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โš—๏ธ Scale-up and Scale-down Introduction Series v1.0

๐Ÿ“– Reading time: 140-170 min ๐Ÿ“Š Level: Intermediate to Advanced ๐Ÿ’ป Code examples: 35

Scale-up and Scale-down Introduction Series v1.0

From Similarity Principles to Machine Learning Predictions - Complete Practical Guide from Lab Scale to Commercial Plants

Series Overview

This series is a 5-chapter educational content that allows step-by-step learning from fundamentals to practice of scale-up and scale-down in chemical processes. It comprehensively covers similarity principles theory, dimensionless number utilization, heat and mass transfer scaling, reaction and mixing scaling, and machine learning-based scale-up predictions.

Features:
- โœ… Practice-oriented: 35 executable Python code examples
- โœ… Systematic structure: 5-chapter structure learning from fundamental theory to latest AI methods
- โœ… Industrial applications: Real examples of pilot plant design and commercial plant optimization
- โœ… Latest technology: Scale-up predictions using machine learning and deep learning

Total learning time: 140-170 minutes (including code execution and exercises)


How to Learn

Recommended Learning Sequence

flowchart TD A[Chapter 1: Fundamentals of Scaling Theory] --> B[Chapter 2: Dimensionless Numbers and Scale-up Rules] B --> C[Chapter 3: Heat and Mass Transfer Scaling] C --> D[Chapter 4: Reactor and Mixing Scaling] D --> E[Chapter 5: Machine Learning-based Scale-up Prediction] style A fill:#e8f5e9 style B fill:#c8e6c9 style C fill:#a5d6a7 style D fill:#81c784 style E fill:#66bb6a

For beginners (learning scaling for the first time):
- Chapter 1 โ†’ Chapter 2 โ†’ Chapter 3 โ†’ Chapter 4 โ†’ Chapter 5
- Required time: 140-170 minutes

For chemical engineering practitioners (with fundamental knowledge):
- Chapter 1 (quick review) โ†’ Chapter 2 โ†’ Chapter 3 โ†’ Chapter 4 โ†’ Chapter 5
- Required time: 110-140 minutes

For scale-up practitioners (with practical experience):
- Chapter 3 โ†’ Chapter 4 โ†’ Chapter 5
- Required time: 80-100 minutes


Chapter Details

Chapter 1: Fundamentals of Scaling Theory

๐Ÿ“– Reading time: 25-30 min ๐Ÿ’ป Code examples: 7 ๐Ÿ“Š Difficulty: Intermediate

Learning Content

  1. Fundamentals of Similarity Principles
    • Geometric similarity
    • Kinematic similarity
    • Dynamic similarity
    • Scale factors and scaling rules
  2. Power Law Scaling
    • Scaling relationships for length, area, and volume
    • Power law theory
    • Scale-up coefficient calculations
  3. Equipment Sizing Calculations
    • Reactor scale-up design
    • Heat exchanger area calculations
    • Tank and piping sizing
  4. Scale-down Optimization
    • Determining scale-down ratios
    • Pilot plant design
    • Experimental design and data acquisition
  5. Economic Scaling
    • Six-tenths rule
    • Equipment cost estimation
    • Determining economically optimal scale

Learning Objectives

Read Chapter 1 โ†’

Chapter 2: Dimensionless Numbers and Scale-up Rules

๐Ÿ“– Reading time: 28-33 min ๐Ÿ’ป Code examples: 7 ๐Ÿ“Š Difficulty: Intermediate to Advanced

Learning Content

  1. Major Dimensionless Numbers
    • Reynolds number (Re) - inertial force vs viscous force
    • Froude number (Fr) - inertial force vs gravity
    • Weber number (We) - inertial force vs surface tension
    • Peclet number (Pe) - advection vs diffusion
  2. Application of Similarity Principles
    • Complete similarity and incomplete similarity
    • Selection of dominant dimensionless numbers
    • Maintaining dimensionless numbers and scale-up
  3. Buckingham ฯ€ Theorem
    • Dimensional analysis theory
    • Derivation of dimensionless groups
    • Organization of experimental data
  4. Setting Scale-up Criteria
    • Constant geometry scale-up
    • Constant Re number scale-up
    • Constant power density scale-up
    • Criteria selection guidelines
  5. Mixing Time Scaling
    • Dimensionless mixing time
    • Mixing time prediction during scale-up
    • Agitation power calculations

