A radial Lagrangian streamtube-ensemble modeling approach and its applications to reactive transport experiments in the subsurface

The reactive transport process in the heterogeneous subsurface can be effectively modeled by using a Lagrangian approach that handles the heterogeneity by separating micromixing from macromixing and accommodates multicomponent and/or nonlinear reactions among mobile and immobile species within the effective “streamtubes.” This method establishes an effective ensemble of streamtubes governing transport in a Cartesian setting, with negligible tracer injection flux. However, subsurface injections often involve a relatively large flux, therefore the flow field near the injection well has a strongly radial component. The effect of this initial, primarily radial, spreading renders the solute flux boundary condition variant over streamtubes making up the downstream Lagrangian ensemble, i.e., centrally-located streamtubes would have a larger boundary condition than laterally-located streamtubes. To model this radial-Cartesian flow and transport process, a dual (two-stage) streamtube ensemble approach is created in this study. The primarily radial flow is first treated with its own streamtube ensemble defined in the streamline coordinates combining radial and Cartesian flow (corresponding to flux due to the injection and the local induced longitudinal hydraulic gradient). The bacterial velocity-dependent attachment kinetics is approximated using colloid filtration theory. The travel time distribution function [TTDF] for this ensemble is determined by numerically simulating transport in the streamline coordinates for an effectively homogeneous media, and by collecting all downstream injectate fluxes at a “transition surface.” Solute flux arriving at the transition surface is then used as a boundary condition for the second stage, consisting of a conventional ensemble of streamtubes that convey solute downstream from the transition surface. The TTDF of the second stage may be obtained through the deconvolution of a breakthrough curve of an inert tracer. Of particular concern is how to “handoff” the solute flux from the radial-Cartesian ensemble to the conventional downstream ensemble, at the transition surface. Two limit cases are studied, and they are complete mixing and no mixing. The dual streamtube ensemble approach is employed to analyze the bromide and bacterial tracer breakthrough curves from the subsurface bacterial transport experiment conducted in October 1999 at a site near Oyster, Virginia.