dickeyd-mixing scale-up.pdf
TRANSCRIPT
Mixing Scale-UpSmall Mistakes Can Mean Big Success
David S. Dickey
MixTech, Inc.
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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
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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
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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
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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
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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
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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
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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
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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
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Multiple Processes
Multiple processes – multiple scale-up
rules
Combination
– dispersion
– chemical reaction
– heat transfer
Use design methods in combination with
scale-up
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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
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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
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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
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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”
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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
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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
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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
(937) 431-144638
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