Chemical Reaction Engineering10_2010

8/7/2019 Chemical Reaction Engineering10_2010

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Reaction Mechanism,Bioreaction and Bioreactors

Lecture 9


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Active Intermediates

Many reaction proceed via formation of active intermediate bycollision or interaction with other molecules

A M A M

+ +

The idea was suggested in 1922 by F.A.Lindermann , acitveintermediates were experimentally observed using

femtosecond spectroscopy by A.Zewail (Nobel Prize 1999)cyclobutane x2 ethylene


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Pseudo Steady-State Hypothesis (PSSH)

Decomposition of the intermediate doesnt occurinstantaneously, activated species have finite life time

Active intermediates react as fast as they are formed, so theirnet rate of formation is zero:

* *1 0

N

A iAir r ==


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Gas-phase decomposition of azomethane intoethane and N 2:

( )3 2 2 6 22CH N C H N +

experimentally found to follow 1 st order at pressures above 1atm

2 nd order below 50mmHg

2 6C H AZOr C

2 6

2C H AZOr C


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Suggested mechanism:

( ) ( ) ( ) ( )1 *3 2 3 2 3 2 3 22 2 2 2 *AZOk CH N CH N CH N CH N + +

( ) 3 *3 2 2 6 22 * AZOk CH N C H N +

( ) ( ) ( ) ( )2 *

3 2 3 2 3 2 3 22 2 2 2*AZOk

CH N CH N CH N CH N + +

21 * 1 *AZO AZO AZOr k C =

the rate laws

2 * 2 * *AZO AZO AZO AZOr k C C =

3 * 3 * *AZO AZO AZOr k C =

* 1 * 2 * 3 * 0AZO AZO AZO AZOr r r r = + +


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solving for C azo* and finding the rate of formation of product:

6

21 3

2 3r

AZOC H

AZO

k k C r

k C k =

+

at low concentrations

6

22 3 1r AZO C H AZO

k C k r k C =

6

1 32 3

2r AZO C H AZO AZO

k k k C k r C kC

k = =

at high concentrations


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Experimentally finding the mechanism:

6

21

1r AZO

C H AZO

k C r

k C =

+

Rule of thumb for developing the mechanism: species having the concentration appearing in the denominatorprobably collide with the active intermediate species having the concentration appearing in the numerator probably

produce the active intermediate


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Enzymatic reactions

lower activation energies for enzymatic pathways lead to

enormous enhancement in reaction rates enzymes are highly specific: one enzyme can usually catalyzeonly one type of reaction

enzymes usually work at mild conditions; at extremetemperatures or pH may unfold losing its activity


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Enzymatic reactions

Two models for enzyme-substrate interaction: thelock-and-key and the induced fit :

both the enzyme molecule and thesubstrate molecule are distorted therefor

stressing and weakining the bond forrearrengement


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Enzymatic reactions

There are six classes ofenzymes

1. Oxidoreductases2. Transferases3. Hydrolases

4. Isomerases5. Lyases6. Ligases

2 2AH B E A BH E + + + +AB C E AC B E + + + +

A E isoA E + +

AB E A B E + + +

A B E AB E + + +

2AB H O E AH BOH E + + + +


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Michaelis-Menten equation

kcat (s -1) the turnover number: the number of substratemolecules converted in a given time on a single enzymemolecule when saturated with the substrate

Km (mol/l) Michaelis constant or affinity constant: measure of

attraction of the enzyme to the substrate

( )( )( )cat t

SM

k E Sr

S K =

+

( )

( )

maxS

M

V Sr

S K

=+


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Evaluation of Michaelis-Menten parameters

Michaelis-Menten plot Lineweaver-Burk plot

Hanes-Woolf plotbetter V

Eadie-Hofstee plotdoesnt bias low concentraion oints

( )

( )

maxS

M

V Sr

S K

=+

( )maxS

S M

r r V K

S

=

( )max max1 1 1M S

K r V V S

= +

( )( )max max

1M S

S K Sr V V = +


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Batch reactor calculations

after integration, in terms of conversion

ureaurea

dN r V

dt = urea urea

dC r

dt =

in liquid

max urea

ureaurea M

V C r

C K =

+

0 0

max

urea urea

urea urea

C C

urea urea M

ureaurea ureaC C

dC C K t dC

r V C

+= =

0

max max

1ln

1

ureaM C X K t

V X V

= +( )0 1urea ureaC C X =

combining with the Michaelis-Menten law

mole balance on urea:


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Briggs-Haldane equation

If the reaction of forming the product from the enzyme-substrate complex is reversible

E S E S E P+ + i

The Briggs-Haldane equation can be derived applying PSSHto the enzyme kinetics:

( )maxmax

/ S P C S

S p p

V C C K r

C K K C

=

+ +


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Effect of Temperature

catalytic breakdown of H 2O2 vs temperature

temperature inactivation

due to enzyme denaturation

rise due to Arrhenius law

optimum


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Enzyme inhibition

Competitive: substrate and inhibition competefor the same site on the enzyme

Uncompetitive: inhibitor deactivates enzyme-substrate complex (doesnt allow to form the

product) Noncompetitive : inhibitor attaches to a

different site on the enzyme


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Inhibition of Enzyme reactions Competitive inhibition


