L9 Reactor Design For Multiple Rxns
L9 Reactor Design For Multiple Rxns
L9 Reactor Design For Multiple Rxns
rA 3 a b 1 1
kA a b
dm mol
C A CB s
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-4
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
dC A L9-6
For the reaction A products rA
dt
For a zero-order reaction -rA = k dCA
k
dt
Plot of CA vs CA
t is a straight
line CA CA0 kt
t
dCA
For a first-order reaction - rA = k CA kCA
ln (CA0/CA) dt
Plot of
ln(CA0/CA) vs t CA0
is a straight line ln kt
t CA
dCA
For a second-order reaction - rA = k CA2 kCA 2
dt
1/CA
Plot of 1/CA vs t 1 1
is a straight line kt
t CA CA0
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-7
ln (t1/2)
1 1 1
t a 1
k a 1 CA CA0a 1
Slope = 1- a
1
CA CA0 at t = t1 2
2
2a 1 1 1
t1 2
k a 1 CA0a 1
ln CA0
2a 1 1
Plot ln(t1/2) vs ln CA0. Get a straight
line with a slope of 1-
ln t1 2 ln
k a 1
1 a lnCA0
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-8
DL FA0 FAe rA DW 0
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-11
k1 B
A
k2 C
Desired product
2) Series reactions k1 k2
A B C
Desired product
k k
4) Complex reactions A B
1 CD A C
2 E
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-12
Parallel Reactions
Purpose: maximizing the desired product in parallel reactions
ED
kD
D (desired) rD kDCAa1CB b1 rD AD e RT CAa1CB b1
A+B EU
kU
U (undesired) rU kUCAa 2 CB b2 rU AUe RT CAa 2 CB b2
E
k T AeRT Rate of disappearance of A: rA rD rU
ED EU
rA ADe RT C Aa1CB b1 AUe RT C Aa2 CB b2
Define the instantaneous rate selectivity, SD/U
ED
rate of formation of D rD AD e RT
C A a1CBb1
SD U sD U EU
rate of formation of U rU A Ue RT
C A a2 CBb2
ED EU
k
SD U D CAa1a2 CB b1 b2 SD U
kU AU
AD
CAa1a2 CB b1 b2
e RT
Goal: Maximize SD/U to maximize production of the desired product
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-13
ED EU ED EU
ED EU ED EU
0 e RT 1 0 e RT 1
RT RT
Specific rate of desired reaction kD
Specific rate of desired reaction increases less rapidly with
kD increases more rapidly with increasing T
increasing T
Use lower T to favor desired
Use higher temperature to favor product formation (not so low that
desired product formation the reaction rate is tiny)
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-14
AD 1.987 298K AD
SD U e molK CAa1a2 SD U 4.6 108 CAa1a2
AU AU
cal cal
T = 100 C 20,000 10,000 kD/U
(373K): mol mol
cal
AD 1.987 373K AD
SD U e mol K CAa1a2 1.4 106 CAa1a2
SD U
AU AU
SD/U is greater at 373K, higher temperature to favors desired product formation
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-15
CAa1a2 CAa1a2
Use large CA Use small CA
c) b1 b2 b1 b2 0 d) b1 b2 b1 b2 0
CBb1b2 CBb1b2
Use large CB Use small CB
How do these concentration requirements affect reactor selection?
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-16
Semi-batch: concentration
Batch: CB0
of one reactant (A as
concentration is shown) is high at t=0 &
CA(t)
CB(t) high at t=0 & progressively drops with
progressively drops increasing time, whereas
with increasing time CA concentration of B can be
kept low at all times
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
kD L9-17
D High C favors desired High CA favors undesired
A+B a1 a2 A a1 a2
product formation product formation
kU (keep CA low)
U
b1 b 2 Batch reactor
PFR/PBR
Side streams feed low CA
High CB CA
When CA & CB are low (end time Semi-batch
favors or position), all rxns will be slow reactor slowly feed High CB
desired A to large amt of B
product PFR/PBR CA CA CA
formation High P for gas-phase rxn, do not CSTRs in
add inert gas (dilutes reactants) series
CA00 CA0
CB00 CB0
b1 b2 CSTR
PFR/PBR w/ side streams feeding
High CB low CB CB
favors Semi-batch
undesired reactor, slowly High CA PFR/PBR
product feed B to large amount of A PFR/PBR w/ high
formation CB CB CB recycle
(keep CB CSTRs in Dilute feed with inerts that are
series easily separated from product
low)
B consumed
Slides courtesy of Prof before&leaving
M L Kraft, Chemical CSTR
Biomolecular Engr Low
n Dept, P if gas
University phaseUrbana-Champaign.
of Illinois,
L9-18
FD ND
flow YD F F
Evaluated
batch YD Evaluated
A0 A at outlet NA0 NA at tfinal
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-19
or PFR/PBR or
n
dCB
dt
k1 CA0ek1t k 2CB
dCB
dt
k 2CB k1 C A0ek1t
Use integrating
factor (reviewed
d CBek 2t k C ek1t ek 2t
k 2 k1t CB k1CA0
1 A0 e k 2 k1
on Compass) dt
CC CA0 CA CB
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.
L9-21
CC CA0 CA CB
topt
The reactor V (for a given 0) and t that maximizes CB occurs when dCB/dt=0
dCB k1CA0
dt
k 2 k1
k1
e k1t
k 2 e k 2t
0
1 k
t opt ln 1
k1 k 2 k 2
V
t so Vopt 0t opt
0
Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.