10.10 Introduction to Chemical Engineering

Course Overview & Study Guide

Why does Chemical Engineering require so much math and computer work?

One of the most important tasks for an engineer is to analyze an existing or proposed product or process. Based on this analysis she or he can determine whether or not it will work properly and safely, and identify potential improvements. Usually the analysis requires assembling a set of equations that describe the system, where some of the equations are thought to be nearly exact, and others are approximations (which can be checked/calibrated by experimental data).

These equations are not much use unless you can solve them. In the real world, the problems engineers work on are very complex, and the equations that result are so complicated that it is not practical to solve them by hand (this is called “finding an analytical solution”). Sometimes an analytical solution exists, but it is often so long and complicated that you would need a computer to evaluate it anyway. So usually engineers use a computer to solve the equations numerically. In this course we will show you how.

Overview of 10.10

In 10.10, we deal with equations you have already heard about: the conservation of energy, the conservation of mass, and the conservation of fundamental particles (e.g. electrons, protons, atomic nuclei). In many situations other things are conserved, too, e.g. when you boil water, the number of H₂O molecules in the universe does not change. As you will see, you can solve an amazing number of important problems using equations that come from these simple conservation laws, and from the fact that the time-derivative of any conserved quantity is zero.

Although it is usually easy to see where each equation comes from, often we have so many equations and so many variables that it becomes challenging to handle them. First, we will give you some tips about how to come up with the appropriate equations systematically, to help avoid errors. To simplify things, we will lump the unknowns together into an array (like a vector), and write the system of equations in matrix-vector notation. In this course we will introduce matrices, and the associated branch of mathematics and computing called Linear Algebra. As you will see, Linear Algebra is also used to fit experimental data to mathematical models, a task Chemical Engineers call Parameter Estimation. Sometimes the equations we will want to solve are nonlinear, so we will use some methods that come from Numerical Analysis and Multivariable Calculus. Towards end of the semester, we will show you how to solve systems of Differential Equations using the computer. We will only introduce the math needed to solve the Chemical Engineering problems, and we will not prove any theorems; by no means does 10.10 replace math subjects such as 18.02, 18.03, and 18.06!

To solve the equations, we will use MATLAB, a computing environment which is extremely well-suited to these sorts of problems. Sometimes we will be able to write our problems in a form which can be solved by a program distributed with MATLAB; in other cases you will write your own computer programs using the MATLAB programming language to solve them. The first four chapters of our textbook, Numerical Methods with Matlab (NMM), are designed to teach you how to use MATLAB; the rest of the book presents the numerical methods (and some background mathematics) that you will need to solve the types of equations frequently encountered by chemical engineers.

Numerical Methods with Matlab is a long book that gives a lot of detailed information, more than we will be able to cover this semester (though if you become a professional engineer you will likely have a use for everything eventually). To help you stay focused on the main points we have provided a study guide.