Semianalytical Solution for Nonequilibrium Sorption of Pollutant Transport in Streams

Abstract

During pollutant transport in a stream, many pollutants get adsorbed in the streambed materials and are subsequently released. A conceptual hybrid-cells-in-series model for adsorption (HCIS-A), which consists of a plug flow zone and two thoroughly mixed zones of unequal residence times, has been developed to simulate adsorption-desorption in addition to advection and dispersion processes. Sorption processes governed by first-order mass exchange kinetics along with advection in the plug flow zone have been solved analytically using the Laplace transform technique. Analytical solutions have been derived for transport of pollutants through the first and second thoroughly mixed zones of the hybrid model considering sorption. Using the convolution technique and ramp kernel coefficients, the pollutants have been routed through all the zones to derive a semianalytical solution at the end of first hybrid unit. The advantages of this conceptual hybrid model are (1) the conversion of the second-order partial differential equation to a first-order ordinary differential equation; (2) the model’s capacity to incorporate variation of stream geometry and flow velocity in different stream reaches; and (3) the model’s capability to incorporate sorption kinetics. The responses of the hybrid model correspond to the finite-difference solutions of the partial differential equation (PDE) that accounts for advection, dispersion, and adsorption. The first arrival time of the pollutant downstream of a point disposal has been estimated. This is not clearly identified in other models. The effect of sorption on pollutant transport was studied and demonstrated in various