Table Of ContentEnvironmental Chemistry and Toxicology L
I
T
T
Environmental Fate and L
E
Transport Analysis
with
E
Compartment Modeling n
v
ir
o
n
m
“... an excellent introduction to compartmental modeling that is well written and e
n
accessible to a wide range of environmental professionals. The text includes suf- t
a
ficient rigor to ensure effective and accurate model applications, while keeping
l
F
the material focused on real-world, practical applications. The downloadable GEM a
software is the only readily available compartmental model with complete flexibil- t
e
ity and extendibility in the model setup. ... Dr. Little’s book and GEM software are a
welcome contributions to the environmental modeling field.” n
d
—Michael Lowry, RTI International, North Carolina
T
r
a
“This is an excellent integration of numerical methods with environmental modeling. n
s
... clearly the best discussion of stability and numerical dispersion available for en- p
vironmental modelers. Dr. Little’s book covers critical topics that too often receive o
r
only a passing mention in more traditional environmental modeling texts.” t
A
—Daniel Gallagher, Department of Civil and Environmental Engineering,
n
Virginia Polytechnic Institute and State University a
ly
s
“Not only does it motivate and explain the basic concepts of compartmental is
w
modeling but it also discusses some of the natural extensions such as incorporating
it
sink and source terms. ... with this book as a resource, the modeler should be well- h
C
informed on how to approach a problem and the issues they should be aware of
o
when analyzing or solving the model.” m
—Ellen Peterson, Carnegie Mellon University, Pennsylvania p
a
r
Environmental Fate and Transport Analysis with Compartment Modeling explains t
m
how to use the powerful, highly flexible, and intuitive compartment approach to
e
estimate the distribution of chemical contaminants in environmental media in time n
t
and space. It includes access to the Generic Environmental Model (GEM), a new
M
software package that implements the compartment approach based on user-
o
prepared input files and solves the resulting mathematical equations. A user-friendly d
e
introduction to environmental compartment modeling for the beginning modeler,
this is a valuable reference for the experienced modeler as well. lin
g
K14060
6000 Broken Sound Parkway, NW
Suite 300, Boca Raton, FL 33487
711 Third Avenue
New York, NY 10017
an informa business
2 Park Square, Milton Park
www.taylorandfrancisgroup.com Abingdon, Oxon OX14 4RN, UK www.crcpress.com
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
MATLAB® and Simulink® are trademarks of The MathWorks, Inc. and are used with permission. The MathWorks does not warrant the
accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® and Simulink® software or related products
does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the
MATLAB® and Simulink® software.
Mathematica® and the Mathematica logo are registered trademarks of Wolfram Research, Inc. (“WRI – www.wolfram.com) and are
used herein with WRI’s permission.
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2012 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20120424
International Standard Book Number-13: 978-1-4398-8797-4 (eBook - PDF)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish
reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the con-
sequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this
publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material
has not been acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form
by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and record-
ing, or in any information storage or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.
com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a
not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a
photocopy license by the CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and
explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
This book is dedicated to my father, Keith K. Little, who inspired
me to be an engineer, and to my doctoral advisor and mentor,
Donald T. Lauria, who gave me a passion for quantitative methods.
Contents
Preface.......................................................................................................................xi
Acknowledgments...................................................................................................xiii
Author.......................................................................................................................xv
Chapter 1 Introduction...........................................................................................1
1.1. GEM.Highlights.........................................................................3
1.2. Getting.Started:.Two.Examples..................................................5
1.2.1. Example.of.Chemical.Risk.Assessment.Problem.........5
1.2.2. Example.of.Mathematical.Problem.............................15
1.3. Organization.and.Suggested.Reading.Strategy........................16
References...........................................................................................16
Chapter 2 GEM.User’s.Guide..............................................................................19
2.1. Two.Alternative.Formulations.of.PRAM-.Like.Model.............19
2.1.1. k /k .Alternative..........................................................19
s ds
2.1.2. K .Alternative..............................................................24
d
2.2. GEM.Input.Files.......................................................................27
2.2.1. Static.Input.Files..........................................................30
2.2.1.2. Environmental.System.Mode.Input.Files....33
2.2.1.3. Equation.Solver.Input.Files.........................53
2.2.2. Dynamic.Input.Files.Using.Shell.Procedure...............54
2.2.3. Other.Control.csv.Inputs.............................................69
2.3. GEM.Output.files.....................................................................72
2.3.1. Simulated.Concentration.Files....................................72
2.3.2. Intermediate.Diagnostic.Files.....................................73
2.3.3. Mass.Balance.Error-.Checking....................................74
Reference.............................................................................................75
Chapter 3 Compartment.Approach,.Transport.Mechanisms,.and.Boundary.
Conditions...........................................................................................77
3.1. Compartment.Approach...........................................................77
3.2. Mass.Balance.Equation.for.Compartment.i.............................79
3.3. System.of.Transport.Mass.Balance.Equations.for.Single.
Chemical...................................................................................83
3.4. System.of.Transport.Mass.Balance.Equations.for.
Multiple.Chemicals..................................................................84
3.5. Extension.to.Porous.Media.......................................................85
vii
viii Contents
3.6. Boundary.Conditions.and.Types.of.Compartments.................87
3.6.1. Fixed.Concentration.Boundary.Conditions.................88
3.6.2. Zero.Gradient.Boundary.Conditions...........................89
3.6.3. Linear.Gradient.Boundary.Conditions........................90
Reference.............................................................................................95
Chapter 4 Source.and.Sink.Terms.......................................................................97
4.1. Linear.Source.and.Sink.Terms.................................................97
4.1.1. Zero-Order.Exogenous.Sink.......................................97
4.1.2. First-Order.Exogenous.Sources.and.Sinks..................98
4.1.3. Cross-.Compartment.First-.Order.Sources.and.Sinks....100
4.1.4. Cross-.Chemical.First-.Order.Sources.and.Sinks.......102
4.1.5. Retardation.Sink.for.Porous.Media...........................102
4.2. System.of.Fate.and.Transport,.Mass.Balance.Equations.
for.Multiple.Chemicals...........................................................107
4.3. Source.and.Sink.Terms.for.Nonlinear.Systems......................114
4.3.1. General.Approach.....................................................114
References.........................................................................................122
Chapter 5 Solution.Techniques.for.Steady-State.Problems...............................123
5.1. Linear.Systems.......................................................................123
5.2. Nonlinear.Systems..................................................................127
5.2.1. Classical.Newton’s.Method.......................................127
5.2.2. Quasi-.Newton.Method.and.Random.Start.
Enhancements.to.Newton’s.Method..........................130
5.3. Accuracy.of.Solutions.............................................................135
5.3.1. Discretization.Error.and.Numerical.Dispersion........135
5.3.2. Positivity.and.Wiggle................................................145
5.3.3. Correcting.for.Numerical.Dispersion.and.Resulting.
Equality.of.the.Two.Differencing.Methods..............149
5.3.4. Quantification.of.Total.Discretization.Error.............154
References.........................................................................................156
Chapter 6 Solution.Techniques.for.Dynamic.Problems.....................................157
6.1. Introduction............................................................................157
6.2. Explicit.Forward.Time.(Euler).Method..................................160
6.2.1. Methodology.............................................................160
6.2.2. Stability.....................................................................163
6.2.3. Numerical.Dispersion................................................165
6.2.4. Comparison.of.FTBS.and.FTCS.Methods................169
6.3. Explicit.Centered.Time.(MacCormack).Method...................192
6.3.1. Methodology.............................................................192
6.3.2. Stability,.Numerical.Dispersion,.and.Wiggle............194