Learning Objectives

Read Chapter 2 โ†’

Chapter 3: Heat and Mass Transfer Scaling

๐Ÿ“– Reading time: 28-33 min ๐Ÿ’ป Code examples: 7 ๐Ÿ“Š Difficulty: Intermediate to Advanced

Learning Content

  1. Heat Transfer Scaling
    • Nusselt number (Nu) - convective heat transfer
    • Prandtl number (Pr) - momentum diffusion vs thermal diffusion
    • Heat exchanger scale-up
    • Reactor temperature control and scaling
  2. Mass Transfer Scaling
    • Sherwood number (Sh) - mass transfer
    • Schmidt number (Sc) - momentum diffusion vs mass diffusion
    • Mass transfer coefficient scaling
    • Mass transfer in multiphase systems
  3. Surface Area to Volume Ratio Effects
    • S/V ratio scaling (โˆ Lโปยน)
    • Changes in heat transfer and cooling capacity
    • Thermal runaway risks during scale-up
  4. Boundary Layer Scaling
    • Laminar and turbulent boundary layers
    • Boundary layer thickness scaling
    • Effects on heat and mass transfer coefficients
  5. Multiphase System Scaling
    • Gas-liquid reactor scale-up
    • Liquid-liquid extraction column scaling
    • Solid-liquid stirred tank scaling

Learning Objectives

Read Chapter 3 โ†’

Chapter 4: Reactor and Mixing Scaling

๐Ÿ“– Reading time: 28-33 min ๐Ÿ’ป Code examples: 7 ๐Ÿ“Š Difficulty: Intermediate to Advanced

Learning Content

  1. Reactor Scaling Theory
    • Damkohler number (Da) - reaction rate vs transport rate
    • Residence time distribution (RTD) scaling
    • Deviation from perfect mixing
  2. Batch Reactor Scale-up
    • Maintaining reaction time
    • Temperature control challenges
    • Maintaining mixing performance
  3. Continuous Stirred Tank Reactor (CSTR) Scale-up
    • Maintaining perfect mixing conditions
    • Setting agitation power density
    • Multi-stage CSTR scaling
  4. Mixing Performance Scaling
    • Macro-mixing and micro-mixing
    • Scale dependence of mixing time
    • Mixing effects in competitive-consecutive reaction systems
    • Impeller type selection
  5. Case Study: Real Process Scale-up
    • Pilot design from lab data
    • Commercial plant design from pilot data
    • Scale-up trouble cases and countermeasures

Learning Objectives

Read Chapter 4 โ†’

Chapter 5: Machine Learning-based Scale-up Prediction

Reading time: 31-41 min ๐Ÿ’ป Code examples: 7 ๐Ÿ“Š Difficulty: Advanced

Learning Content

  1. Data-driven Scale-up Overview
    • Limitations of conventional methods and advantages of machine learning
    • Characteristics of scale-up data
    • Feature engineering
  2. Supervised Learning for Scale-up Prediction
    • Random Forest regression models
    • Gradient Boosting (XGBoost, LightGBM)
    • Neural Network predictions
    • Ensemble learning utilization
  3. Transfer Learning and Domain Adaptation
    • Scale-up prediction with limited data
    • Knowledge transfer from similar processes
    • Transfer Learning implementation
  4. Physics-constrained Machine Learning
    • Physics-Informed Neural Networks (PINN)
    • Learning with dimensionless numbers as features
    • Ensuring consistency with physical laws
  5. Bayesian Optimization for Scale-up Experimental Design
    • Minimizing experimental costs
    • Balance between exploration and exploitation
    • Pilot experiment efficiency
    • Uncertainty quantification

Learning Objectives

Read Chapter 5 โ†’


Overall Learning Outcomes

Upon completing this series, you will acquire the following skills and knowledge:

Knowledge Level (Understanding)

Practical Skills (Doing)

Application Skills (Applying)


FAQ (Frequently Asked Questions)

Q1: How much prerequisite knowledge in chemical engineering is needed?

