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:
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Practice-oriented: 35 executable Python code examples
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Systematic structure: 5-chapter structure learning from fundamental theory to latest AI methods
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Industrial applications: Real examples of pilot plant design and commercial plant optimization
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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
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
Learning Content
- Fundamentals of Similarity Principles
- Geometric similarity
- Kinematic similarity
- Dynamic similarity
- Scale factors and scaling rules
- Power Law Scaling
- Scaling relationships for length, area, and volume
- Power law theory
- Scale-up coefficient calculations
- Equipment Sizing Calculations
- Reactor scale-up design
- Heat exchanger area calculations
- Tank and piping sizing
- Scale-down Optimization
- Determining scale-down ratios
- Pilot plant design
- Experimental design and data acquisition
- Economic Scaling
- Six-tenths rule
- Equipment cost estimation
- Determining economically optimal scale
Learning Objectives
- โ Understand and apply the three types of similarity principles
- โ Calculate scale factors and perform equipment sizing
- โ Perform scale-up design using power laws
- โ Design and optimize pilot plants
- โ Perform scaling calculations considering economics
Chapter 2: Dimensionless Numbers and Scale-up Rules
Learning Content
- 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
- Application of Similarity Principles
- Complete similarity and incomplete similarity
- Selection of dominant dimensionless numbers
- Maintaining dimensionless numbers and scale-up
- Buckingham ฯ Theorem
- Dimensional analysis theory
- Derivation of dimensionless groups
- Organization of experimental data
- Setting Scale-up Criteria
- Constant geometry scale-up
- Constant Re number scale-up
- Constant power density scale-up
- Criteria selection guidelines
- Mixing Time Scaling
- Dimensionless mixing time
- Mixing time prediction during scale-up
- Agitation power calculations
Learning Objectives
- โ Understand and calculate major dimensionless numbers
- โ Determine dominant dimensionless numbers and apply similarity principles
- โ Derive dimensionless numbers using Buckingham ฯ theorem
- โ Select appropriate scale-up criteria
- โ Perform mixing time and agitation power scaling
Chapter 3: Heat and Mass Transfer Scaling
Learning Content
- 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
- 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
- Surface Area to Volume Ratio Effects
- S/V ratio scaling (โ Lโปยน)
- Changes in heat transfer and cooling capacity
- Thermal runaway risks during scale-up
- Boundary Layer Scaling
- Laminar and turbulent boundary layers
- Boundary layer thickness scaling
- Effects on heat and mass transfer coefficients
- Multiphase System Scaling
- Gas-liquid reactor scale-up
- Liquid-liquid extraction column scaling
- Solid-liquid stirred tank scaling
Learning Objectives
- โ Understand and utilize dimensionless numbers for heat and mass transfer
- โ Perform heat transfer scaling for heat exchangers and reactors
- โ Evaluate the effects of S/V ratio changes
- โ Apply boundary layer theory to scaling
- โ Design scale-up for multiphase systems
Chapter 4: Reactor and Mixing Scaling
Learning Content
- Reactor Scaling Theory
- Damkohler number (Da) - reaction rate vs transport rate
- Residence time distribution (RTD) scaling
- Deviation from perfect mixing
- Batch Reactor Scale-up
- Maintaining reaction time
- Temperature control challenges
- Maintaining mixing performance
- Continuous Stirred Tank Reactor (CSTR) Scale-up
- Maintaining perfect mixing conditions
- Setting agitation power density
- Multi-stage CSTR scaling
- Mixing Performance Scaling
- Macro-mixing and micro-mixing
- Scale dependence of mixing time
- Mixing effects in competitive-consecutive reaction systems
- Impeller type selection
- 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
- โ Understand reactor dimensionless numbers and apply to scaling
- โ Perform optimal scale-up design for batch reactors
- โ Perform CSTR scaling calculations and performance predictions
- โ Perform scale-up considering mixing performance
- โ Plan scale-up strategies for real processes
Chapter 5: Machine Learning-based Scale-up Prediction
Learning Content
- Data-driven Scale-up Overview
- Limitations of conventional methods and advantages of machine learning
- Characteristics of scale-up data
- Feature engineering
- Supervised Learning for Scale-up Prediction
- Random Forest regression models
- Gradient Boosting (XGBoost, LightGBM)
- Neural Network predictions
- Ensemble learning utilization
- Transfer Learning and Domain Adaptation
- Scale-up prediction with limited data
- Knowledge transfer from similar processes
- Transfer Learning implementation
- Physics-constrained Machine Learning
- Physics-Informed Neural Networks (PINN)
- Learning with dimensionless numbers as features
- Ensuring consistency with physical laws
- Bayesian Optimization for Scale-up Experimental Design
- Minimizing experimental costs
- Balance between exploration and exploitation
- Pilot experiment efficiency
- Uncertainty quantification
Learning Objectives
- โ Apply machine learning to scale-up predictions
- โ Build and evaluate supervised learning models
- โ Predict from limited data using transfer learning
- โ Implement machine learning models with physical constraints
- โ Optimize experimental design using Bayesian optimization
Overall Learning Outcomes
Upon completing this series, you will acquire the following skills and knowledge:
Knowledge Level (Understanding)
- โ Understand similarity principles (geometric, kinematic, dynamic)
- โ Understand major dimensionless numbers and their physical meanings
- โ Understand heat and mass transfer scaling theory
- โ Understand reactor and mixing system scaling principles
- โ Understand the potential of machine learning-based scale-up predictions
Practical Skills (Doing)
- โ Calculate scale factors and perform equipment sizing
- โ Apply similarity principles using dimensionless numbers
- โ Perform heat and mass transfer coefficient scaling calculations
- โ Perform reactor and mixing tank scale-up design
- โ Predict scale-up using machine learning models
- โ Optimize experimental design using Bayesian optimization
Application Skills (Applying)
- โ Design pilot plants from lab data
- โ Scale up commercial plants from pilot data
- โ Assess scale-up risks and plan countermeasures
- โ Determine optimal scale considering economics
- โ Lead scale-up projects as a process engineer
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. โ
Execute code examples from Chapters 1-2 and become proficient in scale calculations
2. โ
Evaluate scale-up challenges in your company's processes
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Calculate major dimensionless numbers and identify dominant factors
Short-term (1-3 months):
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Launch pilot plant design project
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Practice heat and mass transfer scaling calculations
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Develop scale-up experimental design
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Build machine learning models and collect data
Long-term (6 months or more):
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Execute commercial plant scale-up
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Build scale-up database
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Present at conferences or write papers
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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:
- Typos, errors, technical mistakes: Please report as GitHub repository issues
- Improvement suggestions: New topics, code examples you'd like added, etc.
- Questions: Parts that were difficult to understand, sections needing additional explanation
- Success stories: Projects using what you learned from 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:
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Free viewing and downloading
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Use for educational purposes (classes, study sessions, etc.)
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Modification and derivative works (translation, summarization, etc.)
Conditions:
- ๐ Author credit attribution required
- ๐ Must indicate if modifications were made
- ๐ 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
- 2025-10-26: v1.0 Initial release
Your scale-up learning journey starts here!