Page 68 - The engineering of chemical reactions

52 Reaction Rates, the Batch Reactor, and the Real World

F-l --+ situations.

v
batch tubular
reactor reactor

and the PFTR equation we will solve most often is
dC.
J = uz = vjr(Cj)
dt
We can therefore replace dt by dz/u in all of the preceding differential equations
for the mass balance in the batch reactor and use these equations to describe
reactions during flow through a pipe. This reactor is called the plug-flow tubular
reactor, which is the most important continuous reactor encountered in the chemical
industry.

The preceding example shows that all the previous equations for the batch reactor
can be immediately transformed into the plug-flow tubular reactor simply by replacing
dt + dz/u in the differential equation or by replacing t + L/u in the integrated equation.
We do not have to solve these equations again for this very important flow reactor! It
is important to note, however, that this transformation t + z/u is only valid if the velocity
in the tube is constant. This requires that the tube diameter be constant and that there be no
change in the fluid density as it moves down the tube because of pressure drops, temperature
changes, or changes in the number of moles due to reaction.

Example 2-7 The reaction A + B with k = 0.01 set-t takes place in a continuous-
plug-flow tubular reactor What residence time in the tube is required for 90% conversion?
For 99%? For 99.9%?

Simple application of the equation given previously yields

t = i In 5 = & In 10 = 100 x 2.303 = 230 set
CA
for 90% conversion
t = & In 100 = 100 x 2 x 2.303 = 460 set
for 99% conversion, and

t = & In 1000 = 100 x 3 x 2.303 = 690 set

for 99.9% conversion.