Stochastic-convective transport with nonlinear reactions and mixing: finite streamtube ensemble formulation for multicomponent reaction systems with intra-streamtube dispersion

An effective streamtube ensemble method is: developed to upscale convective -dispersive transport with multicomponent nonlinear reactions in steady non uniform flow. The transport is cast in terms of a finite ensemble of indepe ndent discrete streamtubes that approximate convective transport along macr oscopically averaged pathlines and dispersive transport longitudinally as m icroscopic mixing within streamtubes. The representation of fate and transp ort via a finite ensemble of effective linear streamtubes, allows the treat ment of arbitrarily complex reaction systems involving both homogeneous and heterogeneous reactions, and longitudinal dispersive/diffusive mixing with in streamtubes. This allows the use of reactive-transport codes designed to solve such problems in an Eulerian framework, as opposed to reliance on cl osed-ti,rm (convolutional or canonical) expressions for reactive transport in exclusively convective streamtubes. The approach requires both reactive- transport solutions for a representative ensemble of one-dimensional convec tive-dispersive-reactive streamtubes and the distribution of flux over the streamtube ensemble variants, and it does not allow fur lateral mixing betw een streamtubes. Here, the only ensemble variant is travel time. The discus sion details the way that the conventional Eulerian fate and transport mode l is converted first into an ensemble of transports along three-dimensional streamtubes of unknown geometry, and then to approximate one-dimensional s treamtubes that an designed to honor the important global properties of the transport. Conditions under which such an 'equivalent' ensemble of one-dim ensional streamtubes are described. The breakthrough curve of a nonreactive tracer in the ensemble is expressed as a combined Volterra-Fredholm integr al equation, which serves as the basis for estimation of the distribution o f flux over the variant of the ensemble, travel time. Transient convective speed and the effects of errors in flux distributions are described, and th e method is applied to a demonstration problem involving nonlinear multicom ponent reaction kinetics and strongly nonuniform flow. (C) 2001 Elsevier Sc ience B.V. All rights reserved.