regimes 1to4

8/2/2019 Regimes 1to4

1/59

Rate Determining Step


2/59

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)


3/59

Gas-Solid Reaction


4/59

Design Problem

To emphasize the importance of rate

controlling step


5/59

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


6/59

Reaction

CO2 + 2 NaOH --------> Na2CO3 + H2O

A (g) + B (l) -----> Products


7/59

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?


8/59

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?


9/59

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


10/59

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


11/59

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


12/59

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


13/59

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


14/59

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


15/59

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


16/59

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


17/59

Reason

mol/m3sec

Rate of reaction (intrinsic kinetics) 0.78

Rate of reaction (plant operation) 0.0977


18/59

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)


19/59

Three Phase Reaction

GAS Liquid Solid


20/59

Heterogeneous reaction regimes


21/59

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.


22/59


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


23/59

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


24/59

Regime 1Pure gas (gas side resistance absent)

oB

Ap

*A

Gasside film

Liquidside film

Interface

*oA A

GAS LIQUID

VERY SLOW REACTION


25/59

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.


26/59

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


27/59

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


28/59

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


29/59

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


30/59

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


31/59

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


32/59


Ap

*A

Gasside film

Liquidside film

Interface

0oA

GAS LIQUID

oB

SLOW REACTION


33/59

WHAT IF

*

*1L

m n

l mn o

k a A

k A B


34/59

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


35/59

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)


36/59

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


37/59

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)


38/59

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


39/59

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


40/59

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



41/59


*

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


42/59

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


43/59


Ap

*A

Gasside film

Liquidside film

Interface

0oA

GAS LIQUID

oB

SLOW REACTION * A A A H p

REGIME 1 and 2


44/59

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


45/59


Ap

*A

Gasside film

Liquidside film

Interface

0oA

GAS LIQUID

oB

FAST REACTION

Regime 3


46/59

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


47/59


Ap

*A

Gasside film

Liquidside film

Interface

0oA

GASLIQUID

oB

FAST REACTION * A A A H p

Regime 4


48/59

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


49/59


Ap

*A

Gasside film

Liquidside film

Interface

0o oB A

GASLIQUID

oB

Reactionplane

VERY FAST REACTION

Regime 4


50/59

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


51/59


Ap

*A

Gasside film

Liquidside film

Interface

0o oB A

GASLIQUID

oB

Reactionplane

VERY FAST REACTION * A A A H p

Regime 3 revisited


52/59

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


53/59

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


54/59

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


55/59

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



56/59


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


57/59

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


58/59

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


59/59

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

regimes 1to4

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