chemical reaction engineering - nptel.ac.in · non-isothermal reactors - cstr 0.0 0.2 0.4 0.6 0.8...

Chemical Reaction Engineering Reactor Design

Jayant M. Modak Department of Chemical Engineering Indian Institute of Science, Bangalore

Chemical Reactor Design

Ø Objectives q  Technological

n  Maximum possible product in minimum time n  Desired quantity in minimum time n  Maximum possible product in desired time

q  Economic n  Maximize profit

Chemical Reactor Design

Ø Constraints q  Market

n  Raw materials availability – quality and quantity n  Demand for the product

q  Society/Legislative n  Safety n  Pollution control

q  Technological n  Thermodynamics n  Stoichiometry n  Kinetics

Chemical Reactor Design - Decisions

Ø Type of reactor q  Tubular, Fixed Bed, Stirred tank, Fluidized bed

Ø Mode q  Mass Flow: Batch, Continuous, Semibatch q  Energy: Isothermal, Adiabatic, Co/counter current

Ø Process Intensification q  Combining more than one type of unit operation

Tubular reactor – mass balance

Indian Institute of Science

( ) ( )

( ) 0

j jj j j j j

j j j j j j j jj j j j

ff

C CFlux R uC J R

t z t z

M C u M C M J M Rt z

ut xρ

ρ

∂ ∂∂ ∂+ = + + =∂ ∂ ∂ ∂

⎛ ⎞ ⎛ ⎞∂ ∂+ + =⎜ ⎟ ⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠

∂ ∂+ =∂ ∂

∑ ∑ ∑ ∑

Tubular reactor – energy balance


( )

( ) ( )

( )

1

j

j

T T j jj

T T

T

j

jj

j

jj

j

j Pj

j Pj

jj

jj

jj

j

j

C U F H A H J Qt A z

C U C H Pt t

F

TC Ct

TF C

CH

t

FH

z

JH

z

H

Hz

H Jz z

Jz

∂⎛ ⎛ ⎞ ∂⎜ ⎟ ∂⎝

⎞

⎛ ⎞∂ ∂+ + =⎜ ⎟∂ ∂ ⎝ ⎠∂ ∂= − = +∂ ∂

∂ = +∂

⎛ ⎞∂ = +⎜ ⎟∂ ⎝

⎠⎛ ⎞ ∂⎜ ⎟ ∂⎝ ⎠

∂

⎜ ⎟ ∂⎝ ⎠∂⎛ ⎞

⎜ ⎟ ∂⎝ ⎠∂⎛ ⎞

⎜ ⎟ ∂⎝ ⎠

⎞∂⎠⎠

⎛⎜ ⎟⎝

∑

∑

∑∑

∑

∑

∑

∑

Tubular reactor – energy balance


( )

( )

4

1

4

j

j

j j jj j j i i

j j

j P

rt

r

i

ij

ii t

j

j P

Q U

C F JH A H R H r

t A z z

T TC C

H

T Td

U T T

ut u

T TC C uu d

rt

⎛ ⎞ ∂ ∂⎛ ⎞+⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠⎝ ⎠

∂ ∂ ∂⎛ ⎞ ⎛ ⎞⎛ ⎞⎡ ⎤+ + = Δ⎜ ⎟ ⎜ ⎟⎜ ⎟⎢ ⎥∂ ∂ ∂⎣

⎛ ⎞ ∂ ∂⎛ ⎞+ +⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠

⎦⎝ ⎠=

= −

−⎝

⎝ ⎠

⎠

⎝ ⎠

Δ =

∑ ∑ ∑

∑

∑

∑

Stirred tank reactor – mass and energy balance


( ) ( ) ( )

0

0 0j

jj je j

j P i ii

Kj j jej j

rdTN C F H Hdt

V

dNF F R

dt

A U Tr TH= −⎛ ⎞

− +⎜ ⎟

=

Δ⎠

+

+

−⎝

−

∑∑ ∑

Fixed bed reactor – mass balance

( ) ( )

( )

( )

( )( )

