# Section 1.2.3: Basic Reactors

## The Well-Mixed Reactor

The most common type of chemical reactor consists basically of a tank fitted with a stirrer. The stirrer is meant to ensure that the contents of the vessel are well mixed, so that conditioons everywhere are the same. In mathematical terms this is thus a lumped system.

This type of reactor may be operated in three different ways.

1. The vessel is filled with reatants and the reaction allowed to proceed until a sufficient proportion of these are converted to product. This is called batch operation. It is clearly an unsteady-state situation, and so is described by o.d.e.s with time as the independent variable.
2. Reactants are continuously fed to the reactor at a constant rate and product continuously withdrawn. After the initial startup, this is a steady state situation described by algebraic equations. In this mode of operation the reactor is referred to as a continuous stirred tank reactor or CSTR.
3. In a fed batch reactor typically one reactant is initially charged into the reactor and the second fed to it continuously over a period of time. No product is withdrawn until the reaction period has elapsed, when the feed is stopped and the entire contents removed. The rate at which reactant is supplied may be varied as the reaction proceeds. Mathematically this is almost the same as batch operation.
The other major type of chemical reactor consists of a tube or pipe down which reactants flow continuously and turn into products, leaving at the far end. This is called a tubular or plug-flow reactor or PFR. It is obviously a distributed system since conditions vary spatially along the tube, and possibly also across it. Except during start up and shut down it will normally be operated in a steady state manner.

## Reaction Kinetics

The rate of a chemical reaction depends primarily on the amount of reactants present.

For a unimolecular reaction, e.g.:

A -> products
We can write a rate equation:

R = - V k Can

Here:
• R is the extensive rate (extent) of the reaction in kmol/hr
• V is reactor volume in m³
• k is the rate constant on a per hour basis; its units depend on reaction order
• n is reaction order and may be nonintegral
• Ca is the concentration of species A in kmol/m³
Rdefines the rate at which A disappears and thus at which products are produced.

If n=1 the reaction is said to be First Order and all equations have a particularly simple solution.

For a bimolecular reaction, e.g.:

A + B -> products
Bimolecular reactions are often Second Order and we can write a rate equation:

R = - V k Ca Cb

Where Cb is the concentration of B.

## Reactor Models

1. A CSTR model for a unimolecular reaction appears in handin 2a.
2. The development of a model for a second order fed batch reactor is described in 4.2.3 and used in handin 5.