Chemical Reaction Engineering - NPTel

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Lecture 2: Review of Undergraduate Material. Jayant M. Modak ... H ! +. Reactor Design. Stoichiometry conversion molar flows. Rate of reaction. Mole balances.
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 C H ! C H + H 2 6 2 4 2

Rate of reaction

Mole balances Batch/ CSTR/ PFR Stoichiometry conversion molar flows

Reactor Design

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

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Representation of chemical reaction – single reaction !  Consider

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

!  General

representation: N

"! A j =1

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j

j

=0

Representation of chemical reaction – multiple reactions !  Consider

R chemical reactions in N species A1,

A2,…., AN !  General

representation:

N

"! j =1

ij

A j = 0,

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

Representation of chemical reaction – independent reactions !  Stoichiometric

matrix

" !11 … !1N $ !=$ ! " ! $# ! R1 # ! RN !  Number

of independent reaction

R!=!rank!! "#! $% Indian Institute of Science

% ' ' '&

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 - "

!= Indian Institute of Science

nj " nj0

#j

Molar extent of reaction !  Properties " 

!=

of "

defined for the reaction n j " n j 0 nk " nk 0 != = #j #k

#k $!!nk = nk 0 + nj " nj0 #j

(

" 

Extensive property in moles

" 

Always positive Indian Institute of Science

)

nj " nj0

#j

Conversion of species !  Conversion

X X=

!  Stoichiometrically

nj0 ! nj nj0

limiting species k # nj0 & min!! % ! ( " $ j '

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Cracking of ethane to ethylene C H ! C H + H 2 6 2 4 2 Molar flow at entry Ethane, F10

Molar flow at exit Ethane, F1 Ethylene, F2 …

Stoichiometric tables – Flow reactor !1 A1 + ! 2 A2 + ! 3 A3 + ! 4 A4 = 0 Species

Entry (mol/ min)

A1 F1O Aj j=2,3, 4 FjO I (inerts)

FI0

Total

FT0

Change (mol/ min)

Exit from the reactor (mol/min)

-(F10X) - #j/#1 (F10X)

F1=F10- F10X Fj=Fj0- #j/#1 F10X

-----

FI= FI0 FT=FT0-(!#j/#1)F10X FT=FT0+ ! F10X

Concentrations in terms of conversion P v = Z FT RT P0 v0 = Z0 FT 0 RT0

! % P0 ( % Z ( % T ( % FT ( # " v = v0 ' * ' * ' * ' * P Z T F & ) & ) & ) & # 0 0 T0 ) $

FT = FT 0 + + F10 X FT F10 = 1+ + X = 1 + + y10 X = 1 + , X FT 0 FT 0 % P0 ( % Z ( % T ( v = v0 ' * ' * ' * 1 + , X & P ) & Z0 ) & T0 )

(

)

Concentrations in terms of conversion FA0 CA0 = v0 FA FA0 "FA0X CA = = v v # 1" X $# P $# Z0 $#T0 $ CA =CA0 % &% &% &% & 1 + ! X ' (' P0 (' Z ('T0 ( # )B "b/ aX $# P $# Z0 $#T0 $ CB =CA0 % &% &% &% & 1 + ! X ' (' P0 (' Z ('T0 (

Summary – Stoichiometry of reaction !  Keywords "  "  "  "  "  " 

& concepts

Stoichiometric coefficients Multiple reactions Set of independent reactions Extent of reaction Conversion Stoichiometric tables

Indian Institute of Science

Chemical Reaction Engineering Lecture 3: 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

Thermodynamic considerations !  Equilibrium !  Working !  Heat

conversion

conditions of the reactor

effects in a chemical reaction

Why thermodynamics A! B

A ( B 5 0 0 0 !1 " # $ 6 & T % '

r= 2 .61 )0e

r = 2.6 ! 106 e

C A

2.0

2.0

1.8

1.8

1.2

3

1.4 1.0 0.8 0.6 0.4 0.2 0.0

C A " 3.9 ! 1033 e

# 25000 & "% $ T ('

CA X CB

1.6

CA X CB

CA (mol/dm ), X

3

CA (mol/dm ), X

1.6

# 15000 & "% $ T ('

1.4 1.2 1.0 0.8 0.6 0.4 0.2

0

1

2

3

time (h)

