Semianalytical Solutions for Stream Depletion in Partially Penetrating Streams

Abstract

In the analysis of streamflow depletion, the Hunt (1999) solution has an important advantage because it considers a partially penetrating stream. By extending the Hunt drawdown solution, this paper presents semianalytical solutions for gaining streams that evaluate the induced stream infiltration and base flow reduction separately. Simulation results show that for a given deltah (the initial hydraulic head difference between stream and aquifer beneath the channel), the base flow reduction is in direct proportion to the product of streambed leakage (lambda) and the distance between pumping well and stream (L), and the induced stream infiltration is in inverse proportion to lambdaL. Deltah has a significant effect on the ratio of stream infiltration to base flow reduction. The results from the semianalytical solutions agree well with those from MODFLOW simulations. The semianalytical solutions are useful in the verification of numerical simulations and in the analysis of stream-aquifer interactions where water quantity or quality is concerned.

Streamflow depletion by wells--Understanding and managing the effects of groundwater pumping on streamflow

“…Other factors also affect the relative proportion of captured discharge and induced infiltration. These factors include the pumping rate of the well (with greater rates of induced infiltration occurring for higher pumping rates), the direction of groundwater flow in the aquifer prior to pumping, the distribution of aquifer boundaries near the well (including the presence of impermeable boundaries and other streams), the hydraulic properties of the aquifer and streambank materials, and the penetration depths of the pumped well and stream into the aquifer (Newsom and Wilson, 1988;Morrissey, 1989;Wilson, 1993;Conrad and Beljin, 1996;Chen, 2001;Chen and Yin, 2001;Chen and Shu, 2002;Chen and Chen, 2003;Chen and Yin, 2004;Gannett and Lite, 2004).…”

A general analytical solution for flow to a single horizontal well by Fourier and Laplace transforms

“…The stream depletion rate increases gradually with pumping time and finally approaches one, which reflects most of water comes from the stream, after a certain period of pumping time. Many analytical models treat the stream as a constant-head boundary to estimate stream depletion rate [e.g., [1][2][3]6,17,21]. Some researchers proposed to treat the stream as a variable stream stage represented by a periodic function for seasonal variations or a function changed in space and time for flood wave [7].…”

Analytical solutions for stream‐aquifer flow exchange under varying head asymmetry and river penetration: Comparison to numerical solutions and use in regional groundwater models

“…There have been many studies of the stream‐aquifer interaction using analytical techniques in the recent past [e.g., Zlotnik and Huang , ; Moench and Barlow , ; Butler et al ., ; Chen and Yin , ; Moutsopoulos and Tsihrintzis , ; Akylas and Koussis , ; Sun and Zhan , ; Zlotnik and Tartakovsky , ; Intaraprasong and Zhan , ; Moutsopoulos , ] or purely numerical techniques [ Graham and Butts , ; Gunduz and Aral , ]. These studies have gradually and greatly improved over the early work of Theis.…”