chemical reaction engineering - nptel · chemical reaction engineering lecture 4: review of...

Chemical Reaction Engineering Lecture 2: Review of Undergraduate Material

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

Ethylene production by thermal cracking of ethane

! The thermal cracking of ethane is carried out in multitubular 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 - 680°C "  Tube length 95 m, ethylene conversion – 60%

Indian Institute of Science

Cracking of ethane to ethylene 26 24 2CHCHH!+

Reactor Design

Stoichiometry conversion molar flows

Rate of reaction

Mole balances

Batch/ CSTR/ PFR

Conversion Volume Production rate CSTR +PFR


Topic 1: Basic concepts

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

"  Heat of reaction "  Condition of equilibrium


Representation of chemical reaction – single reaction

! Consider a single chemical reaction in N species A1, A2,…., AN

! General representation:

! jAj = 0j=1

N

"


Representation of chemical reaction – multiple reactions

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

! General representation:

! ijAj = 0j=1

N

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


Representation of chemical reaction – independent reactions

! Stoichiometric matrix

! Number of independent reaction

! =!11 … !1N! " !!R1 # !RN

"

#

$$$

%

&

'''

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


Progress of chemical reaction – single reaction

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

nj0 = number of moles of species j present initially nj = number of moles of species j at any time t

! Molar extent of reaction - "

! =nj " nj0

# j


Molar extent of reaction

! Properties of " "  defined for the reaction

"  Extensive property in moles

"  Always positive

! =nj " nj0

# j

! =nj " nj0

# j

=nk " nk0

#k

$!!nk = nk0 +#k

# j

n j " nj0( )


Conversion of species

! Conversion X

! Stoichiometrically limiting species “k”

X =nj0 ! njnj0

min!! !nj0" j

#

$%&

'(

Cracking of ethane to ethylene 26 24 2CHCHH!+

Molar flow at entry Ethane, F10

Molar flow at exit Ethane, F1 Ethylene, F2 …

Stoichiometric tables – Flow reactor

!1A1 + !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- F10X Aj j=2,3, 4 FjO - #j/#1

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

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

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

Concentrations in terms of conversion

Pv = Z FT RTP0 v0 = Z0 FT 0 RT0

!"#

$#v = v0

P0

P%

&'(

)*ZZ0

%

&'(

)*TT0

%

&'(

)*FT

FT 0

%

&'(

)*

FT = FT 0 + +F10 XFT

FT 0

= 1+ +F10

FT 0

X = 1+ + y10 X = 1+ ,X

v = v0

P0

P%

&'(

)*ZZ0

%

&'(

)*TT0

%

&'(

)*1+ ,X( )

Concentrations in terms of conversion

00

0

0 0

0 00

0 0

0 00

0 0

11

/1

AA

A AAA

A A

BB A

FCvF F XFC

v vZ TX PC C

X P Z T

Z Tb aX PC CX P Z T

!

!

=

"= =

# $ # $" # $# $= % & % &% & % &+' ( ' (' ( ' (# $ # $) " # $# $= % & % &% & % &+' ( ' (' ( ' (

Summary – Stoichiometry of reaction

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


Ethylene production by thermal cracking of ethane

! The thermal cracking of ethane is carried out in multitubular 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 - 680°C "  Tube length 95 m, ethylene conversion – 60%


Thermodynamic considerations

! Equilibrium conversion

! Working conditions of the reactor

! Heat effects in a chemical reaction

Why thermodynamics

1500062.610 T

A

A B

r e C! "#$ %& '

(

= )

A! B

r = 2.6!106 e"

15000T

#$%

&'(CA " 3.9!1033e

"25000

T#$%

&'(CB

0 1 2 3 4 50.00.20.40.60.81.01.21.41.61.82.0

CA

(mol

/dm

3 ), X

time (h)

CA X CB

0 1 2 3 4 50.00.20.40.60.81.01.21.41.61.82.0

CA

(mol

/dm

3 ), X

time (h)

CA X CB

Effect of temperature

A! BT = 320

0 1 2 3 4 50.00.20.40.60.81.01.21.41.61.82.0

CA

(mol

/dm

3 ), X

time (h)

CA X CB

A! BT = 330

0 1 2 3 4 50.00.20.40.60.81.01.21.41.61.82.0

CA

(mol

/dm

3 ), X

time (h)

CA X CB

Chemical Equilibrium

! Consider a reaction ! !jAj = 0 taking place at constant 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 Gibb’s equations


dG = Vdp ! SdT + µ jdnjj=1

N

" ,

Chemical !Potential !µ j =#G#nj

$

%&'

() T ,P,nk

Chemical Equilibrium

! Equilibrium condition


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

N

" nj

!!!G!"

