Stochastic Modelling in Process Technology (eBook)

Herold G. Dehling, Timo Gottschalk, Alex C. Hoffmann (Autoren)

eBook Download: PDF

2007 | 1. Auflage
290 Seiten
Elsevier Science (Verlag)
978-0-08-054897-5 (ISBN)

Infos

There is an ever increasing need for modelling complex processes reliably. Computational modelling techniques, such as CFD and MD may be used as tools to study specific systems, but their emergence has not decreased the need for generic, analytical process models. Multiphase and multicomponent systems, and high-intensity processes displaying a highly complex behaviour are becoming omnipresent in the processing industry.
This book discusses an elegant, but little-known technique for formulating process models in process technology: stochastic process modelling.
The technique is based on computing the probability distribution for a single particle's position in the process vessel, and/or the particle's properties, as a function of time, rather than - as is traditionally done - basing the model on the formulation and solution of differential conservation equations.
Using this technique can greatly simplify the formulation of a model, and even make modelling possible for processes so complex that the traditional method is impracticable.
Stochastic modelling has sporadically been used in various branches of process technology under various names and guises. This book gives, as the first, an overview of this work, and shows how these techniques are similar in nature, and make use of the same basic mathematical tools and techniques.
The book also demonstrates how stochastic modelling may be implemented by describing example cases, and shows how a stochastic model may be formulated for a case, which cannot be described by formulating and solving differential balance equations.

Key Features:
- Introduction to stochastic process modelling as an alternative modelling technique
- Shows how stochastic modelling may be succesful where the traditional technique fails
- Overview of stochastic modelling in process technology in the research literature
- Illustration of the principle by a wide range of practical examples
- In-depth and self-contained discussions
- Points the way to both mathematical and technological research in a new, rewarding field

- Introduction to stochastic process modelling as an alternative modelling technique
- Shows how stochastic modelling may be succesful where the traditional technique fails
- Overview of stochastic modelling in process technology in the research literature
- Illustration of the principle by a wide range of practical examples
- In-depth and self-contained discussions
- Points the way to both mathematical and technological research in a new, rewarding field

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There is an ever increasing need for modelling complex processes reliably. Computational modelling techniques, such as CFD and MD may be used as tools to study specific systems, but their emergence has not decreased the need for generic, analytical process models. Multiphase and multicomponent systems, and high-intensity processes displaying a highly complex behaviour are becoming omnipresent in the processing industry. This book discusses an elegant, but little-known technique for formulating process models in process technology: stochastic process modelling. The technique is based on computing the probability distribution for a single particle's position in the process vessel, and/or the particle's properties, as a function of time, rather than - as is traditionally done - basing the model on the formulation and solution of differential conservation equations. Using this technique can greatly simplify the formulation of a model, and even make modelling possible for processes so complex that the traditional method is impracticable. Stochastic modelling has sporadically been used in various branches of process technology under various names and guises. This book gives, as the first, an overview of this work, and shows how these techniques are similar in nature, and make use of the same basic mathematical tools and techniques. The book also demonstrates how stochastic modelling may be implemented by describing example cases, and shows how a stochastic model may be formulated for a case, which cannot be described by formulating and solving differential balance equations. - Introduction to stochastic process modelling as an alternative modelling technique- Shows how stochastic modelling may be succesful where the traditional technique fails- Overview of stochastic modelling in process technology in the research literature- Illustration of the principle by a wide range of practical examples- In-depth and self-contained discussions- Points the way to both mathematical and technological research in a new, rewarding field

Inhalt

Cover 1
Table of Contents 10
Preface 6
Chapter 1 Modeling in Process Technology 12
1.1 Deterministic Modeling 14
1.2 Stochastic modeling—an Example 31
Chapter 2 Principles of Stochastic Process modeling 40
2.1 Stochastic Process Generalities 40
2.2 Markov Processes 43
2.3 Markov Chains 46
2.4 Long-Term Behavior of Markov Chains 52
2.5 Diffusion processes 58
2.6 First Exit Times and RTD Curves 68
Chapter 3 Batch Fluidized Beds 76
3.1 Flow Regimes 76
3.2 Bubbling Beds 77
3.3 Slugging Fluidized Beds 92
3.4 Stochastic Model Incorporating Interfering Particles 105
Chapter 4 Continuous Systems and RTD 114
4.1 Theory of Danckwerts 114
4.2 Subsequent Work 119
4.3 Danckwerts’ Law Revisited 127
4.4 RTD for Complex Systems 130
Chapter 5 RTD in Continuous Fluidized Beds 144
5.1 Types of beds considered here 144
5.2 Bubbling bed 145
5.3 Fluidized Bed Riser 162
Chapter 6 Mixing and Reactions 172
6.1 Network-of-Zones Modeling 172
6.2 Modeling of Chemical Reactions 189
Chapter 7 Particle Size Manipulation 198
7.1 Physical Phenomena 199
7.2 Principles of PBM 202
7.3 PBM for High-Shear Granulation 209
7.4 Analysis of a Grinding Process 218
Chapter 8 Multiphase Systems 224
8.1 Multiphase System for Bubbling Bed 225
8.2 Gulf Streaming in Fluidized beds 229
8.3 Extension of the Model to include Gulf Streaming 241
8.4 Quantification of the Model Parameters 245
8.5 Model Validation with Data 249
8.6 Review of Too et al. 253
8.7 Danckwerts’ law for a Multiphase Systems 255
8.8 The abstract Multiphase System 257
Chapter 9 Diffusion Limits 260
9.1 Fokker-Planck equation 260
9.2 Limit Process 266
Appendix A Equations for RTD in CSTR and DPF 270
A.1 Ideally Mixed Vessels (CSTRs) in Series 270
A.2 Plug Flow with Axial Dispersion 272
Bibliography 274
Index 286
Mathematics in Science and Engineering 291

Produkt-Details

• Erscheint lt. Verlag: 3.7.2007
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-054897-0 / 0080548970
• ISBN-13: 978-0-08-054897-5 / 9780080548975