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Rate Determining Step
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Heat Exchanger
1 1 1i oU h h
What will be the rate controlling step:
If inside heat transfer is by condensationand outside by convection ????
hi = O(1000-10000)
ho = O(10-1000)
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Gas-Solid Reaction
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Design Problem
To emphasize the importance of rate
controlling step
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Design Problem
In a process of combustion, flue gases contain
carbon dioxide and unreacted air Flow rate: 10 m3/s
Pressure: 1 atm
composition of flue gases
mol %
CO2 5
N2 85
O2 10
We can not send these gases to atmophere, the norms sayCO2 content should be below 100 ppm
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Reaction
CO2 + 2 NaOH --------> Na2CO3 + H2O
A (g) + B (l) -----> Products
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Steps
1. What experiments I should carry out to find the
kinetics (i.e. order and rate constant) of thereaction?
2. What is the heat of reaction? Is it an endothermicor exothermic reaction?
3. What should be the temperature of the reaction?
4. Whether the liquid phase (Aq. NaOH solution) isin batch or it is should be continuous ?
5. What is the amount of NaOH solution I will usefor this reaction?
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Steps
6. What should be the concentration of NaOH
solution?7. what kind of reactor, I will use?
8. What should be the height to diameter ratio forthe reactor selected?
9. If I make a choice of CSTR type reactor, whichimpeller I should use and at what speed I shouldrotate?
10. What provisions I will make to either provide orremove heat from the system?
11. What should be the material of construction ofthe reactor?
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Lab Scale Studies
Kinetics
order with respect to A m 1
order with respect to B n 1
k2 (rate const for reaction) 0.002 m/(mol.s)
Thermodynamics
Reaction exothermic
Heat of reaction 100 kJ/mol of A reacted
Process Conditions
isothermal reaction
T 330 K
Mode of operation
Gas Phase obviously continuousLiquid Phase continuous
Hw 0.000282 kmol/(m.kN/m)
Equilibrium solubility of A 0.002451 kmol/m3
Diffusivity of CO2 1.96E-09 m2/s
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Preliminary Calculation
Flow rate of flue gases 10 m3/s
Pressure 1 atm
Temperature 330 K
R 8.314
To find total molar flow rate, we will use ideal gas law
PV = n (total) R T
N (total) 369.31135 mol/s
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Overall Balance
Composition of flue gasesIN OUT mol wt
mol % mol/s gm/s mol/s gm/mol gm/s mol/s mol %
CO2 5.00 18.47 849.42 ? 46.00 1.00 0.02 0.00
N2 85.00 313.91 8789.61 313.91 28.008789.6
1 313.91 0.89
O2 10.00 36.93 1181.80 36.93 32.001181.8
0 36.93 0.11
total 100.00 369.3110820.8
2 total 350.87
inlet ppm 78498
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Overall Balance
Total moles of CO2 reacted per unit time in - out
18.44389
NaOH moles required per unit time
stiochiometric coeff x moles of CO2 reacted 36.88778
Taking 20 % excess of NaOH flow
NaOH moles required per unit time 44.26534
Liquid phase concentration [Bo] 1 1000 mol/m3
Liquid phase flow rate 0.044265
outlet concentration of liquid phase 200
from experiments he found out that
concentration of CO2 in liquid phase 0.00098 0.98049 mol/m3
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material balance across the reactor
[Bo]in*Q-[Bo]out*Q = 2 * (-rA) V
volume of liquid phase 45.14615 m3
let the gas phase hold up is 0.2
hence liquid phase hold up is 0.8
volume of dispersion 56.43268
provide 20 % excess for gas dispersion
total volume of reactor 67.71922
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Sizing of the reactor
D 4.35 m
H 4.35 m
Design is further continued for impeller
selection, heat transfer aspects. Reactor isfabricated and sent for actual operation
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Actual Plant Operation
outlet [Bo] 800.62 mol/m3moles of [Bo] reacted 8.83 mol/sec
moles of CO2 reacted 4.41 mol/sec
so outlet moles of CO2 14.05 mol/sec
outlet composition in actual operation
mol/s gm/s
CO2 14.05 646.43
N2 313.91 8789.61
O2 36.93 1181.80
outlet PPM = 60881
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What we did not consider
Mass Transfer Rate
Variables of importance
Rate constant (intrinsic kinetics)
Order with respect to all the reactants
Liquid phase concentration
Gas phase concentration
Equilibrium solubility
Gas holdup, bubble size, interfacial area, masstransfer coefficient
Diffusion coefficient
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Reason
mol/m3sec
Rate of reaction (intrinsic kinetics) 0.78
Rate of reaction (plant operation) 0.0977
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Rate controlling step
* *2
3
1 1 1
1 1 1
[ ] [ ][ ]
1 1 1
0.001 2.45 0.002 0.8 200 2.45
0.0977 /
L L o
overall rate mass transfer rate intrinsic kinetic rate
overall rate k a A k B A
overall rate
overall rate mol m s
Slowest step controls the process,
Similar to Heat exchangers (inside and outside HTCand wall resistance)
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Three Phase Reaction
GAS Liquid Solid
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Heterogeneous reaction regimes
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Heterogeneous reactions
A l ZB l products
Transfer of solute A from dispersed phase to
continuous phase
Dispersed phase may be gas / liquid / solid
Continuous phase may be gas / liquid
Reaction of dissolved A with non-volatile liquid phase
reactant B
The rate of transfer depends upon the relative rates of
diffusion and reaction.
