Stochastic Modelling in Process Technology 1st Edition by Herold Dehling, Timo Gottschalk, Alex Hoffmann ISBN 0444520260 9780444520265

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ISBN 10:    0444520260
ISBN 13: 978-0444520265
Author:   Herold G. Dehling, Timo Gottschalk, Alex C. Hoffmann

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

Stochastic Modelling in Process Technology 1st Table of contents:

Chapter 1: Modeling in Process Technology
1.1. Deterministic Modeling
1.2. Stochastic Modeling—An Example

Chapter 2: Principles of Stochastic Process Modeling
2.1. Stochastic Process Generalities
2.2. Markov Processes
2.3. Markov Chains
2.4. Long-Term Behavior of Markov Chains
2.5. Diffusion Processes
2.6. First Exit Times and RTD Curves

Chapter 3: Batch Fluidized Beds
3.1. Flow Regimes
3.2. Bubbling Beds
3.3. Slugging Fluidized Beds
3.4. Stochastic Model Incorporating Interfering Particles

Chapter 4: Continuous Systems and RTD
4.1. Theory of Danckwerts
4.2. Subsequent Work
4.3. Danckwerts’ Law Revisited
4.4. RTD for Complex Systems

Chapter 5: RTD in Continuous Fluidized Beds
5.1. Types of Beds Considered Here
5.2. Bubbling Bed
5.3. Fluidized Bed Riser

Chapter 6: Mixing and Reactions
6.1. Network-of-Zones Modeling
6.2. Modeling of Chemical Reactions

Chapter 7: Particle Size Manipulation
7.1. Physical Phenomena
7.2. Principles of PBM
7.3. PBM for High-Shear Granulation
7.4. Analysis of a Grinding Process

Chapter 8: Multiphase Systems
8.1. Multiphase System for Bubbling Bed
8.2. Gulf Streaming in Fluidized Beds
8.3. Extension of the Model to Include Gulf Streaming
8.4. Quantification of the Model Parameters
8.5. Model Validation with Data
8.6. Review of Too et al.
8.7. Danckwerts’ Law for Multiphase Systems
8.8. The Abstract Multiphase System

Chapter 9: Diffusion Limits
9.1. Fokker-Planck Equation
9.2. Limit Process

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