Mixing Scale-UpSmall Mistakes Can Mean Big Success

David S. Dickey

MixTech, Inc.

1

Previous Mixing Webinars

Fluid Mixing: Still Needed for the Process

Industries in the 21st Century

– Dr. Arthur W. Etchells, III

– February 10, 2010

Identifying Mixing Problems

– Dr. Suzanne Kresta

– June 9, 2010

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Overview of Presentation

Turbulent Mixing – some basics

Geometric Similarity and Scale-up

More Complicated Scale-up

Testing for Limits and Mechanisms

Successful Scale-up

3

Mistakes

Not every day you are told to make

mistakes – some can be good

Mixing scale-up is more than just applying

“Rules of Thumb”

Laboratory and pilot studies should

investigate the effects of mixing on both

success and failure

A good approach to scale-up is often

avoiding failures

4

Mixing Scale-up

Basics of scale-up start with geometric similarity

– the simple approach

Scale-up “Rules” should be the result of a pilot

study, not just the supposition of a mechanism

All studies should look at a range of possible

operating and design conditions

Scale-up results must be both practical and

positive

Mixing becomes more difficult with scale-up

5

Mixing Basics

Typical Nomenclature

T – tank

diameter

D – impeller

diameter

N – rotational

speed

V – tank

volume

6T

DCb

C

H or Z

L

d

W

B

N

Standard Baffles –

for Turbulent Mixing

7Elevation View

Plan View

4 Baffles at 90 deg.

T

T/72

T/12Baffle W idth

Baffle Spacing

Tank Diameter

Geometric Similarity Scale-up

8

W 2

D2

B2

T2

C2

Z2

W 1

D1

B1

T1

C 1

Z1

Reasons for Testing with

Geometric Similarity

Effects of geometry are often the least

known variables in mixing

Different impeller tests

– type of impeller (pitched-blade, hydrofoil, etc.)

– diameter of impeller (D/T)

– number of impellers

– location of impellers – off-bottom clearance

Different mixer types (top, side, angle, etc.)

Basic flow patterns and problems9

Dimensionless Groups

for Mixing

Reynolds number

– inertial / viscous forces

Power number

– applied / inertial forces

Froude number

– inertial / gravity forces

Blend time number

– blending / rotation time

10

ReN

2D N

PN3 5

P

N D

FrN2N D

g

N

nD

NT

Relational QuantitiesTurbulent Conditions & Geometric Similarity

Volume

Tip Speed

Power

– power/volume

Torque

– torque/volume

Blend Time

11

3 5P N D

2 5P N N D

2 3 3V HT T D

tipv N D

1 N

3 5 3 3 2P V N D D N D

2 5 3 2 2V N D D N D

Scale-up with Geometric Similarity

For any positive exponent [n] large scale

rotational speed is smaller than small

scale rotational speed

Practical and reasonable scale-up

12

smalllarge small

large

nD

N ND

Scale-up with Equal Tip Speed

13

large small

large large small small

smalllarge small

large

1

tip

tip tip

v N D

v v

N D N D

DN N

D

n

Scale-up Results with Equal

Tip Speed

Optimistic scale-up

– smallest practical large-scale mixer

– comparable liquid velocities

Some conservatism from increased

Reynolds number

Often used for

– comparable mixing intensities – as observed

– equal drop size for liquid-liquid dispersion

Longer blend time – larger micro-scale

turbulence 14

Scale-up with Equal

Power per Volume

15

3 2

large small

3 2 3 2large large small small

23

smalllarge small

large

23

P V N D

P V P V

N D N D

DN N

D

n

Scale-up Results with Equal

Power per Volume

Conservative scale-up

– largest practical large-scale mixer

– more intense large-scale mixing

Often used for

– maintain local mixing intensity for fast

chemical reactions

– equal mass transfer coefficient in gas

dispersion

Longer blend time – similar micro-scale

turbulence16

Scale-up with Equal

Torque per Volume

17

2 2

large small

2 2 2 2large large small small

smalllarge small

large

same as equal tip speed

different without geometric similarity

1

V N D

V V

N D N D

DN N

D

n

Scale-up Results with Equal

Torque per Volume

Realistic scale-up

– smallest practical large-scale mixer

– comparable liquid velocities

– somewhat independent of D/T

Some conservatism from increased

Reynolds number

Often used for

– comparable mixing intensities – as observed

Longer blend time – larger micro-scale

turbulence 18

Scale-up for Equal

Solids Suspension

19

.

smalllarge small

large

exponent depends on settling velocity

and other factors, such as

geometry and concentration

1 0 6

nD

N ND

n

Scale-up Results with Equal

Solids Suspension

Practical / Empirical scale-up

– exponent depends on particle settling velocity

– low values [n=1] of exponent for slowly settling

particles that follow liquid velocity

– high values [n>2/3] of exponent for rapidly

settling particles

– practical large-scale mixer

Used in combination with other design

experience

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Impractical Scale-up Criteria

