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A Stochastic Model for Unsaturated Steady Flow in Bounded Heterogeneous Formations
No full textUnsaturated steady flow in three dimensional bounded heterogeneous formations is modelled by considering the hydraulic parameters of the conductivity curve as stationary Random Space Functions (RSFs). The corresponding stochastic governing equations are solved by means of a perturbation approach which regards the variances of the logarithms of the saturated hydraulic conductivity (Ks), and the pore scale distribution of the Gardner (1958) model as small quantities. Analytical closed forms (requiring only few quadratures) for the spatial moments of the pressure head are derived, without invoking the unit mean hydraulic assumption. It is found that the flow variables are nonstationary near the boundary (i.e. the water table), and approach stationarity as the vertical distance from the water table increases. The stationary limits and the critical vertical distance at which stationarity is attained depend on soil types as well as infiltrating rates. The smaller the rate is, the larger the critical distance; and the coarser the soil texture is, the smaller the distance. Our results generalize the study of Indelman et al. (1993), and provide a general methodology to tackle more complex unsaturated flows
Una soluzione analitica per il trasporto nei suoli di soluti reattivi in presenza di ridistribuzione
No full textIl presente lavoro illustra una soluzione analitica di tipo perturbativo che descrive il trasporto di soluti reattivi in suoli in presenza di ridistribuzione. La soluzione di tipo perturbativo viene ricavata assumendo che lo scambio di massa tra il suolo e la soluzione circolante sia sufficientemente rapido. A causa della natura singolare del problema considerato, la soluzione perturbata standard è accettabile solo localmente e, di conseguenza, è necessario determinare una seconda soluzione di tipo perturbativo che permetta di descrivere il fenomeno lì dove la soluzione standard non è valida. Le due soluzioni vengono poi raccordate opportunamente per ottenere un’unica espressione valida uniformemente nello spazio e nel tempo
A Stochastic Model for Unsaturated Steady Flow in Bounded Heterogeneous Formations
No full textUnsaturated steady flow in three dimensional bounded heterogeneous formations is modelled by considering the hydraulic parameters of the conductivity curve as stationary Random Space Functions (RSFs). The corresponding stochastic governing equations are solved by means of a perturbation approach which regards the variances of the logarithms of the saturated hydraulic conductivity (Ks), and the pore scale distribution of the Gardner (1958) model as small quantities. Analytical closed forms (requiring only few quadratures) for the spatial moments of the pressure head are derived, without invoking the unit mean hydraulic assumption. It is found that the flow variables are nonstationary near the boundary (i.e. the water table), and approach stationarity as the vertical distance from the water table increases. The stationary limits and the critical vertical distance at which stationarity is attained depend on soil types as well as infiltrating rates. The smaller the rate is, the larger the critical distance; and the coarser the soil texture is, the smaller the distance. Our results generalize the study of Indelman et al. (1993), and provide a general methodology to tackle more complex unsaturated flows
Unsaturated Transport with Linear Kinetic Sorption Under Unsteady Vertical Flow
Full text linkWe consider transport of a solute obeying linear kinetic sorption under unsteady flow conditions. The study relies on the vertical unsaturated flow model developed by Indelman et al. [J. Contam. Hydrol. 32 (1998), 77–97] to account for a cycle of infiltration and redistribution. One of the main features of this type of transport, as compared with the case of a continuous water infiltration, is the finite depth of solute penetration. In the infiltration stage an analytical solution that generalizes the previous results of Lassey [Water Resour. Res. 24 (1988), 343–350] and Severino and Indelman [J. Contam. Hydrol. 70 (2004), 89–115] is derived. This solution accounts for quite general initial solute distributions in both the mobile and immobile concentration. When the redistribution is also considered, two timescales become relevant, namely: (i) the desorption rate k−1, and (ii) the water application time tap. In particular, we have assumed that the quantity ε =(k tap)−1 can be regarded as a small parameter so that a perturbation analytical solution is obtained. At field-scale the concentration is calculated by means of the column model of Dagan and Bresler [Soil Sci. Soc. Am. J. 43 (1979), 461–467], i.e. as ensemble average over an infinite series of randomly distributed and uncorrelated soil columns. It is shown that the heterogeneity of hydraulic properties produces an additional spreading of the plume. An unusual phenomenon of plume contraction is observed at long times of solute propagation during the drying period. The mean solute penetration depth is studied with special emphasis on the impact of the variability of the saturated conductivity upon attaining the maximum solute penetration depth
Variabilità spaziale delle proprietà ideologiche dei suoli in prossimità di una falda idrica
No full textModelling Water Flow and Solute Transport in Heterogeneous Unsaturated Porous Media
No full textNew results concerning flow velocity and solute spreading in an unbounded three dimensional partially saturated heterogeneous porous formation are derived. Assuming that the effective water content is a uniformly distributed constant, and dealing with the recent results of Severino and Santini (2005) on mean vertical steady flows, first order approximation of the velocity covariance, and concurrently of the resultant macrodispersion coefficients are calculated. Generally, the velocity covariance is expressed via two quadratures. These quadratures are further reduced after adopting specific (i.e. exponential) shape for the required (cross)correlation functions. Two particular formation structures which are relevant for the applications, and lead to significant simplifications of the computational aspect are also considered. It is shown that the rate at which the Fickian regime is approached is an intrinsic medium property, whereas the value of the macrodispersion coefficients is also influenced by the mean flow conditions as well as the (cross)variances σ2 of the input parameters. For a medium of given anisotropy structure, the velocity variances reduce as the medium becomes drier (in mean), and it increases with σ2. In order to emphasize the intrinsic nature of the velocity autocorrelation, it is shown the good agreement between our analytical results and the velocity autocorrelation as determined by Russo (1995a) when accounting for groundwater flow normal to the formation bedding. In a similar manner, the intrinsic character of attainment the Fickian regime is demonstrated by comparing the scaled longitudinal macrodispersion coefficients D11(t)/D11(∞) as well as the lateral displacement variance X22(t)/X22(∞)=X33(t)/X33(∞) with the same quantities derived by Russo (1995a) in the case of groundwater flow normal to the formation bedding
Antibiotic prescription in Southern Italian outpatients: Real-world data analysis of prevalence, socioeconomic and sociodemographic variables and geographic variability
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