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Solid Fuels
Combustion and
Gasification
Copyright © 2004 by Marcel Dekker, Inc.
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MECHANICAL ENGINEERING
A Series of Textbooks and Reference Books
Founding Editor
L.L.Faulkner
Columbus Division, Battelle Memorial Institute
and Department of Mechanical Engineering
The Ohio State University
Columbus, Ohio
1. Spring Designerís Handbook, Harold Carlson
2. Computer-Aided Graphics and Design, Daniel L.Ryan
3. Lubrication Fundamentals, J.George Wills
4. Solar Engineering for Domestic Buildings, William A.Himmelman
5. Applied Engineering Mechanics: Statics and Dynamics, G.Boothroyd and
C.Poli
6. Centrifugal Pump Clinic, Igor J.Karassik
7. Computer-Aided Kinetics for Machine Design, Daniel L.Ryan
8. Plastics Products Design Handbook, Part A: Materials and Components;
Part B: Processes and Design for Processes, edited by Edward Miller
9. Turbomachinery: Basic Theory and Applications, Earl Logan, Jr.
10. Vibrations of Shells and Plates, Werner Soedel
11. Flat and Corrugated Diaphragm Design Handbook, Mario Di Giovanni
12. Practical Stress Analysis in Engineering Design, Alexander Blake
13. An Introduction to the Design and Behavior of Bolted Joints, John H.
Bickford
14. Optimal Engineering Design:Principles and Applications, James N.Siddall
15. Spring Manufacturing Handbook, Harold Carlson
16. Industrial Noise Control: Fundamentals and Applications, edited by Lewis
H.Bell
17. Gears andTheirVibration:A Basic Approach to Understanding Gear Noise,
J.Derek Smith
18. Chains for Power Transmission and Material Handling: Design and
Applications Handbook, American Chain Association
19. Corrosion and Corrosion Protection Handbook, edited by Philip A.
Schweitzer
20. Gear Drive Systems: Design and Application, Peter Lynwander
21. Controlling In-Plant Airborne Contaminants: Systems Design and
Calculations, John D.Constance
22. CAD/CAM Systems Planning and Implementation, Charles S.Knox
23. Probabilistic Engineering Design: Principles and Applications, James N.
Siddall
24. Traction Drives: Selection and Application, Frederick W.Heilich III and
Eugene E.Shube
25. Finite Element Methods: An Introduction, Ronald L.Huston and Chris E.
Passerello
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26. Mechanical Fastening of Plastics: An Engineering Handbook, Brayton
Lincoln, Kenneth J.Gomes, and James F.Braden
27. Lubrication in Practice: Second Edition, edited by W.S.Robertson
28. Principles of Automated Drafting, Daniel L.Ryan
29. Practical Seal Design, edited by Leonard J.Martini
30. Engineering Documentation for CAD/CAM Applications, Charles S.Knox
31. Design Dimensioning with Computer Graphics Applications, Jerome C.
Lange
32. Mechanism Analysis: Simplified Graphical and Analytical Techniques,
Lyndon O.Barton
33. CAD/CAM Systems: Justification, Implementation, Productivity
Measurement, Edward J.Preston, George W.Crawford, and Mark
E.Coticchia
34. Steam Plant Calculations Manual, V.Ganapathy
35. Design Assurance for Engineers and Managers, John A.Burgess
36. Heat Transfer Fluids and Systems for Process and Energy Applications,
Jasbir Singh
37. Potential Flows: Computer Graphic Solutions, Robert H.Kirchhoff
38. Computer-Aided Graphics and Design: Second Edition, Daniel L.Ryan
39. Electronically Controlled Proportional Valves: Selection and Application,
Michael J.Tonyan, edited by Tobi Goldoftas
40. Pressure Gauge Handbook, AMETEK, U.S. Gauge Division, edited by
Philip W.Harland
41. Fabric Filtration for Combustion Sources: Fundamentals and Basic
Technology, R.P.Donovan
42. Design of Mechanical Joints, Alexander Blake
43. CAD/CAM Dictionary, Edward J.Preston, George W.Crawford, and Mark
E. Coticchia
44. Machinery Adhesives for Locking, Retaining, and Sealing, Girard
S.Haviland
45. Couplings and Joints: Design, Selection, and Application, Jon R.Mancuso
46. Shaft Alignment Handbook, John Piotrowski
47. BASIC Programs for Steam Plant Engineers: Boilers, Combustion, Fluid
Flow, and Heat Transfer, V.Ganapathy
48. Solving Mechanical Design Problems with Computer Graphics, Jerome
C.Lange
49. Plastics Gearing: Selection and Application, Clifford E.Adams
50. Clutches and Brakes: Design and Selection, William C.Orthwein
51. Transducers in Mechanical and Electronic Design, Harry L.Trietley
52. Metallurgical Applications of Shock-Wave and High-Strain-Rate
Phenomena, edited by Lawrence E.Murr, Karl P.Staudhammer, and Marc
A.Meyers
53. Magnesium Products Design, Robert S.Busk
54. How to Integrate CAD/CAM Systems: Management and Technology,
William D.Engelke
55. Cam Design and Manufacture: Second Edition; with cam design software
for the IBM PC and compatibles, disk included, Preben W.Jensen
56. Solid-State AC Motor Controls: Selection and Application, Sylvester
Campbell
57. Fundamentals of Robotics, David D.Ardayfio
Copyright © 2004 by Marcel Dekker, Inc.
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58. Belt Selection and Application for Engineers, edited by Wallace D.Erickson
59. Developing Three-Dimensional CAD Software with the IBM PC, C.Stan
Wei
60. Organizing Data for CIM Applications, Charles S.Knox, with contributions
by Thomas C.Boos, Ross S.Culverhouse, and Paul F.Muchnicki
61. Computer-Aided Simulation in Railway Dynamics, by RaoV.Dukkipati and
Joseph R.Amyot
62. Fiber-Reinforced Composites: Materials, Manufacturing, and Design, P.K.
Mallick
63. Photoelectric Sensors and Controls: Selection and Application, Scott M.
Juds
64. Finite Element Analysis with Personal Computers, Edward R.Champion,
Jr., and J.Michael Ensminger
65. Ultrasonics: Fundamentals, Technology, Applications: Second Edition,
Revised and Expanded, Dale Ensminger
66. Applied Finite Element Modeling:Practical Problem Solving for Engineers,
Jeffrey M.Steele
67. Measurement and Instrumentation in Engineering: Principles and Basic
Laboratory Experiments, Francis S.Tse and Ivan E.Morse
68. Centrifugal Pump Clinic: Second Edition, Revised and Expanded, Igor J.
Karassik
69. Practical Stress Analysis in Engineering Design: Second Edition, Revised
and Expanded, Alexander Blake
70. An Introduction to the Design and Behavior of Bolted Joints: Second
Edition, Revised and Expanded, John H.Bickford
71. High Vacuum Technology: A Practical Guide, Marsbed H.Hablanian
72. Pressure Sensors: Selection and Application, Duane Tandeske
73. Zinc Handbook: Properties, Processing, and Use in Design, Frank Porter
74. Thermal Fatigue of Metals, Andrzej Weronski and Tadeusz Hejwowski
75. Classical and Modern Mechanisms for Engineers and Inventors, Preben
W.Jensen
76. Handbook of Electronic Package Design, edited by Michael Pecht
77. Shock-Wave and High-Strain-Rate Phenomena in Materials, edited by
Marc A.Meyers, Lawrence E.Murr, and Karl P.Staudhammer
78. Industrial Refrigeration: Principles, Design and Applications, P.C.Koelet
79. Applied Combustion, Eugene L.Keating
80. Engine Oils and Automotive Lubrication, edited by Wilfried J.Bartz
81. Mechanism Analysis: Simplified and Graphical Techniques, Second
Edition, Revised and Expanded, Lyndon O.Barton
82. Fundamental Fluid Mechanics for the Practicing Engineer, James W.
Murdock
83. Fiber-Reinforced Composites: Materials, Manufacturing, and Design,
Second Edition, Revised and Expanded, P.K.Mallick
84. Numerical Methods for Engineering Applications, Edward R.Champion, Jr.
85. Turbomachinery: Basic Theory and Applications, Second Edition, Revised
and Expanded, Earl Logan, Jr.
86. Vibrations of Shells and Plates: Second Edition, Revised and Expanded,
Werner Soedel
87. Steam Plant Calculations Manual:Second Edition, Revised and Expanded,
V.Ganapathy
Copyright © 2004 by Marcel Dekker, Inc.
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88. Industrial Noise Control: Fundamentals and Applications, Second Edition,
Revised and Expanded, Lewis H.Bell and Douglas H.Bell
89. Finite Elements: Their Design and Performance, Richard H.MacNeal
90. Mechanical Properties of Polymers and Composites:Second Edition, Revised
and Expanded, Lawrence E.Nielsen and Robert F.Landel
91. Mechanical Wear Prediction and Prevention, Raymond G.Bayer
92. Mechanical Power Transmission Components, edited by David W.South
and Jon R.Mancuso
93. Handbook of Turbomachinery, edited by Earl Logan, Jr.
94. Engineering Documentation Control Practices and Procedures, Ray E.
Monahan
95. Refractory Linings Thermomechanical Design and Applications, Charles
A.Schacht
96. Geometric Dimensioning and Tolerancing: Applications and Techniques
for Use in Design, Manufacturing, and Inspection, James D.Meadows
97. An Introduction to the Design and Behavior of Bolted Joints:Third Edition,
Revised and Expanded, John H.Bickford
98. Shaft Alignment Handbook:Second Edition, Revised and Expanded, John
Piotrowski
99. Computer-Aided Design of Polymer-Matrix Composite Structures, edited
by Suong Van Hoa
100. Friction Science and Technology, Peter J.Blau
101. Introduction to Plastics and Composites: Mechanical Properties and
Engineering Applications, Edward Miller
102. Practical Fracture Mechanics in Design, Alexander Blake
103. Pump Characteristics and Applications, Michael W.Volk
104. Optical Principles and Technology for Engineers, James E.Stewart
105. Optimizing the Shape of Mechanical Elements and Structures, A.A.Seireg
and Jorge Rodriguez
106. KinematicsandDynamicsofMachinery,VladimÌrStejskalandMichaelVal öek
107. Shaft Seals for Dynamic Applications, Les Horve
108. Reliability-Based Mechanical Design, edited by Thomas A.Cruse
109. Mechanical Fastening, Joining, and Assembly, James A.Speck
110. Turbomachinery Fluid Dynamics and Heat Transfer, edited by Chunill Hah
111. High-Vacuum Technology: A Practical Guide, Second Edition, Revised
and Expanded, Marsbed H.Hablanian
112. Geometric Dimensioning and Tolerancing: Workbook and Answerbook,
James D.Meadows
113. Handbook of Materials Selection for Engineering Applications, edited by
G.T.Murray
114. Handbook of Thermoplastic Piping System Design,Thomas Sixsmith and
Reinhard Hanselka
115. Practical Guide to Finite Elements: A Solid Mechanics Approach, Steven
M.Lepi
116. Applied Computational Fluid Dynamics, edited by Vijay K.Garg
117. Fluid Sealing Technology, Heinz K.Muller and Bernard S.Nau
118. Friction and Lubrication in Mechanical Design, A.A.Seireg
119. Influence Functions and Matrices, Yuri A.Melnikov
120. Mechanical Analysis of Electronic Packaging Systems, Stephen A.
McKeown
Copyright © 2004 by Marcel Dekker, Inc.
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121. Couplings and Joints: Design, Selection, and Application, Second Edition,
Revised and Expanded, Jon R.Mancuso
122. Thermodynamics: Processes and Applications, Earl Logan, Jr.
123. Gear Noise and Vibration, J.Derek Smith
124. Practical Fluid Mechanics for Engineering Applications, John J.Bloomer
125. Handbook of Hydraulic Fluid Technology, edited by George E.Totten
126. Heat Exchanger Design Handbook, T.Kuppan
127. Designing for Product Sound Quality, Richard H.Lyon
128. Probability Applications in Mechanical Design, Franklin E.Fisher and Joy
R.Fisher
129. Nickel Alloys, edited by Ulrich Heubner
130. Rotating Machinery Vibration: Problem Analysis and Troubleshooting,
Maurice L.Adams, Jr.
131. Formulas for Dynamic Analysis, Ronald L.Huston and C.Q.Liu
132. Handbook of Machinery Dynamics, Lynn L.Faulkner and Earl Logan, Jr.
133. Rapid PrototypingTechnology:Selection and Application, Kenneth G.Cooper
134. ReciprocatingMachineryDynamics:DesignandAnalysis,AbdullaS.Rangwala
135. Maintenance Excellence: Optimizing Equipment Life-Cycle Decisions,
edited by John D.Campbell and Andrew K.S.Jardine
136. Practical Guide to Industrial Boiler Systems, Ralph L.Vandagriff
137. Lubrication Fundamentals: Second Edition, Revised and Expanded, D.M.
Pirro and A.A.Wessol
138. Mechanical Life Cycle Handbook: Good Environmental Design and
Manufacturing, edited by Mahendra S.Hundal
139. Micromachining of Engineering Materials, edited by Joseph McGeough
140. Control Strategies for Dynamic Systems:Design and Implementation, John
H.Lumkes, Jr.
141. Practical Guide to Pressure Vessel Manufacturing, Sunil Pullarcot
142. Nondestructive Evaluation: Theory, Techniques, and Applications, edited
by Peter J.Shull
143. Diesel Engine Engineering: Thermodynamics, Dynamics, Design, and
Control, Andrei Makartchouk
144. Handbook of Machine Tool Analysis, loan D.Marinescu, Constantin Ispas,
and Dan Boboc
145. Implementing Concurrent Engineering in Small Companies, Susan
Carlson Skalak
146. Practical Guide to the Packaging of Electronics:Thermal and Mechanical
Design and Analysis, Ali Jamnia
147. Bearing Design in Machinery: Engineering Tribology and Lubrication,
Avraham Harnoy
148. Mechanical Reliability Improvement: Probability and Statistics for
Experimental Testing, R.E.Little
149. Industrial Boilers and Heat Recovery Steam Generators: Design,
Applications, and Calculations, V.Ganapathy
150. The CAD Guidebook: A Basic Manual for Understanding and Improving
Computer-Aided Design, Stephen J.Schoonmaker
151. Industrial Noise Control and Acoustics, Randall F.Barron
152. Mechanical Properties of Engineered Materials, WolÈ Soboyejo
153. Reliability Verification, Testing, and Analysis in Engineering Design, Gary
S.Wasserman
Copyright © 2004 by Marcel Dekker, Inc.
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154. Fundamental Mechanics of Fluids: Third Edition, I.G.Currie
155. Intermediate Heat Transfer, Kau-Fui Vincent Wong
156. HVAC Water Chillers and Cooling Towers:Fundamentals, Application, and
Operation, Herbert W.Stanford III
157. Gear Noise and Vibration: Second Edition, Revised and Expanded, J.
Derek Smith
158. Handbook of Turbomachinery: Second Edition, Revised and Expanded,
edited by Earl Logan, Jr., and Ramendra Roy
159. Piping and Pipeline Engineering: Design, Construction, Maintenance,
Integrity, and Repair, George A.Antaki
160. Turbomachinery: Design and Theory, Rama S.R.Gorla and Aijaz Ahmed
Khan
161. Target Costing: Market-Driven Product Design, M.Bradford Clifton, Henry
M.B.Bird, Robert E.Albano, and Wesley P.Townsend
162. Fluidized Bed Combustion, Simeon N.Oka
163. Theory of Dimensioning: An Introduction to Parameterizing Geometric
Models, Vijay Srinivasan
164. Handbook of Mechanical Alloy Design, edited by George E.Totten, Lin
Xie, and Kiyoshi Funatani
165. Structural Analysis of Polymeric Composite Materials, Mark E.Tuttle
166. Modeling and Simulation for Material Selection and Mechanical Design,
edited by George E.Totten, Lin Xie, and Kiyoshi Funatani
167. Handbook of Pneumatic Conveying Engineering, David Mills, Mark G.
Jones, and Vijay K.Agarwal
168. Clutches and Brakes: Design and Selection, Second Edition, William C.
Orthwein
169. Fundamentals of Fluid Film Lubrication: Second Edition, Bernard J.
Hamrock, Steven R.Schmid, and Bo O.Jacobson
170. Handbook of Lead-Free SolderTechnology for Microelectronic Assemblies,
edited by Karl J.Puttlitz and Kathleen A.Stalter
171. Vehicle Stability, Dean Karnopp
172. Mechanical Wear Fundamentals and Testing: Second Edition, Revised
and Expanded, Raymond G.Bayer
173. Liquid Pipeline Hydraulics, E.Shashi Menon
174. Solid Fuels Combustion and Gasification, Marcio L.de Souza-Santos
175. Mechanical Tolerance Stackup and Analysis, Bryan R.Fischer
176. Engineering Design for Wear, Raymond G.Bayer
177. Vibrations of Shells and Plates: Third Edition, Revised and Expanded,
Werner Soedel
178. Refractories Handbook, edited by Charles A.Schacht
179. Practical Engineering Failure Analysis, Hani Tawancy, Halim Hamid,
Nureddin M.Abbas
180. Mechanical Alloying and Milling, C.Suryanarayana
Additional Volumes in Preparation
Progressing Cavity Pumps, Downhole Pumps, and Mudmotors, Lev Nelik
Design of Automatic Machinery, Stephen J.Derby
Copyright © 2004 by Marcel Dekker, Inc.
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MechanicalVibration:Analysis, Uncertainties, and Control, Second Edition,
Revised and Expanded, Haym Benaroya
Practical Fracture Mechanics in Design: Second Edition, Revised and
Expanded, Arun Shukla
Spring Design with an IBM PC, Al Dietrich
Mechanical Design Failure Analysis: With Failure Analysis System
Software for the IBM PC, David G.Ullman
Copyright © 2004 by Marcel Dekker, Inc.
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Solid Fuels
Combustion and
Gasification
Modeling, Simulation, and
Equipment Operation
State University at Campinas
São Paolo, Brazil
Marcio L.de Souza-Santos
MARCEL DEKKER, INC. NEW YORK • BASEL
Copyright © 2004 by Marcel Dekker, Inc.
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Transferred to Digital Printing 2005
Although great care has been taken to provide accurate and current information, neither the author(s)
nor the publisher, nor anyone else associated with this publication, shall be liable for any loss,
damage, or liability directly or indirectly caused or alleged to be caused by this book. The material
contained herein is not intended to provide specific advice or recommendations for any specific
situation.
Trademark notice: Product or corporate names may be trademarks or registered trademarks and are
used only for identification and explanation without intent to infringe.
Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the Library of Congress.
ISBN: 0-8247-0971-3
Headquarters
Marcel Dekker, Inc., 270 Madison Avenue, NewYork, NY 10016, U.S.A.
tel: 212–696–9000; fax: 212–685–4540
Distribution and Customer Service
Marcel Dekker, Inc., Cimarron Road, Monticello, NewYork 12701, U.S.A.
tel: 800–228–1160; fax: 845–796–1772
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Marcel Dekker AG, Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland
tel: 41–61–260–6300; fax: 41–61–260–6333
World Wide Web
http://www.dekker.com
The publisher offers discounts on this book when ordered in bulk quantities. For more information,
write to Special Sales/Professional Marketing at the headquarters address above.
Copyright © 2004 by Marcel Dekker, Inc. All Rights Reserved.
Neither this book nor any part may be reproduced or transmitted in any form or by any means,
electronic or mechanical, including photocopying, microfilming, and recording, or by any information
storage and retrieval system, without permission in writing from the publisher.
Current printing (last digit):
10 9 8 7 6 5 4 3 2 1
Copyright © 2004 by Marcel Dekker, Inc.
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…the history of science—by far the most successful claim to
knowledge accessible to humans—teaches that the most we can
hope for is successive improvement in our understanding,
learning from our mistakes, an asymptotic approach to the
Universe, but with the proviso that absolute certainty will always
elude us.
Carl Sagan
The Demon-Haunted World: Science as a Candle in the Dark
Ballantine Books, 1996
to Laura, Daniel and Nalva
Copyright © 2004 by Marcel Dekker, Inc.
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v
Preface
Contrary to general perception, the importance of coal and biomass as energy
resources continues to increase. Special attention has been given to biomass
due to its renewable and overall zero carbon dioxide generation aspects.
Therefore, it is not surprising that the number of professionals and graduate
students entering the field of power generation based on solid fuels is increasing.
However, unlike specialized researchers, they are not interested in deep
considerations based on exhaustive literature reviews of specialized texts.