,

,

2

2

,

4

,1 ( , ),

j

B j B j mj

jB j s j ej s f mj

f

rt

e

j P s ej

j

e

h

r j

r

C Flux qt z

CC u C D q

t z z

U T Td

D CYrX X

qT T TC C ut z

Yr

z

r T

ε ε

ε ρρ

λ

λ⎛

∂ ∂+ =∂ ∂

⎛ ⎞⎛ ⎞∂ ∂ ∂+ − =⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟∂ ∂ ∂ ⎝ ⎠⎝ ⎠

−

∂ ∂⎛ ⎞ =⎜ ⎟∂

⎞⎛ ⎞∂ ∂ ∂+ − +⎜ ⎟⎜ ⎟∂ ∂ ∂⎝ ⎠⎝=

∂⎝ ⎠

⎠∑

Psuedohomogenous model


mj

h ii

j

i

q R

q H r

=

= Δ∑

Heterogenous model – external diffusion


( )

( )( )

( )

( ) ( )

3 1

( ) ,

mj g j js p g v j js

v B

h f v s

g v j js j js s

f i ii

v s

q K C C n A K a C C

aR

q h a T T

K a C C R C T

h a HT T r

ε

= − − = − −

= −

= −

− =

Δ

−

− =∑

g g

Heterogenous model – internal diffusion


( )

( )

( )

'

'2 ' ' ' '

2

'2 '

2

''

1 ,

1i

j

ej j

ii

i i ii

j

e

jmj ej v j j

r R

h

Cr D R C T

r r r

Tr H r

H r

r r r

Cq D a R C

r

q

η

η

λ

=

⎛ ⎞∂∂ = −⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠⎛ ⎞∂∂ =⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠

∂= −

−Δ

=∂

=

Δ∑

∑

Non-isothermal reactors - PFR

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

1

2

300

325

3500 10 20 30 40

0.00.51.01.52.0

Concentration temperature

Time (min)

Adiabatic Isothermal

Con

cent

ratio

n


Non-isothermal reactors - CSTR

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0

0.5

1.0

1.5

2.0300

320

340C

once

ntra

tion

Residence time

Tem

pera

ture

Non-isothermal reactors - rate


0.0 0.5 1.0 1.5 2.00

2

4

6

8 r11/rate

C10-C1

Trajectories - Exothermic reaction


300 320 340 360 380 4000.0

0.2

0.4

0.6

0.8

1.0 X

eq

T

Isothermal

Adiabatic

Trajectories - Endothermic reaction


300 320 340 360 380 4000.0

0.2

0.4

0.6

0.8

1.0

Xeq

T

Isothermal

Adiabatic

Optimal temperature trajectories

0.0 0.2 0.4 0.6 0.8 1.00.01

0.1

1

10

100

1/ra

te

conversion

0.0 0.2 0.4 0.6 0.8 1.00.01

0.1

1

10

Rate

conversion

Optimal temperature


0

50

100

150

200

250

300

350

400

450

500

450 500 550 600 650 700

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Temperature K

Exte

nt

Thermal cracking of ethane in tubular reactor

Ø  Ethylene demands – polyethylene, ethylene oxide, ethylene glycol – 20 million tons per annum

Ø  Main Reaction increase in number of moles so steam as inert

Ø  Endothermic reaction - ∆H 34.5 kcal/mol, high

temperature for high equilibrium conversions, increasing temperatures along the length of the reactor

Ø  Side reactions higher conversion yield of side products higher


2 6 2 4 2C H C H H→ +

2 6 3 8 42C H C H CH→ +


Yield conversion diagram for ethane cracking

Ethane cracking reactor


Typical operating condn

•  L = 95 m

• G = 68.68 kg/m2/s

• P inlet 2.99 atm, outlet 1.2 atm

• T inlet 680, outlet 820 C

• Production 10000 tons/coil

Balances

( )

2

2

2

41 ( )

