# Keys To This Book

## Keys To This Book

KEYS TO THIS BOOK We hope that this book will be of interest for engineers, students and applied mathematicians and we wish to give a few reading dire...

KEYS TO THIS BOOK We hope that this book will be of interest for engineers, students and applied mathematicians and we wish to give a few reading directions for an optimal use of it. Chapter 1 presents the main pollutants and their characters of miscibility which justify the foundations of groundwater-pollution studies on miscibledisplacement theories. Chapter 2 outlines the basic elements of dispersion theory, otherwise detailed by Fried and Combarnous (1971), and stresses the derivation of the mathematical representations from laboratory experiments and their limits. Chapter 3 gives the methodological rules for studying a case of groundwater pollution quantitatively. It shows how to handle such a problem and it defines the sequence of operations. To illustrate this methodology, two type-projects are presented that could be used as models of propositions for groundwater-pollution studies (especially in the case of pollution from sanitary landfills). Chapter 6 describes some typical case histories which explain how t o apply the methodology, while Chapter 4 gives the main field experiments and formulas necessary to collect the various pollution parameters and Chapter 5 presents some useful numerical models with their finitedifference discretization. With Chapter 7, we have tried to widen the subject, showing that groundwater pollution is part of larger economical problems linked to the management of water resources. We show that the methodology specific to groundwater pollution described in Chapter 3 is an application of more general methods, supported by mathematical tools and refined mathema tical data-processing methods, which we describe briefly. We then give the basic concepts of an economical and political approach to water resources and groundwater-pollution problems. Although Chapter 8 is a consequence of experimental considerations, it is highly mathematical and theoretical and has been written to show applied mathematicians that even ground-to-ground pollution problems offer very good opportunities of developing their own mathematical research and t o induce them to come into this very applied branch of physics and help it with their mathematical knowledge. Chapter 9 develops the numerical-analysis methods and procedures necessary to set a pollution problem numerically and to solve it on a computer. I t stresses the close interrelationships between the physics of the phenomena and the modelling. Four Appendices have been added t o provide specific information. Appendix I provides basic information on groundwater hydrology, sufficient for a correct understanding of groundwater and pollution flow. Appendix I1 explains the basis of geophysical electrical soundings, which are much-used

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KEYS TO THIS BOOK

field techniques to detect pollution without disturbing the medium and with a restricted number of boreholes. Appendix I11 is a summary of basic algebraic notions, necessary to understand the techniques of Chapter 9: a non-specialist, such as a geologist, should be able to build a mathematical model with Appendix I11 and Chapters 5 and 9. Appendix IV is a description of the international norms for drinking water and provides the concentration thresholds used in pollution studies. An engineer will mostly use Chapters 3, 4, 5, 6 and 9 to obtain a practical knowledge of and practical solutions for his pollution problems. If this practical man is responsible for a whole project, Chapter 7 will be of great help for him. An applied mathematician, or a research scientist will find interest in Chapters 2 and 8 which are theoretical or close to the laboratory. Of course they should read all the other chapters which bring them into the physics of the phenomena. This book can be used as a textbook on the understanding and the quantification of groundwater-pollution problems; we feel that Chapter 8 should then be skipped, except for 58.4.1,which is an introduction to the philosophy of modelling. At the undergraduate level, Chapter 2 on dispersion is a basis for laboratory and mathematical work; at the graduate level, the chapters on methodology ( 3 and 7) and on field experiments should be studied.