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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
Transport of sorptive solutes that undergo a reversible equilibrium sorption reaction with a retardation factor that is negatively correlated with log conductivity was considered. First-order analysis, based on a stochastic continuum presentation of the Eulerian retarded 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 the expected breakthrough of the sorptive solute and the uncertainty in its prediction, under steady, unsaturated flow. The length scales are the vertical distance L to the horizontal control plane (CP), the length scale of the planar source, ≡; the log conductivity correlation scales in the vertical (I(yv)) and the horizontal (I(yh)) directions; and the macroscopic capillary length scale λ. It was demonstrated in this study that as in transport of inert solutes, for a given mean water saturation and gravity-dominated unsaturated flow, both the skewness of the mean breakthrough curve (BTC) of the sorptive solute and the uncertainty in its prediction increase in formations of small ρ = I(yh)/I(yv) and large η = λ/I(yv) and relatively shallow CP (small v = L/I(yv)) and that the uncertainty in the prediction of the mean BTC decreases with increasing size of the planar source (large l = ≡/I(yh)). A new finding of the present study suggests that the relative impact of the chemical heterogeneity of the formation on the skewness of the mean BTC of the sorptive solute and the uncertainty in its prediction increases with increasing p (larger stratification) and decreasing η (coarser-textured soil material). This result stems from the fact that when the mean flow is vertical, both large ρ and small η diminish the impact of the heterogeneity in the physical properties of the formation on the variability of the flow in the longitudinal direction.
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Stochastic analysis of mass flux of sorptive solutes in unsaturated heterogeneous anisotropic 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
Stochastic analysis of mass flux of sorptive solutes in unsaturated heterogeneous anisotropic porous formations
Transport of sorptive solutes that undergo a reversible equilibrium sorption reaction with a retardation factor that is negatively correlated with log conductivity was considered. First-order analysis, based on a stochastic continuum presentation of the Eulerian retarded 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 the expected breakthrough of the sorptive solute and the uncertainty in its prediction, under steady, unsaturated flow. The length scales are the vertical distance L to the horizontal control plane (CP), the length scale of the planar source, ≡; the log conductivity correlation scales in the vertical (I(yv)) and the horizontal (I(yh)) directions; and the macroscopic capillary length scale λ. It was demonstrated in this study that as in transport of inert solutes, for a given mean water saturation and gravity-dominated unsaturated flow, both the skewness of the mean breakthrough curve (BTC) of the sorptive solute and the uncertainty in its prediction increase in formations of small ρ = I(yh)/I(yv) and large η = λ/I(yv) and relatively shallow CP (small v = L/I(yv)) and that the uncertainty in the prediction of the mean BTC decreases with increasing size of the planar source (large l = ≡/I(yh)). A new finding of the present study suggests that the relative impact of the chemical heterogeneity of the formation on the skewness of the mean BTC of the sorptive solute and the uncertainty in its prediction increases with increasing p (larger stratification) and decreasing η (coarser-textured soil material). This result stems from the fact that when the mean flow is vertical, both large ρ and small η diminish the impact of the heterogeneity in the physical properties of the formation on the variability of the flow in the longitudinal direction.
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