4

2

' 1

t

t

jj

t i iij pj

j

f ft b i

jj

ddFmass R

dzddTenergy q z d H r

dz F C

dp f dumomentum u udz d r dz

RT FFuA A p

π

ππ

ξ ρ ρπ

=

⎡ ⎤= + − Δ⎢ ⎥

⎣ ⎦

⎡ ⎤− = + +⎢ ⎥

⎣ ⎦⎡ ⎤⎢ ⎥= = ⎢ ⎥⎢ ⎥⎣ ⎦

∑∑

∑

Simulation of ethane reactor

Hydrogenation of oil

Ø  Major demand – margarine, shortenings, vanaspati

Ø  Vegetable oils – mixture of triglycerides - glycerol and fatty acids

Ø  Fatty acids – saturated (S) , monosaturated (cis, R1 and trans, R2) and diunsaturated (B). Hydrogenation to reduce odor or color, improve stability and increase melting point.

Ø  Product requirements – some polyunsaturated

(health) and R2 ( consistency and higher melting points)

Reactions

2 2

1/ 21 4 5 6,H Hr r C r r C− ∝ − ∝

implies selectivity of monounsaturates over saturates proportional to (CH2)1/2

Yield conversion diagrams

Balances

( ) ( )( ) ( )

( )

2 2 2 2

2

2 2 2 2

2 2 2

1 2

, , ,

,, , , ,

, ,

, , ,

,

0

1 1 1

jj

L v H g H s H j H s

H bL v H g H b S S H b H s

S S H b H s H

L v S SL v

dCmass R j B R R M

dtk a C C R C C

dCk a C C k a C C

dtk a C C R

k a k ak a

= =

− − =

= − − −

= − +

= +

Stirred tank batch reactor Ø  Desired conversion –

batch time Ø  Desired production rate

and batch time – volume

Ø  Based on volume – internal design

Ø  Cooling load ( ) ( )i i K ri

Q V H r A U T T− = −Δ = −∑

Ammonia synthesis

Ø Major demand – Fertilizer, chemicals, explosives, polyamides, pharmaceuticals; 150 million tons per annum

Ø Main reaction Ø High pressure, low temperatures

favorable Ø Catalytic reaction – iron, promoted

ruthenium

12

N2 +32

H2 ! NH3 , !H298K = "45.7 kJ / mol"1

Ammonia synthesis – equilibrium


500 600 700 800 9000.00.10.20.30.40.50.60.70.80.91.0

(A)

1

310

50

100

200

P = 300 atm

A

mm

onia

Mol

frac

tion

Temperature (K)0 100 200 300

0.00.10.20.30.40.50.60.70.80.91.0

(B)

773

723

673

623

573

523

T = 473 K

Am

mon

ia M

ol fr

actio

nPressure (Atm)

Ammonia synthesis - balances


( )

( ) ( )

( )'

2 ' '2

'2

2

,

4

1 ,

1

js j j

f s p rt

iie i i

e

dCmass u R C T

dzdT Uenergy u c T T H rdz d

dCd r D R C Tr dr dr

catalystdTd r H r

r dr dr

η

ρ η

λ

=

= − + −Δ

⎛ ⎞= −⎜ ⎟

⎝ ⎠⎛ ⎞

= Δ⎜ ⎟⎝ ⎠

Reactor simulation

0 1 2 3 4 50

20

40

60

80

100

120

rate at bulk conditions observed rate

rate

Length (m)


0 1 2 3 4 50.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

N2

H2

NH3

m

ol fr

actio

n

Length (m)0 1 2 3 4 5

680700720740760780800820840860

tem

pera

ture

Length (m)

Optimal temperature


0

50

100

150

200

250

300

350

400

450

500

450 500 550 600 650 700

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Temperature K

Exte

nt

Fixed bed reactors


Ammonia – Multibed reactor

400 500 600 700 800 9000.0

0.2

0.4

0.6

0.8

1.0 r=0 r/ T=0 Reactor 1 Reactor 2 Reactor 3

Conversion

Temperature


Fixed bed reactors


Ammonia – Autothermal

400 500 600 700 800 900 10000

50

100

150

200

250

300 Ttop-T1L

Ttop-Tfeed

473 491 513 523 578 623

ΔΤ

Ttop


400 500 600 700 800 900 1000400

500

600

700

800

900

1000

T feed

K

Ttop K

Ammonia – Autothermal

0 1 2 3 4 5 6

500

550

600

650

700

750

800

reactor heat exchanger

Conversion

Length


600 650 700 750 800 850 9000.00.10.20.30.40.50.60.70.8

r=0 ∂r/∂T=0

Conversion

Temperature

Process intensification

Ø Strategy of reduction in physical size of a chemical plant while achieving given objective

Ø 30 – 40 years old concept, reinvented in last decade due to intense competition, scarce resources and stricter environmental norms

Ø Multifunctional reactive systems – several functions are designed to occur simultaneously.

