A model of isotope transport in the unsaturated zone, case study

This work deals with a groundwater flow and solute transport model in the near-surface (predominantly unsaturated) zone. The model is implemented so that it allows simulations of contamination transport from a source located in a geological environment of a rock massif. The groundwater flow model is based on Richards’ equation. Evaporation is computed using the Hamon model. The transport model is able to simulate advection, diffusion, sorption and radioactive decay. Besides the basic model concept, the article also discusses potential cases that could lead to non-physical solutions. On three selected examples, which include, for example, rapidly changing boundary conditions, the article shows the solvability of such cases with the proposed model without unwanted effects, such as negative concentrations or oscillations of solution, that do not correspond to inputs

Modelling of processes in fractured rock using FEM/FVM on multidimensional domains

AbstractThe paper deals with a new approach to the numerical modelling of groundwater flow in compact rock massifs.Empirical knowledge of hydrogeologists is summarized first. There are three types of objects important for the groundwater flow in such massifs—small fractures, which can be replaced by blocks of porous media, large deterministic fractures and lines of intersection of the large fractures. We solve problem of the linear Darcy's flow on each of these three separated domains and then we join them by coupling the equations. We do not require geometrical correspondence between 1D, 2D and 3D meshes, which simplifies the process of the spatial dicretization. The mixed-hybrid FEM with the lowest-order Raviart–Thomas elements is used for approximation of the solution. The advective mass transfer is solved by the FVM on the same discretization as the flow problem.Results of numerical experiments with the model are shown in the end of the paper

A novel approach to modelling of flow in fractured porous medium

summary:There are many problems of groundwater flow in a disrupted rock massifs that should be modelled using numerical models. It can be done via “standard approaches” such as increase of the permeability of the porous medium to account the fracture system (or double-porosity models), or discrete stochastic fracture network models. Both of these approaches appear to have their constraints and limitations, which make them unsuitable for the large- scale long-time hydrogeological calculations. In the article, a new approach to the modelling of groudwater flow in fractured porous medium, which combines the above-mentioned models, is described. This article presents the mathematical formulation and demonstration of numerical results obtained by this new approach. The approach considers three substantial types of objects within a structure of modelled massif important for the groudwater flow – small stochastic fractures, large deterministic fractures, and lines of intersection of the large fractures. The systems of stochastic fractures are represented by blocks of porous medium with suitably set hydraulic conductivity. The large fractures are represented as polygons placed in 3D space and their intersections are represented by lines. Thus flow in 3D porous medium, flow in 2D and 1D fracture systems, and communication among these three systems are modelled together

Direct Probing of Dispersion Quality of ZrO2 Nanoparticles Coated by Polyelectrolyte at Different Concentrated Suspensions.

This study reports useful application of the electrokinetic sonic amplitude (ESA) technique in combination with rheometry and electron microscopy techniques for direct probing the stability of low and high-concentrated zirconia (ZrO2) nanosuspensions in the presence of an alkali-free anionic polyelectrolyte dispersant Dolapix CE64. A comparative study of the electrokinetic characteristics and the rheological behavior of concentrated ZrO2 nanosuspensions has been done. Good agreement was obtained from relationship between the electrokinetic characteristics (zeta potential, ESA signal), viscosity, and its pH dependence for each concentrated ZrO2 nanosuspension with different dispersant concentration in the range of 0.9-1.5 mass%. A nanoscale colloidal hypothesis is proposed to illustrate that the addition of different amounts of dispersant influences on both the stability and the electrokinetic and rheological properties of concentrated ZrO2 nanosuspensions. It is found that an optimum amount of 1.4 mass% dispersant at the inherent pH (>9.2) can be attached fully onto the nanoparticles with sufficient electrosteric dispersion effects, suitable for casting applications. Supplementary scanning electron microscopy (SEM) and high-resolution transmission electron microscopy (HR-TEM) analyses followed by colorization effect were taken to verify the visible interaction between dispersant and nanoparticles surfaces. SEM and HR-TEM images proved the existence of visible coverage of dispersant on the surface of individual nanoparticles and showed that thin polyelectrolyte layers were physically bound onto the particles' surfaces. This study will be of interest to materials scientists and engineers who are dealing with dispersion technology, nanoparticle surface treatments, functionalization, characterization, and application of bio/nanoparticle suspensions at various concentrations using different types of polymers

Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media

Mixed-hybrid finite element discretization of Darcy's law and the continuity equation that describe the potential fluid flow problem in porous media leads to symmetric indefinite saddle-point problems. In this paper we consider solution techniques based on the computation of a null-space basis of the whole or of a part of the left lower off-diagonal block in the system matrix and on the subsequent iterative solution of a projected system. This approach is mainly motivated by the need to solve a sequence of such systems with the same mesh but different material properties. A fundamental cycle null-space basis of the whole off-diagonal block is constructed using the spanning tree of an associated graph. It is shown that such a basis may be theoretically rather ill-conditioned. Alternatively, the orthogonal null-space basis of the sub-block used to enforce continuity over faces can be easily constructed. In the former case, the resulting projected system is symmetric positive definite and so the conjugate gradient method can be applied. The projected system in the latter case remains indefinite and the preconditioned minimal residual method (or the smoothed conjugate gradient method) should be used. The theoretical rate of convergence for both algorithms is discussed and their efficiency is compared in numerical experiments. Copyright © 2006, Kent State University

Mathematical Models of the Underground Water Flow and Transport of Contaminants

Mathematical models of unsteady flow and transport in underground porous media. The governing equations in a compact form. They are discretized by Rothe method in time and by mixed-hybrid finite element method in space. Methods which provide an easy and robust way to solve both the flow and transport problems with mixtures of reacting contaminants. Basic components of such approach