Pumping induced depletion from two streams

We have proved that the Hantush’s model [Hantush MS. Wells near streams with semipervious beds. J Geophys Res 1965;70:2829–38] in a half-domain can be extended to a whole-domain and becomes identical to that of Hunt [Hunt B. Unsteady stream depletion from ground water pumping. Ground Water 1999;37(1):98–102] for a shallow and infinitely narrow stream, provided that the Dupuit assumption is adopted. This proof helps correct a false concept that regards the Hantush’s model as less useful because of its fully penetrating stream assumption. This study deals with interaction of an aquifer with two parallel streams based on the Hantush’s model. Semi-analytical solutions are obtained based on rigorous mass conservation requirement by maintaining continuity of flux and head along the aquifer–streambed boundaries. This study shows that the hydraulic conductivity ratio of the two streambeds appears to be the most important factor controlling the stream–aquifer interaction, followed by a less important role played by the thickness ratio of the two streambeds. When the low-permeability streambeds do not exist, the steady-state stream depletion from one stream is linearly proportional to the ratio of the shortest distance from the pumping well to the other stream over the shortest distance between the two streams. When the low-permeability streambeds are presented, similar conclusion can be drawn except that the stream depletion now also strongly depends on the hydraulic conductivity ratio of the two streambeds. When the values of the hydraulic conductivity of the two streambeds are different by an order of magnitude, the location of the pumping well that receives equal flux from two streams can be off the middle-line between the two streams by nearly 90%.