A: Basic knowledge of fluid mechanics, heat transfer, and mass transfer is desirable. Understanding dimensionless number concepts and reaction engineering fundamentals (residence time, yield, etc.) will enable smooth learning.

Q2: What is the difference between scale-up and scale-down?

A: Scale-up is enlarging from small scale (lab, pilot) to large scale (commercial plant), while scale-down is the opposite. Scale-down is important for designing pilot experiments and determining lab experimental conditions from commercial plant data.

Q3: Is scale-up possible without using machine learning?

A: Yes, it is possible. Conventional methods based on similarity principles and dimensionless numbers learned in Chapters 1-4 have a long track record and are used as standard in many industries. The machine learning methods in Chapter 5 are additional tools when abundant data is available or higher accuracy predictions are needed.

Q4: Which Python libraries are needed?

A: Primarily NumPy, SciPy, Pandas, Matplotlib, and Seaborn are used. For machine learning, scikit-learn, XGBoost, LightGBM, and TensorFlow/PyTorch are recommended. Chapters 1-4 can be executed with only basic scientific computing libraries.

Q5: What should I learn next?

A: The following topics are recommended:
- Process Modeling: CFD simulation and digital twins
- Process Control: Control system design associated with scale changes
- Process Safety: Safety assessment during scale-up (HAZOP, risk assessment)
- Design of Experiments (DOE): Efficient design of pilot experiments


Next Steps

Recommended Actions After Series Completion

Immediate (within 1 week):
1. โœ… Execute code examples from Chapters 1-2 and become proficient in scale calculations
2. โœ… Evaluate scale-up challenges in your company's processes
3. โœ… Calculate major dimensionless numbers and identify dominant factors

Short-term (1-3 months):
1. โœ… Launch pilot plant design project
2. โœ… Practice heat and mass transfer scaling calculations
3. โœ… Develop scale-up experimental design
4. โœ… Build machine learning models and collect data

Long-term (6 months or more):
1. โœ… Execute commercial plant scale-up
2. โœ… Build scale-up database
3. โœ… Present at conferences or write papers
4. โœ… Build career as a scale-up engineer


Feedback and Support

About This Series

This series was created under the supervision of Dr. Yusuke Hashimoto, Tohoku University, as part of the PI Knowledge Hub project.

Creation Date: October 26, 2025
Version: 1.0

We Welcome Your Feedback

We look forward to your feedback to improve this series:

Contact: yusuke.hashimoto.b8@tohoku.ac.jp


License and Terms of Use

This series is published under the CC BY 4.0 (Creative Commons Attribution 4.0 International) license.

What you can do:
- โœ… Free viewing and downloading
- โœ… Use for educational purposes (classes, study sessions, etc.)
- โœ… Modification and derivative works (translation, summarization, etc.)

Conditions:
- ๐Ÿ“Œ Author credit attribution required
- ๐Ÿ“Œ Must indicate if modifications were made
- ๐Ÿ“Œ Contact in advance for commercial use

Details: CC BY 4.0 License Full Text


Let's Get Started!

Are you ready? Start with Chapter 1 and begin your journey into the world of scale-up and scale-down!

Chapter 1: Fundamentals of Scaling Theory โ†’


Update History


Your scale-up learning journey starts here!

References

  1. Montgomery, D. C. (2019). Design and Analysis of Experiments (9th ed.). Wiley.
  2. Box, G. E. P., Hunter, J. S., & Hunter, W. G. (2005). Statistics for Experimenters: Design, Innovation, and Discovery (2nd ed.). Wiley.
  3. Seborg, D. E., Edgar, T. F., Mellichamp, D. A., & Doyle III, F. J. (2016). Process Dynamics and Control (4th ed.). Wiley.
  4. McKay, M. D., Beckman, R. J., & Conover, W. J. (2000). "A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code." Technometrics, 42(1), 55-61.

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