M. N. Pace

An Integrated Media, Integrated Processes Watershed Model – WASH123D: Part 8 – Reactive Chemical Transport in Subsurface Media

A watershed system includes river/stream networks, overland regions, and subsurface media. This paper presents a reaction-based numerical model of reactive chemical transport in subsurface media of watershed systems. Transport of M chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into M reaction extent-transport equations (a reaction extent is a linear combination of species concentrations), each involves one and the only one linearly independent reaction. Thus, the reactive transport problem is viewed from two different points of view. Descirbed with a species-transport equation, the transport of a species is balanced by a linear combinations of rates of all reactions. Described by a reaction extent-transport equation, the rate of a linear independent reaction is balanced by the transport of the linear combination of species. The later description facilitates the decoupling of fast reactions from slow reactions and circumvent the stiffness of reactive transport problems. This is so because the M reaction extent-transport equations can be approximated with three subsets of equations: NE algebraic equations describing NE fast reactions (where NE is the set of linearly independent fast/equilibrium reactions), NKI reactive transport equations of kinetic-variables involving no fast reactions (where NKI is the number of linearly independent slow/kinetic reactions), and NC transport equations of components involving no reaction at all (where NC = M – NE – NKI is the number of components). The elimination of fast reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables and components rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with reaction networks involving both kinetic and equilibrium reactions. A hypothetical three-dimensional example is presented to demonstrate the model application to a field-scale problem involving reactive transport with a complex reaction network.