Design of Reactor

7/31/2019 Design of Reactor

1/31

Design of Reactor

By; Eko Ariyanto, ST., MChemEng

8 November 2007 (Week II)


2/31

dVrdXF AAA )(0

PFR

dt

dXNVr AAA 0)(

Batch

t CA 0 dXA(rA )0XA

AX

A

AA

rdXC

vV

00

0

0A

For constant density systems:

identical performance equation

the same Vis needed to do the job

Single

reactions design batch / plug reactor / CSTR -

Vv0 CA0VFA0

CA0XArA

CSTR

FA0XA (rA )V

We need acomparativestudy


3/31

Single reactions design- CSTR (mixed) / plug reactor -

n

AA

A kCdt

dN

Vr

1General nth order rate equation:30n

n

A

n

AAA

n

AA

AA

mA

Am

X

XX

kCr

XC

F

VC

)1(

)1(11

0

0

0

0

AA

AAA

X

XCC

1

10

p CA0V

FA0

p

CA0dXA

rA0XA 1

kCA0n1

(1 AXA )ndXA

(1 XA )n0

XA

mixed

plug

(1)

2)


4/31


CA0n1

m

CA0n1

p

CA 0

nV

FA 0

m

CA 0

nV

FA0

p

XA1 AXA

1 XA

n

m

1 AXA1 XA

n

dXA0

XA

p

0

0

0 A

A

F

VC

v

VDividing (1) / (2) and

0A


5/31


CA0n1

m

CA0n1 p

XA

1 XA n

m

1 XA 1n

1

n 1

p

CA0n1

m

CA 0n1

p

XA

1 XA

m

ln(1 XA )p

0A

1n 1n


6/31


m

p

Vm

Vp

XA

1 XA n

m

1 XA 1n

1

n 1

p

Plot for various XA and comparethe performance

For equal quantities (FA0) ofthe same feed (CA0):


7/31

Single reactions design- mixed reactor systems / 1st order rxn. -

1

/1

0

N

N

ireactorsN

C

C

k

NN

C

C

kp

0ln1

N

Series of N mixed

Plug flow

p

N

p

N

V

V

RA


8/31

Single reactions design- plug reactor systems -

X1,X2,...XN

Consider:

Nplug flow reactors connected in series

Conversion of component A leaving reactor 1,2,3N

V

FA0

dXA

rAXAiXAf

Vi

FA0

dXA

rXi1Xifor ithreactor

V

F0

Vi

F0i1

N

V1 V2 ...VNF0

dX

r

X0

X1dX

r

X1

X2 ...dX

rXN1XN

dX

rX0XN

N reactors in series

N plug reactor in series conversion = single plug reactor conversion


9/31

Design of parallel reactions- product distribution -

A

Decomposition of A

1

1

a

AR

R Ckdt

dCr

R

S

1k

2k

2

2aA

SS Ck

dtdCr

21

2

1 aa

A

S

R

S

R Ck

k

dC

dC

r

r

2121 ,,, aakk ct. (specific system, given temp.)

adjust & controlAC

(desired product)

(unwanted product)

maximise!!!


10/31


A

Decomposition of A

1

1

a

AR

R Ckdt

dCr

R

S

1k

2k

2

2aA

SS Ck

dtdCr

21

2

1 aa

A

S

R

S

R Ck

k

dC

dC

r

r

2121 ,,, aakk ct. (specific system, given temp.)

adjust & controlAC

(desired product)

(unwanted product)

maximise!!!


11/31

Design of parallel reactions- adjusting CA -

CA low CA high

Mixed flow reactor

Maintaining high conversion

Increasing inerts in feed

Decreasing the pressure ingas-phase systems

Batch / PFR

Maintaining low conversion

Removing inerts in feed

Increasing the pressure ingas-phase systems

CA low or high?

21

2

1 aaA

S

R

S

R Ckk

dCdC

rr


12/31

Design of parallel reactions- adjusting CA -

AR

S

1k

2k

(desired)

(unwanted)

21

2

1 aa

A

S

R

S

R Ck

k

dC

dC

r

r

021

aa CA should be high Batch / plug flow reactor smallsize reactor

CA should be lowMixed flow reactor large size

reactor

21aa .

1

2 ctk

k

dC

dC

r

r

S

R

S

R Product distrib. unaffected by CA

021

aa


13/31

Design of parallel reactions- adjusting k2/k1 -

AR

S

1k

2k

(desired)

(unwanted)

21

2

1 aaA

S

R

S

R Ckk

dCdC

rr

2 ways: Changing the temperature level of operation later!

Using a catalyst selectivity feature the most effective way!


14/31

Design of parallel reactions- summary -

AR

S

1k

2k

(desired)

(unwanted)

High reactant concentration favours the high order reaction

Low reactant concentration

favours the lower order reaction

No effect of concentration reactions with the same order

1

1aA

RR Ck

dtdCr

2

2

a

AS

S Ckdt

dCr

Reactants concentration = key controlling variable:


15/31

Design of parallel reactions- other parallel reactions -

BA R

S

1k

2k

(desired)

(unwanted)

rR dCRdt

k1CA1CB

1

22

2

BA

S

S

CCkdt

dCr

BA

2121

2

1 BAS

R

S

R CC

k

k

dC

dC

r

rMaximise!!!

