Jacob Bear

Seawater Intrusion in Coastal Aquifers — Concepts, Methods and Practices

Preface. List of Contributors. 1. Introduction J. Bear, A.H.-D. Cheng. 2. Geophysical Investigations M.T. Stewart. 3. Geochemical Investigations B.F. Jones, et al. 4. Exploitation, Restoration and Management J.C. van Dam. 5. Conceptual and Mathematical Modeling J. Bear. 6. Analytical Solutions A.H.-D. Cheng, D. Ouazar. 7. Steady Interface in Stratified Aquifers of Random Permeability Distribution G. Dagan, D.G. Zeitoun. 8. USGS SHARP Model H.I. Essaid. 9. USGS SUTRA Code - History, Practical Use, and Application in Hawaii C.I. Voss. 10. Three-Dimensional Model of Coupled Density-Dependent Flow and Miscible Salt Transport G. Gambolati, et al. 11. Modified Eulerian Lagrangian Method for Density Dependent Miscible Transport S. Sorek, et al. 12. Survey of Computer Codes and Case Histories S. Sorek, G.F. Pinder. 13. Seawater Intrusion in the United States L.F. Konikow, T.E. Reilly. 14. Impact of Sea Level Rise in the Netherlands G.H.P. Oude Essink. 15. Movement of Brackish Groundwater Near a Deep-Well Infiltration System in the Netherlands A. Stakelbeek. 16. A Semi-Empirical Approach to Intrusion Monitoring in Israeli Coastal Aquifer A.J. Melloul, D.G. Zeitoun. 17. Nile Delta Aquifer in Egypt M. Sherif. Bibliography. Index.

Macroscopic Modelling of Transport Phenomena in Porous Media. 1: The Continuum Approach

This is the first of two papers presenting a systematic development of a continuum model of a porous medium and of transport processes occurring in it. The concept of a Representative Elementary Volume (REV) as opposed to any arbitrary volume of averaging quantities at the micro-scale, is quantified. A universal criterion for selecting the size of an REV as a function of measurable characteristics of a porous medium and selected tolerance levels of estimation errors, is developed. The rules of spatial averaging are extended by including the effects of both the configuration of the solid matrix and of interphase transfer phenomena within an REV.

On the movement of water bodies injected into aquifers

Abstract The paper deals with artificial replenishment through wells and with the movement of water bodies injected into confined aquifers. The knowledge of such movement is essential for any planning of artificial replenishment of ground water aquifers, both for storage and for mixing purposes. The assumption underlying the present investigations is that the native water in the aquifer and the injected water are two immiscible liquids of different salinities. It is also assumed that differences in density and viscosity are small and may be neglected. Two cases have been investigated: (1) injection through a single well under steady flow conditions into a confined aquifer in which uniform flow takes place, and (2) the movement of injected water bodies under nonsteady flow conditions. In addition to the determination of front shapes, the recovery ratio of injected water in the water pumped through the same well and the extent of mixing in the pumped water, were determined.

Modelling and applications of transport phenomena in porous media

These books are written in very different styles. In a sense they are complementary, though many workers comfortable with the content and presentation of one might find the other relatively unattractive. The first is intended ‘to provide a user-friendly introduction to the topic of convection in porous media . . . (employing) only routine classical mathematics , . . as a review and as a tutorial work ’. It adopts familiar constitutive models for transport of mass momentum and energy in homogeneous saturated porous media, and uses them to solve boundary value problems by standard mathematical techniques. The book is tightly written, the applications are precisely defined and the approach, which relies heavily on dimensionless formulations, will be familiar to most engineering scientists. Within the range of topics chosen it is comprehensive, but it tends not to stress the real difficulties of reducing engineering or geomechanical problems to tractable mathematical form. The second is a collection of separately authored chapters of greatly varying length and content, which has the paradoxical advantage of showing that there are different ways of looking at any given process. Much of it is very formal, and is concerned with setting up the basic continuum models (constitutive relations) that others might use. Three relatively specialized examples (two of these from the nuclear industry) are considered, covering boiling and drying. There is little connection between the various chapters. It should be noted that it is volume 5 in a series on Theory and Applications of Transport in Porous Media. I found considerable overlap with parts of volume 4 : the first long chapter by Bear, which occupies nearly half of volume 5 , is to some extent a digest of volume 4. Neither is as balanced a text from the point of view of an engineering scientist as that reviewed earlier (Theory of Fluid Flows through Natural R O C ~ S , by Barenblatt, Entov & Ryzhik, volume 3 of the Kluwer series, see J . Fluid Mech. 223 (1991), p. 663). Though Nield & Bejan stands very well on its own, it is primarily an academic textbook (and a very good one too) ; I hope that it does not sound churlish to argue that the limitations that academics impose upon themselves to maintain elegance and simplicity detract somewhat from the merit of their work as sources for engineers : real problems arise because of the inadequacies of our existing models, and unless this is emphasized there is a danger that engineers trained by academics-will use inappropriate models. In the case of real porous media, the continuum assumption of an isotropic homogeneous undeforming medium with Darcy-like behaviour always has to be carefully examined : if the mathematical modeller does not carry out such an examination and assess the consequences of any departures from the assumption, the chances are that nobody will. To this extent the rather arid and formal development of continuum equations is an important discipline. An understanding of the relevance of averaging processes and of their consequences for averaged continuum equations should always be emphasized in texts for engineers. I can therefore commend chapter 6 by de Marsily 408 pp. DM128.

