engg 199 reacting flows spring 2006 lecture 4 gas-liquid … · 2006-04-18 · sample calculation...

Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRocheAll rights reserved.

ENGG 199 Reacting FlowsSpring 2006

Lecture 4Gas-Liquid MixingReactor SelectionAgitator Design

ENGG 199 Lecture 4 Slide 2Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved.

Background

Roughly 25 % of processes involve gas-liquid contacting.

A variety of equipment types are used.

Size of vessel and type of equipment will depend on:Concentrations

Kinetics

Diffusivities

Solubilities

May involve reaction or simple transfer between phases.

Similar issues to single-phase mixing and reaction.


Examples

Sulphonation and Chlorination:Fast reactions - Gas is soluble in liquid - High mass and heat transfer required.

Short contact times small reactor volume with high mixing rates.

Oxidation and Hydrogenation:Solubility is low - Many reactions are very exothermic.

Long contact times large reactor volume with high mixing rates.

Fermenters (inc. WWT):Often dilute - Slow reactions.

Long contact times very large reactor volume with low mixing rates.Heat transfer may be important.


Examples

May need to remove dissolved material from liquid:May be contaminant.

May be by-product.

Must be removed affects product quality.

Add inert gas to liquid to strip out contaminant.

Fermentation:Aerobic organisms produce carbon dioxide.

Soluble in reaction mass changes pH.Air supplies oxygen and strips out carbon dioxide.

80 % of air supplied is inert.


Equipment for Gas-Liquid Mixing

From Mixing in the Process Industries


Mass Balance

Molecules transfer from gas into liquid (or vice versa):

Where:a´ is the surface area to volume of a single bubble.

v is the volume of a single bubble.

n is the number of bubbles per unit volume of liquid.

Mass transfer resistance:

Usually, kG >> kL / H so 1 / kG can be neglected.

)(dd

AAA VCt

rVP

HCyvnVaPKG

LGG k

H

kK

11


Mass Balance

Interfacial area per unit volume, a:

Gas hold-up, G:

nvaa

nvG

)(dd

)(dd

)(dd

AA

*

A

AA

*

A

AAA

VCt

rVCCaVk

VCt

rVCxaVk

VCt

rVCyH

PaVk

L

molL

L


Comparison of G-L Contacting Devices

Device kLa(s-1)

V(m3)

kLaV(m3 s-1)

a(m-1)

L

(-)LiquidFlow

GasFlow (W /kg)

AgitatedVessel

0.02 0.2

0.002 100

10-4

3200 0.90 B mixed Int to

B mixed0.5 10

BubbleColumn

0.05 0.1

0.002 300

10-5

320 0.95 Plug Plug 0.01 -

1

PackedTower

0.005 0.02

0.005 300

10-5

6200 0.05 Plug Plug 0.01

0.2

PlateTower

0.01 0.05

0.005 300

10-5

15150 0.15 Int Plug 0.01

0.2

StaticMixer

0.1 20

Up to10

1 20

1000 0.1 0.9

Plug Plug 10 500

From Mixing in the Process Industries .


Choice of Mixing Equipment

A diffuses through film into bulk.

Without reaction, rate of mass transfer per unit area of interface will be:

Maximum mass transfer when CA = 0:

Note: higher mass transfer rate may be achieved if all reaction occurs in film - Enhancement Factor .

1-2-

A

*

AA

*

A s m kmol )()(

CCkCC

Dj Lmol

*

A

*

A )0(Ck

CDj Lmolmax


Choice of Mixing Equipment

Some A will be consumed by reaction within the film.

Maximum possible rate of reaction within unit area of interface will be:

Define Film Conversion Parameter , M:

B

*

ACCkr Rmax

2B

*

A

2

B

*

A

*

A

B

*

A

L

molR

mol

mol

mol

R

mol

R

max

max

k

DCkM

D

D

CD

CCk

CD

CCk

j

rM


M < 0.0004 Infinitely Slow Reaction

Mass transfer keeps concentration of A in the bulk close to the saturation level.

Reactor needs:High liquid hold-up.

Sufficient interfacial area - but not high.

Once kLa is high enough, rate is independent of mixing.

Consider using Bubble Column.

ak

CkC

C

CCkCCakj

L

LR

LRL

B

*

AA

BAA

*

AA

1

)(


0.0004 < M < 4.0 Intermediate Reaction

Reaction consumes A in bulk but not fast enough to drive concentration to 0.

Most of reaction does occur in bulk (V L >> a ).

Must not be mass transfer limited:Need sufficient interfacial area.

Since CA < CA*, mixing can

increase CA:

Consider using Agitated Vessel.

t

CCCkCCak LRL d

d)( A

BAA

*

A


M > 4.0 Instantaneous Reaction

Reaction is so fast, compared to diffusion rate, that all A is consumed in film.

Hence, large a is needed but L is not.

Consider using Motionless Mixer.

Consumption of A steepensconcentration gradient enhancingmass transfer.

Reaction occurs at plane within film:A and B cannot exist together.

Location of film depends on relative diffusivities of A and B.


