Russo, D., Department of Soil Physics, Institute of Soils and Water, Volcani Center, Bet Dagan, Israel, Department of Soil Physics, Institute of Soils and Water, Volcani Center, Bet Dagan 50250, Israel

First-order analysis, based on a stochastic continuum presentation of the Eulerian velocity in a partially saturated porous formation and a general Lagrangian description of the transport, was used to investigate the effects of a few length scales, characteristics of the heterogeneous transport domain, on nonergodic transport of passive solutes and its tendency to ergodic transport in steady state, gravity-dominated, unsaturated flow. Results of the analyses show that, as in ergodic transport, for given finite travel time, t, and fixed length-scale of the planar input zone, l, the principal components of the scaled macrodispersion tensor, D'(ij) (i, j = 1, 2, 3), are controlled by the length-scale ratios ρ = I(yh)/I(yv) and η = λ/I(yv), where I(yv) and I(yh) are the length scales of the formation heterogeneity in the vertical and the horizontal directions, respectively, and λ is the macroscopic capillary length-scale. The results, that for fixed I(yv) and given ρ η, and t, the principal components of D'(ij) are controlled by the ratio l' = l/I(yh) and that they may reach their ergodic limits if l' is sufficiently large, are in agreement with results of previous studies of nonergodic transport in aquifers. New findings obtained in the present investigation suggest that when the mean unsaturated flow is vertical and the typical travel distance is small compared with the travel distance required for the plume to reach its asymptotic, Fickian behavior, the tendency of the principal components of the preasymptotic D'(ij) to their ergodic limits is enhanced by increasing ρ (larger stratification) and decreasing η (coarser-textured soil material). The effects of both ρ and η on the tendency of the transport to its ergodic limit, however, decrease with increasing travel time and vanishes at the large time limit, in which the transport approaches Fickian behavior.

A note on nonergodic transport of a passive solute in partially saturated anisotropic heterogeneous porous formations

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Russo, D., Department of Soil Physics, Institute of Soils and Water, Volcani Center, Bet Dagan, Israel, Department of Soil Physics, Institute of Soils and Water, Volcani Center, Bet Dagan 50250, Israel

A note on nonergodic transport of a passive solute in partially saturated anisotropic heterogeneous porous formations

First-order analysis, based on a stochastic continuum presentation of the Eulerian velocity in a partially saturated porous formation and a general Lagrangian description of the transport, was used to investigate the effects of a few length scales, characteristics of the heterogeneous transport domain, on nonergodic transport of passive solutes and its tendency to ergodic transport in steady state, gravity-dominated, unsaturated flow. Results of the analyses show that, as in ergodic transport, for given finite travel time, t, and fixed length-scale of the planar input zone, l, the principal components of the scaled macrodispersion tensor, D'(ij) (i, j = 1, 2, 3), are controlled by the length-scale ratios ρ = I(yh)/I(yv) and η = λ/I(yv), where I(yv) and I(yh) are the length scales of the formation heterogeneity in the vertical and the horizontal directions, respectively, and λ is the macroscopic capillary length-scale. The results, that for fixed I(yv) and given ρ η, and t, the principal components of D'(ij) are controlled by the ratio l' = l/I(yh) and that they may reach their ergodic limits if l' is sufficiently large, are in agreement with results of previous studies of nonergodic transport in aquifers. New findings obtained in the present investigation suggest that when the mean unsaturated flow is vertical and the typical travel distance is small compared with the travel distance required for the plume to reach its asymptotic, Fickian behavior, the tendency of the principal components of the preasymptotic D'(ij) to their ergodic limits is enhanced by increasing ρ (larger stratification) and decreasing η (coarser-textured soil material). The effects of both ρ and η on the tendency of the transport to its ergodic limit, however, decrease with increasing travel time and vanishes at the large time limit, in which the transport approaches Fickian behavior.

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