Section 4: Dynamic Systems and Differential Algebraic Equations

• 4.1 Ordinary Differential Equations and their Solution
• 4.2 The Systematic Construction of Dynamic Models
• 4.2.1 Introduction
• 4.2.2 Procedure and Example One: Flow into a tank
• 4.2.3 Example Two: Fed Batch Reactor
• 4.2.4 Example Three: Sparged Steam Water Heater
• 4.3 Differential Algebraic Equation Systems
• 4.4 Additional Theory and Notes
• 4.4.1 Steady State Model
• 4.4.2 The Richness of Dynamics
• 4.4.2.1 Analytic Solution of Gravity Outflow Problem with Constant Feed
• 4.4.3 Numerical Solution of an ODE
• 4.4.4 Time constant, Accuracy and Step Size
• 4.4.5 Numerical Instability
• 4.4.6 Systems of ODE's
• 4.4.6.1 Choosing a Step Size for More than One ODE
• 4.4.7 Other Methods: Euler is not the Only Method
• 4.4.7.1 Demonstration that Improved and Modified Euler are Second Order Methods
• 4.4.8 Applications of ODE's
• 4.4.8.1 Implicit Differentiation of Redlich-Kwong equation
• 4.4.9 DAE systems
• 4.4.9.1 DAE Formulation of Flow Controller problem
• 4.4.10 Towards Process Simulation
• 4.4.10.1 Material and energy balance for a tank
• 4.5 Case Study Section
• 4.5.1 Modelling a Simple Control System
• 4.5.2 Modelling a Vaporiser
• 4.5.3 Exercise: Modelling the vaporiser with a control system

Section 4 in printable format

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