Ø Major drive in refining and petrochemicals sector


Catalyst particle in reacting media

Ø  Type A – at catalyst level Ø  Type B – at interphase

transport level Ø  Type C – at intra-reactor

level – separations/heat transfer

Ø  Type D – inter-reactor level by combining two reactor operation with solids recirculation.


Type A Example – bifunctional catalysis

Ø Catalytic reforming to increase the octane number

Ø Conversion of parafins, cyclo parafins and napthenes to aromatics and branced paraffins.

Ø Reactions involved – dehydrogenation, cyclization and isomerization

Ø Pt/SiO2 catalyst


Type B Example – Gas induction reactors


DISPERSIONGAS-LIQUID

STATORDRAFT TUBE

DISPERSING IMPELLER

SUSPENDING IMPELLER

SELF INDUCING IMPELLER

GAS ENTRANCE

DISPERSIONGAS-LIQUID

STATORDRAFT TUBE

DISPERSING IMPELLER

SUSPENDING IMPELLER


GAS-LIQUID

STATORDRAFT TUBE

DISPERSING IMPELLER

SUSPENDING IMPELLER


GAS ENTRANCE

GAS - LIQUID DISPERSION

STATOR DRAFT TUBE

Type C – Intra-reactor operation

Ø Energy transfer – reaction in heat exchanger Ø Momentum transfer – radial flow reactors Ø Mass transfer – reactive- distillation,

absorption


Type C – Momentum transfer

Ø High gas flow rates – ammonia synthesis, styrene from ethylbenzene, flue gas treatments


Type C – Mass transfer

Ø Enhance conversion in equilibrium limited reaction, prevent undesirable reaction, increase rate of product inhibited reactions


Type C – Energy transfer

0 1 2 3 4 5 60.00

0.05

0.10

0.15

0.20

0.25

0.30

Flue gas Process

Temperature

Length


4 2 2

4 2 2 2

3 206 /2 2 803 /

CH H O CO H H kJ molCH O CO H O H kJ mol

+ + Δ =+ + Δ = −

ÉÉ

0 1 2 3 4 5 6

640

680

720

760

800

840

Flue gas Process

Temperature

Length

Type C – Example styrene synthesis


Design considerations and safety


Multiplicity in stirred tank reactor


Explosion in batch reactor


Runaway/Hot spot in tubular reactor


Runaway/Hot spot in tubular reactor


0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.000

0.005

0.010

0.015

0.020

0.012 0.015 0.016 0.0175 0.0176 0.0181

part

ial p

ress

ure

Length0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

600

700

800

0.012 0.015 0.016 0.0175 0.0176 0.0181

temperature

Length

Runaway/Hotspot in tubular reactors


610 620 630 640 650 660

0.004

0.008

0.012

0.016

0.020

Par

tial p

ress

ure

temperature

Sensitive

Insensitive


q=det (A)

>= ±

>

q p

iλ α βα

2

1,2

/ 4

0

=q p2 / 4

>= ±

>

q p

iλ α βα

2

1,2

/ 4

0

>= ±

<

q p

iλ α βα

2

1,2

/ 4

0

<=<

q p

λ α αα

2

1,2 1 2

/ 4

,

' ' 0

<=<

q p

λ α αα

2

1,2 1 2

/ 4

,

' ' 0

<=

> >

q p

λ α αα α α

2

1,2 1 2

1 1 2

/ 4

,

0,

<= >

q p

λ α α

2

1,2 1 2

/ 4

, 0

p=tr (A)

Stability analysis

Ø A state X=0 is said to be stable when given e>0, there exists a d>0 (0<d<e) such that if ||X(0)||<d then ||X(t)|| < e for all t>0

Ø A state X=0 is said to be asymptotically attractive when given m>0, such that if ||X(0)||<m then lim (t→∞) ||X(t)|| =0

Ø A state is asymptotically stable when stable and asymptotically attractive.

