Process Systems Engineering, 2. Modeling and Simulation
Authors: Gani Rafiqul , Cameron Ian , Lucia Angelo , Sin Gürkan , Georgiadis Michael 
Published: October 2012

The article contains sections titled:1.Introduction2.Systematic Modeling Methods and Tools2.1.Introduction2.2.Model Development2.3.Model Types and Forms2.4.Modeling Practice2.4.1.Problem and Model Definition2.4.2.Model Conceptualization2.4.3.Model Data Requirements2.4.4.Model Construction2.4.5.Model Solution2.4.6.Model Verification2.4.7.Model Validation2.4.8.Model Deployment and Maintenance2.5.Computer‐Aided Modeling2.6.Illustrative Example2.6.1.Model Analysis2.6.2.Model Structure2.6.3.Solution Strategy2.6.4.Incremental Modeling2.7.Challenges and Opportunities3.Numerical Methods for Steady‐State Simulation3.1.Introduction3.2.Numerical Methods and Process Simulation3.2.1.Newton's Method and Its Variants3.2.1.1.Newton's Method3.2.1.2.Finite Difference Method3.2.1.3.Broyden's Method3.2.1.4.Hybrid Newton‐Quasi‐Newton Methods3.2.1.5.Thermodynamically Consistent Hybrid Methods3.2.1.6.Other Variants of Newton's Method3.2.2.Direct and Accelerated Direct Substitution3.2.2.1.Direct Substitution3.2.2.2.Newton Acceleration3.2.2.3.Wegstein Accelerated Direct Substitution3.2.2.4.Broyden Accelerated Direct Substitution3.2.2.5.General Dominant Eigenvalue Acceleration3.2.3.Stabilization Method3.2.3.1.Line Searching Procedures3.2.3.2.Trust Region Methods3.2.3.3.Homotopy‐Continuation Methods3.2.4.Complex Domain Methods3.2.5.Optimization‐Based Methods3.2.6.Interval Methods3.3.Numerical Analysis3.3.1.General Convergence Considerations3.3.1.1.Newton's Method and Its Variant3.3.1.2.Direct Substitution and Its Variant3.3.1.3.Stabilization Methods3.3.2.Rates of Convergence3.3.2.1.Newton's Method and Its Variants3.3.2.2.Direct Substitution and Its Variants3.3.2.3.Rates of Convergence in Practice3.3.3.Nonconvergent Behavior3.3.3.1.Periodic and Chaotic Behavior3.3.3.2.Julia Sets3.3.3.3.The Mandelbrot Set3.3.4.Simple Examples3.3.5.Two‐Dimensional Nonadiabatic Continuous Stirred Tank Reactor4.Numerical Methods for Dynamic Simulation4.1.Introduction4.2.Ordinary Differential Equation Models (ODEs)4.2.1.Basic Ideas for Solving ODE Systems4.2.2.Differential Algebraic Equation Models (DAEs)4.2.3.Implicit Simultaneous Solution of DAEs4.2.4.Implicit or Explicit Structured Solutions of DAEs4.2.5.High‐Index DAE Problems4.2.6.Challenges and Opportunities in Dynamic Modeling and Solution5.Numerical Methods for Distributed Model Simulation5.1.Introduction5.2.General Approaches to Solving Distributed System Models5.3.Population Balance Models (PBMs)6.Parameter uncertainty estimation in numerical modeling6.1.Introduction6.2.Theory of Parameter Uncertainty Estimation6.2.1.Frequentist Approach6.2.2.Bayesian Approach6.2.3.Example: Estimation of Parameters of Michaelis–Menten Kinetics6.3.Frequentist Compared to Bayesian Approach7.Simulation Tools7.1.Introduction7.2.Well‐Known General‐Purpose Process Simulation Software Platforms and Applications7.3.Main Features of General‐Purpose Process Simulation Software7.3.1.Aspen Plus7.3.2.Aspen Plus Dynamics7.3.3.Aspen HYSYS7.3.4.gPROMS7.3.5.PRO/II7.3.6.DynSim7.3.7.ROMeo7.3.8.ChemCad7.4.Trends in Process Simulation Engineering7.4.1.Trends in Process Simulation7.4.2.Trends in Model Deployment7.4.3.Trends in Information Technology (IT) Infrastructure7.4.4.Value Creation Opportunities8.Acknowledgments