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Inhibition of Enzyme reactions Uncompetitive inhibition: inhibitor is forming inactive IES

complex


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Inhibition of Enzyme reactions Non-competitive (mixed) inhibition: inhibitor and the substrates

react with the different sites on the enzyme


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Bioreactors

Cells consume nutrients to grow, to produce more cells andto produce the product in question: (I) fueling reactions (nutrient degradation)

(II) synthesis of small molecules (amino acids) (III) synthesis of large molecules (proteins, DNA, RNA)

Cell growth and division

Advantages of bioconversion: mild reaction conditions high yields approaching 100% stereospecific synthesis


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Bioreactors Growth in the reactor

Substrate More Cells ProductCells +

e.g. CO2, water, proteins etc. Batch bioreactor


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Bioreactors Cell growth in bioreactors

adjusting pathways to the new conditions

exp growth: dividing at max rate

stationary phase: lack of some

nutriotients limits cell growth;many important products (e.g.antibiotics) produced at this phase.

Nutritions required: Carbon source

Nitrogen source Oxygen source Phosphate source .


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Bioreactors: Rate laws

Monod equation


g cr C =

maxs

s s

C K C

=+

Specific growthrate

max s cg

s s

C C r K C

=+

In many systems the product can inhibit cells growth (e.g. winemaking)

max s cg obs

s s

C C r k K C

=+ *

1

n

pobs

p

C k C

= product concentrationwhere metabolism ceases

e.g. glucose-to-ethanol: n=0.5, C p*=93g/l


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Bioreactors: Rate laws Other growth equations:

Tessier equation

Moser equation

max 1 exps

g c

C r C

k

=

( )max

1s c

g

s

C C r

kC =

+

usually give better fit in the beginning and in the end of fermentation

Cell death rate (due to harsh environment, mixingshear forces, local depletion in nutrients, toxic

substances)( )d d t t cr k k C C = +

Temperature effect: similar curve with max

natural death

death due to toxic environment


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Bioreactors: Stoichiometry

Yield coefficient for cells and substrate


/ Mass of new cells formed

Mass of substrate consumedC

c sS

C Y C

= =

Yield coefficient for product in the exponential phase/

Mass of product formedMass of new cells formed

Pp c

C

C Y

C

= =

max/

s cp p c

s s

C C r Y

K C =

+


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Yield coefficient for product in the stationary phase

/

Mass of product formedMass of substrate consumed

Pp s

S

C Y

C

= =

Maintenance utilization term, typically m=0.05 h -1.

sm cr mC =

Usually secondary

nutritient

/ / maintancecells

c s p sS Y C Y P + +

/ / s c s g p s p cr Y r Y r mC = + +


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In the exponential phase we cannot separate substrateconsumption for cell growth and product formation

In stationary phase:

/

/

s s c g c

p g p c

r Y r mC

r r Y

= +

=

/ / maintancecells

c s p sS Y C Y P + +

/ / s c s g p s p cr Y r Y r mC = + +

/ /

p sn

psn sn

sn p p snsn sn p p c c

sn sn

k C

r K C

Y k C r Y r mC mC

K C

=+

= + = ++


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Chemostat (CSTR) operation

Mass balance: Cell balance

Substrate balance

0 ( )c

co c g d

dC V v C vC r r V

dt = +

0s

so s s

dC V v C vC rV

dt = +


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Batch operation Mass balance:

Cell balance

Substratebalance

Product balance

( )c g d dC

V r r V dt

=

/ ( )s

s c g c

dC Y r mC

dt =

/ ( )p

p p s s

dC r Y r dt = =

/ ( )s

s p p c

dC Y r mC

dt =

growth phase stationary phase

growth phasestationary phase

/ p p p c g

dC r Y r dt

= =


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Example 7-6 Fermentation of Saccharomyces cerevisae in a batch reactor.

Plot the concentration of cells, substrate, the product andgrowth rate as a function of time.

Initial cell concentration 1g/dm3

, glucose 250g/dm3

( ) ( )

* 3/

/

1max /

3 1

93 / 0.08 /

0.52 0.45 /

0.33 5.6 /

1.7 / 0.01

0.03 /

p c s

p s

p c

s d

C g cm Y g g

n Y g g

h Y g g

K g dm k h

m g substrate g cell h

= =

= =

= =

= =

=


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Physiologically based pharmacokinetics (PBPK)

Chemical reaction engineering approach can be applied topharmacokinetics

With every organ we can associate a certain tissue watervolume (TWV) and flow rates.


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Physiologically based pharmacokinetics (PBPK)

Chemical reaction engineering approach can beapplied to pharmacokinetics


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Problems (for the class) Derive the Briggs-Haldane equation P7-25 (http://www.engin.umich.edu/~cre/07chap/frames.htm).

Methanol has been ingested, and after pumping the stomachmethanol has an initial concentration of C Mi = 0.25 g/dm 3 in thebody:

1. First prove the equations on the left hand side.2. How many grams of ethanol are necessary to retard the

formation of formaldehyde so that it will not reach the level tocause blindness if the ethanol is to be injected immediately?

3. What feed rate of ethanol should be used to preventformaldehyde from reaching a concentration of 0.16 g/dm 3?

Use the following values for V max1 and K M1 for ethanol neglecting the reversereaction of acetaldehyde to ethanol. As a first approximation, use the same valuesfor methanol. Next, vary V max2 the initial methanol concentration (0.1 g/dm 3 < C M

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Chemical Reaction Engineering10_2010