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 -