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Modeling Tools for Environmental Engineers and Scientists © 2002 by CRC Press LLC Modeling Tools for Environmental Engineers and Scientists N. Nirmala Khandan CRC PR ESS Boca Raton London New York Washington, D.C. Library of Congress Cataloging-in-Publication Data Nirmala Khandan, N. Modeling tools for environmental engineers and scientists / N. Nirmala Khandan. p. cm. Includes bibliographical references and index. ISBN 1-56676-995-7 1. Environmental sciences—Mathematical models. 2. Environmental engineering—Mathematical models. I. Title. GE45.M37 K43 2001 628¢.01¢1—dc21 2001052467 This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. 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Visit the CRC Press Web site at www.crcpress.com © 2002 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 1-56676-995-7 Library of Congress Card Number 2001052467 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper Frontmatter 11/9/01 9:30 AM Page v Contents Preface Acknowledgments FUNDAMENTALS 1. INTRODUCTION TO MODELING 1.1 What is Modeling? 1.2 Mathematical Modeling 1.3 Environmental Modeling 1.4 Objectives of This Book Appendix 1.1 Appendix 1.2 2. FUNDAMENTALS OF MATHEMATICAL MODELING 2.1 Definitions and Terminology in Mathematical Modeling 2.2 Steps in Developing Mathematical Models 2.3 Application of the Steps in Mathematical Modeling 3. PRIMER ON MATHEMATICS 3.1 Mathematical Formulations 3.2 Mathematical Analysis 3.3 Examples of Analytical and Computational Methods 3.4 Closure © 2002 by CRC Press LLC Frontmatter 11/9/01 9:30 AM Page vi 4. FUNDAMENTALS OF ENVIRONMENTAL PROCESSES 4.1 Introduction 4.2 Material Content 4.3 Phase Equilibrium 4.4 Environmental Transport Processes 4.5 Interphase Mass Transport 4.6 Environmental Nonreactive Processes 4.7 Environmental Reactive Processes 4.8 Material Balance Appendix 4.1 5. FUNDAMENTALS OF ENGINEERED ENVIRONMENTAL SYSTEMS 5.1 Introduction 5.2 Classifications of Reactors 5.3 Modeling of Homogeneous Reactors 5.4 Modeling of Heterogeneous Reactors 6. FUNDAMENTALS OF NATURAL ENVIRONMENTAL SYSTEMS 6.1 Introduction 6.2 Fundamentals of Modeling Soil Systems 6.3 Fundamentals of Modeling Aquatic Systems Appendix 6.1 7. SOFTWARE FOR DEVELOPING MATHEMATICAL MODELS 7.1 Introduction 7.2 Spreadsheet-Based Software 7.3 Equation Solver-Based Software 7.4 Dynamic Simulation-Based Software 7.5 Common Example Problem: Water Quality Modeling in Lakes 7.6 Closure Appendix 7.1 Appendix 7.2 © 2002 by CRC Press LLC Frontmatter 11/9/01 9:30 AM Page vii APPLICATIONS 8. MODELING OF ENGINEERED ENVIRONMENTAL SYSTEMS 8.1 Introduction 8.2 Modeling Example: Transients in Sequencing Batch Reactors 8.3 Modeling Example: CMFRs in Series for Toxicity Management 8.4 Modeling Example: Municipal Wastewater Treatment 8.5 Modeling Example: Chemical Oxidation 8.6 Modeling Example: Analysis of Catalytic Bed Reactor 8.7 Modeling Example: Waste Management 8.8 Modeling Example: Activated Carbon Treatment 8.9 Modeling Example: Bioregeneration of Activated Carbon 8.10 Modeling Example: Pipe Flow Analysis 8.11 Modeling Example: Oxygen/Nitrogen Transfer in Packed Columns 8.12 Modeling Example: Groundwater Flow Management 8.13 Modeling Example: Diffusion through Porous Media 9. MODELING OF NATURAL ENVIRONMENTAL SYSTEMS 9.1 Introduction 9.2 Modeling Example: Lakes in Series 9.3 Modeling Example: Radionuclides in Lake Sediments 9.4 Modeling Example: Algal Growth in Lakes 9.5 Modeling Example: Contaminant Transport Visualization 9.6 Modeling Example: Methane Emissions from Rice Fields 9.7 Modeling Example: Chemical Equilibrium 9.8 Modeling Example: Toxicological Exposure Evaluation 9.9 Modeling Example: Visualization of Groundwater Flow 9.10 Modeling Example: Air Pollution—Puff Model 9.11 Modeling Example: Air Pollution—Plume Model 9.12 Modeling Example: Fugacity-Based Modeling 9.13 Modeling Example: Well Placement and Water Quality Management BIBLIOGRAPHY © 2002 by CRC Press LLC Frontmatter 11/9/01 9:30 AM Page ix Preface THIS book is not a treatise on environmental modeling. Several excellent books are currently available that do more than justice to the science of environmental modeling. The goal of this book is to bridge the gap between the science of environmental modeling and working models of environmental systems. More specifically, the intent of this book is to bring computer- based modeling within easy reach of subject matter experts and professionals who have shied away from modeling,daunted by the intricacies of computer programming and programming languages. In the past two decades, interest in computer modeling in general and in environmental modeling in particular,have grown significantly. The number of papers and reports published on modeling, the number of specialty con- ferences on modeling held all over the world, and the number of journals dedicated to modeling efforts are evidence of this growth. Several factors such as better understanding of the underlying science, availability of high performance computer facilities, and increased regulatory concerns and pressures have fueled this growth. Scrutiny of those involved in environmental modeling, however, reveals that only a small percentage of experts are active in the modeling