Page 473 - 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

Reactors in Process Engineering 35

V t Upon simplification the resulting ideal plug flow reactor
dN i
˙ n i0 − ˙ n i + r i dV = equation is
0 dt
i. CSTR assumptions. t d ˙ n i
dV = .
r i
1. There is no accumulation in the reactor of any In terms of a reactant A and conversion, this equation can
species i. This implies the reactor is at steady-state be written as
flow conditions. X A
t dX A
V = ˙ n A0 .
dN i
= 0 0 −r A
dt
For the special case of a constant density PFR, the preced-
2. There is perfect mixing in the reactor. This implies
ing equation can be simplified by noting that
no spatial variations of rate in the reactor, and the com-
position of the exit stream is the same as the composition C A0 − C A
X A =
anywhere in the reactor. C A0
V t
dC A [constant volume]
r i dV = r i V t dX A =−
C A0
0
therefore,
These assumptions then give the ideal CSTR design C A
t
equation V =− ˙ n A0 dC A .
C A0 −r A
C A0
t ˙ n i − ˙ n i0
V = . For the special case of a packed bed catalytic reactor with
r i
plug flow, the equation is rewritten in terms of catalyst
If this equation is written for a reactant A, the resulting weight,
equation is
˙ n i

d ˙ n i
t ˙ n A0 − ˙ n A W c = ,
V = . ˙ n i0 r i
−r A
where W c is the weight of catalyst in kg and r the rate

Noting that ˙ n A = ˙ n A0 (1 − X A ), we can rewrite the ideal i −1
constant based on a unit volume of catalyst in mol sec
CSTR design equation in terms of conversion of reactant −1
kg catalyst.
A, as
t X A ˙ n A0
V = . 4. Space Time
−r A
For the special case of constant density or constant volume It is useful to have a measure of time for a flow reactor
of the reacting fluid, this equation is written even though the major design variable is reactor or fluid
volume. A commonly used quantity in industrial reactor
t X A ˙ n A0 ˙ n A0 (C A0 − C A )
V = = . design is space time. Space time is defined as the time
required to process one reactor volume of feed, measured
−r A C A0 (−r A )
at some set of specified conditions. The normal conditions
b. Ideal plug flow reactor design equation. Unre-
chosen are the inlet concentration of a reactant and inlet
acted material flows into the reactor, a pipe or tube that
molar or volumetric flow rate.
has a large enough length and volume to provide suffi-
Volumetric flow rate into the reactor is defined as
cient residence time for the fluid to react before exiting.
˙
The assumption of ideal plug flow indicates that the com- V 0 ≡ ˙ n A0 .
position in the reactor is independent of radial position. C A0
Unlike in a stirred-tank reactor, the composition changes Since time is obtained when total volume is divided by
as the fluid flows down the length of the reactor. The de- volumetric flow rate, a quantity τ called space time is
sign equation for an ideal PFR is derived by a differential defined
material balance assuming steady-state flow in the reactor. t t
V C A0 V
This gives τ = = .
˙
V 0 ˙ n A0
V t
˙ n i + r i dV − (˙ n i + d ˙ n i ) = 0. Since space time is defined for the inlet conditions, it is
0 constant no matter what happens in the reactor. Our design