Pharmaceutical Manufacturing Handbook: Production and

LABORATORY VESSELS AND REACTION CALORIMETERS 147
For reactions with essentially instantaneous kinetics, the reaction rate is limited by
the feed addition rate. For other reactions, particularly if the reactor is operated at
too low of a temperature, a reactant concentration can “ build up, ” eventually reaching
an unsafe level that could lead to a rapid temperature rise and explosion. It is
important for these reactions to monitor the heat fl ow to confi rm that the reactant
concentration is not increasing to unacceptable levels.
3.1.3.6 Rapid Scale - Up Relationships
Lacking knowledge of the larger scale reactor, it is tempting to simply assume that
only the area for heat transfer varies upon scale - up. A natural parameter is the
1
cooling time , defi ned as
( mcp)
r Vρcpφ τco
= =
UA UA
The heat transfer area varies with the square of the vessel diameter, and the volume
varies with the cube of the vessel diameter. Thus the area – volume ratio ( A / V ) varies
with volume as
A
~
V V
1
(20)
1/3 (21)
The inverse cooling time relationship for scale - up from volume V 1 to V 2 is
⎡ UA ⎤ ⎡ UA ⎤
⎣
⎢Vρcpφ⎦
⎥
=
⎣
⎢Vρcpφ⎦
2 1
V
V
1
⎥ ( )
The required reactor - jacket temperature difference on scale - up, with a constant
Lewis number, is
1/3
V2
− j 2 = − j 1(
V ) 1
[ T T ] [ T T ]
so the temperature difference can increase dramatically when a process is scaled up
several orders of magnitude. Reactor - jacket temperature difference constraints can
be particularly important for glass - lined vessels, where the limit is often 75 ° C.
3.1.3.7 Safety under a Cooling System Failure
In the event of a cooling system failure it can be assumed that the reactor operates
adiabatically. The adiabatic temperature rise can be found from
1
The notion of cooling time can be understood by writing (1) and assuming no calibration energy or heat
loss. Then (1) becomes τ co ( dT / dt ) = − ( T − T j ). If a constant temperature difference T − T j is applied, it
will take τ co time units for the reactor temperature to change by the temperature difference.
2
1/3
(22)
(23)