Dynamics of Fluids in Porous Media

Keywords: Ecoulement souterrain ; Milieux poreux Reference Record created on 2004-09-07, modified on 2016-08-08

Potentials and Their Role in Transport in Porous Media

The concept of “capillary,” or “matric,” potentials is commonly used in soil physics to describe water movement in unsaturated soils. The rigorous definition of these and other potentials is presented from fundamental thermodynamic principles at the microscopic level and extended to the macroscopic level by averaging over a representative elementary volume. Of special interest is the treatment of adsorptive surface forces and their associated potentials. Porous medium potentials are extended to a domain containing multiple fluid phases and multiple components. A macroscopic motion equation for a fluid phase (Darcys law) is derived, incorporating the effect of potentials and surface forces. It relates advective fluxes to gradients of macroscopic chemical potentials and temperature. It reduces to the usual form of Darcys law only when the aqueous phase is sufficiently dilute and temperatures are uniform. Kelvins law, which relates relative humidity to matric potential, is extended to the case of multiple multicomponent fluid phases in a porous medium domain. The concept of “irreducible” (or “residual”) wetting fluid saturation and its relationship to capillary pressure, surface forces, and the Gibbs chemical potential, are discussed. Common methods for determining the matric potential are reexamined in light of this work.

Macroscopic modelling of transport phenomena in porous media. 2: Applications to mass, momentum and energy transport

In this second paper, the averaging rules presented in Part 1 are employed in order to develop a general macroscopic balance equation and particular equations for mass, mass of a component, momentum and energy, all of a phase in a porous medium domain. These balance equations involve averaged fluxes. Then macroscopic equations are developed for advective, dispersive and diffusive fluxes, all in terms of averaged state variables of the system. These are combined with the macroscopic balance equations to yield field equations that serve as the core of the mathematical models that describe the transport of extensive quantities in a porous medium domain.It is shown that the methodology of averaging leads to a better understanding of the effective stress concept employed in dealing with transport phenomena in deformable porous media.

Effective and relative permeabilities of anisotropie porous media

A model composed of a three-dimensional orthogonal network of capillary tubes was used to simulate the flow behavior in an unsaturated anisotropic soil. The anisotropy in the networks permeability was introduced by randomly selecting the radii in the three mutually orthogonal directions of the network tubes from three different lognormal probability distributions, one for each direction. These three directions were assumed to be the principal directions of anisotropy. The sample was gradually drained, with only tubes smaller than a certain diameter remaining full at each degree of saturation. Computer experiments were conducted to determine the networks effective permeability as a function of saturation. The main conclusion was that the relationship between saturation and effective permeability depends on direction. Consequently the concept of relative permeability used in unsaturated flow should be limited to isotropic media and not extended to anisotropic ones.

Transport Phenomena in Porous Media — Basic Equations

The objective of this review is to present the methodology of developing the complete description of transport phenomena in a multiphase, deformable porous medium, and to demonstrate this methodology by applying it to the transport of such extensive quantities as volume, mass, component of a phase, momentum and heat.

Optimization of pump-treat-inject (PTI) design for the remediation of a contaminated aquifer: multi-stage design with chance constraints

Abstract A large scale groundwater remediation project using pump-and-treat (PAT) or pump-treat-inject (PTI) cannot be designed as a single time-step operation, because of uncertainties associated with the system. The changes in concentrations in reality may differ significantly from predicted ones. Instead, a multi-stage decision process is formulated and solved as a two-level hierarchical optimization model. Cost serves as the objective function, while contaminant concentration and total cleanup time are constraints. The entire cleanup time is divided into several stages. The number of wells for both pumping and injection is treated as a decision variable in each design stage. At the basic level, well locations and pumping/injection rates are sought so as to maximize mass removal of contaminants. At the upper level, the number of wells for pumping and injection is optimized, so as to minimize the cost, taking maximum contaminant level (MCL) as a constraint. Indices for the equivalent centroid and areal extent of a contaminant plume are proposed and used to initiate well locations at each design stage.