Ø A state is marginally stable when stable but not asymptotically attractive


Examples


( )( )

( )( )

2 5

22 2 2 2

2

22 2 2 2

1

2

1

x y x ydxdt x y x y

y y xdydt x y x y

− +=

+ + + +

−=

+ + + +

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Y

X

dx ydtdy xdt

=

= −

-1.2-1.0-0.8-0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.2

Y

X

Two dimensional system - Eigen values


22

1,202 4T TT D Dλ λ λ− + = ⇒ = ± −

0

Stablenode

Stablefocus

Unstablefocus

D=determinant(A)

T=trace(A)

T2/4-D=0

Unstablenode

Unstable node


0.1 0.00971, 0.988 0.0099,0.9782D Tµ λ= = = =

-50 0 50 100 150 200 250 300 35010

15

20

25

30

35

40

45

-50 0 50 100 150 200 250 300 350

0.00

0.02

0.04

0.06

0.08

0.10

10 20 30 40 50

0.00

0.02

0.04

0.06

0.08

0.10

alpha

Time

beta

Time

beta

alpha

0

Stablenode

Stablefocus

Unstablefocus

D=determinant(A)

T=trace(A)

T2/4-D=0

Unstablenode

Unstable focus


0.5 0.248, 0.751 0.3756 0.3276iD Tµ λ= = = = ±

-50 0 50100150200250300350400450500550600650700750-50

0

50

100

150

200

250

300

350

-50 0 50 100 150 200 250 300 3500.0

0.5

1.0

1.5

2.0

2.5

3.0

-10 0 10 20 30

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2 4 6 8 10 12 14 16 18 20-10-8-6-4-20246810

alpha

Time

beta

Time

beta

alpha

linearized process real process

beta

alpha

0

Stablenode

Stablefocus

Unstablefocus

D=determinant(A)

T=trace(A)

T2/4-D=0

Unstablenode

Stable focus

-50 0 50 100 150 200 250 300 3500.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

-50 0 50 100 150 200 250 300 3501.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.801.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

-2 0 2 4 6 8 10

0.0

0.1

0.2

0.3

alph

a

Time

beta

Time

beta

alpha

Δ a

lpha

alpha


2.0 3.99, 2.98 -1.4900 1.3288iD Tµ λ= = = − = ± 0

Stablenode

Stablefocus

Unstablefocus

D=determinant(A)

T=trace(A)

T2/4-D=0

Unstablenode

Stable node

-50 0 50 100 150 200 250 300 350

0.40

0.45

0.50

0.55

0.60

0.65

-50 0 50 100 150 200 250 300 3501.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

0.40 0.45 0.50 0.55 0.60 0.651.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

alpha

Time

beta

Time

beta

alpha


2.5 6.23, T = -5.21 -3.3614, -1.8525Dµ λ= = = 0

Stablenode

Stablefocus

Unstablefocus

D=determinant(A)

T=trace(A)

T2/4-D=0

Unstablenode

Limit cycle

-50 0 50 100 150 200 250 300 350

0.6

0.8

1.0

1.2

1.4

1.6

-50 0 50 100 150 200 250 300 3500.70.80.91.01.11.21.31.41.5

0.6 0.8 1.0 1.2 1.4 1.60.70.80.91.01.11.21.31.41.5

alpha

Time

beta

Time

beta

alpha


1.005 1.01, T = 0 1.003iDµ λ= = = ± 0

Stablenode

Stablefocus

Unstablefocus

D=determinant(A)

T=trace(A)

