Process Systems Engineering, 2. Modeling and Simulation

1.	Introduction
2.	Systematic Modeling Methods and Tools
2.1.	Introduction
2.2.	Model Development
2.3.	Model Types and Forms
2.4.	Modeling Practice
2.4.1.	Problem and Model Definition
2.4.2.	Model Conceptualization
2.4.3.	Model Data Requirements
2.4.4.	Model Construction
2.4.5.	Model Solution
2.4.6.	Model Verification
2.4.7.	Model Validation
2.4.8.	Model Deployment and Maintenance
2.5.	Computer-Aided Modeling
2.6.	Illustrative Example
2.6.1.	Model Analysis
2.6.2.	Model Structure
2.6.3.	Solution Strategy
2.6.4.	Incremental Modeling
2.7.	Challenges and Opportunities
3.	Numerical Methods for Steady-State Simulation
3.1.	Introduction
3.2.	Numerical Methods and Process Simulation
3.2.1.	Newton's Method and Its Variants
3.2.1.1.	Newton's Method
3.2.1.2.	Finite Difference Method
3.2.1.3.	Broyden's Method
3.2.1.4.	Hybrid Newton-Quasi-Newton Methods
3.2.1.5.	Thermodynamically Consistent Hybrid Methods
3.2.1.6.	Other Variants of Newton's Method
3.2.2.	Direct and Accelerated Direct Substitution
3.2.2.1.	Direct Substitution
3.2.2.2.	Newton Acceleration
3.2.2.3.	Wegstein Accelerated Direct Substitution
3.2.2.4.	Broyden Accelerated Direct Substitution
3.2.2.5.	General Dominant Eigenvalue Acceleration
3.2.3.	Stabilization Method
3.2.3.1.	Line Searching Procedures
3.2.3.2.	Trust Region Methods
3.2.3.3.	Homotopy-Continuation Methods
3.2.4.	Complex Domain Methods
3.2.5.	Optimization-Based Methods
3.2.6.	Interval Methods
3.3.	Numerical Analysis
3.3.1.	General Convergence Considerations
3.3.1.1.	Newton's Method and Its Variant
3.3.1.2.	Direct Substitution and Its Variant
3.3.1.3.	Stabilization Methods
3.3.2.	Rates of Convergence
3.3.2.1.	Newton's Method and Its Variants
3.3.2.2.	Direct Substitution and Its Variants
3.3.2.3.	Rates of Convergence in Practice
3.3.3.	Nonconvergent Behavior
3.3.3.1.	Periodic and Chaotic Behavior
3.3.3.2.	Julia Sets
3.3.3.3.	The Mandelbrot Set
3.3.4.	Simple Examples
3.3.5.	Two-Dimensional Nonadiabatic Continuous Stirred Tank Reactor
4.	Numerical Methods for Dynamic Simulation
4.1.	Introduction
4.2.	Ordinary Differential Equation Models (ODEs)
4.2.1.	Basic Ideas for Solving ODE Systems
4.2.2.	Differential Algebraic Equation Models (DAEs)
4.2.3.	Implicit Simultaneous Solution of DAEs
4.2.4.	Implicit or Explicit Structured Solutions of DAEs
4.2.5.	High-Index DAE Problems
4.2.6.	Challenges and Opportunities in Dynamic Modeling and Solution
5.	Numerical Methods for Distributed Model Simulation
5.1.	Introduction
5.2.	General Approaches to Solving Distributed System Models
5.3.	Population Balance Models (PBMs)
6.	Parameter uncertainty estimation in numerical modeling
6.1.	Introduction
6.2.	Theory of Parameter Uncertainty Estimation
6.2.1.	Frequentist Approach
6.2.2.	Bayesian Approach
6.2.3.	Example: Estimation of Parameters of Michaelis–Menten Kinetics
6.3.	Frequentist Compared to Bayesian Approach
7.	Simulation Tools
7.1.	Introduction
7.2.	Well-Known General-Purpose Process Simulation Software Platforms and Applications
7.3.	Main Features of General-Purpose Process Simulation Software
7.3.1.	Aspen Plus
7.3.2.	Aspen Plus Dynamics
7.3.3.	Aspen HYSYS
7.3.4.	gPROMS
7.3.5.	PRO/II
7.3.6.	DynSim
7.3.7.	ROMeo
7.3.8.	ChemCad
7.4.	Trends in Process Simulation Engineering
7.4.1.	Trends in Process Simulation
7.4.2.	Trends in Model Deployment
7.4.3.	Trends in Information Technology (IT) Infrastructure
7.4.4.	Value Creation Opportunities
8.	Acknowledgments

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