2. The problem
Scaling up processes is difficult
There are three main elements involved in process developments
Thermodynamics
Kinetics
Transfers
Heat
Mass
Momentum
Thermodynamics
Kinetics
Transfers
Heat
Mass
Momentum
Pressure, Temperature,
Concentrations
Velocities, characteristic
dimensions
Lab scale Full scale
Pressure, Temperature,
Concentrations
5. 𝜌𝑖 𝐶 𝑝,𝑖 𝑇𝑖
Solid-solid heat transfer
Mixing is also playing a key role in heat transfer
𝑇 𝑤
𝜌𝑖 𝐶 𝑝,𝑖
𝑑
𝑑𝑡
𝑇𝑖 = 𝛻 ∙ −𝑘𝛻𝑇
• Residence time at
wall is critical
• Probability of hitting
the wall is 𝑓(𝑣)
Heat transfer is 𝒇(𝒗)
𝑣
6. Scale-up
Why are we so far from the real solution when scaling up processes?
Two observations I made
1) We are approaching transfer problems as mixing problems too quickly.
• It limits the possibilities for alternate solutions beyond mixing theory
2) We are spending too much time and $ on models/CFD and not doing the
right experimental work.
• Industrials want an operating point, not a theory.
• All models work just fine for a very small onset of cases, but are totally off with
realistic systems.
7. How do we do scale-up normally?
Maintaining flow regime by scaling up mixing operations
Calculation of
𝒗, 𝑵 𝒑 , 𝑲 𝑻, etc
Identify hydrodynamic
parameters
Extrapolation
to large scale
Large unit
Lab scale
technology
Selection of the
mixing device
Parameters
Selection of mixing
device and power to
keep mixing similar
Application to new
large scale conditions
Process problems
8. How do we approach this?
Maintaining flow regime by scaling up mixing operations
Identify hydrodynamic
parameters
Extrapolation
to large scale
Large unit
Lab scale
technology
Characterization of the
mixing device
Parameters
Selection of mixing
device and power to
keep mixing similar
Application to new
large scale conditions
Optimization of
mixing device
Process problems
Calculation of
𝒗, 𝑵 𝒑 , 𝑲 𝑻, etc
9. Taking a step back
Is it really a mixing problem more so than a problem about transfers?
Transfers
Heat
Mass
Momentum
Mixing
Hydrodynamics
Global transfert
coefficients
P/V
𝑁 𝑄
𝐾 𝑇
Fields Tools
𝛻𝑣 (Shear rates)
𝑣 ∙ 𝑑𝑆 (RTD)
𝑝, 𝑣
Estimation of
Estimation of
11. Example of heat transfer
Classical tire pyrolysis has a big heat transfer problem
Insulating layer
Tires RTD at surface → 0
Heat transfer with tires → 0
In the mixing framework: segregation must be prevented
12. Taking a step back
Is it really a mixing problem more so than a problem about transfers?
Transfers
Heat
Mass
Momentum
Mixing
Hydrodynamics
How can we heat otherwise than using
the wall?
How can we minimize segregation?
Fields Tools
Can we add baffles?
Can we rotate faster/slower?
Particle size?
13. Example of heat transfer
Microwave tire pyrolysis is insensitive to fouling
Insulating layer
Tires RTD at surface → 0
Heat transfer with tires: unchanged
The problem is now to contain microwaves safely in the reactor: that we know how to do!
14. How do we approach this?
Maintaining flow regime by scaling up mixing operations
Identify hydrodynamic
parameters
Extrapolation
to large scale
Large unit
Lab scale
technology
Characterization of the
mixing device
Parameters
Selection of mixing
device and power to
keep mixing similar
Application to new
large scale conditions
Optimization of
mixing device
Process problems
Calculation of
𝒗, 𝑵 𝒑 , 𝑲 𝑻, etc
15. How did we approach this?
Revisiting the technology to maintain proper heating rates
Extrapolation
to large scale
Large unit
Characterization of the
heating device
Parameters
Selection of large scale
MW reactor to keep heating
rate similar
Application to new
large scale conditions
Change to
microwave
heating
Process problems
Identify hydrodynamics
Lab scale
MW reactor
Calculation of
Heating rates, etc
17. Example III
Agitator has two functions
Air
Air
Fluid circulation (momentum transfer)
Air dispersion (mass transfer)
Air
Work
P
18. How do we approach this?
Increasing oxygen transfer by scaling up mixing operations
Identify hydrodynamic
parameters
Extrapolation
to large scale
Large unit
Lab scale
technology
Characterization of the
mixing device
Parameters
Selection of mixing
device and power to
keep mixing similar
Application to new
large scale conditions
Optimization of
sparger to increase
𝑘 𝐿 𝑎
Process problems
Calculation of
𝒗, 𝑵 𝒑 , 𝑲 𝑻, etc
19. Taking a step back
Is it really a mixing problem more so than a problem about transfers?
