engg 199 reacting flows spring 2006 lecture 3 mixing and ... · ideal plug flow reactor tubular or...

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

ENGG 199 Reacting FlowsSpring 2006

Lecture 3Mixing and Chemical Reactions

ENGG 199 Lecture 3 Slide 2Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche All rights reserved

Review of Ideal Chemical Reactors

Reference: Chemical Reaction Engineering by O. LevenspielIdeal Batch Reactor

Ideal Plug Flow Reactor

Ideal Continuous Stirred Tank Reactor

Ideal Semi-Batch Reactor

Consider component A to be limiting reactant, we can define concentration of A, CA, in terms of conversion, XA

AAA

A

AAAAAA

dXCdC

inresultsatingdifferenti

N

NNXwhereXCC

0

0

00 1


Ideal Batch Reactor

AssumptionReactor contents uniformly mixed

AX

A

AA

t

AA

AAAA

AA

Vr

dXNdtt

egratingintandgrearrangindt

dXN

dt

XNd

dt

dNVr

dt

dNVr

onaccumulatireactionbyncedisappearaoutputinput

000

00 1

00

A

A

A C

CA

AX

A

AA

A

AA

A

AA

r

dC

r

dXCt

C

dCdXand

C

CX

systemsdensityttanconsFor

000

00

1liquidofvolumeV

AofconversionX

AofmolesN

liquidofvolume

AofmolesC

A

A

A


Terminology for Continuous Flow Reactors

Space-timetime required to process one reactor volume at specified conditions

Space-velocitynumber of reactor volumes of feed at specified conditions which can be treated in unit time

timeratefeedvolumetric

volumereactor

v

V

time

enteringAmoles

reactorofvolumefeedofvolume

enteringAmoles

F

VC

A

A

0

0

0

11times


Ideal Plug Flow Reactor

Tubular or Pipeline ReactorAssumptions

No mixing in flow (axial) direction

Perfect mixing in radial direction

Af

Af

Af

X

A

AA

X

A

A

AA

X

A

AV

A

AAA

AAAAA

AA

AAAA

r

dXC

v

V

r

dX

CF

V

r

dX

F

dV

egratingint

dVrdXF

ngsubstituti

dXFXFddF

thatnoting

dVrdF

dVrdFFF


000

000

000

0

00 1

0

time

liquidofvolumev

AofconversionXtime

AofmolesF

liquidofvolume

AofmolesC

A

A

A

Af

A

Af C

CA

AX

A

AA

A

AA

A

AA

r

dC

r

dXC

v

V

C

dCdXand

C

CX


0000

00

1

Note similarity with ideal batch reactor


Ideal Continuous Stirred Tank Reactor (CSTR)

CSTR, C-Star, Back-mixed, Mixed-Flow ReactorAssumptions

Reactor contents uniformly mixed

Exit conditions same as reactor conditions

Step change from inlet to outlet conditions

A

AA

A

A

A

A

AA

AAAA

AAA

r

XC

v

V

F

VC

r

X

CF

V

VrXFF

VrFF

naccumlatioreactionbyncedisappearaoutputinput

0

00

0

00

00

0

1

0

A

AA

A

AA

A

AA

r

CC

r

XC

v

V

C

CX


00

0

0

1


Semi-Batch Reactor

Commonly used for specialty chemicalsReactor loaded with one reactant (component A)Add other reactant over time (component B)Called starved feed by chemists

CB is now a more complex function of time

t C

BiB

B

BB

Bi

Bi

Bi

BBBi

B

Cr

dCdtt

dt

VdCVr

VC

F

VCthatnote

systemsdensityttanconsdt

VdCVrF

0 0

)(0

A

A

C

CA

At

AA

r

dCdtt

systemsdensityttanconsdt

VdCVr


00

)(00


Analysis of Batch Reactor Data

In a constant-volume reactor, the rate of disappearance of component A

We often separate rate expression into a concentration-dependent and a concentration-independent term

Rearranging to give

Integrating

Plotting concentration function (LHS) vs. time yields a straight line with slope of k

Ckfdt

dCr A

A ,

Ckfdt

dCr A

A

kdtCf

dCA

tC

CA

A ktdtkCf

dCA

A 00


Example: Irreversible Unimolecular-type First-Order Reaction

productsA

ktAA

A

A

tC

CA

A

AA

A

eCC

ktC

C

dtkC

dC

kCdt

dCr

A

A

0

0

0

ln

0

ktA

A

tX

A

A

AA

AAAAAA

AA

A

eX

ktX

dtkX

dX

Xkdt

dX

dXCdCandXCC

kCdt

dCr

A

1

)1ln(

1

1

1

00

00

In terms of concentration, CA In terms of conversion, XA


Recap of Ideal Reactor Types

Ideal Batch ReactorReactor contents uniformly mixed

Ideal Plug Flow ReactorNo mixing in flow (axial) direction

Perfect mixing in radial direction

Ideal Continuous Stirred Tank ReactorReactor contents uniformly mixed

Exit conditions same as reactor conditions

Step change from inlet to outlet conditions


Assumptions for Reactor Design

Assume that vessel contents are perfectly mixed .

