1Institute of Process Engineering, G25-217, andreas.joerke@ovgu.de

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