Process Control and Dynamics

2.

Mathematical Modeling of Dynamic Systems

2.1.

Modeling Fundamentals

2.1.1.

Purpose of Mathematical Models

2.1.2.

Model Classification

2.1.2.1.

Linear vs Nonlinear Models

2.1.2.2.

Lumped vs Distributed Parameter Models

2.1.2.3.

Deterministic vs Stochastic Models

2.1.3.

Model Development Steps

2.2.

Conservation Principles

2.2.1.

Conservation of Mass

2.2.1.1.

General Mass Balance Equation

2.2.1.2.

Component Mass Balances

2.2.1.3.

Accumulation Terms

2.2.1.4.

Generation and Consumption Terms

2.2.2.

Conservation of Energy

2.2.2.1.

Energy Balance Equations

2.2.2.2.

Enthalpy Balances

2.2.2.3.

Heat Transfer Considerations

2.2.3.

Conservation of Momentum

2.2.3.1.

Momentum Balance Equations

2.2.3.2.

Pressure Drop Relationships

2.3.

Constitutive Relations

2.3.1.

Thermodynamic Relations

2.3.2.

Transport Properties

2.3.3.

Reaction Kinetics

2.3.4.

Equilibrium Relationships

2.4.

Modeling Approaches

2.4.1.

First-Principles Modeling

2.4.2.

Empirical Modeling

2.4.3.

Semi-Empirical Modeling

2.4.4.

Black-Box Modeling

2.5.

Linearization Techniques

2.5.1.

Taylor Series Expansion

2.5.2.

Deviation Variables

2.5.3.

Operating Point Selection

2.5.4.

Validity of Linear Approximations

2.6.

Dynamic Models of Common Process Units

2.6.1.

2.6.1.1.

Single Tank Systems

2.6.1.2.

Multiple Tank Systems

2.6.1.3.

Non-Isothermal Tanks

2.6.2.

Continuous Stirred Tank Reactors

2.6.2.1.

Isothermal CSTR

2.6.2.2.

Non-Isothermal CSTR

2.6.2.3.

Multiple Reaction Systems

2.6.3.

Heat Exchangers

2.6.3.1.

2.6.3.2.

Countercurrent Flow

2.6.3.3.

Shell and Tube Exchangers

2.6.4.

Distillation Systems

2.6.4.1.

Binary Distillation

2.6.4.2.

Multicomponent Systems

2.6.4.3.

2.6.5.

Plug Flow Reactors

2.6.6.

Membrane Separators

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1. Introduction to Process Control

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3. Laplace Transforms and Transfer Functions