Stochastic Modelling in Process Technology
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Table of contents
- Cover
- Table of Contentsix
- Prefacev
- Chapter 1 Modeling in Process Technology1
- 1.1 Deterministic Modeling3
- 1.2 Stochastic modeling—an Example20
- Chapter 2 Principles of Stochastic Process modeling29
- 2.1 Stochastic Process Generalities29
- 2.2 Markov Processes32
- 2.3 Markov Chains35
- 2.4 Long-Term Behavior of Markov Chains41
- 2.5 Diffusion processes47
- 2.6 First Exit Times and RTD Curves57
- Chapter 3 Batch Fluidized Beds65
- 3.1 Flow Regimes65
- 3.2 Bubbling Beds66
- 3.3 Slugging Fluidized Beds81
- 3.4 Stochastic Model Incorporating Interfering Particles94
- Chapter 4 Continuous Systems and RTD103
- 4.1 Theory of Danckwerts103
- 4.2 Subsequent Work108
- 4.3 Danckwerts’ Law Revisited116
- 4.4 RTD for Complex Systems119
- Chapter 5 RTD in Continuous Fluidized Beds133
- 5.1 Types of beds considered here133
- 5.2 Bubbling bed134
- 5.3 Fluidized Bed Riser151
- Chapter 6 Mixing and Reactions161
- 6.1 Network-of-Zones Modeling161
- 6.2 Modeling of Chemical Reactions178
- Chapter 7 Particle Size Manipulation187
- 7.1 Physical Phenomena188
- 7.2 Principles of PBM191
- 7.3 PBM for High-Shear Granulation198
- 7.4 Analysis of a Grinding Process207
- Chapter 8 Multiphase Systems213
- 8.1 Multiphase System for Bubbling Bed214
- 8.2 Gulf Streaming in Fluidized beds218
- 8.3 Extension of the Model to include Gulf Streaming230
- 8.4 Quantification of the Model Parameters234
- 8.5 Model Validation with Data238
- 8.6 Review of Too et al.242
- 8.7 Danckwerts’ law for a Multiphase Systems244
- 8.8 The abstract Multiphase System246
- Chapter 9 Diffusion Limits249
- 9.1 Fokker-Planck equation249
- 9.2 Limit Process255
- Appendix A Equations for RTD in CSTR and DPF259
- A.1 Ideally Mixed Vessels (CSTRs) in Series259
- A.2 Plug Flow with Axial Dispersion261
- Bibliography263
- Index275
- Mathematics in Science and Engineering280
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