POWER NUMBER POWER NUMBER

(1)

( )

dC

dt = K a C _L ^* − C − xQ

**On what and how saturation oxygen koncentration C* depends ?**

On what and how … K

_L

?

On what and how… a ^?

On what and how …. K

_l

a ?

(2)

KEVERÕMÛ

Not mixed reactors Only aeration

LEVEGÕELOSZTÓ

0 z

d_b

dC

dt D C

O

z

= − 

  

 

2 =

0

∂

∂ dC/dt= k

_L

(C*- C).

Oxygen flux through unit surface erea

Fick-law of diffusion Air sparger

(3)

LIQUID FILM

(4)

( )

C = f z Sh Sc Gr , , ,

Sh = g(Sc,Gr)

Dimensionless form

Dimensionless mass transfer coefficient:

Sherwood-number Sherwood-number

There are numerous correlations describing K_l (Sh) as a function of hydrodymanic Behaviour and liquid characteristics

(5)

Definition, explanation general form used for form oxygen m.tr.

REYNOLDS No

PECLET No

SCHMIDT No

O2

b

D d

D

dv

v^b

stream component

konductive

stream component

konvective Pe=

l l

vb

µ ρ

µρ db

dv forces viscous

forces inertial

Re =

l 2

l

D

DO

ρ µ ρ

µ dffusivity

mass

y diffusivit momentum

Sc =

FROUDE No

GRASHOF No

(Archimédes-No)

SHERWOOD No

(dimensionless Mass tr. coeff.)

l 2

D ρ D_O

ρ dffusivity

mass

gL

v

2

force nal

gravitatio

force l

centrifuga Fr =

( )

2 3

b 2

3 d

d

l

g l lg G g

µ ρ ρ ρ µ

ρ

ρ ∆ ⁻

= viscous force force buoyant

r

2

kl

D

kd

O b

D d thickness

film

diameter bubble

Sh=

(6)

2. CALDERBANK CALDERBANK andand MOOMOO--YOUNGYOUNG in most lab and industrial aerated reactors bubbles move up and/or down in groups, clusters ,

they are in interaction with each other (influence each other’s movement) ((single, independently moving bubbles are rare in real situations))

d_b<<<< 2,5 mm d_b>2,5 mm

1 1 1 1

Example for estimating k_l

Sh k d

D

^L ^b

Gr Sc

O

= =

2

0 31

1 3

1

,

3

^Sh ^{k d}

D

^L ^b

Gr Sc

O

= =

2

0 42

1 3

1

,

2

hidrofil materials Small holes

(sintered plates, bubble columns)

Pure water Sieve tray

(7)

felhajtóerõ Buoyant force BUOYANT FORCE

viszkózus visszatartó erõ

b u b o r é k á t m é r õ n õ d_b

Viscous restraining force B u b b l e d i a m e t e r increases BUBBLE DIAMETER INCREASES

VISCOUS RETRAINING FORCE

(8)

ESTIMATION OF

a

d _b

=d

At birth of a bubble there is an equilibrium between buoyant force and restraining force (surface tension on the circumference of the hole.

d g

b d

o 3

6 π∆ρ = π σ

=d _O

levegõ

σσσσ

surface tension

6

2 bubble

one 3

1

f 6

b o

b

d

g

d d π

ρ

σ ₌

 



 



= ∆

How many bubbles are present in the system at a given time?

a i r

(9)

It depends on residence time.

t H

b

v

L

b

=

H_L - liquid heights v - bubble velocity.

v_b is not constant, it varies while moves upward from the hole to the surface.

Bubble velocity: usually terminal v.

at the surface (when explodes into How many bubbles are present in the system at a given time?

v_b - bubble velocity. at the surface (when explodes into the gas phase above.

(10)

a V nqt d d

nqt V d

b b

b

b b

= 1 =

6

2

6

3

π π

Surface of one bubble

Total bubble volume In the reactor

Volume of one bubble b

0

d H 6

a =

Specific surface of one bubble

Hold up =

GAS VOLUME TOTAL VOLUME

HOW CAN WE INREASE?

