The Mathematics of Fluid Flow Through Porous Media

Learn the fundamental concepts that underlie the physics of multiphase flow and transport in porous media with the information in Essentials of Multiphase Flow in Porous Media, which demonstrates the mathematical-physical ways to express and address multiphase flow problems. Find a logical, step-by-step introduction to everything from the simple concepts to the advanced equations useful for addressing real-world problems like infiltration, groundwater contamination, and movement of non-aqueous phase liquids. Discover and apply the governing equations for application to these and other problems in light of the physics that influence system behavior.

The first edition of this book is considered the bible of this topic… Suffice it to say that there is no other published treatise that approaches the depth of treatment offered by this book. The coverage is the state of the published art, while the added contents cover the new known developments in the field. Haisam Osman; Technology Development Manager, United Launch Alliance This long-awaited second edition of a respected text from world leaders in the field of acoustic materials covers the state of the art with a depth of treatment unrivalled elsewhere. Allard and Atalla employ a logical and progressive approach that leads to a thorough understanding of porous material modelling. The first edition of Propagation of Sound in Porous Media introduced the basic theory of acoustics and the related techniques. Research and development in sound absorption has however progressed significantly since the first edition, and the models and methods described, at the time highly technical and specialized, have since become main stream. In this second edition, several original topics have been revisited and practical prediction methods and industrial applications have been added that increase the breadth of its appeal to both academics and practising engineers. New chapters have also been added on numerical modeling in both low (finite element) and high frequency (Transfer Matrix Method). Collating ‘must-have’ information for engineers working in sound and vibration, Propagation of Sound in Porous Media, 2nd edition offers an indisputable reference to a diverse audience; including graduate students and academics in mechanical & civil engineering, acoustics and noise control, as well as practising mechanical, chemical and materials engineers in the automotive, rail, aerospace, building and civil industries.

The book that makes transport in porous media accessible to students and researchers alike Porous Media Transport Phenomena covers the general theories behind flow and transport in porous media—a solid permeated by a network of pores filled with fluid—which encompasses rocks, biological tissues, ceramics, and much more. Designed for use in graduate courses in various disciplines involving fluids in porous materials, and as a reference for practitioners in the field, the text includes exercises and practical applications while avoiding the complex math found in other books, allowing the reader to focus on the central elements of the topic. Covering general porous media applications, including the effects of temperature and particle migration, and placing an emphasis on energy resource development, the book provides an overview of mass, momentum, and energy conservation equations, and their applications in engineered and natural porous media for general applications. Offering a multidisciplinary approach to transport in porous media, material is presented in a uniform format with consistent SI units. An indispensable resource on an extremely wide and varied topic drawn from numerous engineering fields, Porous Media Transport Phenomena includes a solutions manual for all exercises found in the book, additional questions for study purposes, and PowerPoint slides that follow the order of the text.

The book provides the reader with the knowledge, tools, and methods to understand the phenomenon of hysteresis in porous materials. As many challenges have been met only recently, the book summarizes the research results usually found only scattered in the literature, connecting knowledge from traditionally separated research fields to provide a better understanding of the physical phenomena of coupled elastic-fluid systems. The result is an invaluable self-contained reference book for materials scientists, civil, mechanical and construction engineers concerned with development and maintenance of structures made of porous materials.

A unique and timely book on understanding and tailoring the flow of fluids in porous materials Porous media play a key role in chemical processes, gas and water purification, gas storage and the development of new multifunctional materials. Understanding hydrodynamics in porous media is decisive for enabling a wide range of applications in materials science and chemical engineering. This all-encompassing book offers a timely overview of all flow and transport processes in which chemical or physicochemical phenomena such as dissolution, phase transition, reactions, adsorption, diffusion, capillarity, and surface phenomena are essential. It brings together both theoretical and experimental results and includes important industrial applications. Physicochemical Fluid Dynamics in Porous Media: Applications in Geoscience and Petroleum Engineering explains the thermodynamics of phase equilibria for multicomponent fluids, physicochemical models of single-phase and immiscible two-phase flow, based on the macroscopic theory of oil displacement by water. It also covers the theory of two-phase flow with partial miscibility and describes partially miscible flows with phase transitions by means of the negative saturation approach. The final chapters are devoted to flow with chemical reactions, based on the example of in-situ leaching of uranium, and flow with bio-chemical reactions in terms of the underground storage of hydrogen. -Brings together the theoretical and experimental results necessary for the understanding of hydrodynamics in porous media -Covers important industrial applications such as underground leaching of uranium and underground storage of hydrogen -Presents a state-of-the-art overview and summarizes the research results usually found only scattered in the literature Physicochemical Fluid Dynamics in Porous Media: Applications in Geoscience and Petroleum Engineering will appeal to chemical engineers, materials scientists, applied physicists, and mechanical engineers.

