INTRODUCTION

Without doubt, the most important result of developing a mathematical model of a chemical engineering system is the understanding that is gained of what really makes the process “tick”. This insight enables you to strip away from the problem the many extraneous confusion factors and to get to the core of the system. You can see more clearly the cause and effect relationships between the variables.

Mathematical models can be useful in all phases of chemical engineering, from research and development to plant operations and even in business and economic studies.

1. Research and development: determining chemical kinetic mechanisms and parameters form laboratory or pilot plant reaction data; exploring the effects of different operating conditions for optimizations and control studies; aiding in scale up calculations.

2. Design: exploring the sizing and arrangement of processing equipment for dynamic performance; studying the interactions of various parts of the process, particularly when material recycle or heat integration is used; evaluating alternative process and control structures and strategies; simulating start up, shutdown, and emergency situations and procedures.

3. Plant operation troubleshooting control and processing problem; aiding in start up and operator training ; studying the effects of and the requirements for expansion projects; optimizing plant operation. It is usually much cheaper, safer, and faster to conduct the kinds of studies listed above on a mathematical model than experimentally on an operating unit. This is not to say that plant tests are not needed. As we will discuss later, they are a vital part of confirming the validity of the model and of verifying important ideas and recommendations that evolve from the model studies.

We will discuss in this book only deterministic systems that can be described by ordinary of partial differential equations. Most of the emphasis will be on lumped systems ( with one independent variable, time, described by ordinary differential equations). Both English and SI units will be used. You need to be familiar with both.