T2/4-D=0

Unstablenode

Adiabatic CSTR


0 1 2 3 4 5 6 70

20

40

60

80

100 Heat generation Heat removal

τ=60 s τ=10 s τ = 100 s

rate

θ

Adiabatic CSTR – steady state multiplicity

Steady state

Eigenvalues

0.08996, 0.61698

–1.67×10-2 , – 8.68×10-3

0.4957 3.4

–1.67×10-2 7.05×10-3

0.7628 5.2318

–1.74×10-2

–1.66×10-2


0 40 80 120 160 2000.0

0.2

0.4

0.6

0.8

1.0

0

2

4

6

8

10

conversion temperatureco

nver

sion

residence time te

mpe

ratu

re

Adiabatic CSTR – phase plane, transient


0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

10

12

14

Tem

pera

ture

Conversion

Non-ideal flow, mixing and reactions

Ø  If, we know precisely what is happening within the vessel, thus, if we have a complete velocity distribution map for the fluid in the vessel, then we should, in principle, be able to predict the behavior of a vessel as a reactor. Unfortunately, this approach is impractical, even in today’s computer age. Levenspiel, Chemical Reaction Engineering, 1999.

Ø  Mobil Adds Million-Dollar Benefits by Using Flow Simulation to Optimize Refinery Units, Greg Muldowney, Mobil Technology Company, 2007


Ø Bioreactor performance: interactive relation between biosystem and physical environment q  Biotic phase: complex machinary inside cell and

its regulation by external environment q  Abiotic phase: multiphase system with complex

interactions of mass, momentum and energy leading to environmental gradients in space and time


CFD modeling of bioreactors

Anaerobic digestion

Complex polymers


Fermentative B.

ACETOGENESIS

HYDROLYSIS and

ACIDOGENESIS

METHANOGENESIS

Acetate CO2 + H2

CH4 + CO2 CH4+H2O

Homoacetogenic B. Acetoclastic B. Hydrogenophilic B.

Monomers Acidogenic B.

Acetogenic B.

Volatils fatty acids (VFA), alcohols, ...

76 20 4

52 24

72 28


CFD modeling of anaerobic bioreactor

xy

Gas

Leafy biomass

water

1

1.2

1.4 Waste water in

0.15φ

Biogas out

Treated water out

0.15φ

6

Results & Discussion


Contour plot for liquid velocity (m/s) (with Packed bed)

Vector plot for liquid velocity (m/s) (with Packed bed)

PIV – experiments


Experimental verification


Contours of X-direction mean velocity (inlet NRe=7660) (a)experimental and (b ) Simulation results without packed bed

Experimental verification


Contours of X-direction mean velocity (inlet NRe=500) (a)experimental and (b ) Simulation results with packed bed

Improving the performance


Non-ideal flow, mixing and reactions


Residence time distributions

Ø Exit age distribution E(t)dt q  Fraction of material in exit stream which has age

between t and t+dt Ø Cumulative residence time distribution, F(t)

q  Fraction of material in exit stream with age less than t

Ø  Internal age distribution, I(t)dt q  Fraction of material within vessel which has age

between t and t+dt


0

( )( ) ( ') ' ( ), 1 ( ) ( )'

t dF t VF t E t dt or E t F t I tdt F

= = − =∫

Means and moments of distribution

Ø Mean residence time


0 0 0

( ) ( ) ' ( )t tE t dt E t dt tE t dt∞ ∞ ∞

= =∫ ∫ ∫Ø Variance

( )22

0

( )t t E t dtσ∞

= −∫Ø Skewness

( )23 3/ 2

0

( )s t t E t dt σ∞

= −∫

Example


0 2 4 6 8 10 12 140.00

0.05

0.10

0.15

0.20

E

(t)

t0 2 4 6 8 10 12 14

0.0

0.2

0.4

0.6

0.8

1.0

F(t

)

t

0 2 4 6 8 10 12 140.00

0.05

0.10

0.15

0.20

I(t)

t 0 2 4 6 8 10 12 140.0

0.2

0.4

0.6

0.8

t E(t

)