4

5

0.0

0

1

2

3

time (h)

4

5

CB

Effect of temperature A! B T = 330

A! B T = 320 2.0 1.8

1.2

3

3

1.6

1.4 1.0 0.8 0.6 0.4 0.2 0.0

CA X CB

1.8

CA (mol/dm ), X

1.6

CA (mol/dm ), X

2.0

CA X CB

1.4 1.2 1.0 0.8 0.6 0.4 0.2

0

1

2

3

time (h)

4

5

0.0

0

1

2

3

time (h)

4

5

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 N

dG = Vdp ! SdT + " µ j dn j , j =1

$ #G ' Chemical!Potential! µ j = & ) % #n j ( T , P,nk Indian Institute of Science

Chemical Equilibrium N

Gibb's!Equation dG = Vdp ! SdT + " µ j dn j j =1

Progress!of !reaction n j = n j 0 + ! j" !!or!!dn j = ! j d" ! N

!!!!!dG = Vdp " SdT + % # j µ j d$ !  Equilibrium

j =1

condition !! N # !G & %$ (' = * ) j µ j = 0 !" T , P j =1

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Chemical potential !  Perfect

(

y = composition!,!

gas mixture

)

(

)

µ j T , P, y = µ j 0 T , P , y + RT ln !  Non-ideal

(

)

r

r

Py j Pr

gas mixture

(

)

µ j T , P, y = µ j 0 T , P , y + RT ln

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r

r

T = temperature,! P = pressure superscript !r!=!reference P r = 1!atm y r = pure! j f j = fugacity

fj f jr

Chemical potential !  Solution

(

)

µ j (T , P, x ) = µ j 0 T , P r , x r + RT ln ! j x j x = composition!,! T = temperature,! P = pressure superscript !r!=!reference

! = activity!coefficient

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

( )

µ j = µ j0 + RT ln a j N

"! µ j =1

j

j

( )

= " ! j µ j0 + RT " ! j ln a j j

j

$ #j ' !G = !G + RT ln & " a j ) % j ( 0 !G = !G + RT ln K a 0

Equilibrium condition !1 A1 + ! 2 A2 + ! 3 A3 + ! 4 A4 = 0 $ #j ' !G = !G + RT ln & " a j ) = 0 % j ( 0

!G = !G 0 + RT ln K a = 0 0 $ *!G ' $ #j ' K a = & " a j ) = exp & ) % j ( % RT (

Equilibrium constant !1 A1 + ! 2 A2 + ! 3 A3 + ! 4 A4 = 0 0 # & )*G # & "j K a = % ! a j ( = exp % ( $ j ' RT $ '

( )

Pressure

"j & # # K P = % ! Pj ( = % ! Py j $ i ' $ i

Fugacity

"j & # Kf = %! fj ( $ i '

Concentration

"j & # KC = % ! C j ( $ i '

"j

& ('

Equilibrium extent of reaction !1 A1 + ! 2 A2 + ! 3 A3 + ! 4 A4 = 0 # "j & K P = % ! Pj ( $ j '

Pj = y j P =

N j = N j0 + " j)

+ KP = - ! - j ,

% ( N j0 + " j# * ' 'P N + # " * $ j* T0 ' j & )

"j

. 0 0=F # 0 /

( )

Nj NT

P

Extent of reaction and operating conditions !1 A1 + ! 2 A2 + ! 3 A3 + ! 4 A4 = 0 + K P (T ) = - ! - j ,

% ( N j0 + " j# * ' 'P N + # " * $ j* T0 ' j & )

(

"j

. 0 0 = F # , P, N j0 0 /

(

)

)

d d ! &F &F d% # !" ln K P (T ) #$ = F % , P, N j0 = + " $ dY dY &Y &% dY

Extent of reaction and operating conditions !1 A1 + ! 2 A2 + ! 3 A3 + ! 4 A4 = 0

( ) ( )

F ! d! =C dY F' !

