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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