TY - JOUR

T1 - Improvement on the estimation of constant-rate drawdown in large-diameter wells

AU - Chang, Y. C.

AU - Yeh, Hund-Der

AU - Wang, C. T.

PY - 2013

Y1 - 2013

N2 - Papadopulos and Cooper's (PC) solution can be used to describe the drawdown resulting from pumping with a constant rate at a large-diameter well. However, this solution is too complicated to be accurately evaluated due to the oscillatory nature of the Bessel functions. The PC approach resulted in tabulated values of dimensionless drawdown at the well with an accuracy of four or fewer digits for selected values of dimensionless storage coefficient versus dimensionless time. Some researchers have fitted the tabulated values with interpolation formulas that are easy to use in engineering applications. Those formulas may be more accurate if the tabulated values are computed with greater accuracy. In this study, 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. The proposed procedure can evaluate the dimensionless drawdown with greater accuracy and is useful in practice if there is a need for high accuracy for the observation either at the well or in the aquifer at some distance from the pumping well Editor D. Koutsoyiannis Citation Chang, Y.C., Yeh, H.D., and Wang, C.T., 2013. Improvement on the estimation of constant-rate drawdown in large-diameter wells. Hydrological Sciences Journal, 58 (3), 716-727.

AB - Papadopulos and Cooper's (PC) solution can be used to describe the drawdown resulting from pumping with a constant rate at a large-diameter well. However, this solution is too complicated to be accurately evaluated due to the oscillatory nature of the Bessel functions. The PC approach resulted in tabulated values of dimensionless drawdown at the well with an accuracy of four or fewer digits for selected values of dimensionless storage coefficient versus dimensionless time. Some researchers have fitted the tabulated values with interpolation formulas that are easy to use in engineering applications. Those formulas may be more accurate if the tabulated values are computed with greater accuracy. In this study, 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. The proposed procedure can evaluate the dimensionless drawdown with greater accuracy and is useful in practice if there is a need for high accuracy for the observation either at the well or in the aquifer at some distance from the pumping well Editor D. Koutsoyiannis Citation Chang, Y.C., Yeh, H.D., and Wang, C.T., 2013. Improvement on the estimation of constant-rate drawdown in large-diameter wells. Hydrological Sciences Journal, 58 (3), 716-727.

KW - aquifers

KW - constant-rate pumping

KW - drawdown

KW - large-diameter well

KW - numerical approach

KW - wells

UR - http://www.scopus.com/inward/record.url?scp=84876440460&partnerID=8YFLogxK

U2 - 10.1080/02626667.2012.755534

DO - 10.1080/02626667.2012.755534

M3 - Article

AN - SCOPUS:84876440460

SN - 0262-6667

VL - 58

SP - 716

EP - 727

JO - Hydrological Sciences Journal

JF - Hydrological Sciences Journal

IS - 3

ER -