Gerardo Severino

Darcian preferential water flow and solute transport through bimodal porous systems: Experiments and modelling

Soils often exhibit a variety of small-scale heterogeneities such as inter-aggregate pores and voids which partition flow into separate regions. In this paper a methodological approach is discussed for characterizing the hydrological behaviour of a heterogeneous clayey-sandy soil in the presence of structural inter-aggregate pores. For the clay soil examined, it was demonstrated that, coupling the transfer function approach for analyzing BTCs and water retention data obtained with different methods from laboratory studies captures the bimodal geometry of the porous system along with the related existence of fast and slow flow paths. To be effectively and reliably applied this approach requires that the predominant effects of the soil hydrological behaviour near saturation be supported by accurate experimental data of both breakthrough curves (BTCs) and hydraulic functions for high water content values. This would allow the separation of flow phases and hence accurate identification of the processes and related parameters.

On the local concentration probability density function of solutes reacting upon mixing

[1]xa0The probability density function (pdf) of solute concentration is a useful tool for modeling transport of contaminants in heterogeneous aquifers that is increasingly used in risk assessment and, more generally, as a mean to quantify uncertainty in transport modeling. In order to be effective the pdfs should be linked in a simple manner to the spatial variability model of hydraulic properties, pore-scale (local) dispersion, and a suitable parametrization of the geochemical processes. We analyze the pdf and concentration moments of two aqueous species in equilibrium with their precipitate reacting upon mixing in two- and three-dimensional geological formations. The speciation equations, resulting from application of the chromatographic theory, provide the link between concentration pdfs (and moments) of the aqueous species and that of a passive tracer. Within this framework, we investigate the role of pore-scale dispersion and macrodispersion in enhancing mixing, and thus reaction between the aqueous species, in the case of an instantaneous injection of a water with contrasting concentrations with respect to the ambient water under the constraint that in both waters the two aqueous species are in equilibrium with their precipitate. The main conclusion of our analysis is that for the pore-scale dispersion typically observed in natural formations, the local concentration pdfs of both species are far from being Gaussian, and therefore the first two concentration moments provide very limited information of the underlying transport dynamics. Instead, the pdfs provide crucial information for applications, such as the probability of exceeding a given concentration, for example, the regulatory limit, at a particular location within the domain of interest. Furthermore, by analyzing the second-order moments of the concentration, we show that mixing is strongly affected by space dimensionality and that the two-dimensional approach, often used for computational convenience, may severely underestimate reaction rates in real settings.

An indirect assessment on the impact of connectivity of conductivity classes upon longitudinal asymptotic macrodispersivity

Solute transport takes place in heterogeneous porous formations, with the log conductivity, Y = ln K, modeled as a stationary random space function of given univariate normal probability density fu ...

Determining the soil hydraulic conductivity by means of a field scale internal drainage

Abstract Spatial variations of water content in large extents soils (vadose zone) are highly affected by the natural heterogeneity of the porous medium. This implies that the magnitude of the hydraulic properties, especially the conductivity, varies in an irregular manner with scale. Determining mean values of hydraulic properties will not suffice to accurately quantify water flow in the vadose zone. At field scale proper field measurements have to be carried out, similar to standard laboratory methods that also characterize the spatial variability of the hydraulic properties. Toward this aim an internal drainage test has been conducted at Ponticelli site near Naples (Italy) where water content and pressure head were monitored at 50 locations of a 2×50xa0m2 plot. The present paper illustrates a method to quantify the mean value and the spatial variability of the hydraulic parameters needed to calibrate the soil conductivity curve at field scale (hereafter defined as field scale hydraulic conductivity). A stochastic model that regards the hydraulic parameters as random space functions (RSFs) is derived by adopting the stream tube approach of Dagan and Bresler (1979) . Owing to the randomness of the hydraulic parameters, even the water content θ will be a RSF whose mean value (hereafter termed field scale water content) is obtained as an ensemble average over all the realizations of a local analytical solution of Richards equation. It is shown that the most frequent data collection should be carried out in the initial stage of the internal drainage experiment, when the most significant changes in water content occur. The model parameters are obtained by a standard least square optimization procedure using water content data at a certain depth (z=30 cm ) for several times (t=5, 24, 48, 96, 144, 216, 312, 408, 576, 744, 912xa0h). The reliability of the proposed method is then evaluated by comparing the predicted water content with observations at different depths (z=45, 60, 75, and 90xa0cm). The calibration procedure is further verified by comparing the cumulative distribution of measured water content at different times with corresponding distribution obtained from the calibrated model.

Stochastic analysis of well‐type flows in randomly heterogeneous porous formations

[1]xa0Well-type flow takes place in a heterogeneous porous formation where the transmissivity is modeled as a stationary random space function (RSF). General expressions for the covariances of the head and flux are obtained and analyzed. The second-order approximation of the mean radial flux is represented as the product between the solution valid in a homogeneous domain and a distortion term , which adjusts according to the medium heterogeneity. The spatial dependence of the function is studied. In view of the formation identification problem, the equivalent T(eq) and apparent T(ap) transmissivity are computed. The important result is the relationship ( may be either “eq” or “ap”), where TH and TG represent the harmonic and the geometric means of the transmissivity, respectively. The position-dependent weight is explicitly calculated. Indeed, close to the well, it yields , which is understandable in view of the fact that the limit is equivalent to I → ∞, which is the heterogeneity structure of a stratified formation. Nevertheless, the effective transmissivity of a stratified formation is precisely TH. In contrast, far from the well, one has , with the flow being slowly varying in the mean there. It is shown that grows with increasing . In the case of T(eq), the rate of growing is found (similar to Dagan and Lessoff (2007)) to be strongly dependent upon the position in the flow domain, whereas T(ap) is a more robust property. Finally, it is shown how the general results can be used for practical applications.

