Based on previous work on the transport–transformation model of heavy metal pollutants in fluvial rivers, this paper presents the formulation of a two-dimensional model to describe chemical transport–transformation in fluvial rivers by considering basic principles of environmental chemistry, hydraulics and mechanics of sediment transport and recent developments along with three very simplified test cases. The model consists of water flow governing equations, sediment transport governing equations, transport–transformation equation of chemicals and convection–diffusion equations of sorption–desorption kinetics of particulate chemical concentrations on suspended load, bed load and bed sediment. The chemical transport–transformation equation is basically a mass balance equation. It demonstrates how sediment transport affects transport–transformation of chemicals in fluvial rivers. The convection–diffusion equations of sorption–desorption kinetics of chemicals, being an extension of batch reactor experimental results, take both physical transport, i.e. convection and diffusion, and chemical reactions, i.e. sorption–desorption into account. The effects of sediment transport on chemical transport–transformation were clarified through three simple examples. Specifically, the transport–transformation of chemicals in a steady, uniform and equilibrium sediment-laden flow was calculated by applying this model, and results were shown to be rational. Both theoretical analysis and numerical simulation indicated that the transport–transformation of chemicals in sediment-laden flows with a clay-enriched riverbed possesses not only the generality of common tracer pollutants, but also characteristics of transport–transformation induced by sediment motion. Future work will be conducted to present the validation/application of the model with available data.
A high-order exponential ADI scheme for two dimensional time fractional convection–diffusion equations
