Imbedding velocity autocorrelation into simulators for constituent transport through porous media

摘要

Simulation based on the traditional advection-dispersion equation often is inadequate for making fate-transport predictions. The dominant process in transport through porous media is differential advection, which can be characterized statistically through spatial and temporal correlations in the velocity field. A particle tracking scheme that contains appropriate velocity statistics predicts realistic contaminant plumes. A particular generating scheme for random correlated velocities is introduced that can be mathematically transformed to a system of transport equations for parallel media whereby each equation transports a fraction of the contaminant mass, each with its characteristic advection velocity. The rate of transport among the parallel media determines the spectrum of length scales represented. The formulation of a continuum, multi-scale transport model thus follows naturally from the particle tracking scheme. This resulting computational scheme is one familiar to some fracture flow modelers―the multiple-interacting continuum approach. This discussion ties together the correlated random walk, non-local, and multiple-interacting continuum approaches and provides a means for model calibration.