"H Temperature C = RT 2 Pressure Inerts

C=# C=?

%$ j

P

"H = heat of reaction j

%$ j

j

= change in no. of moles

Equilibrium conversion - Exothermic reaction 1.0 Isothermal

0.8

Xeq

0.6

Adiabatic

0.4 0.2 0.0 300 320 340 360 380 400 T

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Equilibrium conversion - Endothermic reaction 1.0 0.8

Xeq

0.6

Adiabatic Isothermal

0.4 0.2 0.0 300 320 340 360 380 400 T

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Equilibrium extent of reaction N

"! j =1

K Pi

ij

Aj = 0,

i = 1, 2, ...., R

# " ij & = % ! Pj ( $ j ' R

N j = N j0 + * " ij) i i =1

Heat of reaction !1 A1 + ! 2 A2 + ! 3 A3 + ! 4 A4 = 0 !H R = # " j h j j

h j (T ) = h + $ 0 j

T

298

C Pj dT

!H R = # " j h + # " j $ 0 j

j

298

j

!H R = !H + # " j $ 0 R

j

T

T

298

C Pj dT

C Pj dT

Summary !  Free

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

Indian Institute of Science

Chemical Reaction Engineering Lecture 4: Review of Undergraduate Material

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

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

Classification of reactions !  Based " 

on the direction of the reaction

Irreversible and reversible reactions

cyclopropane ! propylene trans " butylene ! cis " butylene

Classification of reactions !  Based " 

on number of phases present in the system

Homogenous and heterogeneous reactions

C2 H 6 (g) ! C2 H 4 (g) + H 2 (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

1 d! r= V dt

!=

1 dn j rj = V dt Indian Institute of Science

nj " nj0

#j

Reaction rate !  Consider

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

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

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Reaction rate – power law kinetics !  Consider

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

r = kC C .....C q1 1

q2 2

N

qN N

= k! C j =1

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

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qj j

Reaction rate – law of mass action kinetics !  Consider

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

r = k! C j =1

qj j

(

1 qj = "j #"j 2 Indian Institute of Science

)

Effect of temperature on rate k

40

! E" #$ % T' &R

35

k=A e

30

20 15 k

10 5

10

400

T (K)

500

1

(400, 0.85605)

-1

0 300

k (s )

-1

k (s )

25

0.1 0.01 1E-3 300

(310, 0.00359) (300, 0.0016) 400

T (K)

500

Activation energy

! E " #$ % & RT '

k = Ae

E lnk = ln A# RT

ln (k)

2

ln (k)

0 -2 -4 -6 0.0020

0.0025

0.0030 -1

1/T (K )

0.0035

Reaction rate – reversible reaction !  Consider

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

r = kf !C j =1

qj j

N

" kb ! C

( (

1 qj = #j "#j 2 1 ' qj = #j +#j 2 Indian Institute of Science

j =1

) )

q'j j

Variation of reaction rate with progress of reaction !  Consider

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

r = rf ! rb = k f (T )" C j =1

qj j

! kb (T )" C

C j = C j 0 + #$ j r(# ,T ) = rf (# ,T ) ! rb (# ,T ) Indian Institute of Science

N

j =1

q'j j

Rate contours – endothermic reaction

Extent

100 0.9

90

0.8

80

0.7

70

0.6

60

0.5

50

0.4

40

0.3

30

0.2

20

0.1

10

700

750

800

850

Temperature

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900

950

1000

0

Rate contours – exothermic reaction

Extent

500 0.9

450

0.8

400

0.7

350

0.6

300

0.5

250

0.4

200

0.3

150

0.2

100

0.1

50

450

500

550

600

Temperature K

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650

700

0

Summary !  Rate

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

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