Enhancement Factor

For reaction with negligible gas phase resistance:

A + bB Products

Max. mass transfer rate per unit area without reaction is:

Term inside bracket is Enhancment Factor, E:

*

AA,

BB,*

AAA 1CDb

CDCkr

mol

mol

L

*

AAA Ckr L

alone

transfer massfor

ratereactionwith

transfer mass

of

rateE


Sample Calculation

For a given system, how fast must reaction rate be in each regime?

Diffusivity, Dmol:

Oxygen / Water 2.5 10-9 m2 / s

Hydrogen / Water 5.8 10-9 m2 / s

Chlorine / Water 1.4 10-9 m2 / s

Carbon dioxide / Water 2.0 10-9 m2 / s

Carbon dioxide / Ethanol 4.0 10-9 m2 / s

Sulphur dioxide / Water 1.7 10-9 m2 / s


Sample Calculation

Concentration of liquid phase reactant, CB:For a pure liquid:

For water: CB = 55.55 kmol / m3

Mass transfer coefficient, kL:

Estimate (from Coulson & Richardson) for bubbly flow:

kL= 3 10-4 m / s

MwCB


Estimates of kR

From definition of M:

M = 4.0: kR = 3.24 m3 kmol-1 s-1

M = 0.0004: kR = 3.24 10-4 m3 kmol-1 s-1

Look for some examples .

MM

DC

Mkk

mol

LR 81.0

10255.55)103(

9

24

B

2


Agitator Design

Equipment selection should be made by comparing rates of reaction and mass transfer:

But these are often not known and can be very difficult to measure.

Agitated vessel is very commonly used:Offers compromise of high liquid hold-up and high interfacial area.

Similarities with solid-liquid mixing:Buoyancy causes bubbles to rise and leave liquid phase.

Bubble size is determined by intensity of agitation.

Expect minimum speed for impeller (analogous to NJS for solids suspension)?


Agitator provides energy to:

Break-up bubbles and create interfacial area.

Re-circulate bubbles (prevent plug flow).

Mix the liquid phase.

Suspend solids - if present (catalyst).

Promote heat transfer.

Re-incorporate gas from head space - pure gas only.


Calculations

Need to be able to calculate:

Agitator speed:Minimum speed for dispersion.

Maximum speed required to re-circulate bubbles.

Power:Presence of gas affects power drawn by impeller.

How to account for gas in power calculation?

Mass transfer co-efficient:Power input and gas flow affect mass transfer.

How to estimation of mass transfer co-efficient?


Vessel Geometry

Typical vertical, cylindrical vessel:May have 1/2 baffles with upper impeller to create vortex on surface.

Re-incorporates gas from head space.

Dished heads to withstand pressure.

Often need mechanical seal.

Sometimes H / T > 1.0:Increases pressure increase solubility increase driving force.Increases surface area per unit volume for heat transfer.

Gas introduced low in vessel:Through pipe or sparge ring.

Locate beneath impeller.


Impeller Geometry

Lowest impeller:Main gas dispersing impeller.

Traditionally a Rushton turbine.

New development - concave blade (Smith) turbine.

High local energy dissipation rate high interfacial area.

Upper impeller(s):Another radial flow impeller (Rushton or Smith).

More usually an axial flow impeller (PBT or Hydrofoil).

Recent development:Upward pumping hydrofoils.

Seem to offer several advantages .


Impellers used for Gas Dispersion

Rushton TurbineSmith Turbine

Chemineer BT-6High-solidity Hydrofoil


Nienow et al. (5th Europ Conf on Mixing)


Impeller Speed

At (a):Inertia of gas bubbles dominates flow.

Vessel behaves as bubble column.

Impeller starts rotating:Inertia of liquid flow starts to increase.

Bubbles are driven radially towards wall of vessel.

At (b) - the Flooding Speed:Bubbles reach wall at height of impeller.

At (c) - the Complete Dispersion Speed :Bubbles re-circulate beneath the impeller.


Dimensionless Numbers

These speeds have been measured experimentally:Empirical correlations relating impeller speed and diameter to gas flow rate have been developed.

Dimensionless numbers have been used to correlations.

T

D

g

DNFr

ND

QAeFl G

2

3


Flooding Speed

For Rushton and Smith turbines (0.22 < D / T < 0.55):

For a Rushton turbine: KF = 30.For a Smith turbine: KF = 70.

3/15.3

4

5.32

3

5.3

D

T

DK

gQN

T

D

g

DNK

DN

Q

T

DFrKAe

F

GF

FF

F

G

FFF


Complete Dispersion

For Rushton and Smith turbines (0.22 < D / T < 0.55):

For a Rushton turbine: KCD = 0.2.For a Smith turbine: KCD = 0.4.

2/1

4

2/1

2/12

3

2/1

5.0

)(DK

TgQN

T

D

g

DNK

DN

Q

T

DFrKAe

CD

GCD

CDCD

CD

G

CDCDCD


Power No. vs. Flow No.Smith Turbine - Standard Baffles - No Coil

0

0.5

1

1.5

2

2.5

3

3.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Flow No.

Pow

er N

o.