Obviously, works in that line are very important; however they assume an
audience of accomplished mathematical modelers. Therefore, they do not have
the preoccupation of presenting the details on how, from fundamental and general
equations, it is possible to arrive at a final model for an equipment or process.
Those beginning in the field are not interested in the other extreme, i.e., simple
and mechanistic description of equipment design procedures or instruction
manuals for application of commercial simulation packages. Their main
preoccupations are:
• Sufficient familiarity with the fundamental phenomena taking place in
the equipment or processes
• Knowledge of basic procedures for modeling and simulation of equipment
and systems.
• Elaborate procedures or methods to predict the behavior of the equipment
or processes, mainly for cases where there are no commercially available
simulators. Even when simulators are available, to be able to properly set
the conditions asked as inputs by the simulator, to evaluate the applicability
of possible solutions, and to choose among various alternatives.
• The use those instruments to help solve problems and situations in the
field.
• Building confidence for decision making regarding process improvements
and investments.
Copyright © 2004 by Marcel Dekker, Inc.
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vi Preface
On the other hand, experience shows that a good route to acquire real and testable
understanding of a subject in processing is to develop models and their respective
computer simulators. The feeling of accomplishment achieved when one is
capable of developing one’s own simulator, however simple, is fantastic. This
would be the crowning achievement of accumulated knowledge in the subject.
The simulation program becomes a source of improvements, not to mention
leading to a whole set of other advantages, as detailed later.
The book is essential to graduate students, engineers, and other professionals
with a strong scientific background entering the area of solid fuel combustion
and gasification, but needing a basic introductory course in mathematical
modeling and simulation. The text is based on a course given for many years
for professionals and graduate students.
In view of the hands-on approach, several correlations and equations are
cited from the literature without the preoccupation on mathematical
demonstrations of their validity. References are provided and should be consulted
by those interested in more details.
Despite the specific focus on combustion and gasification, the basic methods
illustrated here can be employed for modeling a wide range of other processes
or equipment commonly found in the processing industry. Operations of
equipment such as boilers, furnaces, incinerators, gasifiers, and any others
associated with combustion or gasification phenomena involves a multitude of
simultaneous processes such as heat, mass and momentum transfers, chemical
kinetics of several reactions, drying, and pyrolysis, etc. These should be
coherently combined to allow reasonable simulation of industrial units or
equipment. This book provides the relevant basic principles.
It is important to emphasize the need for simple models.As mentioned before,
most field or design engineers cannot afford to spend too much time on very
elaborate and complex models. Of course, there are several levels to which
models can be built. Nevertheless, one should be careful with models that are
too simple or too complex. The low extreme normally provides only superficial
information while the other usually takes years to develop and often involves
considerable computational difficulties due to convergence problems or
inconsistencies. In the present text, the model complexity is extended just to
the point necessary to achieve a reasonable representation of the corresponding
equipment. For instance, the examples are limited to two dimensions and most
of the models are based on a one-dimensional approach. This may sound
simplistic; however, the level of detail and usefulness of results from such
simulations are significant. Additionally, the book can also be used as an
introduction to more complex models.
The main strategy of the book is to teach by examples. Besides the significant
fraction of industrial equipment operating with suspensions of pulverized solid
Copyright © 2004 by Marcel Dekker, Inc.
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Preface vii
fuels, the specific cases of moving and fluidized bubbling beds have been selected
because they:
Cover much of the equipment related to combustion and gasification of
solid fuels found in industry. In the particular case of fluidized beds,
the fraction of equipment employing that technique has continually
increased. In fact several more conventional boilers and furnaces
operating with suspensions have been retrofitted to fluidized beds.
Allow easy-to-follow examples of how simplifying assumptions regarding
the operation of real industrial equipment can be set.
Permit relatively quick introduction of fundamental equations without
the need for overly complex treatments.
Provide simple examples applying model and simulation techniques and
how these can be put together to write a simulation program.
Allow easier comparisons between real operational data and simulation
results.
In addition, the book contains basic descriptions of combustion and gasification
processes, including suspension or pneumatic transport. Several fundamental
aspects are common and can be applicable in studies of any technique, such as:
zero-dimensional mass and energy balances, kinetics of gas and solid reactions,
heat and mass transport phenomena and correlations, and pressure losses though
air or gas distributors.
Although the basic concepts of momentum, heat, and mass transfer
phenomena can be found in several texts, the fundamental equations for such
processes are included here, minimizing the need to consult other texts. Concepts
usually learned in graduate-level engineering courses will be sufficient. The
same is valid for thermodynamics, fundamentals of chemical kinetics, and
applied mathematics—mainly concerning aspects of differential equations.
To summarize, the book:
• Shows several constructive and operational features of equipment dealing
with combustion and gasification of solid fuels, such as coal, biomass,
and solid residues, etc.
• Presents basic aspects of solid and gas combustion phenomena
• Introduces the fundamental methodology to formulate a mathematical
model of the above equipments
• Demonstrates possible routes from model to workable computer
simulation program
• Illustrates interpretations of simulation results that may be applied as tools
for improving the performance of existing industrial equipment or for
optimized design of new ones
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viii Preface
of solid-gas systems and main characteristics of combustion and gasification
of zero-dimensional models with the objective of allowing verification of overall
relations between inputs and outputs of any general process, including
combustors and gasifiers.
reactor. Of course, it is not the intention to present any model for flames; that is
beyond the scope of this introductory book. However, it is useful to introduce
standard considerations regarding mathematical modeling and the application
first example of a model for solid fuel combustion and gasification equipment,
program to simulate the model introduced in Chapter 10.
in order to build a workable simulation program. The chapter also presents
comparisons between measured parameters obtained from a real operation of
moving-bed gasifier and results from a simulation program based on the model
several already given enable the writing a computer program for fluidized bed
cases of fluidized bed combustors as Chapter 12 for moving bed combustors
and gasifiers.
Almost all the chapters include exercises. They will stimulate the imagination
and build confidence in solving problems related to modeling and simulation.
The relative degree of difficulty or volume of work expected is indicated by an
increasing number of asterisks—problems marked with four asterisks usually
require solid training in the solution of differential equations or demand
considerable work.
Marcio L.de Souza-Santos
Copyright © 2004 by Marcel Dekker, Inc.
It is organized as follows. Chapter 1 presents some generally applicable notions
concerning modeling and simulation. Chapter 2 shows main characteristics of
solid fuels, such as coals and biomasses. Chapter 3 introduces basic concepts
equipments. Chapter 4 provides formulas and methods to allow first calculations
regarding solid fuel processing. Chapter 5 describes the fundamental equations
Chapter 6 introduces a very basic and simple first-dimension model of a gas
of mass, energy, and momentum transfer equations. Chapter 7 describes the
using the case of moving-bed combustor or gasifier. Chapters 8 and 9 introduce
methods to compute gas-gas and gas-solid reaction rates. Chapter 10 introduces
and constitutive equations and methods that may be used to build a computer
modeling of drying and pyrolysis of solid fuels. Chapter 11 presents auxiliary
Chapter 12 shows how to put together all the information previously given
described earlier. Chapter 13 repeats the same approach used for Chapter 7, but
now pertaining to bubbling fluidized-bed combustors and gasifiers. Chapters
14 and 15 provide correlations and constitutive equations that together with
combustors, boilers, and gasifiers. Chapter 16 has the same objective for the
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ix
Acknowledgments
It is extremely important to acknowledge the help of various colleagues whom
I had the pleasure to work with, in particular to Alan B.Hedley (University of
Sheffield, U.K.), Francisco D.Alves de Souza (Institute for Technological
Research, São Paulo, Brazil), and former colleagues at the Institute of Gas
Technology (Chicago). I appreciate the collaboration of several students and
friends, who pointed out errors and made suggestions. I also thank John Corrigan
and the staff of Marcel Dekker, Inc. for their help during all the aspects of the
publication process. Finally, I am also grateful to the State University of
Campinas (UNICAMP) and colleagues at the Energy Department of Mechanical
Engineering for their support.
Marcio L.de Souza-Santos
Copyright © 2004 by Marcel Dekker, Inc.
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xi
Nomenclature
ai parameters or constants (dimensionless)
a general parameter or coefficient (dimensions depend
on the application) or ratio between the radius of the
nucleus and the original particle or Helmoltz energy (J
kg-1
)
â activity coefficient (dimensionless)
A area (m2
) or ash (in chemical reactions)
ae air excess (dimensionless)
b exergy (J kg-1
)
B coefficient, constant or parameter (dimensions depend
on the application)
c specific heat at constant pressure (J kg-1
K-1
)
C constants or parameters to be defined in each situation
COC1(j) coefficient of component j in the representative formula
of char (after drying and devolatilization of original fuel)
(dimensionless)
COC2(j) coefficient of component j in the representative formula
of coke (due to tar coking) (dimensionless)
COF(j) coefficient of component j in the representative formula
of original solid fuel (dimensionless)
COF(j) coefficient of component j in the representative formula
of original solid fuel (dimensionless)
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xii Nomenclature
COT(j) coefficient of component j in the representative formula
of tar (dimensionless)
COV(j) coefficient of component j in the representative formula
of volatile fraction of the original solid fuel
(dimensionless)
d diameter (m)
dP particle diameter (m)
Dj diffusivity of component j in the phase or media
indicated afterwards (m2
s-1
)
activation energy of reaction i (J kmol-1
)
É factor or fraction (dimensionless)
Ébexp expansion factor of the bed or ratio between its actual
volume and volume at minimum fluidization condition
(dimensionless)
É514 total mass fractional conversion of carbon
fmoist mass fractional conversion of moisture (or fractional
degree of drying)
ÉV mass fractional conversion of volatiles (or degree of
devolatilization)
Éfc mass fraction conversion of fixed carbon
Ém mass fraction of particles kind m among all particles
present in the process (dimensionless)
Éair air excess (dimensionless)
Éfr fuel ratio factor used in reactivity calculations
(dimensionless)
F mass flow (kg s-1
)
g acceleration of gravity (m s-2
) or specific Gibbs function
(J/kg)
G mass flux (kg m-2
s-1
)
variation of Gibbs function related to reaction i (J kmol-1
)
h enthalpy (J kg-1
)
H height (m)
HHV high heat value (J kg-1
)
i inclination relative to the horizontal position (rad)
I variable to indicate the direction of mass flow
concerning a control volume (+1 entering the CV; -1
leaving the CV)
jj mass flux of component j due to diffusion process (kg
m-2
s-1
)
kj kinetic coefficient of reaction i (s-1
) (otherwise, unit
depends on the reaction)
kt specific turbulent kinetic energy (m2
s-2
)
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Nomenclature xiii
k0i preexponential coefficient of reaction i (s-1
) (otherwise,
unit depends on the reaction)
Ki equilibrium coefficient for reaction i (unit depend on
the reaction and notation)
K0i preexponential equilibrium coefficient for reaction i
(unit depend on the reaction and notation)
l mixing length (m)
L coefficient used in devolatilization computations
(dimensionless)
Lgrate length of grate (m)
LT length of tube (m)
LHV low heat value (J kg-1
)
n number of moles
nCP number of chemical species or components
nCV number of control volumes
nG number of chemical species or components in the gas
phase
nS number of chemical species or components in the solid
phase
nSR number of streams
Nj mass flux of component j referred to a fixed frame of
coordinates (kg m-2
s-1
)
M mass (kg)
Mj molecular mass of component j (kmol/kg)
NAr Archimedes number (dimensionless)
NBi Biot number (dimensionless)
NNu Nusselt number (dimensionless)
NPe Peclet number (dimensionless)
NPr Prandtl number (dimensionless)
NRe Reynolds number (dimensionless)
NSc Schmidt number (dimensionless)
NSh Sherwood number (dimensionless)
p index for the particle geometry (0=planar, 1=cylindrical,
3= sphere)
pj partial pressure of component j (Pa)
P pressure (Pa)
q energy flux (W m-2
)
rate of energy generation (+) or consumption (-) of an
equipment or system (W)
r radial coordinate (m)
ri rate of reaction i (for homogeneous reactions: kg m -3
s-
1
; for heterogeneous reactions: kg m-2
s-1
)
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xiv Nomenclature
R equipment radius (m)
R universal gas constant (8314.2 J kmol-1
K-1
)
RC rate of energy transfer to (if positive) or from (if
negative) the indicated phase due to convection [W m-
3
(of reactor volume or volume of the indicates phase)]
Rcond rate of energy transfer to (if positive) or from (if
negative) the indicated phase due to conduction [W m-
3
(of reactor volume or volume of the indicated phase)]
Rh rate of energy transfer to (if positive) or from (if
negative) the indicated phase due to mass transfer
between phases [W m-3
(of reactor volume or volume
of the indicated phase)]
Rj rate of component j generation (if positive) or
consumption (if negative) by chemical reactions (kg
m-3
s-1
). If in molar basis (~) the units are (kmol m-3
s-1
).
Rkind,j rate of component j generation (if positive) or
consumption (if negative) by chemical reactions. Units
vary according to the “kind” of reaction. If the subscript
indicates homogeneous reactions the units are kg m-3
(of gas phase) s-1
, if heterogeneous reactions in kg m-2
(of external or of reacting particles) s-1
.
RM,G,j total rate of production (or consumption if negative) of
gas component j [kg m-3
(of gas phase) s-1
]
RM,S,j total rate of production (or consumption if negative) of
solid-phase component j [kg m-3
(of reacting particles)
s-1
]
RQ rate of energy generation (if positive) or consumption
(if negative) due to chemical reactions [W m-3
(of reactor
volume or volume of the indicated phase)]
RR rate of energy transfer to (if positive) or from (if
negative) the indicated phase due to radiation [W m-3
(of reactor volume or volume of the indicated phase)]
Rheat heating rate imposed on a process (K/s)
s entropy (J kg-1
K-1
)
S cross-sectional area (m2
). If no index, it indicates the
cross-sectional area of the reactor (m2
).
t time (s)
T temperature (K)
T* reference temperature (298 K)
Te ration between activation energy and gas constant ( )
(K)
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Nomenclature xv
u velocity (m s-1
)
U gas superficial velocity (m s-1
) or resistances to mass
transfer (s m-2
)
ureduc reduced gas velocity (dimensionless)
v specific volume (m3
kg-1
)
V volume (m3
)
x coordinate or distance (m)
xj mole fraction of component j (dimensionless)
X elutriation parameter (kg sms1
)
y coordinate (m) or dimensionless variable
Y rate of irreversibility generation at a control volume
(W)
wj mass fraction of component j (dimensionless)
W
.
rate of work generation (+) or consumption (-) by an
equipment or system (W)
z vertical coordinate (m)
Z compressibility factor (dimensionless)
Greek Letters
α coefficient of heat transfer by convection (W m-2
K-1
)
αm relaxation coefficient related to momentum transfer
involving solid phase m (s-1
)
β coefficient (dimensionless) or mass transfer coefficient
(m s-1
)
χ number of atoms of an element (first index) in a
molecule of a chemical component (second index)
unit vector (m)
ε void fraction (dimensionless)
ε‘ emissivity (dimensionless)
εt dissipation rate of specific turbulent kinetic energy
(m2
s-3
)
γ tortuosity factor
Φ Thiele modulus
Γ rate of fines production due to particle attrition (kg s-1
)
η efficiency or effectiveness coefficient
τ efficiency coefficient
ϕ particle sphericity
␭ thermal conductivity (W m-1
K-l
)
Λ parameter related to mass and energy transfer
µ viscosity (kg m-1
s-1
) or chemical potential (J kg -1
)
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xvi Nomenclature
vij stoichiometry coefficient of component j in reaction i
θ angular coordinate
solid particle friability (m-l
)
ρ density (unit depends on the reaction and notation)
ρp apparent density of particle (kg m-3
)
ρj mass basis concentration of component j (kg m-3
) (in
some situations the component j can be indicated by its
formula)
shear stress tensor (Pa)
ω Pitzer’s acentric factor (dimensionless)
ϕ air ratio (dimensionless)
σ Stefan-Boltzmann constant (W m-2
K-4
)
σv Standard deviation for distributed energy
devolatilization model
chemical component formula
ζ particle porosity (m3
of pores/m3
of particle)
ψ mass transfer coefficient (s-1
if between two gas phases,
kmol m-2
s-1
if between gas and solid)
Ω parameter of the Redlich-Kwong equation of state
related to mass and energy transfers.
Other
gradient operator
Laplacian operator
Superscripts
→ rector or tensor
– time averaged
fluctuation or perturbation
~ in molar basis
relative concentration (dimensionless)
‘ number fraction
“ area fraction
“‘ volume fraction
s for particles smaller than the particles whose kind and
level are indicated in the subscript
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(dimensionless) or (only in Appendix C) a parameter
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Nomenclature xvii
Subscripts
Numbers as subscripts may represent sequence of variables, chemical species
or reactions. In the particular case of chemical species the number would be
equal to or greater than 19. In the case of reactions it will be clear when the
number indicates reaction number.The numbering for components and reactions
0 at reference or ideal condition
a at the nucleus-outer-shell interface
A shell or residual layer
air air
app apparent (sometimes this index does not appear and
should be understood, as in, for instance ρp=ρp,app)
aro aromatic
ash ash
av average value
b based on exergy
B bubble
bexp related to the expansion of the bed
bri bridges
bulk bulk
c critical value
C convection contribution (in some obvious situations, it
would represent carbon)
car carbonaceous solid
char char
cond conduction contribution
CIP coated inert particle
CP referred to the chemical component
COF, COV, COT see main nomenclature above
CSP Coke Shell Particle
CV referred to the control volume or equipment
cy related to the cyclone system
d related to drying or dry basis
D bed
daf dry and ash-free basis
dif diffusion contribution
dist distributor
E emulsion
ental relative to enthalpy
entro relative to entropy
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is shown in Tables 8.1 to 8.5.
