Alex Yakirevich

A quasi three-dimensional model for flow and transport in unsaturated and saturated zones: 1. Implementation of the quasi two-dimensional case

A quasi three-dimensional (QUASI 3-D) model is presented for simulating the subsurface water flow and solute transport in the unsaturated and in the saturated zones of soil. The model is based on the assumptions of vertical flow in the unsaturated zone and essentially horizontal groundwater flow. The 1-D Richards equation for the unsaturated zone is coupled at the phreatic surface with the 2-D flow equation for the saturated zone. The latter was obtained by averaging 3-D flow equation in the saturated zone over the aquifer thickness. Unlike the Boussinesq equation for a leaky-phreatic aquifer, the developed model does not contain a storage term with specific yield and a source term for natural replenishment. Instead it includes a water flux term at the phreatic surface through which the Richards equation is linked with the groundwater flow equation. The vertical water flux in the saturated zone is evaluated on the basis of the fluid mass balance equation while the horizontal fluxes, in that equation, are prescribed by Darcy law. A 3-D transport equation is used to simulate the solute migration. A numerical algorithm to solve the problem for the general quasi 3-D case was developed. The developed methodology was exemplified for the quasi 2-D cross-sectional case (QUASI2D). Simulations for three synthetic problems demonstrate good agreement between the results obtained by QUASI2D and two fully 2-D flow and transport codes (SUTRA and 2DSOIL). Yet, simulations with the QUASI2D code were several times faster than those by the SUTRA and the 2DSOIL codes.

A Two-Dimensional Areal Model for Density Dependent Flow Regime

A two-dimensional (2D) plane model of saltwater intrusion was developed, for the simulation of groundwater level and the average solute concentration in a 2D horizontal plane, together with the estimation of the saltwater depth. The proposed approach is of particular interest when assessing the effect of different regional pumping scenarios on groundwater level and its quality. The corresponding MEL2DSLT code was developed on the basis of the Modified Eulerian–Lagrangian (MEL) method to overcome difficulties arising from hyperbolic behavior of flow and transport equations, due to the advective nature of solute transport and heterogeneity of the soil characteristics (permeabilities and dispersivities). The code was verified against the 2D cross sectional model SUTRA and the three-dimensional (3D) model SWICHA. Simulation was conducted concerning the problem of saltwater intrusion in the Khan Yunis portion of the phreatic coastal aquifer of Gaza Strip. After calibrating the model for the aquifer parameters, we investigated its predictions resulting from various regional pumping scenarios using the actual pumping intensity from the year 1985 and extrapolating on the basis of 3.8% annual population growth. Results show a considerable depletion of groundwater level and intrusion of seawater due to excessive pumping.

K+ uptake by root systems grown in soil under salinity: I. A mathematical model

A novel theoretical model is proposed for K+ uptake by intact root systems from saline soil considering interactions with Na+, Ca2+ and Mg2+. The model assumes radial movement of ions towards the root governed by advection and diffusion flux mechanisms, and chemical exchange of the four cations according to Gapon isotherms, with Cl− as the accompanying anion. Influx of K+ to the root surface is assumed as a function of its concentration in the soil solution at the root. This influx is governed by a saturable-cooperative term and a linear term for low and high K+ concentrations, respectively. Influx of Na+, above a critical value of its concentration, increases linearly with its concentration in the soil solution at the root surface. Uptake of Ca+2+ is controlled by the balance between influxes of anions and cations, which induces efflux of H+ or HCO3−, and interacts with calcite in a calcareous soil. The model may provide information about the behavior of ions at the root-soil interface which cannot be measuredin situ.

Multiphase and Multi-component Interactions through the Unsaturated Saturated Zone Field and Model Study

An integrated approach of field and model investigations was implemented to an aquifer underlying urban infrastructure. The study focuses on the transport of Trichloroethylene (TCE) through the unsaturated-saturated zone. Simulations, subject to isothermal conditions, addressed a threedimensional continuum involving three interacting mobile phases: aqueous, NAPL (Non-Aqueous Phase Liquids) and gaseous. The mathematical model considers water, air and TCE as components in equilibrium partitioning between the three mobile fluids, while for the latter we account also for sorption on the solid matrix. Predictions of migration patterns were due to a continuous spill from a single NAPL source situated at the soil surface.

Numerical modeling of coupled hydrological phenomena using the Modified Eulerian-Langrangian method

The chapter presents the advantages of using the Modified Eulerian-Lagrangian (MEL) method for solving the transport of extensive quantities in a porous medium. In this modified formulation, the material derivatives are written in terms of modified velocities. These are the velocities at which the various phase and component variables propagate in the domain, along their respective characteristic curves. It is shown that these velocities depend on the heterogeneity of various solid matrix and fluid properties. Accordingly, an extension to the Peclet number is presented that also accounts for governing equations that may be advective dominant with no reference to the fluid velocity or even when this velocity is not introduced. A mathematical analysis proves that for coupled partial differential equations (PDEs), unlike the Eulerian implicit finite difference scheme the MEL method unconditionally guarantees the absent of spurious oscillations. The MEL formulation is demonstrated for a coupled set of PDEs concerning the problem of saltwater intrusion, with heat transfer. A numerical example suggests that the MEL scheme produces better resolution compared to the Eulerian and the Eulerian-Lagrangian ones.

K+ uptake by root systems grown in soil under salinity: II. Sensitivity analysis

A numerical algorithm for the solution of multicomponent transport of Ca2+, Mg2+, Na+, K+, Cl− in soil and their uptake by plant roots has been developed. The model emphasizes adsorptiondesorption due to cation exchange mechanism, dissolution-precipitation of CaCO3, and pH changes at the root surface controlled by the anion-cation influx balance. A fully implicit finite difference scheme is used for numerical implementation. Sensitivity analysis was conducted to evaluate the effect of each parameter on nutrient uptake. Each parameter (independent of all others) was varied between 0.25 to 4 times its speculated ‘average’ level. Predicted K+ uptake was found to be more sensitive to changes of root radius and the parameter indicating maximal influx of K+. Effective diffusion coefficient and soil moisture are less influential. The influence of CaCO3 dissolution and different kinds of boundary conditions were also considered.

On The Modified Eulerian-Lagrangian MethodFor Solving Coupled Balance Equations In PorousMedia

The paper presents the modified Eulerian-Lagrangian (MEL) method for solving the flow and the transport of extensive quantities in a porous medium. In this modified formulation, the material derivatives are written in terms of modified velocities. These are the velocities at which the various phase and component variables propagate in the domain, along their respective characteristic curves. It is shown that these velocities depend on the heterogeneity of various solid matrix and fluid properties. A numerical analysis proves that unlike the Eulerian and the Eulerian-Lagrangian (EL) implicit difference scheme, the MEL one guarantees the absence of spurious oscillations. 1 Theory The basic MEL characteristics are presented in Bear et alA Here in what follows the MEL formulation is developed for both flow and solute migration. In the case of the flow equation, particles velocity is associated with the gradient of the hydraulic conductivity while for Transactions on Ecology and the Environment vol 17,