If reaction is slow relative to rate of mixing this is true:Vessel will be homogeneous before reaction takes off.

Reaction rate will be determined by average composition.

Even in semi-batch or continuous reactors.

What if reaction is fast compared to mixing rate?

No problem if reaction is non-competitive:

No undesirable by-products.

D

C

B

A


Competitive Reactions

Many valuable chemical reactions are competitive:

Example:Want to make mononitro toluene.

Dinitro toluene is a possible by-product.

So is trinitro toluene (or TNT)!!

If reaction rate is faster than rate of mixing:Concentration gradients determine selectivity (yield of product and by-products).

High concentration of B at feed point.

Reaction is over within a few cm of feed point.

W

B

P

P

B

A

W

C

A

P

B

A


Mixing on the Micro-scale

A + B

P

P + B

W

Well mixed on the micro-scale:

Poorly mixed on the micro-scale:


Time-scales of Mixing

Macro-mixing:- scale of the tank- blend time

Meso-mixing:- scale of the feed zone- dispersion of feed plume

Micro-mixing:- smallest scales of turbulence- diffusion time

10 m


Macro-Mixing

Macro-mixing Time:Time for vessel contents to become homogeneous after addition of tracer .

Important for design of CSTR s - Ratio of Blend to Residence Time and validity of Perfect Back-Mixing assumption.

Correlation for prediction of Blend Time:

Important time-scale for slow reactions (tR > 10 secs):Want blend time to be shorter than reaction time.

By how much?

2

3/195

40.5D

T

NPo


Micro-Mixing

Micro-mixing Time (Bourne et al.):Time for turbulent eddy to shrink from 12 lK to lK.

Called Engulfment Time (eddy containing A engulfs eddy of B).

As engulfment occurs (shrinking in x and y directions), eddy deforms (stretches in z direction).

Shrinkage in x and y directions increases concentration gradients increasing rate of diffusion of A and B.

Hence: Eddy-Deformation-Diffusion (EDD) Model.

Engulfment is rate limiting step:

2/12/1

31.172ln

121E

tE


Meso-Mixing

Meso-mixing Time (Bourne et al.):Semi-batch or continuous reactor - adding B to A.

Time for plume of B to be dispersed in A by local turbulence.

More complicated than micro-mixing:Time is dependent on local mixing conditions and feed rate of B.

Two definitions:

3/13/12

3/43/122

U

qLt

DU

q

DU

qt BC

CB

T

BD


Meso-Mixing

Turbulent diffusivity:

Velocity of bulk flow past feed point:

Meso-mixing includes dilution effect (want high Q):

What is more important; generation of turbulence or flow?

3/43/13/1)( DllluDT

TIPQQ

SWEPT

UND

NDN

A

QU 4

42

3

Q

q

U

qt BB

D


Meso-Mixing/ Micromixing

Important for anti-solvent addition crystallization processMeso-mixing Time (Bourne et al.):

Semi-batch or continuous reactor - adding B to ATime for plume of B to be dispersed in A by local turbulence.

Time is dependent on local mixing conditions and feed rate of B

Important to identify the rate limiting step for successful scale-up

Micromixing refers to the smallest scales of mixing that can affect particle size

Multi-environment Mixing Models incorporating models such as IEM (Interaction by exchange with the mean)Improved prediction of product selectivity, crystal size and associated properties


Meso-Mixing

More complicated than micro-mixing:Time is dependent on local mixing (turbulence and flow) conditions and feed rate of B

Keep Damkohler number constant on scale-up

Corrsin meso-mixing time

)( raten dissipatio turbulent theis

)(point feed past theity bulk veloc theis

)( rate feedreactant theis

where

2

32

3

3/1

sm

smU

smB

q

U

qt BC

Reference: G.K. Patterson, E.L. Paul, S.M. Kresta, A.W. Etchells III, Mixing and Chemical Reactions, Chapter 13 in the Handbook of Industrial Mixing, edited by E.L. Paul, V.A. Atimo-Obeng, S.M. Kresta, John Wiley & Sons, 2003

mixBRE tCkDa 0


What happens on Scale-Up?