efforts; namely those who also happen to be skilled in computer programming. For the rest of us, computer modeling has remained a challenging task until recently. A new breed of software authoring packages has now become available that enables nonprogrammers to develop their own models without having to learn programming languages. These packages feature English-like syntax and easy-to-use yet extremely powerful mathematical, analytical, computational, and graphical functions, and user-friendly interfaces. They can drastically reduce the time, effort, and programming skills required to develop professional quality user-friendly models. This book describes eight such software packages, and, with over 50 modeling examples, illustrates how they can be adapted for almost any type of modeling project. © 2002 by CRC Press LLC Frontmatter 11/9/01 9:30 AM Page x The contents of this book are organized into nine chapters. Chapter 1 is an introduction to modeling. Chapter 2 focuses on the science and art of mathematical modeling. Chapter 3 contains a primer on mathematics with examples of computer implementation of standard mathematical calculi. Chapters 4,5, and 6 contain reviews of the fundamentals of environmental processes,engineered systems, and natural systems, respectively. Chapter 7 describes and compares the eight software packages selected here for developing environmental models. Chapters 8 and 9 are devoted entirely to modeling examples covering engineered and natural systems,respectively. The book can be of benefit to those who have been yearning to venture into modeling,as well as to those who have been using traditional language-based approaches for modeling. In the academic world,this book can be used as the main text to cultivate computer modeling skills at the freshman or junior levels. It can be used as a companion text in “fate and transport” or “environmental modeling” types of courses. It can be useful to graduate students planning to incorporate some form of modeling into their research. Faculty can benefit from this book in developing special purpose models for teaching, research,publication,or consulting. Practicing professionals may find it useful to develop custom models for limited use, preliminary analysis, and fea- sibility studies. Suggested uses of this book by different audiences at different levels are included in Chapter 1. As a final note, this book should not be taken as a substitute for the user manuals that accompany software packages; rather, it takes off from where the user manuals stop,and demonstrates the types of finished products (models,in this case) that can be developed by integrating the features of the software. This book can, perhaps, be compared to a road map, which can take nonprogrammers from the problem statement to a working computer-based mathematical model. Different types of vehicles can be used for the journey. The intention here is not to teach how to drive the vehicles but rather to point out the effort required by the different vehicles,their capabilities,advantages, disadvantages,special features,and limitations. © 2002 by CRC Press LLC Frontmatter 11/9/01 9:30 AM Page xi Acknowledgments Iwould like to acknowledge several individuals who, directly or indirectly, were responsible for giving me the strength,confidence,opportunity,and support to venture into this project. First,I would like to recognize all my teachers in Sri Lanka,some of whom probably did not even know me by name. Yet,they gave me a rigorous education, particularly in mathematics, for which I am forever thankful. I also want to acknowledge the continuing encouragement, guidance, motivation, and friendship of Professor Richard Speece, to whom I gratefully attribute my academic career. The five years that I shared with Professor Speece have been immensely satisfying and most productive. I want to thank my department head, Professor Kenneth White, for supporting my efforts throughout my academic tenure, without which I could not have found the time or the resources to embark on this project. Thanks to my departmental colleagues and the administration at New Mexico State University for allowing me to go on sabbatical leave to complete this project. The donation of full versions of software packages by MathSoft,Inc.,The Mathworks,Inc.,Universal Technical Systems,Inc.,Wolfram Research,Inc., and High Performance Systems, Inc., is gratefully acknowledged. The support,encouragement,and patience of Dr. Joseph Eckenrode and his editorial staff at Technomic Publishing Co., Inc. (now owned by CRC Press LLC) is fully appreciated. I am indebted to my grandparents and to my parents for the sacrifices they made to ensure that I received the finest education from the earliest age; and to the families of my sister and sister-in-law for their support and compassion, particularly during my graduate studies. Finally, I am thankful to my wife Gnana and our sons Rajeev and Sanjeev,for their support,understanding,and tolerance throughout this and many other projects, which took much of my time and attention away from them. Sanjeev also contributed to this work directly in setting up some of the models and by sharing some of the agonies and ecstasies of computer programming. © 2002 by CRC Press LLC