tutorial chemical reaction engineering - otto von … · 1institute of process engineering,...
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1Institute of Process Engineering, G25-217, [email protected]
Tutorial Chemical Reaction Engineering:
Dipl.-Ing. Andreas Jörke1
11. Real reactors, residence time distribution and selectivity / yield for reaction networks
28-Jun-16
Ideal: no mixing (PFTR) or perfect mixing (CSTR)
Technical reality is in between those cases!
For technical / real reactors:
Measurements and modeling of the mixing state
Calculation of e.g. conversion for the mixing state
CRE: Real reactors and reaction networks 2 28-Jun-16
S S+P
Bypass flow
„dead zones“
CSTR PFTR
Fluid elements take different ways through packed bed
Radial flow velocity profile because of bypass flows at low dT/dP (<10)
Tutorial CRE: Residence time distribution
CRE: Real reactors and reaction networks 3 28-Jun-16
PFTR BR
CSTR
real
reactant 0
0
reactant
Da
"time given"
"time needed"
r T
c
Tutorial CRE: Residence time distribution
Characterization of residence time distribution with measurement of pulse or step responses
Description of pulse response with statistical moments
Normalized pulse response:
1. moment: mean residence time
2. moment: variance
CRE: Real reactors and reaction networks 4 28-Jun-16
t 0
C
0 t
C
t
S
t
S
Differentiation
1
0
dt
E t S t S t t
0
dt
t E t t
22
0
dt
t E t t
Tutorial CRE: Residence time distribution
Tutorial CRE: Residence time distribution
Ideal reactors vs. cascade model (N CSTR’s)
PFTR:
CSTR:
Cascade:
CRE: Real reactors and reaction networks 5 28-Jun-16
2R 0V
V
… 1 2 3 4 N-1 N
Norm
. Puls
e r
esponse E
(t)
Norm. residence time τ(t)
∞
2 2RV
V
22C R
R
V V NN
V V N
Tutorial CRE: Residence time distribution
Dispersion model: Tubular reactors
Introduction of an axial dispersion term in the mass balance
Characterization possible with Bodenstein-Number Bo:
PFTR assumption is reasonable if Bo > 100 and dT/dP > 10
CRE: Real reactors and reaction networks 6 28-Jun-16
, ,
1 1
div 0M M
ii i j j i i i j j
j j
c Vj r c J r
t z A
ax
d
d
ii
cJ D
z
2
ax ,21
0M
i ii j j
j
c cVD r
A z z
ax ax
"convective mass tranfer"Bo
"diffusive mass transfer"
V L vL
AD D
2 22R
2
2 8THO
Bo Bo
V
V
Tutorial CRE: Residence time distribution
Segregation model: Tubular reactors
Splitting of a tubular reactor into parallel PFTR‘s with different length (residence time, conversion)
Calculation of the mean conversion from the residence time distribution possible:
CRE: Real reactors and reaction networks 7 28-Jun-16
0
dt
X X t E t t
Tutorial CRE: Real tubular reactor
10.1 Real tubular reactor: Tracer experiment
CRE: Real reactors and reaction networks 8 28-Jun-16
Tcool
Tcool
2 2 1 1
tracermin min mol l min
144 0 0 0
64 4 0.3 0.0375
16 8 0.5 0.0625
0 12 0.5 0.0625
16 16 0.4 0.05
64 20 0.2 0.025
144 24 0.1 0.0125
256 28 0 0
t t c E
1 1
0
0
2 22 2
0
d
d 12 min
d 30.4 min
i
it
i i
it
i i
it
E t S t S t t S t S t t
t E t t t E t t
t E t t t E t t
A Br
Ar kc
10.045 mink
Tutorial CRE: Real tubular reactor
Part b: Number of STR for equivalent cascade
Part c: Conversion for cascade model
Mass balances of all CSTR‘s in cascade
CRE: Real reactors and reaction networks 9 28-Jun-16
Tcool
Tcool
2
24.74 5N
A Br
Ar kc
10.045 mink
Acascade 0
A
1 40 %Nc
Xc
0AA A
R
1AA A
R
1AA A
R
d 10
d
d 10
d
d 10
d
II I
A
ii i i
A
NN N N
A
cc c kc
t
cc c kc
t
cc c kc
t
1
AA
R1
NN c
ck
1
AA
R1
ii c
ck
A
0
A
1
1
N
N
c
ck
N
Tutorial CRE: Real tubular reactor
Part d: Conversion for segregation model
Conversion as function of time? Analogy between PFTR and batch reactor!
CRE: Real reactors and reaction networks 10 28-Jun-16
Tcool
Tcool
A Br
Ar kc
10.045 mink
seg
0
d 40 %i i
it
X X t E t t X t E t t
0AA A A
AA 0
A
dexp
d
1 1 exp
i i
i i
ckc c t c kt
cX t kt
c
2 2 1 1
tracer Amin min mol l min
144 0 0 0 0
64 4 0.3 0.0375 0.16
16 8 0.5 0.0625 0.30
0 12 0.5 0.0625 0.42
16 16 0.4 0.05 0.51
64 20 0.2 0.025 0.59
144 24 0.1 0.0125 0.66
256 28 0 0 0.72
t t c E X
Cascade model and segregation model
give the same result!
Tutorial CRE: Selectivity / yield for networks
10.2: Yield and selectivity for series reactions
Part a: Maximum yield of B for CSTR
Maximum yield 1. derivative = 0 (product rule)
CRE: Real reactors and reaction networks 11 28-Jun-16
1 2A B Cr r
0
A A 1 A
B1 A 2 B
C2 B
10
0
0
c c k c
ck c k c
ck c
0
AA
11
cc
k
0
1 AB
1 2
11
k cc
k k
B 1B 0
A1 2
11
c kY
ck k
2
B 1 1
22
21 21 2
d0
1d 1 11
Y k k
k kk k
B,max
1
21 1 22
1 1
1Y
k
k k kk
0
B B BB 0 0
A A
c c cY
c c
Tutorial CRE: Selectivity / yield for networks
10.2: Yield and selectivity for series reactions
Part b: Maximum yield of B for BR/PFTR
Maximum yield 1. derivative = 0
CRE: Real reactors and reaction networks 12 28-Jun-16
1 2A B Cr r
0
B B BB 0 0
A A
c c cY
c c
A1 A
B1 A 2 B
C2 B
d
d
d
d
d
d
ck c
ck c k c
ck c
0
A A 1expc c k
1 20
B 1 A
2 1
exp expk kc k c
k k
1 2BB 10
A 2 1
exp expk kcY k
c k k
B,max
2 2 1 1 2 1B1
2 1 2 1
exp exp lnd0
dY
k k k k k kYk
k k k k
Tutorial CRE: Selectivity / yield for networks
More than one reaction: Reaction network!
Series reaction:
Parallel reaction:
High selectivity to desired product!
Differential selectivity:
CRE: Real reactors and reaction networks 13 28-Jun-16
1 2 2 BB,series
1 1 A
1B,parallel
21 2
1
produced product
consumed reactant
1 PFTR, low conversion
1 PFTR or CSTR
1
dS
r r k cdS
r k c
rdS
kr r
k
1 2A B Cr r
1
2
A B
A C
r
r