An analytical solution for a radial collector well near a stream with a low-permeability streambed

SummaryRadial collector wells are often constructed near a stream to obtain more water and produce smaller drawdown in comparison with traditional vertical wells. This paper aims at developing a mathematical model for describing head distributions induced by pumping in a radial collector well near a stream in an unconfined aquifer. A low permeable streambed between the stream and the aquifer is considered. The first-order free surface equation is used to describe the movement of water table. A point-sink solution of the model is developed first by a general transform combining Fourier sine and cosine transforms and then by Fourier transform and Laplace transform. The transient solution of head distributions for different well types such as the horizontal well or radial collector well can be obtained by integrating the point-sink solution along the well. Based on Darcy’s law and the developed solution, an equation for temporal stream depletion rate describing filtration from the stream is then obtained. The steady-state solutions for filtration can be obtained from the transient solution when neglecting the exponential term associated with time. It is found that steady-state filtration depends only on the ratio of streambed permeability over aquifer permeability. Steady-state filtration equals water extraction from a well when the ratio is larger than 10−2. The streambed is regarded as completely impermeable when the ratio is less than 10−7. Additionally, the lowest water table happens near the well before occurrence of filtration. The lowest water table moves landward and away from the well after filtration occurs.

► An analytical solution is developed to describe flow induced by a collector well.
► Steady depletion depends only on the ratio of streambed permeability to aquifer one.
► A well with laterals toward a stream produces large depletion and small drawdown.
► The water level predicted by the present solution agrees with the field data.