NONLOCAL REACTIVE TRANSPORT WITH PHYSICAL AND CHEMICAL HETEROGENEITY - LOCALIZATION ERRORS

The origin of nonlocality in ''macroscale'' models for subsurface chem ical transport is illustrated. It is argued that media that are either nonperiodic (e.g., media with evolving heterogeneity) or periodic vie wed on a scale wherein a unit cell is discernible must display some no nlocality in the mean. A metaphysical argument suggests that owing to the scarcity of information on natural scales of heterogeneity and on scales of observation associated with an instrument window, constituti ve theories for the mean concentration should at the outset of any mod eling effort always be considered nonlocal. The intuitive appeal to no nlocality is reinforced with an analytical derivation of the constitut ive theory for a conservative tracer without appeal to any mathematica l approximations. Deng et al. (1993) present a first-order, nonlocal, Eulerian theory for transport of a conservative solute in an infinite nondeforming domain under steady flow conditions. Hu et al. (this issu e) extended these results to account for nonequilibrium linear sorptio n with random partition coefficient K-d but deterministic constant rea ction rate K-r. These theories are localized herein, and comparisons a re made between the fully nonlocal (FNL), nonlocal in time (NLT), and fully localized (FL) theories. For conservative transport, there is li ttle difference between the first-order FL and FNL models for spatial moments up to and including the third. However, for conservative trans port the first-order NLT model differs significantly from the FNL mode l in the third spatial moments. For reactive transport, all spatial mo ments differ between the FNL and FL models. The second transverse-hori zontal and third longitudinal-horizontal moments for the NLT model dif fer from the FNL model. These results suggest that localized first-ord er transport models for conservative tracers are reasonable if only lo wer-order moments are desired. However, when the chemical reacts with its environment, the localization approximation can lead to significan t error in all moments, and a FNL model will in general be required fo r accurate simulation.