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Heterogeneous reactions
Mass TransferRate
Reaction Rate
Regime 1 very slowreactions
High Low
Regime 2 slow reactions Comparable
Slightly low
Comparable
Slightly high
Regime 3 fast reactions Low High
Regime 4 Instantaneousreactions
Low High
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Notations
[C] : concentration of species, mol/m3
[A*] : equilibrium solubilty, mol/m3
RA : specific rate of absorption, mol/m2s
a : interfacial area, m2/m3
kL : true liquid side mass transfer coefficient, m/s HA : Henrys constant
pA : partial pressure of gas A, Pa
DA
: Diffusion coeff of A in liquid, m2/s
L : liquid hold-up
kmn : intrinsic kinetics rate constant
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Regime 1Pure gas (gas side resistance absent)
oB
Ap
*A
Gasside film
Liquidside film
Interface
*oA A
GAS LIQUID
VERY SLOW REACTION
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REGIME 1: VERY SLOW REACTIONS
The rate of reaction between the dissolved A and B is
very much slower than the rate of transfer of A from gas
to liquid phase. The liquid phase will be saturated with
solute A at any moment and the rate of formation of the
products will be determined by kinetics of homogeneous
chemical reaction. The diffusional factors are unimportant
in this regime.
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Regime 1
*
* *
1:
1
m n
A l mn o
m n
L l mn o
R a k A B
criterion for regime
k a A k A B
volumetric rate of mass transfer
rate of homogeneous chemical reaction
A Ar R a
R i b i b l d i id
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Reaction between isobutylene and acetic acid
Reaction temperature = 30 oC
First order with respect to isobutylene and acetic
acid
Rate constant = 1.2 cm3/mol sec
Catalyst concentration = 10 % w/w
[Bo] = [AcOH]=15 x 10-3 mol/cm3
Liquid phase hold up = 0.75
kLa =0.15 to 0.4 s-1
R i 1
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Regime 1
Liquid phase air oxidation of ethyl benzene
Reactor: Stirred vessel Temperature: below 130 0C
Industrial range: 115 125 0C
0.0E+00
4.0E-06
8.0E-06
1.2E-05
1.6E-05
2.0E-05
0 200 400 600 800 1000
Stirring Speed, rpm
Rateof
Absorption,mol/cm3s
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Liquid-Liquid reaction (Oils)
Alkylation of Benzene, first step in manufacture ofalkyl benzene sulphonates, used as detergents
0.0E+00
1.0E-06
2.0E-06
3.0E-06
4.0E-06
0 500 1000 1500 2000 2500
Stirring Speed, rpm
RateofAbsorption,mol/cm3
REGIME 2 SLOW REACTIONS
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REGIME 2: SLOW REACTIONS
The rate of reaction between the dissolved A and B is
much faster than the rate of transfer of A from gas to
liquid phase. The liquid phase concentration of A will be
almost zero at any moment and the rate of formation of
the products will be determined by rate of transfer of A
from gas phase to liquid phase. The diffusional factors
are important in this regime.
