HR: 0800h
AN: H51F-0422    [Abstracts]
TI: Effects of Boundaries and Conditioning on Macrodispersivity
AU: * Morales-Casique, E
EM: emorales@hwr.arizona.edu
AF: Department of Hydrology and Water Resources, The University of Arizona, 1133 E. North Campus Drive, Tucson, AZ 85721 United States
AU: Neuman, S P
EM: neuman@hwr.arizona.edu
AF: Department of Hydrology and Water Resources, The University of Arizona, 1133 E. North Campus Drive, Tucson, AZ 85721 United States
AU: Guadagnini, A
EM: alberto.guadagnini@polimi.it
AF: Dipartimento di Ingegneria Idraulica Ambientale, Infrastrutture Viarie, Rilevamento, Politecnico di Milano, Piazza L. Da Vinci, 32, Milano, 20133 Italy
AB: We have shown previously that it is computationally feasible to obtain accurate, unbiased predictions of non-reactive solute transport in bounded randomly heterogeneous porous media, and to assess the corresponding predictive uncertainty, by means of an iterative finite element algorithm based on recursive approximations of exact nonlocal conditional moment equations. The solution deteriorates with increasing log hydraulic conductivity variance and Peclet number due to our disregard of third (and possibly higher) velocity moments, which we show gain significance as these parameters increase due to the departure of both longitudinal and transverse velocities from Gaussian behavior. The solution improves with conditioning as the magnitude of third order velocity moments diminishes and the distribution of velocities at conditioning points approaches Gaussian. Even though our nonlocal solution does not entail macrodispersivities, we nevertheless found it instructive to compute space-time localized (conditional and unconditional quasi-Fickian) macrodispersion coefficients for the centroid of a two-dimensional mean plume and compare with similar-order unconditional analytic solutions for preasymptotic (at infinite Peclet number) and asymptotic (at finite Peclet numbers) regimes in an infinite domain. We found that shortening the length of the domain and/or approaching the downstream boundary causes the unconditional longitudinal macrodispersion coefficient D₁₁ and its temporal rate of change to increase. The unconditional transverse macrodispersion coefficient D₂₂ associated with a relatively long domain is very close to its analytic value for an infinite domain and infinite Peclet number except at large time as the plume approaches the downstream boundary; with diminishing domain length, D₂₂ falls below the analytical solution. This behavior is explained by the effect of boundaries on the velocity covariance and Green's function whose space-time integral defines D₁₁ and D₂₂. Both the longitudinal and transverse quasi-Fickian macrodispersion coefficients D₁₁ and D₂₂, as well as their temporal rates of change, are reduced significantly by conditioning. This finding is consistent not only with out theory but also with an earlier observation by Neuman [1990], based on world-wide tracer test results, that the rate at which apparent longitudinal dispersivity increases with scale (represented by travel distance or time) diminishes with conditioning. In preliminary runs conducted on a relatively small grid without optimizing our algorithms and without parallelization, the moment solutions required considerably less computer time than did corresponding Monte Carlo simulations.
DE: 1832 Groundwater transport
DE: 1847 Modeling
DE: 1869 Stochastic hydrology
SC: Hydrology [H]
MN: Fall Meeting 2005