The interface between fresh and salt groundwater in heterogeneous aquifers: a numerical approach

In this paper we study the behavior of a sharp interface between fresh and salt groundwater, in horizontally extended heterogeneous aquifers. The heterogeneities considered are discontinuities in intrinsic permeability. Each fluid has a constant, but different specific weight, while the viscosities are equal. The difference in specific weight induces fluid movement, which in turn causes motion of the interface. We are especially interested in the behavior of interfaces crossing discontinuities in permeability. The governing equations are an elliptic equation for the stream function, coupled with an interface motion equation for the time evolution of the interface. A finite element method is used to solve the equation for the stream function and a front tracking scheme to compute the time evolution of the (discrete) interface movement. We compare numerical results with some (semi-)analytical results of simplified interface problems in both homogeneous and heterogeneous aquifers. Some attention is given to hydrodynamically instable situations, i.e. when a heavier fluid is on top of a lighter fluid

High-concentration-gradient dispersion in porous media : experiments, analysis and approximations

Various experimental and theoretical studies have shown that Fick's law, based on the assumption of a linear relation between solute dispersive mass flux and concentration gradient, is not valid when high concentration gradients are encountered in a porous medium. The value of the macrodispersivity is found to decrease as the magnitude of the concentration gradient increases. The classical, linear theory does not provide an explanation for this phenomenon. A recently developed theory suggests a nonlinear relation between concentration gradient and dispersive mass flux, introducing a new parameter in addition to the longitudinal and transversal dispersivities. Once a unique set of relevant parameters has been determined (experimentally), the nonlinear theory provides satisfactory results, matching experimental data of column tests, over a wide range of density differences between resident and invading fluids. The lower limit of the nonlinear theory, i.e. very low (tracer) density differences, recovers the linear formulation of Fick's law. The equations describing high concentration brine transport are a fluid mass balance, a salt mass balance in combination with a nonlinear dispersive mass flux equation, Darcy's law and an equation of state. We study the resulting set of nonlinear partial differential equations and derive explicit (exact) and semi-explicit solutions, under various assumptions. A comparison is made between mathematical solutions, numerical solutions and experimental data. The results indicate that the simple explicit solution can be used to simulate experiments in a wide range of density differences, given a unique set of experimentally determined parameters. The analysis shows that enhanced flow due to the compressibility effect, which is caused by local fluid density variations, is neglectable in all cases considered. The linear formulation of Fick's law appears to give an upperbound for magnitude of the compressibility effect

Brine transport in porous media

In this paper we use a Von Mises transformation to study brine transport in porous media. The model involves mass balance equations for fluid and salt, Darcy's law and an equation of state, relating the salt mass fraction to the fluid density. Application of the Von Mises transformation recasts the model equations into a single nonlinear diffusion equation. A further reduction is possible if the problem admits similarity. This yields a formulation in terms of a boundary value problem for an ordinary differential equation which can be treated by semi-analytical means. Three specific similarity problems are considered in detail: (i) One-dimensional, stable displacement of fresh water and brine in a porous column, (ii) Flow of fresh water along the surface of a salt rock, (iii) Mixing of parallel layers of brine and fresh water

On the interaction between gravity forces and dispersive brine fronts in micro-heterogeneous porous media

The concepts of homogenization theory are employed to derive a macro-scale brine transport equation for micro-heterogeneous porous medium of layered structure under assumptions of validity of classical Darcy's law and Fick's law at the local scale. Derived macro-scale model is analogous to the so-called phase field equations. The obtained results are verified with direct numerical experiment. © 2004 Elsevier Ltd. All rights reserved

Density-dependent dispersion in heterogeneous porous media Part II: Comparison with nonlinear models

The results of a series of high-resolution numerical experiments are used to test and compare three nonlinear models for high-concentration-gradient dispersion. Gravity stable miscible displacement is considered. The first model, introduced by Hassanizadeh, is a modification of Fick's law which involves a second-order term in the dispersive flux equation and an additional dispersion parameter β. The numerical experiments confirm the dependency of β on the flow rate. In addition, a dependency on travelled distance is observed. The model can successfully be applied to nearly homogeneous media (σ2 = 0.1), but additional fitting is required for more heterogeneous media. The second and third models are based on homogenization of the local scale equations describing density-dependent transport. Egorov considers media that are heterogeneous on the Darcy scale, whereas Demidov starts at the pore-scale level. Both approaches result in a macroscopic balance equation in which the dispersion coefficient is a function of the dimensionless density gradient. In addition, an expression for the concentration variance is derived. For small σ2, Egorov's model predictions are in satisfactory agreement with the numerical experiments without the introduction of any new parameters. Demidov's model involves an additional fitting parameter, but can be applied to more heterogeneous media as well. © 2007

Brine transport in porous media self-similar solutions

In this paper we analyze a model for brine transport in porous media, which includes a mass balance for the fluid, a mass balance for salt, Darcy's law and an equation of state, which relates the fluid density to the salt mass fraction. This model incorporates the effect of local volume changes due to variations in the salt concentration. Density variations affect the compressibility of the fluid, which in turn cause additional movement of fluid. Two specific situations are investigated that lead to self similarity. We study the relative importance of the compressibility effect in terms of the relative density difference. Semi-analytical solutions are obtained as well as asymptotic expressions in terms of the relative density difference. It is found that the volume changes have a small but noticeable effect on the mass transport only when the salt concentration gradients are large. Some results on the simultaneous transport of brine and dissolved (radioactive) tracers are presented

Crack-sealing bacteria and multi-usage bamboo

The Sultan Qaboos Academic Chair for Quantitative Water Management assists with a holistic solution for drought problems in the Chinese province Yunna

The Oman Water Challenge: Wettskills 2012

In the framework of the State Visit of HM Queen Beatrix to Oman Prof. Dr. Ruud J. Schotting, Sultan Qaboos Chair of Quantitative Water Management at Utrecht University/ Roosevelt Academy, was invited to Oman to assist with the Wetskills competition. The Academic Chair is an initiative of the Netherlands-Oman Foundation and its industrial supporters that funded its first four years. Prof. Schotting reports