R i 2
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Regime 2
*
* *
2 :
1
A L
m n
l mn o L
R a k a A
criterion for regime
k A B k a A
rate of homogeneous chemical reactionvolumetric rate of mass transfer
A Ar R a
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Regime 2Pure gas (gas side resistance absent)
Ap
*A
Gasside film
Liquidside film
Interface
0oA
GAS LIQUID
oB
SLOW REACTION
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WHAT IF
*
*1L
m n
l mn o
k a A
k A B
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Between Regime 1 and 2Pure gas (gas side resistance absent)
BETWEEN VERY SLOW AND SLOW REACTION
Ap
*A
Gasside film
Liquidside film
Interface
0oA
GAS LIQUID
oB
0oA
B R i 1 d 2
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Between Regime 1 and 2
*
*
1
*
1
1 1
1 1 1
m n
A l mn o o
L o
nA L l n o
A LR
n
LR L l n o
R a k A B
k a A A
A
R a k a k B
R a k a A
k a k a k B
1 1 1i oU h h
Regime ??? (Polymers)
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Regime ??? (Polymers)
Absorption of phosphine in an aqueous solution offormaldehyde and hydrochloric acid
The product (Tetrakis(hydroxymethyl) phosphoniumchloride) is an important intermediate in manufacture offlame-resistant ploymers
T = 27 0C
Kmn = 1.84 x 103
[A*] = 1 x 10-5 mol/cm3
[HCHO] = 0.001 mol/cm3
[HCl] = 0.0005 mol/cm3
Liquid hold up = 0.8
kLa = 0.2 s-1
Pollution control
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Pollution control
Absorption of CO2 in carbonate solution
k2[Bo]=1.2 s-1
a = 200 m2/m3
kLa = 0.08 s-1
First order with respect to both A and B
DAk2[Bo]=1.6 x 10-5 (cm/sec)2
Regime ?? (Oils)
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Regime ?? (Oils)
Hydrochlorination of olefins (C12-C18):manufacturing of biodegradable detergents
Temperature : 25 55 0C
First order w.r.to olefin and half order w.r.to HCl
Rate constant: 0.017
[A*] = 1.2 x 10-4 mol/cm3
[Bo] = 3.5 x 10-3 mol/cm3
Liquid hold up = 0.8
kLa = 0.03 s-1
Depending on the kLa, reaction belongs to eitherregime 2 or between 2 and 3.
Dyestuff Pharma and polymers
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Dyestuff, Pharma and polymers
Nitration of aromatic compounds like benzene,toluene, phenol and naphthhalene, formanufacture of intermediates in dyestuff, pharmaand polymers
Two phases, organic and aqueous
Experimentally it has been found that rate ofnitration is diffusion controlled,
means Regime ???
B t i 1 d 2
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Between regime 1 and 2
n-butylacetate + NaOH ------------> Sodium Acetate + Butanol
This is liquid liquid reaction. N-butylacetate is pure liquid and NaOH is 1 N solution.
The product butanol goes to organic phase and Sodium acetate remains in aquaous phase
Time (s) Normality RAa [A*] [Bo] 1/[Bo] [A*]/Ra
gmol/lit gmol/cm3sgmol/cm3 (gmol/cm3 (cm3/gmaol)
0 1.01 2.93E-06 3.41E-05 1.01E-03 990 1.16E+01
100 0.76 2.19E-06 3.31E-05 7.56E-04 1323 1.51E+01
200 0.57 1.64E-06 3.23E-05 5.66E-04 1768 1.97E+01
300 0.42 1.23E-06 3.17E-05 4.23E-04 2363 2.58E+01
400 0.32 9.18E-07 3.13E-05 3.17E-04 3158 3.41E+01500 0.24 6.87E-07 3.10E-05 2.37E-04 4220 4.51E+01
600 0.15 4.32E-07 3.07E-05 1.49E-04 6713 7.11E+01
Between regime 1 and 2
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Between regime 1 and 2
*
1
1 1n
A L l n o
A
R a k a k B
y = 0.0104x + 1.3266
R
2
= 1
0
20
40
60
80
0 2000 4000 6000 8000
1/[Bo]
[A*]/RAa
1
0.72
100
L
n
k a
k
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Regime 1gaseous mixture (gas side resistance present)
* A A A H p
oB
Ap
*A
Gasside film
Liquidside film
Interface
*oA A
GAS LIQUID
VERY SLOW REACTION
Liquid side
Gas side
A I
AA
A
AA
A
I
I II
I
I I
I
I
I
Regime 2
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Regime 2gaseous mixture (gas side resistance present)
Ap
*A
Gasside film
Liquidside film
Interface
0oA
GAS LIQUID
oB
SLOW REACTION * A A A H p
REGIME 1 and 2
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REGIME 1 and 2One more criterion
The amount of dissolved solute that reacts in thediffusional film adjacent to the phase boundary compared
to that which reaches the liquid bulk in the unreacted state
should be negligible. Practically no reaction occurs in the
liquid side film.
1*2
11
mn
mn A o
L
k D B Am
Mk
R i 3
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Regime 3Pure gas (gas side resistance absent)
Ap
*A
Gasside film
Liquidside film
Interface
0oA
GAS LIQUID
oB
FAST REACTION
Regime 3
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Regime 3
1
*
*
2
1 1
mn
mn A o
L
A L
k D B A
mMk
R k A M
1. The expression for regime 3 is similar to regime 2, but in
regime 3, one extra term appears which is higher than 1.
2. The rate of absorption of solute A is enhanced due to chemical
reaction occuring in the film.3. So in some cases, reactions are forced to regime 3, to get an
advantage of the enhanced level of mass transfer, so that total
volume of the reactor/separator can be brought down.