021

021

021

021


16/31

Design of parallel reactions- contacting patterns -

Batch process

021

021

021

021

021

021

2121

2

1 BAS

R

S

R CCk

k

dC

dC

r

r


17/31


Continuous process

021

021

021

021

021

021

2121

2

1 BAS

R

S

R CCkk

dCdC

rr

Slide 19Slide 25


18/31


Example 1:For the following reactions:

BA TR

US

1k

2k

(desired)

(unwanted)

3.05.1

1 BATR CCk

dt

dC

dt

dC

8.15.02 BA

US CCkdtdC

dtdC BA

Order the contacting schemes from most desirable to least desirable


19/31


Example 1 Solution:

rR k1CA1.5

CB0.3

rS k2CA0.5

CB1.8

rR

rS

k1

k2

CACB1.5

Maximise CA high, CB low (most important)


20/31

Design of parallel reactions- fractional yield -

A RKnowing the rate equations - we can determine the product distribution &reactor size

Instantaneous fractional yield of R

moles R formedmoles A reacted

dCR

dCA

Overall fractional yield of R

all R formedall A reacted

CRf

CA 0 CAf C

Rf

(CA )in reactor

Selectivity

selectivity moles of desired product formed

moles of undesired material formed


21/31

Design of parallel reactions- fractional yield for PFR / MFR -

PFR CA is changing through the reactor

CAf composition everywhere

p 1

CA0 CAfdCACA0

CAf 1CA

dCACA0

CAf

MFR

m evaluated at CAf

m dpdCA

at CAf

p 1

CAmdCACA0

CAf

PFR / MFR relationships


22/31

Design of parallel reactions- fractional yield for series of MFR -

MFR in series Overall yield = sum (fractional yields) weighted by theamount of reaction occurring in each vessel

N mixed 1(CA0 CA1)2(CA1 CA2) ...N(CA,N1 CA,N)

CA0 CAN

CRf (CA0 CAf)

For any type of reactor:

Very useful!!!


23/31

Design of parallel reactions- graphical representation of CRf -

p 1CAdCACA0

CAf

CRf (CA0 CAf)

m evaluated at CAf

CRf (CA0 CAf)

CRf

CRf

CRf

N mixed 1(CA0 CA1) ...N(CA,N1 CA ,N)

CA0 CAN

CRf (CA0 CAf)


24/31

Design of parallel reactions- graphical representation / types of flow -

Which type of flow gives the best product distribution?

Mixed flow isbest

Plug flow is best

Mixed up to CA1follow by plugflow

the largest area


25/31


Example 2:Consider the aqueous reactions:

(desired)

(unwanted)

CRf=?

BA1k

2k

S

R

dCR

dt1.0CA

1.5CB0.3

dCS

dt1.0C

A

0.5CB

1.8

Equal volumetric flow rates of A and B

Each stream has C=20 mol/lof reactant

90% conversion of A


26/31


Example 2 Solution:

R

A

dCR

dCR dCS

1.0CA1.5

CB0.3

1.0CA1.5

CB0.3 1.0CA

0.5CB

1.8

CA

CA CB1.5

Af

A

C

CA

AfA

p dCCC 00

1

a) Plug Flow

)1(0 AAAf XCC

BA1k

2k

S

R

10

1 5.0

1

10 5.1 19

1

110

1

A

A

AA

AAp

C

dC

CC

dCC

BA CC


27/31


Example 2 Solution:

p 1

9

dCA

1 CA0.51

10

CA0.5 x CA x

2

dCA 2xdx

p

1

9

2xdx

1 x110

2

9 dx

dx

1 x110

1

10

0.32

CRf (CA0 CAf) 9(0.32) lmolCRf /86.2

CSf (1 )(CA0 CAf) 9(10.32) lmolCSf /14.6


28/31


Example 2 Solution:

lmolCRf /5.4

lmolCSf /5.4

b) Mixed Flow

m evaluated at CAf

5.01

15.05.1

ABA

Aexit

CCC

C

BA CC

)5.0(9)( 0 AfARf CCC

)5.01(9))(1( 0 AfASf CCC


29/31


Example 2 Solution:

lmolCRf /85.7

lmolCSf /15.1

c) Plug flow A Mixed flow B

)87.0(9)( 0 AfARf CCC

)87.01(9))(1( 0 AfASf CCC

Af

A

C

CA

AfA

p dCCC 00

1

87.0118

1

)1(18

1

119

1 19

1

19

1

1

19 5.1

1

19 5.1

A

AA

A

AA

BA

AAp

C

dCdC

C

dCC

CC

dCC


30/31


Example 2 Solution:Summary

Plug Flow:

Mixed Flow:

Plug A / Mixed B

32.0 AR

5.0 AR

87.0 AR

lmolCRf /86.2

lmolCRf

/85.7

lmolCRf /5.4


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Design of Reactor