stoic hi o kinetics

7/29/2019 Stoic Hi o Kinetics

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Chemical Reaction EngineeringLecture 2: Review of Undergraduate Material

Jayant M. Modak

Department of Chemical Engineering

Indian Institute of Science, Bangalore


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Ethylene production by thermal cracking of ethane

!The thermal cracking of ethane is carried out inmultitubular reactor. Typical production capacity

of each tube is 10000 Tons per annum.

!Reactor specifications:" Feed to the reactor: ethane + steam (?)" Inlet pressure - 2.99 atm; temperature - 680C" Tube length 95 m, ethylene conversion 60%

Indian Institute of Science


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Cracking of ethane to ethylene

26 24CH

C!

Reactor Design

Stoichiometryconversionmolar flows

Rate ofreaction

Molebalances

Batch/CSTR/PFR

Conversion

Volume

Production rate

CSTR +PFR


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Topic 1: Basic concepts

!Representation of reaction!Extent of reaction and conversion!Thermodynamics and chemical reactions

" Heat of reaction" Condition of equilibrium


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Representation of chemical reaction single reaction

!Consider a single chemical reaction in N speciesA1, A2,., AN

!General representation:

!jAj

= 0

j=1

N

"


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Representation of chemical reaction multiple reactions

!Consider R chemical reactions in N species A1,A2,., AN

!General representation:!ijAj = 0

j=1

N

" , i = 1,!2,!.........,!R


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Representation of chemical reaction independent reactions

!Stoichiometric matrix

!Number of independent reaction

! =

!11 !

1N

! " !!R1

# !RN

"

#

$

$$

%

&

'

''

R!=!rank!! !"# $%


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Progress of chemical reaction single reaction

!Consider a reaction !!jAj = 0 taking place in aclosed system

nj0 = number of moles of speciesjpresent initially

nj = number of moles of speciesjat any time t

!Molar extent of reaction - "

! =

nj" n

j0

#j


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Molar extent of reaction

!Properties of"" defined for the reaction

" Extensive property in moles

"Always positive

! =

nj" n

j0

#j

! =

nj " nj0

#j

=n

k " nk0

#k

$!!nk = nk0 + #k#j

nj " nj0( )


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Conversion of species

!Conversion X

!Stoichiometrically limiting species k

X=n

j0! nj

nj0

min!! ! nj0"

j

#

$

%&

'

(


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Cracking of ethane to ethylene

26 24CHC!

Molar flow at

entry

Ethane, F10

Molar flow at

exit

Ethane, F1Ethylene, F2


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Stoichiometric tables Flow reactor

!

1

A1

+!

2

A2

+ !

3

A3

+!

4

A4

= 0

Species Entry(mol/

min)

Change(mol/

min)

Exit from the reactor(mol/min)

A1 F1O -(F10X) F1=F10- F10XAj j=2,3, 4 FjO - #j/#1

(F10X)Fj=Fj0- #j/#1 F10X

I (inerts) FI0 ----- FI= FI0

Total FT0 FT=FT0-(!#j/#1)F10XFT=FT0+!F10X


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Concentrations in terms of conversion

Pv = Z FT RTP

0v0= Z

0F

T0RT

0

!"#$#

v = v0

P0

P%&'

()*

ZZ

0

%&'

()*

TT0

%&'

()*

FT

FT0

%&'

()*

FT= F

T0+ +F

10X

FT

FT0

= 1+ +F10

FT0

X= 1+ +y10X= 1+ ,X

v=

v0

P0

P

%

&'

(

)*

Z

Z0

%

&'

(

)*

T

T0

%

&'

(

)*1+ ,

X( )


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Concentrations in terms of conversion

0

0

0

0 0

0 0

0

0 0

0 0

0

0 0

1

1

/

1

A

A

A AA

A

A A

B

B A

FC

v

F F XFC

v v

Z TX PC C

X P Z T

Z Tb aX P C C

X P Z T

!

!

=

"= =

# $ # $ " # $# $= % & % & % & % &

+' ( ' (' ( ' ( # $ #) " # $# $

= % & %% & % &+' ( ' (


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Summary Stoichiometry of reaction

!Keywords & concepts" Stoichiometric coefficients" Multiple reactions" Set of independent reactions" Extent of reaction" Conversion" Stoichiometric tables



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Ethylene production by thermal cracking of ethane

!The thermal cracking of ethane is carried out inmultitubular reactor. Typical production capacity

of each tube is 10000 Tons per annum.

!Reactor specifications:" Feed to the reactor: ethane + steam (?)" Inlet pressure - 2.99 atm; temperature - 680C" Tube length 95 m, ethylene conversion 60%



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Chemical Equilibrium

!Consider a reaction !!jAj = 0 taking place atconstant temperature T and pressure P. The

system will spontaneously change in the direction

of increasing entropy, reaching equilibrium when

entropy can not increase further.!Free energy and Gibbs equations


dG = Vdp ! SdT+ jdnjj=1

N

" ,

Chemical !Potential !j = #G#nj$%& '()T,P,nk


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Chemical Equilibrium

!Equilibrium condition


Gibb 's!Equation dG = Vdp ! SdT+ jdj=1

N

" nj

!!!G

!"#$%

&'(T,P

=

)jjj=1

N

*=

0

!!!!!dG

=

Vdp"SdT

+ #jjd

$

j=1

N

%

Progress!of!reaction nj = nj0 + !j"!!or !!dnj = !jd"!