Lab reactor will run at 100 s RPM.

Scaling-up with constant blend time is (almost) impossible:

Typical lab reactor is 1 ft diameter - typical plant reactor is 6 ft diameter:

Power input increases by 65 = 7776 times.

Power input per unit mass increases by 62 = 36 times.

Uneconomic to scale-up with constant blend time.

25

S

L

S

L

S

L

S

L

D

D

D

D

P

P


Scaling-Up Fast Chemical Reactions

For competitive reactions ONLY!

Scale-up at constant power input per unit mass:Blend time will get longer.

Outcome of fast chemical reaction is determined by local mixing conditions at feed point:

Determined by the local mixing rate.

The local energy dissipation rate.

Conditions in bulk of vessel are unimportant.

What factors affect the design of the mixing system (impeller and feed method become important) for a fast, competitive chemical reaction?


Damkohler Number

Damkohler Number is ratio of reaction rate to mixing rate.

Since reaction rate is fast all B will be consumed close to feed point.

Reaction rate will be determined by concentration at which B is fed to reaction (NOT vessel averaged concentration).

Increase mixing rate, smaller Damkohler No.

Controlling mechanism may change from micro- to meso-mixing.

DBRDEBRE tCkDatCkDa 00

:or


Typical plot of Waste vs. Damkohler No.


Effect of Feed Location

Feed at location of highest mixing and energy dissipation rate:

Into the impeller zone.

Effect has been well characterized and reported.

Care must be taken in the mechanical design of the pipe:Flow induced vibration.

Fatigue failures.

What happens if feed of B shuts off?Will reactor contents migrate into feed pipe?

May have to feed above liquid surface for safety reasons.


Selectivity versus Feed Location

Location B makes6 - 8 x more waste thanLocations A or D.


Effect of Impeller Type

So far, have compared impellers in terms of vessel average power input per unit mass - affects blend time.

When compared at the same average PPM, some impellers have higher PPM in the impeller zone than others.

Define ratio of maximum energy dissipation rate (or PPM) to vessel average, K:

Measure K for various impeller types and geometries.

KMAX


Results from Zhou & Kresta (U of Alberta)

For T / 3 impellers @ T / 3 off-bottom clearance with standard baffles:Pitched blade turbine: K = 38.3

Hydrofoil: K = 26.5

Rushton turbine: K = 47.7


Hydrofoil: K = 19.2



Hydrofoil: K = 46.3



Conclusion

An impeller which is considered efficient for blending will have a large diameter relative to the vessel.

An impeller which is considered efficient for micro-mixing applications will have a small diameter.

Need to define and understand mixing requirements!!

Need to consider other aspects of reactor design in determining best impeller type:

May need several mixing operations (blending and micro-mixing).

Especially Heat Transfer.


Effect of Feed Rate

At low feed rates, micro-mixing controls:Engulfment of small-scale eddies.

Feed jet is dispersed quickly.

As feed rate, qB, increases mechanism changes:Dispersion of feed jet takes longer than engulfment.

Change in mechanism.

A critical feed time (or feed rate) can be identified:t > tCRIT Micro-mixing controls.

t < tCRIT Meso-mixing controls.


Selectivity versus Feed Time


Scale-Up Problem

Operation of lab reactors:High power input per unit mass.

Short blend time.

Slow feed rate.

Operation of plant reactors:Can operate at same power input per unit mass.

Longer blend time.

Same micro-mixing time.

Feed rate determined by productivity (batches per day):Lab may be micro-mixing controlled.

Plant will probably be meso-mixing controlled.


Best Place to Operate

The most cost effective operation will be at the knee of the curve:

At the boundary between meso- and micro-mixing control.

Increasing power input does not increase yield:Yield is determined by kinetics to the right of the knee.

Slow down feed rate (increase feed time):Not acceptable.

Feed rate determined by productivity requirements.

qB is local feed rate:If total feed rate increases - consider multiple feed points.


In Industry .

Often do not know kinetics.

Sometimes do not even know mechanism.

Can make estimates of mixing rates.

If speed of chemistry does not change (constant temperature and concentrations):

Constant Mixing Rate = Constant Da

Scale-up keeping appropriate mixing rate constant.

engg 199 reacting flows spring 2006 lecture 3 mixing and ... · ideal plug flow reactor tubular or...

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