(11)

OXYGEN MASS TRANSFER IN MIXED REACTOR

steril tömítés habtörõ

hûtõvíz spirál

törõlap

flat blade turbinakeverõ

(12)

(13)

(14)

MSG, JAPAN MSG, JAPAN HOFU

63420 GALLON 100 FEET

(15)

ROLE OFMIXING:

-Energy input to the liquid

moving heat -Dispersion of bubbling gas in the liquid

BUBLE FORMATION, MASS TRANSFER

P/V

K

_L

a

BUBLE FORMATION, MASS TRANSFER -Separation of gas from liquid

REVERSE MASS TRANSFER

-good mixing of the dissolved and suspended materials in the liquid GENERAL MIXING FUNCTION

CO

₂

substrates, products...

(16)

propellerkeverõ

h

_r

d

_w

lapátkeverõ

egyenes lapátú nyitott turbinakeverõ

(flat blade)

d

_s

d

_i

paddle

(17)

(18)

(19)

(20)

primary

liquid stream

secondary

liquid stream liquid stream

Bubble motion

at small gas velocity

Bubble motion

at large gas velocity good g/f dispersion

flooding

(21)

P AD N Fr W D

D D

H

i

D

m n i

i

T i

L i

= 

  

  

  

  

  

 

5 3

ρ

α β γ

Re ...

Power uptake of the mixing device

ρ - specific density

N – revolution rate of mixer.

µ

= dvρ Re

: ált.

µ ND ρ µ

.ND ρ Re D

2 i i

i







 

= 

=

mixing Re

sebesség kerületi

NDπ

= µ Re : ált.

µ Re µ

=

 

 

=

( )

 



 

= 

= g gL

N D gD

N

Fr D

ⁱ

i i

2 2 2

= v Fr : see.

Mixing Fr

(22)

P = ′ A D N ⁵ _i ³ ρ Re ^m Fr ⁿ

For a bioreactor of a given geometry

Power number (Ne=Newton-szám vagy Eu=Euler-szám) :

N P

D N

A Fr

P

i

m n

=

₅ ₃

= ′

ρ Re

(23)

POWER NUMBER

6 BLADE PADDLE

4 BLADE PADDLE with baffles without baffles

POWER NUMBER

PROPELLER

4 BLADE PADDLE

N_P=A’Re^-1 N_P=A’

′ ρ

= A D⁵_i N³

2 P

3 i N D A P = ′µ

(24)

3 2

2 3

/ 4

/ m

ker

rate aeration l

superficia apparent

i i

i

ND F s

m ND

D m

s F

sebessége ületi

keverő

Na = = =

π π

P

^g

= f Na ( )

P decrease when aerating

6 BLADE TURBINE good g/l dispersion

0,25-0,4

Aeration number

AERATION NUMBER*10-² PADDLE IMPELLER

bad g/l dispersion flooding

(25)

K a P

V v N

L

g

∝ 

s

  

 

0 4

0 4 0 5 ,

, ,

For lab fermentors

K a P

V v N

L

g

∝  s

  

 

α β 0 5 ,

_generally

αααα ββββ scale dependent constants, 0,3  0,95 0,5067

POWER NUMBER POWER NUMBER

( )

dC

dt = K a C L * − C − xQ

On what and how saturation oxygen koncentration C* depends ?

On what and how … K

?

On what and how… a ?

On what and how …. K

a ?

dC

dt D C

z

= − 

  

 

∂

∂ dC/dt= k

(C*- C).

( )

C = f z Sh Sc Gr , , ,

Sh = g(Sc,Gr)

( )

Sh k d

D

Gr Sc

= =

0 31

,

Sh k d

D

Gr Sc

= =

0 42

,

a

d b

=d

d g

b d

o 3

6

π∆ρ = π σ

=d O

σσσσ

6

f 6

d

g

d d π

ρ

σ =

 



 



= ∆

t H

v

=

a V nqt d d

nqt V d

= 1 =

6

6

π π

d H 6

a =

Hold up =

P/V

K

a

CO

h

d

d

d

P AD N Fr W D

D D

H

dt = K a C _L ^* − C − xQ

**On what and how saturation oxygen koncentration C* depends ?**

On what and how… a ^?

^Sh ^{k d}

d _b

=d _O

σ ₌

P = ′ A D N ⁵ _i ³ ρ Re ^m Fr ⁿ

dt = K a C _L ^* − C − xQ