Multicomponent exchange and subsurface solute transport: Characteristics, coherence, and the Riemann Problem

Abstract

When water of one chemical composition is displaced by water of another, there is a change in composition at any point within the flow system which may occur more or less rapidly, depending on both the hydraulics and chemistry of the system. For many applications it is possible to decouple the hydraulic and chemical analyses, and later combine them for prediction of effluent compositions from well fields or concentration histories at observation wells. When an advection‐reaction model is used, the displacement problem is described mathematically as a Riemann problem. In this paper the Riemann problem is solved for the ternary exchange system using the method of characteristics. The pattern of composition changes is found to follow the right eigenvector paths in composition space, and the eigenvalues provide composition‐dependent retardation functions. The hydraulics is treated fairly generally and allows one to consider steady uniform or nonuniform flow fields or stochastic flow models. Both laboratory and field applictions are presented.