Regime 3
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Regime 3gaseous mixture (gas side resistance present)
Ap
*A
Gasside film
Liquidside film
Interface
0oA
GASLIQUID
oB
FAST REACTION * A A A H p
Regime 4
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Regime 4
The reaction is potentially so fast that the solute
A and reactant B can not co-exist.
At a certain distance from the interface, a
reaction plane is formed at which the solute andthe reactant are consumed instantaneously.
Regime 4
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Regime 4Pure gas (gas side resistance absent)
Ap
*A
Gasside film
Liquidside film
Interface
0o oB A
GASLIQUID
oB
Reactionplane
VERY FAST REACTION
Regime 4
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Regime 4
*
1*
*
*
* 1
21
1*
o BA L
A
mnmn A o
o B
L A
oA B
L A
BD R k ADZ A
criterion
k D B AB Dm
k DZ A
BR D enhancement factork A DZ A
Regime 4
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Regime 4gaseous mixture (gas side resistance present)
Ap
*A
Gasside film
Liquidside film
Interface
0o oB A
GASLIQUID
oB
Reactionplane
VERY FAST REACTION * A A A H p
Regime 3 revisited
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Regime 3 revisited
*
1*
1*
*
2
1 1
21
A L
mn
mn A o
L
mn
mn A oo B
L A
R k A M
k D B A
mMk
k D B A B Dm
k DZ A
Alkaline hydrolysis of formate
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Alkaline hydrolysis of formate
HCOOR + OH- HCOO-+ROH
Alkaline hydrolysis of isobornyl formate, step inmanufacture of camphor
First order w. r. to each reactant
[A*] = 5 x 10-5 mol/cm3
[Bo] = 2 x 10-3 mol/cm3
kL = 0.003 cm/s
DA = 8 x 10-6 cm2/s
DB = 2.12 x 10-5 cm2/s
k2 = 3 x 104 cm3/mol.s
Human body
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Human body
Absorption of oxygen in red cells of the blood
DO2 = 7.0 x 10-6
cm2
/s DHb = 7.5 x 10
-8 cm2/s
PPO2 = 0.21 atm
HO2in Hb
= 9.4 x 10-7 mol/cm3 atm
kL = 0.01 cm/s
[Hb] = 2 x 10-5 mol/cm3
k2 = 1.8 x 109 cm3/mol s
Regimes 1- 4
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g
oB
Ap
*A
Gasside film
Liquidside film
Interface
*oA A
GAS LIQUID
oB
Ap
*A
Gasside film
Liquidside film
Interface
*oA A
oB
Ap
*A
Gasside film
Liquidside film
Interface
*oA A
GAS LIQUID
Ap
*A
Gasside film
Liquidside film
Interface
0oA
GAS LIQUID
oBA
p
*A
Gasside film
Liquidside film
Interface
0oA
GAS LIQUID
oB oB
Ap
*A
Gasside film
Liquidside film
Interface
0oA
GAS LIQUID
oBAp
*A
Gasside film
Liquidside film
Interface
0oA
GAS LIQUID
oB oBA
p
*A
Gasside film
Liquidside film
Interface
0o oB A
GAS LIQUID
oB
Reactionplane
Ap
*A
Gasside film
Liquidside film
Interface
0o oB A
GAS LIQUID
oB oB
Reactionplane
Heterogeneous reactions
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Heterogeneous reactions
Regime 4
Regime 3
Regime 2
Regime 1
Regime 4
Regime 3
Regime 2
Regime 1
*
m n
A l mn o R a k A B
*
A LR a k a A
1
*2
1
mn
mn A o
L
k D B Am
Mk
*A L R k A M
** 1
o BA L
A
B D R k A
DZ A
What is required
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q
Kinetics of gas-liquid reaction
Diffusivity of gas and liquid reactant
Solubility of the gas or the gases
Interfacial area
Mass transfer coefficient
Factors affecting overall rate of absorption
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g p
Factor Regime 1 Regime 2 Regime 3 Regime 4
[Bo] + - + +[A*] + + + / - +Interfacial area
- + + +Liquid hold up + - - -MTC (liquid side) - + - +MTC (gas side) - + + +Rate constant + - + -
Effect of k and holdup
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Effect of kL and holdup
Regime Effect on the specific rate of absorption (RA) of
[A*] [Bo] Speed of
stirring
Phase hold up
Regime 1 [A*]m
[Bo]n
No Yes
Regime 2 [A*]1 [Bo]0 Yes No
Regime 3 [A*](m+1)/2
[Bo]n/2
No No
Regime 4 [A*]0
[Bo]1
Yes No