Equal Reynolds number – small mixer

Equal Froude number – large mixer

Equal blend time – very large mixer

21

2

smalllarge small

large

DN N

D

12

smalllarge small

large

DN N

D

0

smalllarge small small

large

DN N N

D

More Complicated Scale-up

Not all scale-up should use geometric

similarity

Not all scale-up can be done with

geometric similarity – lack of available

equipment

Which scale-up method applies in

complicated or multiple processes

– primary process result

– secondary process result

22

Geometric Similarity Does Not Work

for Equal Heat Transfer per Volume

23

T T

large small

large small

2 3

large small

same , ,

Q Q

V V

h A h A

V V

T A D V D

h h

D D

Agitated Heat Transfer

24

Nu Re Pr2 1

3 3

2 2 42 3 3 3

2 13 3

large small

2 2 2 23 3 3 3

large small

1

smalllarge small

large

k

h T h D N D N D

h hh N D

D D

N D N D

DN N

D

Area per Volume Scale-up

Area increases as square of diameter

Volume increases as cube of diameter

Area per Volume decreases as diameter

increases

Problem for heat transfer – temperature

control

Problem for other area per volume

processes

25

Non-Geometric Scale-up

Size change by geometric similarity

– usually to correct tank diameter

Adjust volume

– increase volume for taller tank

– decrease volume for shorter tank

Adjust impeller diameter or type

Make adjustments in large scale

– equal power/volume

– equal torque/volume

– equal tip speed

26

Multiple Processes

Multiple processes – multiple scale-up

rules

Combination

– dispersion

– chemical reaction

– heat transfer

Use design methods in combination with

scale-up

27

Scale-up Depends on Testing

At a minimum test at multiple impeller

speeds in small scale

Investigate both success and failure

Most processes require some minimum

level of agitation

A few processes have a maximum level of

agitation

Hopefully find a successful range

28

Scale-up “Rules” Can Be Unreliable

The conventional “rules” for scale-up are based

on an assumption that the primary mixing

mechanism is known

Rarely is any single mechanism clearly “known”

and exceptions are common

My “First Rule of Mixing” is that “All of the Other

Rules Have Exceptions”

Two remaining options for scale-up

– test for mechanisms

– be conservative

29

Testing for Mechanisms

If the only variable tested in a pilot study is

rotational speed – increasing speed means

– increased power

– increased torque

– increased tip speed

– which one?

If studies of the same process are conducted with

different size impellers and different speeds

– equal power, equal torque, or equal tip speed can be

observed independently

Tests at different scales may also identify scale-

up mechanisms 30

Be Conservative

The most conservative and still practical

scale-up is equal power per volume

Equal power per volume may result in

extremely large full-scale mixers, unless

applied to a failure or near failure in the

small scale

Less conservative scale-up like equal tip

speed or torque per volume may be

applied to a clearly successful

(conservative) small-scale result 31

Reasons for Conservatism

Certain and rapid start-up

– reduced impeller size easy

– larger mixer size costly and slow

Possibility of future capacity increase

– de-bottleneck plant for higher throughput

Cost of mixing equipment small compared

to total plant

– mixer may convert raw materials to products

– mixing is often essential for process success

32

The Most Important Test Result

The most important test result may be a small-

scale failure

The conditions which caused the small-scale

failure must be avoided with scale-up to a large-

scale process

Avoid having a large failure by finding your

potential failures in the small scale

“Make your mistakes on the small scale”

“Make your money on the large scale”

33

Be Sure That Failures Are

Documented

Failures occur often in the laboratory, but

knowing about them may help the

developers in the pilot plant

Failures in the pilot plant may help

engineers when designing or operating

the plant

By the time a process reaches the large

scale plant, the failures should be known

and avoided

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The Development/Scale-up Process

Laboratory tests and information should

help the pilot plant conduct good tests

The pilot plant should explore operating

limits for the full-scale process

The full-scale process should take

advantage of laboratory and pilot-plant

results

A scale-up decision cannot be an

afterthought when testing is finished

35

Mixing Scale-up

Mixing scale-up can be done by different

methods

– geometric similarity

– scale-up rules

– process design methods

– intermediate scale results

No one method always works

Knowing the limits of mixing requirements

always helps

36

More Information

Handbook of Industrial Mixing

– Science and Practice

Chapters on many aspects of mixing

– scale-up recommendations and examples throughout

Editors: Edward L. Paul, Victor A. Atiemo-Obeng, and

Suzanne M. Kresta

John Wiley & Sons, 2004

Plenty of other published articles on

mixing

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Mixing Scale-UpSmall Mistakes Can Mean Big Success

David S. Dickey

MixTech, Inc.

www.mixtech.com

d.dickey@mixtech.com

(937) 431-144638

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