Applications of Markov Chains in Chemical Engineering (eBook)

A. Tamir (Autor)

eBook Download: PDF

1998 | 1. Auflage
604 Seiten
Elsevier Science (Verlag)
978-0-08-052739-0 (ISBN)

Infos

Markov chains make it possible to predict the future state of a system from its present state ignoring its past history. Surprisingly, despite the widespread use of Markov chains in many areas of science and technology, their applications in chemical engineering have been relatively meager. A possible reason for this phenomenon might be that books containing material on this subject have been written in such a way that the simplicity of Markov chains has been shadowed by the tedious mathematical derivations. Thus, the major objective of writing this book has been to try to change this situation.

There are many advantages, detailed in Chapter 1, of using the discrete Markov-chain model in chemical engineering. Probably, the most important advantage is that physical models can be presented in a unified description via state vector and a one-step transition probability matrix. Consequently, a process is demonstrated solely by the probability of a system to occupy or not occupy a state.

The book has been written in an easy and understandable form, where complex mathematical derivations are abandoned. The fundamentals of Markov chains are presented in Chapter 2 with examples from the bible, art and real life problems. An extremely wide collection is given of examples viz., reactions, reactors, reactions and reactors as well as combined processes, including their solution and a graphical presentation of it, all of which demonstrates the usefulness of applying Markov chains in chemical engineering.

Inhalt

Cover 1
Copyright Page 5
Contents 10
Chapter 0. Biblical Origins and Artistic Demonstrations of Markov Chains-a Humorous Introduction 14
Chapter 1.Why Write this Book? 19
Chapter 2. Fundamentals of Markov Chains 24
2.1 Markov Chains Discrete in Time and Space 24
2.2 Markov Chains Discrete in Space and Continuous in Time 145
2.3 Markov Chains Continuous in Space and Time 183
2.4 Concluding Remarks 193
2.5 Artistic Ending of the Chapter 193
Chapter 3. Applications of Markov Chains in Chemical Reactions 199
3.1 Modeling the Probabilities in Chemical Reactions 200
3.2 Application and Verification of the Modeling 206
3.3 Major Conclusions and General Guidelines for Applying the Modeling 217
3.4 Application of Kinetic Models to Artistic Paintings 217
3.5 Introduction to Modeling of Chemical Reactions 223
3.6 Single Step Irreversible Reaction 226
3.7 Single Step Reversible Reactions 232
3.8 Consecutive Irreversible Reactions 241
3.9 Consecutive Reversible Reactions 250
3.10 Parallel Reactions Single and Consecutive Irreversible Reaction Steps 263
3.11 Parallel Reactions Single and Consecutive Reversible Reaction Steps 300
3.12 Chain Reactions 314
3.13 Oscillating Reactions [55-69] 318
3.14 Non-Existing Reactions with a Beautiful Progression Route 336
Chapter 4. Applications of Markov Chains in Chemical Reactors 347
4.1 Modeling The Probabilities in Flow Systems 348
4.2 Application of the Modeling and General Guidelines 362
4.3 Perfectly Mixed Reactor Systems 366
4.4 Plug Flow-Perfectly Mixed Reactor Systems 419
4.5 Impinging-Stream Systems 475
Chapter 5. Applications of Markov Chains in Chemical Processes 511
5.1 Modeling of the Probabilities 511
5.2 Application of the Modeling and General Guidelines 534
Nomenclature 603
References 612

Produkt-Details

• Erscheint lt. Verlag: 26.8.1998
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Chemie ► Technische Chemie
• Themenwelt: Technik ► Umwelttechnik / Biotechnologie
• ISBN-10: 0-08-052739-6 / 0080527396
• ISBN-13: 978-0-08-052739-0 / 9780080527390