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xviii Nomenclature
eq equilibrium condition
exer relative to exergy
f formation at 298 K and 1 atm
fl fluid
F freeboard
fc fixed-carbon
fuel related to fuel
G gas phase
h transfer of energy due to mass transfer
H related to the circulation of particles in a fluidized bed
(in some obvious situations, it would represent
hydrogen)
hom related to homogeneous (or gas-gas) reactions
het related to heterogeneous (or gas-solid) reactions
i
I as at the feeding point
∞ at the gas phase far from the particle surface
iCO component number
iCV control volume (or equipment) number
iSR stream number
j chemical component (numbers are described in Chapter
8)
J related to the internal surface or internal dimension
K related to the recycling of particles, collected in the
cyclone, to the bed
l chemical element
L at the leaving point or condition
lam laminar condition
m physical phase (carbonaceous solid, m=1; limestone or
dolomite, m=2; inert solid, m=3; gas, m=4)
mratio mixing ratio
M mmass generation or transfer
max maximum condition
mb minimum bubbling condition
min minimum condition
mf minimum fluidization condition
moist moisture or water
mon monomers
mtp metaplast
orif orifices in the distributor plate
N nucleus or core (in some obvious situations, it would
represent nitrogen)
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reaction i (numbers are described in Chapter 8)
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Nomenclature xix
O at the referred to external or outside surface (in some
obvious situations, it would represent oxygen)
p particle (if no other indication, property of particle is
related to apparent value)
P at constant pressure
per peripheral groups
pores related to particle pores
plenum average conditions in the plenum below the distributor
plate or device
Q chemical reactions
r at reduced condition
R related to radiative heat transfer
real related to real or skeletal density of solid particles
sat at saturation condition
S solid phase or particles (if indicated for a property, such
as density, it means apparent particle density)
SR referred to the stream
sit immobile recombination sites
T terminal value or referred to tubes
tar tar
to mixing-take-over value
tur turbulent condition
U unexposed-core or shrinking-core model
v related to devolatilization
V volatile
W wall
X exposed-core model
Y related to entrainment of particles
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xxi
Contents
Preface v
Nomenclature xi
1 Basic Remarks on Modeling and Simulation 1
1.1 Experiment and Simulation 1
1.2 A Classification for Mathematical Models 10
1.3 Exercises 17
2 Solid Fuels 18
2.1 Introduction 18
2.2 Physical Properties 19
2.3 Chemical Properties 21
2.4 Thermal Treatment 24
2.5 Gasification and Combustion 35
2.6 Exercises 37
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xxii Contents
3 Equipment and Processes 38
3.1 Introduction 38
3.2 Elements of Gas-Solid Systems 38
3.3 Moving Bed 43
3.4 Fluidized Bed 48
3.5 Suspension or Pneumatic Transport 63
3.6 Some Aspects Related to Fuels 67
4 Basic Calculations 69
4.1 Introduction 69
4.2 Computation of Some Basic Parameters 70
4.3 Tips on Calculations 80
4.4 Observations 83
Exercises 83
5 Zero-Dimensional Models 86
5.1 Introduction 86
5.2 Basic Equations 87
5.3 Species Balance and Exiting Composition 93
5.4 Useful Relations 99
5.5 Summary for 0D-S Model 105
5.6 Flame Temperature 106
Exercises 109
6 Introduction to One-Dimensional, Steady-State Models 112
6.1 Definitions 112
6.2 Fundamental Equations 113
6.3 Final Comments 125
Exercises 126
7 Moving-Bed Combustion and Gasification Model 127
7.1 Introduction 127
7.2 The Model 128
Exercises 144
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Contents xxiii
8 Chemical Reactions 146
8.1 Homogeneous/Heterogeneous Reactions 146
8.2 Numbering Chemical Components 147
8.3 A System of Chemical Reactions 147
8.4 Stoichiometry 150
8.5 Kinetics 152
8.6 Final Notes 157
Exercises 159
9 Heterogeneous Reactions 160
9.1 Introduction 160
9.2 General Form of the Problem 163
9.3 Generalized Treatment 172
9.4 Other Heterogeneous Reactions 174
Exercises 174
10 Drying and Devolatilization 178
10.1 Drying 178
10.2 Devolatilization 181
Exercises 208
11 Auxiliary Equations and Basic Calculations 209
11.1 Introduction 209
11.2 Total Production Rates 209
11.3 Thiele Modulus 214
11.4 Diffusivities 215
11.5 Reactivity 218
11.6 Core Dimensions 219
11.7 Heat and Mass Transfer Coefficients 220
11.8 Energy-Related Parameters 222
11.9 A Few Immediate Applications 225
11.10 Pressure Losses 233
Exercises 243
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xxiv Contents
12 Moving-Bed Simulation Program and Results 245
12.1 Introduction 245
12.2 From Model to Simulation Program 245
12.3 Samples of Results 254
Exercises 261
13 Fluidized-Bed Combustion and Gasification Model 264
13.1 Introduction 264
13.2 The Mathematical Model 264
13.3 Boundary Conditions 276
Exercises 280
14 Fluidization Dynamics 282
14.1 Introduction 282
14.2 Splitting of Gas Injected into a Bed 283
14.3 Bubble Characteristics and Behavior 288
14.4 Circulation of Solid Particles 291
14.5 Entrainment and Elutriation 300
14.6 Particle Size Distribution 302
14.7 Recycling of Particles 304
14.8 Segregation 305
14.9 Areas and Volumes at Freeboard Section 306
14.10 Mass and Volume Fractions of Solids 307
14.11 Further Studies 308
Exercises 308
15 Auxiliary Parameters Related to Fluidized-Bed Processes 309
15.1 Introduction 309
15.2 Mass Transfers 309
15.3 Heat Transfers 312
15.4 Parameters Related to Reaction Rates 322
16 Fluidized-Bed Simulation Program and Results 323
16.1 The Block Diagram 323
16.2 Samples of Results 326
16.3 Exercises 364
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Contents xxv
Appendix A The Fundamental Equations of Transport Phenomena 366
Appendix B Notes on Thermodynamics 372
B.1 Heat and Work 372
B.2 Chemical Equilibrium Equation 374
B.3 Specific Heat 376
B.4 Correction for Departure from Ideal Behavior 376
B.5 Generalized 0D-S Models 379
B.6 Heat Values 386
B.7 Representative Formation Enthalpy of a Solid Fuel 387
Appendix C Possible Improvements on Modeling Heterogeneous
Reactions 389
C.1 General Mass Balance for a Particle 390
C.2 Generalized Energy Balance for a Particle 390
Appendix D Improvements on Various Aspects 396
D.1 Rate of Particles Circulation in the Fluidized Bed 396
D.2 Improvements on the Fluidized-Bed Equipment Simulator (FBES) 399
Appendix E Basics of Turbulent Flow 400
E.1 Momentum Transfer 400
E.2 Heat and Mass Transfers 403
E.3 Reaction Kinetics 404
Appendix F Classifications of Modeling for Bubbling Fluidized-Bed
Equipment 406
F.1 Main Aspects 406
Appendix G Basics Techniques of Kinetics Determination 408
References 412
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Solid Fuels
Combustion and
Gasification
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1
1
Basic Remarks on Modeling and
Simulation
1.1 EXPERIMENT AND SIMULATION
Over the years, among other comments, I have heard remarks such as:
• “If the equipment is working, why all the effort to simulate it?”
• “Can’t we just find the optimum operational point by experimentation?”
The basic answer to the first question is: Because it is always possible to improve
and, given an objective, to optimize an existing operation. Optimization not
only increases competitiveness of a company but may also determine its chances
of survival. For the second question the answer is: Because experimentation is
much more expensive than computation. In addition, if any variable of the
original process changes, the costly experimentally achieved optimum is no
longer valid. As an example, if a thermoelectric power unit starts receiving a
coal with properties different from the one previously used, the optimum
operational point would not be the same. It is also important to remember that
the experimentally found optimum at a given scale is not applicable to any
other scale, even if several conditions remain the same. In fact, no company
today can afford not to use computer simulation to seek optimized design or
operation of its industrial processes.
Apparently, one may think that these remarks could hide some sort of
prejudice against experimental methods. Nothing could be further from the truth.
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2 Chapter 1
There is no valid theory without experimentation. A model or theory is not
applicable unless experimentally verifiable. In other words, a mathematical
model and consequent simulation program, no matter how sophisticated, is
useless if it cannot reproduce the real operation it is intended to simulate
within an acceptable degree of deviation. Of course, it would also not be able
to predict the behavior of future equipment with some degree of confidence,
and therefore it would also be useless as design tool.
Before going any further, let us consideration some experimental and
theoretical procedures.
1.1.1 The Experimental Method
One may ask about the conditions that allow the application of experimental
method to obtain or infer valid information concerning the behavior of a process.
For this, the following definitions are necessary:
• Controlled variables are those whose values can, within a certain range,
be imposed freely, for example, the temperature of a bath heated by
electrical resistances.
• Observed variables are those whose values can be measured, directly or
indirectly. An example is the thermal conductivity of the fluid in the bath
where the temperature has been controlled.
Experiments are a valid source of information if during the course of tests the
observed variables are solely affected by the controlled variables. Any other
variable should be maintained at constant value.
Example 1.1 Let us imagine that someone is interested in determining the
dependence on temperature of thermal conductivity of a bath or solution with
a given composition and under a given pressure. Therefore, the observed
variable would be the thermal conductivity, and the solution average temperature
the controlled one. Thus, the bath thermal conductivity would be measured at
various levels of its temperature. During the tests, the chemical composition
and pressure of the previous bath should be maintained constant. In doing so,
it will be possible to correlate cause and effect, i.e., the values of observed and
controlled variables. These correlations may take the form of graphs or
mathematical expressions.
Example 1.2 The SO2 absorption by limestone can be represented by the
following reaction:
Experiments to determine the kinetics of the reaction should be conducted under
carefully chosen conditions; for example,
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Basic Remarks on Modeling and Simulation 3
• The sample of limestone should be put in a barge where it is exposed to
various mixtures of SO2 and O2.
• The pressure should be maintained constant.
• The sample of limestone should have its maximum particle size reduced
to a point where no interference of particle size on the reaction rate could
be noticed. The interference is caused by the resistance to mass transfer
of gas components through the porous structure of the particle.
• The temperature should be controlled. This can be achieved by electrical
heating of the barge. In addition, influences of temperature differences
between the various regions of the sample should be reduced or eliminated.
This can be accomplished by using thin layers of sample and through
high heat transfer coefficients between gas and solid sample. One method
would be to increase the Reynolds number or the relative velocity between
gas and particles. Of course, this has limitations because the gas stream
should carry no solid.
• The concentrations of reactants (SO2 and O2) in the involving atmosphere
should be controlled or kept constant. Therefore, a fresh supply of the
reacting mixture should be guaranteed.
• Each test should be designed to take samples of the CaO and CaSO4
mixture for analysis throughout the experiment, so; the number of
controlled variables could be reduced to temperature and concentration
of SO2 and O2 in the incoming gas stream.
The conversion of CaO into CaSO4 would be the observed variable and it would
be measured against time.
In addition, the number of experimental tests should be as high as possible
to eliminate bias. This is possible to verify by quantitative means.
Even after all these precautions, the determined kinetics is valid only for the
particular kind of limestone because possible catalyst or poisoning activity due
to presence of other chemical components in the original limestone has not
been taken into account.
The above examples show the typical scientific experimental procedure. It
allows observations that may be applied to understand the phenomenon. Within
an established range of conditions, the conclusions do not depend on a particular
situation. Therefore, they can be generalized and used in mathematical models
that combine several other phenomena.
It is also important to be aware that experimental optimization of a process
presents stringent limitations due to:
1. Variables: The number of variables that interfere in a given process is
usually much higher than the number of controllable variables. Imposed
variation on a single input may represent variations on several process
conditions and, as consequence, on several observed variables.
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4 Chapter 1
2. Scale effects: Physical-chemical properties of substances handled by the
process do not obey a linear dependence with the equipment geometry
such as length, area, and volume. For instance, one may double the volume
of a chemical reactor, but this does not double the density or viscosity of
streams entering or leaving the reactor.
In some cases, scaling-up does not even allow geometry similarity with the
experimental or pilot unit. To better illustrate the point of false inference on the
validity of an experimental procedure, let us refer to the following example.
Example 1.3 Someone is intending to scale-up a simple chemical reactor, as
shown in Figure 1.1. The reactants A and B are continuously injected and the
reaction between them is exothermic. The product C, diluted in the exit stream,
leaves the reactor continuously. Water is used as cooling fluid and runs inside
the jacket. The agitator maintains the reacting media as homogeneously as
possible. There is also an optimum temperature that leads to a maximum output
of the C component. Let us suppose that the optimization of this operation was
carried and the correct water flow into the jacket was found in order to give the
maximum concentration of C in the product. To achieve this, a pilot was built
and through experiments the best operational condition was set. Now, the
engineering intends to build a reactor to deliver a mass flow of C ten times
higher than the achieved in the pilot.
Someone proposed to keep the same geometric shape of the pilot, which is
H/D (H=level filled with fluid, D=diameter) equal to 2. However, to obtain the
same concentration of C in the products, the residence time of reactants in the
volume should be maintained. Residence time τ is usually defined by
FIG. 1.1 Scheme of a water-jacketed reactor.
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Basic Remarks on Modeling and Simulation 5
(1.1)
where V is the volume of the reactor (filled with liquid reactants), ρ is the
average density of the fluid and F is the mass flow of injected fluids into the
reactor. Assuming a cylindrical shape reactor, the volume is given by
(1.2)
The relation should be set in order to maintain the same residence time.
V=10V0 (1.3)
where index 0 indicates the pilot dimensions. To keep H/D ratio equal to 2, the
new diameter would be
D=101/3
D0 (1.4)
The area for heat transfer (neglecting the bottom) is given by
A=πHD (1.5)
Therefore, the area ratio would be
(1.6)
Using 1.4,
A=102/3
A0 (1.7)
By this option, the industrial-scale reactor would have a heat exchange area just
4.64 times larger than the one at the pilot unit. The cooling would not be as
efficient as before.
Reversibly, if one tries to multiply the reactor wall area by 10, the volume
would be much larger than 10 times the volume of the pilot.Actually, this would
increase the residence time of the reactants by more than 31 times. This is not
desirable because:
• The investment in the new reactor would be much larger than intended.
• The reactants would sit idle in the reactor, or the residence time of the
reactants would be much larger than the time found through optimization
tests.
The only possibility is to modify the H/D ratio in order to maintain the same
area/volume relation as found in the pilot. The only solution is a diameter equal
to the diameter of the pilot. Therefore, to multiply the volume by 10, the new
length of level would be 10 times the length of the pilot. This solution would
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6 Chapter 1
not be very convenient from the operational point of view, not for the layout of
the plant where it would be installed.
This demonstrates that not even a similar geometric shape could be kept in a
scaling-up process. To maintain the shape of the pilot and multiply the volume
by 10, a solution might be to insert a coil inside the reactor to provide the extra
heat transfer area.
Example 1.4 Another example is given in the case of a boiler. Someone
wants to optimize the design of a boiler by experimental tests with a small pilot
unit.The unit is composed of a furnace with a tube bank, and coal is continuously
fed into it. Water runs into the tube bank and the bank can be partially retreated
from the furnace in a way to vary the heat exchange area. The tests show that,
by maintaining a given fuel input, there is a certain area of tubes that leads to a
maximum rate of steam generation. The reason rests on two main influences,
which play an important role in the boiler efficiency, as follows:
1. If the tube area increases, the heat transfer between the furnace and the
tubes increases, leading to an increase in steam production. However,
after a certain point, increases in the tube area lead to decreases in the
average temperature in the furnace. Decreases in temperature decrease
carbon conversion or fuel utilization and, therefore, decrease the rate of
energy transferred to tubes for steam generation.
2. If the area of tubes decreases, the average temperature in the furnace
increases and the carbon conversion increases. Therefore, more coal is
converted to provide energy and may possibly leading to increases in the
steam generation. However, after a certain point, due to insufficient tube
area for heat transfer, the effect is just to increase the temperature of the
gases in the chimney, therefore decreasing the efficiency of the boiler.
In this way, the optimum or maximum efficiency for the boiler operation should
be an intermediate point. However, it is not easy to find a solution because it
would necessitate considering a great number of processes or phenomena, e.g.,
heat transfers of all kind between the particle, gases, and tubes, mass transfers
among gases and particles, momentum transfers among those phases, several
chemical reactions. To achieve this by experimental procedure would be a
nightmare, if impossible.
Example 1.5 Following the previous example, let us now imagine that
someone tries to design a larger boiler, for instance, one to consume twice the
previous amount of fuel. Among other possibilities, he could imagine two
alternatives:
a. To maintain the same ratio between the total area of tube surface and the
mass flow of coal feeding (or energy input) employed at the optimum
condition found at the pilot;
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Basic Remarks on Modeling and Simulation 7
b. To maintain the same ratio between the total area of tube surface and the
combustor volume employed at the optimum experimental condition.
A very likely answer to this dilemma is: Neither of the above alternatives is the
correct one.
To better explain, let us consider the following relations, which are very
strong simplifications of the problem:
(1.8)
(1.9)
where
= total rate energy input to the boiler furnace, (W)
ƒc = fraction of fuel that is consumed in the furnace (dimensionless from
0 to 1). The unreacted fuel leaves the furnace with the stack gas or in
the ashes.
F = fuel feeding rate, kg/s
hc = combustion enthalpy of the injected fuel, J/kg
η = boiler efficiency, i.e., the ratio between the injected energy (through
the fuel) into the furnace and the amount used to generate steam.
A = total area of tube surface, m2
n = coefficient used to accommodate an approximate equation that
accounts the differences between the laws of radiative and convective
heat transfer processes;
ΔT = average difference between the fluid that runs inside the tubes and
the furnace interior, K
αav = equivalent global (or average between inside and outside coefficients
of the tubes) heat transfer (includes convection and radiation)
between the fluid that runs inside the tubes and the furnace interior,
W m-2
K-n
)
Equations 1.8 and 1.9 are combined to write
(1.10)
Let us examine alternative (‘a’).As seen by Eq. 1.10, the area of tubes seems to
be proportional to the fuel-feeding rate. However, assuming the same tube bank
configuration as in the pilot, the bank area would not be linearly proportional to
the furnace volume. Therefore, the average velocity of gases crossing the tube
bank will be different from the values found in the pilot. As the heat transfer
coefficient is a strong function of that velocity, it will also change. Looking at
Eq. 1.10, it is easy to conclude that alternative (a) will not work. If one tries to
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8 Chapter 1
maintain the increase the volume at the same proportion of the tube bank area,
the residence time (see Eq. 1.1) will not be the same as in the pilot. Therefore,
the fuel conversion and the boiler efficiency will not be the same as the pilot,
and alternative (b) would not work either.
1.1.2 The Theoretical Method
It is too difficult for the human mind to interpret any phenomenon where more
than three variables are involved. It is not a coincidence that the graphical
representation of influences is also limited to that number of variables. Some
researchers make invalid extrapolations of the experimental method and apply
the results to multidimensional problems. For instance, try to infer the above
kinetics of SO2 absorption using a boiler combustor where coal and limestone are
added.As temperature and concentration (among several other variables) change
from point to point in the combustion chamber, no real control over the influencing
variables is possible in this case. The best that can be accomplished is the
verification of some interdependence. The result of such a study might be used in
the optimization of a particular application without the pretension to generalize
the results or to apply them to other situations, despite possible similarities.
On the other hand, the theoretical method is universal. If based on fundamental
equations (mass, momentum, and energy conservation) and correlations obtained
from well-conducted experimental procedure, the theoretical approach does
not suffer from limitations due to the number of variables involved. Therefore,
mathematical modeling is not a matter of sophistication, but the only possible
method to understand complex processes. In addition, the simple fact that a
simulation program is capable of being processed to generate information that
describes, within reasonable degree of deviations, the behavior of a real operation
is in itself a strong indication of the coherence of the mathematical structure.
The most important properties of mathematical modeling and the respective
simulation program can be summarized as follows:
• Mathematical modeling requires much fewer financial resources than the
experimental investigation.
• It can be applied to study the conditions at areas of difficult or impossible
access or where uncertainties in measurements are implicit. Such
conditions may include very high temperatures, as usually found in
combustion and gasification processes. Added to that, these processes
normally involve various phases with moving boundaries, turbulence, etc.
• It can be extended to infer the behavior of a process far from the tested
experimental range.
• It allows a much better understanding of the experimental data and results
and therefore can be used to complement the acquired knowledge from
experimental tests.
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Basic Remarks on Modeling and Simulation 9
• Mathematical modeling can be used to optimize the experimental
procedure and to avoid tests at uninteresting or even dangerous range of
operations.
• It can be employed during the scaling-up phase in order to achieve an
optimized design of the equipment or process unit. This brings substantial
savings of time and money because it eliminates or drastically reduces
the need for intermediate pilot scales.
• The model and respective program are not “static.” In other words, they
can be improved at any time to expand the range of application, reliability,
or to decrease the time necessary for the computations.
• The model and the program can also be improved with more and better
information available from experimental investigations. The results
published in the literature concerning the basic phenomena involved in
the simulated process or system can be seen as a constant source of
information. Therefore, the program can be seen as a “reservoir of
knowledge.”
Mathematical modeling is not a task but a process. The development of a
mathematical model, and its respective computer simulation program, is not a
linear sequence where each step follows the one before. The process is composed
by a series of forward and backward movements where each block or task is
repeatedly revisited.
One should be suspicious of simple answers. Nature is complex and the
process of modeling it is an effort to represent it as closely as possible. The best
that can be done is to improve the approximations in order to decrease deviations
from the reality. A good simulation program should be capable of reproducing
measured operational data within an acceptable level of deviation. In most cases,
even deviations have a limit that cannot be surpassed. These are established by
several constraints, among them:
• Intrinsic errors in correlation obtained through experimental procedures
(due to limitations in the precisions of measurements)
• Available knowledge (literature or personal experience)
• Basic level of modeling adopted (zero, one, or more dimensions)
Therefore, only approximations—sometimes crude—of the reality are
possible.
It is advisable to go from simple to complex, not the other way around.
Modeling is an evolutionary movement. Usually, there is a long way from the
very first model to the more elaborate version. The first model should of course
be mathematically consistent and at the same time very simple. It is important
to include very few effects in the first trial. Several hypothesis and simplifications
Copyright © 2004 by Marcel Dekker, Inc.
These, as well other factors, are better discussed at Chapter 12.
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10 Chapter 1
should be assumed; otherwise, the risk of not achieving a working model would
be great. If one starts from the very simple, results might be obtained from
computations. Then, comparisons against experimental or equipment operational
data may provide information for improving the model. Measurements of
variables during industrial operations seldom present fluctuations below 5% in
relation to an average value. For instance, the average temperature of a stack
gas released from an industrial boiler can easily fluctuate 30 K, for an average
of 600 K. Therefore, if a model has already produced that kind of deviation
against measured or published values, it might be better to consider stopping.
Improvements in a model should be accomplished mainly by eliminating
one (and just one) simplifying hypothesis at a time, followed by verification if
the new version leads to representations closer to reality. If not, eliminate another
hypothesis, and so on. On the other hand, if one starts from complex models,
not even computational results may be obtainable. Even so, there would be
little chance to identify where improvements should be made. If one needs to
travel, it is better to have a runningVolkswagen Beetle than a Mercedes without
wheels.