Transfers
Heat
Mass
Momentum
Mixing
Hydrodynamics
How can we transfer more oxygen in
the broth?
What agitator and conditions will
increase 𝑘 𝐿 𝑎?
Fields Tools
Can we increase P/V ratio?
Can we increase shear to reduce
bubble size (agitator design, number
etc)?
20. Aerobic fermentation
Oxygen limiting process – how to increase oxygen transfer
Air
Air
Work
P
We need more oxygen
a) Agitator design (𝑘 𝐿 𝑎)
a) Reduce bubble size
b) Increase shear rate
b) Increase the gradient (no mixer
involved)
𝑞 = 𝑘 𝐿 𝑎(𝐶∗
𝐵 − 𝐶 𝐵)
21. Aerobic fermentation
Playing with the equilibrium to speed-up transfer
𝑃 (𝑎𝑡𝑚)
1
7
𝑑𝑥 𝑂2
𝑑𝑡
= 𝑘 𝐿 𝑎(𝟕 − 𝑥)
𝑃 (𝑎𝑡𝑚)
1 2
7
14
𝑑𝑥 𝑂2
𝑑𝑡
= 𝑘 𝐿 𝑎(𝟏𝟒 − 𝑥)
𝑥 𝑂2
𝑚𝑔/𝐿
𝑥 𝑂2
𝑚𝑔/𝐿
24. Aerobic fermentation
Recirculating on high pressure offside sparger
Air
Air
P
Compressed
air 2 bars
Porous
diffuser
Air saturation
at 2 bars
More oxygen
in the broth
150% increase in
production rate
25. Few observations
Scaling up is challenging when hydrodynamics is involved
• Maintaining similar hydrodynamic conditions is often impossible
• Velocity field
• Pressure field
• Power to volume
• Hydrodynamics is responsible for scale-up problems because it
impacts local transfers
• The solution is not always mixing!
• The solution can lie in a different approach.
• Must ensure that the problem is really a problem of mixing and not a problem of
transfer.
26. Second observation
We are spending too much time and $ on models/CFD and not doing the right experimental work
• We need an operating point, not a theory!
• CFD and computer simulations provide solution to the Navier-Stokes equation
and solves for P and 𝒗 fields.
• Problem when using CFD for scale-up in real conditions
• They require numerous constitutive equations that increase with increasing
number of phases
• Turbulence is still an issue
• Resolution is cut off to cut computational time
• Complex boundary conditions create poor numerical conditioning
• At the end of this, CFD does not give mixing and transfer values, it gives 𝒗 and P
fields.
27. CAD
simulations
How we do computer design now?
Using CFD models to reproduce lab data and give scale-up guidance
Lab work
Iteration on parameters
to fit experiments
Generate
large scale
mesh
Optimum
parameters
Results
(mixing time
etc)
Iteration on geometries
and components
Optimum
config
Commercial
design
Extrapolation zone
28. 3D printing
the geometry
How can we use computer now?
How can we do the right experiment to get a working point?
Large scale
geometry
Results
(mixing time
etc)
Iteration on geometries
and components until satisfactory
Optimum
config
Commercial
design
Large scale
exp
Non-intrusive
methods
Materials range
Wide size range
30. Velocity field
Rushton Turbine
0 0.5 1
0
0.2
0.4
0.6
0.8
1
r/R
z/H
−1 −0.5 0
0
0.2
0.4
0.6
0.8
1
r/R
z/H
RPTCFD
30
Flat surface for CFD simulations
Use of zero-thickness baffles
Velocity fields can be recovered
Time series analysis is well established for extracting mixing information on flows
