# Chemical reactor

A chemical reactor is a process unit which combines one or more chemicals into another by promoting a chemical reaction. Reactors can be run as flow systems or as batch systems.

The design equation for a chemical reactor is based directly on the general balance equation

$F_{j0} - F_j + \int^V{r_jdV} = \frac{dN_j}{dt}$[1]

where

j is a specific species (chemical) in the system
Fj0 is the molar flow rate into the system of species j
Fj is the molar flow rate out of the system of species j
rj is the rate of appearance of species j[2]
V is volume in which the reactor takes place
Nj is the number of moles of species j

The design equation is typically performed on the limiting reactant of a reaction.

## Batch Reactor

A batch reactor is the simplest form of a chemical reactor. A batch reactor is simply a vessel of fixed or variable volume which has no material flows into or out of the system. A batch reactor could be as small as a beaker in a chemistry lab, or as large as a 1,000 gallon fermenter in a large scale brewery.

### Design Equation

Since batch reactors have no in or out flows, Fj0 and Fj are both equal to 0. If the reactor is assumed to be perfectly mixed, then there are no spacial variations of rj (in other words, rj is a constant and can be taken outside of the integral. Thus, the design equation for a batch reactor is

$r_jV = \frac{dN_j}{dt}$.

### Uses

Batch reactors are useful for

• small-scale operations
• testing new processes
• manufacturing expensive products
• very slow processes (such as biological reactions)

## Continuous Stirred-Tank Reactor

A continuous stirred-tank reactor (CSTR) is a well mixed tank with a flow of material flowing both into and out of it.

### Design Equation

Like a batch reactor, CSTRs can be assumed to be well mixed. Additionally, CSTRs are almost always run at steady state, thus the differential term of the design equation is 0. The design equation for a CSTR is

Fj0 - Fj + rjV = 0

Since the well mixed assumption means that conditions anywhere in the tank are equal to conditions at the exit, rj is evaluated at the conditions of the exit stream.

## Notes

1. Fogler, H. Scott. Elements of Chemical Reaction Engineering, 4e. Pearson Education: 2006.
2. Since the design equation is performed on a reactant, the rate of appearance is actually negative. For this reason -rj is often substituted, to represent dissapearance of the reactant.