What are models?
representation of a system or process to analyze, predict, and understand its behavior.
What are implicit vs. explicit models?
Implicit Models:
Assumptions are hidden.
Consistency of assumptions is untested.
Logical consequences and relation to data are unknown.
Explicit Models:
Assumptions are detailed and can be studied.
Written as equation systems.
Focus on mechanistic models based on physical laws.
Why do we focus on explicit models in MTS?
Assumptions are clearly laid out and studied.
Allows for detailed analysis and understanding.
Based on mechanistic models following physical laws.
Enables systematic and scientific validation.
What are mechanistic vs. data-driven models?
Mechanistic Models:
Based on physical laws and principles.
Equation systems representing real-world processes.
Data-Driven Models:
Based on learning from data (e.g., machine learning).
Utilizes statistical and computational techniques.
Can be hybridized with mechanistic models for better accurac
Name reasons to model.
Explain phenomena.
Guide data collection.
Illuminate core dynamics.
Suggest analogies.
Discover new questions.
Promote scientific thinking.
Bound outcomes to plausible ranges.
Illuminate uncertainties.
Offer crisis options in real-time.
Demonstrate trade-offs.
Challenge robustness of theories.
Expose inconsistencies with data.
Train practitioners.
Discipline policy dialogue.
Educate the public.
Reveal complexity or simplicit
What information is needed to model a chemical plant?
Process design and equipment specifications.
Chemical reactions and kinetics.
Thermodynamic data.
Material and energy balances.
Control strategies and dynamics.
Environmental and safety considerations.
What could be the desired information to get out of a model for a chemical plant?
Efficiency and yield of processes.
Safety and environmental impact.
Resource utilization and cost efficiency.
Optimal operating conditions.
Dynamic behavior and control strategies.
Potential improvements and innovations.
What are the key methods/ideas to eliminate one or more spatial dimensions and time-dependence?
Dimensional Analysis: Simplify by analyzing units and scaling laws.
Symmetry and Aspect Ratios: Use symmetry to reduce dimensions.
Quasi-steady-state Assumptions: Assume certain dynamics are in steady-state.
Time-scale Separation: Identify dominant processes over different time scales.
Why are consistent assumptions not enough to yield an accurate model?
Assumptions may oversimplify complex systems.
External factors and variability may not be accounted for.
Accurate data and validation are required for reliability.
Models need to adapt to real-world deviations.
What type of process quantities exist?
Extensive Quantities: Depend on system size (e.g., mass, volume).
Intensive Quantities: Independent of size (e.g., temperature, pressure).
State Variables: Define system state (e.g., concentrations).
Fluxes: Flow rates of quantities across boundaries.
How do we distinguish model equations?
Balance Equations: Conservations laws (mass, energy).
Constitutive Equations: Material-specific relations.
Closure Equations: Supplementary equations for closure.
Boundary Equations: Define system boundaries and interfaces.
What is hybrid mechanistic/data-driven modeling?
Combines mechanistic models (physical laws) with data-driven approaches.
Uses machine learning to enhance prediction and adaptation.
Integrates empirical data with theoretical models for accuracy.
Useful in complex systems with incomplete knowledge.
Name important steps of the modeling process.
Define the problem and objectives.
Choose balance envelopes and interconnections.
Decide on resolution (temporal and spatial).
Select quantities to be balanced.
Formulate balance equations.
Select constitutive relations.
Check for well-posedness.
Implement in a modeling environment.
What kind of model equations exist?
Algebraic Equations: Relationships between variables.
Differential Equations: Rate of change over time.
Partial Differential Equations: Changes across space and time.
Integro-differential Equations: Combined integration and differentiation.
Stochastic Equations: Incorporate randomness and uncertainty.
Name modeling examples and briefly explain their respective modeling concept.
Spherical Earth Model: Assumptions of a perfect sphere for calculating circumference.
Biorefinery Control: Optimizing chemical processes using mass and energy balances.
Polymerization Reactor: Modeling kinetics and transport phenomena for product quality.
Baking Bread: Understanding heat and mass transfer in convection ovens.
Last changed4 months ago