Integrating Hydrogeochemical and Geophysical Data for Testing a Finite Volume Based Numerical Model for Saltwater Intrusion

In this paper, hydrogeological and geophysical data are used to validate a numerical model developed to predict seawater intrusion into coastal aquifers. The cell-centered finite volume method is adopted here to solve the set of coupled partial differential equations describing the motion of saltwater and freshwater separated by a sharp interface. These equations are based on the Dupuit approximation and are obtained from integration of 3D flow equations for fresh and salt water zones over the vertical dimension. In order to have flexibility upon complex configurations domain, non structured grid meshing is utilized. To approximate the diffusion fluxes, Green-Gauss type reconstruction, based on diamond-cell and least squares interpolation, is performed. The model is first validated using academic test case studies with known closed form solutions. The mathematical model has been calibrated using hydrogeochemical and geophysical data. The geophysical method applied in this study has been a frequency domain electromagnetic method. In this method the apparent electrical conductivity is measured by induction using two separate hand-held transmitter and receiver coils. During the operation the transmitter coil is energized by a low frequency alternating current that radiates an electromagnetic field and the receiver coil detects the resulting field. Taking into account the relationship between the bulk conductivity of the subsoil and the conductivity of groundwater, EM soundings have been interpreted to provide complementary information to hydrogeochemical data to outline the fresh–saltwater interface. This methodology has been applied to the case of saltwater intrusion into the Llobregat delta aquifer, near Barcelona, Spain.     

A Stochastic Model for Particulate Suspension Flow in Porous Media

A population balance model for a particulate suspension transport with size exclusion capture of particles by porous rock is derived. The model accounts for particle flux reduction and pore space accessibility due to restriction for large particles to move through smaller pores – a particle is captured by a smaller pore and passes through a larger pore. Analytical solutions are obtained for a uniform pore size medium, and also for a medium with small pore size variation. For both cases, the equations for averaged concentrations significantly differ from the classical deep bed filtration model.     

Salt Water Intrusion in a Three-dimensional Groundwater System in The Netherlands: A Numerical Study

Salt water intrusion is investigated in a coastal groundwater system in the northern part of the province Noord-Holland, The Netherlands. Density dependent groundwater flow is modeled in three-dimensions with MOCDENS3D. This computer code is a version of MOC3D (Konikow et al., 1996) that has been adapted to simulate transient density-driven groundwater flow. Results from the model suggests that in this Dutch hydrogeologic system a severe and irreversible salinisation is already occurring. Within a few tens to hundreds of years, the salinity of the shallow aquifer is estimated to increase substantially. This salinisation process is a result of human activities such as the reclamation of the low-lying areas during the past centuries. Without changing the present boundary conditions, seepage into the low-lying areas will decrease slightly because of predicted increases in groundwater salinity. However, the rate in salt load through the Holocene aquitard into the low-lying areas will increase significantly due to an increase in salinity in the shallow aquifer. In addition, a relative sea level rise of 0.5m per century will intensify the salinisation process, causing an enormous increase in salt load in all low-lying areas in this part of The Netherlands.     

Corner Singularities and Regularity of Weak Solutions for the Two-Dimensional Lamé Equations on Domains with Angular Corners

This paper is concerned with corner singularities of weak solutions of boundary value problems in the theory of plane linearized elasticity. The presence of angular corner points or points at which the type of boundary conditions changes yields generally local singularities in the solution. This singular behavior in the vicinity of such points can be described with the help of asymptotic singular representations for the solution, which essentially depend on the zeros of certain transcendental functions. These transcendental functions will be derived and analyzed for all ten possible combinations of boundary conditions, generated by the four basic ones, prescribing in the tangential and normal direction of the boundary, respectively, either the displacement or the tractions. The regularity of the corresponding weak solutions will be investigated. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Two-Equation Model for Heat Conduction in Porous Media (I: Theory)

A two-equation model is presented which describes the conservation of heat in each phase of a porous medium in which diffusion is the predominant means of heat transfer, and of which the phases are not in thermal equilibrium with each other. The model is derived using the method of local volume averaging. This formulation, together with the introduction of characteristic temperature distributions, yields the definition of an effective and a coupled thermal conductivity tensor.     

A Two-Equation Model for Heat Conduction in Porous Media (II: Application)

The formulism of a two-equation model for heat conduction in porous media, developed in a previous paper, is applied to the case of steady state one-dimensional heat transfer in a porous medium that is made up of geometrically similar units of similar size and of ordered spatial distribution. For this case study, the model-predicted locally volume-averaged temperature distributions for the solid and the fluid phase are compared to a numerical solution at a microscopic level, showing excellent agreement.