1.2 A CLASSIFICATION FOR MATHEMATICAL MODELS
1.2.1 Phenomenological versus Analogical Models
Industrial equipment or processes operate by receiving physical inputs,
processing those inputs, and delivering physical outputs. Among the usual
physical inputs and outputs there are:
• Mass flows
• Compositions
• Temperatures
• Pressures
In addition to these variables, heat and work may be exchanged through the
control surface.
The internal physical phenomena are the processes that transform inputs
into outputs. The phenomenological model intends to reproduce these processes
as closely as possible. The phenomenological models are based on:
• Fundamental equations,*
such as laws of thermodynamics and laws of
mass, energy, and momentum conservation.
* The fundamental laws of thermodynamics are found in any undergraduate and graduate-level
conservation are found in any text of transport phenomena, such as Refs. 1–4. In addition,Appendix
A summarizes the most important for the purposes of the present book. The constitutive equations
necessary for the models present in the following chapters will be described during the discussions.
Copyright © 2004 by Marcel Dekker, Inc.
textbook. The main relations are repeated in Chapter 5 and Appendix B. Those related to
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Basic Remarks on Modeling and Simulation 11
• Constitutive equations, which are usually based on empirical or
semiempirical correlations
The combination of fundamental laws or equations and constitutive correlations
may lead to valid models. These models are valid within the same range of the
employed correlations. This brings some assurance that phenomenological
models reflect reality in that range.
Analogy models, although useful for relatively simple systems or processes,
just mimic the behavior of a process, and therefore do not reflect reality.
Examples of analogy models are, for instance, those based on mass-and-spring
systems or on electric circuits.
The computer simulation program based on a phenomenological model
receives the input data, treats them according to the model in which it is based
upon, and delivers the output or results. However, depending on the degree of
sophistication, the model might provide much more information than simple
descriptions of the properties and characteristics of the output streams. As
mentioned before, it is extremely important to properly understand the role
of process variables that are not accessible for direct or even indirect
measurement. That information might be useful in the design controlling
systems. In addition, the process of building up the phenomenological model
requires the setting of relationships linking the various variables. Therefore,
the combination of experimental observations with the theoretical
interpretation usually leads to a much better understanding of the physical
operation.
The phenomenological models can be classified according several criteria.
The first branching is set according to the amount of space dimensions considered
in the model. Therefore, three levels are possible.
A second branching considers the inclusion of time as a variable. If it is not
included, the model is called steady state; otherwise, it is a dynamic model. In
addition, several other levels can be added, for instance,
• If laminar or turbulent flow conditions are assumed
• If dissipative effects such as those provided by terms containing viscosity,
thermal conductivity, and diffusivity are included
The list could go on. However, in order to keep a simple basic classification for
this introductory text, only the aspects of dimension and time are considered.A
simple notation will be followed:
1. Zero-dimensional-steady, or 0D-S. It is the simplest level of modeling
and includes neither dimension nor time as variable.
2. Three-dimensional-dynamic, or 3D-D. It includes three space dimensions
and time as variables.
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1.2.2 Steady-State Models
Although the definition of steady-state regime is widely employed, some
confusion may arise if not clearly understood. Therefore, let us take some lines
to state it before further considerations.
In relation to a given set of space coordinates, a steady-state regime for a
control volume*
will be established if:
1. The control surface does not deform or move.
2. The mass flows and space average properties of each input and output
stream remain constant.
3. The rates of heat and work exchanges between the control volume and
surrounds are constant.
4. Although conditions inside the control volume differ from point to point,
they remain constant at each position.
Most of industrial equipments operate at steady-state conditions. Rigorously,
there is no such thing as a perfect steady-state operation. Even for operations
that are supposed to be steady, some degree of fluctuations against time in
variables such as temperature, concentration, or velocities occur. On the other
hand, most of the time, several industrial processes operate within a range of
conditions not very far from an average. Therefore, a good portion of those can
be treated as such with high or at least reasonable accuracy.
1.2.2.1 0D-S Models
Zero-dimensional-steady models set relations between input and output variables
of a system or control volume without considering the details of the phenomena
occurring inside that system or control volume. Therefore, no description or
evaluation of temperature, velocity, or concentration profiles in the studied
equipment is possible.
Despite that, 0D-S models are very useful, mainly if an overall analysis of
an equipment, or system composed of several equipments, is intended.
Depending on the complexity of internal phenomena and the available
information about a process or system, this may be the only achievable level of
modeling. However, it should not be taken for granted because it may involve
serious difficulties, mainly when many subsystems (or equipment) are considered
in a single system.
Since there is no description on how processes occur related to space, 0D-S
models require assumptions such as chemical and thermodynamic equilibrium
conditions of the output stream. On the other hand, hypotheses such as these
could constitute oversimplifications and lead to false conclusions because:
*
Copyright © 2004 by Marcel Dekker, Inc.
See Appendix B, Section B.1.
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Basic Remarks on Modeling and Simulation 13
• Rigorously, equilibrium at exiting streams would require infinite
residence time of the chemical components or substances inside the
equipment. Typical residence time of several classes of reactors,
combustors, and gasifiers are seconds to minutes. Therefore, conditions
far from equilibrium might be expected.
• Determination of equilibrium composition at exiting streams requires the
value of their temperatures. However, to estimate those temperatures, one
needs to perform energy balance or balances. For that, the compositions
and temperatures of the streams should be known to allow computation
of enthalpies or internal energies of the exiting streams. Reiterative
processes work well if the exiting streams are composed by just one or
two components. However, reiterative processes with several nested
convergence problems might become awkward computational problems.
Most of these situations take huge amounts of time to achieve solutions,
or even to impossibilities of arriving at solutions.
• If the process includes gas-solid reactions—as in combustors or
gasifiers—the conversion of reacting solid (coal or biomass, for instance)
is usually unknown and therefore should be guessed. On the other hand,
the bulk of conversion occurs at points of high temperature inside the
equipment. That temperature is usually much higher than the
temperatures of exiting streams (gas or solid particles). Therefore, to
accomplish the energy balance for the control volume, one needs to
guess some sort of average representative temperature at which the
reactions and equilibrium should be computed.Apart from being artificial
under the point of view of phenomenology, guesses of such average
temperature usually are completely arbitrary. Experimental conditions
should therefore be used to calibrate such models. Experimental
conditions differ from one case to another and are therefore not reliable
when a general model for a process or equipment operation is sought.
Therefore, 0D-S models are very limited or might even lead to wrong
conclusions. This is also valid for 0D-D models. In addition, they are
not capable of predicting a series of possible operational problems
because, despite relatively low temperatures of exiting streams, internal
temperatures could surpass:
Limits of integrity of wall materials
Explosion limits
Values that start runaway processes, etc.
• 0D-S models are also extremely deficient in cases of combustion and
gasification of solids because pyrolysis or devolatilization is present. That
very complex process introduces gases and complex mixtures of organic
and inorganic substances at particular regions of the equipment. The
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14 Chapter 1
compositions of those streams have strong influence on the composition
and temperature of the exiting gas, even if equilibrium is assumed.
1.2.2.2 1D-S Models
The second level of modeling is to assume that all properties or conditions
inside the equipment vary only at one space coordinate. They constitute a
considerable improvement in quality and quantity of information provided by
the zero-dimensional models. Equilibrium hypotheses are no longer necessary
and profiles of the variables, such as temperature, pressures, and compositions,
throughout the willequipment can be determined. Of course, they might not be
enough to properly represent processes where severe variations of temperature,
concentration, and other parameters occur in more than one dimension.
1.2.2.3 2D-S Models
Two-dimensional models may be necessary in cases where the variations in a
second dimension can no longer be neglected. As an example, let us imagine
the difference between a laminar flow and a plug-flow reactor. Figure 1.2
illustrates a reactor where exothermic reactions are occurring and heat can be
exchanged with the environment through the external wall.
In Figure 1.2a, the variations of temperature and composition in the axial
direction are added to the variations in the radial direction. It is easy to imagine
FIG. 1.2 Schematic views of (a) a laminar flow and (b) a plug-flow reactor.
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Basic Remarks on Modeling and Simulation 15
that, due to the relatively smaller temperatures at the layer of fluid near the
walls, small changes in composition provoked by chemical reactions occur there.
This is a typical system that may require two-dimensional modeling to account
for the correct exit conditions; otherwise, the average concentration at the exiting
point cannot be computed with some degree of precision.
Reversibly, plug-flow processes provide flat temperature, velocity, and
concentration profiles. Highly turbulent flow or presence of packing inside the
reactor provide the possibility to assume plug-flow regimes. Of course, the thin
layer near the wall experiences drastic variations of temperature, but this is not
a representative portion of the flowing mass. Therefore, a fair assumption is
that variations in the radial coordinate could be neglected, as compared with
variations in composition and temperature at the axial direction. This is a typical
case where a 1D-S model might lead to good results.
1.2.2.4 3D-S Models
Due to their usual complexity, 3D-S models are seldom adopted. However, they
may, in some cases, be necessary. By this approach, all space coordinates are
considered. On the other hand, if the model and simulation procedure are
successful, a great deal of information about the process is obtained. For instance,
imposed to the flowing fluid. In some of these cases a cylindrical symmetry can
be assumed and a two-dimensional model might be enough for a good
representation of the process, but for asymmetrical geometries 3D models are
usually necessary.An example of such a process occurs inside commercial boilers
burning pulverized fuels. Most of the combustion chambers have rectangular
cross sections and internal buffers are usually present, not to mention tube banks.
no symmetry assumption is possible or reasonable. On the other hand, and as
everything in life, there is a price to be paid. Let us imagine what would be
necessary to set a complete model. First, it would require the solution of the
complete Navier-Stokes, or momentum conservation, equations. These should
be combined with the equations of energy and mass conservation applied for all
chemical species. All these equations ought to be written for three directions and
solved throughout the reactor. Second, the number of boundary conditions is also
high. Most of the time, these conditions involve not just given or known values at
interfaces, but also derivatives. Moreover, boundary conditions might require
complex geometric descriptions. For example, the injections of reactant streams
at the feeding section may be made by such a complex distributing system that
even setting the boundary condition would be difficult. When correlations and
constitutive equations for all these parameters are included, the final set of
mathematical equations is awesome. However, commercially available
computational fluid dynamics (CFD) have evolved and are capable of solving
Copyright © 2004 by Marcel Dekker, Inc.
let us imagine the laminar-flow reactor (Figure 1.2a), where rotation or vortex is
Since rotational flows as well as strong reversing flows are present (see Fig. 3.11),
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16 Chapter 1
suchsystems.Verygoodresultsareobtainable,particularlyforsingle-phasesystems
(gas-gas, for instance). Nonetheless, combustion and gasification of solid fuels
still present considerable difficulties, mainly for cases of combustion and
gasification of suspensions or pneumatic transported pulverized fuels.
On the other hand, one must question the use of such an amount of information.
Is it necessary to predict the details of the velocities, concentration, and
temperature profiles in all directions inside the equipment? What is the cost-
benefit situation in this case? Departing from a previous one- or two-dimensional
model, would this three-dimensional model be capable of decreasing the
deviations between simulation and real operation to a point that the time and
money invested in it would be justifiable? Is it useful to have a model that generates
deviations below the measurement errors? Finally, what would be necessary to
measure in order to validate such a model against real operations?
In this line, let us ask what sort of variables are usually possible to measure
and what is the degree of precision or certainty of such measurements.
Anyone who works or has worked in an industrial plant operation knows
that is not easy to measure temperature profiles inside the given equipment. In
addition, if combustion of solid fuel is taking place, composition profiles of gas
streams and composition of solids are extremely difficult to determine.
Alternatively, average values of temperatures, pressures, mass flows, and
compositions of entering and leaving streams can be measured. Sometimes,
average values of variables within a few points inside the equipment are
obtainable.This illustrates the fact that those involved in mathematical modeling
of particular equipment or process should be acquainted with its real operation.
This would provide a valuable training that might be very useful when he or
she decides to develop a simulation model and program. If that is not possible,
it is advisable to keep in contact with people involved in such operations, as
well to read as many papers or reports as possible on descriptions of operations
of industrial or pilot units. This will be very rewarding at the time that
simplification hypothesis of a model needs to be made.
1.2.3 Dynamic, or nD-D, Models
Added to the above considerations, models might include time as a variable,
and are therefore called dynamic models.
Some processes are designed to provide progressive or repetitive (regular or
not) increasing or decreasing values of input or output values of temperature,
concentration, velocities, pressure, etc. Batch operation reactors and internal
combustion engines are examples of such processes.
Dynamic models are also useful or necessary when control strategies are to
be set or for cases where starting-up and/or stopping-up procedures should be
monitored or controlled. Safety or economics may require that.
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Basic Remarks on Modeling and Simulation 17
Most of the considerations made above regarding the necessity of including
more dimensions for steady-state models are also valid for dynamic ones.
1.2.4 Which Level to Attack?
Chosing among the various levels of modeling should be based on necessity.
Sophisticationisnotaguaranteeforquality.Thesameistrueforextremesimplicity,
which could lead to false or naive hypothesis about complex phenomena.
The following suggestions may serve as a guide:
1. If steady-state process, it is advisable to start from a 0D-S model (or from
a 0D-D model if dynamic). Even if this is not the desired level to reach, it
is useful just to verify if the conception or ideas about the overall operation
of the equipment or process are coherent or not. Overall mass and energy
conservation should always hold.
2. Comparison between simulation results and measured values should be
made. As seen, measurements in industrial operations always present
relatively high deviations. Unless more details within the equipment are
necessary, the present level might be satisfactory if it has already produced
equal or lower deviations between simulation and measured values.
3. If they do not compare well, at least within a reasonable degree of
approximation, the model equations must be revisited. Hypothesis and
simplifications should also be reevaluated. Then, the process should start
again from step 2. It may also be possible that due to reasons already
explained, the present level of attack cannot properly simulate the process.
The reasons for that are discussed above. In addition, depending on the
deviations produced by the previous level or the need for more detailed
information. In any of those circumstances, it might be necessary to add
a dimension.
4. Before starting a higher and more sophisticated level of modeling, it is
advisable to verify what can be measured in the equipment pilot or the
industrial unit to be simulated. In addition, it should be verified that the
measurements and available information would be enough for
comparisons against results from the next simulation level. If not sufficient,
the value of stepping up the model should receive serious consideration.
EXERCISES
1.1* Discuss others possibilities for the design of the reactor and solving the
scaling-up contradictions, as described in Example 1.3.
1.2** Based on the considerations made in Example 1.4, develop some
suggestions for a feasible scaling up of the boiler.
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18
2
Solid Fuels
2.1 INTRODUCTION
This chapter describes the fundamental properties of carbonaceous solid fuels
most used in commercial combustion and gastification processes. The objective
is to introduce the main characteristics of most common solid fuels and their
behavior under heating. No mathematical treatments are presented at this stage.
This chapter mainly shows qualitative aspects of drying and pyrolysis, leaving
From a practical point of view, industrially employed solid carbonaceous
fuels can be classified in three main categories:
1. Coals
2. Biomass
3. Other
Carbonaceous fuels are complex collections of organic polymers consisting
mainly of aromatic chains combined by hydrocarbons and other atoms such as
oxygen, nitrogen, sulfur, potassium, sodium. Coals are mainly the results of
slow deterioration of biomass. The degree of that deterioration determines the
coal rank. For instance, the lower degree of deterioration is found in lignites
and the maximum are found in anthracites. Intermediary stages are the
Copyright © 2004 by Marcel Dekker, Inc.
quantifications to Chapter 10. Combustion and gasification reactions will be
detailed in Chapters 8 and 9.
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Solid Fuels 19
subbituminous and bituminous coals. Therefore, the coal physical and chemical
properties are functions of its age, and the most important are discussed below.
2.2 PHYSICAL PROPERTIES
Among the principal aspects concerning the physical properties of solid fuels
there are:
• Size or particle size distribution
• Shape of particles
• Porosity of particles
Of course, the size of particles plays a fundamental role in combustion and
gasification processes.
Prior of feeding into combustors or gasifiers, a solid fuel usually passes
through a grinding process to reduce particle sizes. The degree of reduction
depends on the requirements of applications. Most of combustors and gasifiers
cover the range from 10-6
to 10-2
m.
The method of grinding is also important. Some solid fuels present special
characteristics, which might lead to serious problems for the combustor or gasifier
feeding devices. For instance, fibrous materials, such as sugar-cane bagasse, have
ends with a broomlike structure. They allow entangling among fibers, leading to
formation of large agglomerates inside the hopper.This might prevent the bagasse
to continuously flow down to the feeding screws. Sophisticated design and costly
systems are necessary to ensure steady feeding operation. Many grinding processes
dramatically increase the fraction of particles with those broomlike ends, but that
can be largely avoided by applying rotary knife cutters.
Any sample of particles covers a wide range of sizes. The particle size
distribution is provided after a laboratory determination where several techniques
can be applied. The most used is still the series of screens, piled in vertical
stacks where the aperture of the net decreases from the top to the bottom. A
sample of particles is deposited on the top of the pile, usually with 5–15 screens,
and a gentle rocking movement is applied to the whole system. After a time, if
no significant change is verified on the amounts retained by the screens, the
mass remaining at each one is measured.A list of the percentage of the original
sample against the screen aperture is provided. The natural distribution usually
nears a normal probabilistic curve. The apertures of screens follow standard
It is easy to imagine that smaller particles carried by gas stream tend to be
consumedfasterandeasierthanbiggerones.Therefore,theparticlesizedistribution
influences not only the rate at which the fuel reacts with oxygen and other gases,
but also almost all other aspects of combustor and gasifiers operations. Of course,
to repeat and report all computations for each particle size would be rather
Copyright © 2004 by Marcel Dekker, Inc.
sizes. More details will be described in Chapter 4.
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20 Chapter 2
cumbersome. That is why all mathematical models use some sort of average
phenomena found in combustors and gasifiers.The rates of gas-solid reactions—
among them the oxidation of carbonaceous solids or combustion—depend on
the available surface area of the particle. Therefore, for the same volume, the
particle with higher surface area should lead to faster consumption. Of course,
the minimum would be found for spherical particles. However, the problem is
not so simple, mainly because the available area of pores surfaces inside the
particle and mass transfer phenomena influence the consumption rate. In
addition, the form of particles has a strong influence on the momentum transfers
between the particles and the gas stream that carries them.Among the parameters,
there is the terminal velocity. The most-used parameter to describe the shape of
a particle is sphericity, given by
(2.1)
Of course, sphericity tends to 1 for particles approaching spherical shape, and
to smaller values for particles departing from that. That concept is very useful
because solid particles found in nature, or even preprocessed ones, are seldom
spherical. For most of the coal, limestone, and sand particles, the sphericity
ranges from 0.6 to 0.9. The value of 0.7 may be used if no better information is
available.Wood chips—usually used to feed the process in paper mills—present
sphericity around 0.2. Sphericity of particles is mainly dictated by the grinding
or preparation process, and it is easily determined by laboratorial tests. Likewise,
for several other particle properties, sphericity also suffers strong variation during
combustion or gasification processes.
Fuel solids are usually very porous. Normally more than half of particle volume
is empty due to tunnels that crisscross its interior.A good portion of these tunnels
have microscopic diameters. This leads to considerably high values for the total
areaoftheirsurfacespermassofparticle,andfiguresaround500m2
/garecommon.
However, there is some controversy on the methods to determine the internal area
of pores, and much has been written on the subject, as illustrated by Gadiou et al.
[5]. In any case, the above value demonstrates the importance of pores and their
structures on the rate of heterogeneous or gas-solid reactions.
The porosity can be calculated using two different definitions of density:
• Apparent particle density ρapp, which is the ratio between the mass of an
average particle and its volume, including the void volumes of internal
pores. A wide range of values can be found even for a single species of
Copyright © 2004 by Marcel Dekker, Inc.
diameter.Thereareseveraldefinitionsorinterpretationforsuchanaverage;Chapter
In addition to the size of particles, their shape strongly influences several
4 presents the various definitions and methodology to compute them.
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Solid Fuels 21
fuel, but for the sake of examples, typical values for coals fall around
1100 and 700 kg/m3
for woods.
• Real density ρreal, which is the ratio between the mass of an average particle
and its volume, excluding the volumes occupied by internal pores.Again,
a wide range of values can be found even for a single species of fuel, but
typical values for coals fall around 2200 and 1400 kg/m3
for woods.
