the Bessel functions. They gave tabulated values of dimensionless drawdown at the well with an accuracy of four digits for various values of dimensionless storage coefficient versus dimensionless time. There were two articles proposed interpolation formulas to represent the tabulated values for easy use in engineering applications. Those formulas may have better results if the accuracy of the tabulated values is improved. In this paper, we propose an efficient numerical procedure including a root search scheme to find the roots of the integrand, Gaussian quadrature for numerical integration, and Shanks transform to accelerate convergence of infinite series. This procedure can evaluate the dimensionless drawdown with an accuracy of six digits at least. The results are expressed in tabular forms for the dimensionless drawdown in terms of dimensionless distance and dimensionless time. These results are practically useful if good accuracy is needed for the observation either at the well or some distance from the pumping well.
Year: 2009