# 8.19: Untitled Page 208

## Chapter 8

Figure 8.12. Batch reactor start‐up process

flow rate Q and a concentration o

c . When the reactor is full, the stream of o

A

species A is shut off and the system proceeds in the normal manner for a batch reactor. During the start‐up time, the volume of fluid in the reactor can be expressed as

V( t)  V Q t

(3)

o

o

and the final volume of the fluid is given by

V

V Q t

(4)

1

o

o 1

Here t is the start‐up time. In this problem you are asked to determine the 1

concentration of species A during the start‐up time and all subsequent times.

The analysis for the start‐up time can be simplified by means of the transformation

(

y t)   c V( t)

(5)

A

and use of the initial condition

I.C.

y  0 , t  0

(6)

After you have determined y( t) you can easily determine  c  during the start-A

up period. The concentration at t t then becomes the initial condition for the 1

analysis of the system for all subsequent times. Often one simplifies the analysis of a batch reactor by assuming that the time required to fill the reactor is   Transient Material Balances

389

negligible. Use your solution to this problem to identify what is meant by

“negligible” for this particular problem.

8‐13. In the perfectly mixed continuous stirred tank reactor illustrated in Figure 8.13a, species A undergoes an irreversible reaction to form products according to

k

A 

products,

R

 

A

k c

(1)

A

The original volume of fluid in the reactor is V and the original volumetric flow o

rate into and out of the reactor is Q . The concentration of species A entering the o

reactor is fixed at

o

c and under steady state operating conditions the A

concentration at the exit (and therefore the concentration in the reactor) is  c  .

A

Part (a). Determine the concentration  c  under steady state operating A

conditions.   