Equations and their physical interpretation in numerical modeling of heavy metals in fluvial rivers

Based on the previous work on the transport-transformation of heavy metal pollutants in fluvial rivers, this paper presented the formulation of a two-dimensional model to describe heavy metal transport-transformation in fluvial rivers by considering basic principles of environmental chemistry, hydraulics, 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 heavy metal pollutants, and convection-diffusion equations of adsorption-desorption kinetics of particulate heavy metal concentrations on suspended load, bed load and bed sediment. The heavy metal transport-transformation equation is basically a mass balance equation, which demonstrates how sediment transport affects transport-transformation of heavy metals in fluvial rivers. The convection-diffusion equations of adsorption-desorption kinetics of heavy metals, being an extension of batch reactor experimental results and a major advancement of the previous work, take both physical transport, i.e. convection and diffusion and chemical reactions, i.e. adsorption-desorption into account. Effects of sediment transport on heavy metal transport-transformation were clarified through three examples. Specifically, the transport-transformation of heavy metals 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 heavy metals in sediment-laden flows with 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 validation/application of the model with available data.