Analytical solution and analysis for solute transport in streams with diffusive transfer in the hyporheic zone

• Analytical solutions of solute transport in streams with hyporheic zone are derived.
• Solutions are in excellent agreement with the experimental findings.
• Performing parameter sensitivity analysis becomes easy due to analytical solutions.
• Our solutions can be used as a tool to verify the related numerical schemes.
• Our solutions can be reliably used to analyze solute transport processes in streams.

Solute transport in streams with diffusive transfer in the hyporheic zone is studied. Analytical solution of the diffusive transfer model is obtained by means of Laplace transform. Solutions are derived for a general situation, in which the concentration at the injection point is a function of time. In order to illustrate the use of present analytical solution, physical transport parameters are estimated for the observed data of Uvas Creek tracer experiment for chloride concentration and also of Wkra river tracer experiment. The concentration–time breakthrough curves obtained from the analytical solutions are found to be in good agreement with the observed as well as numerical concentration–time breakthrough curve. Step concentration–time profile and continuous concentration–time profile are considered as upstream boundary conditions for conservative solute. An instantaneous injection of solute is taken as an upstream boundary condition for reactive solute. It is noticed that with the increase in the value of porosity, the solute concentration in the main channel decreases. With the decrease in the value of Péclet number in the hyporheic zone, the overall solute concentration in the main channel decreases. Due to increase in the value of the sorption rate coefficient in the hyporheic zone, solute particles once enter into the hyporheic zone, reside for a longer time in the hyporheic zone. A sensitivity analysis is performed in order to identify the critical parameters for conservative as well as for reactive solute. It is found that the ratio of cross-sectional areas is much more sensitive compared to the other parameters for conservative solute. The Damköhler number in the hyporheic zone is the most sensitive parameter among all the parameters for reactive solute. The above observations indicate that the analytical solution can be reliably applied for the analysis of tracer experiments.