t

Experimental determination of RTD

Ø Convolution integral


0 0

( ) ( ') ( ') ( ') ( ')t t

e o oC t C t t E t dt C t E t t dt= − = −∫ ∫Ø Pulse input

0

( ) ( ) ( )e eE t C t C t dt∞

= ∫Ø Step input

0( ) ( )eF t C t C=

Determination of RTD from model

Ø CSTR


( )1( ) expE t t ττ

= −

Ø PFR

( ) ( ), ( ) ( )E t t F t H tδ τ τ= − = −

Ø PFR-CSTR or CSTR-PFR 0

( ) 1 exp

p

pp

s s

tE t t

t

ττ

ττ τ

<= −⎛ ⎞

≥⎜ ⎟⎝ ⎠

RTD and reactions

Ø  kinetics of the reaction Ø  the RTD of fluid in the reactor Ø  the earliness or lateness of fluid mixing in the

reactor Ø whether the fluid is a micro or macro fluid


Example – second order reaction


0 2 4 6 8 100.0

0.2

0.4

0.6

0.8

1.0C

/C0

kτC0

CSTR-PF PF-CSTR PF CSTR PF(τ=4) CSTR(τ=4)

Macro- and Micromixing

Ø Macromixing – distribution of residence times in the reactor

Ø Micromixing – description of how molecules of different ages interaction with each other q  Complete segregation – all molecules of same

age group remain together until they exit the reactor

q  Complete micromixing – molecules of different age group are completely mixed

Ø  the earliness or lateness of fluid mixing in the reactor

Ø whether the fluid is a micro or macro fluid Indian Institute of Science

Zero parameter models

Ø Complete segregation


0

( ) ( )sC C t E t dt∞

= ∫

Model


00

( ) (0) ( ) ( )

( ) ( ) (0) 0

s

ss

dC R C C C C C t E t dtdtdC C t E t Cdt

∞

= = =

= =

∫

( ) ( ) ( )

( )

( )

2

2

2

0, 0,1 11( )

1( 1 )1

s

z dC dC dz dct t z zz dt dz dt dz

dC R Cdz zdC E z z Cdz z

= ∞ ≡ = = −−

=−

−=−

Zero parameter models

Ø Maxiumum mixedness


( )10 10( )( ) ( 0)

1 ( )dC ER C C C C Cd F

λ λλ λ= − − − = =

−

Example – second order reaction


0.01 0.1 1 10 100 1000

0.0

0.2

0.4

0.6

0.8

1.0 maximum mixedness complete segregation 2 CSTRs

C/C

0

kτC0

1 10 100 10000.0

0.2

0.4 maximum mixedness complete segregation 2 CSTRs

Example – mass transfer and reaction


1 10 100 1000 100000.0

0.1

0.2

0.3

0.4

0.5

0.6

CA

e

r(µm)

maximum mixedness segregated flow

0 2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

Con

cent

ratio

nθ

CA (r=1µm) CB

CA (r=100µm) CB

One parameter models

Ø Tanks – in - series


12 1( ) exp

( 1)!

N n

NN t ntE tN N

στ τ

− ⎛ ⎞= =⎜ ⎟− ⎝ ⎠

One parameter models

Ø Axial dispersion model


( )2 1 11 1 PeePe Pe

σ −⎡ ⎤= − −⎢ ⎥⎣ ⎦

RTD


0 20.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1 2 3 4

10

4

2

1

E(t)

t

0.0 0.5 1.0 1.5 2.00

1

2

3

4

5

6

7

dispersion model500

4050

E(t)

t

Transient in PFR


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0 t

0 0.25 0.5 0.75

: :

2.5

C

z

Compartment models


Example


0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Yie

ldB

ρ

1 CSTR 2 CSTR

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Con

vers

ion A

ρ

1 CSTR 2 CSTR


Rate contours –reversible reaction

0

0

0

00

0.1

0.1

0.1

0.1

0.1

1

1

11

10

1010

100100

Temperature

α'

300 310 320 330 340 350 360 370 380 390 4000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Fludized bed catalytic convertors


Fluidised bed reactor


Solid volume fraction

chemical reaction engineering - nptel.ac.in · non-isothermal reactors - cstr 0.0 0.2 0.4 0.6 0.8...

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