Analytical solutions for contaminant transport in streams

The importance of the effect of surface/ground water interactions on contaminant transport in streams and rivers has been greatly recognized in the last two decades. Bencala and Walters (1983) [Bencala, K.E., Walters, R.A., 1983. Simulation of solute transport in a mountain pool-and-riffle stream – a transient storage model. Water Resources Research 19 (3), 718–724.] developed a mathematical model for the transient storage zone to represent the movement of solute from main streams into stagnant zones and back to the main stream. This model calculates the concentrations of a main channel and a storage zone and the transient storage is represented by the mass exchange due to the concentration difference between the stream and the storage zone. Later, Kazezyılmaz-Alhan and Medina (2006) [Kazezyılmaz-Alhan, C.M., Medina Jr., M.A., 2006. Stream solute transport incorporating hyporheic zone processes. Journal of Hydrology 329 (1–2), 26–38.] made several improvements to this transient storage model by incorporating advection and dispersion into the hyporheic zone and representing the mass transport between the channel and hyporheic zone by mass flux terms. In this study, analytical solutions are derived for both transient storage models for the cases of continuous and finite injections of a tracer. The analytical solutions provide the researchers with computational speed in obtaining results for contaminant transport problems, and a means to check the validity of the numerical models. The analytical solutions are compared to the numerical solutions for hypothetical problems. Comparison of results shows that the numerical and analytical solutions are in very good agreement.