This new edition brings the fascinating and intriguing history of mathematics to life The Second Edition of this internationally acclaimed text has been thoroughly revised, updated, and reorganized to give readers a fresh perspective on the evolution of mathematics. Written by one of the world's leading experts on the history of mathematics, the book details the key historical developments in the field, providing an understanding and appreciation of how mathematics influences today's science, art, music, literature, and society. In the first edition, each chapter was devoted to a single culture. This Second Edition is organized by subject matter: a general survey of mathematics in many cultures, arithmetic, geometry, algebra, analysis, and mathematical inference. This new organization enables students to focus on one complete topic and, at the same time, compare how different cultures approached each topic. Many new photographs and diagrams have been added to this edition to enhance the presentation. The text is divided into seven parts: The World of Mathematics and the Mathematics of the World, including the origin and prehistory of mathematics, cultural surveys, and women mathematicians Numbers, including counting, calculation, ancient number theory, and numbers and number theory in modern mathematics Color Plates, illustrating the impact of mathematics on civilizations from Egypt to Japan to Mexico to modern Europe Space, including measurement, Euclidean geometry, post-Euclidean geometry, and modern geometrics Algebra, including problems leading to algebra, equations and methods, and modern algebra Analysis, including the calculus, real, and complex analysis Mathematical Inference, including probability and statistics, and logic and set theory As readers progress through the text, they learn about the evolution of each topic, how different cultures devised their own solutions, and how these solutions enabled the cultures to develop and progress. In addition, readers will meet some of the greatest mathematicians of the ages, who helped lay the groundwork for today's science and technology. The book's lively approach makes it appropriate for anyone interested in learning how the field of mathematics came to be what it is today. It can also serve as a textbook for undergraduate or graduate-level courses. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

Praise for the Second Edition «An amazing assemblage of worldwide contributions in mathematics and, in addition to use as a course book, a valuable resource . . . essential.» —CHOICE This Third Edition of The History of Mathematics examines the elementary arithmetic, geometry, and algebra of numerous cultures, tracing their usage from Mesopotamia, Egypt, Greece, India, China, and Japan all the way to Europe during the Medieval and Renaissance periods where calculus was developed. Aimed primarily at undergraduate students studying the history of mathematics for science, engineering, and secondary education, the book focuses on three main ideas: the facts of who, what, when, and where major advances in mathematics took place; the type of mathematics involved at the time; and the integration of this information into a coherent picture of the development of mathematics. In addition, the book features carefully designed problems that guide readers to a fuller understanding of the relevant mathematics and its social and historical context. Chapter-end exercises, numerous photographs, and a listing of related websites are also included for readers who wish to pursue a specialized topic in more depth. Additional features of The History of Mathematics, Third Edition include: Material arranged in a chronological and cultural context Specific parts of the history of mathematics presented as individual lessons New and revised exercises ranging between technical, factual, and integrative Individual PowerPoint presentations for each chapter and a bank of homework and test questions (in addition to the exercises in the book) An emphasis on geography, culture, and mathematics In addition to being an ideal coursebook for undergraduate students, the book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the history of mathematics.

A porous medium is composed of a solid matrix and its geometrical complement: the pore space. This pore space can be occupied by one or more fluids. The understanding of transport phenomena in porous media is a challenging intellectual task. This book provides a detailed analysis of the aspects required for the understanding of many experimental techniques in the field of porous media transport phenomena. It is aimed at students or engineers who may not be looking specifically to become theoreticians in porous media, but wish to integrate knowledge of porous media with their previous scientific culture, or who may have encountered them when dealing with a technological problem. While avoiding the details of the more mathematical and abstract developments of the theories of macroscopization, the author gives as accurate and rigorous an idea as possible of the methods used to establish the major laws of macroscopic behavior in porous media. He also illustrates the constitutive laws and equations by demonstrating some of their classical applications. Priority is to put forward the constitutive laws in concrete circumstances without going into technical detail. This second volume in the three-volume series focuses on transport and transfer from homogeneous phases to porous media, and isothermal transport in the pore space.

Despite of many years of studies, predicting fluid flow, heat, and chemical transport in fractured-porous media remains a challenge for scientists and engineers worldwide. This monograph is the third in a series on the dynamics of fluids and transport in fractured rock published by the American Geophysical Union (Geophysical Monograph Series, Vol. 162, 2005; and Geophysical Monograph, No. 122, 2000). This monograph is dedicated to the late Dr. Paul Witherspoon for his seminal influence on the development of ideas and methodologies and the birth of contemporary fractured rock hydrogeology, including such fundamental and applied problems as environmental remediation; exploitation of oil, gas, and geothermal resources; disposal of spent nuclear fuel; and geotechnical engineering. This monograph addresses fundamental and applied scientific questions and is intended to assist scientists and practitioners bridge gaps in the current scientific knowledge in the areas of theoretical fluids dynamics, field measurements, and experiments for different practical applications. Readers of this book will include researchers, engineers, and professionals within academia, Federal agencies, and industry, as well as graduate/undergraduate students involved in theoretical, experimental, and numerical modeling studies of fluid dynamics and reactive chemical transport in the unsaturated and saturated zones, including studies pertaining to petroleum and geothermal reservoirs, environmental management and remediation, mining, gas storage, and radioactive waste isolation in underground repositories. Volume highlights include discussions of the following: Fundamentals of using a complex systems approach to describe flow and transport in fractured-porous media. Methods of Field Measurements and Experiments Collective behavior and emergent properties of complex fractured rock systems Connection to the surrounding environment Multi-disciplinary research for different applications