5 SCFM

10 SCFM

20 SCFM

30 SCFM

40 SCFM

53 SCFM

0 SCFM


Gas Cavity Structures


Power Input

As impeller rotates:High pressure region is formed on front of blades.

Low pressure region is formed on back of blades.

Gas cavities form in low pressure regions:Reduces drag on impeller.

Reduces power required to move impeller reduces Po.

Five cavity structures have been identified:6 vortex cavities.

6 clinging cavities.

3 clinging and 3 large cavities on alternate blades.

6 large cavities of different size (3 - 3 structure).

6 ragged cavities (flooded impeller).


Ratio of Gassed to Ungassed Power

Vortex and clinging cavities little effect on power draw.

Power drops as 3-3 cavity structure forms.

Once ragged cavities form slight increase in power draw.

Ratio of gassed to ungassed power is dependent on impeller type.

A great deal of work has been done to find impellers that minimize the fall in power.

Smith and Upward Pumping turbines and others.


Prediction of Gassed Power

For Rushton turbines:

Calderbank (1958) fitted two straight lines to curve:

Volesky (1979):

035.0:for 85.162.0

035.0:for 6.121

AeAeP

P

AeAeP

P

U

G

U

G

5/1

3/2

424/1

10.0gwV

DN

NV

Q

P

P G

U

G


Prediction of Gassed Power

Bakker, Smith & Myers (Chemical Engineering, 199x):

a b c d

Rushton 0.72 0.72 24 0.25

Smith 0.12 0.44 12 0.37

)tanh()(1 cAeFrabP

P d

U

G


Gas Hold-Up

Gas hold-up, G, is ratio of gas volume to total volume of dispersion.It is affected by:

Bubble size generated by impeller.

Distribution and circulation of bubbles throughout liquid.

Growth (due to coalescence) of bubbles during circulation.

Interfacial tension between gas and liquid determines:How much energy is required to break-up bubbles.

How likely are bubbles to coalesce as they collide.

Hold-up is important because:

32

6d

a G


Estimation of Gas Hold-Up

Experimental measurements.

Best correlation in terms of (gassed) power input per unit mass and superficial gas velocity.

Chapman (1983):

Chapman correlated hold-up data from two sizes of Rushton turbine and two pitched blade turbines pumping up and down.

Similar exponents found in other work.

67.031.097.1 SGGG U


CFD:- Aeration: Gas Holdup in Eulerian

Contours of GasVolume Fraction

Contours of vorticity magnitude(0-100) display on an iso-surface of contant gas volume fraction (0.25)

NA = 0.043 << Namax = 0.45Pg/Pu = 0.7 (0.83 for single impeller system; experiments)


Mass Transfer Co-efficient

Researchers measure and correlate kLa.

Best correlation in terms of (gassed) power input per unit mass and superficial gas velocity.

Muskett (1987)

Van t Riet (1979)Non-coalescing, salt solutions, typical of fermentations

Epsilon turbulent energy dissipation rateCalculated directly from CFD analysis

Estimate using Power/Mass in the impeller swept volume

Absolute kLa not required, but relative values compared to verifiable small-scale reactor

49.041.0 )vvm( Tak GL

2.07.0 )vvm( Tak GL


G and kLa

kLa and G are related:

From turbulence theory and experiments:

Relationship between hold-up and superficial gas velocity?

32

6d

kak GLL

4.0

4.0

32

6 GGLL

G

kak

d


CFD:- Volumetric Mass Transfer Coefficient (KLa)


Scale-Up

Gas flow is usually specified in terms of liquid volume:Defines productivity of vessel.

Kmols of gas processed per unit time.

Expressed as vessel volumes per minute (vvm s) of gas:e.g. 1000 gallon vessel with 500 GPM gas flow 0.5 vvm.

Especially true if mixed gas (e.g. air) is fed to the reactor:Gas bubble will be depleted of reacting gas decreasing driving force.

What happens to mass transfer rate on scale-up?


Scale-Up

Scaling-up with constant vvm s:

On scale-up:

Superficial gas velocity increases on scale-up

kLa will increase if vvm & are constant on scale-up

TT

QU

TQ

2

3

S

L

SSG

LSG

T

T

U

U

,

,


Driving Force

In order to calculate driving force need to know CA*.

For pure gas this is (relatively) easy.

For mixed gas need to know representative gas composition.

In stirred tank, gas phase is back-mixed:Assume that gas composition is that of exit gas.

Not always true, especially in tall tanks (fermenters).

Gas composition has been measured and modeled (see Mann, Vlaev et al., UMIST).


Boiling Reactors

Boiling reactors are often used:Remove a solvent.

Remove heat of reaction.

Etc. etc.

Vapour is generated by boil-up.

What happens to power draw?

In gassed system, power draw decreases due to cavities forming in low pressure region on back of blades.


Boiling Reactors

How will cavity form in boiling reactor?

Pressure in zone at back of blades must be less than the saturated vapour pressure of the liquid.

Static head of liquid will suppress cavity formation.

Power draw will not decrease (in most circumstances):Especially on scale-up.

What will happen when gas is sparged into a boiling reactor?

engg 199 reacting flows spring 2006 lecture 4 gas-liquid … · 2006-04-18 · sample calculation...

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