A Numerical Stream/River Water Quality Model for TMDL Studies

Abstract

This paper presents the development of a numerical model to simulate sediment and reactive chemical transport in river/stream networks. Through the decomposition of the system of species transport equations via Gauss-Jordan column reduction of the reaction network, fast reactions and slow reactions are decoupled, which enables robust numerical integrations. Species reactive transport equations are transformed into three subsets: a set of nonlinear algebraic equations representing equilibrium reactions, a set of transport equations of kinetic-variables in terms of kinetically controlled reaction rates, and a set of transport equations of chemical components. As a result, the model uses kinetic-variables and components rather than biogeochemical species as primary dependent variables, which reduces the number of transport equations and simplifies reaction terms in the equations. For each time step, we first solve the advection-dispersion transport equations of kinetic-variables and components. We then solve the reactive chemical system node by node to obtain concentrations of all species. Two example problems are employed to demonstrate the design capability of the model, in simulating sediment and chemical transport, chemicals in both mobile water phase and immobile water phase, and both kinetic and equilibrium reactions. Based on the application of the eutrophication example, the deficiency of current practices in the water quality modeling is discussed and potential improvements over current practices using this model are addressed.