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The governing equations are discussed for the flow of salt solution with significant density variations through a porous medium. Equations for mass conservation, salt conservation, and momentum conservation are formulated in terms of the mass fraction weighted average velocity and the mass fraction of concentrated salt solution, and the underlying approximations are considered. These equations are incorporated in the finite element groundwater code NAMMU and applied to test case 5 of level 1 of the international HYDROCOiN project. This test case proposed to model the groundwater flow over a hypothetical salt dome. The nonlinearities arising from the density variation and from a velocitydependent dispersion tensor made the problem very hard: we had to use special techniques including mixed interpolation finite elements and parameter stepping. Starting from a related problem involving a large diffusivity we obtained a series of solutions at successively smaller values of dispersion. Our final solution is to a physically realistic problem very similar to that specified. We draw general conclusions relevant to modeling these flows and have built confidence in our numerical code. INTRODUCTIONMany countries are currently considering disposal of radioactive waste by burial in geological formations. The most likely way in which radionuclides from buried waste might return to the biosphere is through dissolution and transport by flowing groundwater. This involves many complicated physical and chemical processes; to understand these processes and predict the groundwater flow and transport over the very long time scales involved, it is necessary to use mathematical models. These models are generally solved numerically.Normally, porous medium models are used for groundwater flow and transport. Usually, the density of the groundwater is nearly constant. It may vary slightly as a result of small variations in either temperature or pressure or as a result of the presence of trace quantities of dissolved contaminants. However, the density can sometimes vary considerably, for example, in strong saline solutions, and this can affect the flow significantly. This type of flow is relevant to those countries that are contemplating waste burial in stable salt formations. Similar flows can also be encountered around repositories near the coast, where seawater might percolate into neighboring rocks.In this paper we discuss the equations that are appropriate for describing flows in which the fluid density is strongly dependent upon concentration. We focus, in particular, on the quantities which appear in the equations, the averaging procedures used, and the underlying assumptions that are made. Then we discuss the numerical solution of an example problem using NAMMU [Atkinson et al., 1985-], a very flexible groundwater flow code developed in Theoretical Physics Division at Hatwell. The example problem is one of the test cases that was proposed for study by the participants in the international HYDROCOIN collaboration for verification and ...

A field example of measuring the dispersive properties of a single fracture in fractured plutonic rock is presented. The experimental technique involves injecting a slug of conservative tracer into a “steady” groundwater flow field established between a pumping and recharging borehole and monitoring the tracer breakthrough by sampling the withdrawal water directly. The breakthrough curves from two experiments were analyzed with a model which describes the flow field geometry either analytically or numerically and solves for hydrodynamic dispersion analytically. A longitudinal dispersivity of 1.40 m was estimated by fitting the model to each set of field data. The magnitude of the dispersion was determined to be independent of dispersive effects created by flow through the borehole instrumentation and thought to be purely hydrodynamic in nature.

The distortion by a linear flow of the electric double layer around a small particle is studied for the case of a charge cloud which is thick in comparison with the particle radius and for arbitrary flow strengths, including those which are strong enough to produce a significant distortion of the cloud. For weak flows a second-order-fluid approximation is obtained for the stress contribution for a dilute suspension of such particles. For arbitrarily strong flows integral representations of the charge density and numerical calculations of the stress contribution are given for three representative flows: simple shear, axisymmetric strain and two-dimensional straining motion.