31. Do we really need 𝒗 ?
Most of our work needs transfer rates and RTDs , i.e. the integrated form
0 0.5 1
0
0.2
0.4
0.6
0.8
1
r/R
z/H
−1 −0.5 0
0
0.2
0.4
0.6
0.8
1
r/R
z/H
Typically we start with
the velocity field
Then …
We integrate the trajectories of a set Ω of
particles flowing on the field to calculate
• Lyapunov exponents
• Diffusion coefficients
• Residence time distribution
• Some sort of « Mixing efficiency »
−0.1 0 0.1
0
0.1
0.2
r (m)
Z(m)
𝒗
Ω
𝑑𝑡
32. Working with 𝒙 𝒕
1) Using time series analysis for extraction of dynamic properties
Flow dimensions
Lyapunov exponents
Entropies
Particle tracer time-series
Lypanunov exponent: sensitivity to initial
conditions Doucet et al. Granular Matter, 10 (2008), 133-138
33. Measuring mixing with 𝒙 𝒕
2) Using time series analysis for evaluation of mixing rate
Normalized position of a cluster of
particles from time series
Doucet et al. CheRD, 86 (2008), 1313-1321
Calculate correlation
between 𝑥 𝑡 and 𝑥(𝑡0)
for each particles
𝐶𝑖𝑗 = 𝜌 X𝑖
𝑡
, X𝑗
0
M = CC 𝑇
• First eigenvalue of M is
related to mixing rate
• First eigenvector of M is
the direction of minimum
mixing
At 𝑡0, correlation is 1, system is NOT mixed
At 𝑡 → ∞, correlation tends to limit value,
• system is mixed (=0)
• or not (≠0)
34. What if we have 𝒙 𝒕 instead
3) We can extract mapping functions like Markov chains
𝑡 𝑛 𝑡 𝑛+1
P
𝑋 𝑛 𝑋 𝑛+1 = P𝑋 𝑛
35. What if we have 𝒙 𝒕 instead
We can extract mapping functions like Markov chains
𝑡 𝑛 𝑡 𝑛+1
P
𝑋 𝑛 𝑋 𝑛+1 = P𝑋 𝑛
36. What if we have 𝒙 𝒕 instead
We can extract mapping functions like Markov chains
𝑡 𝑛 𝑡 𝑛+1
P
𝑋 𝑛 𝑋 𝑛+1 = P𝑋 𝑛
37. Mixing with mapping functions
Extracting dynamical information from stochastic models
Levin et al. Markov Chains and Mixing Times
Limit distribution (eigen problem)
Mixing time
Entropies
XP = 𝜆X
X 𝑘 − 𝝅 ≤ 𝐶 𝜆∗
𝑘
𝛑P = 𝛑
𝜏(𝜀) ≥
ln(2𝜀)
ln 𝜆∗
38. Examples
Application to a rotating drum
Doucet et al. Computers and Chem. Eng., 32 (2008), 1334-1341
CFDMapping
Mixing
dynamics
Invariant distribution
39. Examples
Application to a rotating drum
Doucet et al. Computers and Chem. Eng., 32 (2008), 1334-1341
CFDMapping
Mixing
dynamics
Eigenvalue spectrum
𝜏 1/𝑒 ≥
ln 2𝜀
ln 𝜆∗
=
ln
2
𝑒
ln 0.9962
= 81
40. The 3D printing
Example of solid-solid mixing in plastic degradation
1. Several iterations of the
drum were made.
2. The segregation
patterns were observed
rapidly
3. Baffle orientations was
changed
4. The RTDs were
determined
5. After validated at small
scale, a larger prototype
was built
41. The pilot prototyping
Example of solid-solid mixing in plastic degradation
Catalyst attrition
Dynamic angle of repose
Catalyst/fines segregation
42. Conclusions
Scaling up processes is difficult because transfers are not kept similar
1. Mixing is often guilty because it is used to promote transfers.
a) If transfers are affected, take a step back
b) Consider the transfer problem and consider it at the transfer level
c) See if an alternate technology can solve the transfer problem
2. CFD is limitative in predicting the mixing performance at different scale
because of the constitutive equations limitations
a) Keep in mind we need a working point, not a theory.
b) CAD can be used to build various 3D printed geometries and test real fluid in
similar flow conditions before building a pilot unit
c) Modern non-intrusive techniques can be used to measure mixing in a
Lagrangian way and more rapidly than converging a simulation
d) Time-series analysis and a variety of stochastic techniques can be used to
analyse the performance without the velocity field.