The porosity is defined as the ratio between the volumes occupied by all pores
inside a particle and its total volume (including pores). It can be easily
demonstrated that
(2.2)
Typical values of porosity are around 0.5 (or 50%).
2.3 CHEMICAL PROPERTIES
The composition and molecular structures found in any carbonaceous fuel, such
as coal and biomass, are very complex. They involve a substantial variety of
inorganic and organic compounds. The largest portion are organic and arranged
in hydrocarbon chains where, apart from C, H, O, and N, several other atoms
are present, such as S, Fe, Ca, Al, Si, Zn, Na, K, Mg, Cl, heavy metals, etc.
There is a vast literature on coal structure (e.g., Refs. 6–8). On the other hand,
the literature also shows that most of coal architecture is still ignored.
Among the differences between biomass and coals, there is the carbon-to-
hydrogen ratio, with higher values for the last ones. Therefore, the C/H ratio
can be seen as a vector of time. The principal reason rests on the fact that products
from decomposition are light gases and organic liquids with higher proportion
of hydrogen—or lower C/H ratio—than the original biomass. For instance,
biomass present C/H ratios around 10, lignites around 14, bituminous coals
average around 17, while anthracites average around 30. Therefore, the final
stage of decomposition is almost pure carbon. On the other hand, one should be
careful not to equate the fuel rank with its value for applications. For instance,
high volatile content is very important in pulverized combustion because
facilitates the solid fuel ignition.
There are relatively simple analyses to determine the basic fractions and
atomic composition, which can be applied to almost all carbonaceous solid
fuels. The simplest one is called proximate analysis and includes the following
categories:
• Moisture, which is determined by maintaining a sample of solid fuel in an
inert atmosphere at 378 K and near ambient pressure until no variation of
Copyright © 2004 by Marcel Dekker, Inc.
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Solido Fuels Combustion & Gasification.pdf

  • 2. Solid Fuels Combustion and Gasification Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 3. MECHANICAL ENGINEERING A Series of Textbooks and Reference Books Founding Editor L.L.Faulkner Columbus Division, Battelle Memorial Institute and Department of Mechanical Engineering The Ohio State University Columbus, Ohio 1. Spring Designerís Handbook, Harold Carlson 2. Computer-Aided Graphics and Design, Daniel L.Ryan 3. Lubrication Fundamentals, J.George Wills 4. Solar Engineering for Domestic Buildings, William A.Himmelman 5. Applied Engineering Mechanics: Statics and Dynamics, G.Boothroyd and C.Poli 6. Centrifugal Pump Clinic, Igor J.Karassik 7. Computer-Aided Kinetics for Machine Design, Daniel L.Ryan 8. Plastics Products Design Handbook, Part A: Materials and Components; Part B: Processes and Design for Processes, edited by Edward Miller 9. Turbomachinery: Basic Theory and Applications, Earl Logan, Jr. 10. Vibrations of Shells and Plates, Werner Soedel 11. Flat and Corrugated Diaphragm Design Handbook, Mario Di Giovanni 12. Practical Stress Analysis in Engineering Design, Alexander Blake 13. An Introduction to the Design and Behavior of Bolted Joints, John H. Bickford 14. Optimal Engineering Design:Principles and Applications, James N.Siddall 15. Spring Manufacturing Handbook, Harold Carlson 16. Industrial Noise Control: Fundamentals and Applications, edited by Lewis H.Bell 17. Gears andTheirVibration:A Basic Approach to Understanding Gear Noise, J.Derek Smith 18. Chains for Power Transmission and Material Handling: Design and Applications Handbook, American Chain Association 19. Corrosion and Corrosion Protection Handbook, edited by Philip A. Schweitzer 20. Gear Drive Systems: Design and Application, Peter Lynwander 21. Controlling In-Plant Airborne Contaminants: Systems Design and Calculations, John D.Constance 22. CAD/CAM Systems Planning and Implementation, Charles S.Knox 23. Probabilistic Engineering Design: Principles and Applications, James N. Siddall 24. Traction Drives: Selection and Application, Frederick W.Heilich III and Eugene E.Shube 25. Finite Element Methods: An Introduction, Ronald L.Huston and Chris E. Passerello Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 4. 26. Mechanical Fastening of Plastics: An Engineering Handbook, Brayton Lincoln, Kenneth J.Gomes, and James F.Braden 27. Lubrication in Practice: Second Edition, edited by W.S.Robertson 28. Principles of Automated Drafting, Daniel L.Ryan 29. Practical Seal Design, edited by Leonard J.Martini 30. Engineering Documentation for CAD/CAM Applications, Charles S.Knox 31. Design Dimensioning with Computer Graphics Applications, Jerome C. Lange 32. Mechanism Analysis: Simplified Graphical and Analytical Techniques, Lyndon O.Barton 33. CAD/CAM Systems: Justification, Implementation, Productivity Measurement, Edward J.Preston, George W.Crawford, and Mark E.Coticchia 34. Steam Plant Calculations Manual, V.Ganapathy 35. Design Assurance for Engineers and Managers, John A.Burgess 36. Heat Transfer Fluids and Systems for Process and Energy Applications, Jasbir Singh 37. Potential Flows: Computer Graphic Solutions, Robert H.Kirchhoff 38. Computer-Aided Graphics and Design: Second Edition, Daniel L.Ryan 39. Electronically Controlled Proportional Valves: Selection and Application, Michael J.Tonyan, edited by Tobi Goldoftas 40. Pressure Gauge Handbook, AMETEK, U.S. Gauge Division, edited by Philip W.Harland 41. Fabric Filtration for Combustion Sources: Fundamentals and Basic Technology, R.P.Donovan 42. Design of Mechanical Joints, Alexander Blake 43. CAD/CAM Dictionary, Edward J.Preston, George W.Crawford, and Mark E. Coticchia 44. Machinery Adhesives for Locking, Retaining, and Sealing, Girard S.Haviland 45. Couplings and Joints: Design, Selection, and Application, Jon R.Mancuso 46. Shaft Alignment Handbook, John Piotrowski 47. BASIC Programs for Steam Plant Engineers: Boilers, Combustion, Fluid Flow, and Heat Transfer, V.Ganapathy 48. Solving Mechanical Design Problems with Computer Graphics, Jerome C.Lange 49. Plastics Gearing: Selection and Application, Clifford E.Adams 50. Clutches and Brakes: Design and Selection, William C.Orthwein 51. Transducers in Mechanical and Electronic Design, Harry L.Trietley 52. Metallurgical Applications of Shock-Wave and High-Strain-Rate Phenomena, edited by Lawrence E.Murr, Karl P.Staudhammer, and Marc A.Meyers 53. Magnesium Products Design, Robert S.Busk 54. How to Integrate CAD/CAM Systems: Management and Technology, William D.Engelke 55. Cam Design and Manufacture: Second Edition; with cam design software for the IBM PC and compatibles, disk included, Preben W.Jensen 56. Solid-State AC Motor Controls: Selection and Application, Sylvester Campbell 57. Fundamentals of Robotics, David D.Ardayfio Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 5. 58. Belt Selection and Application for Engineers, edited by Wallace D.Erickson 59. Developing Three-Dimensional CAD Software with the IBM PC, C.Stan Wei 60. Organizing Data for CIM Applications, Charles S.Knox, with contributions by Thomas C.Boos, Ross S.Culverhouse, and Paul F.Muchnicki 61. Computer-Aided Simulation in Railway Dynamics, by RaoV.Dukkipati and Joseph R.Amyot 62. Fiber-Reinforced Composites: Materials, Manufacturing, and Design, P.K. Mallick 63. Photoelectric Sensors and Controls: Selection and Application, Scott M. Juds 64. Finite Element Analysis with Personal Computers, Edward R.Champion, Jr., and J.Michael Ensminger 65. Ultrasonics: Fundamentals, Technology, Applications: Second Edition, Revised and Expanded, Dale Ensminger 66. Applied Finite Element Modeling:Practical Problem Solving for Engineers, Jeffrey M.Steele 67. Measurement and Instrumentation in Engineering: Principles and Basic Laboratory Experiments, Francis S.Tse and Ivan E.Morse 68. Centrifugal Pump Clinic: Second Edition, Revised and Expanded, Igor J. Karassik 69. Practical Stress Analysis in Engineering Design: Second Edition, Revised and Expanded, Alexander Blake 70. An Introduction to the Design and Behavior of Bolted Joints: Second Edition, Revised and Expanded, John H.Bickford 71. High Vacuum Technology: A Practical Guide, Marsbed H.Hablanian 72. Pressure Sensors: Selection and Application, Duane Tandeske 73. Zinc Handbook: Properties, Processing, and Use in Design, Frank Porter 74. Thermal Fatigue of Metals, Andrzej Weronski and Tadeusz Hejwowski 75. Classical and Modern Mechanisms for Engineers and Inventors, Preben W.Jensen 76. Handbook of Electronic Package Design, edited by Michael Pecht 77. Shock-Wave and High-Strain-Rate Phenomena in Materials, edited by Marc A.Meyers, Lawrence E.Murr, and Karl P.Staudhammer 78. Industrial Refrigeration: Principles, Design and Applications, P.C.Koelet 79. Applied Combustion, Eugene L.Keating 80. Engine Oils and Automotive Lubrication, edited by Wilfried J.Bartz 81. Mechanism Analysis: Simplified and Graphical Techniques, Second Edition, Revised and Expanded, Lyndon O.Barton 82. Fundamental Fluid Mechanics for the Practicing Engineer, James W. Murdock 83. Fiber-Reinforced Composites: Materials, Manufacturing, and Design, Second Edition, Revised and Expanded, P.K.Mallick 84. Numerical Methods for Engineering Applications, Edward R.Champion, Jr. 85. Turbomachinery: Basic Theory and Applications, Second Edition, Revised and Expanded, Earl Logan, Jr. 86. Vibrations of Shells and Plates: Second Edition, Revised and Expanded, Werner Soedel 87. Steam Plant Calculations Manual:Second Edition, Revised and Expanded, V.Ganapathy Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 6. 88. Industrial Noise Control: Fundamentals and Applications, Second Edition, Revised and Expanded, Lewis H.Bell and Douglas H.Bell 89. Finite Elements: Their Design and Performance, Richard H.MacNeal 90. Mechanical Properties of Polymers and Composites:Second Edition, Revised and Expanded, Lawrence E.Nielsen and Robert F.Landel 91. Mechanical Wear Prediction and Prevention, Raymond G.Bayer 92. Mechanical Power Transmission Components, edited by David W.South and Jon R.Mancuso 93. Handbook of Turbomachinery, edited by Earl Logan, Jr. 94. Engineering Documentation Control Practices and Procedures, Ray E. Monahan 95. Refractory Linings Thermomechanical Design and Applications, Charles A.Schacht 96. Geometric Dimensioning and Tolerancing: Applications and Techniques for Use in Design, Manufacturing, and Inspection, James D.Meadows 97. An Introduction to the Design and Behavior of Bolted Joints:Third Edition, Revised and Expanded, John H.Bickford 98. Shaft Alignment Handbook:Second Edition, Revised and Expanded, John Piotrowski 99. Computer-Aided Design of Polymer-Matrix Composite Structures, edited by Suong Van Hoa 100. Friction Science and Technology, Peter J.Blau 101. Introduction to Plastics and Composites: Mechanical Properties and Engineering Applications, Edward Miller 102. Practical Fracture Mechanics in Design, Alexander Blake 103. Pump Characteristics and Applications, Michael W.Volk 104. Optical Principles and Technology for Engineers, James E.Stewart 105. Optimizing the Shape of Mechanical Elements and Structures, A.A.Seireg and Jorge Rodriguez 106. KinematicsandDynamicsofMachinery,VladimÌrStejskalandMichaelVal öek 107. Shaft Seals for Dynamic Applications, Les Horve 108. Reliability-Based Mechanical Design, edited by Thomas A.Cruse 109. Mechanical Fastening, Joining, and Assembly, James A.Speck 110. Turbomachinery Fluid Dynamics and Heat Transfer, edited by Chunill Hah 111. High-Vacuum Technology: A Practical Guide, Second Edition, Revised and Expanded, Marsbed H.Hablanian 112. Geometric Dimensioning and Tolerancing: Workbook and Answerbook, James D.Meadows 113. Handbook of Materials Selection for Engineering Applications, edited by G.T.Murray 114. Handbook of Thermoplastic Piping System Design,Thomas Sixsmith and Reinhard Hanselka 115. Practical Guide to Finite Elements: A Solid Mechanics Approach, Steven M.Lepi 116. Applied Computational Fluid Dynamics, edited by Vijay K.Garg 117. Fluid Sealing Technology, Heinz K.Muller and Bernard S.Nau 118. Friction and Lubrication in Mechanical Design, A.A.Seireg 119. Influence Functions and Matrices, Yuri A.Melnikov 120. Mechanical Analysis of Electronic Packaging Systems, Stephen A. McKeown Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 7. 121. Couplings and Joints: Design, Selection, and Application, Second Edition, Revised and Expanded, Jon R.Mancuso 122. Thermodynamics: Processes and Applications, Earl Logan, Jr. 123. Gear Noise and Vibration, J.Derek Smith 124. Practical Fluid Mechanics for Engineering Applications, John J.Bloomer 125. Handbook of Hydraulic Fluid Technology, edited by George E.Totten 126. Heat Exchanger Design Handbook, T.Kuppan 127. Designing for Product Sound Quality, Richard H.Lyon 128. Probability Applications in Mechanical Design, Franklin E.Fisher and Joy R.Fisher 129. Nickel Alloys, edited by Ulrich Heubner 130. Rotating Machinery Vibration: Problem Analysis and Troubleshooting, Maurice L.Adams, Jr. 131. Formulas for Dynamic Analysis, Ronald L.Huston and C.Q.Liu 132. Handbook of Machinery Dynamics, Lynn L.Faulkner and Earl Logan, Jr. 133. Rapid PrototypingTechnology:Selection and Application, Kenneth G.Cooper 134. ReciprocatingMachineryDynamics:DesignandAnalysis,AbdullaS.Rangwala 135. Maintenance Excellence: Optimizing Equipment Life-Cycle Decisions, edited by John D.Campbell and Andrew K.S.Jardine 136. Practical Guide to Industrial Boiler Systems, Ralph L.Vandagriff 137. Lubrication Fundamentals: Second Edition, Revised and Expanded, D.M. Pirro and A.A.Wessol 138. Mechanical Life Cycle Handbook: Good Environmental Design and Manufacturing, edited by Mahendra S.Hundal 139. Micromachining of Engineering Materials, edited by Joseph McGeough 140. Control Strategies for Dynamic Systems:Design and Implementation, John H.Lumkes, Jr. 141. Practical Guide to Pressure Vessel Manufacturing, Sunil Pullarcot 142. Nondestructive Evaluation: Theory, Techniques, and Applications, edited by Peter J.Shull 143. Diesel Engine Engineering: Thermodynamics, Dynamics, Design, and Control, Andrei Makartchouk 144. Handbook of Machine Tool Analysis, loan D.Marinescu, Constantin Ispas, and Dan Boboc 145. Implementing Concurrent Engineering in Small Companies, Susan Carlson Skalak 146. Practical Guide to the Packaging of Electronics:Thermal and Mechanical Design and Analysis, Ali Jamnia 147. Bearing Design in Machinery: Engineering Tribology and Lubrication, Avraham Harnoy 148. Mechanical Reliability Improvement: Probability and Statistics for Experimental Testing, R.E.Little 149. Industrial Boilers and Heat Recovery Steam Generators: Design, Applications, and Calculations, V.Ganapathy 150. The CAD Guidebook: A Basic Manual for Understanding and Improving Computer-Aided Design, Stephen J.Schoonmaker 151. Industrial Noise Control and Acoustics, Randall F.Barron 152. Mechanical Properties of Engineered Materials, WolÈ Soboyejo 153. Reliability Verification, Testing, and Analysis in Engineering Design, Gary S.Wasserman Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 8. 154. Fundamental Mechanics of Fluids: Third Edition, I.G.Currie 155. Intermediate Heat Transfer, Kau-Fui Vincent Wong 156. HVAC Water Chillers and Cooling Towers:Fundamentals, Application, and Operation, Herbert W.Stanford III 157. Gear Noise and Vibration: Second Edition, Revised and Expanded, J. Derek Smith 158. Handbook of Turbomachinery: Second Edition, Revised and Expanded, edited by Earl Logan, Jr., and Ramendra Roy 159. Piping and Pipeline Engineering: Design, Construction, Maintenance, Integrity, and Repair, George A.Antaki 160. Turbomachinery: Design and Theory, Rama S.R.Gorla and Aijaz Ahmed Khan 161. Target Costing: Market-Driven Product Design, M.Bradford Clifton, Henry M.B.Bird, Robert E.Albano, and Wesley P.Townsend 162. Fluidized Bed Combustion, Simeon N.Oka 163. Theory of Dimensioning: An Introduction to Parameterizing Geometric Models, Vijay Srinivasan 164. Handbook of Mechanical Alloy Design, edited by George E.Totten, Lin Xie, and Kiyoshi Funatani 165. Structural Analysis of Polymeric Composite Materials, Mark E.Tuttle 166. Modeling and Simulation for Material Selection and Mechanical Design, edited by George E.Totten, Lin Xie, and Kiyoshi Funatani 167. Handbook of Pneumatic Conveying Engineering, David Mills, Mark G. Jones, and Vijay K.Agarwal 168. Clutches and Brakes: Design and Selection, Second Edition, William C. Orthwein 169. Fundamentals of Fluid Film Lubrication: Second Edition, Bernard J. Hamrock, Steven R.Schmid, and Bo O.Jacobson 170. Handbook of Lead-Free SolderTechnology for Microelectronic Assemblies, edited by Karl J.Puttlitz and Kathleen A.Stalter 171. Vehicle Stability, Dean Karnopp 172. Mechanical Wear Fundamentals and Testing: Second Edition, Revised and Expanded, Raymond G.Bayer 173. Liquid Pipeline Hydraulics, E.Shashi Menon 174. Solid Fuels Combustion and Gasification, Marcio L.de Souza-Santos 175. Mechanical Tolerance Stackup and Analysis, Bryan R.Fischer 176. Engineering Design for Wear, Raymond G.Bayer 177. Vibrations of Shells and Plates: Third Edition, Revised and Expanded, Werner Soedel 178. Refractories Handbook, edited by Charles A.Schacht 179. Practical Engineering Failure Analysis, Hani Tawancy, Halim Hamid, Nureddin M.Abbas 180. Mechanical Alloying and Milling, C.Suryanarayana Additional Volumes in Preparation Progressing Cavity Pumps, Downhole Pumps, and Mudmotors, Lev Nelik Design of Automatic Machinery, Stephen J.Derby Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 9. MechanicalVibration:Analysis, Uncertainties, and Control, Second Edition, Revised and Expanded, Haym Benaroya Practical Fracture Mechanics in Design: Second Edition, Revised and Expanded, Arun Shukla Spring Design with an IBM PC, Al Dietrich Mechanical Design Failure Analysis: With Failure Analysis System Software for the IBM PC, David G.Ullman Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 10. Solid Fuels Combustion and Gasification Modeling, Simulation, and Equipment Operation State University at Campinas São Paolo, Brazil Marcio L.de Souza-Santos MARCEL DEKKER, INC. NEW YORK • BASEL Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 11. Transferred to Digital Printing 2005 Although great care has been taken to provide accurate and current information, neither the author(s) nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage, or liability directly or indirectly caused or alleged to be caused by this book. The material contained herein is not intended to provide specific advice or recommendations for any specific situation. Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress. ISBN: 0-8247-0971-3 Headquarters Marcel Dekker, Inc., 270 Madison Avenue, NewYork, NY 10016, U.S.A. tel: 212–696–9000; fax: 212–685–4540 Distribution and Customer Service Marcel Dekker, Inc., Cimarron Road, Monticello, NewYork 12701, U.S.A. tel: 800–228–1160; fax: 845–796–1772 Eastern Hemisphere Distribution Marcel Dekker AG, Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41–61–260–6300; fax: 41–61–260–6333 World Wide Web http://www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright © 2004 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 12. …the history of science—by far the most successful claim to knowledge accessible to humans—teaches that the most we can hope for is successive improvement in our understanding, learning from our mistakes, an asymptotic approach to the Universe, but with the proviso that absolute certainty will always elude us. Carl Sagan The Demon-Haunted World: Science as a Candle in the Dark Ballantine Books, 1996 to Laura, Daniel and Nalva Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 13. v Preface Contrary to general perception, the importance of coal and biomass as energy resources continues to increase. Special attention has been given to biomass due to its renewable and overall zero carbon dioxide generation aspects. Therefore, it is not surprising that the number of professionals and graduate students entering the field of power generation based on solid fuels is increasing. However, unlike specialized researchers, they are not interested in deep considerations based on exhaustive literature reviews of specialized texts. Obviously, works in that line are very important; however they assume an audience of accomplished mathematical modelers. Therefore, they do not have the preoccupation of presenting the details on how, from fundamental and general equations, it is possible to arrive at a final model for an equipment or process. Those beginning in the field are not interested in the other extreme, i.e., simple and mechanistic description of equipment design procedures or instruction manuals for application of commercial simulation packages. Their main preoccupations are: • Sufficient familiarity with the fundamental phenomena taking place in the equipment or processes • Knowledge of basic procedures for modeling and simulation of equipment and systems. • Elaborate procedures or methods to predict the behavior of the equipment or processes, mainly for cases where there are no commercially available simulators. Even when simulators are available, to be able to properly set the conditions asked as inputs by the simulator, to evaluate the applicability of possible solutions, and to choose among various alternatives. • The use those instruments to help solve problems and situations in the field. • Building confidence for decision making regarding process improvements and investments. Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 14. vi Preface On the other hand, experience shows that a good route to acquire real and testable understanding of a subject in processing is to develop models and their respective computer simulators. The feeling of accomplishment achieved when one is capable of developing one’s own simulator, however simple, is fantastic. This would be the crowning achievement of accumulated knowledge in the subject. The simulation program becomes a source of improvements, not to mention leading to a whole set of other advantages, as detailed later. The book is essential to graduate students, engineers, and other professionals with a strong scientific background entering the area of solid fuel combustion and gasification, but needing a basic introductory course in mathematical modeling and simulation. The text is based on a course given for many years for professionals and graduate students. In view of the hands-on approach, several correlations and equations are cited from the literature without the preoccupation on mathematical demonstrations of their validity. References are provided and should be consulted by those interested in more details. Despite the specific focus on combustion and gasification, the basic methods illustrated here can be employed for modeling a wide range of other processes or equipment commonly found in the processing industry. Operations of equipment such as boilers, furnaces, incinerators, gasifiers, and any others associated with combustion or gasification phenomena involves a multitude of simultaneous processes such as heat, mass and momentum transfers, chemical kinetics of several reactions, drying, and pyrolysis, etc. These should be coherently combined to allow reasonable simulation of industrial units or equipment. This book provides the relevant basic principles. It is important to emphasize the need for simple models.As mentioned before, most field or design engineers cannot afford to spend too much time on very elaborate and complex models. Of course, there are several levels to which models can be built. Nevertheless, one should be careful with models that are too simple or too complex. The low extreme normally provides only superficial information while the other usually takes years to develop and often involves considerable computational difficulties due to convergence problems or inconsistencies. In the present text, the model complexity is extended just to the point necessary to achieve a reasonable representation of the corresponding equipment. For instance, the examples are limited to two dimensions and most of the models are based on a one-dimensional approach. This may sound simplistic; however, the level of detail and usefulness of results from such simulations are significant. Additionally, the book can also be used as an introduction to more complex models. The main strategy of the book is to teach by examples. Besides the significant fraction of industrial equipment operating with suspensions of pulverized solid Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 15. Preface vii fuels, the specific cases of moving and fluidized bubbling beds have been selected because they: Cover much of the equipment related to combustion and gasification of solid fuels found in industry. In the particular case of fluidized beds, the fraction of equipment employing that technique has continually increased. In fact several more conventional boilers and furnaces operating with suspensions have been retrofitted to fluidized beds. Allow easy-to-follow examples of how simplifying assumptions regarding the operation of real industrial equipment can be set. Permit relatively quick introduction of fundamental equations without the need for overly complex treatments. Provide simple examples applying model and simulation techniques and how these can be put together to write a simulation program. Allow easier comparisons between real operational data and simulation results. In addition, the book contains basic descriptions of combustion and gasification processes, including suspension or pneumatic transport. Several fundamental aspects are common and can be applicable in studies of any technique, such as: zero-dimensional mass and energy balances, kinetics of gas and solid reactions, heat and mass transport phenomena and correlations, and pressure losses though air or gas distributors. Although the basic concepts of momentum, heat, and mass transfer phenomena can be found in several texts, the fundamental equations for such processes are included here, minimizing the need to consult other texts. Concepts usually learned in graduate-level engineering courses will be sufficient. The same is valid for thermodynamics, fundamentals of chemical kinetics, and applied mathematics—mainly concerning aspects of differential equations. To summarize, the book: • Shows several constructive and operational features of equipment dealing with combustion and gasification of solid fuels, such as coal, biomass, and solid residues, etc. • Presents basic aspects of solid and gas combustion phenomena • Introduces the fundamental methodology to formulate a mathematical model of the above equipments • Demonstrates possible routes from model to workable computer simulation program • Illustrates interpretations of simulation results that may be applied as tools for improving the performance of existing industrial equipment or for optimized design of new ones Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 16. viii Preface of solid-gas systems and main characteristics of combustion and gasification of zero-dimensional models with the objective of allowing verification of overall relations between inputs and outputs of any general process, including combustors and gasifiers. reactor. Of course, it is not the intention to present any model for flames; that is beyond the scope of this introductory book. However, it is useful to introduce standard considerations regarding mathematical modeling and the application first example of a model for solid fuel combustion and gasification equipment, program to simulate the model introduced in Chapter 10. in order to build a workable simulation program. The chapter also presents comparisons between measured parameters obtained from a real operation of moving-bed gasifier and results from a simulation program based on the model several already given enable the writing a computer program for fluidized bed cases of fluidized bed combustors as Chapter 12 for moving bed combustors and gasifiers. Almost all the chapters include exercises. They will stimulate the imagination and build confidence in solving problems related to modeling and simulation. The relative degree of difficulty or volume of work expected is indicated by an increasing number of asterisks—problems marked with four asterisks usually require solid training in the solution of differential equations or demand considerable work. Marcio L.de Souza-Santos Copyright © 2004 by Marcel Dekker, Inc. It is organized as follows. Chapter 1 presents some generally applicable notions concerning modeling and simulation. Chapter 2 shows main characteristics of solid fuels, such as coals and biomasses. Chapter 3 introduces basic concepts equipments. Chapter 4 provides formulas and methods to allow first calculations regarding solid fuel processing. Chapter 5 describes the fundamental equations Chapter 6 introduces a very basic and simple first-dimension model of a gas of mass, energy, and momentum transfer equations. Chapter 7 describes the using the case of moving-bed combustor or gasifier. Chapters 8 and 9 introduce methods to compute gas-gas and gas-solid reaction rates. Chapter 10 introduces and constitutive equations and methods that may be used to build a computer modeling of drying and pyrolysis of solid fuels. Chapter 11 presents auxiliary Chapter 12 shows how to put together all the information previously given described earlier. Chapter 13 repeats the same approach used for Chapter 7, but now pertaining to bubbling fluidized-bed combustors and gasifiers. Chapters 14 and 15 provide correlations and constitutive equations that together with combustors, boilers, and gasifiers. Chapter 16 has the same objective for the Download From Boilersinfo.com
  • 17. ix Acknowledgments It is extremely important to acknowledge the help of various colleagues whom I had the pleasure to work with, in particular to Alan B.Hedley (University of Sheffield, U.K.), Francisco D.Alves de Souza (Institute for Technological Research, São Paulo, Brazil), and former colleagues at the Institute of Gas Technology (Chicago). I appreciate the collaboration of several students and friends, who pointed out errors and made suggestions. I also thank John Corrigan and the staff of Marcel Dekker, Inc. for their help during all the aspects of the publication process. Finally, I am also grateful to the State University of Campinas (UNICAMP) and colleagues at the Energy Department of Mechanical Engineering for their support. Marcio L.de Souza-Santos Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 18. xi Nomenclature ai parameters or constants (dimensionless) a general parameter or coefficient (dimensions depend on the application) or ratio between the radius of the nucleus and the original particle or Helmoltz energy (J kg-1 ) â activity coefficient (dimensionless) A area (m2 ) or ash (in chemical reactions) ae air excess (dimensionless) b exergy (J kg-1 ) B coefficient, constant or parameter (dimensions depend on the application) c specific heat at constant pressure (J kg-1 K-1 ) C constants or parameters to be defined in each situation COC1(j) coefficient of component j in the representative formula of char (after drying and devolatilization of original fuel) (dimensionless) COC2(j) coefficient of component j in the representative formula of coke (due to tar coking) (dimensionless) COF(j) coefficient of component j in the representative formula of original solid fuel (dimensionless) COF(j) coefficient of component j in the representative formula of original solid fuel (dimensionless) Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 19. xii Nomenclature COT(j) coefficient of component j in the representative formula of tar (dimensionless) COV(j) coefficient of component j in the representative formula of volatile fraction of the original solid fuel (dimensionless) d diameter (m) dP particle diameter (m) Dj diffusivity of component j in the phase or media indicated afterwards (m2 s-1 ) activation energy of reaction i (J kmol-1 ) É factor or fraction (dimensionless) Ébexp expansion factor of the bed or ratio between its actual volume and volume at minimum fluidization condition (dimensionless) É514 total mass fractional conversion of carbon fmoist mass fractional conversion of moisture (or fractional degree of drying) ÉV mass fractional conversion of volatiles (or degree of devolatilization) Éfc mass fraction conversion of fixed carbon Ém mass fraction of particles kind m among all particles present in the process (dimensionless) Éair air excess (dimensionless) Éfr fuel ratio factor used in reactivity calculations (dimensionless) F mass flow (kg s-1 ) g acceleration of gravity (m s-2 ) or specific Gibbs function (J/kg) G mass flux (kg m-2 s-1 ) variation of Gibbs function related to reaction i (J kmol-1 ) h enthalpy (J kg-1 ) H height (m) HHV high heat value (J kg-1 ) i inclination relative to the horizontal position (rad) I variable to indicate the direction of mass flow concerning a control volume (+1 entering the CV; -1 leaving the CV) jj mass flux of component j due to diffusion process (kg m-2 s-1 ) kj kinetic coefficient of reaction i (s-1 ) (otherwise, unit depends on the reaction) kt specific turbulent kinetic energy (m2 s-2 ) Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 20. Nomenclature xiii k0i preexponential coefficient of reaction i (s-1 ) (otherwise, unit depends on the reaction) Ki equilibrium coefficient for reaction i (unit depend on the reaction and notation) K0i preexponential equilibrium coefficient for reaction i (unit depend on the reaction and notation) l mixing length (m) L coefficient used in devolatilization computations (dimensionless) Lgrate length of grate (m) LT length of tube (m) LHV low heat value (J kg-1 ) n number of moles nCP number of chemical species or components nCV number of control volumes nG number of chemical species or components in the gas phase nS number of chemical species or components in the solid phase nSR number of streams Nj mass flux of component j referred to a fixed frame of coordinates (kg m-2 s-1 ) M mass (kg) Mj molecular mass of component j (kmol/kg) NAr Archimedes number (dimensionless) NBi Biot number (dimensionless) NNu Nusselt number (dimensionless) NPe Peclet number (dimensionless) NPr Prandtl number (dimensionless) NRe Reynolds number (dimensionless) NSc Schmidt number (dimensionless) NSh Sherwood number (dimensionless) p index for the particle geometry (0=planar, 1=cylindrical, 3= sphere) pj partial pressure of component j (Pa) P pressure (Pa) q energy flux (W m-2 ) rate of energy generation (+) or consumption (-) of an equipment or system (W) r radial coordinate (m) ri rate of reaction i (for homogeneous reactions: kg m -3 s- 1 ; for heterogeneous reactions: kg m-2 s-1 ) Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 21. xiv Nomenclature R equipment radius (m) R universal gas constant (8314.2 J kmol-1 K-1 ) RC rate of energy transfer to (if positive) or from (if negative) the indicated phase due to convection [W m- 3 (of reactor volume or volume of the indicates phase)] Rcond rate of energy transfer to (if positive) or from (if negative) the indicated phase due to conduction [W m- 3 (of reactor volume or volume of the indicated phase)] Rh rate of energy transfer to (if positive) or from (if negative) the indicated phase due to mass transfer between phases [W m-3 (of reactor volume or volume of the indicated phase)] Rj rate of component j generation (if positive) or consumption (if negative) by chemical reactions (kg m-3 s-1 ). If in molar basis (~) the units are (kmol m-3 s-1 ). Rkind,j rate of component j generation (if positive) or consumption (if negative) by chemical reactions. Units vary according to the “kind” of reaction. If the subscript indicates homogeneous reactions the units are kg m-3 (of gas phase) s-1 , if heterogeneous reactions in kg m-2 (of external or of reacting particles) s-1 . RM,G,j total rate of production (or consumption if negative) of gas component j [kg m-3 (of gas phase) s-1 ] RM,S,j total rate of production (or consumption if negative) of solid-phase component j [kg m-3 (of reacting particles) s-1 ] RQ rate of energy generation (if positive) or consumption (if negative) due to chemical reactions [W m-3 (of reactor volume or volume of the indicated phase)] RR rate of energy transfer to (if positive) or from (if negative) the indicated phase due to radiation [W m-3 (of reactor volume or volume of the indicated phase)] Rheat heating rate imposed on a process (K/s) s entropy (J kg-1 K-1 ) S cross-sectional area (m2 ). If no index, it indicates the cross-sectional area of the reactor (m2 ). t time (s) T temperature (K) T* reference temperature (298 K) Te ration between activation energy and gas constant ( ) (K) Copyright © 2004 by Marcel Dekker, Inc. ∼ Download From Boilersinfo.com
  • 22. Nomenclature xv u velocity (m s-1 ) U gas superficial velocity (m s-1 ) or resistances to mass transfer (s m-2 ) ureduc reduced gas velocity (dimensionless) v specific volume (m3 kg-1 ) V volume (m3 ) x coordinate or distance (m) xj mole fraction of component j (dimensionless) X elutriation parameter (kg sms1 ) y coordinate (m) or dimensionless variable Y rate of irreversibility generation at a control volume (W) wj mass fraction of component j (dimensionless) W . rate of work generation (+) or consumption (-) by an equipment or system (W) z vertical coordinate (m) Z compressibility factor (dimensionless) Greek Letters α coefficient of heat transfer by convection (W m-2 K-1 ) αm relaxation coefficient related to momentum transfer involving solid phase m (s-1 ) β coefficient (dimensionless) or mass transfer coefficient (m s-1 ) χ number of atoms of an element (first index) in a molecule of a chemical component (second index) unit vector (m) ε void fraction (dimensionless) ε‘ emissivity (dimensionless) εt dissipation rate of specific turbulent kinetic energy (m2 s-3 ) γ tortuosity factor Φ Thiele modulus Γ rate of fines production due to particle attrition (kg s-1 ) η efficiency or effectiveness coefficient τ efficiency coefficient ϕ particle sphericity ␭ thermal conductivity (W m-1 K-l ) Λ parameter related to mass and energy transfer µ viscosity (kg m-1 s-1 ) or chemical potential (J kg -1 ) Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 23. xvi Nomenclature vij stoichiometry coefficient of component j in reaction i θ angular coordinate solid particle friability (m-l ) ρ density (unit depends on the reaction and notation) ρp apparent density of particle (kg m-3 ) ρj mass basis concentration of component j (kg m-3 ) (in some situations the component j can be indicated by its formula) shear stress tensor (Pa) ω Pitzer’s acentric factor (dimensionless) ϕ air ratio (dimensionless) σ Stefan-Boltzmann constant (W m-2 K-4 ) σv Standard deviation for distributed energy devolatilization model chemical component formula ζ particle porosity (m3 of pores/m3 of particle) ψ mass transfer coefficient (s-1 if between two gas phases, kmol m-2 s-1 if between gas and solid) Ω parameter of the Redlich-Kwong equation of state related to mass and energy transfers. Other gradient operator Laplacian operator Superscripts → rector or tensor – time averaged fluctuation or perturbation ~ in molar basis relative concentration (dimensionless) ‘ number fraction “ area fraction “‘ volume fraction s for particles smaller than the particles whose kind and level are indicated in the subscript Copyright © 2004 by Marcel Dekker, Inc. (dimensionless) or (only in Appendix C) a parameter Download From Boilersinfo.com
  • 24. Nomenclature xvii Subscripts Numbers as subscripts may represent sequence of variables, chemical species or reactions. In the particular case of chemical species the number would be equal to or greater than 19. In the case of reactions it will be clear when the number indicates reaction number.The numbering for components and reactions 0 at reference or ideal condition a at the nucleus-outer-shell interface A shell or residual layer air air app apparent (sometimes this index does not appear and should be understood, as in, for instance ρp=ρp,app) aro aromatic ash ash av average value b based on exergy B bubble bexp related to the expansion of the bed bri bridges bulk bulk c critical value C convection contribution (in some obvious situations, it would represent carbon) car carbonaceous solid char char cond conduction contribution CIP coated inert particle CP referred to the chemical component COF, COV, COT see main nomenclature above CSP Coke Shell Particle CV referred to the control volume or equipment cy related to the cyclone system d related to drying or dry basis D bed daf dry and ash-free basis dif diffusion contribution dist distributor E emulsion ental relative to enthalpy entro relative to entropy Copyright © 2004 by Marcel Dekker, Inc. is shown in Tables 8.1 to 8.5. Download From Boilersinfo.com
  • 25. xviii Nomenclature eq equilibrium condition exer relative to exergy f formation at 298 K and 1 atm fl fluid F freeboard fc fixed-carbon fuel related to fuel G gas phase h transfer of energy due to mass transfer H related to the circulation of particles in a fluidized bed (in some obvious situations, it would represent hydrogen) hom related to homogeneous (or gas-gas) reactions het related to heterogeneous (or gas-solid) reactions i I as at the feeding point ∞ at the gas phase far from the particle surface iCO component number iCV control volume (or equipment) number iSR stream number j chemical component (numbers are described in Chapter 8) J related to the internal surface or internal dimension K related to the recycling of particles, collected in the cyclone, to the bed l chemical element L at the leaving point or condition lam laminar condition m physical phase (carbonaceous solid, m=1; limestone or dolomite, m=2; inert solid, m=3; gas, m=4) mratio mixing ratio M mmass generation or transfer max maximum condition mb minimum bubbling condition min minimum condition mf minimum fluidization condition moist moisture or water mon monomers mtp metaplast orif orifices in the distributor plate N nucleus or core (in some obvious situations, it would represent nitrogen) Copyright © 2004 by Marcel Dekker, Inc. reaction i (numbers are described in Chapter 8) Download From Boilersinfo.com
  • 26. Nomenclature xix O at the referred to external or outside surface (in some obvious situations, it would represent oxygen) p particle (if no other indication, property of particle is related to apparent value) P at constant pressure per peripheral groups pores related to particle pores plenum average conditions in the plenum below the distributor plate or device Q chemical reactions r at reduced condition R related to radiative heat transfer real related to real or skeletal density of solid particles sat at saturation condition S solid phase or particles (if indicated for a property, such as density, it means apparent particle density) SR referred to the stream sit immobile recombination sites T terminal value or referred to tubes tar tar to mixing-take-over value tur turbulent condition U unexposed-core or shrinking-core model v related to devolatilization V volatile W wall X exposed-core model Y related to entrainment of particles Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 27. xxi Contents Preface v Nomenclature xi 1 Basic Remarks on Modeling and Simulation 1 1.1 Experiment and Simulation 1 1.2 A Classification for Mathematical Models 10 1.3 Exercises 17 2 Solid Fuels 18 2.1 Introduction 18 2.2 Physical Properties 19 2.3 Chemical Properties 21 2.4 Thermal Treatment 24 2.5 Gasification and Combustion 35 2.6 Exercises 37 Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 28. xxii Contents 3 Equipment and Processes 38 3.1 Introduction 38 3.2 Elements of Gas-Solid Systems 38 3.3 Moving Bed 43 3.4 Fluidized Bed 48 3.5 Suspension or Pneumatic Transport 63 3.6 Some Aspects Related to Fuels 67 4 Basic Calculations 69 4.1 Introduction 69 4.2 Computation of Some Basic Parameters 70 4.3 Tips on Calculations 80 4.4 Observations 83 Exercises 83 5 Zero-Dimensional Models 86 5.1 Introduction 86 5.2 Basic Equations 87 5.3 Species Balance and Exiting Composition 93 5.4 Useful Relations 99 5.5 Summary for 0D-S Model 105 5.6 Flame Temperature 106 Exercises 109 6 Introduction to One-Dimensional, Steady-State Models 112 6.1 Definitions 112 6.2 Fundamental Equations 113 6.3 Final Comments 125 Exercises 126 7 Moving-Bed Combustion and Gasification Model 127 7.1 Introduction 127 7.2 The Model 128 Exercises 144 Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 29. Contents xxiii 8 Chemical Reactions 146 8.1 Homogeneous/Heterogeneous Reactions 146 8.2 Numbering Chemical Components 147 8.3 A System of Chemical Reactions 147 8.4 Stoichiometry 150 8.5 Kinetics 152 8.6 Final Notes 157 Exercises 159 9 Heterogeneous Reactions 160 9.1 Introduction 160 9.2 General Form of the Problem 163 9.3 Generalized Treatment 172 9.4 Other Heterogeneous Reactions 174 Exercises 174 10 Drying and Devolatilization 178 10.1 Drying 178 10.2 Devolatilization 181 Exercises 208 11 Auxiliary Equations and Basic Calculations 209 11.1 Introduction 209 11.2 Total Production Rates 209 11.3 Thiele Modulus 214 11.4 Diffusivities 215 11.5 Reactivity 218 11.6 Core Dimensions 219 11.7 Heat and Mass Transfer Coefficients 220 11.8 Energy-Related Parameters 222 11.9 A Few Immediate Applications 225 11.10 Pressure Losses 233 Exercises 243 Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 30. xxiv Contents 12 Moving-Bed Simulation Program and Results 245 12.1 Introduction 245 12.2 From Model to Simulation Program 245 12.3 Samples of Results 254 Exercises 261 13 Fluidized-Bed Combustion and Gasification Model 264 13.1 Introduction 264 13.2 The Mathematical Model 264 13.3 Boundary Conditions 276 Exercises 280 14 Fluidization Dynamics 282 14.1 Introduction 282 14.2 Splitting of Gas Injected into a Bed 283 14.3 Bubble Characteristics and Behavior 288 14.4 Circulation of Solid Particles 291 14.5 Entrainment and Elutriation 300 14.6 Particle Size Distribution 302 14.7 Recycling of Particles 304 14.8 Segregation 305 14.9 Areas and Volumes at Freeboard Section 306 14.10 Mass and Volume Fractions of Solids 307 14.11 Further Studies 308 Exercises 308 15 Auxiliary Parameters Related to Fluidized-Bed Processes 309 15.1 Introduction 309 15.2 Mass Transfers 309 15.3 Heat Transfers 312 15.4 Parameters Related to Reaction Rates 322 16 Fluidized-Bed Simulation Program and Results 323 16.1 The Block Diagram 323 16.2 Samples of Results 326 16.3 Exercises 364 Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 31. Contents xxv Appendix A The Fundamental Equations of Transport Phenomena 366 Appendix B Notes on Thermodynamics 372 B.1 Heat and Work 372 B.2 Chemical Equilibrium Equation 374 B.3 Specific Heat 376 B.4 Correction for Departure from Ideal Behavior 376 B.5 Generalized 0D-S Models 379 B.6 Heat Values 386 B.7 Representative Formation Enthalpy of a Solid Fuel 387 Appendix C Possible Improvements on Modeling Heterogeneous Reactions 389 C.1 General Mass Balance for a Particle 390 C.2 Generalized Energy Balance for a Particle 390 Appendix D Improvements on Various Aspects 396 D.1 Rate of Particles Circulation in the Fluidized Bed 396 D.2 Improvements on the Fluidized-Bed Equipment Simulator (FBES) 399 Appendix E Basics of Turbulent Flow 400 E.1 Momentum Transfer 400 E.2 Heat and Mass Transfers 403 E.3 Reaction Kinetics 404 Appendix F Classifications of Modeling for Bubbling Fluidized-Bed Equipment 406 F.1 Main Aspects 406 Appendix G Basics Techniques of Kinetics Determination 408 References 412 Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 32. Solid Fuels Combustion and Gasification Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 33. 1 1 Basic Remarks on Modeling and Simulation 1.1 EXPERIMENT AND SIMULATION Over the years, among other comments, I have heard remarks such as: • “If the equipment is working, why all the effort to simulate it?” • “Can’t we just find the optimum operational point by experimentation?” The basic answer to the first question is: Because it is always possible to improve and, given an objective, to optimize an existing operation. Optimization not only increases competitiveness of a company but may also determine its chances of survival. For the second question the answer is: Because experimentation is much more expensive than computation. In addition, if any variable of the original process changes, the costly experimentally achieved optimum is no longer valid. As an example, if a thermoelectric power unit starts receiving a coal with properties different from the one previously used, the optimum operational point would not be the same. It is also important to remember that the experimentally found optimum at a given scale is not applicable to any other scale, even if several conditions remain the same. In fact, no company today can afford not to use computer simulation to seek optimized design or operation of its industrial processes. Apparently, one may think that these remarks could hide some sort of prejudice against experimental methods. Nothing could be further from the truth. Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 34. 2 Chapter 1 There is no valid theory without experimentation. A model or theory is not applicable unless experimentally verifiable. In other words, a mathematical model and consequent simulation program, no matter how sophisticated, is useless if it cannot reproduce the real operation it is intended to simulate within an acceptable degree of deviation. Of course, it would also not be able to predict the behavior of future equipment with some degree of confidence, and therefore it would also be useless as design tool. Before going any further, let us consideration some experimental and theoretical procedures. 1.1.1 The Experimental Method One may ask about the conditions that allow the application of experimental method to obtain or infer valid information concerning the behavior of a process. For this, the following definitions are necessary: • Controlled variables are those whose values can, within a certain range, be imposed freely, for example, the temperature of a bath heated by electrical resistances. • Observed variables are those whose values can be measured, directly or indirectly. An example is the thermal conductivity of the fluid in the bath where the temperature has been controlled. Experiments are a valid source of information if during the course of tests the observed variables are solely affected by the controlled variables. Any other variable should be maintained at constant value. Example 1.1 Let us imagine that someone is interested in determining the dependence on temperature of thermal conductivity of a bath or solution with a given composition and under a given pressure. Therefore, the observed variable would be the thermal conductivity, and the solution average temperature the controlled one. Thus, the bath thermal conductivity would be measured at various levels of its temperature. During the tests, the chemical composition and pressure of the previous bath should be maintained constant. In doing so, it will be possible to correlate cause and effect, i.e., the values of observed and controlled variables. These correlations may take the form of graphs or mathematical expressions. Example 1.2 The SO2 absorption by limestone can be represented by the following reaction: Experiments to determine the kinetics of the reaction should be conducted under carefully chosen conditions; for example, Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 35. Basic Remarks on Modeling and Simulation 3 • The sample of limestone should be put in a barge where it is exposed to various mixtures of SO2 and O2. • The pressure should be maintained constant. • The sample of limestone should have its maximum particle size reduced to a point where no interference of particle size on the reaction rate could be noticed. The interference is caused by the resistance to mass transfer of gas components through the porous structure of the particle. • The temperature should be controlled. This can be achieved by electrical heating of the barge. In addition, influences of temperature differences between the various regions of the sample should be reduced or eliminated. This can be accomplished by using thin layers of sample and through high heat transfer coefficients between gas and solid sample. One method would be to increase the Reynolds number or the relative velocity between gas and particles. Of course, this has limitations because the gas stream should carry no solid. • The concentrations of reactants (SO2 and O2) in the involving atmosphere should be controlled or kept constant. Therefore, a fresh supply of the reacting mixture should be guaranteed. • Each test should be designed to take samples of the CaO and CaSO4 mixture for analysis throughout the experiment, so; the number of controlled variables could be reduced to temperature and concentration of SO2 and O2 in the incoming gas stream. The conversion of CaO into CaSO4 would be the observed variable and it would be measured against time. In addition, the number of experimental tests should be as high as possible to eliminate bias. This is possible to verify by quantitative means. Even after all these precautions, the determined kinetics is valid only for the particular kind of limestone because possible catalyst or poisoning activity due to presence of other chemical components in the original limestone has not been taken into account. The above examples show the typical scientific experimental procedure. It allows observations that may be applied to understand the phenomenon. Within an established range of conditions, the conclusions do not depend on a particular situation. Therefore, they can be generalized and used in mathematical models that combine several other phenomena. It is also important to be aware that experimental optimization of a process presents stringent limitations due to: 1. Variables: The number of variables that interfere in a given process is usually much higher than the number of controllable variables. Imposed variation on a single input may represent variations on several process conditions and, as consequence, on several observed variables. Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 36. 4 Chapter 1 2. Scale effects: Physical-chemical properties of substances handled by the process do not obey a linear dependence with the equipment geometry such as length, area, and volume. For instance, one may double the volume of a chemical reactor, but this does not double the density or viscosity of streams entering or leaving the reactor. In some cases, scaling-up does not even allow geometry similarity with the experimental or pilot unit. To better illustrate the point of false inference on the validity of an experimental procedure, let us refer to the following example. Example 1.3 Someone is intending to scale-up a simple chemical reactor, as shown in Figure 1.1. The reactants A and B are continuously injected and the reaction between them is exothermic. The product C, diluted in the exit stream, leaves the reactor continuously. Water is used as cooling fluid and runs inside the jacket. The agitator maintains the reacting media as homogeneously as possible. There is also an optimum temperature that leads to a maximum output of the C component. Let us suppose that the optimization of this operation was carried and the correct water flow into the jacket was found in order to give the maximum concentration of C in the product. To achieve this, a pilot was built and through experiments the best operational condition was set. Now, the engineering intends to build a reactor to deliver a mass flow of C ten times higher than the achieved in the pilot. Someone proposed to keep the same geometric shape of the pilot, which is H/D (H=level filled with fluid, D=diameter) equal to 2. However, to obtain the same concentration of C in the products, the residence time of reactants in the volume should be maintained. Residence time τ is usually defined by FIG. 1.1 Scheme of a water-jacketed reactor. Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 37. Basic Remarks on Modeling and Simulation 5 (1.1) where V is the volume of the reactor (filled with liquid reactants), ρ is the average density of the fluid and F is the mass flow of injected fluids into the reactor. Assuming a cylindrical shape reactor, the volume is given by (1.2) The relation should be set in order to maintain the same residence time. V=10V0 (1.3) where index 0 indicates the pilot dimensions. To keep H/D ratio equal to 2, the new diameter would be D=101/3 D0 (1.4) The area for heat transfer (neglecting the bottom) is given by A=πHD (1.5) Therefore, the area ratio would be (1.6) Using 1.4, A=102/3 A0 (1.7) By this option, the industrial-scale reactor would have a heat exchange area just 4.64 times larger than the one at the pilot unit. The cooling would not be as efficient as before. Reversibly, if one tries to multiply the reactor wall area by 10, the volume would be much larger than 10 times the volume of the pilot.Actually, this would increase the residence time of the reactants by more than 31 times. This is not desirable because: • The investment in the new reactor would be much larger than intended. • The reactants would sit idle in the reactor, or the residence time of the reactants would be much larger than the time found through optimization tests. The only possibility is to modify the H/D ratio in order to maintain the same area/volume relation as found in the pilot. The only solution is a diameter equal to the diameter of the pilot. Therefore, to multiply the volume by 10, the new length of level would be 10 times the length of the pilot. This solution would Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 38. 6 Chapter 1 not be very convenient from the operational point of view, not for the layout of the plant where it would be installed. This demonstrates that not even a similar geometric shape could be kept in a scaling-up process. To maintain the shape of the pilot and multiply the volume by 10, a solution might be to insert a coil inside the reactor to provide the extra heat transfer area. Example 1.4 Another example is given in the case of a boiler. Someone wants to optimize the design of a boiler by experimental tests with a small pilot unit.The unit is composed of a furnace with a tube bank, and coal is continuously fed into it. Water runs into the tube bank and the bank can be partially retreated from the furnace in a way to vary the heat exchange area. The tests show that, by maintaining a given fuel input, there is a certain area of tubes that leads to a maximum rate of steam generation. The reason rests on two main influences, which play an important role in the boiler efficiency, as follows: 1. If the tube area increases, the heat transfer between the furnace and the tubes increases, leading to an increase in steam production. However, after a certain point, increases in the tube area lead to decreases in the average temperature in the furnace. Decreases in temperature decrease carbon conversion or fuel utilization and, therefore, decrease the rate of energy transferred to tubes for steam generation. 2. If the area of tubes decreases, the average temperature in the furnace increases and the carbon conversion increases. Therefore, more coal is converted to provide energy and may possibly leading to increases in the steam generation. However, after a certain point, due to insufficient tube area for heat transfer, the effect is just to increase the temperature of the gases in the chimney, therefore decreasing the efficiency of the boiler. In this way, the optimum or maximum efficiency for the boiler operation should be an intermediate point. However, it is not easy to find a solution because it would necessitate considering a great number of processes or phenomena, e.g., heat transfers of all kind between the particle, gases, and tubes, mass transfers among gases and particles, momentum transfers among those phases, several chemical reactions. To achieve this by experimental procedure would be a nightmare, if impossible. Example 1.5 Following the previous example, let us now imagine that someone tries to design a larger boiler, for instance, one to consume twice the previous amount of fuel. Among other possibilities, he could imagine two alternatives: a. To maintain the same ratio between the total area of tube surface and the mass flow of coal feeding (or energy input) employed at the optimum condition found at the pilot; Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 39. Basic Remarks on Modeling and Simulation 7 b. To maintain the same ratio between the total area of tube surface and the combustor volume employed at the optimum experimental condition. A very likely answer to this dilemma is: Neither of the above alternatives is the correct one. To better explain, let us consider the following relations, which are very strong simplifications of the problem: (1.8) (1.9) where = total rate energy input to the boiler furnace, (W) ƒc = fraction of fuel that is consumed in the furnace (dimensionless from 0 to 1). The unreacted fuel leaves the furnace with the stack gas or in the ashes. F = fuel feeding rate, kg/s hc = combustion enthalpy of the injected fuel, J/kg η = boiler efficiency, i.e., the ratio between the injected energy (through the fuel) into the furnace and the amount used to generate steam. A = total area of tube surface, m2 n = coefficient used to accommodate an approximate equation that accounts the differences between the laws of radiative and convective heat transfer processes; ΔT = average difference between the fluid that runs inside the tubes and the furnace interior, K αav = equivalent global (or average between inside and outside coefficients of the tubes) heat transfer (includes convection and radiation) between the fluid that runs inside the tubes and the furnace interior, W m-2 K-n ) Equations 1.8 and 1.9 are combined to write (1.10) Let us examine alternative (‘a’).As seen by Eq. 1.10, the area of tubes seems to be proportional to the fuel-feeding rate. However, assuming the same tube bank configuration as in the pilot, the bank area would not be linearly proportional to the furnace volume. Therefore, the average velocity of gases crossing the tube bank will be different from the values found in the pilot. As the heat transfer coefficient is a strong function of that velocity, it will also change. Looking at Eq. 1.10, it is easy to conclude that alternative (a) will not work. If one tries to Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 40. 8 Chapter 1 maintain the increase the volume at the same proportion of the tube bank area, the residence time (see Eq. 1.1) will not be the same as in the pilot. Therefore, the fuel conversion and the boiler efficiency will not be the same as the pilot, and alternative (b) would not work either. 1.1.2 The Theoretical Method It is too difficult for the human mind to interpret any phenomenon where more than three variables are involved. It is not a coincidence that the graphical representation of influences is also limited to that number of variables. Some researchers make invalid extrapolations of the experimental method and apply the results to multidimensional problems. For instance, try to infer the above kinetics of SO2 absorption using a boiler combustor where coal and limestone are added.As temperature and concentration (among several other variables) change from point to point in the combustion chamber, no real control over the influencing variables is possible in this case. The best that can be accomplished is the verification of some interdependence. The result of such a study might be used in the optimization of a particular application without the pretension to generalize the results or to apply them to other situations, despite possible similarities. On the other hand, the theoretical method is universal. If based on fundamental equations (mass, momentum, and energy conservation) and correlations obtained from well-conducted experimental procedure, the theoretical approach does not suffer from limitations due to the number of variables involved. Therefore, mathematical modeling is not a matter of sophistication, but the only possible method to understand complex processes. In addition, the simple fact that a simulation program is capable of being processed to generate information that describes, within reasonable degree of deviations, the behavior of a real operation is in itself a strong indication of the coherence of the mathematical structure. The most important properties of mathematical modeling and the respective simulation program can be summarized as follows: • Mathematical modeling requires much fewer financial resources than the experimental investigation. • It can be applied to study the conditions at areas of difficult or impossible access or where uncertainties in measurements are implicit. Such conditions may include very high temperatures, as usually found in combustion and gasification processes. Added to that, these processes normally involve various phases with moving boundaries, turbulence, etc. • It can be extended to infer the behavior of a process far from the tested experimental range. • It allows a much better understanding of the experimental data and results and therefore can be used to complement the acquired knowledge from experimental tests. Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 41. Basic Remarks on Modeling and Simulation 9 • Mathematical modeling can be used to optimize the experimental procedure and to avoid tests at uninteresting or even dangerous range of operations. • It can be employed during the scaling-up phase in order to achieve an optimized design of the equipment or process unit. This brings substantial savings of time and money because it eliminates or drastically reduces the need for intermediate pilot scales. • The model and respective program are not “static.” In other words, they can be improved at any time to expand the range of application, reliability, or to decrease the time necessary for the computations. • The model and the program can also be improved with more and better information available from experimental investigations. The results published in the literature concerning the basic phenomena involved in the simulated process or system can be seen as a constant source of information. Therefore, the program can be seen as a “reservoir of knowledge.” Mathematical modeling is not a task but a process. The development of a mathematical model, and its respective computer simulation program, is not a linear sequence where each step follows the one before. The process is composed by a series of forward and backward movements where each block or task is repeatedly revisited. One should be suspicious of simple answers. Nature is complex and the process of modeling it is an effort to represent it as closely as possible. The best that can be done is to improve the approximations in order to decrease deviations from the reality. A good simulation program should be capable of reproducing measured operational data within an acceptable level of deviation. In most cases, even deviations have a limit that cannot be surpassed. These are established by several constraints, among them: • Intrinsic errors in correlation obtained through experimental procedures (due to limitations in the precisions of measurements) • Available knowledge (literature or personal experience) • Basic level of modeling adopted (zero, one, or more dimensions) Therefore, only approximations—sometimes crude—of the reality are possible. It is advisable to go from simple to complex, not the other way around. Modeling is an evolutionary movement. Usually, there is a long way from the very first model to the more elaborate version. The first model should of course be mathematically consistent and at the same time very simple. It is important to include very few effects in the first trial. Several hypothesis and simplifications Copyright © 2004 by Marcel Dekker, Inc. These, as well other factors, are better discussed at Chapter 12. Download From Boilersinfo.com
  • 42. 10 Chapter 1 should be assumed; otherwise, the risk of not achieving a working model would be great. If one starts from the very simple, results might be obtained from computations. Then, comparisons against experimental or equipment operational data may provide information for improving the model. Measurements of variables during industrial operations seldom present fluctuations below 5% in relation to an average value. For instance, the average temperature of a stack gas released from an industrial boiler can easily fluctuate 30 K, for an average of 600 K. Therefore, if a model has already produced that kind of deviation against measured or published values, it might be better to consider stopping. Improvements in a model should be accomplished mainly by eliminating one (and just one) simplifying hypothesis at a time, followed by verification if the new version leads to representations closer to reality. If not, eliminate another hypothesis, and so on. On the other hand, if one starts from complex models, not even computational results may be obtainable. Even so, there would be little chance to identify where improvements should be made. If one needs to travel, it is better to have a runningVolkswagen Beetle than a Mercedes without wheels. 1.2 A CLASSIFICATION FOR MATHEMATICAL MODELS 1.2.1 Phenomenological versus Analogical Models Industrial equipment or processes operate by receiving physical inputs, processing those inputs, and delivering physical outputs. Among the usual physical inputs and outputs there are: • Mass flows • Compositions • Temperatures • Pressures In addition to these variables, heat and work may be exchanged through the control surface. The internal physical phenomena are the processes that transform inputs into outputs. The phenomenological model intends to reproduce these processes as closely as possible. The phenomenological models are based on: • Fundamental equations,* such as laws of thermodynamics and laws of mass, energy, and momentum conservation. * The fundamental laws of thermodynamics are found in any undergraduate and graduate-level conservation are found in any text of transport phenomena, such as Refs. 1–4. In addition,Appendix A summarizes the most important for the purposes of the present book. The constitutive equations necessary for the models present in the following chapters will be described during the discussions. Copyright © 2004 by Marcel Dekker, Inc. textbook. The main relations are repeated in Chapter 5 and Appendix B. Those related to Download From Boilersinfo.com
  • 43. Basic Remarks on Modeling and Simulation 11 • Constitutive equations, which are usually based on empirical or semiempirical correlations The combination of fundamental laws or equations and constitutive correlations may lead to valid models. These models are valid within the same range of the employed correlations. This brings some assurance that phenomenological models reflect reality in that range. Analogy models, although useful for relatively simple systems or processes, just mimic the behavior of a process, and therefore do not reflect reality. Examples of analogy models are, for instance, those based on mass-and-spring systems or on electric circuits. The computer simulation program based on a phenomenological model receives the input data, treats them according to the model in which it is based upon, and delivers the output or results. However, depending on the degree of sophistication, the model might provide much more information than simple descriptions of the properties and characteristics of the output streams. As mentioned before, it is extremely important to properly understand the role of process variables that are not accessible for direct or even indirect measurement. That information might be useful in the design controlling systems. In addition, the process of building up the phenomenological model requires the setting of relationships linking the various variables. Therefore, the combination of experimental observations with the theoretical interpretation usually leads to a much better understanding of the physical operation. The phenomenological models can be classified according several criteria. The first branching is set according to the amount of space dimensions considered in the model. Therefore, three levels are possible. A second branching considers the inclusion of time as a variable. If it is not included, the model is called steady state; otherwise, it is a dynamic model. In addition, several other levels can be added, for instance, • If laminar or turbulent flow conditions are assumed • If dissipative effects such as those provided by terms containing viscosity, thermal conductivity, and diffusivity are included The list could go on. However, in order to keep a simple basic classification for this introductory text, only the aspects of dimension and time are considered.A simple notation will be followed: 1. Zero-dimensional-steady, or 0D-S. It is the simplest level of modeling and includes neither dimension nor time as variable. 2. Three-dimensional-dynamic, or 3D-D. It includes three space dimensions and time as variables. Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 44. 12 Chapter 1 1.2.2 Steady-State Models Although the definition of steady-state regime is widely employed, some confusion may arise if not clearly understood. Therefore, let us take some lines to state it before further considerations. In relation to a given set of space coordinates, a steady-state regime for a control volume* will be established if: 1. The control surface does not deform or move. 2. The mass flows and space average properties of each input and output stream remain constant. 3. The rates of heat and work exchanges between the control volume and surrounds are constant. 4. Although conditions inside the control volume differ from point to point, they remain constant at each position. Most of industrial equipments operate at steady-state conditions. Rigorously, there is no such thing as a perfect steady-state operation. Even for operations that are supposed to be steady, some degree of fluctuations against time in variables such as temperature, concentration, or velocities occur. On the other hand, most of the time, several industrial processes operate within a range of conditions not very far from an average. Therefore, a good portion of those can be treated as such with high or at least reasonable accuracy. 1.2.2.1 0D-S Models Zero-dimensional-steady models set relations between input and output variables of a system or control volume without considering the details of the phenomena occurring inside that system or control volume. Therefore, no description or evaluation of temperature, velocity, or concentration profiles in the studied equipment is possible. Despite that, 0D-S models are very useful, mainly if an overall analysis of an equipment, or system composed of several equipments, is intended. Depending on the complexity of internal phenomena and the available information about a process or system, this may be the only achievable level of modeling. However, it should not be taken for granted because it may involve serious difficulties, mainly when many subsystems (or equipment) are considered in a single system. Since there is no description on how processes occur related to space, 0D-S models require assumptions such as chemical and thermodynamic equilibrium conditions of the output stream. On the other hand, hypotheses such as these could constitute oversimplifications and lead to false conclusions because: * Copyright © 2004 by Marcel Dekker, Inc. See Appendix B, Section B.1. Download From Boilersinfo.com
