An evaluation of analytical solutions to estimate drawdowns and stream depletions by wells

Abstract

Analytical solutions for computing drawdowns and streamflow depletion rates often neglect conditions that exist in typical stream‐aquifer systems. These conditions can include (1) partial penetration of the aquifer by the stream, (2) presence of a streambed clogging layer, (3) aquifer storage available to the pumping well from areas beyond the stream, and (4) hydraulic disconnection between the stream and the well. A methodology is presented for estimating extended flow lengths and other parameters used to approximate the increased head losses created by partially penetrating streams and clogging layer resistance effects. The computed stream depletion rates and drawdown distributions from several analytical solutions (Theis, 1941; Glover and Balmer, 1954; Jacob, 1950; Hantush, 1965) were compared to those obtained using a two‐dimensional groundwater flow model. The stream geometry was approximated as a semicircle. Numerical simulation results indicate that, because of the use of simplifying assumptions, the analytical solutions can misrepresent aquifer drawdown distributions and overestimate stream depletion rates. Assuming that a correct simulation of the stream depletion phenomenon is provided by the numerical model, the error associated with each of the simplifying assumptions was determined. At a time of 58.5 days after pumping began, errors in computed stream depletion rates due to neglect of partial penetration were 20%, those due to neglect of clogging layer resistance were 45%, and those due to neglect of storage in areas beyond the stream were 21%. Neglecting hydraulic disconnection had only a minor effect (i.e., an error of 1% only at a time of 58.5 days after pumping began) on computed stream depletion rates and a noticeable effect on aquifer drawdown distributions.