Travel time approach to kinetically sorbing solute by diverging radial flows through heterogeneous porous formations

[1]xa0Diverging radial flow takes place in a heterogeneous porous medium where the log conductivity Y = ln K is modeled as a stationary random space function (RSF). The flow is steady, and is generated by a fully penetrating well. A linearly sorbing solute is injected through the well envelope, and we aim at computing the average flux concentration (breakthrough curve). A relatively simple solution for this difficult problem is achieved by adopting, similar to Indelman and Dagan (1999), a few simplifying assumptions: (i) a thick aquifer of large horizontal extent, (ii) mildly heterogeneous medium, (iii) strongly anisotropic formation, and (iv) large Peclet number. By introducing an appropriate Lagrangian framework, three-dimensional transport is mapped onto a one-dimensional domain (τ, t) where τ and t represent the fluid travel and current time, respectively. Central for this approach is the probability density function of the RSF τthat is derived consistently with the adopted assumptions stated above. Based on this, it is shown that the travel time can be regarded as a Gaussian random variable only in the far field. The breakthrough curves are analyzed to assess the impact of the hydraulic as well as reactive parameters. Finally, the travel time approach is tested against a forced-gradient transport experiment and shows good agreement.

Macrodispersion by diverging radial flows in randomly heterogeneous porous media

Radial flow takes place in a heterogeneous porous formation where the transmissivity T is modelled as a stationary random space function (RSF). The steady flow is driven by a given rate, and the mean velocity is radial. A pulse-like of a tracer is injected in the porous formation, and the thin plume spreads due to the fluctuations of the velocity which results a RSF as well. Transport is characterized by the mean front, and by the second spatial moment of the plume. We are primarily interested in tracer macrodispersion modelling. With the neglect of pore-scale dispersion, macrodispersion coefficients are computed at the second order of approximation, without neglecting the head-gradient fluctuations. Although transport is non-ergodic at the source, it is shown that ergodicity is achieved at small distances from the source. This is due to the fact that close to the source local velocities are quite large, and therefore solute particles become uncorrelated very soon. Under ergodic conditions, we compare macrodispersion mechanism in radial flows with that occurring in mean uniform flows. At short distances the spreading effect is highly enhanced by the large variability of the flow field, whereas at large distances transport exhibits a lesser dispersion due to the reduction of velocities. This supports the explanation provided by Indelman and Dagan (1999) to justify why the macrodispersivity is found smaller than that pertaining to mean uniform flows. The model is tested against a tracer transport experiment (Fernàndez-Garcia et al., 2004) by comparing the theoretical and experimental breakthrough curves. The accordance with real data, that is achieved without any fitting to concentration values, strengthens the capability of the proposed model to grasp the main features of such an experiment, the approximations as well as experimental uncertainties notwithstanding.

A note on transport of a pulse of nonlinearly reactive solute in a heterogeneous formation

Saturated flow takes place in geological formations of spatially variable permeability which is regarded as a stationary random space function of given statistical moments. The flow is assumed to be uniform in the mean and the Eulerian velocity field has stationary fluctuations. Water carries solutes that react according to the nonlinear equilibrium Freundlich isotherm. Neglecting pore scale dispersion (high Peclet number), we study the behavior of an initially finite pulse injection of constant concentration.Mean flux-averaged concentration is derived in a simple manner by using the previously determined solution of transport in a homogeneous one-dimensional medium and the Lagrangian methodology developed by Cvetkovic and Dagan [5] to model reactive transport in a three-dimensional flow field.The mean breakthrough curves are computed and the combined effect of reactive parameters and heterogeneity upon reduction of the concentration peak is investigated. Furthermore, with the aid of temporal moments, we determine equivalent reaction and macrodispersion coefficients pertinent to a homogeneous medium.

Modelling Water Flow and Solute Transport in Heterogeneous Unsaturated Porous Media

New 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 (Advances in Water Resources 2005;28:964–974) 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 that are relevant for the applications and lead to significant simplifications of the computational aspect are also considered.

Mining Geostatistics to Quantify the Spatial Variability of Certain Soil Flow Properties

The functional dependence of the relative unsaturated hydraulic conductivity (UHC) Kr (ź) exp(αź) upon the matric potential ź, L, via the soil-dependent parameter α, L-1, has been traditionally regarded as a deterministic process (i.e. α ~ constant). However, in the practical applications one is concerned with flow domains of large extents where α undergoes to significant spatial variations as consequence of the disordered soils structure. To account for such a variability (hereafter also termed as heterogeneity) we adopt the mining geostatistical approach, which regards α as a random space function (RSF). To quantify the heterogeneity of α, estimates of local-values were obtained from ~ 100 locations along a trench where an internal drainage test was conducted. The analysis of the statistical moments of α demonstrates (in line with the current literature on the matter) that the log-transform ź ln α can be regarded as a structureless, normally distributed, RSF. An novel implementation of the present study in the context of the Internet of Things (IoT) is outlined.