Page 472 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

P1: GNH/GUR P2: GPJ Final Pages
Encyclopedia of Physical Science and Technology EN014A-654 July 28, 2001 16:35

34 Reactors in Process Engineering

or Y A0 ν (0.5)(2)
E A = = = 1.0.
t

1 V dC A C A dV t |ν A | |−1|

−r A =− t + ,
V dt dt
c. Summary of ideal batch reactor design
or
equations.
t
dC A C A dV i. General case.
−r A =− + .
dt V t dt
1 dN i N i
From thermodynamics, assuming ideal solutions, we can t = r i C i ≡ t
V dt V
derive an expression relating the volume at any conversion
t
C i d(ln V )
with the original volume, dC i + = r i
dt dt

t t N A0 ν i V i
V = V 1 + t X A , N A0 − N A
0
|ν A |V ∼
0 X A = [for reactant A]
N A0
where V i is the molar specific volume of componenti. This
t
expression is usually simplified by defining an expansion V 0 dX A
C A0 t =−r A .
factor in terms of any reactant; for A, V dt
ii. Constant temperature and pressure ideal solution.
N A0 ν i V i
E A ≡
|ν A |V t
0 C A0 ν i V i
E A ≡
and |ν A |
t
t
V = V (1 + E A X A ). C A0 dC A
0
=−r A
This changes the ideal batch reactor equation to C A0 + E A C A dt
iii. Ideal gas.
C A0 dX A
−r A = ,
1 + E A X A dt Y A0 ν
E A ≡
where |ν A |
C A0 ν i V i
E A ≡ C A0 dX A
|ν A | =−r A
1 + E A C A dt
and assumes constant temperature, pressure, and ideal
iv. Constant volume.
solutions.
For the special case of an ideal gas mixture, dC i
= r i
dt
Y A0 P
C A0 =
RT dX A
C A0 =−r A .
and dt
RT
V i = 3. Single Ideal Flow Reactor
P
which leads to an easy formula to calculate the change in For batch reactors, time is the key design variable. The
volume factor. batch reactor design equations answer the question: How
Y A0 ν long does it take to obtain a specified conversion or
E A = ,
|ν A | concentration?
With flow reactors, volume is the key design variable.
where Y A0 is the initial mole fraction of A, ν the sum of
For a given feed rate, how big must the reactor be to get a
the stoichiometric numbers, and |ν A | the stoichiometric
specified conversion?
number of component A.
iii. Example.A → 3R. Given that the feed is 50% A
a. Ideal continuous-stirred tank reactor design
and 50% inerts, calculate E A . By stoichiometry,
equations. Very well-mixed unreacted material flows
|ν A |=|−1|= 1 into a vessel, reacts, and exits the reactor along with
converted product. Starting with the general reactor de-
ν = ν i = 3 − 1 = 2
sign equation, several assumptions are made to reduce the
Y A0 = Y 10 = 0.50 equation to a usable form.