#$%

&'( T ,P

= ) jµ jj=1

N

* = 0

!!!!!dG = Vdp " SdT + # jµ jd$j=1

N

%

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

Chemical potential

! Perfect gas mixture

! Non-ideal gas mixture


µ j T ,P, y( ) = µ j0 T ,Pr , yr( ) + RT ln PyjPr

y = composition!,!T = temperature,!P = pressuresuperscript !r !=!referencePr = 1!atmyr = pure! jf j = fugacity

µ j T ,P, y( ) = µ j0 T ,Pr , yr( ) + RT ln f j

f jr

Chemical potential

! Solution


µ j T ,P, x( ) = µ j0 T ,Pr , xr( ) + RT ln! j x j

x = composition!,!T = temperature,!P = pressuresuperscript !r !=!reference! = activity!coefficient

Free energy change

µ j = µ j0 + RT ln aj( ) !1A1 + !2 A2 + !3 A3 + !4 A4 = 0

! jµ j

j=1

N

" = ! jµ j0j" + RT ! j ln aj( )

j"

!G = !G0 + RT ln "

ja j# j$

%&'()

!G = !G0 + RT ln Ka

Equilibrium condition

!1A1 + !2 A2 + !3 A3 + !4 A4 = 0

!G = !G0 + RT ln "j

a j# j$

%&'()= 0

!G = !G0 + RT ln Ka = 0

Ka = "j

a j# j$

%&'()= exp

*!G0

RT$

%&'

()

Equilibrium constant

!1A1 + !2 A2 + !3 A3 + !4 A4 = 0

Ka = !j

a j

" j#$%

&'(= exp

)*G0

RT#

$%&

'(

Pressure KP = !i

Pj

" j#$%

&'( = !

iPy j( )" j#

$%&'(

Fugacity K f = !i

f j

" j#$%

&'(

Concentration KC = !i

C j

" j#$%

&'(

Equilibrium extent of reaction

!1A1 + !2 A2 + !3 A3 + !4 A4 = 0

KP = !j

Pj" j#

$%&'(

Pj = y j P =N j

NT

P

N j = N j0 + " j)

KP = !j

PN j0 + " j#

NT 0 +# " jj$

%

&

'''

(

)

***

" j+

,

---

.

/

000= F #( )

Extent of reaction and operating conditions

!1A1 + !2 A2 + !3 A3 + !4 A4 = 0

KP (T ) = !j

PN j0 + " j#

NT 0 +# " jj$

%

&

'''

(

)

***

" j+

,

---

.

/

000= F # , P, N j0( )

d

dYln KP (T )!" #$ =

ddY

F % , P, N j0( )!"

#$ =

&F&Y

+&F&%

d%dY

Extent of reaction and operating conditions

!1A1 + !2 A2 + !3 A3 + !4 A4 = 0

d!dY

= CF !( )F ' !( )

Temperature C ="HRT 2 "H = heat of reaction

Pressure C = #$ j

j%

P$ j = change in no. of moles

j%

Inerts C = ?


Equilibrium conversion - Exothermic reaction

300 320 340 360 380 4000.0

0.2

0.4

0.6

0.8

1.0 X

eq

T

Isothermal

Adiabatic


Equilibrium conversion - Endothermic reaction

300 320 340 360 380 4000.0

0.2

0.4

0.6

0.8

1.0 X

eq

T

Isothermal

Adiabatic

Equilibrium extent of reaction

! ij Aj

j=1

N

" = 0, i = 1, 2, ...., R

KPi = !j

Pj"ij#

$%&'(

N j = N j0 + " ij) ii=1

R

*

Heat of reaction

!HR = " jhjj#

hj (T ) = hj0 + CPj dT

298

T

$!HR = " jhj

0

j# + " j

j# CPj dT

298

T

$

!HR = !HR0 + " j

j# CPj dT

298

T

$

!1A1 + !2 A2 + !3 A3 + !4 A4 = 0

Summary

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



Chemical Kinetics: Basic concepts

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

! Rate of simple reactions

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


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

cyclopropane! propylene

trans " butylene! cis " butylene


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

C2H6 (g)! C2H 4 (g) + H2 (g)

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


Rate of chemical reaction – single reaction

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

! Rate of reaction - r

r = 1Vd!dt

! =nj " nj0

# j

rj =1Vdnjdt


Reaction rate


r = r(T ,P, y1, y 2 ...yN !1)= r(T ,P,C1,C 2 ...CN !1)= r(T ,C1,C 2 ...CN !1,CN )


Reaction rate – power law kinetics


qj is the order of the reaction wrt species Aj q = ! qj is the overall order !

r = kC1q1C2

q2 .....CNqN = k Cj

qj

j=1

N

!


Reaction rate – law of mass action kinetics


r = k Cjqj

j=1

N

!

qj =12

" j #" j( )

Effect of temperature on rate

300 400 5000

5

10

15

20

25

30

35

40

k (s-1

)

T (K)

k

300 400 5001E-3

0.01

0.1

1

10

k (s-1

)

T (K)

k

(400, 0.85605)

(310, 0.00359)

(300, 0.0016)

ERTk Ae! "#$ %& '=

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

ERTk AeEk ART

! "#$ %& '=

= #


Reaction rate – reversible reaction


r = k f Cjqj

j=1

N

! " kb Cjqj'

j=1

N

!

qj =12

# j "# j( )q 'j =

12

# j + # j( )


Variation of reaction rate with progress of reaction


r = rf ! rb = k f (T ) Cjqj

j=1

N

" ! kb (T ) Cjqj'

j=1

N

"Cj = Cj0 +#$ j

r(#,T ) = rf (#,T ) ! rb (#,T )


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

Exte

nt


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

Exte

nt

Summary

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


chemical reaction engineering - nptel · chemical reaction engineering lecture 4: review of...

Documents