Adiabatic Plug Flow Reactor with Recycle

​
recycle ratio
13
fresh feed temperature
T
f
(K)
300
guess
T
0
until the correct value of
T
f
is calculated below
PFR feed temperature
T
0
(K)
411
A first-order reaction is carried out in an adiabatic plug flow reactor (PFR) with recycle. The fresh feed concentration is known. Select the fresh feed temperature
T
f
and the recycle ratio with sliders. The correct exit temperature
T
e
is obtained iteratively: the PFR feed temperature
T
0
is guessed with the slider (and the feed concentration to the PFR calculated using the adiabatic relation between temperature and concentration), the PFR mass and energy balances are solved to determine
T
f
and
C
A,f
, and an energy balance around the mixing point before the PFR is then solved to determine the calculated
T
f
. Next, guess
T
0
until the calculated
T
f
(black arrow on the left) equals the
T
f
value (the center of the green circle). The graph shows the temperature in the PFR as a function of distance using the guessed value for
T
0
. Multiple solutions are obtained under some conditions, and the solution observed depends on how the reactor is started up. High recycle ratios approach continuous stirred-tank reactor (CSTR) behavior.

Details

Mass and energy balance:
T
dz
=-k
C
A
ΔH
u
0
C
A,0
Cp
,
d
C
A
dz
=-k
C
A
/
u
0
,
k=
k
o
-
Ea
RT
e
,
T
f
=(1+ξ)
T
0
-ξ
T
e
,
u
0
=
u
f
(1+ξ)
,
where
T
is temperature (K),
z
is length down the reactor (m),
u
0
is the velocity of the stream exiting the reactor (m/s),
C
A,0
is concentration of
A
entering the reactor (
mol/
3
m
),
Cp
is heat capacity (
J/[
3
m
K]
),
ΔH
is heat of reaction (J/mol),
k
is the rate constant (1/s),
C
A
is concentration of reactant
A
(
mol/
3
m
),
k
o
is a pre-exponential factor (1/s),
T
0
and
T
e
are the temperatures of the stream entering and exiting the reactor (K),
T
f
is the fresh feed temperature (K),
Ea
is activation energy (J/mol),
R
is the ideal gas constant (J/[mol K]),
ξ
is the recycle ratio, and
u
f
is the velocity of the fresh feed (m/s).
The screencast video at[1] shows how to use this Demonstration.

References

[1] Adiabatic Plug Flow Reactor with Recycle. www.colorado.edu/learncheme/kinetics/AdiabaticPFRRecycle.html.

External Links

Isothermal Plug Flow Reactor with Recycle

Permanent Citation

Rachael L. Baumann, John L. Falconer
​
​"Adiabatic Plug Flow Reactor with Recycle"​
​http://demonstrations.wolfram.com/AdiabaticPlugFlowReactorWithRecycle/​
​Wolfram Demonstrations Project​
​Published: January 21, 2014