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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
Indian Institute of Science
Topic 1: Basic concepts
! Representation of reaction ! Extent of reaction and conversion ! Thermodynamics and chemical reactions
" Heat of reaction " Condition of equilibrium
Indian Institute of Science
Representation of chemical reaction – single reaction
! Consider a single chemical reaction in N species A1, A2,…., AN
! General representation:
! jAj = 0j=1
N
"
Indian Institute of Science
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
Indian Institute of Science
Representation of chemical reaction – independent reactions
! Stoichiometric matrix
! Number of independent reaction
! =!11 … !1N! " !!R1 # !RN
"
#
$$$
%
&
'''
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 - "
! =nj " nj0
# j
Indian Institute of Science
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( )
Indian Institute of Science
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
!
!
=
"= =
# $ # $" # $# $= % & % &% & % &+' ( ' (' ( ' (# $ # $) " # $# $= % & % &% & % &+' ( ' (' ( ' (
Summary – Stoichiometry of reaction
! Keywords & concepts " Stoichiometric coefficients " Multiple reactions " Set of independent reactions " Extent of reaction " Conversion " Stoichiometric tables
Indian Institute of Science
Chemical Reaction Engineering Lecture 3: Review of Undergraduate Material
Jayant M. Modak Department of Chemical Engineering Indian Institute of Science, Bangalore
Ethylene production by thermal cracking of ethane
! The thermal cracking of ethane is carried out in multitubular reactor. Typical production capacity of each tube is 10000 Tons per annum.
! Reactor specifications:
" Feed to the reactor: ethane + steam (?) " Inlet pressure - 2.99 atm; temperature - 680°C " Tube length 95 m, ethylene conversion – 60%
Indian Institute of Science
Thermodynamic considerations
! Equilibrium conversion
! Working conditions of the reactor
! Heat effects in a chemical reaction
Why thermodynamics
1500062.610 T
A
A B
r e C! "#$ %& '
(
= )
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
Indian Institute of Science
dG = Vdp ! SdT + µ jdnjj=1
N
" ,
Chemical !Potential !µ j =#G#nj
$
%&'
() T ,P,nk
Chemical Equilibrium
! Equilibrium condition
Indian Institute of Science
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
Indian Institute of Science
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
Indian Institute of Science
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 = ?
Indian Institute of Science
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
Indian Institute of Science
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
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
Indian Institute of Science
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
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
C2H6 (g)! C2H 4 (g) + H2 (g)
CO2 (g) + NaOH (l)! NaHCO3(l)
Indian Institute of Science
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
Indian Institute of Science
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 ...CN !1)= r(T ,C1,C 2 ...CN !1,CN )
Indian Institute of Science
Reaction rate – power law kinetics
! Consider a reaction ! !jAj = 0 taking place in a closed, isothermal, constant pressure system
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
!
Indian Institute of Science
Reaction rate – law of mass action kinetics
! Consider a reaction ! !jAj = 0 taking place in a closed, isothermal, constant pressure system
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
! "#$ %& '=
= #
Indian Institute of Science
Reaction rate – reversible reaction
! Consider a reaction ! !jAj = 0 taking place in a closed, isothermal, constant pressure system
r = k f Cjqj
j=1
N
! " kb Cjqj'
j=1
N
!
qj =12
# j "# j( )q 'j =
12
# j + # j( )
Indian Institute of Science
Variation of reaction rate with progress of reaction
! Consider a reaction ! !jAj = 0 taking place in a closed, isothermal, constant pressure system
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 )
Indian Institute of Science
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
Indian Institute of Science
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