Page 106 - The engineering of chemical reactions

90 Single Reactions in Continuous Isothermal Reactors

CA&
CB = CA0 - CA = ~
1 +kt
if CB~ = 0.

Example 3-l The reaction A -+ B, r = kCA occurs in CSTR with 90% conversion. If
k = 0.5 mini,CAM = 2 moles/liter, and u = 4 liter/min, what residence time and reactor

volume will be required?

From the preceding equation we have
t= CAo - CA = CAo - CA 2.0 - 0.2 1.8 = 18 min
r(CA) kCA = 0.5 x 0.2 = 0.1
The reactor volume is
V = ut = 4 x 18 = 72 liters
Note that this problem is even easier than for a batch reactor because for the CSTR
we just have to solve an algebraic equation rather than a differential equation.
For second-order kinetics, r = kc:, the CSTR mass-balance equation becomes

CA0 - CA = tkC;

$b so we must solve a quadratic in CA to obtain
#$ H
#a -1 + (1 + ‘tktC,#2
%I% CA =
2kr

Throughout this book the reaction we will focus on for many examples will be variations

of the preceding reaction: A + B, r = kCA, CA0 = 2 moles/liter, k = 0.5 min-l,u, = 4
liter/min. We will compare it for several reactors in this chapter, and in Chapters 5 and 6
we will examine it for nonisothermal reactors. Watch for it.

i Example 3-2 The reaction A + B, r = kc:, occurs in CSTR with 90% conversion. If
’ k = 0.5 liter mole-i mint, CA,, = 2 moles/liter, and u = 4 liter/min, what residence time
and reactor volume will be required?
!(I#
‘“$
1:;.
:ij From the above equation we have
2.0 - 0.2 1.8
t= CAo - CA CAo - CA = 90 min
r (CA) = kc; = 0.5 x (0.2)2 = 0.02
The reactor volume is
V = ur = 4 x 90 = 360 liters
For nth-order kinetics in a CSTR we can easily solve for T