Alessandro Santini

Numerical analysis of one-dimensional unsaturated flow in layered soils

Abstract The paper deals with numerical solutions to the Richards equation to simulate one-dimensional flow processes in the unsaturated zone of layered soil profiles. The equation is expressed in the pressure-based form and a finite-difference algorithm is developed for accurately estimating the values of the hydraulic conductivity between two neighboring nodes positioned in different soil layers, often referred to as the interlayer hydraulic conductivity. The algorithm is based upon flux conservation and continuity of pressure potential at the interface between two consecutive layers, and does not add significantly to simulation run time. The validity of the model is established for a number of test problems by comparing numerical results with the analytical solutions developed by Srivastava and Yeh29 which hold for vertical infiltration towards the water table in a two-layer soil profile. The results show a significant reduction in relative mass balance errors when using the proposed model. Some specific insights into its numerical performance are also gained by comparisons with a numerical model in which the more common geometric averaging operator acts on the interlayer conductivities.

Determining soil hydraulic functions from evaporation experiments by a parameter estimation Approach: Experimental verifications and numerical studies

A parameter estimation method is developed for the determination of unsaturated soil hydraulic properties from evaporation experiments under laboratory conditions. Variables used in the inversion procedure are soil water pressure heads at various positions and total soil weights, both measured as a function of time during the experiment. Unknown parameters of different analytical expressions used to describe the soil hydraulic properties are estimated by coupling a finite difference solution of the Richards equation with a nonlinear optimization problem. This problem is formulated by minimizing the deviations between the numerical solution of the transient flow process and the real system response measured during the experiment. Minimization of the objective function is performed using a version of the Levenberg-Marquardts method; the procedure also provides information about the uncertainty in parameter estimates. The performance of the selected parametric relationships is evaluated, and the applicability and accuracy of the proposed inverse method are shown by comparing estimated water retention and hydraulic conductivity functions with experimental results obtained via the instantaneous profile method. Parameter sensitivity analyses and stability of the inverse solutions are discussed with reference to the originally designed evaporation experiment and to an evaporation method that is developed with a view to reducing experimental efforts. Further insights into the properties of existence and uniqueness of inverse solutions are gained by examining contour plots of the objective functions under varying experimental conditions. The results confirm the reliability and flexibility of the proposed method and suggest that the evaporation flux imposed at the upper soil surface may determine the well posedness of the optimization problem.

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.

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.