  • 45. Basic Remarks on Modeling and Simulation 13 • Rigorously, equilibrium at exiting streams would require infinite residence time of the chemical components or substances inside the equipment. Typical residence time of several classes of reactors, combustors, and gasifiers are seconds to minutes. Therefore, conditions far from equilibrium might be expected. • Determination of equilibrium composition at exiting streams requires the value of their temperatures. However, to estimate those temperatures, one needs to perform energy balance or balances. For that, the compositions and temperatures of the streams should be known to allow computation of enthalpies or internal energies of the exiting streams. Reiterative processes work well if the exiting streams are composed by just one or two components. However, reiterative processes with several nested convergence problems might become awkward computational problems. Most of these situations take huge amounts of time to achieve solutions, or even to impossibilities of arriving at solutions. • If the process includes gas-solid reactions—as in combustors or gasifiers—the conversion of reacting solid (coal or biomass, for instance) is usually unknown and therefore should be guessed. On the other hand, the bulk of conversion occurs at points of high temperature inside the equipment. That temperature is usually much higher than the temperatures of exiting streams (gas or solid particles). Therefore, to accomplish the energy balance for the control volume, one needs to guess some sort of average representative temperature at which the reactions and equilibrium should be computed.Apart from being artificial under the point of view of phenomenology, guesses of such average temperature usually are completely arbitrary. Experimental conditions should therefore be used to calibrate such models. Experimental conditions differ from one case to another and are therefore not reliable when a general model for a process or equipment operation is sought. Therefore, 0D-S models are very limited or might even lead to wrong conclusions. This is also valid for 0D-D models. In addition, they are not capable of predicting a series of possible operational problems because, despite relatively low temperatures of exiting streams, internal temperatures could surpass: Limits of integrity of wall materials Explosion limits Values that start runaway processes, etc. • 0D-S models are also extremely deficient in cases of combustion and gasification of solids because pyrolysis or devolatilization is present. That very complex process introduces gases and complex mixtures of organic and inorganic substances at particular regions of the equipment. The Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 46. 14 Chapter 1 compositions of those streams have strong influence on the composition and temperature of the exiting gas, even if equilibrium is assumed. 1.2.2.2 1D-S Models The second level of modeling is to assume that all properties or conditions inside the equipment vary only at one space coordinate. They constitute a considerable improvement in quality and quantity of information provided by the zero-dimensional models. Equilibrium hypotheses are no longer necessary and profiles of the variables, such as temperature, pressures, and compositions, throughout the willequipment can be determined. Of course, they might not be enough to properly represent processes where severe variations of temperature, concentration, and other parameters occur in more than one dimension. 1.2.2.3 2D-S Models Two-dimensional models may be necessary in cases where the variations in a second dimension can no longer be neglected. As an example, let us imagine the difference between a laminar flow and a plug-flow reactor. Figure 1.2 illustrates a reactor where exothermic reactions are occurring and heat can be exchanged with the environment through the external wall. In Figure 1.2a, the variations of temperature and composition in the axial direction are added to the variations in the radial direction. It is easy to imagine FIG. 1.2 Schematic views of (a) a laminar flow and (b) a plug-flow reactor. Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 47. Basic Remarks on Modeling and Simulation 15 that, due to the relatively smaller temperatures at the layer of fluid near the walls, small changes in composition provoked by chemical reactions occur there. This is a typical system that may require two-dimensional modeling to account for the correct exit conditions; otherwise, the average concentration at the exiting point cannot be computed with some degree of precision. Reversibly, plug-flow processes provide flat temperature, velocity, and concentration profiles. Highly turbulent flow or presence of packing inside the reactor provide the possibility to assume plug-flow regimes. Of course, the thin layer near the wall experiences drastic variations of temperature, but this is not a representative portion of the flowing mass. Therefore, a fair assumption is that variations in the radial coordinate could be neglected, as compared with variations in composition and temperature at the axial direction. This is a typical case where a 1D-S model might lead to good results. 1.2.2.4 3D-S Models Due to their usual complexity, 3D-S models are seldom adopted. However, they may, in some cases, be necessary. By this approach, all space coordinates are considered. On the other hand, if the model and simulation procedure are successful, a great deal of information about the process is obtained. For instance, imposed to the flowing fluid. In some of these cases a cylindrical symmetry can be assumed and a two-dimensional model might be enough for a good representation of the process, but for asymmetrical geometries 3D models are usually necessary.An example of such a process occurs inside commercial boilers burning pulverized fuels. Most of the combustion chambers have rectangular cross sections and internal buffers are usually present, not to mention tube banks. no symmetry assumption is possible or reasonable. On the other hand, and as everything in life, there is a price to be paid. Let us imagine what would be necessary to set a complete model. First, it would require the solution of the complete Navier-Stokes, or momentum conservation, equations. These should be combined with the equations of energy and mass conservation applied for all chemical species. All these equations ought to be written for three directions and solved throughout the reactor. Second, the number of boundary conditions is also high. Most of the time, these conditions involve not just given or known values at interfaces, but also derivatives. Moreover, boundary conditions might require complex geometric descriptions. For example, the injections of reactant streams at the feeding section may be made by such a complex distributing system that even setting the boundary condition would be difficult. When correlations and constitutive equations for all these parameters are included, the final set of mathematical equations is awesome. However, commercially available computational fluid dynamics (CFD) have evolved and are capable of solving Copyright © 2004 by Marcel Dekker, Inc. let us imagine the laminar-flow reactor (Figure 1.2a), where rotation or vortex is Since rotational flows as well as strong reversing flows are present (see Fig. 3.11), Download From Boilersinfo.com
  • 48. 16 Chapter 1 suchsystems.Verygoodresultsareobtainable,particularlyforsingle-phasesystems (gas-gas, for instance). Nonetheless, combustion and gasification of solid fuels still present considerable difficulties, mainly for cases of combustion and gasification of suspensions or pneumatic transported pulverized fuels. On the other hand, one must question the use of such an amount of information. Is it necessary to predict the details of the velocities, concentration, and temperature profiles in all directions inside the equipment? What is the cost- benefit situation in this case? Departing from a previous one- or two-dimensional model, would this three-dimensional model be capable of decreasing the deviations between simulation and real operation to a point that the time and money invested in it would be justifiable? Is it useful to have a model that generates deviations below the measurement errors? Finally, what would be necessary to measure in order to validate such a model against real operations? In this line, let us ask what sort of variables are usually possible to measure and what is the degree of precision or certainty of such measurements. Anyone who works or has worked in an industrial plant operation knows that is not easy to measure temperature profiles inside the given equipment. In addition, if combustion of solid fuel is taking place, composition profiles of gas streams and composition of solids are extremely difficult to determine. Alternatively, average values of temperatures, pressures, mass flows, and compositions of entering and leaving streams can be measured. Sometimes, average values of variables within a few points inside the equipment are obtainable.This illustrates the fact that those involved in mathematical modeling of particular equipment or process should be acquainted with its real operation. This would provide a valuable training that might be very useful when he or she decides to develop a simulation model and program. If that is not possible, it is advisable to keep in contact with people involved in such operations, as well to read as many papers or reports as possible on descriptions of operations of industrial or pilot units. This will be very rewarding at the time that simplification hypothesis of a model needs to be made. 1.2.3 Dynamic, or nD-D, Models Added to the above considerations, models might include time as a variable, and are therefore called dynamic models. Some processes are designed to provide progressive or repetitive (regular or not) increasing or decreasing values of input or output values of temperature, concentration, velocities, pressure, etc. Batch operation reactors and internal combustion engines are examples of such processes. Dynamic models are also useful or necessary when control strategies are to be set or for cases where starting-up and/or stopping-up procedures should be monitored or controlled. Safety or economics may require that. Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 49. Basic Remarks on Modeling and Simulation 17 Most of the considerations made above regarding the necessity of including more dimensions for steady-state models are also valid for dynamic ones. 1.2.4 Which Level to Attack? Chosing among the various levels of modeling should be based on necessity. Sophisticationisnotaguaranteeforquality.Thesameistrueforextremesimplicity, which could lead to false or naive hypothesis about complex phenomena. The following suggestions may serve as a guide: 1. If steady-state process, it is advisable to start from a 0D-S model (or from a 0D-D model if dynamic). Even if this is not the desired level to reach, it is useful just to verify if the conception or ideas about the overall operation of the equipment or process are coherent or not. Overall mass and energy conservation should always hold. 2. Comparison between simulation results and measured values should be made. As seen, measurements in industrial operations always present relatively high deviations. Unless more details within the equipment are necessary, the present level might be satisfactory if it has already produced equal or lower deviations between simulation and measured values. 3. If they do not compare well, at least within a reasonable degree of approximation, the model equations must be revisited. Hypothesis and simplifications should also be reevaluated. Then, the process should start again from step 2. It may also be possible that due to reasons already explained, the present level of attack cannot properly simulate the process. The reasons for that are discussed above. In addition, depending on the deviations produced by the previous level or the need for more detailed information. In any of those circumstances, it might be necessary to add a dimension. 4. Before starting a higher and more sophisticated level of modeling, it is advisable to verify what can be measured in the equipment pilot or the industrial unit to be simulated. In addition, it should be verified that the measurements and available information would be enough for comparisons against results from the next simulation level. If not sufficient, the value of stepping up the model should receive serious consideration. EXERCISES 1.1* Discuss others possibilities for the design of the reactor and solving the scaling-up contradictions, as described in Example 1.3. 1.2** Based on the considerations made in Example 1.4, develop some suggestions for a feasible scaling up of the boiler. Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com
  • 50. 18 2 Solid Fuels 2.1 INTRODUCTION This chapter describes the fundamental properties of carbonaceous solid fuels most used in commercial combustion and gastification processes. The objective is to introduce the main characteristics of most common solid fuels and their behavior under heating. No mathematical treatments are presented at this stage. This chapter mainly shows qualitative aspects of drying and pyrolysis, leaving From a practical point of view, industrially employed solid carbonaceous fuels can be classified in three main categories: 1. Coals 2. Biomass 3. Other Carbonaceous fuels are complex collections of organic polymers consisting mainly of aromatic chains combined by hydrocarbons and other atoms such as oxygen, nitrogen, sulfur, potassium, sodium. Coals are mainly the results of slow deterioration of biomass. The degree of that deterioration determines the coal rank. For instance, the lower degree of deterioration is found in lignites and the maximum are found in anthracites. Intermediary stages are the Copyright © 2004 by Marcel Dekker, Inc. quantifications to Chapter 10. Combustion and gasification reactions will be detailed in Chapters 8 and 9. Download From Boilersinfo.com
  • 51. Solid Fuels 19 subbituminous and bituminous coals. Therefore, the coal physical and chemical properties are functions of its age, and the most important are discussed below. 2.2 PHYSICAL PROPERTIES Among the principal aspects concerning the physical properties of solid fuels there are: • Size or particle size distribution • Shape of particles • Porosity of particles Of course, the size of particles plays a fundamental role in combustion and gasification processes. Prior of feeding into combustors or gasifiers, a solid fuel usually passes through a grinding process to reduce particle sizes. The degree of reduction depends on the requirements of applications. Most of combustors and gasifiers cover the range from 10-6 to 10-2 m. The method of grinding is also important. Some solid fuels present special characteristics, which might lead to serious problems for the combustor or gasifier feeding devices. For instance, fibrous materials, such as sugar-cane bagasse, have ends with a broomlike structure. They allow entangling among fibers, leading to formation of large agglomerates inside the hopper.This might prevent the bagasse to continuously flow down to the feeding screws. Sophisticated design and costly systems are necessary to ensure steady feeding operation. Many grinding processes dramatically increase the fraction of particles with those broomlike ends, but that can be largely avoided by applying rotary knife cutters. Any sample of particles covers a wide range of sizes. The particle size distribution is provided after a laboratory determination where several techniques can be applied. The most used is still the series of screens, piled in vertical stacks where the aperture of the net decreases from the top to the bottom. A sample of particles is deposited on the top of the pile, usually with 5–15 screens, and a gentle rocking movement is applied to the whole system. After a time, if no significant change is verified on the amounts retained by the screens, the mass remaining at each one is measured.A list of the percentage of the original sample against the screen aperture is provided. The natural distribution usually nears a normal probabilistic curve. The apertures of screens follow standard It is easy to imagine that smaller particles carried by gas stream tend to be consumedfasterandeasierthanbiggerones.Therefore,theparticlesizedistribution influences not only the rate at which the fuel reacts with oxygen and other gases, but also almost all other aspects of combustor and gasifiers operations. Of course, to repeat and report all computations for each particle size would be rather Copyright © 2004 by Marcel Dekker, Inc. sizes. More details will be described in Chapter 4. Download From Boilersinfo.com
  • 52. 20 Chapter 2 cumbersome. That is why all mathematical models use some sort of average phenomena found in combustors and gasifiers.The rates of gas-solid reactions— among them the oxidation of carbonaceous solids or combustion—depend on the available surface area of the particle. Therefore, for the same volume, the particle with higher surface area should lead to faster consumption. Of course, the minimum would be found for spherical particles. However, the problem is not so simple, mainly because the available area of pores surfaces inside the particle and mass transfer phenomena influence the consumption rate. In addition, the form of particles has a strong influence on the momentum transfers between the particles and the gas stream that carries them.Among the parameters, there is the terminal velocity. The most-used parameter to describe the shape of a particle is sphericity, given by (2.1) Of course, sphericity tends to 1 for particles approaching spherical shape, and to smaller values for particles departing from that. That concept is very useful because solid particles found in nature, or even preprocessed ones, are seldom spherical. For most of the coal, limestone, and sand particles, the sphericity ranges from 0.6 to 0.9. The value of 0.7 may be used if no better information is available.Wood chips—usually used to feed the process in paper mills—present sphericity around 0.2. Sphericity of particles is mainly dictated by the grinding or preparation process, and it is easily determined by laboratorial tests. Likewise, for several other particle properties, sphericity also suffers strong variation during combustion or gasification processes. Fuel solids are usually very porous. Normally more than half of particle volume is empty due to tunnels that crisscross its interior.A good portion of these tunnels have microscopic diameters. This leads to considerably high values for the total areaoftheirsurfacespermassofparticle,andfiguresaround500m2 /garecommon. However, there is some controversy on the methods to determine the internal area of pores, and much has been written on the subject, as illustrated by Gadiou et al. [5]. In any case, the above value demonstrates the importance of pores and their structures on the rate of heterogeneous or gas-solid reactions. The porosity can be calculated using two different definitions of density: • Apparent particle density ρapp, which is the ratio between the mass of an average particle and its volume, including the void volumes of internal pores. A wide range of values can be found even for a single species of Copyright © 2004 by Marcel Dekker, Inc. diameter.Thereareseveraldefinitionsorinterpretationforsuchanaverage;Chapter In addition to the size of particles, their shape strongly influences several 4 presents the various definitions and methodology to compute them. Download From Boilersinfo.com
  • 53. Solid Fuels 21 fuel, but for the sake of examples, typical values for coals fall around 1100 and 700 kg/m3 for woods. • Real density ρreal, which is the ratio between the mass of an average particle and its volume, excluding the volumes occupied by internal pores.Again, a wide range of values can be found even for a single species of fuel, but typical values for coals fall around 2200 and 1400 kg/m3 for woods. The porosity is defined as the ratio between the volumes occupied by all pores inside a particle and its total volume (including pores). It can be easily demonstrated that (2.2) Typical values of porosity are around 0.5 (or 50%). 2.3 CHEMICAL PROPERTIES The composition and molecular structures found in any carbonaceous fuel, such as coal and biomass, are very complex. They involve a substantial variety of inorganic and organic compounds. The largest portion are organic and arranged in hydrocarbon chains where, apart from C, H, O, and N, several other atoms are present, such as S, Fe, Ca, Al, Si, Zn, Na, K, Mg, Cl, heavy metals, etc. There is a vast literature on coal structure (e.g., Refs. 6–8). On the other hand, the literature also shows that most of coal architecture is still ignored. Among the differences between biomass and coals, there is the carbon-to- hydrogen ratio, with higher values for the last ones. Therefore, the C/H ratio can be seen as a vector of time. The principal reason rests on the fact that products from decomposition are light gases and organic liquids with higher proportion of hydrogen—or lower C/H ratio—than the original biomass. For instance, biomass present C/H ratios around 10, lignites around 14, bituminous coals average around 17, while anthracites average around 30. Therefore, the final stage of decomposition is almost pure carbon. On the other hand, one should be careful not to equate the fuel rank with its value for applications. For instance, high volatile content is very important in pulverized combustion because facilitates the solid fuel ignition. There are relatively simple analyses to determine the basic fractions and atomic composition, which can be applied to almost all carbonaceous solid fuels. The simplest one is called proximate analysis and includes the following categories: • Moisture, which is determined by maintaining a sample of solid fuel in an inert atmosphere at 378 K and near ambient pressure until no variation of Copyright © 2004 by Marcel Dekker, Inc. Download From Boilersinfo.com