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Chemical potential

!Solution


jT,P,x( ) = j0 T,P

r,x

r( ) + RTln!jxj

x = composition!,!T = temperature,!P = pressure

superscript!r !=!reference!= activity!coefficient


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Free energy change

j=

j0+RTln a

j( )

!

1

A1

+!2

A2

+ !3

A3

+ !4

A4

= 0

!j

j

j=1

N

" = !jj0j" +RT !j ln aj( )

j"

!G = !G0 +RTln "j

aj

#j

$

%&

'

()

!G = !G

0+RTlnK

a


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Equilibrium condition

!1A

1+!

2A

2+ !

3A

3+!

4A

4= 0

!G = !G0 + RTln "j

aj

#j

$%&

'()= 0

!G = !G0

+ RTlnKa = 0

Ka= "

j

aj

#j

$%&

'()= exp

*!G0

RT

$

%&'

()


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Equilibrium extent of reaction

!1A

1+!

2A

2+ !

3A

3+!

4A

4= 0

KP= !

j

Pj

"j

#$%

&'(

Pj= y

jP=

Nj

NT

P

Nj = Nj0 +"j)

KP= !

j

PN

j0+"

j#

NT0 +# "jj$

%

&

'''

(

)

***

"j+

,

---

.

/

000

=F #( )


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Extent of reaction and operating conditions

!

1

A1

+ !

2

A2

+!

3

A3

+!

4

A4

= 0

KP(T) = !

j

PN

j0+ "

j#

NT0

+# "

jj$

%

&

''

'

(

)

**

*

"j+

,

--

-

.

/

00

0

= F #,P,Nj0( )

d

dYlnK

P(T)!" #$ =

d

dYF %,P,N

j0( )!" #$ =&F

&Y+

&F

&%

d%

dY


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Extent of reaction and operating conditions

!

1

A1

+ !

2

A2

+!

3

A3

+!

4

A4

= 0

d!

dY= C

F !( )F' !( )

Temperature C="H

RT2 "H= heatofreaction

Pressure C= #

$j

j

%

P$

j=changeinno. ofmoles

j

%

Inerts C= ?


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Equilibrium conversion - Endothermic reaction

300 320 340 360 380 4000.0

0.2

0.4

0.6

0.8

1.0

Xe

q

T

Isothermal

Adiabatic


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Heat of reaction

!HR= "

jhj

j

#

hj (T) = hj0

+ CPj dT298

T

$!H

R= "

jhj

0

j

# + "jj

# CPj dT298T

$

!HR = !HR0 + "j

j# CPj dT298T

$

!

1

A1

+ !

2

A2

+!

3

A3

+!

4

A4

= 0


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Summary

!Free energy!Chemical potential!Condition of Equilibrium!Equilibrium constant!Equilibrium extent of reaction!Operating conditions



36/51

Chemical Reaction EngineeringLecture 4: Review of Undergraduate Material

Jayant M. Modak

Department of Chemical Engineering

Indian Institute of Science, Bangalore


37/51

Indian Institute of

Chemical Kinetics: Basic concepts

!Kinetics of irreversible and reversible reactions" Power law kinetics" Law of mass action kinetics

!Rate of simple reactions


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Classification of reactions

!Based on mechanism of the reaction" Elementary and nonelementary reactions

Example: chlorination of nitric oxide to give nitrosyl chloride

2NO + Cl2! 2NOCl


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!Based on the direction of the reaction" Irreversible and reversible reactions

cyclopropane! propylene

trans " butylene! cis " butylene


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!Based on number of phases present in the system" Homogenous and heterogeneous reactions

C2H

6(g)! C

2H

4(g) + H

2(g)

CO2 (g) + NaOH(l)! NaHCO3(l)


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Indian Institute of

Rate of chemical reaction single reaction

!Consider a reaction !!jAj = 0 taking place in aclosed, isothermal, constant pressure system

!Rate of reaction - rr =

1

Vd!

dt! =

nj" n

j0

#j

rj =1

V

dnj

dt


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Indian Institute of

Reaction rate

!Consider a reaction !!jAj = 0 taking place in aclosed, isothermal, constant pressure system

r = r(T,P,y1

,y2

...yN!

1

)

= r(T,P,C1,C2 ...CN!1)

= r(T,C1,C

2...CN!1,CN)


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Activation energy

0.0020 0.0025 0.0030 0.0035

-6

-4

-2

0

2

ln

(k)

1/T (K-1)

ln (k)

ln ln

E

RTk Ae

Ek A

R

! "#$ %& '=

= #


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Indian Institute of

Rate contours endothermic reaction

0

10

20

30

40

50

60

70

80

90

100

700 750 800 850 900 950 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Temperature

Ex

tent


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Indian Institute of

Rate contours exothermic reaction

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

Extent


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Summary

!Rate of reaction!Power law kinetics!Law of mass action kinetics!Exothermic and endothermic reactions

Indian Institute of

stoic hi o kinetics

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