An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 6 – Sediment and Reactive Chemical Transport in Stream/River Networks

Abstract

A watershed system includes river/stream networks, overland regions, and subsurface media. This paper presents a numerical model of sediment and reactive chemical transport in river/stream networks of watershed systems. The distribution of mobile suspended sediments and immobile bed sediments is controlled by hydrological transport as well as erosion and deposition processes. The distribution and fate of chemical species with a variety of chemical and physical processes is mathematically described by a system of advective-dispersive-reactive species- transport equations. Each equation in the system simply states that the rate of increase of a species is due to hydrology transport and the production rate from all reactions contributing to the species. The system is very stiff if some of reactions are very fast; in the limit with infinite rates. To circumvent the stiff problem, fast reactions must be decoupled from slow reactions. A matrix decomposition procedure is performed via the Gauss-Jordan column reduction of the reaction network. After matrix decomposition, the system of species-transport equations is transformed to a system of reaction extent-transport equations, in which one and only one linearly independent reaction rate appears in any reaction- extent equation. This facilitates the decoupling of fast reactions from slow reactions. Each of the reaction-extent transport equations with the one and only one fast reaction is then approximated with an algebraic equation and its reaction- extent is called an equilibrium variable. Thus the system of reaction-extent transport equations is reduced three subsets: (1) algebraic equations, (2) kinetic- variable transport equations, and (3) component transport equations. A variety of numerical methods are investigated for solving the mixed differential and algebraic equations (DAE). Two verification examples are compared with analytical solutions to demonstrate the correctness of and to emphasize the need of implementing various numerical options and coupling strategies for application-dependent simulations. A hypothetical example is employed to demonstrate the capability of the model to simulate both sediment and reactive chemical transport and to handle complex reaction networks involving both slow and fast reactions.