Wells near streams with semipervious beds

Abstract

Currently used formulas for the drawdown distribution and the rate and total volume of river depletion resulting from wells pumping nearby are based primarily on the assumption that the bed of the stream is as permeable as the aquifer it completely cuts through. These formulas have been empirically modified to be approximately applicable when the stream bed is semipervious and is partially penetrating the aquifer. This modification is based on the assumption that the resistance to flow due to the partial penetration and the semiperviousness of the stream bed can be reasonably replaced by its equivalent owing to flow through a horizontal additional stretch of the main aquifer. This additional length is determined empirically by using pumping test data in conjunction with the drawdown equation for the substitute system. In the present study, the approach to the problem is to replace the resistance to flow due to the semiperviousness of the bed of the stream by an equivalent resistance due to a horizontal flow through a semipervious layer of insignificant storage capacity which is lying between the aquifer and the channel of the stream. The conjecture is that this approach is closer to reality and, consequently, yields flow formulas that reproduce the flow conditions in the actual system more closely. Except for the unsteady drawdown equation, this approach has led to flow equations that are as easy as their counterparts now in use. Tabulation of the function involved in the unsteady drawdown equation is not difficult, and, once completed, the equation becomes as easy to use as any other simple formula. Quantitative comparison between results of the old and the new approaches are presented graphically. A procedure using the steady-state drawdown equation is outlined for obtaining the transmissivity of the aquifer, the effective distance to the stream, and the ‘retardation coefficient’ of the channel lining.